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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Authenticated Data Structures As Functors - Archive of Formal Proofs</title><meta name="description" content="Authenticated data structures allow several systems to convince each other that they are referring to the same data structure, even if each of them knows..."><meta property="og:title" content="Authenticated Data Structures As Functors" />
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<h1 >
<span class='first'>A</span>uthenticated <span class='first'>D</span>ata <span class='first'>S</span>tructures as <span class='first'>F</span>unctors</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/maric">Ognjen Marić</a> <a class="obfuscated" data="eyJob3N0IjpbIm15bm9zZWZyb3plIiwiY29tIl0sInVzZXIiOlsib2dpIiwiYWZwIl19">📧</a>
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<p class="date">April 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Authenticated data structures allow several systems to convince each
other that they are referring to the same data structure, even if each
of them knows only a part of the data structure. Using inclusion
proofs, knowledgeable systems can selectively share their knowledge
with other systems and the latter can verify the authenticity of what
is being shared. In this article, we show how to modularly define
authenticated data structures, their inclusion proofs, and operations
thereon as datatypes in Isabelle/HOL, using a shallow embedding.
Modularity allows us to construct complicated trees from reusable
building blocks, which we call Merkle functors. Merkle functors
include sums, products, and function spaces and are closed under
composition and least fixpoints. As a practical application, we model
the hierarchical transactions of <a
href="https://www.canton.io">Canton</a>, a
practical interoperability protocol for distributed ledgers, as
authenticated data structures. This is a first step towards
formalizing the Canton protocol and verifying its integrity and
security guarantees.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session ADS_Functor</h3>
<ul>
<li><a href="../theories/ads_functor/#Merkle_Interface">Merkle_Interface</a></li>
<li><a href="../theories/ads_functor/#ADS_Construction">ADS_Construction</a></li>
<li><a href="../theories/ads_functor/#Generic_ADS_Construction">Generic_ADS_Construction</a></li>
<li><a href="../theories/ads_functor/#Inclusion_Proof_Construction">Inclusion_Proof_Construction</a></li>
<li><a href="../theories/ads_functor/#Canton_Transaction_Tree">Canton_Transaction_Tree</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">ADS_Functor-AFP</p><pre id="copy-text">@article{ADS_Functor-AFP,
author = {Andreas Lochbihler and Ognjen Marić},
title = {Authenticated Data Structures As Functors},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/ADS_Functor.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/AI_Planning_Languages_Semantics.html b/web/entries/AI_Planning_Languages_Semantics.html
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<h1 >
<span class='first'>A</span><span class='first'>I</span> <span class='first'>P</span>lanning <span class='first'>L</span>anguages <span class='first'>S</span>emantics</h1>
<div>
<p><a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a href="http://home.in.tum.de/~mansour/">🌐</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">October 29, 2020</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is an Isabelle/HOL formalisation of the semantics of the
multi-valued planning tasks language that is used by the planning
system Fast-Downward, the STRIPS fragment of the Planning Domain
Definition Language (PDDL), and the STRIPS soundness meta-theory
developed by Vladimir Lifschitz. It also contains formally verified
checkers for checking the well-formedness of problems specified in
either language as well the correctness of potential solutions. The
formalisation in this entry was described in an earlier publication.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/artificial-intelligence">Computer science/Artificial intelligence</a></li></ul>
<h3>Session AI_Planning_Languages_Semantics</h3>
<ul>
<li><a href="../theories/ai_planning_languages_semantics/#Error_Monad_Add">Error_Monad_Add</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#Option_Monad_Add">Option_Monad_Add</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#SASP_Semantics">SASP_Semantics</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#SASP_Checker">SASP_Checker</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#PDDL_STRIPS_Semantics">PDDL_STRIPS_Semantics</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#PDDL_STRIPS_Checker">PDDL_STRIPS_Checker</a></li>
<li><a href="../theories/ai_planning_languages_semantics/#Lifschitz_Consistency">Lifschitz_Consistency</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Certification_Monads.html">Certification Monads</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Propositional_Proof_Systems.html">Propositional Proof Systems</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Verified_SAT_Based_AI_Planning.html">Verified SAT-Based AI Planning</a></li></ul>
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<p style="display:none;" id="bibtex-filename">AI_Planning_Languages_Semantics-AFP</p><pre id="copy-text">@article{AI_Planning_Languages_Semantics-AFP,
author = {Mohammad Abdulaziz and Peter Lammich},
title = {AI Planning Languages Semantics},
journal = {Archive of Formal Proofs},
month = {October},
year = {2020},
note = {\url{https://isa-afp.org/entries/AI_Planning_Languages_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
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- <a href="https://www.isa-afp.org/release/afp-AI_Planning_Languages_Semantics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-AI_Planning_Languages_Semantics-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-AI_Planning_Languages_Semantics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AI_Planning_Languages_Semantics-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-AI_Planning_Languages_Semantics-2020-10-30.tar.gz">Oct 30, 2020</a>: Isabelle2020
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<h1 >
<span class='first'>L</span>oop <span class='first'>F</span>reedom of the (<span class='first'>U</span>ntimed) <span class='first'>A</span><span class='first'>O</span><span class='first'>D</span><span class='first'>V</span> <span class='first'>R</span>outing <span class='first'>P</span>rotocol</h1>
<div>
<p><a href="../authors/bourke">Timothy Bourke</a> <a href="http://www.tbrk.org">🌐</a> and <a href="../authors/hoefner">Peter Höfner</a> <a href="http://www.hoefner-online.de/">🌐</a>
</p>
<p class="date">October 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
The Ad hoc On-demand Distance Vector (AODV) routing protocol allows
the nodes in a Mobile Ad hoc Network (MANET) or a Wireless Mesh
Network (WMN) to know where to forward data packets. Such a protocol
is ‘loop free’ if it never leads to routing decisions that forward
packets in circles.
<p>
This development mechanises an existing pen-and-paper proof of loop
freedom of AODV. The protocol is modelled in the Algebra of
Wireless Networks (AWN), which is the subject of an earlier paper
and AFP mechanization. The proof relies on a novel compositional
approach for lifting invariants to networks of nodes.
</p><p>
We exploit the mechanization to analyse several variants of AODV and
show that Isabelle/HOL can re-establish most proof obligations
automatically and identify exactly the steps that are no longer valid.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session AODV</h3>
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<li><a href="../theories/aodv/#Aodv_Data">Aodv_Data</a></li>
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<li><a href="../theories/aodv/#Aodv">Aodv</a></li>
<li><a href="../theories/aodv/#Aodv_Predicates">Aodv_Predicates</a></li>
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<li><a href="../theories/aodv/#Seq_Invariants">Seq_Invariants</a></li>
<li><a href="../theories/aodv/#Quality_Increases">Quality_Increases</a></li>
<li><a href="../theories/aodv/#OAodv">OAodv</a></li>
<li><a href="../theories/aodv/#Global_Invariants">Global_Invariants</a></li>
<li><a href="../theories/aodv/#Loop_Freedom">Loop_Freedom</a></li>
<li><a href="../theories/aodv/#Aodv_Loop_Freedom">Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#A_Norreqid">A_Norreqid</a></li>
<li><a href="../theories/aodv/#A_Aodv_Data">A_Aodv_Data</a></li>
<li><a href="../theories/aodv/#A_Aodv_Message">A_Aodv_Message</a></li>
<li><a href="../theories/aodv/#A_Aodv">A_Aodv</a></li>
<li><a href="../theories/aodv/#A_Aodv_Predicates">A_Aodv_Predicates</a></li>
<li><a href="../theories/aodv/#A_Fresher">A_Fresher</a></li>
<li><a href="../theories/aodv/#A_Seq_Invariants">A_Seq_Invariants</a></li>
<li><a href="../theories/aodv/#A_Quality_Increases">A_Quality_Increases</a></li>
<li><a href="../theories/aodv/#A_OAodv">A_OAodv</a></li>
<li><a href="../theories/aodv/#A_Global_Invariants">A_Global_Invariants</a></li>
<li><a href="../theories/aodv/#A_Loop_Freedom">A_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#A_Aodv_Loop_Freedom">A_Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#B_Fwdrreps">B_Fwdrreps</a></li>
<li><a href="../theories/aodv/#B_Aodv_Data">B_Aodv_Data</a></li>
<li><a href="../theories/aodv/#B_Aodv_Message">B_Aodv_Message</a></li>
<li><a href="../theories/aodv/#B_Aodv">B_Aodv</a></li>
<li><a href="../theories/aodv/#B_Aodv_Predicates">B_Aodv_Predicates</a></li>
<li><a href="../theories/aodv/#B_Fresher">B_Fresher</a></li>
<li><a href="../theories/aodv/#B_Seq_Invariants">B_Seq_Invariants</a></li>
<li><a href="../theories/aodv/#B_Quality_Increases">B_Quality_Increases</a></li>
<li><a href="../theories/aodv/#B_OAodv">B_OAodv</a></li>
<li><a href="../theories/aodv/#B_Global_Invariants">B_Global_Invariants</a></li>
<li><a href="../theories/aodv/#B_Loop_Freedom">B_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#B_Aodv_Loop_Freedom">B_Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#C_Gtobcast">C_Gtobcast</a></li>
<li><a href="../theories/aodv/#C_Aodv_Data">C_Aodv_Data</a></li>
<li><a href="../theories/aodv/#C_Aodv_Message">C_Aodv_Message</a></li>
<li><a href="../theories/aodv/#C_Aodv">C_Aodv</a></li>
<li><a href="../theories/aodv/#C_Aodv_Predicates">C_Aodv_Predicates</a></li>
<li><a href="../theories/aodv/#C_Fresher">C_Fresher</a></li>
<li><a href="../theories/aodv/#C_Seq_Invariants">C_Seq_Invariants</a></li>
<li><a href="../theories/aodv/#C_Quality_Increases">C_Quality_Increases</a></li>
<li><a href="../theories/aodv/#C_OAodv">C_OAodv</a></li>
<li><a href="../theories/aodv/#C_Global_Invariants">C_Global_Invariants</a></li>
<li><a href="../theories/aodv/#C_Loop_Freedom">C_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#C_Aodv_Loop_Freedom">C_Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#D_Fwdrreqs">D_Fwdrreqs</a></li>
<li><a href="../theories/aodv/#D_Aodv_Data">D_Aodv_Data</a></li>
<li><a href="../theories/aodv/#D_Aodv_Message">D_Aodv_Message</a></li>
<li><a href="../theories/aodv/#D_Aodv">D_Aodv</a></li>
<li><a href="../theories/aodv/#D_Aodv_Predicates">D_Aodv_Predicates</a></li>
<li><a href="../theories/aodv/#D_Fresher">D_Fresher</a></li>
<li><a href="../theories/aodv/#D_Seq_Invariants">D_Seq_Invariants</a></li>
<li><a href="../theories/aodv/#D_Quality_Increases">D_Quality_Increases</a></li>
<li><a href="../theories/aodv/#D_OAodv">D_OAodv</a></li>
<li><a href="../theories/aodv/#D_Global_Invariants">D_Global_Invariants</a></li>
<li><a href="../theories/aodv/#D_Loop_Freedom">D_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#D_Aodv_Loop_Freedom">D_Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#E_All_ABCD">E_All_ABCD</a></li>
<li><a href="../theories/aodv/#E_Aodv_Data">E_Aodv_Data</a></li>
<li><a href="../theories/aodv/#E_Aodv_Message">E_Aodv_Message</a></li>
<li><a href="../theories/aodv/#E_Aodv">E_Aodv</a></li>
<li><a href="../theories/aodv/#E_Aodv_Predicates">E_Aodv_Predicates</a></li>
<li><a href="../theories/aodv/#E_Fresher">E_Fresher</a></li>
<li><a href="../theories/aodv/#E_Seq_Invariants">E_Seq_Invariants</a></li>
<li><a href="../theories/aodv/#E_Quality_Increases">E_Quality_Increases</a></li>
<li><a href="../theories/aodv/#E_OAodv">E_OAodv</a></li>
<li><a href="../theories/aodv/#E_Global_Invariants">E_Global_Invariants</a></li>
<li><a href="../theories/aodv/#E_Loop_Freedom">E_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#E_Aodv_Loop_Freedom">E_Aodv_Loop_Freedom</a></li>
<li><a href="../theories/aodv/#All">All</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/AWN.html">Mechanization of the Algebra for Wireless Networks (AWN)</a></li></ul>
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<p style="display:none;" id="bibtex-filename">AODV-AFP</p><pre id="copy-text">@article{AODV-AFP,
author = {Timothy Bourke and Peter Höfner},
title = {Loop freedom of the (untimed) AODV routing protocol},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/AODV.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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\ No newline at end of file
diff --git a/web/entries/AVL-Trees.html b/web/entries/AVL-Trees.html
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<h1 >
<span class='first'>A</span><span class='first'>V</span><span class='first'>L</span> <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/pusch">Cornelia Pusch</a>
</p>
<p class="date">March 19, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Two formalizations of AVL trees with room for extensions. The first formalization is monolithic and shorter, the second one in two stages, longer and a bit simpler. The final implementation is the same. If you are interested in developing this further, please contact <tt>gerwin.klein@nicta.com.au</tt>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 11, 2011</dt>
<dd>Ondrej Kuncar added delete function</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session AVL-Trees</h3>
<ul>
<li><a href="../theories/avl-trees/#AVL">AVL</a></li>
<li><a href="../theories/avl-trees/#AVL2">AVL2</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">AVL-Trees-AFP</p><pre id="copy-text">@article{AVL-Trees-AFP,
author = {Tobias Nipkow and Cornelia Pusch},
title = {AVL Trees},
journal = {Archive of Formal Proofs},
month = {March},
year = {2004},
note = {\url{https://isa-afp.org/entries/AVL-Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>M</span>echanization of the <span class='first'>A</span>lgebra for <span class='first'>W</span>ireless <span class='first'>N</span>etworks (<span class='first'>A</span><span class='first'>W</span><span class='first'>N</span>)</h1>
<div>
<p><a href="../authors/bourke">Timothy Bourke</a> <a href="http://www.tbrk.org">🌐</a>
</p>
<p class="date">March 8, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
AWN is a process algebra developed for modelling and analysing
protocols for Mobile Ad hoc Networks (MANETs) and Wireless Mesh
Networks (WMNs). AWN models comprise five distinct layers:
sequential processes, local parallel compositions, nodes, partial
networks, and complete networks.</p>
<p>
This development mechanises the original operational semantics of
AWN and introduces a variant 'open' operational semantics that
enables the compositional statement and proof of invariants across
distinct network nodes. It supports labels (for weakening
invariants) and (abstract) data state manipulations. A framework for
compositional invariant proofs is developed, including a tactic
(inv_cterms) for inductive invariant proofs of sequential processes,
lifting rules for the open versions of the higher layers, and a rule
for transferring lifted properties back to the standard semantics. A
notion of 'control terms' reduces proof obligations to the subset of
subterms that act directly (in contrast to operators for combining
terms and joining processes).</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session AWN</h3>
<ul>
<li><a href="../theories/awn/#Lib">Lib</a></li>
<li><a href="../theories/awn/#TransitionSystems">TransitionSystems</a></li>
<li><a href="../theories/awn/#Invariants">Invariants</a></li>
<li><a href="../theories/awn/#OInvariants">OInvariants</a></li>
<li><a href="../theories/awn/#AWN">AWN</a></li>
<li><a href="../theories/awn/#AWN_SOS">AWN_SOS</a></li>
<li><a href="../theories/awn/#AWN_Cterms">AWN_Cterms</a></li>
<li><a href="../theories/awn/#AWN_Labels">AWN_Labels</a></li>
<li><a href="../theories/awn/#Inv_Cterms">Inv_Cterms</a></li>
<li><a href="../theories/awn/#AWN_SOS_Labels">AWN_SOS_Labels</a></li>
<li><a href="../theories/awn/#Pnet">Pnet</a></li>
<li><a href="../theories/awn/#Closed">Closed</a></li>
<li><a href="../theories/awn/#OAWN_SOS">OAWN_SOS</a></li>
<li><a href="../theories/awn/#OAWN_SOS_Labels">OAWN_SOS_Labels</a></li>
<li><a href="../theories/awn/#OPnet">OPnet</a></li>
<li><a href="../theories/awn/#ONode_Lifting">ONode_Lifting</a></li>
<li><a href="../theories/awn/#OPnet_Lifting">OPnet_Lifting</a></li>
<li><a href="../theories/awn/#OClosed_Lifting">OClosed_Lifting</a></li>
<li><a href="../theories/awn/#AWN_Invariants">AWN_Invariants</a></li>
<li><a href="../theories/awn/#OAWN_Invariants">OAWN_Invariants</a></li>
<li><a href="../theories/awn/#OAWN_Convert">OAWN_Convert</a></li>
<li><a href="../theories/awn/#Qmsg">Qmsg</a></li>
<li><a href="../theories/awn/#Qmsg_Lifting">Qmsg_Lifting</a></li>
<li><a href="../theories/awn/#OClosed_Transfer">OClosed_Transfer</a></li>
<li><a href="../theories/awn/#AWN_Main">AWN_Main</a></li>
<li><a href="../theories/awn/#Toy">Toy</a></li>
<li><a href="../theories/awn/#AWN_Term_Graph">AWN_Term_Graph</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/AODV.html">Loop freedom of the (untimed) AODV routing protocol</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">AWN-AFP</p><pre id="copy-text">@article{AWN-AFP,
author = {Timothy Bourke},
title = {Mechanization of the Algebra for Wireless Networks (AWN)},
journal = {Archive of Formal Proofs},
month = {March},
year = {2014},
note = {\url{https://isa-afp.org/entries/AWN.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-AWN-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Abortable_Linearizable_Modules.html b/web/entries/Abortable_Linearizable_Modules.html
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<h1 >
<span class='first'>A</span>bortable <span class='first'>L</span>inearizable <span class='first'>M</span>odules</h1>
<div>
<p><a href="../authors/guerraoui">Rachid Guerraoui</a> <a class="obfuscated" data="eyJob3N0IjpbImVwZmwiLCJjaCJdLCJ1c2VyIjpbInJhY2hpZCIsImd1ZXJyYW91aSJdfQ==">📧</a>, <a href="../authors/kuncak">Viktor Kuncak</a> <a href="http://lara.epfl.ch/~kuncak/">🌐</a> and <a href="../authors/losa">Giuliano Losa</a> <a class="obfuscated" data="eyJob3N0IjpbImVwZmwiLCJjaCJdLCJ1c2VyIjpbImdpdWxpYW5vIiwibG9zYSJdfQ==">📧</a>
</p>
<p class="date">March 1, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We define the Abortable Linearizable Module automaton (ALM for short)
and prove its key composition property using the IOA theory of
HOLCF. The ALM is at the heart of the Speculative Linearizability
framework. This framework simplifies devising correct speculative
algorithms by enabling their decomposition into independent modules
that can be analyzed and proved correct in isolation. It is
particularly useful when working in a distributed environment, where
the need to tolerate faults and asynchrony has made current
monolithic protocols so intricate that it is no longer tractable to
check their correctness. Our theory contains a typical example of a
refinement proof in the I/O-automata framework of Lynch and Tuttle.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Abortable_Linearizable_Modules</h3>
<ul>
<li><a href="../theories/abortable_linearizable_modules/#Sequences">Sequences</a></li>
<li><a href="../theories/abortable_linearizable_modules/#IOA">IOA</a></li>
<li><a href="../theories/abortable_linearizable_modules/#RDR">RDR</a></li>
<li><a href="../theories/abortable_linearizable_modules/#SLin">SLin</a></li>
<li><a href="../theories/abortable_linearizable_modules/#Simulations">Simulations</a></li>
<li><a href="../theories/abortable_linearizable_modules/#Idempotence">Idempotence</a></li>
<li><a href="../theories/abortable_linearizable_modules/#Consensus">Consensus</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Abortable_Linearizable_Modules-AFP</p><pre id="copy-text">@article{Abortable_Linearizable_Modules-AFP,
author = {Rachid Guerraoui and Viktor Kuncak and Giuliano Losa},
title = {Abortable Linearizable Modules},
journal = {Archive of Formal Proofs},
month = {March},
year = {2012},
note = {\url{https://isa-afp.org/entries/Abortable_Linearizable_Modules.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Abortable_Linearizable_Modules-2012-03-02.tar.gz">Mar 2, 2012</a>: Isabelle2011-1
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<h1 >
<span class='first'>A</span>bstract <span class='first'>I</span>nterpretation of <span class='first'>A</span>nnotated <span class='first'>C</span>ommands</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">November 23, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is the Isabelle formalization of the material decribed in the
eponymous <a href="https://doi.org/10.1007/978-3-642-32347-8_9">ITP 2012 paper</a>.
It develops a generic abstract interpreter for a
while-language, including widening and narrowing. The collecting
semantics and the abstract interpreter operate on annotated commands:
the program is represented as a syntax tree with the semantic
information directly embedded, without auxiliary labels. The aim of
the formalization is simplicity, not efficiency or
precision. This is motivated by the inclusion of the material in a
theorem prover based course on semantics. A similar (but more
polished) development is covered in the book
<a href="https://doi.org/10.1007/978-3-319-10542-0">Concrete Semantics</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Abs_Int_ITP2012</h3>
<ul>
<li><a href="../theories/abs_int_itp2012/#Complete_Lattice_ix">Complete_Lattice_ix</a></li>
<li><a href="../theories/abs_int_itp2012/#ACom">ACom</a></li>
<li><a href="../theories/abs_int_itp2012/#Collecting">Collecting</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_Int0">Abs_Int0</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_State">Abs_State</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_Int1">Abs_Int1</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_Int2">Abs_Int2</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_Int2_ivl">Abs_Int2_ivl</a></li>
<li><a href="../theories/abs_int_itp2012/#Abs_Int3">Abs_Int3</a></li>
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<p style="display:none;" id="bibtex-filename">Abs_Int_ITP2012-AFP</p><pre id="copy-text">@article{Abs_Int_ITP2012-AFP,
author = {Tobias Nipkow},
title = {Abstract Interpretation of Annotated Commands},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Abs_Int_ITP2012.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Abstract-Hoare-Logics.html b/web/entries/Abstract-Hoare-Logics.html
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<h1 >
<span class='first'>A</span>bstract <span class='first'>H</span>oare <span class='first'>L</span>ogics</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">August 8, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These therories describe Hoare logics for a number of imperative language constructs, from while-loops to mutually recursive procedures. Both partial and total correctness are treated. In particular a proof system for total correctness of recursive procedures in the presence of unbounded nondeterminism is presented.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T. (2002). Hoare Logics in Isabelle/HOL. Proof and System-Reliability, 341–367. <a href="https://doi.org/10.1007/978-94-010-0413-8_11">https://doi.org/10.1007/978-94-010-0413-8_11</a>
</li><li>
Nipkow, T. (2002). Hoare Logics for Recursive Procedures and Unbounded Nondeterminism. Lecture Notes in Computer Science, 103–119. <a href="https://doi.org/10.1007/3-540-45793-3_8">https://doi.org/10.1007/3-540-45793-3_8</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/MOD2001.html">Open access</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/csl02.html">Open access</a>
</li></ul>
<h3>Session Abstract-Hoare-Logics</h3>
<ul>
<li><a href="../theories/abstract-hoare-logics/#Lang">Lang</a></li>
<li><a href="../theories/abstract-hoare-logics/#Hoare">Hoare</a></li>
<li><a href="../theories/abstract-hoare-logics/#Termi">Termi</a></li>
<li><a href="../theories/abstract-hoare-logics/#HoareTotal">HoareTotal</a></li>
<li><a href="../theories/abstract-hoare-logics/#PLang">PLang</a></li>
<li><a href="../theories/abstract-hoare-logics/#PHoare">PHoare</a></li>
<li><a href="../theories/abstract-hoare-logics/#PTermi">PTermi</a></li>
<li><a href="../theories/abstract-hoare-logics/#PHoareTotal">PHoareTotal</a></li>
<li><a href="../theories/abstract-hoare-logics/#PsLang">PsLang</a></li>
<li><a href="../theories/abstract-hoare-logics/#PsHoare">PsHoare</a></li>
<li><a href="../theories/abstract-hoare-logics/#PsTermi">PsTermi</a></li>
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<p style="display:none;" id="bibtex-filename">Abstract-Hoare-Logics-AFP</p><pre id="copy-text">@article{Abstract-Hoare-Logics-AFP,
author = {Tobias Nipkow},
title = {Abstract Hoare Logics},
journal = {Archive of Formal Proofs},
month = {August},
year = {2006},
note = {\url{https://isa-afp.org/entries/Abstract-Hoare-Logics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Abstract-Hoare-Logics-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Abstract-Hoare-Logics-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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diff --git a/web/entries/Abstract-Rewriting.html b/web/entries/Abstract-Rewriting.html
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+++ b/web/entries/Abstract-Rewriting.html
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<h1 >
<span class='first'>A</span>bstract <span class='first'>R</span>ewriting</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">June 14, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an Isabelle formalization of abstract rewriting (see, e.g.,
the book by Baader and Nipkow). First, we define standard relations like
<i>joinability</i>, <i>meetability</i>, <i>conversion</i>, etc. Then, we
formalize important properties of abstract rewrite systems, e.g.,
confluence and strong normalization. Our main concern is on strong
normalization, since this formalization is the basis of <a
href="http://cl-informatik.uibk.ac.at/software/ceta">CeTA</a> (which is
mainly about strong normalization of term rewrite systems). Hence lemmas
involving strong normalization constitute by far the biggest part of this
theory. One of those is Newman's lemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>October 16, 2013</dt>
<dd>Generalized delta-orders from rationals to Archimedean fields.</dd><dt>September 17, 2010</dt>
<dd>Added theories defining several (ordered)
semirings related to strong normalization and giving some standard
instances. <br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Abstract-Rewriting</h3>
<ul>
<li><a href="../theories/abstract-rewriting/#Seq">Seq</a></li>
<li><a href="../theories/abstract-rewriting/#Abstract_Rewriting">Abstract_Rewriting</a></li>
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author = {Christian Sternagel and René Thiemann},
title = {Abstract Rewriting},
journal = {Archive of Formal Proofs},
month = {June},
year = {2010},
note = {\url{https://isa-afp.org/entries/Abstract-Rewriting.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Abstract_Completeness.html b/web/entries/Abstract_Completeness.html
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<h1 >
<span class='first'>A</span>bstract <span class='first'>C</span>ompleteness</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a href="http://www21.in.tum.de/~blanchet">🌐</a>, <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
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<p class="date">April 16, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A formalization of an abstract property of possibly infinite derivation trees (modeled by a codatatype), representing the core of a proof (in Beth/Hintikka style) of the first-order logic completeness theorem, independent of the concrete syntax or inference rules. This work is described in detail in the IJCAR 2014 publication by the authors.
The abstract proof can be instantiated for a wide range of Gentzen and tableau systems as well as various flavors of FOL---e.g., with or without predicates, equality, or sorts. Here, we give only a toy example instantiation with classical propositional logic. A more serious instance---many-sorted FOL with equality---is described elsewhere [Blanchette and Popescu, FroCoS 2013].</div>
<h3>License</h3>
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<h3>Session Abstract_Completeness</h3>
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<li><a href="../theories/abstract_completeness/#Abstract_Completeness">Abstract_Completeness</a></li>
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<ul class="horizontal-list"><li><a href="../entries/FOL_Seq_Calc3.html">A Naive Prover for First-Order Logic</a></li><li><a href="../entries/FOL_Seq_Calc2.html">A Sequent Calculus Prover for First-Order Logic with Functions</a></li><li><a href="../entries/Abstract_Soundness.html">Abstract Soundness</a></li><li><a href="../entries/Incredible_Proof_Machine.html">The meta theory of the Incredible Proof Machine</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Abstract_Completeness-AFP</p><pre id="copy-text">@article{Abstract_Completeness-AFP,
author = {Jasmin Christian Blanchette and Andrei Popescu and Dmitriy Traytel},
title = {Abstract Completeness},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/Abstract_Completeness.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span>bstract <span class='first'>S</span>oundness</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamFzbWluIiwiYmxhbmNoZXR0ZSJdfQ==">📧</a>, <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">February 10, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A formalized coinductive account of the abstract development of
Brotherston, Gorogiannis, and Petersen [APLAS 2012], in a slightly
more general form since we work with arbitrary infinite proofs, which
may be acyclic. This work is described in detail in an article by the
authors, published in 2017 in the <em>Journal of Automated
Reasoning</em>. The abstract proof can be instantiated for
various formalisms, including first-order logic with inductive
predicates.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Abstract_Soundness</h3>
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<h3>Depends on</h3>
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<ul class="horizontal-list"><li><a href="../entries/FOL_Seq_Calc3.html">A Naive Prover for First-Order Logic</a></li><li><a href="../entries/FOL_Seq_Calc2.html">A Sequent Calculus Prover for First-Order Logic with Functions</a></li></ul>
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<li><a href="../entries/Relational_Paths.html">Relational Characterisations of Paths</a></li>
<li><a href="../entries/FOL_Seq_Calc1.html">A Sequent Calculus for First-Order Logic</a></li>
<li><a href="../entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></li>
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<p style="display:none;" id="bibtex-filename">Abstract_Soundness-AFP</p><pre id="copy-text">@article{Abstract_Soundness-AFP,
author = {Jasmin Christian Blanchette and Andrei Popescu and Dmitriy Traytel},
title = {Abstract Soundness},
journal = {Archive of Formal Proofs},
month = {February},
year = {2017},
note = {\url{https://isa-afp.org/entries/Abstract_Soundness.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span>ckermann's <span class='first'>F</span>unction <span class='first'>I</span>s <span class='first'>N</span>ot <span class='first'>P</span>rimitive <span class='first'>R</span>ecursive</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">March 23, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Ackermann's function is defined in the usual way and a number of
its elementary properties are proved. Then, the primitive recursive
functions are defined inductively: as a predicate on the functions
that map lists of numbers to numbers. It is shown that every
primitive recursive function is strictly dominated by Ackermann's
function. The formalisation follows an earlier one by Nora Szasz.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li></ul>
<h3>Session Ackermanns_not_PR</h3>
<ul>
<li><a href="../theories/ackermanns_not_pr/#Primrec">Primrec</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Ackermanns_not_PR-AFP</p><pre id="copy-text">@article{Ackermanns_not_PR-AFP,
author = {Lawrence C. Paulson},
title = {Ackermann&#39;s Function Is Not Primitive Recursive},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/Ackermanns_not_PR.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Actuarial_Mathematics.html b/web/entries/Actuarial_Mathematics.html
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<h1 >
<span class='first'>A</span>ctuarial <span class='first'>M</span>athematics</h1>
<div>
<p><a href="../authors/ito">Yosuke Ito</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZ2xhY2llcjM0NSJdfQ==">📧</a>
</p>
<p class="date">January 23, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Actuarial Mathematics is a theory in applied mathematics, which is
mainly used for determining the prices of insurance products and
evaluating the liability of a company associating with insurance
contracts. It is related to calculus, probability theory and financial
theory, etc. In this entry, I formalize the very basic part of
Actuarial Mathematics in Isabelle/HOL. The first formalization is
about the theory of interest which deals with interest rates, present
value factors, an annuity certain, etc. I have already formalized the
basic part of Actuarial Mathematics in Coq
(https://github.com/Yosuke-Ito-345/Actuary). This entry is currently
the partial translation and a little generalization of the Coq
formalization. The further translation in Isabelle/HOL is now
proceeding.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Actuarial_Mathematics</h3>
<ul>
<li><a href="../theories/actuarial_mathematics/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/actuarial_mathematics/#Interest">Interest</a></li></ul><div class="flex-wrap">
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author = {Yosuke Ito},
title = {Actuarial Mathematics},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Actuarial_Mathematics.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>F</span>ormalisation of an <span class='first'>A</span>daptive <span class='first'>S</span>tate <span class='first'>C</span>ounting <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/sachtleben">Robert Sachtleben</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1icmVtZW4iLCJkZSJdLCJ1c2VyIjpbInJvYl9zYWMiXX0=">📧</a>
</p>
<p class="date">August 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a formalisation of a refinement of an adaptive
state counting algorithm, used to test for reduction between finite
state machines. The algorithm has been originally presented by Hierons
in the paper <a
href="https://doi.org/10.1109/TC.2004.85">Testing from a
Non-Deterministic Finite State Machine Using Adaptive State
Counting</a>. Definitions for finite state machines and
adaptive test cases are given and many useful theorems are derived
from these. The algorithm is formalised using mutually recursive
functions, for which it is proven that the generated test suite is
sufficient to test for reduction against finite state machines of a
certain fault domain. Additionally, the algorithm is specified in a
simple WHILE-language and its correctness is shown using Hoare-logic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Adaptive_State_Counting</h3>
<ul>
<li><a href="../theories/adaptive_state_counting/#FSM">FSM</a></li>
<li><a href="../theories/adaptive_state_counting/#FSM_Product">FSM_Product</a></li>
<li><a href="../theories/adaptive_state_counting/#ATC">ATC</a></li>
<li><a href="../theories/adaptive_state_counting/#ASC_LB">ASC_LB</a></li>
<li><a href="../theories/adaptive_state_counting/#ASC_Suite">ASC_Suite</a></li>
<li><a href="../theories/adaptive_state_counting/#ASC_Sufficiency">ASC_Sufficiency</a></li>
<li><a href="../theories/adaptive_state_counting/#ASC_Hoare">ASC_Hoare</a></li>
<li><a href="../theories/adaptive_state_counting/#ASC_Example">ASC_Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/FSM_Tests.html">Verified Complete Test Strategies for Finite State Machines</a></li>
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<p style="display:none;" id="bibtex-filename">Adaptive_State_Counting-AFP</p><pre id="copy-text">@article{Adaptive_State_Counting-AFP,
author = {Robert Sachtleben},
title = {Formalisation of an Adaptive State Counting Algorithm},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/Adaptive_State_Counting.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Affine_Arithmetic.html b/web/entries/Affine_Arithmetic.html
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<h1 >
<span class='first'>A</span>ffine <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>
</p>
<p class="date">February 7, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We give a formalization of affine forms as abstract representations of zonotopes.
We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division.
Expressions involving those operations can automatically be turned into (executable) functions approximating the original
expression in affine arithmetic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 20, 2017</dt>
<dd>linear approximations for all symbols from the floatarith data
type</dd><dt>January 31, 2015</dt>
<dd>added algorithm for zonotope/hyperplane intersection<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Affine_Arithmetic</h3>
<ul>
<li><a href="../theories/affine_arithmetic/#Affine_Arithmetic_Auxiliarities">Affine_Arithmetic_Auxiliarities</a></li>
<li><a href="../theories/affine_arithmetic/#Executable_Euclidean_Space">Executable_Euclidean_Space</a></li>
<li><a href="../theories/affine_arithmetic/#Affine_Form">Affine_Form</a></li>
<li><a href="../theories/affine_arithmetic/#Floatarith_Expression">Floatarith_Expression</a></li>
<li><a href="../theories/affine_arithmetic/#Straight_Line_Program">Straight_Line_Program</a></li>
<li><a href="../theories/affine_arithmetic/#Affine_Approximation">Affine_Approximation</a></li>
<li><a href="../theories/affine_arithmetic/#Counterclockwise">Counterclockwise</a></li>
<li><a href="../theories/affine_arithmetic/#Counterclockwise_Vector">Counterclockwise_Vector</a></li>
<li><a href="../theories/affine_arithmetic/#Counterclockwise_2D_Strict">Counterclockwise_2D_Strict</a></li>
<li><a href="../theories/affine_arithmetic/#Polygon">Polygon</a></li>
<li><a href="../theories/affine_arithmetic/#Counterclockwise_2D_Arbitrary">Counterclockwise_2D_Arbitrary</a></li>
<li><a href="../theories/affine_arithmetic/#Intersection">Intersection</a></li>
<li><a href="../theories/affine_arithmetic/#Affine_Code">Affine_Code</a></li>
<li><a href="../theories/affine_arithmetic/#Optimize_Integer">Optimize_Integer</a></li>
<li><a href="../theories/affine_arithmetic/#Optimize_Float">Optimize_Float</a></li>
<li><a href="../theories/affine_arithmetic/#Print">Print</a></li>
<li><a href="../theories/affine_arithmetic/#Float_Real">Float_Real</a></li>
<li><a href="../theories/affine_arithmetic/#Ex_Affine_Approximation">Ex_Affine_Approximation</a></li>
<li><a href="../theories/affine_arithmetic/#Ex_Ineqs">Ex_Ineqs</a></li>
<li><a href="../theories/affine_arithmetic/#Ex_Inter">Ex_Inter</a></li>
<li><a href="../theories/affine_arithmetic/#Affine_Arithmetic">Affine_Arithmetic</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Taylor_Models.html">Taylor Models</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
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<p style="display:none;" id="bibtex-filename">Affine_Arithmetic-AFP</p><pre id="copy-text">@article{Affine_Arithmetic-AFP,
author = {Fabian Immler},
title = {Affine Arithmetic},
journal = {Archive of Formal Proofs},
month = {February},
year = {2014},
note = {\url{https://isa-afp.org/entries/Affine_Arithmetic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Aggregation_Algebras.html b/web/entries/Aggregation_Algebras.html
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matrices and for edge weights in graphs. We verify the correctness of
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<h1 >
<span class='first'>A</span>ggregation <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">September 15, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop algebras for aggregation and minimisation for weight
matrices and for edge weights in graphs. We verify the correctness of
Prim's and Kruskal's minimum spanning tree algorithms based
on these algebras. We also show numerous instances of these algebras
based on linearly ordered commutative semigroups.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>December 9, 2020</dt>
<dd>moved Hoare logic to HOL-Hoare, moved spanning trees to Relational_Minimum_Spanning_Trees
(revision dbb9bfaf4283)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Aggregation_Algebras</h3>
<ul>
<li><a href="../theories/aggregation_algebras/#Semigroups_Big">Semigroups_Big</a></li>
<li><a href="../theories/aggregation_algebras/#Aggregation_Algebras">Aggregation_Algebras</a></li>
<li><a href="../theories/aggregation_algebras/#Matrix_Aggregation_Algebras">Matrix_Aggregation_Algebras</a></li>
<li><a href="../theories/aggregation_algebras/#Linear_Aggregation_Algebras">Linear_Aggregation_Algebras</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stone_Kleene_Relation_Algebras.html">Stone-Kleene Relation Algebras</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Relational_Minimum_Spanning_Trees.html">Relational Minimum Spanning Tree Algorithms</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Aggregation_Algebras-AFP</p><pre id="copy-text">@article{Aggregation_Algebras-AFP,
author = {Walter Guttmann},
title = {Aggregation Algebras},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Aggregation_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Aggregation_Algebras-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Aggregation_Algebras-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Akra_Bazzi.html b/web/entries/Akra_Bazzi.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Akra-Bazzi theorem and the Master theorem - Archive of Formal Proofs</title><meta name="description" content="This article contains a formalisation of the Akra-Bazzi method based on a proof by Leighton. It is a generalisation of the well-known Master Theorem for..."><meta property="og:title" content="The Akra-Bazzi theorem and the Master theorem" />
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<h1 >
<span class='first'>T</span>he <span class='first'>A</span>kra-<span class='first'>B</span>azzi <span class='first'>T</span>heorem and the <span class='first'>M</span>aster <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">July 14, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article contains a formalisation of the Akra-Bazzi method
based on a proof by Leighton. It is a generalisation of the well-known
Master Theorem for analysing the complexity of Divide & Conquer algorithms.
We also include a generalised version of the Master theorem based on the
Akra-Bazzi theorem, which is easier to apply than the Akra-Bazzi theorem
itself.
<p>
Some proof methods that facilitate applying the Master theorem are also
included. For a more detailed explanation of the formalisation and the
proof methods, see the accompanying paper (publication forthcoming).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Akra_Bazzi</h3>
<ul>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi_Library">Akra_Bazzi_Library</a></li>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi_Asymptotics">Akra_Bazzi_Asymptotics</a></li>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi_Real">Akra_Bazzi_Real</a></li>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi">Akra_Bazzi</a></li>
<li><a href="../theories/akra_bazzi/#Master_Theorem">Master_Theorem</a></li>
<li><a href="../theories/akra_bazzi/#Eval_Numeral">Eval_Numeral</a></li>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi_Method">Akra_Bazzi_Method</a></li>
<li><a href="../theories/akra_bazzi/#Akra_Bazzi_Approximation">Akra_Bazzi_Approximation</a></li>
<li><a href="../theories/akra_bazzi/#Master_Theorem_Examples">Master_Theorem_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Closest_Pair_Points.html">Closest Pair of Points Algorithms</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Akra_Bazzi-AFP</p><pre id="copy-text">@article{Akra_Bazzi-AFP,
author = {Manuel Eberl},
title = {The Akra-Bazzi theorem and the Master theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2015},
note = {\url{https://isa-afp.org/entries/Akra_Bazzi.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2015-07-24.tar.gz">Jul 24, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Akra_Bazzi-2015-07-15.tar.gz">Jul 15, 2015</a>: Isabelle2015
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<h1 >
<span class='first'>A</span>lgebraic <span class='first'>N</span>umbers in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>, <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a> and <a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsic2ViYXN0aWFhbiIsImpvb3N0ZW4iXX0=">📧</a>
with contributions from <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 22, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Based on existing libraries for matrices, factorization of rational polynomials, and Sturm's theorem, we formalized algebraic numbers in Isabelle/HOL. Our development serves as an implementation for real and complex numbers, and it admits to compute roots and completely factorize real and complex polynomials, provided that all coefficients are rational numbers. Moreover, we provide two implementations to display algebraic numbers, an injective and expensive one, or a faster but approximative version.
</p><p>
To this end, we mechanized several results on resultants, which also required us to prove that polynomials over a unique factorization domain form again a unique factorization domain.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 16, 2017</dt>
<dd>Use certified Berlekamp-Zassenhaus factorization, use subresultant algorithm for computing resultants, improved bisection algorithm</dd><dt>January 29, 2016</dt>
<dd>Split off Polynomial Interpolation and Polynomial Factorization<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Algebraic_Numbers</h3>
<ul>
<li><a href="../theories/algebraic_numbers/#Algebraic_Numbers_Prelim">Algebraic_Numbers_Prelim</a></li>
<li><a href="../theories/algebraic_numbers/#Bivariate_Polynomials">Bivariate_Polynomials</a></li>
<li><a href="../theories/algebraic_numbers/#Resultant">Resultant</a></li>
<li><a href="../theories/algebraic_numbers/#Algebraic_Numbers">Algebraic_Numbers</a></li>
<li><a href="../theories/algebraic_numbers/#Sturm_Rat">Sturm_Rat</a></li>
<li><a href="../theories/algebraic_numbers/#Factors_of_Int_Poly">Factors_of_Int_Poly</a></li>
<li><a href="../theories/algebraic_numbers/#Min_Int_Poly">Min_Int_Poly</a></li>
<li><a href="../theories/algebraic_numbers/#Algebraic_Numbers_Pre_Impl">Algebraic_Numbers_Pre_Impl</a></li>
<li><a href="../theories/algebraic_numbers/#Cauchy_Root_Bound">Cauchy_Root_Bound</a></li>
<li><a href="../theories/algebraic_numbers/#Real_Algebraic_Numbers">Real_Algebraic_Numbers</a></li>
<li><a href="../theories/algebraic_numbers/#Real_Roots">Real_Roots</a></li>
<li><a href="../theories/algebraic_numbers/#Complex_Roots_Real_Poly">Complex_Roots_Real_Poly</a></li>
<li><a href="../theories/algebraic_numbers/#Compare_Complex">Compare_Complex</a></li>
<li><a href="../theories/algebraic_numbers/#Interval_Arithmetic">Interval_Arithmetic</a></li>
<li><a href="../theories/algebraic_numbers/#Complex_Algebraic_Numbers">Complex_Algebraic_Numbers</a></li>
<li><a href="../theories/algebraic_numbers/#Show_Real_Alg">Show_Real_Alg</a></li>
<li><a href="../theories/algebraic_numbers/#Show_Real_Approx">Show_Real_Approx</a></li>
<li><a href="../theories/algebraic_numbers/#Show_Real_Precise">Show_Real_Precise</a></li>
<li><a href="../theories/algebraic_numbers/#Algebraic_Number_Tests">Algebraic_Number_Tests</a></li>
<li><a href="../theories/algebraic_numbers/#Algebraic_Numbers_External_Code">Algebraic_Numbers_External_Code</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li><li><a href="../entries/Cubic_Quartic_Equations.html">Solving Cubic and Quartic Equations</a></li><li><a href="../entries/BenOr_Kozen_Reif.html">The BKR Decision Procedure for Univariate Real Arithmetic</a></li><li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li><li><a href="../entries/LLL_Basis_Reduction.html">A verified LLL algorithm</a></li><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
<li><a href="../entries/Cubic_Quartic_Equations.html">Solving Cubic and Quartic Equations</a></li>
<li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li>
<li><a href="../entries/Complex_Geometry.html">Complex Geometry</a></li>
<li><a href="../entries/Transcendence_Series_Hancl_Rucki.html">The Transcendence of Certain Infinite Series</a></li>
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<p style="display:none;" id="bibtex-filename">Algebraic_Numbers-AFP</p><pre id="copy-text">@article{Algebraic_Numbers-AFP,
author = {René Thiemann and Akihisa Yamada and Sebastiaan J. C. Joosten},
title = {Algebraic Numbers in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Algebraic_Numbers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Algebraic_Numbers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Algebraic_Numbers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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</li><li>
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<h1 >
<span class='first'>P</span>rogram <span class='first'>C</span>onstruction and <span class='first'>V</span>erification <span class='first'>C</span>omponents <span class='first'>B</span>ased on <span class='first'>K</span>leene <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInZpY3RvciIsImdvbWVzIl19">📧</a> and <a href="../authors/struth">Georg Struth</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJnIiwic3RydXRoIl19">📧</a>
</p>
<p class="date">June 18, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Variants of Kleene algebra support program construction and
verification by algebraic reasoning. This entry provides a
verification component for Hoare logic based on Kleene algebra with
tests, verification components for weakest preconditions and strongest
postconditions based on Kleene algebra with domain and a component for
step-wise refinement based on refinement Kleene algebra with tests. In
addition to these components for the partial correctness of while
programs, a verification component for total correctness based on
divergence Kleene algebras and one for (partial correctness) of
recursive programs based on domain quantales are provided. Finally we
have integrated memory models for programs with pointers and a program
trace semantics into the weakest precondition component.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Algebraic_VCs</h3>
<ul>
<li><a href="../theories/algebraic_vcs/#VC_KAT_scratch">VC_KAT_scratch</a></li>
<li><a href="../theories/algebraic_vcs/#VC_KAD_scratch">VC_KAD_scratch</a></li>
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<li><a href="../theories/algebraic_vcs/#VC_KAT">VC_KAT</a></li>
<li><a href="../theories/algebraic_vcs/#VC_KAT_Examples">VC_KAT_Examples</a></li>
<li><a href="../theories/algebraic_vcs/#VC_KAT_Examples2">VC_KAT_Examples2</a></li>
<li><a href="../theories/algebraic_vcs/#RKAT">RKAT</a></li>
<li><a href="../theories/algebraic_vcs/#RKAT_Models">RKAT_Models</a></li>
<li><a href="../theories/algebraic_vcs/#VC_RKAT">VC_RKAT</a></li>
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<li><a href="../theories/algebraic_vcs/#Domain_Quantale">Domain_Quantale</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li><li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Algebraic_VCs-AFP</p><pre id="copy-text">@article{Algebraic_VCs-AFP,
author = {Victor B. F. Gomes and Georg Struth},
title = {Program Construction and Verification Components Based on Kleene Algebra},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Algebraic_VCs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span>llen's <span class='first'>I</span>nterval <span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/ghourabi">Fadoua Ghourabi</a>
</p>
<p class="date">September 29, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Allen’s interval calculus is a qualitative temporal representation of
time events. Allen introduced 13 binary relations that describe all
the possible arrangements between two events, i.e. intervals with
non-zero finite length. The compositions are pertinent to
reasoning about knowledge of time. In particular, a consistency
problem of relation constraints is commonly solved with a guideline
from these compositions. We formalize the relations together with an
axiomatic system. We proof the validity of the 169 compositions of
these relations. We also define nests as the sets of intervals that
share a meeting point. We prove that nests give the ordering
properties of points without introducing a new datatype for points.
[1] J.F. Allen. Maintaining Knowledge about Temporal Intervals. In
Commun. ACM, volume 26, pages 832–843, 1983. [2] J. F. Allen and P. J.
Hayes. A Common-sense Theory of Time. In Proceedings of the 9th
International Joint Conference on Artificial Intelligence (IJCAI’85),
pages 528–531, 1985.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session Allen_Calculus</h3>
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<p style="display:none;" id="bibtex-filename">Allen_Calculus-AFP</p><pre id="copy-text">@article{Allen_Calculus-AFP,
author = {Fadoua Ghourabi},
title = {Allen&#39;s Interval Calculus},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Allen_Calculus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Amicable_Numbers.html b/web/entries/Amicable_Numbers.html
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<h1 >
<span class='first'>A</span>micable <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a>
</p>
<p class="date">August 4, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalisation of Amicable Numbers, involving some relevant
material including Euler's sigma function, some relevant
definitions, results and examples as well as rules such as
Th&#257;bit ibn Qurra's Rule, Euler's Rule, te
Riele's Rule and Borho's Rule with breeders.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Amicable_Numbers</h3>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Pratt_Certificate.html">Pratt&rsquo;s Primality Certificates</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Amicable_Numbers-AFP</p><pre id="copy-text">@article{Amicable_Numbers-AFP,
author = {Angeliki Koutsoukou-Argyraki},
title = {Amicable Numbers},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/Amicable_Numbers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Amicable_Numbers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Amicable_Numbers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>A</span>mortized <span class='first'>C</span>omplexity <span class='first'>V</span>erified</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">July 7, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A framework for the analysis of the amortized complexity of functional
data structures is formalized in Isabelle/HOL and applied to a number of
standard examples and to the folowing non-trivial ones: skew heaps,
splay trees, splay heaps and pairing heaps.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 14, 2016</dt>
<dd>Moved pairing heaps from here to the new Pairing_Heap</dd><dt>July 12, 2016</dt>
<dd>Moved splay heaps from here to Splay_Tree<br></dd><dt>March 17, 2015</dt>
<dd>Added pairing heaps by Hauke Brinkop.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T., & Brinkop, H. (2018). Amortized Complexity Verified. Journal of Automated Reasoning, 62(3), 367–391. <a href="https://doi.org/10.1007/s10817-018-9459-3">https://doi.org/10.1007/s10817-018-9459-3</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jar18.html">Open access</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Amortized_analysis">Wikipedia</a>
</li></ul>
<h3>Session Amortized_Complexity</h3>
<ul>
<li><a href="../theories/amortized_complexity/#Amortized_Framework0">Amortized_Framework0</a></li>
<li><a href="../theories/amortized_complexity/#Amortized_Framework">Amortized_Framework</a></li>
<li><a href="../theories/amortized_complexity/#Amortized_Examples">Amortized_Examples</a></li>
<li><a href="../theories/amortized_complexity/#Priority_Queue_ops_merge">Priority_Queue_ops_merge</a></li>
<li><a href="../theories/amortized_complexity/#Skew_Heap_Analysis">Skew_Heap_Analysis</a></li>
<li><a href="../theories/amortized_complexity/#Lemmas_log">Lemmas_log</a></li>
<li><a href="../theories/amortized_complexity/#Splay_Tree_Analysis_Base">Splay_Tree_Analysis_Base</a></li>
<li><a href="../theories/amortized_complexity/#Splay_Tree_Analysis">Splay_Tree_Analysis</a></li>
<li><a href="../theories/amortized_complexity/#Splay_Tree_Analysis_Optimal">Splay_Tree_Analysis_Optimal</a></li>
<li><a href="../theories/amortized_complexity/#Priority_Queue_ops">Priority_Queue_ops</a></li>
<li><a href="../theories/amortized_complexity/#Splay_Heap_Analysis">Splay_Heap_Analysis</a></li>
<li><a href="../theories/amortized_complexity/#Pairing_Heap_Tree_Analysis">Pairing_Heap_Tree_Analysis</a></li>
<li><a href="../theories/amortized_complexity/#Pairing_Heap_Tree_Analysis2">Pairing_Heap_Tree_Analysis2</a></li>
<li><a href="../theories/amortized_complexity/#Pairing_Heap_List1_Analysis">Pairing_Heap_List1_Analysis</a></li>
<li><a href="../theories/amortized_complexity/#Pairing_Heap_List1_Analysis2">Pairing_Heap_List1_Analysis2</a></li>
<li><a href="../theories/amortized_complexity/#Pairing_Heap_List2_Analysis">Pairing_Heap_List2_Analysis</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Pairing_Heap.html">Pairing Heap</a></li><li><a href="../entries/Skew_Heap.html">Skew Heap</a></li><li><a href="../entries/Splay_Tree.html">Splay Tree</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Root_Balanced_Tree.html">Root-Balanced Tree</a></li><li><a href="../entries/Dynamic_Tables.html">Parameterized Dynamic Tables</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Amortized_Complexity-AFP</p><pre id="copy-text">@article{Amortized_Complexity-AFP,
author = {Tobias Nipkow},
title = {Amortized Complexity Verified},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/Amortized_Complexity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2015-05-28.tar.gz">May 28, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2015-05-19.tar.gz">May 19, 2015</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Amortized_Complexity-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li></ul>
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diff --git a/web/entries/AnselmGod.html b/web/entries/AnselmGod.html
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<h1 >
<span class='first'>A</span>nselm's <span class='first'>G</span>od in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/blumson">Ben Blumson</a> <a href="https://philpeople.org/profiles/ben-blumson">🌐</a>
</p>
<p class="date">September 6, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Paul Oppenheimer and Edward Zalta's formalisation of
Anselm's ontological argument for the existence of God is
automated by embedding a free logic for definite descriptions within
Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session AnselmGod</h3>
<ul>
<li><a href="../theories/anselmgod/#AnselmGod">AnselmGod</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">AnselmGod-AFP</p><pre id="copy-text">@article{AnselmGod-AFP,
author = {Ben Blumson},
title = {Anselm&#39;s God in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {September},
year = {2017},
note = {\url{https://isa-afp.org/entries/AnselmGod.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-AnselmGod-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-AnselmGod-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-AnselmGod-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2017-09-18.tar.gz">Sep 18, 2017</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2017-09-11.tar.gz">Sep 11, 2017</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AnselmGod-2017-09-08.tar.gz">Sep 8, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Applicative_Lifting.html b/web/entries/Applicative_Lifting.html
--- a/web/entries/Applicative_Lifting.html
+++ b/web/entries/Applicative_Lifting.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Applicative Lifting - Archive of Formal Proofs</title><meta name="description" content="Applicative functors augment computations with effects by lifting function application to types which model the effects. As the structure of the..."><meta property="og:title" content="Applicative Lifting" />
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<h1 >
<span class='first'>A</span>pplicative <span class='first'>L</span>ifting</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/schneider">Joshua Schneider</a>
</p>
<p class="date">December 22, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Applicative functors augment computations with effects by lifting function application to types which model the effects. As the structure of the computation cannot depend on the effects, applicative expressions can be analysed statically. This allows us to lift universally quantified equations to the effectful types, as observed by Hinze. Thus, equational reasoning over effectful computations can be reduced to pure types.
</p><p>
This entry provides a package for registering applicative functors and two proof methods for lifting of equations over applicative functors. The first method normalises applicative expressions according to the laws of applicative functors. This way, equations whose two sides contain the same list of variables can be lifted to every applicative functor.
</p><p>
To lift larger classes of equations, the second method exploits a number of additional properties (e.g., commutativity of effects) provided the properties have been declared for the concrete applicative functor at hand upon registration.
</p><p>
We declare several types from the Isabelle library as applicative functors and illustrate the use of the methods with two examples: the lifting of the arithmetic type class hierarchy to streams and the verification of a relabelling function on binary trees. We also formalise and verify the normalisation algorithm used by the first proof method.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 10, 2016</dt>
<dd>implemented automatic derivation of lifted combinator reductions;
support arbitrary lifted relations using relators;
improved compatibility with locale interpretation
(revision ec336f354f37)<br></dd><dt>March 3, 2016</dt>
<dd>added formalisation of lifting with combinators<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Applicative_Lifting</h3>
<ul>
<li><a href="../theories/applicative_lifting/#Applicative">Applicative</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Environment">Applicative_Environment</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Option">Applicative_Option</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Sum">Applicative_Sum</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Set">Applicative_Set</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_List">Applicative_List</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_DNEList">Applicative_DNEList</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Monoid">Applicative_Monoid</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Filter">Applicative_Filter</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_State">Applicative_State</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Stream">Applicative_Stream</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Open_State">Applicative_Open_State</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_PMF">Applicative_PMF</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Probability_List">Applicative_Probability_List</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Star">Applicative_Star</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Vector">Applicative_Vector</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Functor">Applicative_Functor</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Environment_Algebra">Applicative_Environment_Algebra</a></li>
<li><a href="../theories/applicative_lifting/#Stream_Algebra">Stream_Algebra</a></li>
<li><a href="../theories/applicative_lifting/#Tree_Relabelling">Tree_Relabelling</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Examples">Applicative_Examples</a></li>
<li><a href="../theories/applicative_lifting/#Joinable">Joinable</a></li>
<li><a href="../theories/applicative_lifting/#Beta_Eta">Beta_Eta</a></li>
<li><a href="../theories/applicative_lifting/#Combinators">Combinators</a></li>
<li><a href="../theories/applicative_lifting/#Idiomatic_Terms">Idiomatic_Terms</a></li>
<li><a href="../theories/applicative_lifting/#Abstract_AF">Abstract_AF</a></li>
<li><a href="../theories/applicative_lifting/#Applicative_Test">Applicative_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CryptHOL.html">CryptHOL</a></li><li><a href="../entries/Stern_Brocot.html">The Stern-Brocot Tree</a></li><li><a href="../entries/Free-Groups.html">Free Groups</a></li><li><a href="../entries/Locally-Nameless-Sigma.html">Locally Nameless Sigma Calculus</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Applicative_Lifting-AFP</p><pre id="copy-text">@article{Applicative_Lifting-AFP,
author = {Andreas Lochbihler and Joshua Schneider},
title = {Applicative Lifting},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Applicative_Lifting.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Applicative_Lifting-2015-12-22.tar.gz">Dec 22, 2015</a>: Isabelle2015
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<h1 >
<span class='first'>V</span>erified <span class='first'>A</span>pproximation <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/essmann">Robin Eßmann</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsicm9iaW4iLCJlc3NtYW5uIl19">📧</a>, <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>, <a href="../authors/robillard">Simon Robillard</a> <a href="https://simon-robillard.net/">🌐</a> and <a href="../authors/sulejmani">Ujkan Sulejmani</a>
</p>
<p class="date">January 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the first formal verification of approximation algorithms
for NP-complete optimization problems: vertex cover, set cover, independent set,
center selection, load balancing, and bin packing. The proofs correct incompletenesses
in existing proofs and improve the approximation ratio in one case.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 29, 2021</dt>
<dd>added theory Center_Selection by Ujkan Sulejmani</dd><dt>February 8, 2021</dt>
<dd>added theory Approx_SC_Hoare (Set Cover) by Robin Eßmann<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/approximation">Computer science/Algorithms/Approximation</a></li></ul>
<h3>Session Approximation_Algorithms</h3>
<ul>
<li><a href="../theories/approximation_algorithms/#Approx_VC_Hoare">Approx_VC_Hoare</a></li>
<li><a href="../theories/approximation_algorithms/#Approx_SC_Hoare">Approx_SC_Hoare</a></li>
<li><a href="../theories/approximation_algorithms/#Approx_MIS_Hoare">Approx_MIS_Hoare</a></li>
<li><a href="../theories/approximation_algorithms/#Approx_LB_Hoare">Approx_LB_Hoare</a></li>
<li><a href="../theories/approximation_algorithms/#Approx_BP_Hoare">Approx_BP_Hoare</a></li>
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<p style="display:none;" id="bibtex-filename">Approximation_Algorithms-AFP</p><pre id="copy-text">@article{Approximation_Algorithms-AFP,
author = {Robin Eßmann and Tobias Nipkow and Simon Robillard and Ujkan Sulejmani},
title = {Verified Approximation Algorithms},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Approximation_Algorithms.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Approximation_Algorithms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Approximation_Algorithms-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span> <span class='first'>T</span>heory of <span class='first'>A</span>rchitectural <span class='first'>D</span>esign <span class='first'>P</span>atterns</h1>
<div>
<p><a href="../authors/marmsoler">Diego Marmsoler</a> <a href="http://marmsoler.com">🌐</a>
</p>
<p class="date">March 1, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The following document formalizes and verifies several architectural
design patterns. Each pattern specification is formalized in terms of
a locale where the locale assumptions correspond to the assumptions
which a pattern poses on an architecture. Thus, pattern specifications
may build on top of each other by interpreting the corresponding
locale. A pattern is verified using the framework provided by the AFP
entry Dynamic Architectures. Currently, the document consists of
formalizations of 4 different patterns: the singleton, the publisher
subscriber, the blackboard pattern, and the blockchain pattern.
Thereby, the publisher component of the publisher subscriber pattern
is modeled as an instance of the singleton pattern and the blackboard
pattern is modeled as an instance of the publisher subscriber pattern.
In general, this entry provides the first steps towards an overall
theory of architectural design patterns.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 8, 2019</dt>
<dd>adapting the terminology: honest instead of trusted, dishonest instead of untrusted (revision 7af3431a22ae)</dd><dt>May 25, 2018</dt>
<dd>changing the major assumption for blockchain architectures from alternative minings to relative mining frequencies (revision 5043c5c71685)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session Architectural_Design_Patterns</h3>
<ul>
<li><a href="../theories/architectural_design_patterns/#Singleton">Singleton</a></li>
<li><a href="../theories/architectural_design_patterns/#Publisher_Subscriber">Publisher_Subscriber</a></li>
<li><a href="../theories/architectural_design_patterns/#Blackboard">Blackboard</a></li>
<li><a href="../theories/architectural_design_patterns/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/architectural_design_patterns/#RF_LTL">RF_LTL</a></li>
<li><a href="../theories/architectural_design_patterns/#Blockchain">Blockchain</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/DynamicArchitectures.html">Dynamic Architectures</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Architectural_Design_Patterns-AFP</p><pre id="copy-text">@article{Architectural_Design_Patterns-AFP,
author = {Diego Marmsoler},
title = {A Theory of Architectural Design Patterns},
journal = {Archive of Formal Proofs},
month = {March},
year = {2018},
note = {\url{https://isa-afp.org/entries/Architectural_Design_Patterns.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Architectural_Design_Patterns-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Architectural_Design_Patterns-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Architectural_Design_Patterns-2018-03-01.tar.gz">Mar 1, 2018</a>: Isabelle2017
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diff --git a/web/entries/Aristotles_Assertoric_Syllogistic.html b/web/entries/Aristotles_Assertoric_Syllogistic.html
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<h1 >
<span class='first'>A</span>ristotle's <span class='first'>A</span>ssertoric <span class='first'>S</span>yllogistic</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a>
</p>
<p class="date">October 8, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise with Isabelle/HOL some basic elements of Aristotle's
assertoric syllogistic following the <a
href="https://plato.stanford.edu/entries/aristotle-logic/">article from the Stanford Encyclopedia of Philosophy by Robin Smith.</a> To
this end, we use a set theoretic formulation (covering both individual
and general predication). In particular, we formalise the deductions
in the Figures and after that we present Aristotle's
metatheoretical observation that all deductions in the Figures can in
fact be reduced to either Barbara or Celarent. As the formal proofs
prove to be straightforward, the interest of this entry lies in
illustrating the functionality of Isabelle and high efficiency of
Sledgehammer for simple exercises in philosophy.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session Aristotles_Assertoric_Syllogistic</h3>
<ul>
<li><a href="../theories/aristotles_assertoric_syllogistic/#AristotlesAssertoric">AristotlesAssertoric</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Aristotles_Assertoric_Syllogistic-AFP</p><pre id="copy-text">@article{Aristotles_Assertoric_Syllogistic-AFP,
author = {Angeliki Koutsoukou-Argyraki},
title = {Aristotle&#39;s Assertoric Syllogistic},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/Aristotles_Assertoric_Syllogistic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Aristotles_Assertoric_Syllogistic-2019-10-17.tar.gz">Oct 17, 2019</a>: Isabelle2019
</li></ul>
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diff --git a/web/entries/Arith_Prog_Rel_Primes.html b/web/entries/Arith_Prog_Rel_Primes.html
--- a/web/entries/Arith_Prog_Rel_Primes.html
+++ b/web/entries/Arith_Prog_Rel_Primes.html
@@ -1,171 +1,173 @@
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<h1 >
<span class='first'>A</span>rithmetic <span class='first'>P</span>rogressions and <span class='first'>R</span>elative <span class='first'>P</span>rimes</h1>
<div>
<p><a href="../authors/caballero">José Manuel Rodríguez Caballero</a> <a href="https://josephcmac.github.io/">🌐</a>
</p>
<p class="date">February 1, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article provides a formalization of the solution obtained by the
author of the Problem “ARITHMETIC PROGRESSIONS” from the
<a href="https://www.ocf.berkeley.edu/~wwu/riddles/putnam.shtml">
Putnam exam problems of 2002</a>. The statement of the problem is
as follows: For which integers <em>n</em> > 1 does the set of positive
integers less than and relatively prime to <em>n</em> constitute an
arithmetic progression?</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Arith_Prog_Rel_Primes</h3>
<ul>
<li><a href="../theories/arith_prog_rel_primes/#Arith_Prog_Rel_Primes">Arith_Prog_Rel_Primes</a></li></ul><div class="flex-wrap">
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author = {José Manuel Rodríguez Caballero},
title = {Arithmetic progressions and relative primes},
journal = {Archive of Formal Proofs},
month = {February},
year = {2020},
note = {\url{https://isa-afp.org/entries/Arith_Prog_Rel_Primes.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Arith_Prog_Rel_Primes-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Arith_Prog_Rel_Primes-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Arith_Prog_Rel_Primes-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Arith_Prog_Rel_Primes-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Arith_Prog_Rel_Primes-2020-02-10.tar.gz">Feb 10, 2020</a>: Isabelle2019
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diff --git a/web/entries/ArrowImpossibilityGS.html b/web/entries/ArrowImpossibilityGS.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Arrow and Gibbard-Satterthwaite - Archive of Formal Proofs</title><meta name="description" content="This article formalizes two proofs of Arrow&#39;s impossibility theorem due to Geanakoplos and derives the Gibbard-Satterthwaite theorem as a corollary. One..."><meta property="og:title" content="Arrow and Gibbard-Satterthwaite" />
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<h1 >
<span class='first'>A</span>rrow and <span class='first'>G</span>ibbard-<span class='first'>S</span>atterthwaite</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">September 1, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes two proofs of Arrow's impossibility theorem due to Geanakoplos and derives the Gibbard-Satterthwaite theorem as a corollary. One formalization is based on utility functions, the other one on strict partial orders.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T. (2009). Social Choice Theory in HOL. Journal of Automated Reasoning, 43(3), 289–304. <a href="https://doi.org/10.1007/s10817-009-9147-4">https://doi.org/10.1007/s10817-009-9147-4</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/arrow.html">Open access</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem">Wikipedia</a>
</li></ul>
<h3>Session ArrowImpossibilityGS</h3>
<ul>
<li><a href="../theories/arrowimpossibilitygs/#Arrow_Utility">Arrow_Utility</a></li>
<li><a href="../theories/arrowimpossibilitygs/#Arrow_Order">Arrow_Order</a></li>
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<p style="display:none;" id="bibtex-filename">ArrowImpossibilityGS-AFP</p><pre id="copy-text">@article{ArrowImpossibilityGS-AFP,
author = {Tobias Nipkow},
title = {Arrow and Gibbard-Satterthwaite},
journal = {Archive of Formal Proofs},
month = {September},
year = {2008},
note = {\url{https://isa-afp.org/entries/ArrowImpossibilityGS.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-ArrowImpossibilityGS-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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</li><li>
<a href="https://www.isa-afp.org/release/afp-ArrowImpossibilityGS-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-ArrowImpossibilityGS-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-ArrowImpossibilityGS-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-ArrowImpossibilityGS-2009-09-29.tar.gz">Sep 29, 2009</a>: Isabelle2009
</li><li>
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<h1 >
<span class='first'>A</span>ttack <span class='first'>T</span>rees in <span class='first'>I</span>sabelle for <span class='first'>G</span><span class='first'>D</span><span class='first'>P</span><span class='first'>R</span> <span class='first'>C</span>ompliance of <span class='first'>I</span>o<span class='first'>T</span> <span class='first'>H</span>ealthcare <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/kammueller">Florian Kammüller</a> <a href="http://www.cs.mdx.ac.uk/people/florian-kammueller/">🌐</a>
</p>
<p class="date">April 27, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this article, we present a proof theory for Attack Trees. Attack
Trees are a well established and useful model for the construction of
attacks on systems since they allow a stepwise exploration of high
level attacks in application scenarios. Using the expressiveness of
Higher Order Logic in Isabelle, we develop a generic
theory of Attack Trees with a state-based semantics based on Kripke
structures and CTL. The resulting framework
allows mechanically supported logic analysis of the meta-theory of the
proof calculus of Attack Trees and at the same time the developed
proof theory enables application to case studies. A central
correctness and completeness result proved in Isabelle establishes a
connection between the notion of Attack Tree validity and CTL. The
application is illustrated on the example of a healthcare IoT system
and GDPR compliance verification.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Attack_Trees</h3>
<ul>
<li><a href="../theories/attack_trees/#MC">MC</a></li>
<li><a href="../theories/attack_trees/#AT">AT</a></li>
<li><a href="../theories/attack_trees/#Infrastructure">Infrastructure</a></li>
<li><a href="../theories/attack_trees/#GDPRhealthcare">GDPRhealthcare</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Attack_Trees-AFP</p><pre id="copy-text">@article{Attack_Trees-AFP,
author = {Florian Kammüller},
title = {Attack Trees in Isabelle for GDPR compliance of IoT healthcare systems},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Attack_Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Auto2_HOL.html b/web/entries/Auto2_HOL.html
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+++ b/web/entries/Auto2_HOL.html
@@ -1,188 +1,190 @@
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<h1 >
<span class='first'>A</span>uto2 <span class='first'>P</span>rover</h1>
<div>
<p><a href="../authors/zhan">Bohua Zhan</a> <a href="http://lcs.ios.ac.cn/~bzhan/">🌐</a>
</p>
<p class="date">November 20, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Auto2 is a saturation-based heuristic prover for higher-order logic,
implemented as a tactic in Isabelle. This entry contains the
instantiation of auto2 for Isabelle/HOL, along with two basic
examples: solutions to some of the Pelletier’s problems, and
elementary number theory of primes.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Auto2_HOL</h3>
<ul>
<li><a href="../theories/auto2_hol/#Auto2_Setup">Auto2_Setup</a></li>
<li><a href="../theories/auto2_hol/#Auto2_HOL_Extra_Setup">Auto2_HOL_Extra_Setup</a></li>
<li><a href="../theories/auto2_hol/#HOL_Base">HOL_Base</a></li>
<li><a href="../theories/auto2_hol/#Auto2_HOL_Setup">Auto2_HOL_Setup</a></li>
<li><a href="../theories/auto2_hol/#Logic_Thms">Logic_Thms</a></li>
<li><a href="../theories/auto2_hol/#Order_Thms">Order_Thms</a></li>
<li><a href="../theories/auto2_hol/#Arith_Thms">Arith_Thms</a></li>
<li><a href="../theories/auto2_hol/#Set_Thms">Set_Thms</a></li>
<li><a href="../theories/auto2_hol/#Lists_Thms">Lists_Thms</a></li>
<li><a href="../theories/auto2_hol/#Auto2_Main">Auto2_Main</a></li>
<li><a href="../theories/auto2_hol/#Auto2_Test">Auto2_Test</a></li>
<li><a href="../theories/auto2_hol/#Pelletier">Pelletier</a></li>
<li><a href="../theories/auto2_hol/#Primes_Ex">Primes_Ex</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Auto2_Imperative_HOL.html">Verifying Imperative Programs using Auto2</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Auto2_HOL-AFP</p><pre id="copy-text">@article{Auto2_HOL-AFP,
author = {Bohua Zhan},
title = {Auto2 Prover},
journal = {Archive of Formal Proofs},
month = {November},
year = {2018},
note = {\url{https://isa-afp.org/entries/Auto2_HOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_HOL-2018-11-29.tar.gz">Nov 29, 2018</a>: Isabelle2018
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diff --git a/web/entries/Auto2_Imperative_HOL.html b/web/entries/Auto2_Imperative_HOL.html
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<h1 >
<span class='first'>V</span>erifying <span class='first'>I</span>mperative <span class='first'>P</span>rograms <span class='first'>U</span>sing <span class='first'>A</span>uto2</h1>
<div>
<p><a href="../authors/zhan">Bohua Zhan</a> <a href="http://lcs.ios.ac.cn/~bzhan/">🌐</a>
</p>
<p class="date">December 21, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains the application of auto2 to verifying functional
and imperative programs. Algorithms and data structures that are
verified include linked lists, binary search trees, red-black trees,
interval trees, priority queue, quicksort, union-find, Dijkstra's
algorithm, and a sweep-line algorithm for detecting rectangle
intersection. The imperative verification is based on Imperative HOL
and its separation logic framework. A major goal of this work is to
set up automation in order to reduce the length of proof that the user
needs to provide, both for verifying functional programs and for
working with separation logic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Auto2_Imperative_HOL</h3>
<ul>
<li><a href="../theories/auto2_imperative_hol/#Mapping_Str">Mapping_Str</a></li>
<li><a href="../theories/auto2_imperative_hol/#Lists_Ex">Lists_Ex</a></li>
<li><a href="../theories/auto2_imperative_hol/#BST">BST</a></li>
<li><a href="../theories/auto2_imperative_hol/#Partial_Equiv_Rel">Partial_Equiv_Rel</a></li>
<li><a href="../theories/auto2_imperative_hol/#Union_Find">Union_Find</a></li>
<li><a href="../theories/auto2_imperative_hol/#Connectivity">Connectivity</a></li>
<li><a href="../theories/auto2_imperative_hol/#Arrays_Ex">Arrays_Ex</a></li>
<li><a href="../theories/auto2_imperative_hol/#Dijkstra">Dijkstra</a></li>
<li><a href="../theories/auto2_imperative_hol/#Interval">Interval</a></li>
<li><a href="../theories/auto2_imperative_hol/#Interval_Tree">Interval_Tree</a></li>
<li><a href="../theories/auto2_imperative_hol/#Quicksort">Quicksort</a></li>
<li><a href="../theories/auto2_imperative_hol/#Indexed_PQueue">Indexed_PQueue</a></li>
<li><a href="../theories/auto2_imperative_hol/#RBTree">RBTree</a></li>
<li><a href="../theories/auto2_imperative_hol/#Rect_Intersect">Rect_Intersect</a></li>
<li><a href="../theories/auto2_imperative_hol/#SepLogic_Base">SepLogic_Base</a></li>
<li><a href="../theories/auto2_imperative_hol/#SepAuto">SepAuto</a></li>
<li><a href="../theories/auto2_imperative_hol/#GCD_Impl">GCD_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#LinkedList">LinkedList</a></li>
<li><a href="../theories/auto2_imperative_hol/#BST_Impl">BST_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#RBTree_Impl">RBTree_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Arrays_Impl">Arrays_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Quicksort_Impl">Quicksort_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Union_Find_Impl">Union_Find_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Connectivity_Impl">Connectivity_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#DynamicArray">DynamicArray</a></li>
<li><a href="../theories/auto2_imperative_hol/#Indexed_PQueue_Impl">Indexed_PQueue_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Dijkstra_Impl">Dijkstra_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#IntervalTree_Impl">IntervalTree_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Rect_Intersect_Impl">Rect_Intersect_Impl</a></li>
<li><a href="../theories/auto2_imperative_hol/#Sep_Examples">Sep_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Auto2_HOL.html">Auto2 Prover</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Separation_Logic_Unbounded.html">Unbounded Separation Logic</a></li>
<li><a href="../entries/Skip_Lists.html">Skip Lists</a></li>
<li><a href="../entries/Hoare_Time.html">Hoare Logics for Time Bounds</a></li>
<li><a href="../entries/Treaps.html">Treaps</a></li>
<li><a href="../entries/Complx.html">COMPLX: A Verification Framework for Concurrent Imperative Programs</a></li>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Auto2_Imperative_HOL/document.pdf">Proof
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Auto2_Imperative_HOL/session_graph.pdf">Dependencies</a></nav>
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<p style="display:none;" id="bibtex-filename">Auto2_Imperative_HOL-AFP</p><pre id="copy-text">@article{Auto2_Imperative_HOL-AFP,
author = {Bohua Zhan},
title = {Verifying Imperative Programs using Auto2},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Auto2_Imperative_HOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-Auto2_Imperative_HOL-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Auto2_Imperative_HOL-2019-01-22.tar.gz">Jan 22, 2019</a>: Isabelle2018
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/AutoFocus-Stream.html b/web/entries/AutoFocus-Stream.html
--- a/web/entries/AutoFocus-Stream.html
+++ b/web/entries/AutoFocus-Stream.html
@@ -1,198 +1,200 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics - Archive of Formal Proofs</title><meta name="description" content="We formalize the AutoFocus Semantics (a time-synchronous subset of the Focus formalism) as stream processing functions on finite and infinite message..."><meta property="og:title" content="AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics" />
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<h1 >
<span class='first'>A</span>uto<span class='first'>F</span>ocus <span class='first'>S</span>tream <span class='first'>P</span>rocessing for <span class='first'>S</span>ingle-<span class='first'>C</span>locking and <span class='first'>M</span>ulti-<span class='first'>C</span>locking <span class='first'>S</span>emantics</h1>
<div>
<p><a href="../authors/trachtenherz">David Trachtenherz</a>
</p>
<p class="date">February 23, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the AutoFocus Semantics (a time-synchronous subset of the Focus formalism) as stream processing functions on finite and infinite message streams represented as finite/infinite lists. The formalization comprises both the conventional single-clocking semantics (uniform global clock for all components and communications channels) and its extension to multi-clocking semantics (internal execution clocking of a component may be a multiple of the external communication clocking). The semantics is defined by generic stream processing functions making it suitable for simulation/code generation in Isabelle/HOL. Furthermore, a number of AutoFocus semantics properties are formalized using definitions from the IntervalLogic theories.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session AutoFocus-Stream</h3>
<ul>
<li><a href="../theories/autofocus-stream/#ListSlice">ListSlice</a></li>
<li><a href="../theories/autofocus-stream/#AF_Stream">AF_Stream</a></li>
<li><a href="../theories/autofocus-stream/#AF_Stream_Exec">AF_Stream_Exec</a></li>
<li><a href="../theories/autofocus-stream/#IL_AF_Stream">IL_AF_Stream</a></li>
<li><a href="../theories/autofocus-stream/#IL_AF_Stream_Exec">IL_AF_Stream_Exec</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nat-Interval-Logic.html">Interval Temporal Logic on Natural Numbers</a></li></ul>
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</div>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/AutoFocus-Stream/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">AutoFocus-Stream-AFP</p><pre id="copy-text">@article{AutoFocus-Stream-AFP,
author = {David Trachtenherz},
title = {AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics},
journal = {Archive of Formal Proofs},
month = {February},
year = {2011},
note = {\url{https://isa-afp.org/entries/AutoFocus-Stream.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2013-03-08.tar.gz">Mar 8, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-AutoFocus-Stream-2011-02-24.tar.gz">Feb 24, 2011</a>: Isabelle2011
</li></ul>
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</html>
\ No newline at end of file
diff --git a/web/entries/Automated_Stateful_Protocol_Verification.html b/web/entries/Automated_Stateful_Protocol_Verification.html
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<h1 >
<span class='first'>A</span>utomated <span class='first'>S</span>tateful <span class='first'>P</span>rotocol <span class='first'>V</span>erification</h1>
<div>
<p><a href="../authors/hess">Andreas V. Hess</a> <a class="obfuscated" data="eyJob3N0IjpbImR0dSIsImRrIl0sInVzZXIiOlsiYXZoZSJdfQ==">📧</a>, <a href="../authors/moedersheim">Sebastian Mödersheim</a> <a href="https://people.compute.dtu.dk/samo/">🌐</a>, <a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a>
</p>
<p class="date">April 8, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In protocol verification we observe a wide spectrum from fully
automated methods to interactive theorem proving with proof assistants
like Isabelle/HOL. In this AFP entry, we present a fully-automated
approach for verifying stateful security protocols, i.e., protocols
with mutable state that may span several sessions. The approach
supports reachability goals like secrecy and authentication. We also
include a simple user-friendly transaction-based protocol
specification language that is embedded into Isabelle.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Automated_Stateful_Protocol_Verification</h3>
<ul>
<li><a href="../theories/automated_stateful_protocol_verification/#Transactions">Transactions</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Term_Abstraction">Term_Abstraction</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Stateful_Protocol_Model">Stateful_Protocol_Model</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Term_Variants">Term_Variants</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Term_Implication">Term_Implication</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Stateful_Protocol_Verification">Stateful_Protocol_Verification</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Eisbach_Protocol_Verification">Eisbach_Protocol_Verification</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#ml_yacc_lib">ml_yacc_lib</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#trac_term">trac_term</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#trac_fp_parser">trac_fp_parser</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#trac_protocol_parser">trac_protocol_parser</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#trac">trac</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#PSPSP">PSPSP</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#introduction">introduction</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#KeyserverEx">KeyserverEx</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#manual">manual</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Keyserver">Keyserver</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Keyserver2">Keyserver2</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Keyserver_Composition">Keyserver_Composition</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#PKCS_Model03">PKCS_Model03</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#PKCS_Model07">PKCS_Model07</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#PKCS_Model09">PKCS_Model09</a></li>
<li><a href="../theories/automated_stateful_protocol_verification/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stateful_Protocol_Composition_and_Typing.html">Stateful Protocol Composition and Typing</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Proof_Strategy_Language.html">Proof Strategy Language</a></li>
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<p style="display:none;" id="bibtex-filename">Automated_Stateful_Protocol_Verification-AFP</p><pre id="copy-text">@article{Automated_Stateful_Protocol_Verification-AFP,
author = {Andreas V. Hess and Sebastian Mödersheim and Achim D. Brucker and Anders Schlichtkrull},
title = {Automated Stateful Protocol Verification},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Automated_Stateful_Protocol_Verification.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Automated_Stateful_Protocol_Verification-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Automated_Stateful_Protocol_Verification-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Automated_Stateful_Protocol_Verification-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automated_Stateful_Protocol_Verification-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automated_Stateful_Protocol_Verification-2020-05-20.tar.gz">May 20, 2020</a>: Isabelle2020
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diff --git a/web/entries/Automatic_Refinement.html b/web/entries/Automatic_Refinement.html
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<h1 >
<span class='first'>A</span>utomatic <span class='first'>D</span>ata <span class='first'>R</span>efinement</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJsYW1taWNoIl19">📧</a>
</p>
<p class="date">October 2, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the Autoref tool for Isabelle/HOL, which automatically
refines algorithms specified over abstract concepts like maps
and sets to algorithms over concrete implementations like red-black-trees,
and produces a refinement theorem. It is based on ideas borrowed from
relational parametricity due to Reynolds and Wadler.
The tool allows for rapid prototyping of verified, executable algorithms.
Moreover, it can be configured to fine-tune the result to the user~s needs.
Our tool is able to automatically instantiate generic algorithms, which
greatly simplifies the implementation of executable data structures.
<p>
This AFP-entry provides the basic tool, which is then used by the
Refinement and Collection Framework to provide automatic data refinement for
the nondeterminism monad and various collection datastructures.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Automatic_Refinement</h3>
<ul>
<li><a href="../theories/automatic_refinement/#Refine_Util_Bootstrap1">Refine_Util_Bootstrap1</a></li>
<li><a href="../theories/automatic_refinement/#Mpat_Antiquot">Mpat_Antiquot</a></li>
<li><a href="../theories/automatic_refinement/#Mk_Term_Antiquot">Mk_Term_Antiquot</a></li>
<li><a href="../theories/automatic_refinement/#Refine_Util">Refine_Util</a></li>
<li><a href="../theories/automatic_refinement/#Attr_Comb">Attr_Comb</a></li>
<li><a href="../theories/automatic_refinement/#Named_Sorted_Thms">Named_Sorted_Thms</a></li>
<li><a href="../theories/automatic_refinement/#Prio_List">Prio_List</a></li>
<li><a href="../theories/automatic_refinement/#Tagged_Solver">Tagged_Solver</a></li>
<li><a href="../theories/automatic_refinement/#Anti_Unification">Anti_Unification</a></li>
<li><a href="../theories/automatic_refinement/#Misc">Misc</a></li>
<li><a href="../theories/automatic_refinement/#Foldi">Foldi</a></li>
<li><a href="../theories/automatic_refinement/#Indep_Vars">Indep_Vars</a></li>
<li><a href="../theories/automatic_refinement/#Select_Solve">Select_Solve</a></li>
<li><a href="../theories/automatic_refinement/#Mk_Record_Simp">Mk_Record_Simp</a></li>
<li><a href="../theories/automatic_refinement/#Refine_Lib">Refine_Lib</a></li>
<li><a href="../theories/automatic_refinement/#Param_Chapter">Param_Chapter</a></li>
<li><a href="../theories/automatic_refinement/#Relators">Relators</a></li>
<li><a href="../theories/automatic_refinement/#Param_Tool">Param_Tool</a></li>
<li><a href="../theories/automatic_refinement/#Param_HOL">Param_HOL</a></li>
<li><a href="../theories/automatic_refinement/#Parametricity">Parametricity</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Phases">Autoref_Phases</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Data">Autoref_Data</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Tagging">Autoref_Tagging</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Id_Ops">Autoref_Id_Ops</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Fix_Rel">Autoref_Fix_Rel</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Relator_Interface">Autoref_Relator_Interface</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Translate">Autoref_Translate</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Gen_Algo">Autoref_Gen_Algo</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Chapter">Autoref_Chapter</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Tool">Autoref_Tool</a></li>
<li><a href="../theories/automatic_refinement/#Autoref_Bindings_HOL">Autoref_Bindings_HOL</a></li>
<li><a href="../theories/automatic_refinement/#Automatic_Refinement">Automatic_Refinement</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Van_Emde_Boas_Trees.html">van Emde Boas Trees</a></li><li><a href="../entries/Dict_Construction.html">Dictionary Construction</a></li><li><a href="../entries/IP_Addresses.html">IP Addresses</a></li><li><a href="../entries/ROBDD.html">Algorithms for Reduced Ordered Binary Decision Diagrams</a></li><li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li><li><a href="../entries/Network_Security_Policy_Verification.html">Network Security Policy Verification</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li><li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Automatic_Refinement-AFP</p><pre id="copy-text">@article{Automatic_Refinement-AFP,
author = {Peter Lammich},
title = {Automatic Data Refinement},
journal = {Archive of Formal Proofs},
month = {October},
year = {2013},
note = {\url{https://isa-afp.org/entries/Automatic_Refinement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Automatic_Refinement-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
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<h1 >
<span class='first'>A</span>xiom <span class='first'>S</span>ystems for <span class='first'>C</span>ategory <span class='first'>T</span>heory in <span class='first'>F</span>ree <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a> and <a href="../authors/scott">Dana Scott</a> <a href="http://www.cs.cmu.edu/~scott/">🌐</a>
</p>
<p class="date">May 23, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document provides a concise overview on the core results of our
previous work on the exploration of axioms systems for category
theory. Extending the previous studies
(http://arxiv.org/abs/1609.01493) we include one further axiomatic
theory in our experiments. This additional theory has been suggested
by Mac Lane in 1948. We show that the axioms proposed by Mac Lane are
equivalent to the ones we studied before, which includes an axioms set
suggested by Scott in the 1970s and another axioms set proposed by
Freyd and Scedrov in 1990, which we slightly modified to remedy a
minor technical issue.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session AxiomaticCategoryTheory</h3>
<ul>
<li><a href="../theories/axiomaticcategorytheory/#AxiomaticCategoryTheory">AxiomaticCategoryTheory</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">AxiomaticCategoryTheory-AFP</p><pre id="copy-text">@article{AxiomaticCategoryTheory-AFP,
author = {Christoph Benzmüller and Dana Scott},
title = {Axiom Systems for Category Theory in Free Logic},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/AxiomaticCategoryTheory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/BDD.html b/web/entries/BDD.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>BDD Normalisation - Archive of Formal Proofs</title><meta name="description" content="We present the verification of the normalisation of a binary decision diagram (BDD). The normalisation follows the original algorithm presented by Bryant..."><meta property="og:title" content="BDD Normalisation" />
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<h1 >
<span class='first'>B</span><span class='first'>D</span><span class='first'>D</span> <span class='first'>N</span>ormalisation</h1>
<div>
<p><a href="../authors/ortner">Veronika Ortner</a> and <a href="../authors/schirmer">Norbert Schirmer</a>
</p>
<p class="date">February 29, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the verification of the normalisation of a binary decision diagram (BDD). The normalisation follows the original algorithm presented by Bryant in 1986 and transforms an ordered BDD in a reduced, ordered and shared BDD. The verification is based on Hoare logics.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session BDD</h3>
<ul>
<li><a href="../theories/bdd/#BinDag">BinDag</a></li>
<li><a href="../theories/bdd/#General">General</a></li>
<li><a href="../theories/bdd/#ProcedureSpecs">ProcedureSpecs</a></li>
<li><a href="../theories/bdd/#EvalProof">EvalProof</a></li>
<li><a href="../theories/bdd/#LevellistProof">LevellistProof</a></li>
<li><a href="../theories/bdd/#ShareRepProof">ShareRepProof</a></li>
<li><a href="../theories/bdd/#ShareReduceRepListProof">ShareReduceRepListProof</a></li>
<li><a href="../theories/bdd/#RepointProof">RepointProof</a></li>
<li><a href="../theories/bdd/#NormalizeTotalProof">NormalizeTotalProof</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></li></ul>
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<p style="display:none;" id="bibtex-filename">BDD-AFP</p><pre id="copy-text">@article{BDD-AFP,
author = {Veronika Ortner and Norbert Schirmer},
title = {BDD Normalisation},
journal = {Archive of Formal Proofs},
month = {February},
year = {2008},
note = {\url{https://isa-afp.org/entries/BDD.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/BD_Security_Compositional.html b/web/entries/BD_Security_Compositional.html
--- a/web/entries/BD_Security_Compositional.html
+++ b/web/entries/BD_Security_Compositional.html
@@ -1,201 +1,203 @@
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<h1 >
<span class='first'>C</span>ompositional <span class='first'>B</span><span class='first'>D</span> <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">August 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Building on a previous <a
href="https://www.isa-afp.org/entries/Bounded_Deducibility_Security.html">AFP
entry</a> that formalizes the Bounded-Deducibility Security (BD
Security) framework <a href="https://doi.org/10.4230/LIPIcs.ITP.2021.3">[1]</a>,
we formalize compositionality and transport theorems for information
flow security. These results allow lifting BD Security properties from
individual components specified as transition systems, to a
composition of systems specified as communicating products of
transition systems. The underlying ideas of these results are
presented in the papers <a href="https://doi.org/10.4230/LIPIcs.ITP.2021.3">[1]</a>
and <a href="https://doi.org/10.1109/SP.2017.24">[2]</a>.
The latter paper also describes a major case study where these results
have been used: on verifying the CoSMeDis distributed social media
platform (itself formalized as an <a
href="https://www.isa-afp.org/entries/CoSMeDis.html">AFP
entry</a> that builds on this entry).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session BD_Security_Compositional</h3>
<ul>
<li><a href="../theories/bd_security_compositional/#Composing_Security">Composing_Security</a></li>
<li><a href="../theories/bd_security_compositional/#Trivial_Security">Trivial_Security</a></li>
<li><a href="../theories/bd_security_compositional/#Transporting_Security">Transporting_Security</a></li>
<li><a href="../theories/bd_security_compositional/#Composing_Security_Network">Composing_Security_Network</a></li>
<li><a href="../theories/bd_security_compositional/#Independent_Secrets">Independent_Secrets</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bounded_Deducibility_Security.html">Bounded-Deducibility Security</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CoSMeDis.html">CoSMeDis: A confidentiality-verified distributed social media platform</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Hales_Jewett.html">The Hales–Jewett Theorem</a></li>
<li><a href="../entries/Irrationals_From_THEBOOK.html">Irrational numbers from THE BOOK</a></li>
<li><a href="../entries/Core_SC_DOM.html">The Safely Composable DOM</a></li>
<li><a href="../entries/Goedel_Incompleteness.html">An Abstract Formalization of Gödel&rsquo;s Incompleteness Theorems</a></li>
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">BD_Security_Compositional-AFP</p><pre id="copy-text">@article{BD_Security_Compositional-AFP,
author = {Thomas Bauereiss and Andrei Popescu},
title = {Compositional BD Security},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/BD_Security_Compositional.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>B</span>ounded <span class='first'>N</span>atural <span class='first'>F</span>unctors <span class='first'>W</span>ith <span class='first'>C</span>ovariance and <span class='first'>C</span>ontravariance</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/schneider">Joshua Schneider</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbImpvc2h1YSIsInNjaG5laWRlciJdfQ==">📧</a>
</p>
<p class="date">April 24, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Bounded natural functors (BNFs) provide a modular framework for the
construction of (co)datatypes in higher-order logic. Their functorial
operations, the mapper and relator, are restricted to a subset of the
parameters, namely those where recursion can take place. For certain
applications, such as free theorems, data refinement, quotients, and
generalised rewriting, it is desirable that these operations do not
ignore the other parameters. In this article, we formalise the
generalisation BNF<sub>CC</sub> that extends the mapper
and relator to covariant and contravariant parameters. We show that
<ol> <li> BNF<sub>CC</sub>s are closed under
functor composition and least and greatest fixpoints,</li>
<li> subtypes inherit the BNF<sub>CC</sub> structure
under conditions that generalise those for the BNF case,
and</li> <li> BNF<sub>CC</sub>s preserve
quotients under mild conditions.</li> </ol> These proofs
are carried out for abstract BNF<sub>CC</sub>s similar to
the AFP entry BNF Operations. In addition, we apply the
BNF<sub>CC</sub> theory to several concrete functors.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session BNF_CC</h3>
<ul>
<li><a href="../theories/bnf_cc/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/bnf_cc/#Axiomatised_BNF_CC">Axiomatised_BNF_CC</a></li>
<li><a href="../theories/bnf_cc/#Composition">Composition</a></li>
<li><a href="../theories/bnf_cc/#Fixpoints">Fixpoints</a></li>
<li><a href="../theories/bnf_cc/#Subtypes">Subtypes</a></li>
<li><a href="../theories/bnf_cc/#Quotient_Preservation">Quotient_Preservation</a></li>
<li><a href="../theories/bnf_cc/#Operation_Examples">Operation_Examples</a></li>
<li><a href="../theories/bnf_cc/#Concrete_Examples">Concrete_Examples</a></li>
<li><a href="../theories/bnf_cc/#DDS">DDS</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">BNF_CC-AFP</p><pre id="copy-text">@article{BNF_CC-AFP,
author = {Andreas Lochbihler and Joshua Schneider},
title = {Bounded Natural Functors with Covariance and Contravariance},
journal = {Archive of Formal Proofs},
month = {April},
year = {2018},
note = {\url{https://isa-afp.org/entries/BNF_CC.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-BNF_CC-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-BNF_CC-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-BNF_CC-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-BNF_CC-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-BNF_CC-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-BNF_CC-2018-04-25.tar.gz">Apr 25, 2018</a>: Isabelle2017
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<h1 >
<span class='first'>O</span>perations on <span class='first'>B</span>ounded <span class='first'>N</span>atural <span class='first'>F</span>unctors</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamFzbWluIiwiYmxhbmNoZXR0ZSJdfQ==">📧</a>, <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">December 19, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes the closure property of bounded natural functors
(BNFs) under seven operations. These operations and the corresponding
proofs constitute the core of Isabelle's (co)datatype package. To
be close to the implemented tactics, the proofs are deliberately
formulated as detailed apply scripts. The (co)datatypes together with
(co)induction principles and (co)recursors are byproducts of the
fixpoint operations LFP and GFP. Composition of BNFs is subdivided
into four simpler operations: Compose, Kill, Lift, and Permute. The
N2M operation provides mutual (co)induction principles and
(co)recursors for nested (co)datatypes.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session BNF_Operations</h3>
<ul>
<li><a href="../theories/bnf_operations/#LFP">LFP</a></li>
<li><a href="../theories/bnf_operations/#GFP">GFP</a></li>
<li><a href="../theories/bnf_operations/#Compose">Compose</a></li>
<li><a href="../theories/bnf_operations/#Kill">Kill</a></li>
<li><a href="../theories/bnf_operations/#Lift">Lift</a></li>
<li><a href="../theories/bnf_operations/#Permute">Permute</a></li>
<li><a href="../theories/bnf_operations/#N2M">N2M</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">BNF_Operations-AFP</p><pre id="copy-text">@article{BNF_Operations-AFP,
author = {Jasmin Christian Blanchette and Andrei Popescu and Dmitriy Traytel},
title = {Operations on Bounded Natural Functors},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/BNF_Operations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-BNF_Operations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-BNF_Operations-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-BNF_Operations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-BNF_Operations-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-BNF_Operations-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-BNF_Operations-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-BNF_Operations-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>I</span>mperative <span class='first'>I</span>mplementation of <span class='first'>B</span>-<span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/muendler">Niels Mündler</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsibiIsIm11ZW5kbGVyIl19">📧</a>
</p>
<p class="date">February 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work, we use the interactive theorem prover Isabelle/HOL to
verify an imperative implementation of the classical B-tree data
structure invented by Bayer and McCreight [ACM 1970]. The
implementation supports set membership, insertion, deletion, iteration and range queries with efficient binary search for intra-node navigation. This is
accomplished by first specifying the structure abstractly in the
functional modeling language HOL and proving functional correctness.
Using manual refinement, we derive an imperative implementation in
Imperative/HOL. We show the validity of this refinement using the
separation logic utilities from the <a
href="https://www.isa-afp.org/entries/Refine_Imperative_HOL.html">
Isabelle Refinement Framework </a> . The code can be exported to
the programming languages SML, OCaml and Scala.
This entry contains two developments:
<dl>
<dt>B-Trees</dt>
<dd>This formalisation is discussed in greater detail in the corresponding <a
href="https://mediatum.ub.tum.de/1596550">Bachelor's
Thesis</a>.</dd>
<dt>B+-Trees:</dt>
<dd>This formalisation also supports range queries and is discussed in a paper published at ICTAC 2022.</dd>
</dl>
Change history:
[2022-08-16]: Added formalisations of B+-Trees</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 2, 2021</dt>
<dd>Add implementation and proof of correctness of imperative deletion operations.
Further add the option to export code to OCaml.
<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-management-systems">Computer science/Data management systems</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session BTree</h3>
<ul>
<li><a href="../theories/btree/#BTree">BTree</a></li>
<li><a href="../theories/btree/#BTree_Height">BTree_Height</a></li>
<li><a href="../theories/btree/#BTree_Set">BTree_Set</a></li>
<li><a href="../theories/btree/#BTree_Split">BTree_Split</a></li>
<li><a href="../theories/btree/#BPlusTree">BPlusTree</a></li>
<li><a href="../theories/btree/#BPlusTree_Split">BPlusTree_Split</a></li>
<li><a href="../theories/btree/#BPlusTree_Set">BPlusTree_Set</a></li>
<li><a href="../theories/btree/#BPlusTree_Range">BPlusTree_Range</a></li>
<li><a href="../theories/btree/#BPlusTree_SplitCE">BPlusTree_SplitCE</a></li>
<li><a href="../theories/btree/#Array_SBlit">Array_SBlit</a></li>
<li><a href="../theories/btree/#Partially_Filled_Array">Partially_Filled_Array</a></li>
<li><a href="../theories/btree/#Basic_Assn">Basic_Assn</a></li>
<li><a href="../theories/btree/#BTree_Imp">BTree_Imp</a></li>
<li><a href="../theories/btree/#BTree_ImpSet">BTree_ImpSet</a></li>
<li><a href="../theories/btree/#Imperative_Loops">Imperative_Loops</a></li>
<li><a href="../theories/btree/#BTree_ImpSplit">BTree_ImpSplit</a></li>
<li><a href="../theories/btree/#Flatten_Iter_Spec">Flatten_Iter_Spec</a></li>
<li><a href="../theories/btree/#Flatten_Iter">Flatten_Iter</a></li>
<li><a href="../theories/btree/#Inst_Ex_Assn">Inst_Ex_Assn</a></li>
<li><a href="../theories/btree/#BPlusTree_Imp">BPlusTree_Imp</a></li>
<li><a href="../theories/btree/#BPlusTree_ImpSplit">BPlusTree_ImpSplit</a></li>
<li><a href="../theories/btree/#BPlusTree_ImpSet">BPlusTree_ImpSet</a></li>
<li><a href="../theories/btree/#Partially_Filled_Array_Iter">Partially_Filled_Array_Iter</a></li>
<li><a href="../theories/btree/#BPlusTree_Iter_OneWay">BPlusTree_Iter_OneWay</a></li>
<li><a href="../theories/btree/#Subst_Mod_Mult_AC">Subst_Mod_Mult_AC</a></li>
<li><a href="../theories/btree/#BPlusTree_Iter">BPlusTree_Iter</a></li>
<li><a href="../theories/btree/#BPlusTree_ImpRange">BPlusTree_ImpRange</a></li>
<li><a href="../theories/btree/#BPlusTree_ImpSplitCE">BPlusTree_ImpSplitCE</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Solidity.html">Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</a></li>
<li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li>
<li><a href="../entries/Prpu_Maxflow.html">Formalizing Push-Relabel Algorithms</a></li>
<li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li>
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<p style="display:none;" id="bibtex-filename">BTree-AFP</p><pre id="copy-text">@article{BTree-AFP,
author = {Niels Mündler},
title = {A Verified Imperative Implementation of B-Trees},
journal = {Archive of Formal Proofs},
month = {February},
year = {2021},
note = {\url{https://isa-afp.org/entries/BTree.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-BTree-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-BTree-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-BTree-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-BTree-2021-02-26.tar.gz">Feb 26, 2021</a>: Isabelle2021
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diff --git a/web/entries/Banach_Steinhaus.html b/web/entries/Banach_Steinhaus.html
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<h1 >
<span class='first'>B</span>anach-<span class='first'>S</span>teinhaus <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/unruh">Dominique Unruh</a> <a href="https://www.ut.ee/~unruh/">🌐</a> <a class="obfuscated" data="eyJob3N0IjpbInV0IiwiZWUiXSwidXNlciI6WyJ1bnJ1aCJdfQ==">📧</a> and <a href="../authors/caballero">José Manuel Rodríguez Caballero</a> <a href="https://josephcmac.github.io/">🌐</a> <a class="obfuscated" data="eyJob3N0IjpbInV0IiwiZWUiXSwidXNlciI6WyJqb3NlIiwibWFudWVsIiwicm9kcmlndWV6IiwiY2FiYWxsZXJvIl19">📧</a>
</p>
<p class="date">May 2, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize in Isabelle/HOL a result
due to S. Banach and H. Steinhaus known as
the Banach-Steinhaus theorem or Uniform boundedness principle: a
pointwise-bounded family of continuous linear operators from a Banach
space to a normed space is uniformly bounded. Our approach is an
adaptation to Isabelle/HOL of a proof due to A. Sokal.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Banach_Steinhaus</h3>
<ul>
<li><a href="../theories/banach_steinhaus/#Banach_Steinhaus_Missing">Banach_Steinhaus_Missing</a></li>
<li><a href="../theories/banach_steinhaus/#Banach_Steinhaus">Banach_Steinhaus</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Complex_Bounded_Operators.html">Complex Bounded Operators</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Banach_Steinhaus-AFP</p><pre id="copy-text">@article{Banach_Steinhaus-AFP,
author = {Dominique Unruh and José Manuel Rodríguez Caballero},
title = {Banach-Steinhaus Theorem},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Banach_Steinhaus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Banach_Steinhaus-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Banach_Steinhaus-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Banach_Steinhaus-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Belief_Revision.html b/web/entries/Belief_Revision.html
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<h1 >
<span class='first'>B</span>elief <span class='first'>R</span>evision <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/fouillard">Valentin Fouillard</a> <a class="obfuscated" data="eyJob3N0IjpbImxpbXNpIiwiZnIiXSwidXNlciI6WyJ2YWxlbnRpbiIsImZvdWlsbGFyZCJdfQ==">📧</a>, <a href="../authors/taha">Safouan Taha</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsic2Fmb3VhbiIsInRhaGEiXX0=">📧</a>, <a href="../authors/boulanger">Frédéric Boulanger</a> <a class="obfuscated" data="eyJob3N0IjpbImNlbnRyYWxlc3VwZWxlYyIsImZyIl0sInVzZXIiOlsiZnJlZGVyaWMiLCJib3VsYW5nZXIiXX0=">📧</a> and <a href="../authors/sabouret">Nicolas Sabouret</a>
</p>
<p class="date">October 19, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David
Makinson (AGM), “On the Logic of Theory Change: Partial Meet
Contraction and Revision Functions” launches a large and rapidly
growing literature that employs formal models and logics to handle
changing beliefs of a rational agent and to take into account new
piece of information observed by this agent. In 2011, a review book
titled "AGM 25 Years: Twenty-Five Years of Research in Belief
Change" was edited to summarize the first twenty five years of
works based on AGM. This HOL-based AFP entry is a faithful
formalization of the AGM operators (e.g. contraction, revision,
remainder ...) axiomatized in the original paper. It also contains the
proofs of all the theorems stated in the paper that show how these
operators combine. Both proofs of Harper and Levi identities are
established.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session Belief_Revision</h3>
<ul>
<li><a href="../theories/belief_revision/#AGM_Logic">AGM_Logic</a></li>
<li><a href="../theories/belief_revision/#AGM_Remainder">AGM_Remainder</a></li>
<li><a href="../theories/belief_revision/#AGM_Contraction">AGM_Contraction</a></li>
<li><a href="../theories/belief_revision/#AGM_Revision">AGM_Revision</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Belief_Revision-AFP</p><pre id="copy-text">@article{Belief_Revision-AFP,
author = {Valentin Fouillard and Safouan Taha and Frédéric Boulanger and Nicolas Sabouret},
title = {Belief Revision Theory},
journal = {Archive of Formal Proofs},
month = {October},
year = {2021},
note = {\url{https://isa-afp.org/entries/Belief_Revision.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Bell_Numbers_Spivey.html b/web/entries/Bell_Numbers_Spivey.html
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<h1 >
<span class='first'>S</span>pivey's <span class='first'>G</span>eneralized <span class='first'>R</span>ecurrence for <span class='first'>B</span>ell <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">May 4, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry defines the Bell numbers as the cardinality of set partitions for
a carrier set of given size, and derives Spivey's generalized recurrence
relation for Bell numbers following his elegant and intuitive combinatorial
proof.
<p>
As the set construction for the combinatorial proof requires construction of
three intermediate structures, the main difficulty of the formalization is
handling the overall combinatorial argument in a structured way.
The introduced proof structure allows us to compose the combinatorial argument
from its subparts, and supports to keep track how the detailed proof steps are
related to the overall argument. To obtain this structure, this entry uses set
monad notation for the set construction's definition, introduces suitable
predicates and rules, and follows a repeating structure in its Isar proof.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Bell_Numbers_Spivey</h3>
<ul>
<li><a href="../theories/bell_numbers_spivey/#Bell_Numbers">Bell_Numbers</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Card_Partitions.html">Cardinality of Set Partitions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Twelvefold_Way.html">The Twelvefold Way</a></li><li><a href="../entries/Card_Equiv_Relations.html">Cardinality of Equivalence Relations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Bell_Numbers_Spivey-AFP</p><pre id="copy-text">@article{Bell_Numbers_Spivey-AFP,
author = {Lukas Bulwahn},
title = {Spivey&#39;s Generalized Recurrence for Bell Numbers},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Bell_Numbers_Spivey.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Bell_Numbers_Spivey-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Bell_Numbers_Spivey-2016-05-04.tar.gz">May 4, 2016</a>: Isabelle2016
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diff --git a/web/entries/BenOr_Kozen_Reif.html b/web/entries/BenOr_Kozen_Reif.html
--- a/web/entries/BenOr_Kozen_Reif.html
+++ b/web/entries/BenOr_Kozen_Reif.html
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<h1 >
<span class='first'>T</span>he <span class='first'>B</span><span class='first'>K</span><span class='first'>R</span> <span class='first'>D</span>ecision <span class='first'>P</span>rocedure for <span class='first'>U</span>nivariate <span class='first'>R</span>eal <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/cordwell">Katherine Cordwell</a> <a href="https://www.cs.cmu.edu/~kcordwel/">🌐</a>, <a href="../authors/tan">Yong Kiam Tan</a> <a href="https://www.cs.cmu.edu/~yongkiat/">🌐</a> and <a href="../authors/platzer">André Platzer</a> <a href="https://www.cs.cmu.edu/~aplatzer/">🌐</a>
</p>
<p class="date">April 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the univariate case of Ben-Or, Kozen, and Reif's
decision procedure for first-order real arithmetic (the BKR
algorithm). We also formalize the univariate case of Renegar's
variation of the BKR algorithm. The two formalizations differ
mathematically in minor ways (that have significant impact on the
multivariate case), but are quite similar in proof structure. Both
rely on sign-determination (finding the set of consistent sign
assignments for a set of polynomials). The method used for
sign-determination is similar to Tarski's original quantifier
elimination algorithm (it stores key information in a matrix
equation), but with a reduction step to keep complexity low.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session BenOr_Kozen_Reif</h3>
<ul>
<li><a href="../theories/benor_kozen_reif/#More_Matrix">More_Matrix</a></li>
<li><a href="../theories/benor_kozen_reif/#BKR_Algorithm">BKR_Algorithm</a></li>
<li><a href="../theories/benor_kozen_reif/#Matrix_Equation_Construction">Matrix_Equation_Construction</a></li>
<li><a href="../theories/benor_kozen_reif/#BKR_Proofs">BKR_Proofs</a></li>
<li><a href="../theories/benor_kozen_reif/#BKR_Decision">BKR_Decision</a></li>
<li><a href="../theories/benor_kozen_reif/#Renegar_Algorithm">Renegar_Algorithm</a></li>
<li><a href="../theories/benor_kozen_reif/#Renegar_Proofs">Renegar_Proofs</a></li>
<li><a href="../theories/benor_kozen_reif/#Renegar_Decision">Renegar_Decision</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Sturm_Tarski.html">The Sturm-Tarski Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">BenOr_Kozen_Reif-AFP</p><pre id="copy-text">@article{BenOr_Kozen_Reif-AFP,
author = {Katherine Cordwell and Yong Kiam Tan and André Platzer},
title = {The BKR Decision Procedure for Univariate Real Arithmetic},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/BenOr_Kozen_Reif.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-BenOr_Kozen_Reif-2021-04-25.tar.gz">Apr 25, 2021</a>: Isabelle2021
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diff --git a/web/entries/Berlekamp_Zassenhaus.html b/web/entries/Berlekamp_Zassenhaus.html
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<h1 >
<span class='first'>T</span>he <span class='first'>F</span>actorization <span class='first'>A</span>lgorithm of <span class='first'>B</span>erlekamp and <span class='first'>Z</span>assenhaus</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a>, <a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsic2ViYXN0aWFhbiIsImpvb3N0ZW4iXX0=">📧</a>, <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">October 14, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We formalize the Berlekamp-Zassenhaus algorithm for factoring
square-free integer polynomials in Isabelle/HOL. We further adapt an
existing formalization of Yun’s square-free factorization algorithm to
integer polynomials, and thus provide an efficient and certified
factorization algorithm for arbitrary univariate polynomials.
</p>
<p>The algorithm first performs a factorization in the prime field GF(p) and
then performs computations in the integer ring modulo p^k, where both
p and k are determined at runtime. Since a natural modeling of these
structures via dependent types is not possible in Isabelle/HOL, we
formalize the whole algorithm using Isabelle’s recent addition of
local type definitions.
</p>
<p>Through experiments we verify that our algorithm factors polynomials of degree
100 within seconds.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Berlekamp_Zassenhaus</h3>
<ul>
<li><a href="../theories/berlekamp_zassenhaus/#Finite_Field">Finite_Field</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Arithmetic_Record_Based">Arithmetic_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Finite_Field_Record_Based">Finite_Field_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Matrix_Record_Based">Matrix_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#More_Missing_Multiset">More_Missing_Multiset</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Unique_Factorization">Unique_Factorization</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Unique_Factorization_Poly">Unique_Factorization_Poly</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Poly_Mod">Poly_Mod</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Poly_Mod_Finite_Field">Poly_Mod_Finite_Field</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Karatsuba_Multiplication">Karatsuba_Multiplication</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Polynomial_Record_Based">Polynomial_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Poly_Mod_Finite_Field_Record_Based">Poly_Mod_Finite_Field_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Chinese_Remainder_Poly">Chinese_Remainder_Poly</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Berlekamp_Type_Based">Berlekamp_Type_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Distinct_Degree_Factorization">Distinct_Degree_Factorization</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Finite_Field_Factorization">Finite_Field_Factorization</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Finite_Field_Factorization_Record_Based">Finite_Field_Factorization_Record_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Hensel_Lifting">Hensel_Lifting</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Hensel_Lifting_Type_Based">Hensel_Lifting_Type_Based</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Berlekamp_Hensel">Berlekamp_Hensel</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Square_Free_Int_To_Square_Free_GFp">Square_Free_Int_To_Square_Free_GFp</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Suitable_Prime">Suitable_Prime</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Degree_Bound">Degree_Bound</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Mahler_Measure">Mahler_Measure</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Factor_Bound">Factor_Bound</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Sublist_Iteration">Sublist_Iteration</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Reconstruction">Reconstruction</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Code_Abort_Gcd">Code_Abort_Gcd</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Berlekamp_Zassenhaus">Berlekamp_Zassenhaus</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Gcd_Finite_Field_Impl">Gcd_Finite_Field_Impl</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Square_Free_Factorization_Int">Square_Free_Factorization_Int</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Factorize_Int_Poly">Factorize_Int_Poly</a></li>
<li><a href="../theories/berlekamp_zassenhaus/#Factorize_Rat_Poly">Factorize_Rat_Poly</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Efficient-Mergesort.html">Efficient Mergesort</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/Subresultants.html">Subresultants</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CRYSTALS-Kyber.html">CRYSTALS-Kyber</a></li><li><a href="../entries/Number_Theoretic_Transform.html">Number Theoretic Transform</a></li><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li><li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li><li><a href="../entries/LLL_Basis_Reduction.html">A verified LLL algorithm</a></li><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Types_To_Sets_Extension.html">Extension of Types-To-Sets</a></li>
<li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li>
<li><a href="../entries/LLL_Factorization.html">A verified factorization algorithm for integer polynomials with polynomial complexity</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Berlekamp_Zassenhaus-AFP</p><pre id="copy-text">@article{Berlekamp_Zassenhaus-AFP,
author = {Jose Divasón and Sebastiaan J. C. Joosten and René Thiemann and Akihisa Yamada},
title = {The Factorization Algorithm of Berlekamp and Zassenhaus},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Berlekamp_Zassenhaus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2018-09-07.tar.gz">Sep 7, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Berlekamp_Zassenhaus-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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diff --git a/web/entries/Bernoulli.html b/web/entries/Bernoulli.html
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<h1 >
<span class='first'>B</span>ernoulli <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">January 24, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Bernoulli numbers were first discovered in the closed-form
expansion of the sum 1<sup>m</sup> +
2<sup>m</sup> + &hellip; + n<sup>m</sup>
for a fixed m and appear in many other places. This entry provides
three different definitions for them: a recursive one, an explicit
one, and one through their exponential generating function.</p>
<p>In addition, we prove some basic facts, e.g. their relation
to sums of powers of integers and that all odd Bernoulli numbers
except the first are zero, and some advanced facts like their
relationship to the Riemann zeta function on positive even
integers.</p>
<p>We also prove the correctness of the
Akiyama&ndash;Tanigawa algorithm for computing Bernoulli numbers
with reasonable efficiency, and we define the periodic Bernoulli
polynomials (which appear e.g. in the Euler&ndash;MacLaurin
summation formula and the expansion of the log-Gamma function) and
prove their basic properties.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Bernoulli</h3>
<ul>
<li><a href="../theories/bernoulli/#Bernoulli">Bernoulli</a></li>
<li><a href="../theories/bernoulli/#Periodic_Bernpoly">Periodic_Bernpoly</a></li>
<li><a href="../theories/bernoulli/#Bernoulli_FPS">Bernoulli_FPS</a></li>
<li><a href="../theories/bernoulli/#Bernoulli_Zeta">Bernoulli_Zeta</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Khovanskii_Theorem.html">Khovanskii's Theorem</a></li><li><a href="../entries/Lambert_W.html">The Lambert W Function on the Reals</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li><li><a href="../entries/Euler_MacLaurin.html">The Euler–MacLaurin Formula</a></li><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Bernoulli-AFP</p><pre id="copy-text">@article{Bernoulli-AFP,
author = {Lukas Bulwahn and Manuel Eberl},
title = {Bernoulli Numbers},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/Bernoulli.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Bernoulli-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Bernoulli-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Bernoulli-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Bernoulli-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Bernoulli-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Bernoulli-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Bernoulli-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Bernoulli-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bernoulli-2017-01-24.tar.gz">Jan 24, 2017</a>: Isabelle2016-1
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<h1 >
<span class='first'>B</span>ertrand's <span class='first'>P</span>ostulate</h1>
<div>
<p><a href="../authors/biendarra">Julian Biendarra</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
with contributions from <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">January 17, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Bertrand's postulate is an early result on the
distribution of prime numbers: For every positive integer n, there
exists a prime number that lies strictly between n and 2n.
The proof is ported from John Harrison's formalisation
in HOL Light. It proceeds by first showing that the property is true
for all n greater than or equal to 600 and then showing that it also
holds for all n below 600 by case distinction. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Bertrands_Postulate</h3>
<ul>
<li><a href="../theories/bertrands_postulate/#Bertrand">Bertrand</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Pratt_Certificate.html">Pratt&rsquo;s Primality Certificates</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Triangle.html">Basic Geometric Properties of Triangles</a></li>
<li><a href="../entries/Fourier.html">Fourier Series</a></li>
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<li><a href="../entries/Ptolemys_Theorem.html">Ptolemy&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Bertrands_Postulate-AFP</p><pre id="copy-text">@article{Bertrands_Postulate-AFP,
author = {Julian Biendarra and Manuel Eberl},
title = {Bertrand&#39;s postulate},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/Bertrands_Postulate.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Bertrands_Postulate-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Bertrands_Postulate-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Bertrands_Postulate-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Bertrands_Postulate-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
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diff --git a/web/entries/Bicategory.html b/web/entries/Bicategory.html
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@@ -1,217 +1,219 @@
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<h1 >
<span class='first'>B</span>icategories</h1>
<div>
<p><a href="../authors/stark">Eugene W. Stark</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwic3Rvbnlicm9vayIsImVkdSJdLCJ1c2VyIjpbInN0YXJrIl19">📧</a>
</p>
<p class="date">January 6, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Taking as a starting point the author's previous work on
developing aspects of category theory in Isabelle/HOL, this article
gives a compatible formalization of the notion of
"bicategory" and develops a framework within which formal
proofs of facts about bicategories can be given. The framework
includes a number of basic results, including the Coherence Theorem,
the Strictness Theorem, pseudofunctors and biequivalence, and facts
about internal equivalences and adjunctions in a bicategory. As a
driving application and demonstration of the utility of the framework,
it is used to give a formal proof of a theorem, due to Carboni,
Kasangian, and Street, that characterizes up to biequivalence the
bicategories of spans in a category with pullbacks. The formalization
effort necessitated the filling-in of many details that were not
evident from the brief presentation in the original paper, as well as
identifying a few minor corrections along the way.
</p><p>
Revisions made subsequent to the first version of this article added
additional material on pseudofunctors, pseudonatural transformations,
modifications, and equivalence of bicategories; the main thrust being
to give a proof that a pseudofunctor is a biequivalence if and only
if it can be extended to an equivalence of bicategories.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 22, 2021</dt>
<dd>Added new material: "concrete bicategories" and "bicategory of categories".
(revision 49d3aa43c180)<br></dd><dt>November 4, 2020</dt>
<dd>Added new material on equivalence of bicategories, with associated changes.
(revision 472cb2268826)<br>
</dd><dt>February 15, 2020</dt>
<dd>Move ConcreteCategory.thy from Bicategory to Category3 and use it systematically.
Make other minor improvements throughout.
(revision a51840d36867)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session Bicategory</h3>
<ul>
<li><a href="../theories/bicategory/#IsomorphismClass">IsomorphismClass</a></li>
<li><a href="../theories/bicategory/#Prebicategory">Prebicategory</a></li>
<li><a href="../theories/bicategory/#Bicategory">Bicategory</a></li>
<li><a href="../theories/bicategory/#Coherence">Coherence</a></li>
<li><a href="../theories/bicategory/#CanonicalIsos">CanonicalIsos</a></li>
<li><a href="../theories/bicategory/#Subbicategory">Subbicategory</a></li>
<li><a href="../theories/bicategory/#InternalEquivalence">InternalEquivalence</a></li>
<li><a href="../theories/bicategory/#Pseudofunctor">Pseudofunctor</a></li>
<li><a href="../theories/bicategory/#Strictness">Strictness</a></li>
<li><a href="../theories/bicategory/#InternalAdjunction">InternalAdjunction</a></li>
<li><a href="../theories/bicategory/#PseudonaturalTransformation">PseudonaturalTransformation</a></li>
<li><a href="../theories/bicategory/#EquivalenceOfBicategories">EquivalenceOfBicategories</a></li>
<li><a href="../theories/bicategory/#SpanBicategory">SpanBicategory</a></li>
<li><a href="../theories/bicategory/#Tabulation">Tabulation</a></li>
<li><a href="../theories/bicategory/#BicategoryOfSpans">BicategoryOfSpans</a></li>
<li><a href="../theories/bicategory/#Modification">Modification</a></li>
<li><a href="../theories/bicategory/#ConcreteBicategory">ConcreteBicategory</a></li>
<li><a href="../theories/bicategory/#CatBicat">CatBicat</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/MonoidalCategory.html">Monoidal Categories</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Bicategory-AFP</p><pre id="copy-text">@article{Bicategory-AFP,
author = {Eugene W. Stark},
title = {Bicategories},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Bicategory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Bicategory-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Bicategory-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Bicategory-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bicategory-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/BinarySearchTree.html b/web/entries/BinarySearchTree.html
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<h1 >
<span class='first'>B</span>inary <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/kuncak">Viktor Kuncak</a> <a href="http://lara.epfl.ch/~kuncak/">🌐</a>
</p>
<p class="date">April 5, 2004</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The correctness is shown of binary search tree operations (lookup, insert and remove) implementing a set. Two versions are given, for both structured and linear (tactic-style) proofs. An implementation of integer-indexed maps is also verified.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session BinarySearchTree</h3>
<ul>
<li><a href="../theories/binarysearchtree/#BinaryTree">BinaryTree</a></li>
<li><a href="../theories/binarysearchtree/#BinaryTree_Map">BinaryTree_Map</a></li>
<li><a href="../theories/binarysearchtree/#BinaryTree_TacticStyle">BinaryTree_TacticStyle</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">BinarySearchTree-AFP</p><pre id="copy-text">@article{BinarySearchTree-AFP,
author = {Viktor Kuncak},
title = {Binary Search Trees},
journal = {Archive of Formal Proofs},
month = {April},
year = {2004},
note = {\url{https://isa-afp.org/entries/BinarySearchTree.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>G</span>eneral <span class='first'>T</span>heory of <span class='first'>S</span>yntax <span class='first'>W</span>ith <span class='first'>B</span>indings</h1>
<div>
<p><a href="../authors/gheri">Lorenzo Gheri</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibG9yIiwiZ2hlcmkiXX0=">📧</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">April 6, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a theory of syntax with bindings that has been developed
and refined over the last decade to support several large
formalization efforts. Terms are defined for an arbitrary number of
constructors of varying numbers of inputs, quotiented to
alpha-equivalence and sorted according to a binding signature. The
theory includes many properties of the standard operators on terms:
substitution, swapping and freshness. It also includes bindings-aware
induction and recursion principles and support for semantic
interpretation. This work has been presented in the ITP 2017 paper “A
Formalized General Theory of Syntax with Bindings”.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Binding_Syntax_Theory</h3>
<ul>
<li><a href="../theories/binding_syntax_theory/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/binding_syntax_theory/#QuasiTerms_Swap_Fresh">QuasiTerms_Swap_Fresh</a></li>
<li><a href="../theories/binding_syntax_theory/#QuasiTerms_PickFresh_Alpha">QuasiTerms_PickFresh_Alpha</a></li>
<li><a href="../theories/binding_syntax_theory/#QuasiTerms_Environments_Substitution">QuasiTerms_Environments_Substitution</a></li>
<li><a href="../theories/binding_syntax_theory/#Pick">Pick</a></li>
<li><a href="../theories/binding_syntax_theory/#Equiv_Relation2">Equiv_Relation2</a></li>
<li><a href="../theories/binding_syntax_theory/#Transition_QuasiTerms_Terms">Transition_QuasiTerms_Terms</a></li>
<li><a href="../theories/binding_syntax_theory/#Terms">Terms</a></li>
<li><a href="../theories/binding_syntax_theory/#Well_Sorted_Terms">Well_Sorted_Terms</a></li>
<li><a href="../theories/binding_syntax_theory/#Iteration">Iteration</a></li>
<li><a href="../theories/binding_syntax_theory/#Semantic_Domains">Semantic_Domains</a></li>
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<p style="display:none;" id="bibtex-filename">Binding_Syntax_Theory-AFP</p><pre id="copy-text">@article{Binding_Syntax_Theory-AFP,
author = {Lorenzo Gheri and Andrei Popescu},
title = {A General Theory of Syntax with Bindings},
journal = {Archive of Formal Proofs},
month = {April},
year = {2019},
note = {\url{https://isa-afp.org/entries/Binding_Syntax_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>B</span>inomial <span class='first'>H</span>eaps and <span class='first'>S</span>kew <span class='first'>B</span>inomial <span class='first'>H</span>eaps</h1>
<div>
<p><a href="../authors/meis">Rene Meis</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1tdWVuc3RlciIsImRlIl0sInVzZXIiOlsicmVuZSIsIm1laXMiXX0=">📧</a>, <a href="../authors/nielsen">Finn Nielsen</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1tdWVuc3RlciIsImRlIl0sInVzZXIiOlsiZmlubiIsIm5pZWxzZW4iXX0=">📧</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">October 28, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implement and prove correct binomial heaps and skew binomial heaps.
Both are data-structures for priority queues.
While binomial heaps have logarithmic <em>findMin</em>, <em>deleteMin</em>,
<em>insert</em>, and <em>meld</em> operations,
skew binomial heaps have constant time <em>findMin</em>, <em>insert</em>,
and <em>meld</em> operations, and only the <em>deleteMin</em>-operation is
logarithmic. This is achieved by using <em>skew links</em> to avoid
cascading linking on <em>insert</em>-operations, and <em>data-structural
bootstrapping</em> to get constant-time <em>findMin</em> and <em>meld</em>
operations. Our implementation follows the paper by Brodal and Okasaki.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Binomial Heaps in <a href="https://functional-algorithms-verified.org">Functional Algorithms, Verified!</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Binomial_heap">Wikipedia</a>
</li></ul>
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<li><a href="../theories/binomial-heaps/#SkewBinomialHeap">SkewBinomialHeap</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Binomial-Heaps-AFP</p><pre id="copy-text">@article{Binomial-Heaps-AFP,
author = {Rene Meis and Finn Nielsen and Peter Lammich},
title = {Binomial Heaps and Skew Binomial Heaps},
journal = {Archive of Formal Proofs},
month = {October},
year = {2010},
note = {\url{https://isa-afp.org/entries/Binomial-Heaps.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Heaps-2010-10-28.tar.gz">Oct 28, 2010</a>: Isabelle2009-2
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\ No newline at end of file
diff --git a/web/entries/Binomial-Queues.html b/web/entries/Binomial-Queues.html
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<h1 >
<span class='first'>F</span>unctional <span class='first'>B</span>inomial <span class='first'>Q</span>ueues</h1>
<div>
<p><a href="../authors/neumann">René Neumann</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJyZW5lIiwibmV1bWFubiJdfQ==">📧</a>
</p>
<p class="date">October 28, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Priority queues are an important data structure and efficient implementations of them are crucial. We implement a functional variant of binomial queues in Isabelle/HOL and show its functional correctness. A verification against an abstract reference specification of priority queues has also been attempted, but could not be achieved to the full extent.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Binomial-Queues</h3>
<ul>
<li><a href="../theories/binomial-queues/#PQ">PQ</a></li>
<li><a href="../theories/binomial-queues/#Binomial_Queue">Binomial_Queue</a></li>
<li><a href="../theories/binomial-queues/#PQ_Implementation">PQ_Implementation</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Binomial-Queues-AFP</p><pre id="copy-text">@article{Binomial-Queues-AFP,
author = {René Neumann},
title = {Functional Binomial Queues},
journal = {Archive of Formal Proofs},
month = {October},
year = {2010},
note = {\url{https://isa-afp.org/entries/Binomial-Queues.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Binomial-Queues-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/BirdKMP.html b/web/entries/BirdKMP.html
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+++ b/web/entries/BirdKMP.html
@@ -1,189 +1,191 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Putting the `K&#39; into Bird&#39;s derivation of Knuth-Morris-Pratt string matching - Archive of Formal Proofs</title><meta name="description" content="Richard Bird and collaborators have proposed a derivation of an
intricate cyclic program that implements the Morris-Pratt string
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<h1 >
<span class='first'>P</span>utting the `<span class='first'>K</span>' <span class='first'>I</span>nto <span class='first'>B</span>ird's <span class='first'>D</span>erivation of <span class='first'>K</span>nuth-<span class='first'>M</span>orris-<span class='first'>P</span>ratt <span class='first'>S</span>tring <span class='first'>M</span>atching</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">August 25, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Richard Bird and collaborators have proposed a derivation of an
intricate cyclic program that implements the Morris-Pratt string
matching algorithm. Here we provide a proof of total correctness for
Bird's derivation and complete it by adding Knuth's
optimisation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session BirdKMP</h3>
<ul>
<li><a href="../theories/birdkmp/#HOLCF_ROOT">HOLCF_ROOT</a></li>
<li><a href="../theories/birdkmp/#Theory_Of_Lists">Theory_Of_Lists</a></li>
<li><a href="../theories/birdkmp/#KMP">KMP</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HOLCF-Prelude.html">HOLCF-Prelude</a></li></ul>
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<li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li>
<li><a href="../entries/Imperative_Insertion_Sort.html">Imperative Insertion Sort</a></li>
<li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li>
<li><a href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></li>
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<p style="display:none;" id="bibtex-filename">BirdKMP-AFP</p><pre id="copy-text">@article{BirdKMP-AFP,
author = {Peter Gammie},
title = {Putting the `K&#39; into Bird&#39;s derivation of Knuth-Morris-Pratt string matching},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/BirdKMP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-BirdKMP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-BirdKMP-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-BirdKMP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-BirdKMP-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-BirdKMP-2020-09-02.tar.gz">Sep 2, 2020</a>: Isabelle2020
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diff --git a/web/entries/Blue_Eyes.html b/web/entries/Blue_Eyes.html
--- a/web/entries/Blue_Eyes.html
+++ b/web/entries/Blue_Eyes.html
@@ -1,168 +1,170 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Solution to the xkcd Blue Eyes puzzle - Archive of Formal Proofs</title><meta name="description" content="In a puzzle published by Randall Munroe, perfect logicians forbidden from communicating are stranded on an island, and may only leave once they have..."><meta property="og:title" content="Solution to the xkcd Blue Eyes puzzle" />
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<h1 >
<span class='first'>S</span>olution to the <span class='first'>X</span>kcd <span class='first'>B</span>lue <span class='first'>E</span>yes <span class='first'>P</span>uzzle</h1>
<div>
<p><a href="../authors/kadzioka">Maya Kądziołka</a> <a class="obfuscated" data="eyJob3N0IjpbImNvbXBpbGVyY3JpbSIsImVzIl0sInVzZXIiOlsiYWZwIl19">📧</a>
</p>
<p class="date">January 30, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In a <a href="https://xkcd.com/blue_eyes.html">puzzle published by
Randall Munroe</a>, perfect logicians forbidden
from communicating are stranded on an island, and may only leave once
they have figured out their own eye color. We present a method of
modeling the behavior of perfect logicians and formalize a solution of
the puzzle.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session Blue_Eyes</h3>
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<li><a href="../theories/blue_eyes/#Blue_Eyes">Blue_Eyes</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Blue_Eyes-AFP</p><pre id="copy-text">@article{Blue_Eyes-AFP,
author = {Maya Kądziołka},
title = {Solution to the xkcd Blue Eyes puzzle},
journal = {Archive of Formal Proofs},
month = {January},
year = {2021},
note = {\url{https://isa-afp.org/entries/Blue_Eyes.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>B</span>ondy's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/avigad">Jeremy Avigad</a> <a href="http://www.andrew.cmu.edu/user/avigad/">🌐</a> and <a href="../authors/hetzl">Stefan Hetzl</a> <a href="http://www.logic.at/people/hetzl/">🌐</a>
</p>
<p class="date">October 27, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A proof of Bondy's theorem following B. Bollabas, Combinatorics, 1986, Cambridge University Press.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Bondy</h3>
<ul>
<li><a href="../theories/bondy/#Bondy">Bondy</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Bondy-AFP</p><pre id="copy-text">@article{Bondy-AFP,
author = {Jeremy Avigad and Stefan Hetzl},
title = {Bondy&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {October},
year = {2012},
note = {\url{https://isa-afp.org/entries/Bondy.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>B</span>oolean <span class='first'>E</span>xpression <span class='first'>C</span>heckers</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 8, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides executable checkers for the following properties of
boolean expressions: satisfiability, tautology and equivalence. Internally,
the checkers operate on binary decision trees and are reasonably efficient
(for purely functional algorithms).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 23, 2015</dt>
<dd>Salomon Sickert added an interface that does not require the usage of the Boolean formula datatype. Furthermore the general Mapping type is used instead of an association list.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Boolean_Expression_Checkers</h3>
<ul>
<li><a href="../theories/boolean_expression_checkers/#Boolean_Expression_Checkers">Boolean_Expression_Checkers</a></li>
<li><a href="../theories/boolean_expression_checkers/#Boolean_Expression_Checkers_AList_Mapping">Boolean_Expression_Checkers_AList_Mapping</a></li>
<li><a href="../theories/boolean_expression_checkers/#Boolean_Expression_Example">Boolean_Expression_Example</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li><li><a href="../entries/LTL_to_DRA.html">Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Boolean_Expression_Checkers-AFP</p><pre id="copy-text">@article{Boolean_Expression_Checkers-AFP,
author = {Tobias Nipkow},
title = {Boolean Expression Checkers},
journal = {Archive of Formal Proofs},
month = {June},
year = {2014},
note = {\url{https://isa-afp.org/entries/Boolean_Expression_Checkers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Boolean_Expression_Checkers-2014-06-08.tar.gz">Jun 8, 2014</a>: Isabelle2013-2
</li></ul>
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\ No newline at end of file
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<h1 >
<span class='first'>B</span>oolos's <span class='first'>C</span>urious <span class='first'>I</span>nference in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/ketland">Jeffrey Ketland</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamVmZnJleWtldGxhbmQiXX0=">📧</a>
</p>
<p class="date">June 20, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1987, George Boolos gave an interesting and vivid concrete example
of the considerable speed-up afforded by higher-order logic over
first-order logic. (A phenomenon first noted by Kurt Gödel in 1936.)
Boolos's example concerned an inference $I$ with five premises,
and a conclusion, such that the shortest derivation of the conclusion
from the premises in a standard system for first-order logic is
astronomically huge; while there exists a second-order derivation
whose length is of the order of a page or two. Boolos gave a short
sketch of that second-order derivation, which relies on the
comprehension principle of second-order logic. Here, Boolos's
inference is formalized into fourteen lemmas, each quickly verified by
the automated-theorem-proving assistant Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session Boolos_Curious_Inference</h3>
<ul>
<li><a href="../theories/boolos_curious_inference/#Boo1">Boo1</a></li>
<li><a href="../theories/boolos_curious_inference/#Boo2">Boo2</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Boolos_Curious_Inference-AFP</p><pre id="copy-text">@article{Boolos_Curious_Inference-AFP,
author = {Jeffrey Ketland},
title = {Boolos&#39;s Curious Inference in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/Boolos_Curious_Inference.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <ul><li>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Boolos_Curious_Inference-2022-07-04.tar.gz">Jul 4, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Bounded_Deducibility_Security.html b/web/entries/Bounded_Deducibility_Security.html
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<h1 >
<span class='first'>B</span>ounded-<span class='first'>D</span>educibility <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a>
</p>
<p class="date">April 22, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalization of bounded-deducibility security (BD
security), a flexible notion of information-flow security applicable
to arbitrary transition systems. It generalizes Sutherland's
classic notion of nondeducibility by factoring in declassification
bounds and trigger, whereas nondeducibility states that, in a
system, information cannot flow between specified sources and sinks,
BD security indicates upper bounds for the flow and triggers under
which these upper bounds are no longer guaranteed.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>August 12, 2021</dt>
<dd>Generalised BD Security from I/O automata to nondeterministic
transition systems, with the former retained as an instance of the
latter (renaming locale BD_Security to BD_Security_IO).
Generalise unwinding conditions to allow making more than one
transition at a time when constructing alternative traces.
Add results about the expressivity of declassification triggers vs.
bounds, due to Thomas Bauereiss (added as author).</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Bounded_Deducibility_Security</h3>
<ul>
<li><a href="../theories/bounded_deducibility_security/#Trivia">Trivia</a></li>
<li><a href="../theories/bounded_deducibility_security/#Filtermap">Filtermap</a></li>
<li><a href="../theories/bounded_deducibility_security/#Transition_System">Transition_System</a></li>
<li><a href="../theories/bounded_deducibility_security/#IO_Automaton">IO_Automaton</a></li>
<li><a href="../theories/bounded_deducibility_security/#Abstract_BD_Security">Abstract_BD_Security</a></li>
<li><a href="../theories/bounded_deducibility_security/#BD_Security_TS">BD_Security_TS</a></li>
<li><a href="../theories/bounded_deducibility_security/#BD_Security_IO">BD_Security_IO</a></li>
<li><a href="../theories/bounded_deducibility_security/#BD_Security_Triggers">BD_Security_Triggers</a></li>
<li><a href="../theories/bounded_deducibility_security/#BD_Security_Unwinding">BD_Security_Unwinding</a></li>
<li><a href="../theories/bounded_deducibility_security/#Compositional_Reasoning">Compositional_Reasoning</a></li>
<li><a href="../theories/bounded_deducibility_security/#Bounded_Deducibility_Security">Bounded_Deducibility_Security</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CoCon.html">CoCon: A Confidentiality-Verified Conference Management System</a></li><li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li><li><a href="../entries/CoSMed.html">CoSMed: A confidentiality-verified social media platform</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Bounded_Deducibility_Security-AFP</p><pre id="copy-text">@article{Bounded_Deducibility_Security-AFP,
author = {Andrei Popescu and Peter Lammich and Thomas Bauereiss},
title = {Bounded-Deducibility Security},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/Bounded_Deducibility_Security.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Bounded_Deducibility_Security-2014-04-24.tar.gz">Apr 24, 2014</a>: Isabelle2013-2
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+++ b/web/entries/Buchi_Complementation.html
@@ -1,204 +1,206 @@
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<h1 >
<span class='first'>B</span>üchi <span class='first'>C</span>omplementation</h1>
<div>
<p><a href="../authors/brunner">Julian Brunner</a> <a href="http://www21.in.tum.de/~brunnerj/">🌐</a>
</p>
<p class="date">October 19, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a verified implementation of rank-based Büchi
Complementation. The verification is done in three steps: <ol>
<li>Definition of odd rankings and proof that an automaton
rejects a word iff there exists an odd ranking for it.</li>
<li>Definition of the complement automaton and proof that it
accepts exactly those words for which there is an odd
ranking.</li> <li>Verified implementation of the
complement automaton using the Isabelle Collections
Framework.</li> </ol></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Buchi_Complementation</h3>
<ul>
<li><a href="../theories/buchi_complementation/#Alternate">Alternate</a></li>
<li><a href="../theories/buchi_complementation/#Graph">Graph</a></li>
<li><a href="../theories/buchi_complementation/#Ranking">Ranking</a></li>
<li><a href="../theories/buchi_complementation/#Complementation">Complementation</a></li>
<li><a href="../theories/buchi_complementation/#Complementation_Implement">Complementation_Implement</a></li>
<li><a href="../theories/buchi_complementation/#Formula">Formula</a></li>
<li><a href="../theories/buchi_complementation/#Complementation_Final">Complementation_Final</a></li>
<li><a href="../theories/buchi_complementation/#Complementation_Build">Complementation_Build</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Gale_Shapley.html">Gale-Shapley Algorithm</a></li>
<li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li>
<li><a href="../entries/Weight_Balanced_Trees.html">Weight-Balanced Trees</a></li>
<li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li>
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<p style="display:none;" id="bibtex-filename">Buchi_Complementation-AFP</p><pre id="copy-text">@article{Buchi_Complementation-AFP,
author = {Julian Brunner},
title = {Büchi Complementation},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Buchi_Complementation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Budan_Fourier.html b/web/entries/Budan_Fourier.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Budan-Fourier Theorem and Counting Real Roots with Multiplicity - Archive of Formal Proofs</title><meta name="description" content="This entry is mainly about counting and approximating real roots (of a
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<h1 >
<span class='first'>T</span>he <span class='first'>B</span>udan-<span class='first'>F</span>ourier <span class='first'>T</span>heorem and <span class='first'>C</span>ounting <span class='first'>R</span>eal <span class='first'>R</span>oots <span class='first'>W</span>ith <span class='first'>M</span>ultiplicity</h1>
<div>
<p><a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">September 2, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry is mainly about counting and approximating real roots (of a
polynomial) with multiplicity. We have first formalised the
Budan-Fourier theorem: given a polynomial with real coefficients, we
can calculate sign variations on Fourier sequences to over-approximate
the number of real roots (counting multiplicity) within an interval.
When all roots are known to be real, the over-approximation becomes
tight: we can utilise this theorem to count real roots exactly. It is
also worth noting that Descartes' rule of sign is a direct
consequence of the Budan-Fourier theorem, and has been included in
this entry. In addition, we have extended previous formalised
Sturm's theorem to count real roots with multiplicity, while the
original Sturm's theorem only counts distinct real roots.
Compared to the Budan-Fourier theorem, our extended Sturm's
theorem always counts roots exactly but may suffer from greater
computational cost.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Budan_Fourier</h3>
<ul>
<li><a href="../theories/budan_fourier/#BF_Misc">BF_Misc</a></li>
<li><a href="../theories/budan_fourier/#Budan_Fourier">Budan_Fourier</a></li>
<li><a href="../theories/budan_fourier/#Sturm_Multiple_Roots">Sturm_Multiple_Roots</a></li>
<li><a href="../theories/budan_fourier/#Descartes_Roots_Test">Descartes_Roots_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Sturm_Tarski.html">The Sturm-Tarski Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Three_Circles.html">The Theorem of Three Circles</a></li><li><a href="../entries/Winding_Number_Eval.html">Evaluate Winding Numbers through Cauchy Indices</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Budan_Fourier-AFP</p><pre id="copy-text">@article{Budan_Fourier-AFP,
author = {Wenda Li},
title = {The Budan-Fourier Theorem and Counting Real Roots with Multiplicity},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Budan_Fourier.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Budan_Fourier-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Budan_Fourier-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Buffons_Needle.html b/web/entries/Buffons_Needle.html
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@@ -1,183 +1,185 @@
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<h1 >
<span class='first'>B</span>uffon's <span class='first'>N</span>eedle <span class='first'>P</span>roblem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">June 6, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In the 18th century, Georges-Louis Leclerc, Comte de Buffon posed and
later solved the following problem, which is often called the first
problem ever solved in geometric probability: Given a floor divided
into vertical strips of the same width, what is the probability that a
needle thrown onto the floor randomly will cross two strips? This
entry formally defines the problem in the case where the needle's
position is chosen uniformly at random in a single strip around the
origin (which is equivalent to larger arrangements due to symmetry).
It then provides proofs of the simple solution in the case where the
needle's length is no greater than the width of the strips and
the more complicated solution in the opposite case.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Buffons_Needle</h3>
<ul>
<li><a href="../theories/buffons_needle/#Buffons_Needle">Buffons_Needle</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Buffons_Needle-AFP</p><pre id="copy-text">@article{Buffons_Needle-AFP,
author = {Manuel Eberl},
title = {Buffon&#39;s Needle Problem},
journal = {Archive of Formal Proofs},
month = {June},
year = {2017},
note = {\url{https://isa-afp.org/entries/Buffons_Needle.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Buffons_Needle-2017-06-06.tar.gz">Jun 6, 2017</a>: Isabelle2016-1
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<h1 >
<span class='first'>C</span>hamber <span class='first'>C</span>omplexes, <span class='first'>C</span>oxeter <span class='first'>S</span>ystems, and <span class='first'>B</span>uildings</h1>
<div>
<p><a href="../authors/sylvestre">Jeremy Sylvestre</a> <a href="http://ualberta.ca/~jsylvest/">🌐</a>
</p>
<p class="date">July 1, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a basic formal framework for the theory of chamber
complexes and Coxeter systems, and for buildings as thick chamber
complexes endowed with a system of apartments. Along the way, we
develop some of the general theory of abstract simplicial complexes
and of groups (relying on the <i>group_add</i> class for the basics),
including free groups and group presentations, and their universal
properties. The main results verified are that the deletion condition
is both necessary and sufficient for a group with a set of generators
of order two to be a Coxeter system, and that the apartments in a
(thick) building are all uniformly Coxeter.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Buildings</h3>
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<li><a href="../theories/buildings/#Prelim">Prelim</a></li>
<li><a href="../theories/buildings/#Algebra">Algebra</a></li>
<li><a href="../theories/buildings/#Simplicial">Simplicial</a></li>
<li><a href="../theories/buildings/#Chamber">Chamber</a></li>
<li><a href="../theories/buildings/#Coxeter">Coxeter</a></li>
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<p style="display:none;" id="bibtex-filename">Buildings-AFP</p><pre id="copy-text">@article{Buildings-AFP,
author = {Jeremy Sylvestre},
title = {Chamber Complexes, Coxeter Systems, and Buildings},
journal = {Archive of Formal Proofs},
month = {July},
year = {2016},
note = {\url{https://isa-afp.org/entries/Buildings.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/BytecodeLogicJmlTypes.html b/web/entries/BytecodeLogicJmlTypes.html
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<h1 >
<span class='first'>A</span> <span class='first'>B</span>ytecode <span class='first'>L</span>ogic for <span class='first'>J</span><span class='first'>M</span><span class='first'>L</span> and <span class='first'>T</span>ypes</h1>
<div>
<p><a href="../authors/beringer">Lennart Beringer</a> and <a href="../authors/hofmann">Martin Hofmann</a> <a href="http://www.tcs.informatik.uni-muenchen.de/~mhofmann">🌐</a>
</p>
<p class="date">December 12, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains the Isabelle/HOL sources underlying the paper <i>A bytecode logic for JML and types</i> by Beringer and Hofmann, updated to Isabelle 2008. We present a program logic for a subset of sequential Java bytecode that is suitable for representing both, features found in high-level specification language JML as well as interpretations of high-level type systems. To this end, we introduce a fine-grained collection of assertions, including strong invariants, local annotations and VDM-reminiscent partial-correctness specifications. Thanks to a goal-oriented structure and interpretation of judgements, verification may proceed without recourse to an additional control flow analysis. The suitability for interpreting intensional type systems is illustrated by the proof-carrying-code style encoding of a type system for a first-order functional language which guarantees a constant upper bound on the number of objects allocated throughout an execution, be the execution terminating or non-terminating. Like the published paper, the formal development is restricted to a comparatively small subset of the JVML, lacking (among other features) exceptions, arrays, virtual methods, and static fields. This shortcoming has been overcome meanwhile, as our paper has formed the basis of the Mobius base logic, a program logic for the full sequential fragment of the JVML. Indeed, the present formalisation formed the basis of a subsequent formalisation of the Mobius base logic in the proof assistant Coq, which includes a proof of soundness with respect to the Bicolano operational semantics by Pichardie.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session BytecodeLogicJmlTypes</h3>
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<li><a href="../theories/bytecodelogicjmltypes/#Reachability">Reachability</a></li>
<li><a href="../theories/bytecodelogicjmltypes/#Sound">Sound</a></li>
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<p style="display:none;" id="bibtex-filename">BytecodeLogicJmlTypes-AFP</p><pre id="copy-text">@article{BytecodeLogicJmlTypes-AFP,
author = {Lennart Beringer and Martin Hofmann},
title = {A Bytecode Logic for JML and Types},
journal = {Archive of Formal Proofs},
month = {December},
year = {2008},
note = {\url{https://isa-afp.org/entries/BytecodeLogicJmlTypes.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>ommunicating <span class='first'>C</span>oncurrent <span class='first'>K</span>leene <span class='first'>A</span>lgebra for <span class='first'>D</span>istributed <span class='first'>S</span>ystems <span class='first'>S</span>pecification</h1>
<div>
<p><a href="../authors/buyse">Maxime Buyse</a> <a class="obfuscated" data="eyJob3N0IjpbInBvbHl0ZWNobmlxdWUiLCJlZHUiXSwidXNlciI6WyJtYXhpbWUiLCJidXlzZSJdfQ==">📧</a> and <a href="../authors/jaskolka">Jason Jaskolka</a> <a href="https://carleton.ca/jaskolka/">🌐</a>
</p>
<p class="date">August 6, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Communicating Concurrent Kleene Algebra (C²KA) is a mathematical
framework for capturing the communicating and concurrent behaviour of
agents in distributed systems. It extends Hoare et al.'s
Concurrent Kleene Algebra (CKA) with communication actions through the
notions of stimuli and shared environments. C²KA has applications in
studying system-level properties of distributed systems such as
safety, security, and reliability. In this work, we formalize results
about C²KA and its application for distributed systems specification.
We first formalize the stimulus structure and behaviour structure
(CKA). Next, we combine them to formalize C²KA and its properties.
Then, we formalize notions and properties related to the topology of
distributed systems and the potential for communication via stimuli
and via shared environments of agents, all within the algebraic
setting of C²KA.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session C2KA_DistributedSystems</h3>
<ul>
<li><a href="../theories/c2ka_distributedsystems/#Stimuli">Stimuli</a></li>
<li><a href="../theories/c2ka_distributedsystems/#CKA">CKA</a></li>
<li><a href="../theories/c2ka_distributedsystems/#C2KA">C2KA</a></li>
<li><a href="../theories/c2ka_distributedsystems/#Topology_C2KA">Topology_C2KA</a></li>
<li><a href="../theories/c2ka_distributedsystems/#Communication_C2KA">Communication_C2KA</a></li></ul><div class="flex-wrap">
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outline</a>
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<p style="display:none;" id="bibtex-filename">C2KA_DistributedSystems-AFP</p><pre id="copy-text">@article{C2KA_DistributedSystems-AFP,
author = {Maxime Buyse and Jason Jaskolka},
title = {Communicating Concurrent Kleene Algebra for Distributed Systems Specification},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/C2KA_DistributedSystems.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-C2KA_DistributedSystems-2019-08-06.tar.gz">Aug 6, 2019</a>: Isabelle2019
</li></ul>
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diff --git a/web/entries/CAVA_Automata.html b/web/entries/CAVA_Automata.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The CAVA Automata Library - Archive of Formal Proofs</title><meta name="description" content="We report on the graph and automata library that is used in the fully verified LTL model checker CAVA. As most components of CAVA use some type of graphs..."><meta property="og:title" content="The CAVA Automata Library" />
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<h1 >
<span class='first'>T</span>he <span class='first'>C</span><span class='first'>A</span><span class='first'>V</span><span class='first'>A</span> <span class='first'>A</span>utomata <span class='first'>L</span>ibrary</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">May 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We report on the graph and automata library that is used in the fully
verified LTL model checker CAVA.
As most components of CAVA use some type of graphs or automata, a common
automata library simplifies assembly of the components and reduces
redundancy.
<p>
The CAVA Automata Library provides a hierarchy of graph and automata
classes, together with some standard algorithms.
Its object oriented design allows for sharing of algorithms, theorems,
and implementations between its classes, and also simplifies extensions
of the library.
Moreover, it is integrated into the Automatic Refinement Framework,
supporting automatic refinement of the abstract automata types to
efficient data structures.
<p>
Note that the CAVA Automata Library is work in progress. Currently, it
is very specifically tailored towards the requirements of the CAVA model
checker.
Nevertheless, the formalization techniques presented here allow an
extension of the library to a wider scope. Moreover, they are not
limited to graph libraries, but apply to class hierarchies in general.
<p>
The CAVA Automata Library is described in the paper: Peter Lammich, The
CAVA Automata Library, Isabelle Workshop 2014.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session CAVA_Base</h3>
<ul>
<li><a href="../theories/cava_base/#Statistics">Statistics</a></li>
<li><a href="../theories/cava_base/#Code_String">Code_String</a></li>
<li><a href="../theories/cava_base/#CAVA_Code_Target">CAVA_Code_Target</a></li>
<li><a href="../theories/cava_base/#CAVA_Base">CAVA_Base</a></li>
<li><a href="../theories/cava_base/#Lexord_List">Lexord_List</a></li>
<li><a href="../theories/cava_base/#All_Of_CAVA_Base">All_Of_CAVA_Base</a></li></ul>
<h3>Session CAVA_Automata</h3>
<ul>
<li><a href="../theories/cava_automata/#Digraph_Basic">Digraph_Basic</a></li>
<li><a href="../theories/cava_automata/#Digraph">Digraph</a></li>
<li><a href="../theories/cava_automata/#Automata">Automata</a></li>
<li><a href="../theories/cava_automata/#Lasso">Lasso</a></li>
<li><a href="../theories/cava_automata/#Simulation">Simulation</a></li>
<li><a href="../theories/cava_automata/#Step_Conv">Step_Conv</a></li>
<li><a href="../theories/cava_automata/#Stuttering_Extension">Stuttering_Extension</a></li>
<li><a href="../theories/cava_automata/#Digraph_Impl">Digraph_Impl</a></li>
<li><a href="../theories/cava_automata/#Automata_Impl">Automata_Impl</a></li>
<li><a href="../theories/cava_automata/#All_Of_CAVA_Automata">All_Of_CAVA_Automata</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li><li><a href="../entries/DFS_Framework.html">A Framework for Verifying Depth-First Search Algorithms</a></li><li><a href="../entries/Formal_SSA.html">Verified Construction of Static Single Assignment Form</a></li><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li><li><a href="../entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></li><li><a href="../entries/Promela.html">Promela Formalization</a></li><li><a href="../entries/Gabow_SCC.html">Verified Efficient Implementation of Gabow&rsquo;s Strongly Connected Components Algorithm</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li></ul>
</div>
</div>
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outline</a>
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document</a>
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<p style="display:none;" id="bibtex-filename">CAVA_Automata-AFP</p><pre id="copy-text">@article{CAVA_Automata-AFP,
author = {Peter Lammich},
title = {The CAVA Automata Library},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/CAVA_Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-CAVA_Automata-2014-05-29.tar.gz">May 29, 2014</a>: Isabelle2013-2
</li></ul>
</div>
</div>
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diff --git a/web/entries/CAVA_LTL_Modelchecker.html b/web/entries/CAVA_LTL_Modelchecker.html
--- a/web/entries/CAVA_LTL_Modelchecker.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Fully Verified Executable LTL Model Checker - Archive of Formal Proofs</title><meta name="description" content="We present an LTL model checker whose code has been completely verified
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ully <span class='first'>V</span>erified <span class='first'>E</span>xecutable <span class='first'>L</span><span class='first'>T</span><span class='first'>L</span> <span class='first'>M</span>odel <span class='first'>C</span>hecker</h1>
<div>
<p><a href="../authors/esparza">Javier Esparza</a> <a href="https://www7.in.tum.de/~esparza/">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>, <a href="../authors/neumann">René Neumann</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJyZW5lIiwibmV1bWFubiJdfQ==">📧</a>, <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>, <a href="../authors/schimpf">Alexander Schimpf</a> <a class="obfuscated" data="eyJob3N0IjpbImluZm9ybWF0aWsiLCJ1bmktZnJlaWJ1cmciLCJkZSJdLCJ1c2VyIjpbInNjaGltcGZhIl19">📧</a> and <a href="../authors/smaus">Jan-Georg Smaus</a> <a href="http://www.irit.fr/~Jan-Georg.Smaus">🌐</a>
</p>
<p class="date">May 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an LTL model checker whose code has been completely verified
using the Isabelle theorem prover. The checker consists of over 4000
lines of ML code. The code is produced using the Isabelle Refinement
Framework, which allows us to split its correctness proof into (1) the
proof of an abstract version of the checker, consisting of a few hundred
lines of ``formalized pseudocode'', and (2) a verified refinement step
in which mathematical sets and other abstract structures are replaced by
implementations of efficient structures like red-black trees and
functional arrays. This leads to a checker that,
while still slower than unverified checkers, can already be used as a
trusted reference implementation against which advanced implementations
can be tested.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Esparza, J., Lammich, P., Neumann, R., Nipkow, T., Schimpf, A., & Smaus, J.-G. (2013). A Fully Verified Executable LTL Model Checker. Lecture Notes in Computer Science, 463–478. <a href="https://doi.org/10.1007/978-3-642-39799-8_31">https://doi.org/10.1007/978-3-642-39799-8_31</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/cav13.html">Open access</a>
</li><li>
<a href="https://cava.in.tum.de">Projekt home page</a>
</li></ul>
<h3>Session SM_Base</h3>
<ul></ul>
<h3>Session SM</h3>
<ul>
<li><a href="../theories/sm/#LTS">LTS</a></li>
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<li><a href="../theories/sm/#SM_Ample_Impl">SM_Ample_Impl</a></li>
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<h3>Session CAVA_Setup</h3>
<ul></ul>
<h3>Session CAVA_LTL_Modelchecker</h3>
<ul>
<li><a href="../theories/cava_ltl_modelchecker/#NDFS_SI_Statistics">NDFS_SI_Statistics</a></li>
<li><a href="../theories/cava_ltl_modelchecker/#NDFS_SI">NDFS_SI</a></li>
<li><a href="../theories/cava_ltl_modelchecker/#CAVA_Abstract">CAVA_Abstract</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/DFS_Framework.html">A Framework for Verifying Depth-First Search Algorithms</a></li><li><a href="../entries/Partial_Order_Reduction.html">Partial Order Reduction</a></li><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li><li><a href="../entries/Gabow_SCC.html">Verified Efficient Implementation of Gabow&rsquo;s Strongly Connected Components Algorithm</a></li><li><a href="../entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></li><li><a href="../entries/Promela.html">Promela Formalization</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Knuth_Morris_Pratt.html">The string search algorithm by Knuth, Morris and Pratt</a></li>
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<p style="display:none;" id="bibtex-filename">CAVA_LTL_Modelchecker-AFP</p><pre id="copy-text">@article{CAVA_LTL_Modelchecker-AFP,
author = {Javier Esparza and Peter Lammich and René Neumann and Tobias Nipkow and Alexander Schimpf and Jan-Georg Smaus},
title = {A Fully Verified Executable LTL Model Checker},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/CAVA_LTL_Modelchecker.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span><span class='first'>C</span><span class='first'>S</span> in <span class='first'>N</span>ominal <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/bengtson">Jesper Bengtson</a> <a href="http://www.itu.dk/people/jebe">🌐</a>
</p>
<p class="date">May 29, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise a large portion of CCS as described in Milner's book 'Communication and Concurrency' using the nominal datatype package in Isabelle. Our results include many of the standard theorems of bisimulation equivalence and congruence, for both weak and strong versions. One main goal of this formalisation is to keep the machine-checked proofs as close to their pen-and-paper counterpart as possible.
<p>
This entry is described in detail in <a href="http://www.itu.dk/people/jebe/files/thesis.pdf">Bengtson's thesis</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session CCS</h3>
<ul>
<li><a href="../theories/ccs/#Agent">Agent</a></li>
<li><a href="../theories/ccs/#Tau_Chain">Tau_Chain</a></li>
<li><a href="../theories/ccs/#Weak_Cong_Semantics">Weak_Cong_Semantics</a></li>
<li><a href="../theories/ccs/#Weak_Semantics">Weak_Semantics</a></li>
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<li><a href="../theories/ccs/#Strong_Sim_SC">Strong_Sim_SC</a></li>
<li><a href="../theories/ccs/#Strong_Bisim">Strong_Bisim</a></li>
<li><a href="../theories/ccs/#Strong_Sim_Pres">Strong_Sim_Pres</a></li>
<li><a href="../theories/ccs/#Strong_Bisim_Pres">Strong_Bisim_Pres</a></li>
<li><a href="../theories/ccs/#Struct_Cong">Struct_Cong</a></li>
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<li><a href="../theories/ccs/#Weak_Bisim_Pres">Weak_Bisim_Pres</a></li>
<li><a href="../theories/ccs/#Weak_Cong_Sim_Pres">Weak_Cong_Sim_Pres</a></li>
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<p style="display:none;" id="bibtex-filename">CCS-AFP</p><pre id="copy-text">@article{CCS-AFP,
author = {Jesper Bengtson},
title = {CCS in nominal logic},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/CCS.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-CCS-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-CCS-2012-06-14.tar.gz">Jun 14, 2012</a>: Isabelle2012
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<h1 >
<span class='first'>F</span>ormal <span class='first'>S</span>pecification of a <span class='first'>G</span>eneric <span class='first'>S</span>eparation <span class='first'>K</span>ernel</h1>
<div>
<p><a href="../authors/verbeek">Freek Verbeek</a> <a class="obfuscated" data="eyJob3N0IjpbIm91IiwibmwiXSwidXNlciI6WyJGcmVlayIsIlZlcmJlZWsiXX0=">📧</a>, <a href="../authors/tverdyshev">Sergey Tverdyshev</a> <a class="obfuscated" data="eyJob3N0IjpbInN5c2dvIiwiY29tIl0sInVzZXIiOlsic3R2Il19">📧</a>, <a href="../authors/havle">Oto Havle</a> <a class="obfuscated" data="eyJob3N0IjpbInN5c2dvIiwiY29tIl0sInVzZXIiOlsib2hhIl19">📧</a>, <a href="../authors/blasum">Holger Blasum</a> <a class="obfuscated" data="eyJob3N0IjpbInN5c2dvIiwiY29tIl0sInVzZXIiOlsiaG9sZ2VyIiwiYmxhc3VtIl19">📧</a>, <a href="../authors/langenstein">Bruno Langenstein</a> <a class="obfuscated" data="eyJob3N0IjpbImRma2kiLCJkZSJdLCJ1c2VyIjpbImxhbmdlbnN0ZWluIl19">📧</a>, <a href="../authors/stephan">Werner Stephan</a> <a class="obfuscated" data="eyJob3N0IjpbImRma2kiLCJkZSJdLCJ1c2VyIjpbInN0ZXBoYW4iXX0=">📧</a>, <a href="../authors/nemouchi">Yakoub Nemouchi</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsibmVtb3VjaGkiXX0=">📧</a>, <a href="../authors/feliachi">Abderrahmane Feliachi</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYWJkZXJyYWhtYW5lIiwiZmVsaWFjaGkiXX0=">📧</a>, <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a> and <a href="../authors/schmaltz">Julien Schmaltz</a> <a class="obfuscated" data="eyJob3N0IjpbIm91IiwibmwiXSwidXNlciI6WyJKdWxpZW4iLCJTY2htYWx0eiJdfQ==">📧</a>
</p>
<p class="date">July 18, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Intransitive noninterference has been a widely studied topic in the last
few decades. Several well-established methodologies apply interactive
theorem proving to formulate a noninterference theorem over abstract
academic models. In joint work with several industrial and academic partners
throughout Europe, we are helping in the certification process of PikeOS, an
industrial separation kernel developed at SYSGO. In this process,
established theories could not be applied. We present a new generic model of
separation kernels and a new theory of intransitive noninterference. The
model is rich in detail, making it suitable for formal verification of
realistic and industrial systems such as PikeOS. Using a refinement-based
theorem proving approach, we ensure that proofs remain manageable.</p>
<p>
This document corresponds to the deliverable D31.1 of the EURO-MILS
Project <a href="http://www.euromils.eu">http://www.euromils.eu</a>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CISC-Kernel</h3>
<ul>
<li><a href="../theories/cisc-kernel/#Option_Binders">Option_Binders</a></li>
<li><a href="../theories/cisc-kernel/#List_Theorems">List_Theorems</a></li>
<li><a href="../theories/cisc-kernel/#K">K</a></li>
<li><a href="../theories/cisc-kernel/#SK">SK</a></li>
<li><a href="../theories/cisc-kernel/#ISK">ISK</a></li>
<li><a href="../theories/cisc-kernel/#CISK">CISK</a></li>
<li><a href="../theories/cisc-kernel/#Step_configuration">Step_configuration</a></li>
<li><a href="../theories/cisc-kernel/#Step_policies">Step_policies</a></li>
<li><a href="../theories/cisc-kernel/#Step">Step</a></li>
<li><a href="../theories/cisc-kernel/#Step_invariants">Step_invariants</a></li>
<li><a href="../theories/cisc-kernel/#Step_vpeq">Step_vpeq</a></li>
<li><a href="../theories/cisc-kernel/#Step_vpeq_locally_respects">Step_vpeq_locally_respects</a></li>
<li><a href="../theories/cisc-kernel/#Step_vpeq_weakly_step_consistent">Step_vpeq_weakly_step_consistent</a></li>
<li><a href="../theories/cisc-kernel/#Separation_kernel_model">Separation_kernel_model</a></li>
<li><a href="../theories/cisc-kernel/#Link_separation_kernel_model_to_CISK">Link_separation_kernel_model_to_CISK</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">CISC-Kernel-AFP</p><pre id="copy-text">@article{CISC-Kernel-AFP,
author = {Freek Verbeek and Sergey Tverdyshev and Oto Havle and Holger Blasum and Bruno Langenstein and Werner Stephan and Yakoub Nemouchi and Abderrahmane Feliachi and Burkhart Wolff and Julien Schmaltz},
title = {Formal Specification of a Generic Separation Kernel},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/CISC-Kernel.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ramework for <span class='first'>E</span>stablishing <span class='first'>S</span>trong <span class='first'>E</span>ventual <span class='first'>C</span>onsistency for <span class='first'>C</span>onflict-<span class='first'>F</span>ree <span class='first'>R</span>eplicated <span class='first'>D</span>atatypes</h1>
<div>
<p><a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInZpY3RvciIsImdvbWVzIl19">📧</a>, <a href="../authors/kleppmann">Martin Kleppmann</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbIm1hcnRpbiIsImtsZXBwbWFubiJdfQ==">📧</a>, <a href="../authors/mulligan">Dominic P. Mulligan</a> <a class="obfuscated" data="eyJob3N0IjpbImdvb2dsZW1haWwiLCJjb20iXSwidXNlciI6WyJkb21pbmljIiwicCIsIm11bGxpZ2FuIl19">📧</a> and <a href="../authors/beresford">Alastair R. Beresford</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJhcmIzMyJdfQ==">📧</a>
</p>
<p class="date">July 7, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work, we focus on the correctness of Conflict-free Replicated
Data Types (CRDTs), a class of algorithm that provides strong eventual
consistency guarantees for replicated data. We develop a modular and
reusable framework for verifying the correctness of CRDT algorithms.
We avoid correctness issues that have dogged previous mechanised
proofs in this area by including a network model in our formalisation,
and proving that our theorems hold in all possible network behaviours.
Our axiomatic network model is a standard abstraction that accurately
reflects the behaviour of real-world computer networks. Moreover, we
identify an abstract convergence theorem, a property of order
relations, which provides a formal definition of strong eventual
consistency. We then obtain the first machine-checked correctness
theorems for three concrete CRDTs: the Replicated Growable Array, the
Observed-Remove Set, and an Increment-Decrement Counter.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session CRDT</h3>
<ul>
<li><a href="../theories/crdt/#Util">Util</a></li>
<li><a href="../theories/crdt/#Convergence">Convergence</a></li>
<li><a href="../theories/crdt/#Network">Network</a></li>
<li><a href="../theories/crdt/#Ordered_List">Ordered_List</a></li>
<li><a href="../theories/crdt/#RGA">RGA</a></li>
<li><a href="../theories/crdt/#Counter">Counter</a></li>
<li><a href="../theories/crdt/#ORSet">ORSet</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/IMAP-CRDT.html">The IMAP CmRDT</a></li></ul>
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<p style="display:none;" id="bibtex-filename">CRDT-AFP</p><pre id="copy-text">@article{CRDT-AFP,
author = {Victor B. F. Gomes and Martin Kleppmann and Dominic P. Mulligan and Alastair R. Beresford},
title = {A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/CRDT.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/CRYSTALS-Kyber.html b/web/entries/CRYSTALS-Kyber.html
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<h1 >
<span class='first'>C</span><span class='first'>R</span><span class='first'>Y</span><span class='first'>S</span><span class='first'>T</span><span class='first'>A</span><span class='first'>L</span><span class='first'>S</span>-<span class='first'>K</span>yber</h1>
<div>
<p><a href="../authors/kreuzer">Katharina Kreuzer</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiayIsImtyZXV6ZXIiXX0=">📧</a>
</p>
<p class="date">September 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes the specification and the algorithm of the
cryptographic scheme CRYSTALS-KYBER with multiplication using the
Number Theoretic Transform and verifies its (1-δ)-correctness proof.
CRYSTALS-KYBER is a key encapsulation mechanism in lattice-based
post-quantum cryptography. This entry formalizes the key generation,
encryption and decryption algorithms and shows that the algorithm
decodes correctly under a highly probable assumption
((1-δ)-correctness). Moreover, the Number Theoretic Transform (NTT) in
the case of Kyber and the convolution theorem thereon is formalized.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CRYSTALS-Kyber</h3>
<ul>
<li><a href="../theories/crystals-kyber/#Kyber_spec">Kyber_spec</a></li>
<li><a href="../theories/crystals-kyber/#Mod_Plus_Minus">Mod_Plus_Minus</a></li>
<li><a href="../theories/crystals-kyber/#Abs_Qr">Abs_Qr</a></li>
<li><a href="../theories/crystals-kyber/#Compress">Compress</a></li>
<li><a href="../theories/crystals-kyber/#Crypto_Scheme">Crypto_Scheme</a></li>
<li><a href="../theories/crystals-kyber/#Kyber_Values">Kyber_Values</a></li>
<li><a href="../theories/crystals-kyber/#Mod_Ring_Numeral">Mod_Ring_Numeral</a></li>
<li><a href="../theories/crystals-kyber/#NTT_Scheme">NTT_Scheme</a></li>
<li><a href="../theories/crystals-kyber/#Crypto_Scheme_NTT">Crypto_Scheme_NTT</a></li>
<li><a href="../theories/crystals-kyber/#Powers3844">Powers3844</a></li>
<li><a href="../theories/crystals-kyber/#Kyber_NTT_Values">Kyber_NTT_Values</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Number_Theoretic_Transform.html">Number Theoretic Transform</a></li></ul>
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<p style="display:none;" id="bibtex-filename">CRYSTALS-Kyber-AFP</p><pre id="copy-text">@article{CRYSTALS-Kyber-AFP,
author = {Katharina Kreuzer},
title = {CRYSTALS-Kyber},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/CRYSTALS-Kyber.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The HOL-CSP Refinement Toolkit - Archive of Formal Proofs</title><meta name="description" content="We use a formal development for CSP, called HOL-CSP2.0, to analyse a
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span>-<span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>R</span>efinement <span class='first'>T</span>oolkit</h1>
<div>
<p><a href="../authors/taha">Safouan Taha</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsic2Fmb3VhbiIsInRhaGEiXX0=">📧</a>, <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a> and <a href="../authors/ye">Lina Ye</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsibGluYSIsInllIl19">📧</a>
</p>
<p class="date">November 19, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We use a formal development for CSP, called HOL-CSP2.0, to analyse a
family of refinement notions, comprising classic and new ones. This
analysis enables to derive a number of properties that allow to deepen
the understanding of these notions, in particular with respect to
specification decomposition principles for the case of infinite sets
of events. The established relations between the refinement relations
help to clarify some obscure points in the CSP literature, but also
provide a weapon for shorter refinement proofs. Furthermore, we
provide a framework for state-normalisation allowing to formally
reason on parameterised process architectures. As a result, we have a
modern environment for formal proofs of concurrent systems that allow
for the combination of general infinite processes with locally finite
ones in a logically safe way. We demonstrate these
verification-techniques for classical, generalised examples: The
CopyBuffer for arbitrary data and the Dijkstra's Dining
Philosopher Problem of arbitrary size.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session CSP_RefTK</h3>
<ul>
<li><a href="../theories/csp_reftk/#Introduction">Introduction</a></li>
<li><a href="../theories/csp_reftk/#Assertions_ext">Assertions_ext</a></li>
<li><a href="../theories/csp_reftk/#Properties">Properties</a></li>
<li><a href="../theories/csp_reftk/#Fix_ind_ext">Fix_ind_ext</a></li>
<li><a href="../theories/csp_reftk/#Process_norm">Process_norm</a></li>
<li><a href="../theories/csp_reftk/#CopyBuffer_props">CopyBuffer_props</a></li>
<li><a href="../theories/csp_reftk/#DiningPhilosophers">DiningPhilosophers</a></li>
<li><a href="../theories/csp_reftk/#Conclusion">Conclusion</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HOL-CSP.html">HOL-CSP Version 2.0</a></li></ul>
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<p style="display:none;" id="bibtex-filename">CSP_RefTK-AFP</p><pre id="copy-text">@article{CSP_RefTK-AFP,
author = {Safouan Taha and Burkhart Wolff and Lina Ye},
title = {The HOL-CSP Refinement Toolkit},
journal = {Archive of Formal Proofs},
month = {November},
year = {2020},
note = {\url{https://isa-afp.org/entries/CSP_RefTK.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/CYK.html b/web/entries/CYK.html
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@@ -1,179 +1,181 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A formalisation of the Cocke-Younger-Kasami algorithm - Archive of Formal Proofs</title><meta name="description" content="The theory provides a formalisation of the Cocke-Younger-Kasami
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalisation of the <span class='first'>C</span>ocke-<span class='first'>Y</span>ounger-<span class='first'>K</span>asami <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/bortin">Maksym Bortin</a> <a class="obfuscated" data="eyJob3N0IjpbIm5pY3RhIiwiY29tIiwiYXUiXSwidXNlciI6WyJtYWtzeW0iLCJib3J0aW4iXX0=">📧</a>
</p>
<p class="date">April 27, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory provides a formalisation of the Cocke-Younger-Kasami
algorithm (CYK for short), an approach to solving the word problem
for context-free languages. CYK decides if a word is in the
languages generated by a context-free grammar in Chomsky normal form.
The formalized algorithm is executable.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session CYK</h3>
<ul>
<li><a href="../theories/cyk/#CYK">CYK</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">CYK-AFP</p><pre id="copy-text">@article{CYK-AFP,
author = {Maksym Bortin},
title = {A formalisation of the Cocke-Younger-Kasami algorithm},
journal = {Archive of Formal Proofs},
month = {April},
year = {2016},
note = {\url{https://isa-afp.org/entries/CYK.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory for <span class='first'>Z</span><span class='first'>F</span><span class='first'>C</span> in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>I</span><span class='first'>I</span>: <span class='first'>E</span>lementary <span class='first'>T</span>heory of 1-<span class='first'>C</span>ategories</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article provides a formalization of the foundations of the theory
of 1-categories in the object logic ZFC in HOL of the formal proof
assistant Isabelle. The article builds upon the foundations that were
established in the AFP entry <i>Category Theory for ZFC in HOL
I: Foundations: Design Patterns, Set Theory, Digraphs,
Semicategories</i>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>November 7, 2021</dt>
<dd>added a definition of a dagger monoidal category (revision c9ed46c09de9)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session CZH_Elementary_Categories</h3>
<ul>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Introduction">CZH_ECAT_Introduction</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Category">CZH_ECAT_Category</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Small_Category">CZH_ECAT_Small_Category</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Functor">CZH_ECAT_Functor</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Small_Functor">CZH_ECAT_Small_Functor</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_NTCF">CZH_ECAT_NTCF</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Small_NTCF">CZH_ECAT_Small_NTCF</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_PCategory">CZH_ECAT_PCategory</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Subcategory">CZH_ECAT_Subcategory</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Simple">CZH_ECAT_Simple</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Discrete">CZH_ECAT_Discrete</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_SS">CZH_ECAT_SS</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Parallel">CZH_ECAT_Parallel</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Comma">CZH_ECAT_Comma</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Rel">CZH_ECAT_Rel</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Par">CZH_ECAT_Par</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Set">CZH_ECAT_Set</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_GRPH">CZH_ECAT_GRPH</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_SemiCAT">CZH_ECAT_SemiCAT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_DG_CAT">CZH_DG_CAT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_SMC_CAT">CZH_SMC_CAT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_CAT">CZH_ECAT_CAT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_DG_FUNCT">CZH_DG_FUNCT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_SMC_FUNCT">CZH_SMC_FUNCT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_FUNCT">CZH_ECAT_FUNCT</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Hom">CZH_ECAT_Hom</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Cone">CZH_ECAT_Cone</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Small_Cone">CZH_ECAT_Small_Cone</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Yoneda">CZH_ECAT_Yoneda</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Order">CZH_ECAT_Order</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Small_Order">CZH_ECAT_Small_Order</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Ordinal">CZH_ECAT_Ordinal</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_CSimplicial">CZH_ECAT_CSimplicial</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Structure_Example">CZH_ECAT_Structure_Example</a></li>
<li><a href="../theories/czh_elementary_categories/#CZH_ECAT_Conclusions">CZH_ECAT_Conclusions</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Universal_Constructions.html">Category Theory for ZFC in HOL III: Universal Constructions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/CZH_Universal_Constructions.html">Category Theory for ZFC in HOL III: Universal Constructions</a></li>
<li><a href="../entries/Conditional_Simplification.html">Conditional Simplification</a></li>
<li><a href="../entries/Conditional_Transfer_Rule.html">Conditional Transfer Rule</a></li>
<li><a href="../entries/Intro_Dest_Elim.html">IDE: Introduction, Destruction, Elimination</a></li>
<li><a href="../entries/Recursion-Addition.html">Recursion Theorem in ZF</a></li>
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<p style="display:none;" id="bibtex-filename">CZH_Elementary_Categories-AFP</p><pre id="copy-text">@article{CZH_Elementary_Categories-AFP,
author = {Mihails Milehins},
title = {Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/CZH_Elementary_Categories.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-CZH_Elementary_Categories-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CZH_Elementary_Categories-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CZH_Elementary_Categories-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory for <span class='first'>Z</span><span class='first'>F</span><span class='first'>C</span> in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>I</span>: <span class='first'>F</span>oundations: <span class='first'>D</span>esign <span class='first'>P</span>atterns, <span class='first'>S</span>et <span class='first'>T</span>heory, <span class='first'>D</span>igraphs, <span class='first'>S</span>emicategories</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article provides a foundational framework for the formalization
of category theory in the object logic ZFC in HOL of the formal proof
assistant Isabelle. More specifically, this article provides a
formalization of canonical set-theoretic constructions internalized in
the type <i>V</i> associated with the ZFC in HOL,
establishes a design pattern for the formalization of mathematical
structures using sequences and locales, and showcases the developed
infrastructure by providing formalizations of the elementary theories
of digraphs and semicategories. The methodology chosen for the
formalization of the theories of digraphs and semicategories (and
categories in future articles) rests on the ideas that were originally
expressed in the article <i>Set-Theoretical Foundations of
Category Theory</i> written by Solomon Feferman and Georg
Kreisel. Thus, in the context of this work, each of the aforementioned
mathematical structures is represented as a term of the type
<i>V</i> embedded into a stage of the von Neumann
hierarchy.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session CZH_Foundations</h3>
<ul>
<li><a href="../theories/czh_foundations/#CZH_Sets_MIF">CZH_Sets_MIF</a></li>
<li><a href="../theories/czh_foundations/#CZH_Utilities">CZH_Utilities</a></li>
<li><a href="../theories/czh_foundations/#CZH_Introduction">CZH_Introduction</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Introduction">CZH_Sets_Introduction</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Sets">CZH_Sets_Sets</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Nat">CZH_Sets_Nat</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_BRelations">CZH_Sets_BRelations</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_IF">CZH_Sets_IF</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Equipollence">CZH_Sets_Equipollence</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Cardinality">CZH_Sets_Cardinality</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Ordinals">CZH_Sets_Ordinals</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_FSequences">CZH_Sets_FSequences</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_FBRelations">CZH_Sets_FBRelations</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_VNHS">CZH_Sets_VNHS</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_NOP">CZH_Sets_NOP</a></li>
<li><a href="../theories/czh_foundations/#HOL_CContinuum">HOL_CContinuum</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_ZQR">CZH_Sets_ZQR</a></li>
<li><a href="../theories/czh_foundations/#CZH_EX_Replacement">CZH_EX_Replacement</a></li>
<li><a href="../theories/czh_foundations/#CZH_EX_TS">CZH_EX_TS</a></li>
<li><a href="../theories/czh_foundations/#CZH_EX_Algebra">CZH_EX_Algebra</a></li>
<li><a href="../theories/czh_foundations/#CZH_Sets_Conclusions">CZH_Sets_Conclusions</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Introduction">CZH_DG_Introduction</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Digraph">CZH_DG_Digraph</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Small_Digraph">CZH_DG_Small_Digraph</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_DGHM">CZH_DG_DGHM</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Small_DGHM">CZH_DG_Small_DGHM</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_TDGHM">CZH_DG_TDGHM</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Small_TDGHM">CZH_DG_Small_TDGHM</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_PDigraph">CZH_DG_PDigraph</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Subdigraph">CZH_DG_Subdigraph</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Simple">CZH_DG_Simple</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_GRPH">CZH_DG_GRPH</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Rel">CZH_DG_Rel</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Par">CZH_DG_Par</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Set">CZH_DG_Set</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_Conclusions">CZH_DG_Conclusions</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Introduction">CZH_SMC_Introduction</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Semicategory">CZH_SMC_Semicategory</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Small_Semicategory">CZH_SMC_Small_Semicategory</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Semifunctor">CZH_SMC_Semifunctor</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Small_Semifunctor">CZH_SMC_Small_Semifunctor</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_NTSMCF">CZH_SMC_NTSMCF</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Small_NTSMCF">CZH_SMC_Small_NTSMCF</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_PSemicategory">CZH_SMC_PSemicategory</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Subsemicategory">CZH_SMC_Subsemicategory</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Simple">CZH_SMC_Simple</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Rel">CZH_SMC_Rel</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Par">CZH_SMC_Par</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Set">CZH_SMC_Set</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_GRPH">CZH_SMC_GRPH</a></li>
<li><a href="../theories/czh_foundations/#CZH_DG_SemiCAT">CZH_DG_SemiCAT</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_SemiCAT">CZH_SMC_SemiCAT</a></li>
<li><a href="../theories/czh_foundations/#CZH_SMC_Conclusions">CZH_SMC_Conclusions</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Conditional_Simplification.html">Conditional Simplification</a></li><li><a href="../entries/Intro_Dest_Elim.html">IDE: Introduction, Destruction, Elimination</a></li><li><a href="../entries/ZFC_in_HOL.html">Zermelo Fraenkel Set Theory in Higher-Order Logic</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Elementary_Categories.html">Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/CZH_Elementary_Categories.html">Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</a></li>
<li><a href="../entries/CZH_Universal_Constructions.html">Category Theory for ZFC in HOL III: Universal Constructions</a></li>
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<p style="display:none;" id="bibtex-filename">CZH_Foundations-AFP</p><pre id="copy-text">@article{CZH_Foundations-AFP,
author = {Mihails Milehins},
title = {Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/CZH_Foundations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-CZH_Foundations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CZH_Foundations-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CZH_Foundations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CZH_Foundations-2021-10-05.tar.gz">Oct 5, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-CZH_Foundations-2021-09-14.tar.gz">Sep 14, 2021</a>: Isabelle2021
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diff --git a/web/entries/CZH_Universal_Constructions.html b/web/entries/CZH_Universal_Constructions.html
--- a/web/entries/CZH_Universal_Constructions.html
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory for <span class='first'>Z</span><span class='first'>F</span><span class='first'>C</span> in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>I</span><span class='first'>I</span><span class='first'>I</span>: <span class='first'>U</span>niversal <span class='first'>C</span>onstructions</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The article provides a formalization of elements of the theory of
universal constructions for 1-categories (such as limits, adjoints and
Kan extensions) in the object logic ZFC in HOL of the formal proof
assistant Isabelle. The article builds upon the foundations
established in the AFP entry <i>Category Theory for ZFC in HOL
II: Elementary Theory of 1-Categories</i>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 16, 2022</dt>
<dd>creation and preservation of limits (revision 68412a363595)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session CZH_Universal_Constructions</h3>
<ul>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Introduction">CZH_UCAT_Introduction</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Universal">CZH_UCAT_Universal</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Limit">CZH_UCAT_Limit</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Limit_IT">CZH_UCAT_Limit_IT</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Limit_Product">CZH_UCAT_Limit_Product</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Limit_Pullback">CZH_UCAT_Limit_Pullback</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Limit_Equalizer">CZH_UCAT_Limit_Equalizer</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Pointed">CZH_UCAT_Pointed</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Representable">CZH_UCAT_Representable</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Complete">CZH_UCAT_Complete</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Comma">CZH_UCAT_Comma</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Set">CZH_UCAT_Set</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Adjoints">CZH_UCAT_Adjoints</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Kan">CZH_UCAT_Kan</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_PWKan">CZH_UCAT_PWKan</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_PWKan_Example">CZH_UCAT_PWKan_Example</a></li>
<li><a href="../theories/czh_universal_constructions/#CZH_UCAT_Conclusions">CZH_UCAT_Conclusions</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Elementary_Categories.html">Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li>
<li><a href="../entries/Conditional_Simplification.html">Conditional Simplification</a></li>
<li><a href="../entries/Conditional_Transfer_Rule.html">Conditional Transfer Rule</a></li>
<li><a href="../entries/Intro_Dest_Elim.html">IDE: Introduction, Destruction, Elimination</a></li>
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<p style="display:none;" id="bibtex-filename">CZH_Universal_Constructions-AFP</p><pre id="copy-text">@article{CZH_Universal_Constructions-AFP,
author = {Mihails Milehins},
title = {Category Theory for ZFC in HOL III: Universal Constructions},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/CZH_Universal_Constructions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-CZH_Universal_Constructions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CZH_Universal_Constructions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CZH_Universal_Constructions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CZH_Universal_Constructions-2021-10-05.tar.gz">Oct 5, 2021</a>: Isabelle2021
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diff --git a/web/entries/CakeML.html b/web/entries/CakeML.html
--- a/web/entries/CakeML.html
+++ b/web/entries/CakeML.html
@@ -1,258 +1,260 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>CakeML - Archive of Formal Proofs</title><meta name="description" content="CakeML is a functional programming language with a proven-correct
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<h1 >
<span class='first'>C</span>ake<span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a> and <a href="../authors/zhang">Yu Zhang</a>
with contributions from <a href="../authors/pohjola">Johannes Åman Pohjola</a>
</p>
<p class="date">March 12, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">CakeML is a functional programming language with a proven-correct
compiler and runtime system. This entry contains an unofficial version
of the CakeML semantics that has been exported from the Lem
specifications to Isabelle. Additionally, there are some hand-written
theory files that adapt the exported code to Isabelle and port proofs
from the HOL4 formalization, e.g. termination and equivalence proofs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session LEM</h3>
<ul>
<li><a href="../theories/lem/#Lem_bool">Lem_bool</a></li>
<li><a href="../theories/lem/#Lem_basic_classes">Lem_basic_classes</a></li>
<li><a href="../theories/lem/#Lem_tuple">Lem_tuple</a></li>
<li><a href="../theories/lem/#Lem_function">Lem_function</a></li>
<li><a href="../theories/lem/#Lem_maybe">Lem_maybe</a></li>
<li><a href="../theories/lem/#Lem_num">Lem_num</a></li>
<li><a href="../theories/lem/#LemExtraDefs">LemExtraDefs</a></li>
<li><a href="../theories/lem/#Lem">Lem</a></li>
<li><a href="../theories/lem/#Lem_list">Lem_list</a></li>
<li><a href="../theories/lem/#Lem_either">Lem_either</a></li>
<li><a href="../theories/lem/#Lem_set_helpers">Lem_set_helpers</a></li>
<li><a href="../theories/lem/#Lem_set">Lem_set</a></li>
<li><a href="../theories/lem/#Lem_map">Lem_map</a></li>
<li><a href="../theories/lem/#Lem_string">Lem_string</a></li>
<li><a href="../theories/lem/#Lem_word">Lem_word</a></li>
<li><a href="../theories/lem/#Lem_show">Lem_show</a></li>
<li><a href="../theories/lem/#Lem_sorting">Lem_sorting</a></li>
<li><a href="../theories/lem/#Lem_relation">Lem_relation</a></li>
<li><a href="../theories/lem/#Lem_pervasives">Lem_pervasives</a></li>
<li><a href="../theories/lem/#Lem_function_extra">Lem_function_extra</a></li>
<li><a href="../theories/lem/#Lem_assert_extra">Lem_assert_extra</a></li>
<li><a href="../theories/lem/#Lem_maybe_extra">Lem_maybe_extra</a></li>
<li><a href="../theories/lem/#Lem_map_extra">Lem_map_extra</a></li>
<li><a href="../theories/lem/#Lem_num_extra">Lem_num_extra</a></li>
<li><a href="../theories/lem/#Lem_set_extra">Lem_set_extra</a></li>
<li><a href="../theories/lem/#Lem_list_extra">Lem_list_extra</a></li>
<li><a href="../theories/lem/#Lem_string_extra">Lem_string_extra</a></li>
<li><a href="../theories/lem/#Lem_show_extra">Lem_show_extra</a></li>
<li><a href="../theories/lem/#Lem_machine_word">Lem_machine_word</a></li>
<li><a href="../theories/lem/#Lem_pervasives_extra">Lem_pervasives_extra</a></li></ul>
<h3>Session CakeML</h3>
<ul>
<li><a href="../theories/cakeml/#Doc_Generated">Doc_Generated</a></li>
<li><a href="../theories/cakeml/#Lib">Lib</a></li>
<li><a href="../theories/cakeml/#Namespace">Namespace</a></li>
<li><a href="../theories/cakeml/#FpSem">FpSem</a></li>
<li><a href="../theories/cakeml/#Ast">Ast</a></li>
<li><a href="../theories/cakeml/#AstAuxiliary">AstAuxiliary</a></li>
<li><a href="../theories/cakeml/#Ffi">Ffi</a></li>
<li><a href="../theories/cakeml/#SemanticPrimitives">SemanticPrimitives</a></li>
<li><a href="../theories/cakeml/#SmallStep">SmallStep</a></li>
<li><a href="../theories/cakeml/#BigStep">BigStep</a></li>
<li><a href="../theories/cakeml/#BigSmallInvariants">BigSmallInvariants</a></li>
<li><a href="../theories/cakeml/#Evaluate">Evaluate</a></li>
<li><a href="../theories/cakeml/#LibAuxiliary">LibAuxiliary</a></li>
<li><a href="../theories/cakeml/#NamespaceAuxiliary">NamespaceAuxiliary</a></li>
<li><a href="../theories/cakeml/#PrimTypes">PrimTypes</a></li>
<li><a href="../theories/cakeml/#SemanticPrimitivesAuxiliary">SemanticPrimitivesAuxiliary</a></li>
<li><a href="../theories/cakeml/#SimpleIO">SimpleIO</a></li>
<li><a href="../theories/cakeml/#Tokens">Tokens</a></li>
<li><a href="../theories/cakeml/#TypeSystem">TypeSystem</a></li>
<li><a href="../theories/cakeml/#TypeSystemAuxiliary">TypeSystemAuxiliary</a></li>
<li><a href="../theories/cakeml/#Doc_Proofs">Doc_Proofs</a></li>
<li><a href="../theories/cakeml/#Semantic_Extras">Semantic_Extras</a></li>
<li><a href="../theories/cakeml/#Evaluate_Termination">Evaluate_Termination</a></li>
<li><a href="../theories/cakeml/#Evaluate_Clock">Evaluate_Clock</a></li>
<li><a href="../theories/cakeml/#Evaluate_Single">Evaluate_Single</a></li>
<li><a href="../theories/cakeml/#Big_Step_Determ">Big_Step_Determ</a></li>
<li><a href="../theories/cakeml/#Big_Step_Total">Big_Step_Total</a></li>
<li><a href="../theories/cakeml/#Big_Step_Fun_Equiv">Big_Step_Fun_Equiv</a></li>
<li><a href="../theories/cakeml/#Big_Step_Unclocked">Big_Step_Unclocked</a></li>
<li><a href="../theories/cakeml/#Big_Step_Clocked">Big_Step_Clocked</a></li>
<li><a href="../theories/cakeml/#Big_Step_Unclocked_Single">Big_Step_Unclocked_Single</a></li>
<li><a href="../theories/cakeml/#Matching">Matching</a></li>
<li><a href="../theories/cakeml/#CakeML_Code">CakeML_Code</a></li>
<li><a href="../theories/cakeml/#CakeML_Quickcheck">CakeML_Quickcheck</a></li>
<li><a href="../theories/cakeml/#CakeML_Compiler">CakeML_Compiler</a></li>
<li><a href="../theories/cakeml/#Compiler_Test">Compiler_Test</a></li>
<li><a href="../theories/cakeml/#Code_Test_Haskell">Code_Test_Haskell</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/IEEE_Floating_Point.html">A Formal Model of IEEE Floating Point Arithmetic</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/LambdaAuth.html">Formalization of Generic Authenticated Data Structures</a></li>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/CakeML/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/CakeML/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">CakeML-AFP</p><pre id="copy-text">@article{CakeML-AFP,
author = {Lars Hupel and Yu Zhang},
title = {CakeML},
journal = {Archive of Formal Proofs},
month = {March},
year = {2018},
note = {\url{https://isa-afp.org/entries/CakeML.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-CakeML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CakeML-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CakeML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/CakeML_Codegen.html b/web/entries/CakeML_Codegen.html
--- a/web/entries/CakeML_Codegen.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Verified Code Generator from Isabelle/HOL to CakeML - Archive of Formal Proofs</title><meta name="description" content="This entry contains the formalization that accompanies my PhD thesis
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>C</span>ode <span class='first'>G</span>enerator <span class='first'>F</span>rom <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> to <span class='first'>C</span>ake<span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">July 8, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains the formalization that accompanies my PhD thesis
(see https://lars.hupel.info/research/codegen/). I develop a verified
compilation toolchain from executable specifications in Isabelle/HOL
to CakeML abstract syntax trees. This improves over the
state-of-the-art in Isabelle by providing a trustworthy procedure for
code generation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session CakeML_Codegen</h3>
<ul>
<li><a href="../theories/cakeml_codegen/#ML_Utils">ML_Utils</a></li>
<li><a href="../theories/cakeml_codegen/#Compiler_Utils">Compiler_Utils</a></li>
<li><a href="../theories/cakeml_codegen/#Code_Utils">Code_Utils</a></li>
<li><a href="../theories/cakeml_codegen/#CakeML_Utils">CakeML_Utils</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Utils">Test_Utils</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_Terms">Doc_Terms</a></li>
<li><a href="../theories/cakeml_codegen/#Terms_Extras">Terms_Extras</a></li>
<li><a href="../theories/cakeml_codegen/#HOL_Datatype">HOL_Datatype</a></li>
<li><a href="../theories/cakeml_codegen/#Constructors">Constructors</a></li>
<li><a href="../theories/cakeml_codegen/#Consts">Consts</a></li>
<li><a href="../theories/cakeml_codegen/#Strong_Term">Strong_Term</a></li>
<li><a href="../theories/cakeml_codegen/#Sterm">Sterm</a></li>
<li><a href="../theories/cakeml_codegen/#Pterm">Pterm</a></li>
<li><a href="../theories/cakeml_codegen/#Term_as_Value">Term_as_Value</a></li>
<li><a href="../theories/cakeml_codegen/#Value">Value</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_CupCake">Doc_CupCake</a></li>
<li><a href="../theories/cakeml_codegen/#CupCake_Env">CupCake_Env</a></li>
<li><a href="../theories/cakeml_codegen/#CupCake_Semantics">CupCake_Semantics</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_Rewriting">Doc_Rewriting</a></li>
<li><a href="../theories/cakeml_codegen/#General_Rewriting">General_Rewriting</a></li>
<li><a href="../theories/cakeml_codegen/#Rewriting_Term">Rewriting_Term</a></li>
<li><a href="../theories/cakeml_codegen/#Rewriting_Nterm">Rewriting_Nterm</a></li>
<li><a href="../theories/cakeml_codegen/#Rewriting_Pterm_Elim">Rewriting_Pterm_Elim</a></li>
<li><a href="../theories/cakeml_codegen/#Rewriting_Pterm">Rewriting_Pterm</a></li>
<li><a href="../theories/cakeml_codegen/#Rewriting_Sterm">Rewriting_Sterm</a></li>
<li><a href="../theories/cakeml_codegen/#Big_Step_Sterm">Big_Step_Sterm</a></li>
<li><a href="../theories/cakeml_codegen/#Big_Step_Value">Big_Step_Value</a></li>
<li><a href="../theories/cakeml_codegen/#Big_Step_Value_ML">Big_Step_Value_ML</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_Preproc">Doc_Preproc</a></li>
<li><a href="../theories/cakeml_codegen/#Eval_Class">Eval_Class</a></li>
<li><a href="../theories/cakeml_codegen/#Embed">Embed</a></li>
<li><a href="../theories/cakeml_codegen/#Eval_Instances">Eval_Instances</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_Backend">Doc_Backend</a></li>
<li><a href="../theories/cakeml_codegen/#CakeML_Setup">CakeML_Setup</a></li>
<li><a href="../theories/cakeml_codegen/#CakeML_Backend">CakeML_Backend</a></li>
<li><a href="../theories/cakeml_codegen/#CakeML_Correctness">CakeML_Correctness</a></li>
<li><a href="../theories/cakeml_codegen/#CakeML_Byte">CakeML_Byte</a></li>
<li><a href="../theories/cakeml_codegen/#Doc_Compiler">Doc_Compiler</a></li>
<li><a href="../theories/cakeml_codegen/#Composition">Composition</a></li>
<li><a href="../theories/cakeml_codegen/#Compiler">Compiler</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Composition">Test_Composition</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Print">Test_Print</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Embed_Data">Test_Embed_Data</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Embed_Data2">Test_Embed_Data2</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Embed_Tree">Test_Embed_Tree</a></li>
<li><a href="../theories/cakeml_codegen/#Test_Datatypes">Test_Datatypes</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML.html">CakeML</a></li><li><a href="../entries/Constructor_Funs.html">Constructor Functions</a></li><li><a href="../entries/Dict_Construction.html">Dictionary Construction</a></li><li><a href="../entries/Higher_Order_Terms.html">An Algebra for Higher-Order Terms</a></li><li><a href="../entries/Huffman.html">The Textbook Proof of Huffman&rsquo;s Algorithm</a></li><li><a href="../entries/Pairing_Heap.html">Pairing Heap</a></li><li><a href="../entries/Root_Balanced_Tree.html">Root-Balanced Tree</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Containers.html">Light-weight Containers</a></li>
<li><a href="../entries/XML.html">XML</a></li>
<li><a href="../entries/Imperative_Insertion_Sort.html">Imperative Insertion Sort</a></li>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/CakeML_Codegen/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/CakeML_Codegen/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">CakeML_Codegen-AFP</p><pre id="copy-text">@article{CakeML_Codegen-AFP,
author = {Lars Hupel},
title = {A Verified Code Generator from Isabelle/HOL to CakeML},
journal = {Archive of Formal Proofs},
month = {July},
year = {2019},
note = {\url{https://isa-afp.org/entries/CakeML_Codegen.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-CakeML_Codegen-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-CakeML_Codegen-2019-07-11.tar.gz">Jul 11, 2019</a>: Isabelle2019
</li></ul>
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diff --git a/web/entries/Call_Arity.html b/web/entries/Call_Arity.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Safety of Call Arity - Archive of Formal Proofs</title><meta name="description" content="We formalize the Call Arity analysis, as implemented in GHC, and prove both functional correctness and, more interestingly, safety (i.e. the transformation..."><meta property="og:title" content="The Safety of Call Arity" />
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>afety of <span class='first'>C</span>all <span class='first'>A</span>rity</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a href="http://pp.ipd.kit.edu/~breitner">🌐</a>
</p>
<p class="date">February 20, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the Call Arity analysis, as implemented in GHC, and prove
both functional correctness and, more interestingly, safety (i.e. the
transformation does not increase allocation).
<p>
We use syntax and the denotational semantics from the entry
"Launchbury", where we formalized Launchbury's natural semantics for
lazy evaluation.
<p>
The functional correctness of Call Arity is proved with regard to that
denotational semantics. The operational properties are shown with
regard to a small-step semantics akin to Sestoft's mark 1 machine,
which we prove to be equivalent to Launchbury's semantics.
<p>
We use Christian Urban's Nominal2 package to define our terms and make
use of Brian Huffman's HOLCF package for the domain-theoretical
aspects of the development.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 16, 2015</dt>
<dd>This entry now builds on top of the Launchbury entry,
and the equivalency proof of the natural and the small-step semantics
was added.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Call_Arity</h3>
<ul>
<li><a href="../theories/call_arity/#BalancedTraces">BalancedTraces</a></li>
<li><a href="../theories/call_arity/#SestoftConf">SestoftConf</a></li>
<li><a href="../theories/call_arity/#Sestoft">Sestoft</a></li>
<li><a href="../theories/call_arity/#SestoftCorrect">SestoftCorrect</a></li>
<li><a href="../theories/call_arity/#Arity">Arity</a></li>
<li><a href="../theories/call_arity/#AEnv">AEnv</a></li>
<li><a href="../theories/call_arity/#Arity-Nominal">Arity-Nominal</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisSig">ArityAnalysisSig</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisAbinds">ArityAnalysisAbinds</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisSpec">ArityAnalysisSpec</a></li>
<li><a href="../theories/call_arity/#TrivialArityAnal">TrivialArityAnal</a></li>
<li><a href="../theories/call_arity/#Cardinality-Domain">Cardinality-Domain</a></li>
<li><a href="../theories/call_arity/#CardinalityAnalysisSig">CardinalityAnalysisSig</a></li>
<li><a href="../theories/call_arity/#ConstOn">ConstOn</a></li>
<li><a href="../theories/call_arity/#CardinalityAnalysisSpec">CardinalityAnalysisSpec</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisStack">ArityAnalysisStack</a></li>
<li><a href="../theories/call_arity/#NoCardinalityAnalysis">NoCardinalityAnalysis</a></li>
<li><a href="../theories/call_arity/#TransformTools">TransformTools</a></li>
<li><a href="../theories/call_arity/#AbstractTransform">AbstractTransform</a></li>
<li><a href="../theories/call_arity/#EtaExpansion">EtaExpansion</a></li>
<li><a href="../theories/call_arity/#EtaExpansionSafe">EtaExpansionSafe</a></li>
<li><a href="../theories/call_arity/#ArityStack">ArityStack</a></li>
<li><a href="../theories/call_arity/#ArityEtaExpansion">ArityEtaExpansion</a></li>
<li><a href="../theories/call_arity/#ArityEtaExpansionSafe">ArityEtaExpansionSafe</a></li>
<li><a href="../theories/call_arity/#ArityTransform">ArityTransform</a></li>
<li><a href="../theories/call_arity/#ArityConsistent">ArityConsistent</a></li>
<li><a href="../theories/call_arity/#ArityTransformSafe">ArityTransformSafe</a></li>
<li><a href="../theories/call_arity/#Set-Cpo">Set-Cpo</a></li>
<li><a href="../theories/call_arity/#Env-Set-Cpo">Env-Set-Cpo</a></li>
<li><a href="../theories/call_arity/#CoCallGraph">CoCallGraph</a></li>
<li><a href="../theories/call_arity/#CoCallAnalysisSig">CoCallAnalysisSig</a></li>
<li><a href="../theories/call_arity/#AList-Utils-HOLCF">AList-Utils-HOLCF</a></li>
<li><a href="../theories/call_arity/#CoCallGraph-Nominal">CoCallGraph-Nominal</a></li>
<li><a href="../theories/call_arity/#CoCallAnalysisBinds">CoCallAnalysisBinds</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisFix">ArityAnalysisFix</a></li>
<li><a href="../theories/call_arity/#CoCallFix">CoCallFix</a></li>
<li><a href="../theories/call_arity/#CoCallAnalysisImpl">CoCallAnalysisImpl</a></li>
<li><a href="../theories/call_arity/#CallArityEnd2End">CallArityEnd2End</a></li>
<li><a href="../theories/call_arity/#SestoftGC">SestoftGC</a></li>
<li><a href="../theories/call_arity/#CardArityTransformSafe">CardArityTransformSafe</a></li>
<li><a href="../theories/call_arity/#CoCallAritySig">CoCallAritySig</a></li>
<li><a href="../theories/call_arity/#CoCallAnalysisSpec">CoCallAnalysisSpec</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisFixProps">ArityAnalysisFixProps</a></li>
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<li><a href="../theories/call_arity/#TTreeAnalysisSig">TTreeAnalysisSig</a></li>
<li><a href="../theories/call_arity/#CoCallGraph-TTree">CoCallGraph-TTree</a></li>
<li><a href="../theories/call_arity/#CoCallImplTTree">CoCallImplTTree</a></li>
<li><a href="../theories/call_arity/#Cardinality-Domain-Lists">Cardinality-Domain-Lists</a></li>
<li><a href="../theories/call_arity/#TTreeAnalysisSpec">TTreeAnalysisSpec</a></li>
<li><a href="../theories/call_arity/#CoCallImplTTreeSafe">CoCallImplTTreeSafe</a></li>
<li><a href="../theories/call_arity/#TTreeImplCardinality">TTreeImplCardinality</a></li>
<li><a href="../theories/call_arity/#TTreeImplCardinalitySafe">TTreeImplCardinalitySafe</a></li>
<li><a href="../theories/call_arity/#CallArityEnd2EndSafe">CallArityEnd2EndSafe</a></li>
<li><a href="../theories/call_arity/#ArityAnalysisCorrDenotational">ArityAnalysisCorrDenotational</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Launchbury.html">The Correctness of Launchbury&rsquo;s Natural Semantics for Lazy Evaluation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Call_Arity-AFP</p><pre id="copy-text">@article{Call_Arity-AFP,
author = {Joachim Breitner},
title = {The Safety of Call Arity},
journal = {Archive of Formal Proofs},
month = {February},
year = {2015},
note = {\url{https://isa-afp.org/entries/Call_Arity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>ardinality of <span class='first'>E</span>quivalence <span class='first'>R</span>elations</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">May 24, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides formulae for counting the number of equivalence
relations and partial equivalence relations over a finite carrier set
with given cardinality. To count the number of equivalence relations,
we provide bijections between equivalence relations and set
partitions, and then transfer the main results of the two AFP entries,
Cardinality of Set Partitions and Spivey's Generalized Recurrence for
Bell Numbers, to theorems on equivalence relations. To count the
number of partial equivalence relations, we observe that counting
partial equivalence relations over a set A is equivalent to counting
all equivalence relations over all subsets of the set A. From this
observation and the results on equivalence relations, we show that the
cardinality of partial equivalence relations over a finite set of
cardinality n is equal to the n+1-th Bell number.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Card_Equiv_Relations</h3>
<ul>
<li><a href="../theories/card_equiv_relations/#Card_Equiv_Relations">Card_Equiv_Relations</a></li>
<li><a href="../theories/card_equiv_relations/#Card_Partial_Equiv_Relations">Card_Partial_Equiv_Relations</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bell_Numbers_Spivey.html">Spivey&rsquo;s Generalized Recurrence for Bell Numbers</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Equivalence_Relation_Enumeration.html">Enumeration of Equivalence Relations</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
<li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li>
<li><a href="../entries/Card_Multisets.html">Cardinality of Multisets</a></li>
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<p style="display:none;" id="bibtex-filename">Card_Equiv_Relations-AFP</p><pre id="copy-text">@article{Card_Equiv_Relations-AFP,
author = {Lukas Bulwahn},
title = {Cardinality of Equivalence Relations},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Card_Equiv_Relations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+++ b/web/entries/Card_Multisets.html
@@ -1,190 +1,192 @@
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<h1 >
<span class='first'>C</span>ardinality of <span class='first'>M</span>ultisets</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">June 26, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry provides three lemmas to count the number of multisets
of a given size and finite carrier set. The first lemma provides a
cardinality formula assuming that the multiset's elements are chosen
from the given carrier set. The latter two lemmas provide formulas
assuming that the multiset's elements also cover the given carrier
set, i.e., each element of the carrier set occurs in the multiset at
least once.</p> <p>The proof of the first lemma uses the argument of
the recurrence relation for counting multisets. The proof of the
second lemma is straightforward, and the proof of the third lemma is
easily obtained using the first cardinality lemma. A challenge for the
formalization is the derivation of the required induction rule, which
is a special combination of the induction rules for finite sets and
natural numbers. The induction rule is derived by defining a suitable
inductive predicate and transforming the predicate's induction
rule.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Card_Multisets</h3>
<ul>
<li><a href="../theories/card_multisets/#Card_Multisets">Card_Multisets</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Twelvefold_Way.html">The Twelvefold Way</a></li></ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Card_Multisets/document.pdf">Proof
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author = {Lukas Bulwahn},
title = {Cardinality of Multisets},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Card_Multisets.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Card_Multisets-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Card_Multisets-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Card_Multisets-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Multisets-2016-06-26.tar.gz">Jun 26, 2016</a>: Isabelle2016
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Card_Number_Partitions.html b/web/entries/Card_Number_Partitions.html
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<h1 >
<span class='first'>C</span>ardinality of <span class='first'>N</span>umber <span class='first'>P</span>artitions</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">January 14, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a basic library for number partitions, defines the
two-argument partition function through its recurrence relation and relates
this partition function to the cardinality of number partitions. The main
proof shows that the recursively-defined partition function with arguments
n and k equals the cardinality of number partitions of n with exactly k parts.
The combinatorial proof follows the proof sketch of Theorem 2.4.1 in
Mazur's textbook `Combinatorics: A Guided Tour`. This entry can serve as
starting point for various more intrinsic properties about number partitions,
the partition function and related recurrence relations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Card_Number_Partitions</h3>
<ul>
<li><a href="../theories/card_number_partitions/#Additions_to_Main">Additions_to_Main</a></li>
<li><a href="../theories/card_number_partitions/#Number_Partition">Number_Partition</a></li>
<li><a href="../theories/card_number_partitions/#Card_Number_Partitions">Card_Number_Partitions</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Twelvefold_Way.html">The Twelvefold Way</a></li><li><a href="../entries/Euler_Partition.html">Euler&rsquo;s Partition Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Card_Number_Partitions-AFP</p><pre id="copy-text">@article{Card_Number_Partitions-AFP,
author = {Lukas Bulwahn},
title = {Cardinality of Number Partitions},
journal = {Archive of Formal Proofs},
month = {January},
year = {2016},
note = {\url{https://isa-afp.org/entries/Card_Number_Partitions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-Card_Number_Partitions-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Number_Partitions-2016-01-14.tar.gz">Jan 14, 2016</a>: Isabelle2015
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Card_Partitions.html b/web/entries/Card_Partitions.html
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@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>C</span>ardinality of <span class='first'>S</span>et <span class='first'>P</span>artitions</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">December 12, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory's main theorem states that the cardinality of set partitions of
size k on a carrier set of size n is expressed by Stirling numbers of the
second kind. In Isabelle, Stirling numbers of the second kind are defined
in the AFP entry `Discrete Summation` through their well-known recurrence
relation. The main theorem relates them to the alternative definition as
cardinality of set partitions. The proof follows the simple and short
explanation in Richard P. Stanley's `Enumerative Combinatorics: Volume 1`
and Wikipedia, and unravels the full details and implicit reasoning steps
of these explanations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Card_Partitions</h3>
<ul>
<li><a href="../theories/card_partitions/#Set_Partition">Set_Partition</a></li>
<li><a href="../theories/card_partitions/#Injectivity_Solver">Injectivity_Solver</a></li>
<li><a href="../theories/card_partitions/#Card_Partitions">Card_Partitions</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Discrete_Summation.html">Discrete Summation</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Design_Theory.html">Combinatorial Design Theory</a></li><li><a href="../entries/Falling_Factorial_Sum.html">The Falling Factorial of a Sum</a></li><li><a href="../entries/Twelvefold_Way.html">The Twelvefold Way</a></li><li><a href="../entries/Bell_Numbers_Spivey.html">Spivey&rsquo;s Generalized Recurrence for Bell Numbers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Card_Partitions-AFP</p><pre id="copy-text">@article{Card_Partitions-AFP,
author = {Lukas Bulwahn},
title = {Cardinality of Set Partitions},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Card_Partitions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Card_Partitions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Card_Partitions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Card_Partitions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Card_Partitions-2015-12-13.tar.gz">Dec 13, 2015</a>: Isabelle2015
</li></ul>
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<h1 >
<span class='first'>T</span>he <span class='first'>C</span>artan <span class='first'>F</span>ixed <span class='first'>P</span>oint <span class='first'>T</span>heorems</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">March 8, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Cartan fixed point theorems concern the group of holomorphic
automorphisms on a connected open set of C<sup>n</sup>. Ciolli et al.
have formalised the one-dimensional case of these theorems in HOL
Light. This entry contains their proofs, ported to Isabelle/HOL. Thus
it addresses the authors' remark that "it would be important to write
a formal proof in a language that can be read by both humans and
machines".</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Cartan_FP</h3>
<ul>
<li><a href="../theories/cartan_fp/#Cartan">Cartan</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Cartan_FP-AFP</p><pre id="copy-text">@article{Cartan_FP-AFP,
author = {Lawrence C. Paulson},
title = {The Cartan Fixed Point Theorems},
journal = {Archive of Formal Proofs},
month = {March},
year = {2016},
note = {\url{https://isa-afp.org/entries/Cartan_FP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Cartan_FP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>G</span>enerating <span class='first'>C</span>ases <span class='first'>F</span>rom <span class='first'>L</span>abeled <span class='first'>S</span>ubgoals</h1>
<div>
<p><a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">July 21, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle/Isar provides named cases to structure proofs. This article
contains an implementation of a proof method <tt>casify</tt>, which can
be used to easily extend proof tools with support for named cases. Such
a proof tool must produce labeled subgoals, which are then interpreted
by <tt>casify</tt>.
<p>
As examples, this work contains verification condition generators
producing named cases for three languages: The Hoare language from
<tt>HOL/Library</tt>, a monadic language for computations with failure
(inspired by the AutoCorres tool), and a language of conditional
expressions. These VCGs are demonstrated by a number of example programs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li><li><a href="../topics/computer-science/programming-languages/misc">Computer science/Programming languages/Misc</a></li></ul>
<h3>Session Case_Labeling</h3>
<ul>
<li><a href="../theories/case_labeling/#Case_Labeling">Case_Labeling</a></li>
<li><a href="../theories/case_labeling/#Labeled_Hoare">Labeled_Hoare</a></li>
<li><a href="../theories/case_labeling/#Labeled_Hoare_Examples">Labeled_Hoare_Examples</a></li>
<li><a href="../theories/case_labeling/#Conditionals">Conditionals</a></li>
<li><a href="../theories/case_labeling/#Monadic_Language">Monadic_Language</a></li>
<li><a href="../theories/case_labeling/#Case_Labeling_Examples">Case_Labeling_Examples</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Planarity_Certificates.html">Planarity Certificates</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Case_Labeling-AFP</p><pre id="copy-text">@article{Case_Labeling-AFP,
author = {Lars Noschinski},
title = {Generating Cases from Labeled Subgoals},
journal = {Archive of Formal Proofs},
month = {July},
year = {2015},
note = {\url{https://isa-afp.org/entries/Case_Labeling.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Case_Labeling-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Case_Labeling-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Case_Labeling-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Case_Labeling-2015-08-17.tar.gz">Aug 17, 2015</a>: Isabelle2015
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Case_Labeling-2015-07-24.tar.gz">Jul 24, 2015</a>: Isabelle2015
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diff --git a/web/entries/Catalan_Numbers.html b/web/entries/Catalan_Numbers.html
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@@ -1,187 +1,189 @@
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<h1 >
<span class='first'>C</span>atalan <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">June 21, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>In this work, we define the Catalan numbers <em>C<sub>n</sub></em>
and prove several equivalent definitions (including some closed-form
formulae). We also show one of their applications (counting the number
of binary trees of size <em>n</em>), prove the asymptotic growth
approximation <em>C<sub>n</sub> &sim; 4<sup>n</sup> / (&radic;<span
style="text-decoration: overline">&pi;</span> &middot;
n<sup>1.5</sup>)</em>, and provide reasonably efficient executable
code to compute them.</p> <p>The derivation of the closed-form
formulae uses algebraic manipulations of the ordinary generating
function of the Catalan numbers, and the asymptotic approximation is
then done using generalised binomial coefficients and the Gamma
function. Thanks to these highly non-elementary mathematical tools,
the proofs are very short and simple.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Catalan_Numbers</h3>
<ul>
<li><a href="../theories/catalan_numbers/#Catalan_Auxiliary_Integral">Catalan_Auxiliary_Integral</a></li>
<li><a href="../theories/catalan_numbers/#Catalan_Numbers">Catalan_Numbers</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li></ul>
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author = {Manuel Eberl},
title = {Catalan Numbers},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Catalan_Numbers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Catalan_Numbers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Catalan_Numbers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Catalan_Numbers-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Catalan_Numbers-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Catalan_Numbers-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory to <span class='first'>Y</span>oneda's <span class='first'>L</span>emma</h1>
<div>
<p><a href="../authors/keefe">Greg O&rsquo;Keefe</a> <a href="http://users.rsise.anu.edu.au/~okeefe/">🌐</a>
</p>
<p class="date">April 21, 2005</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development proves Yoneda's lemma and aims to be readable by humans. It only defines what is needed for the lemma: categories, functors and natural transformations. Limits, adjunctions and other important concepts are not included.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>April 23, 2010</dt>
<dd>The definition of the constant <tt>equinumerous</tt> was slightly too weak in the original submission and has been fixed in revision <a href="https://foss.heptapod.net/isa-afp/afp-devel/-/commit/3498bb1e4c7ba468db8588eb7184c1849641f7d3">8c2b5b3c995f</a>.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session Category</h3>
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<li><a href="../theories/category/#Cat">Cat</a></li>
<li><a href="../theories/category/#SetCat">SetCat</a></li>
<li><a href="../theories/category/#Functors">Functors</a></li>
<li><a href="../theories/category/#HomFunctors">HomFunctors</a></li>
<li><a href="../theories/category/#NatTrans">NatTrans</a></li>
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<p style="display:none;" id="bibtex-filename">Category-AFP</p><pre id="copy-text">@article{Category-AFP,
author = {Greg O'Keefe},
title = {Category Theory to Yoneda&#39;s Lemma},
journal = {Archive of Formal Proofs},
month = {April},
year = {2005},
note = {\url{https://isa-afp.org/entries/Category.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Category2.html b/web/entries/Category2.html
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/katovsky">Alexander Katovsky</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJhcGszMiJdfQ==">📧</a>
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<p class="date">June 20, 2010</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article presents a development of Category Theory in Isabelle/HOL. A Category is defined using records and locales. Functors and Natural Transformations are also defined. The main result that has been formalized is that the Yoneda functor is a full and faithful embedding. We also formalize the completeness of many sorted monadic equational logic. Extensive use is made of the HOLZF theory in both cases. For an informal description see <a href="http://www.srcf.ucam.org/~apk32/Isabelle/Category/Cat.pdf">here [pdf]</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session Category2</h3>
<ul>
<li><a href="../theories/category2/#Category">Category</a></li>
<li><a href="../theories/category2/#Universe">Universe</a></li>
<li><a href="../theories/category2/#MonadicEquationalTheory">MonadicEquationalTheory</a></li>
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<li><a href="../theories/category2/#NatTrans">NatTrans</a></li>
<li><a href="../theories/category2/#SetCat">SetCat</a></li>
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<p style="display:none;" id="bibtex-filename">Category2-AFP</p><pre id="copy-text">@article{Category2-AFP,
author = {Alexander Katovsky},
title = {Category Theory},
journal = {Archive of Formal Proofs},
month = {June},
year = {2010},
note = {\url{https://isa-afp.org/entries/Category2.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>ategory <span class='first'>T</span>heory <span class='first'>W</span>ith <span class='first'>A</span>djunctions and <span class='first'>L</span>imits</h1>
<div>
<p><a href="../authors/stark">Eugene W. Stark</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwic3Rvbnlicm9vayIsImVkdSJdLCJ1c2VyIjpbInN0YXJrIl19">📧</a>
</p>
<p class="date">June 26, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
This article attempts to develop a usable framework for doing category
theory in Isabelle/HOL. Our point of view, which to some extent
differs from that of the previous AFP articles on the subject, is to
try to explore how category theory can be done efficaciously within
HOL, rather than trying to match exactly the way things are done using
a traditional approach. To this end, we define the notion of category
in an "object-free" style, in which a category is represented by a
single partial composition operation on arrows. This way of defining
categories provides some advantages in the context of HOL, including
the ability to avoid the use of records and the possibility of
defining functors and natural transformations simply as certain
functions on arrows, rather than as composite objects. We define
various constructions associated with the basic notions, including:
dual category, product category, functor category, discrete category,
free category, functor composition, and horizontal and vertical
composite of natural transformations. A "set category" locale is
defined that axiomatizes the notion "category of all sets at a type
and all functions between them," and a fairly extensive set of
properties of set categories is derived from the locale assumptions.
The notion of a set category is used to prove the Yoneda Lemma in a
general setting of a category equipped with a "hom embedding," which
maps arrows of the category to the "universe" of the set category. We
also give a treatment of adjunctions, defining adjunctions via left
and right adjoint functors, natural bijections between hom-sets, and
unit and counit natural transformations, and showing the equivalence
of these definitions. We also develop the theory of limits, including
representations of functors, diagrams and cones, and diagonal
functors. We show that right adjoint functors preserve limits, and
that limits can be constructed via products and equalizers. We
characterize the conditions under which limits exist in a set
category. We also examine the case of limits in a functor category,
ultimately culminating in a proof that the Yoneda embedding preserves
limits.
</p><p>
Revisions made subsequent to the first version of this article added
material on equivalence of categories, cartesian categories,
categories with pullbacks, categories with finite limits, and
cartesian closed categories. A construction was given of the category
of hereditarily finite sets and functions between them, and it was
shown that this category is cartesian closed.
Using "ZFC_in_HOL", a construction was also given of the (large)
category of small sets and functions between them, and it was shown
that this category is small-complete.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 22, 2021</dt>
<dd>Minor changes to sublocale declarations related to functor/natural transformation to
avoid issues with global interpretations reported 2/2/2021 by Filip Smola.
(revision 49d3aa43c180)<br></dd><dt>November 4, 2020</dt>
<dd>Minor modifications and extensions made in conjunction with the addition
of new material to Bicategory.
(revision 472cb2268826)<br>
</dd><dt>July 10, 2020</dt>
<dd>Added new material, mostly centered around cartesian categories.
(revision 06640f317a79)<br>
</dd><dt>February 15, 2020</dt>
<dd>Move ConcreteCategory.thy from Bicategory to Category3 and use it systematically.
Make other minor improvements throughout.
(revision a51840d36867)<br>
</dd><dt>May 29, 2018</dt>
<dd>Revised axioms for the category locale. Introduced notation for composition and "in hom".
(revision 8318366d4575)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session Category3</h3>
<ul>
<li><a href="../theories/category3/#Category">Category</a></li>
<li><a href="../theories/category3/#DualCategory">DualCategory</a></li>
<li><a href="../theories/category3/#ConcreteCategory">ConcreteCategory</a></li>
<li><a href="../theories/category3/#EpiMonoIso">EpiMonoIso</a></li>
<li><a href="../theories/category3/#InitialTerminal">InitialTerminal</a></li>
<li><a href="../theories/category3/#Functor">Functor</a></li>
<li><a href="../theories/category3/#Subcategory">Subcategory</a></li>
<li><a href="../theories/category3/#SetCategory">SetCategory</a></li>
<li><a href="../theories/category3/#SetCat">SetCat</a></li>
<li><a href="../theories/category3/#ProductCategory">ProductCategory</a></li>
<li><a href="../theories/category3/#NaturalTransformation">NaturalTransformation</a></li>
<li><a href="../theories/category3/#BinaryFunctor">BinaryFunctor</a></li>
<li><a href="../theories/category3/#FunctorCategory">FunctorCategory</a></li>
<li><a href="../theories/category3/#Yoneda">Yoneda</a></li>
<li><a href="../theories/category3/#Adjunction">Adjunction</a></li>
<li><a href="../theories/category3/#EquivalenceOfCategories">EquivalenceOfCategories</a></li>
<li><a href="../theories/category3/#FreeCategory">FreeCategory</a></li>
<li><a href="../theories/category3/#DiscreteCategory">DiscreteCategory</a></li>
<li><a href="../theories/category3/#Limit">Limit</a></li>
<li><a href="../theories/category3/#CategoryWithPullbacks">CategoryWithPullbacks</a></li>
<li><a href="../theories/category3/#CartesianCategory">CartesianCategory</a></li>
<li><a href="../theories/category3/#CategoryWithFiniteLimits">CategoryWithFiniteLimits</a></li>
<li><a href="../theories/category3/#CartesianClosedCategory">CartesianClosedCategory</a></li>
<li><a href="../theories/category3/#HFSetCat">HFSetCat</a></li>
<li><a href="../theories/category3/#ZFC_SetCat">ZFC_SetCat</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></li><li><a href="../entries/ZFC_in_HOL.html">Zermelo Fraenkel Set Theory in Higher-Order Logic</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MonoidalCategory.html">Monoidal Categories</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MonoidalCategory.html">Monoidal Categories</a></li>
<li><a href="../entries/Incompleteness.html">Gödel&rsquo;s Incompleteness Theorems</a></li>
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<p style="display:none;" id="bibtex-filename">Category3-AFP</p><pre id="copy-text">@article{Category3-AFP,
author = {Eugene W. Stark},
title = {Category Theory with Adjunctions and Limits},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Category3.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>auchy's <span class='first'>M</span>ean <span class='first'>T</span>heorem and the <span class='first'>C</span>auchy-<span class='first'>S</span>chwarz <span class='first'>I</span>nequality</h1>
<div>
<p><a href="../authors/porter">Benjamin Porter</a>
</p>
<p class="date">March 14, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document presents the mechanised proofs of two popular theorems attributed to Augustin Louis Cauchy - Cauchy's Mean Theorem and the Cauchy-Schwarz Inequality.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Cauchy</h3>
<ul>
<li><a href="../theories/cauchy/#CauchysMeanTheorem">CauchysMeanTheorem</a></li>
<li><a href="../theories/cauchy/#CauchySchwarz">CauchySchwarz</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Cauchy-AFP</p><pre id="copy-text">@article{Cauchy-AFP,
author = {Benjamin Porter},
title = {Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality},
journal = {Archive of Formal Proofs},
month = {March},
year = {2006},
note = {\url{https://isa-afp.org/entries/Cauchy.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Cauchy-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Cauchy-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Cauchy-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Cauchy-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Cauchy-2006-03-14.tar.gz">Mar 14, 2006</a>: Isabelle2005
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diff --git a/web/entries/Cayley_Hamilton.html b/web/entries/Cayley_Hamilton.html
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@@ -1,183 +1,185 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>C</span>ayley-<span class='first'>H</span>amilton <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/adelsberger">Stephan Adelsberger</a> <a href="http://nm.wu.ac.at/nm/sadelsbe">🌐</a>, <a href="../authors/hetzl">Stefan Hetzl</a> <a href="http://www.logic.at/people/hetzl/">🌐</a> and <a href="../authors/pollak">Florian Pollak</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZmxvcmlhbiIsInBvbGxhayJdfQ==">📧</a>
</p>
<p class="date">September 15, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains a proof of the Cayley-Hamilton theorem
based on the development of matrices in HOL/Multivariate Analysis.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Cayley_Hamilton</h3>
<ul>
<li><a href="../theories/cayley_hamilton/#Square_Matrix">Square_Matrix</a></li>
<li><a href="../theories/cayley_hamilton/#Cayley_Hamilton">Cayley_Hamilton</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Cayley_Hamilton-AFP</p><pre id="copy-text">@article{Cayley_Hamilton-AFP,
author = {Stephan Adelsberger and Stefan Hetzl and Florian Pollak},
title = {The Cayley-Hamilton Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Cayley_Hamilton.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Cayley_Hamilton-2014-09-16.tar.gz">Sep 16, 2014</a>: Isabelle2014
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diff --git a/web/entries/Certification_Monads.html b/web/entries/Certification_Monads.html
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<h1 >
<span class='first'>C</span>ertification <span class='first'>M</span>onads</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">October 3, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides several monads intended for the development of stand-alone certifiers via code generation from Isabelle/HOL. More specifically, there are three flavors of error monads (the sum type, for the case where all monadic functions are total; an instance of the former, the so called check monad, yielding either success without any further information or an error message; as well as a variant of the sum type that accommodates partial functions by providing an explicit bottom element) and a parser monad built on top. All of this monads are heavily used in the IsaFoR/CeTA project which thus provides many examples of their usage.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Certification_Monads</h3>
<ul>
<li><a href="../theories/certification_monads/#Error_Syntax">Error_Syntax</a></li>
<li><a href="../theories/certification_monads/#Error_Monad">Error_Monad</a></li>
<li><a href="../theories/certification_monads/#Check_Monad">Check_Monad</a></li>
<li><a href="../theories/certification_monads/#Strict_Sum">Strict_Sum</a></li>
<li><a href="../theories/certification_monads/#Parser_Monad">Parser_Monad</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Partial_Function_MR.html">Mutually Recursive Partial Functions</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
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<ul class="horizontal-list"><li><a href="../entries/AI_Planning_Languages_Semantics.html">AI Planning Languages Semantics</a></li><li><a href="../entries/WOOT_Strong_Eventual_Consistency.html">Strong Eventual Consistency of the Collaborative Editing Framework WOOT</a></li><li><a href="../entries/XML.html">XML</a></li></ul>
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<li><a href="../entries/Transitive-Closure-II.html">Executable Transitive Closures</a></li>
<li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li>
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<p style="display:none;" id="bibtex-filename">Certification_Monads-AFP</p><pre id="copy-text">@article{Certification_Monads-AFP,
author = {Christian Sternagel and René Thiemann},
title = {Certification Monads},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/Certification_Monads.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Certification_Monads-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Certification_Monads-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Certification_Monads-2014-10-08.tar.gz">Oct 8, 2014</a>: Isabelle2014
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diff --git a/web/entries/Chandy_Lamport.html b/web/entries/Chandy_Lamport.html
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@@ -1,178 +1,180 @@
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>P</span>roof of the <span class='first'>C</span>handy--<span class='first'>L</span>amport <span class='first'>D</span>istributed <span class='first'>S</span>napshot <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/fiedler">Ben Fiedler</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbImJlbiIsImZpZWRsZXIiXX0=">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">July 21, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a suitable distributed system model and implementation of the
Chandy--Lamport distributed snapshot algorithm [ACM Transactions on
Computer Systems, 3, 63-75, 1985]. Our main result is a formal
termination and correctness proof of the Chandy--Lamport algorithm and
its use in stable property detection.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Chandy_Lamport</h3>
<ul>
<li><a href="../theories/chandy_lamport/#Distributed_System">Distributed_System</a></li>
<li><a href="../theories/chandy_lamport/#Trace">Trace</a></li>
<li><a href="../theories/chandy_lamport/#Util">Util</a></li>
<li><a href="../theories/chandy_lamport/#Swap">Swap</a></li>
<li><a href="../theories/chandy_lamport/#Snapshot">Snapshot</a></li>
<li><a href="../theories/chandy_lamport/#Co_Snapshot">Co_Snapshot</a></li>
<li><a href="../theories/chandy_lamport/#Example">Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Chandy_Lamport-AFP</p><pre id="copy-text">@article{Chandy_Lamport-AFP,
author = {Ben Fiedler and Dmitriy Traytel},
title = {A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm},
journal = {Archive of Formal Proofs},
month = {July},
year = {2020},
note = {\url{https://isa-afp.org/entries/Chandy_Lamport.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Chord_Segments.html b/web/entries/Chord_Segments.html
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<h1 >
<span class='first'>I</span>ntersecting <span class='first'>C</span>hords <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">October 11, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a geometric proof of the intersecting chords
theorem. The theorem states that when two chords intersect each other
inside a circle, the products of their segments are equal. After a
short review of existing proofs in the literature, I decided to use a
proof approach that employs reasoning about lengths of line segments,
the orthogonality of two lines and the Pythagoras Law. Hence, one can
understand the formalized proof easily with the knowledge of a few
general geometric facts that are commonly taught in high-school. This
theorem is the 55th theorem of the Top 100 Theorems list.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Chord_Segments</h3>
<ul>
<li><a href="../theories/chord_segments/#Chord_Segments">Chord_Segments</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Triangle.html">Basic Geometric Properties of Triangles</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Ptolemys_Theorem.html">Ptolemy&rsquo;s Theorem</a></li>
<li><a href="../entries/Euler_Partition.html">Euler&rsquo;s Partition Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Chord_Segments-AFP</p><pre id="copy-text">@article{Chord_Segments-AFP,
author = {Lukas Bulwahn},
title = {Intersecting Chords Theorem},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Chord_Segments.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>I</span>sabelle/<span class='first'>C</span>ircus</h1>
<div>
<p><a href="../authors/feliachi">Abderrahmane Feliachi</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYWJkZXJyYWhtYW5lIiwiZmVsaWFjaGkiXX0=">📧</a>, <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a> and <a href="../authors/gaudel">Marie-Claude Gaudel</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsibWNnIl19">📧</a>
with contributions from <a href="../authors/wenzel">Makarius Wenzel</a> <a class="obfuscated" data="eyJob3N0IjpbInNrZXRpcyIsIm5ldCJdLCJ1c2VyIjpbIm1ha2FyaXVzIl19">📧</a>
</p>
<p class="date">May 27, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Circus specification language combines elements for complex data and behavior specifications, using an integration of Z and CSP with a refinement calculus. Its semantics is based on Hoare and He's Unifying Theories of Programming (UTP). Isabelle/Circus is a formalization of the UTP and the Circus language in Isabelle/HOL. It contains proof rules and tactic support that allows for proofs of refinement for Circus processes (involving both data and behavioral aspects).
<p>
The Isabelle/Circus environment supports a syntax for the semantic definitions which is close to textbook presentations of Circus. This article contains an extended version of corresponding VSTTE Paper together with the complete formal development of its underlying commented theories.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 5, 2014</dt>
<dd>More polishing, shorter proofs, added Circus syntax, added Makarius Wenzel as contributor.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session Circus</h3>
<ul>
<li><a href="../theories/circus/#Var">Var</a></li>
<li><a href="../theories/circus/#Relations">Relations</a></li>
<li><a href="../theories/circus/#Designs">Designs</a></li>
<li><a href="../theories/circus/#Reactive_Processes">Reactive_Processes</a></li>
<li><a href="../theories/circus/#CSP_Processes">CSP_Processes</a></li>
<li><a href="../theories/circus/#Circus_Actions">Circus_Actions</a></li>
<li><a href="../theories/circus/#Var_list">Var_list</a></li>
<li><a href="../theories/circus/#Denotational_Semantics">Denotational_Semantics</a></li>
<li><a href="../theories/circus/#Circus_Syntax">Circus_Syntax</a></li>
<li><a href="../theories/circus/#Refinement">Refinement</a></li>
<li><a href="../theories/circus/#Refinement_Example">Refinement_Example</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Circus-AFP</p><pre id="copy-text">@article{Circus-AFP,
author = {Abderrahmane Feliachi and Burkhart Wolff and Marie-Claude Gaudel},
title = {Isabelle/Circus},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Circus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Circus-2012-05-29.tar.gz">May 29, 2012</a>: Isabelle2012
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<h1 >
<span class='first'>C</span>lean - <span class='first'>A</span>n <span class='first'>A</span>bstract <span class='first'>I</span>mperative <span class='first'>P</span>rogramming <span class='first'>L</span>anguage and <span class='first'>I</span>ts <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/tuong">Frédéric Tuong</a> <a href="https://www.lri.fr/~ftuong/">🌐</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a>
</p>
<p class="date">October 4, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Clean is based on a simple, abstract execution model for an imperative
target language. “Abstract” is understood in contrast to “Concrete
Semantics”; alternatively, the term “shallow-style embedding” could be
used. It strives for a type-safe notion of program-variables, an
incremental construction of the typed state-space, support of
incremental verification, and open-world extensibility of new type
definitions being intertwined with the program definitions. Clean is
based on a “no-frills” state-exception monad with the usual
definitions of bind and unit for the compositional glue of state-based
computations. Clean offers conditionals and loops supporting C-like
control-flow operators such as break and return. The state-space
construction is based on the extensible record package. Direct
recursion of procedures is supported. Clean’s design strives for
extreme simplicity. It is geared towards symbolic execution and proven
correct verification tools. The underlying libraries of this package,
however, deliberately restrict themselves to the most elementary
infrastructure for these tasks. The package is intended to serve as
demonstrator semantic backend for Isabelle/C, or for the
test-generation techniques.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages">Computer science/Programming languages</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Clean</h3>
<ul>
<li><a href="../theories/clean/#Lens_Laws">Lens_Laws</a></li>
<li><a href="../theories/clean/#Optics">Optics</a></li>
<li><a href="../theories/clean/#MonadSE">MonadSE</a></li>
<li><a href="../theories/clean/#Seq_MonadSE">Seq_MonadSE</a></li>
<li><a href="../theories/clean/#Symbex_MonadSE">Symbex_MonadSE</a></li>
<li><a href="../theories/clean/#Clean">Clean</a></li>
<li><a href="../theories/clean/#Hoare_MonadSE">Hoare_MonadSE</a></li>
<li><a href="../theories/clean/#Hoare_Clean">Hoare_Clean</a></li>
<li><a href="../theories/clean/#Clean_Symbex">Clean_Symbex</a></li>
<li><a href="../theories/clean/#Test_Clean">Test_Clean</a></li>
<li><a href="../theories/clean/#Clean_Main">Clean_Main</a></li>
<li><a href="../theories/clean/#IsPrime">IsPrime</a></li>
<li><a href="../theories/clean/#LinearSearch">LinearSearch</a></li>
<li><a href="../theories/clean/#Quicksort">Quicksort</a></li>
<li><a href="../theories/clean/#Quicksort_concept">Quicksort_concept</a></li>
<li><a href="../theories/clean/#SquareRoot_concept">SquareRoot_concept</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Clean-AFP</p><pre id="copy-text">@article{Clean-AFP,
author = {Frédéric Tuong and Burkhart Wolff},
title = {Clean - An Abstract Imperative Programming Language and its Theory},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/Clean.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Clean-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Clique_and_Monotone_Circuits.html b/web/entries/Clique_and_Monotone_Circuits.html
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<h1 >
<span class='first'>C</span>lique <span class='first'>I</span>s <span class='first'>N</span>ot <span class='first'>S</span>olvable by <span class='first'>M</span>onotone <span class='first'>C</span>ircuits of <span class='first'>P</span>olynomial <span class='first'>S</span>ize</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">May 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> Given a graph $G$ with $n$ vertices and a number $s$, the
decision problem Clique asks whether $G$ contains a fully connected
subgraph with $s$ vertices. For this NP-complete problem there exists
a non-trivial lower bound: no monotone circuit of a size that is
polynomial in $n$ can solve Clique. </p><p> This entry
provides an Isabelle/HOL formalization of a concrete lower bound (the
bound is $\sqrt[7]{n}^{\sqrt[8]{n}}$ for the fixed choice of $s =
\sqrt[4]{n}$), following a proof by Gordeev. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Clique_and_Monotone_Circuits</h3>
<ul>
<li><a href="../theories/clique_and_monotone_circuits/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/clique_and_monotone_circuits/#Monotone_Formula">Monotone_Formula</a></li>
<li><a href="../theories/clique_and_monotone_circuits/#Assumptions_and_Approximations">Assumptions_and_Approximations</a></li>
<li><a href="../theories/clique_and_monotone_circuits/#Clique_Large_Monotone_Circuits">Clique_Large_Monotone_Circuits</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li><li><a href="../entries/Sunflowers.html">The Sunflower Lemma of Erdős and Rado</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li>
<li><a href="../entries/Concurrent_Revisions.html">Formalization of Concurrent Revisions</a></li>
<li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li>
<li><a href="../entries/Prime_Harmonic_Series.html">The Divergence of the Prime Harmonic Series</a></li>
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<p style="display:none;" id="bibtex-filename">Clique_and_Monotone_Circuits-AFP</p><pre id="copy-text">@article{Clique_and_Monotone_Circuits-AFP,
author = {René Thiemann},
title = {Clique is not solvable by monotone circuits of polynomial size},
journal = {Archive of Formal Proofs},
month = {May},
year = {2022},
note = {\url{https://isa-afp.org/entries/Clique_and_Monotone_Circuits.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Clique_and_Monotone_Circuits-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Clique_and_Monotone_Circuits-2022-05-08.tar.gz">May 8, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/ClockSynchInst.html b/web/entries/ClockSynchInst.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Instances of Schneider&#39;s generalized protocol of clock synchronization - Archive of Formal Proofs</title><meta name="description" content="F. B. Schneider (&#34;Understanding protocols for Byzantine clock synchronization&#34;) generalizes a number of protocols for Byzantine fault-tolerant clock..."><meta property="og:title" content="Instances of Schneider&#39;s generalized protocol of clock synchronization" />
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<h1 >
<span class='first'>I</span>nstances of <span class='first'>S</span>chneider's <span class='first'>G</span>eneralized <span class='first'>P</span>rotocol of <span class='first'>C</span>lock <span class='first'>S</span>ynchronization</h1>
<div>
<p><a href="../authors/barsotti">Damián Barsotti</a> <a href="http://www.cs.famaf.unc.edu.ar/~damian/">🌐</a>
</p>
<p class="date">March 15, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">F. B. Schneider ("Understanding protocols for Byzantine clock synchronization") generalizes a number of protocols for Byzantine fault-tolerant clock synchronization and presents a uniform proof for their correctness. In Schneider's schema, each processor maintains a local clock by periodically adjusting each value to one computed by a convergence function applied to the readings of all the clocks. Then, correctness of an algorithm, i.e. that the readings of two clocks at any time are within a fixed bound of each other, is based upon some conditions on the convergence function. To prove that a particular clock synchronization algorithm is correct it suffices to show that the convergence function used by the algorithm meets Schneider's conditions. Using the theorem prover Isabelle, we formalize the proofs that the convergence functions of two algorithms, namely, the Interactive Convergence Algorithm (ICA) of Lamport and Melliar-Smith and the Fault-tolerant Midpoint algorithm of Lundelius-Lynch, meet Schneider's conditions. Furthermore, we experiment on handling some parts of the proofs with fully automatic tools like ICS and CVC-lite. These theories are part of a joint work with Alwen Tiu and Leonor P. Nieto <a href="http://users.rsise.anu.edu.au/~tiu/clocksync.pdf">"Verification of Clock Synchronization Algorithms: Experiments on a combination of deductive tools"</a> in proceedings of AVOCS 2005. In this work the correctness of Schneider schema was also verified using Isabelle (entry <a href="GenClock.html">GenClock</a> in AFP).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session ClockSynchInst</h3>
<ul>
<li><a href="../theories/clocksynchinst/#ICAInstance">ICAInstance</a></li>
<li><a href="../theories/clocksynchinst/#LynchInstance">LynchInstance</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">ClockSynchInst-AFP</p><pre id="copy-text">@article{ClockSynchInst-AFP,
author = {Damián Barsotti},
title = {Instances of Schneider&#39;s generalized protocol of clock synchronization},
journal = {Archive of Formal Proofs},
month = {March},
year = {2006},
note = {\url{https://isa-afp.org/entries/ClockSynchInst.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>losest <span class='first'>P</span>air of <span class='first'>P</span>oints <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/rau">Martin Rau</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsibWFydGluIiwicmF1Il19">📧</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">January 13, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides two related verified divide-and-conquer algorithms
solving the fundamental <em>Closest Pair of Points</em>
problem in Computational Geometry. Functional correctness and the
optimal running time of <em>O</em>(<em>n</em> log <em>n</em>) are
proved. Executable code is generated which is empirically competitive
with handwritten reference implementations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 14, 2020</dt>
<dd>Incorporate Time_Monad of the AFP entry Root_Balanced_Tree.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/geometry">Computer science/Algorithms/Geometry</a></li></ul><h3>Related publications</h3>
<ul><li>
Rau, M., & Nipkow, T. (2020). Verification of Closest Pair of Points Algorithms. Lecture Notes in Computer Science, 341–357. <a href="https://doi.org/10.1007/978-3-030-51054-1_20">https://doi.org/10.1007/978-3-030-51054-1_20</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Closest_pair_of_points_problem">Wikipedia</a>
</li></ul>
<h3>Session Closest_Pair_Points</h3>
<ul>
<li><a href="../theories/closest_pair_points/#Common">Common</a></li>
<li><a href="../theories/closest_pair_points/#Closest_Pair">Closest_Pair</a></li>
<li><a href="../theories/closest_pair_points/#Closest_Pair_Alternative">Closest_Pair_Alternative</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Akra_Bazzi.html">The Akra-Bazzi theorem and the Master theorem</a></li><li><a href="../entries/Root_Balanced_Tree.html">Root-Balanced Tree</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Closest_Pair_Points-AFP</p><pre id="copy-text">@article{Closest_Pair_Points-AFP,
author = {Martin Rau and Tobias Nipkow},
title = {Closest Pair of Points Algorithms},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Closest_Pair_Points.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/CoCon.html b/web/entries/CoCon.html
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<h1 >
<span class='first'>C</span>o<span class='first'>C</span>on: <span class='first'>A</span> <span class='first'>C</span>onfidentiality-<span class='first'>V</span>erified <span class='first'>C</span>onference <span class='first'>M</span>anagement <span class='first'>S</span>ystem</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJsYW1taWNoIl19">📧</a> and <a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a>
</p>
<p class="date">August 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains the confidentiality verification of the
(functional kernel of) the CoCon conference management system [<a
href="https://doi.org/10.1007/978-3-319-08867-9_11">1</a>,
<a href="https://doi.org/10.1007/s10817-020-09566-9">2</a>].
The confidentiality properties refer to the documents managed by the
system, namely papers, reviews, discussion logs and
acceptance/rejection decisions, and also to the assignment of
reviewers to papers. They have all been formulated as instances of BD
Security [<a href="https://doi.org/10.4230/LIPIcs.ITP.2021.3">3</a>,
<a href="https://www.isa-afp.org/entries/Bounded_Deducibility_Security.html">4</a>]
and verified using the BD Security unwinding technique.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CoCon</h3>
<ul>
<li><a href="../theories/cocon/#Prelim">Prelim</a></li>
<li><a href="../theories/cocon/#System_Specification">System_Specification</a></li>
<li><a href="../theories/cocon/#Automation_Setup">Automation_Setup</a></li>
<li><a href="../theories/cocon/#Safety_Properties">Safety_Properties</a></li>
<li><a href="../theories/cocon/#Observation_Setup">Observation_Setup</a></li>
<li><a href="../theories/cocon/#Paper_Intro">Paper_Intro</a></li>
<li><a href="../theories/cocon/#Paper_Value_Setup">Paper_Value_Setup</a></li>
<li><a href="../theories/cocon/#Paper_Aut_PC">Paper_Aut_PC</a></li>
<li><a href="../theories/cocon/#Paper_Aut">Paper_Aut</a></li>
<li><a href="../theories/cocon/#Paper_All">Paper_All</a></li>
<li><a href="../theories/cocon/#Review_Intro">Review_Intro</a></li>
<li><a href="../theories/cocon/#Review_Value_Setup">Review_Value_Setup</a></li>
<li><a href="../theories/cocon/#Review_RAut">Review_RAut</a></li>
<li><a href="../theories/cocon/#Review_RAut_NCPC">Review_RAut_NCPC</a></li>
<li><a href="../theories/cocon/#Review_RAut_NCPC_PAut">Review_RAut_NCPC_PAut</a></li>
<li><a href="../theories/cocon/#Review_All">Review_All</a></li>
<li><a href="../theories/cocon/#Discussion_Intro">Discussion_Intro</a></li>
<li><a href="../theories/cocon/#Discussion_Value_Setup">Discussion_Value_Setup</a></li>
<li><a href="../theories/cocon/#Discussion_NCPC">Discussion_NCPC</a></li>
<li><a href="../theories/cocon/#Discussion_All">Discussion_All</a></li>
<li><a href="../theories/cocon/#Decision_Intro">Decision_Intro</a></li>
<li><a href="../theories/cocon/#Decision_Value_Setup">Decision_Value_Setup</a></li>
<li><a href="../theories/cocon/#Decision_NCPC">Decision_NCPC</a></li>
<li><a href="../theories/cocon/#Decision_NCPC_Aut">Decision_NCPC_Aut</a></li>
<li><a href="../theories/cocon/#Decision_All">Decision_All</a></li>
<li><a href="../theories/cocon/#Reviewer_Assignment_Intro">Reviewer_Assignment_Intro</a></li>
<li><a href="../theories/cocon/#Reviewer_Assignment_Value_Setup">Reviewer_Assignment_Value_Setup</a></li>
<li><a href="../theories/cocon/#Reviewer_Assignment_NCPC">Reviewer_Assignment_NCPC</a></li>
<li><a href="../theories/cocon/#Reviewer_Assignment_NCPC_Aut">Reviewer_Assignment_NCPC_Aut</a></li>
<li><a href="../theories/cocon/#Reviewer_Assignment_All">Reviewer_Assignment_All</a></li>
<li><a href="../theories/cocon/#Traceback_Properties">Traceback_Properties</a></li>
<li><a href="../theories/cocon/#All_BD_Security_Instances_for_CoCon">All_BD_Security_Instances_for_CoCon</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bounded_Deducibility_Security.html">Bounded-Deducibility Security</a></li><li><a href="../entries/Fresh_Identifiers.html">Fresh identifiers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">CoCon-AFP</p><pre id="copy-text">@article{CoCon-AFP,
author = {Andrei Popescu and Peter Lammich and Thomas Bauereiss},
title = {CoCon: A Confidentiality-Verified Conference Management System},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/CoCon.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-CoCon-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>C</span>o<span class='first'>S</span><span class='first'>M</span>e<span class='first'>D</span>is: <span class='first'>A</span> <span class='first'>C</span>onfidentiality-<span class='first'>V</span>erified <span class='first'>D</span>istributed <span class='first'>S</span>ocial <span class='first'>M</span>edia <span class='first'>P</span>latform</h1>
<div>
<p><a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">August 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains the confidentiality verification of the
(functional kernel of) the CoSMeDis distributed social media platform
presented in [<a href="https://doi.org/10.1109/SP.2017.24">1</a>].
CoSMeDis is a multi-node extension the CoSMed prototype social media
platform [<a href="https://doi.org/10.1007/978-3-319-43144-4_6">2</a>,
<a href="https://doi.org/10.1007/s10817-017-9443-3">3</a>,
<a href="https://www.isa-afp.org/entries/CoSMed.html">4</a>].
The confidentiality properties are formalized as instances of BD
Security [<a href="https://doi.org/10.4230/LIPIcs.ITP.2021.3">5</a>,
<a href="https://www.isa-afp.org/entries/Bounded_Deducibility_Security.html">6</a>].
The lifting of confidentiality properties from single nodes to the
entire CoSMeDis network is performed using compositionality and
transport theorems for BD Security, which are described in [<a
href="https://doi.org/10.1109/SP.2017.24">1</a>]
and formalized in a separate <a
href="https://www.isa-afp.org/entries/BD_Security_Compositional.html">AFP
entry</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CoSMeDis</h3>
<ul>
<li><a href="../theories/cosmedis/#Prelim">Prelim</a></li>
<li><a href="../theories/cosmedis/#System_Specification">System_Specification</a></li>
<li><a href="../theories/cosmedis/#API_Network">API_Network</a></li>
<li><a href="../theories/cosmedis/#Automation_Setup">Automation_Setup</a></li>
<li><a href="../theories/cosmedis/#Safety_Properties">Safety_Properties</a></li>
<li><a href="../theories/cosmedis/#Post_Intro">Post_Intro</a></li>
<li><a href="../theories/cosmedis/#Post_Observation_Setup_ISSUER">Post_Observation_Setup_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Post_Unwinding_Helper_ISSUER">Post_Unwinding_Helper_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Post_Value_Setup_ISSUER">Post_Value_Setup_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Post_ISSUER">Post_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Post_Observation_Setup_RECEIVER">Post_Observation_Setup_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Post_Unwinding_Helper_RECEIVER">Post_Unwinding_Helper_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Post_Value_Setup_RECEIVER">Post_Value_Setup_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Post_RECEIVER">Post_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Post_COMPOSE2">Post_COMPOSE2</a></li>
<li><a href="../theories/cosmedis/#Post_Network">Post_Network</a></li>
<li><a href="../theories/cosmedis/#DYNAMIC_Post_Value_Setup_ISSUER">DYNAMIC_Post_Value_Setup_ISSUER</a></li>
<li><a href="../theories/cosmedis/#DYNAMIC_Post_ISSUER">DYNAMIC_Post_ISSUER</a></li>
<li><a href="../theories/cosmedis/#DYNAMIC_Post_COMPOSE2">DYNAMIC_Post_COMPOSE2</a></li>
<li><a href="../theories/cosmedis/#DYNAMIC_Post_Network">DYNAMIC_Post_Network</a></li>
<li><a href="../theories/cosmedis/#Independent_Post_Observation_Setup_ISSUER">Independent_Post_Observation_Setup_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Independent_DYNAMIC_Post_Value_Setup_ISSUER">Independent_DYNAMIC_Post_Value_Setup_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Independent_DYNAMIC_Post_ISSUER">Independent_DYNAMIC_Post_ISSUER</a></li>
<li><a href="../theories/cosmedis/#Independent_Post_Observation_Setup_RECEIVER">Independent_Post_Observation_Setup_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Independent_Post_Value_Setup_RECEIVER">Independent_Post_Value_Setup_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Independent_Post_RECEIVER">Independent_Post_RECEIVER</a></li>
<li><a href="../theories/cosmedis/#Independent_DYNAMIC_Post_Network">Independent_DYNAMIC_Post_Network</a></li>
<li><a href="../theories/cosmedis/#Independent_Posts_Network">Independent_Posts_Network</a></li>
<li><a href="../theories/cosmedis/#Post_All">Post_All</a></li>
<li><a href="../theories/cosmedis/#Friend_Intro">Friend_Intro</a></li>
<li><a href="../theories/cosmedis/#Friend_Observation_Setup">Friend_Observation_Setup</a></li>
<li><a href="../theories/cosmedis/#Friend_State_Indistinguishability">Friend_State_Indistinguishability</a></li>
<li><a href="../theories/cosmedis/#Friend_Openness">Friend_Openness</a></li>
<li><a href="../theories/cosmedis/#Friend_Value_Setup">Friend_Value_Setup</a></li>
<li><a href="../theories/cosmedis/#Friend">Friend</a></li>
<li><a href="../theories/cosmedis/#Friend_Network">Friend_Network</a></li>
<li><a href="../theories/cosmedis/#Friend_All">Friend_All</a></li>
<li><a href="../theories/cosmedis/#Friend_Request_Intro">Friend_Request_Intro</a></li>
<li><a href="../theories/cosmedis/#Friend_Request_Value_Setup">Friend_Request_Value_Setup</a></li>
<li><a href="../theories/cosmedis/#Friend_Request">Friend_Request</a></li>
<li><a href="../theories/cosmedis/#Friend_Request_Network">Friend_Request_Network</a></li>
<li><a href="../theories/cosmedis/#Friend_Request_All">Friend_Request_All</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Intro">Outer_Friend_Intro</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend">Outer_Friend</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Issuer_Observation_Setup">Outer_Friend_Issuer_Observation_Setup</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Issuer_State_Indistinguishability">Outer_Friend_Issuer_State_Indistinguishability</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Issuer_Openness">Outer_Friend_Issuer_Openness</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Issuer_Value_Setup">Outer_Friend_Issuer_Value_Setup</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Issuer">Outer_Friend_Issuer</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Receiver_Observation_Setup">Outer_Friend_Receiver_Observation_Setup</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Receiver_State_Indistinguishability">Outer_Friend_Receiver_State_Indistinguishability</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Receiver_Value_Setup">Outer_Friend_Receiver_Value_Setup</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Receiver">Outer_Friend_Receiver</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_Network">Outer_Friend_Network</a></li>
<li><a href="../theories/cosmedis/#Outer_Friend_All">Outer_Friend_All</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li><li><a href="../entries/Fresh_Identifiers.html">Fresh identifiers</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
<li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li>
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<p style="display:none;" id="bibtex-filename">CoSMeDis-AFP</p><pre id="copy-text">@article{CoSMeDis-AFP,
author = {Thomas Bauereiss and Andrei Popescu},
title = {CoSMeDis: A confidentiality-verified distributed social media platform},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/CoSMeDis.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>C</span>o<span class='first'>S</span><span class='first'>M</span>ed: <span class='first'>A</span> <span class='first'>C</span>onfidentiality-<span class='first'>V</span>erified <span class='first'>S</span>ocial <span class='first'>M</span>edia <span class='first'>P</span>latform</h1>
<div>
<p><a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">August 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains the confidentiality verification of the
(functional kernel of) the CoSMed social media platform. The
confidentiality properties are formalized as instances of BD Security
[<a href="https://doi.org/10.4230/LIPIcs.ITP.2021.3">1</a>,
<a href="https://www.isa-afp.org/entries/Bounded_Deducibility_Security.html">2</a>].
An innovation in the deployment of BD Security compared to previous
work is the use of dynamic declassification triggers, incorporated as
part of inductive bounds, for providing stronger guarantees that
account for the repeated opening and closing of access windows. To
further strengthen the confidentiality guarantees, we also prove
"traceback" properties about the accessibility decisions
affecting the information managed by the system.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CoSMed</h3>
<ul>
<li><a href="../theories/cosmed/#Prelim">Prelim</a></li>
<li><a href="../theories/cosmed/#System_Specification">System_Specification</a></li>
<li><a href="../theories/cosmed/#Automation_Setup">Automation_Setup</a></li>
<li><a href="../theories/cosmed/#Safety_Properties">Safety_Properties</a></li>
<li><a href="../theories/cosmed/#Observation_Setup">Observation_Setup</a></li>
<li><a href="../theories/cosmed/#Post_Intro">Post_Intro</a></li>
<li><a href="../theories/cosmed/#Post_Value_Setup">Post_Value_Setup</a></li>
<li><a href="../theories/cosmed/#Post">Post</a></li>
<li><a href="../theories/cosmed/#Friend_Intro">Friend_Intro</a></li>
<li><a href="../theories/cosmed/#Friend_Value_Setup">Friend_Value_Setup</a></li>
<li><a href="../theories/cosmed/#Friend">Friend</a></li>
<li><a href="../theories/cosmed/#Friend_Request_Intro">Friend_Request_Intro</a></li>
<li><a href="../theories/cosmed/#Friend_Request_Value_Setup">Friend_Request_Value_Setup</a></li>
<li><a href="../theories/cosmed/#Friend_Request">Friend_Request</a></li>
<li><a href="../theories/cosmed/#Traceback_Intro">Traceback_Intro</a></li>
<li><a href="../theories/cosmed/#Post_Visibility_Traceback">Post_Visibility_Traceback</a></li>
<li><a href="../theories/cosmed/#Friend_Traceback">Friend_Traceback</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bounded_Deducibility_Security.html">Bounded-Deducibility Security</a></li><li><a href="../entries/Fresh_Identifiers.html">Fresh identifiers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">CoSMed-AFP</p><pre id="copy-text">@article{CoSMed-AFP,
author = {Thomas Bauereiss and Andrei Popescu},
title = {CoSMed: A confidentiality-verified social media platform},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/CoSMed.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span>n <span class='first'>E</span>xample of a <span class='first'>C</span>ofinitary <span class='first'>G</span>roup in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/kastermans">Bart Kastermans</a> <a href="http://kasterma.net">🌐</a>
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<p class="date">August 4, 2009</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the usual proof that the group generated by the function k -> k + 1 on the integers gives rise to a cofinitary group.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session CofGroups</h3>
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<p style="display:none;" id="bibtex-filename">CofGroups-AFP</p><pre id="copy-text">@article{CofGroups-AFP,
author = {Bart Kastermans},
title = {An Example of a Cofinitary Group in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {August},
year = {2009},
note = {\url{https://isa-afp.org/entries/CofGroups.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>oinductive</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
with contributions from <a href="../authors/hoelzl">Johannes Hölzl</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJob2VsemwiXX0=">📧</a>
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<p class="date">February 12, 2010</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article collects formalisations of general-purpose coinductive data types and sets. Currently, it contains coinductive natural numbers, coinductive lists, i.e. lazy lists or streams, infinite streams, coinductive terminated lists, coinductive resumptions, a library of operations on coinductive lists, and a version of König's lemma as an application for coinductive lists.<br>The initial theory was contributed by Paulson and Wenzel. Extensions and other coinductive formalisations of general interest are welcome.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 3, 2014</dt>
<dd>ccpo structure on codatatypes used to define ldrop, ldropWhile, lfilter, lconcat as least fixpoint;
ccpo topology on coinductive lists contributed by Johannes Hölzl;
added examples
(revision 23cd8156bd42)<br></dd><dt>September 20, 2013</dt>
<dd>stream theory uses type and operations from HOL/BNF/Examples/Stream
(revision 692809b2b262)<br>
</dd><dt>March 13, 2013</dt>
<dd>construct codatatypes with the BNF package and adjust the definitions and proofs,
setup for lifting and transfer packages
(revision f593eda5b2c0)<br>
</dd><dt>June 27, 2012</dt>
<dd>new codatatype stream with operations (with contributions by Peter Gammie)
(revision dd789a56473c)<br>
</dd><dt>July 20, 2011</dt>
<dd>new codatatype resumption
(revision 811364c776c7)<br>
</dd><dt>February 1, 2011</dt>
<dd>lazy implementation of coinductive (terminated) lists for the code generator
(revision 6034973dce83)<br>
</dd><dt>August 17, 2010</dt>
<dd>Koenig's lemma as an example application for coinductive lists
(revision f81ce373fa96)<br>
</dd><dt>August 4, 2010</dt>
<dd>terminated lazy lists: setup for quotient package;
more lemmas
(revision 6ead626f1d01)<br>
</dd><dt>June 28, 2010</dt>
<dd>new codatatype terminated lazy lists
(revision e12de475c558)<br>
</dd><dt>June 10, 2010</dt>
<dd>coinductive lists: setup for quotient package
(revision 015574f3bf3c)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Coinductive</h3>
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<li><a href="../theories/coinductive/#Coinductive_Nat">Coinductive_Nat</a></li>
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<li><a href="../theories/coinductive/#Quotient_TLList">Quotient_TLList</a></li>
<li><a href="../theories/coinductive/#Coinductive">Coinductive</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Partial_Order_Reduction.html">Partial Order Reduction</a></li><li><a href="../entries/CakeML.html">CakeML</a></li><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/DynamicArchitectures.html">Dynamic Architectures</a></li><li><a href="../entries/CryptHOL.html">CryptHOL</a></li><li><a href="../entries/Parity_Game.html">Positional Determinacy of Parity Games</a></li><li><a href="../entries/Stream_Fusion_Code.html">Stream Fusion in HOL with Code Generation</a></li><li><a href="../entries/Probabilistic_Noninterference.html">Probabilistic Noninterference</a></li><li><a href="../entries/Markov_Models.html">Markov Models</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li><li><a href="../entries/Lazy-Lists-II.html">Lazy Lists II</a></li><li><a href="../entries/Topology.html">Topology</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Coinductive-AFP</p><pre id="copy-text">@article{Coinductive-AFP,
author = {Andreas Lochbihler},
title = {Coinductive},
journal = {Archive of Formal Proofs},
month = {February},
year = {2010},
note = {\url{https://isa-afp.org/entries/Coinductive.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2010-02-15.tar.gz">Feb 15, 2010</a>: Isabelle2009-1
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<a href="https://www.isa-afp.org/release/afp-Coinductive-2010-02-14.tar.gz">Feb 14, 2010</a>: Isabelle2009-1
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>odatatype of <span class='first'>F</span>ormal <span class='first'>L</span>anguages</h1>
<div>
<p><a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">November 15, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We define formal languages as a codataype of infinite trees
branching over the alphabet. Each node in such a tree indicates whether the
path to this node constitutes a word inside or outside of the language. This
codatatype is isormorphic to the set of lists representation of languages,
but caters for definitions by corecursion and proofs by coinduction.</p>
<p>Regular operations on languages are then defined by primitive corecursion.
A difficulty arises here, since the standard definitions of concatenation and
iteration from the coalgebraic literature are not primitively
corecursive-they require guardedness up-to union/concatenation.
Without support for up-to corecursion, these operation must be defined as a
composition of primitive ones (and proved being equal to the standard
definitions). As an exercise in coinduction we also prove the axioms of
Kleene algebra for the defined regular operations.</p>
<p>Furthermore, a language for context-free grammars given by productions in
Greibach normal form and an initial nonterminal is constructed by primitive
corecursion, yielding an executable decision procedure for the word problem
without further ado.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Coinductive_Languages</h3>
<ul>
<li><a href="../theories/coinductive_languages/#Coinductive_Language">Coinductive_Language</a></li>
<li><a href="../theories/coinductive_languages/#Coinductive_Regular_Set">Coinductive_Regular_Set</a></li>
<li><a href="../theories/coinductive_languages/#Context_Free_Grammar">Context_Free_Grammar</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MSO_Regex_Equivalence.html">Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</a></li>
<li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li>
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<p style="display:none;" id="bibtex-filename">Coinductive_Languages-AFP</p><pre id="copy-text">@article{Coinductive_Languages-AFP,
author = {Dmitriy Traytel},
title = {A Codatatype of Formal Languages},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/Coinductive_Languages.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Coinductive_Languages-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Coinductive_Languages-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Coinductive_Languages-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Coinductive_Languages-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>C</span>ollections <span class='first'>F</span>ramework</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
with contributions from <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/tuerk">Thomas Tuerk</a>
</p>
<p class="date">November 25, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides an efficient, extensible, machine checked collections framework. The library adopts the concepts of interface, implementation and generic algorithm from object-oriented programming and implements them in Isabelle/HOL. The framework features the use of data refinement techniques to refine an abstract specification (using high-level concepts like sets) to a more concrete implementation (using collection datastructures, like red-black-trees). The code-generator of Isabelle/HOL can be used to generate efficient code.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 25, 2012</dt>
<dd>New iterator foundation by Tuerk. Various maintenance changes.<br></dd><dt>October 10, 2011</dt>
<dd>SetSpec: Added operations: sng, isSng, bexists, size_abort, diff, filter, iterate_rule_insertP
MapSpec: Added operations: sng, isSng, iterate_rule_insertP, bexists, size, size_abort, restrict,
map_image_filter, map_value_image_filter
Some maintenance changes<br>
</dd><dt>December 1, 2010</dt>
<dd>New Interfaces: Priority Queues, Annotated Lists. Implemented by finger trees, (skew) binomial queues.<br></dd><dt>October 8, 2010</dt>
<dd>New Interfaces: OrderedSet, OrderedMap, List.
Fifo now implements list-interface: Function names changed: put/get --> enqueue/dequeue.
New Implementations: ArrayList, ArrayHashMap, ArrayHashSet, TrieMap, TrieSet.
Invariant-free datastructures: Invariant implicitely hidden in typedef.
Record-interfaces: All operations of an interface encapsulated as record.
Examples moved to examples subdirectory.<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
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<li><a href="../theories/collections/#Idx_Iterator">Idx_Iterator</a></li>
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<li><a href="../theories/collections/#RBT_add">RBT_add</a></li>
<li><a href="../theories/collections/#Dlist_add">Dlist_add</a></li>
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<li><a href="../theories/collections/#Partial_Equivalence_Relation">Partial_Equivalence_Relation</a></li>
<li><a href="../theories/collections/#ICF_Tools">ICF_Tools</a></li>
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<li><a href="../theories/collections/#ICF_Spec_Base">ICF_Spec_Base</a></li>
<li><a href="../theories/collections/#MapSpec">MapSpec</a></li>
<li><a href="../theories/collections/#Robdd">Robdd</a></li>
<li><a href="../theories/collections/#Locale_Code_Ex">Locale_Code_Ex</a></li>
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<li><a href="../theories/collections/#SetAbstractionIterator">SetAbstractionIterator</a></li>
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<li><a href="../theories/collections/#PrioByAnnotatedList">PrioByAnnotatedList</a></li>
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<li><a href="../theories/collections/#Trie_Impl">Trie_Impl</a></li>
<li><a href="../theories/collections/#Trie2">Trie2</a></li>
<li><a href="../theories/collections/#TrieMapImpl">TrieMapImpl</a></li>
<li><a href="../theories/collections/#ArrayHashMap_Impl">ArrayHashMap_Impl</a></li>
<li><a href="../theories/collections/#ArrayHashMap">ArrayHashMap</a></li>
<li><a href="../theories/collections/#ArrayMapImpl">ArrayMapImpl</a></li>
<li><a href="../theories/collections/#MapStdImpl">MapStdImpl</a></li>
<li><a href="../theories/collections/#ListSetImpl">ListSetImpl</a></li>
<li><a href="../theories/collections/#ListSetImpl_Invar">ListSetImpl_Invar</a></li>
<li><a href="../theories/collections/#ListSetImpl_NotDist">ListSetImpl_NotDist</a></li>
<li><a href="../theories/collections/#ListSetImpl_Sorted">ListSetImpl_Sorted</a></li>
<li><a href="../theories/collections/#RBTSetImpl">RBTSetImpl</a></li>
<li><a href="../theories/collections/#HashSet">HashSet</a></li>
<li><a href="../theories/collections/#TrieSetImpl">TrieSetImpl</a></li>
<li><a href="../theories/collections/#ArrayHashSet">ArrayHashSet</a></li>
<li><a href="../theories/collections/#ArraySetImpl">ArraySetImpl</a></li>
<li><a href="../theories/collections/#SetStdImpl">SetStdImpl</a></li>
<li><a href="../theories/collections/#Fifo">Fifo</a></li>
<li><a href="../theories/collections/#BinoPrioImpl">BinoPrioImpl</a></li>
<li><a href="../theories/collections/#SkewPrioImpl">SkewPrioImpl</a></li>
<li><a href="../theories/collections/#FTAnnotatedListImpl">FTAnnotatedListImpl</a></li>
<li><a href="../theories/collections/#FTPrioImpl">FTPrioImpl</a></li>
<li><a href="../theories/collections/#FTPrioUniqueImpl">FTPrioUniqueImpl</a></li>
<li><a href="../theories/collections/#ICF_Impl">ICF_Impl</a></li>
<li><a href="../theories/collections/#ICF_Refine_Monadic">ICF_Refine_Monadic</a></li>
<li><a href="../theories/collections/#ICF_Autoref">ICF_Autoref</a></li>
<li><a href="../theories/collections/#ICF_Entrypoints_Chapter">ICF_Entrypoints_Chapter</a></li>
<li><a href="../theories/collections/#Collections">Collections</a></li>
<li><a href="../theories/collections/#CollectionsV1">CollectionsV1</a></li>
<li><a href="../theories/collections/#Collections_Entrypoints_Chapter">Collections_Entrypoints_Chapter</a></li>
<li><a href="../theories/collections/#Refine_Dflt">Refine_Dflt</a></li>
<li><a href="../theories/collections/#Refine_Dflt_ICF">Refine_Dflt_ICF</a></li>
<li><a href="../theories/collections/#Refine_Dflt_Only_ICF">Refine_Dflt_Only_ICF</a></li>
<li><a href="../theories/collections/#Userguides_Chapter">Userguides_Chapter</a></li>
<li><a href="../theories/collections/#Refine_Monadic_Userguide">Refine_Monadic_Userguide</a></li>
<li><a href="../theories/collections/#ICF_Userguide">ICF_Userguide</a></li></ul>
<h3>Session Collections_Examples</h3>
<ul>
<li><a href="../theories/collections_examples/#Examples_Chapter">Examples_Chapter</a></li>
<li><a href="../theories/collections_examples/#Collection_Autoref_Examples_Chapter">Collection_Autoref_Examples_Chapter</a></li>
<li><a href="../theories/collections_examples/#Succ_Graph">Succ_Graph</a></li>
<li><a href="../theories/collections_examples/#Coll_Test">Coll_Test</a></li>
<li><a href="../theories/collections_examples/#Simple_DFS">Simple_DFS</a></li>
<li><a href="../theories/collections_examples/#ICF_Test">ICF_Test</a></li>
<li><a href="../theories/collections_examples/#ICF_Only_Test">ICF_Only_Test</a></li>
<li><a href="../theories/collections_examples/#Nested_DFS">Nested_DFS</a></li>
<li><a href="../theories/collections_examples/#Combined_TwoSat">Combined_TwoSat</a></li>
<li><a href="../theories/collections_examples/#Collection_Autoref_Examples">Collection_Autoref_Examples</a></li>
<li><a href="../theories/collections_examples/#Refine_Monadic_Examples_Chapter">Refine_Monadic_Examples_Chapter</a></li>
<li><a href="../theories/collections_examples/#Bfs_Impl">Bfs_Impl</a></li>
<li><a href="../theories/collections_examples/#Foreach_Refine">Foreach_Refine</a></li>
<li><a href="../theories/collections_examples/#Refine_Fold">Refine_Fold</a></li>
<li><a href="../theories/collections_examples/#Refine_Monadic_Examples">Refine_Monadic_Examples</a></li>
<li><a href="../theories/collections_examples/#ICF_Examples_Chapter">ICF_Examples_Chapter</a></li>
<li><a href="../theories/collections_examples/#itp_2010">itp_2010</a></li>
<li><a href="../theories/collections_examples/#Exploration">Exploration</a></li>
<li><a href="../theories/collections_examples/#Exploration_DFS">Exploration_DFS</a></li>
<li><a href="../theories/collections_examples/#PerformanceTest">PerformanceTest</a></li>
<li><a href="../theories/collections_examples/#ICF_Examples">ICF_Examples</a></li>
<li><a href="../theories/collections_examples/#Collection_Examples">Collection_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Binomial-Heaps.html">Binomial Heaps and Skew Binomial Heaps</a></li><li><a href="../entries/Finger-Trees.html">Finger Trees</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li><li><a href="../entries/Trie.html">Trie</a></li><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Safe_Range_RC.html">Making Arbitrary Relational Calculus Queries Safe-Range</a></li><li><a href="../entries/FOL_Seq_Calc2.html">A Sequent Calculus Prover for First-Order Logic with Functions</a></li><li><a href="../entries/Gale_Shapley.html">Gale-Shapley Algorithm</a></li><li><a href="../entries/Kruskal.html">Kruskal&rsquo;s Algorithm for Minimum Spanning Forest</a></li><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/ROBDD.html">Algorithms for Reduced Ordered Binary Decision Diagrams</a></li><li><a href="../entries/Formal_SSA.html">Verified Construction of Static Single Assignment Form</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/Abstract_Completeness.html">Abstract Completeness</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li><li><a href="../entries/Dijkstra_Shortest_Path.html">Dijkstra&rsquo;s Shortest Path Algorithm</a></li><li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Tree-Automata.html">Tree Automata</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Gabow_SCC.html">Verified Efficient Implementation of Gabow&rsquo;s Strongly Connected Components Algorithm</a></li>
<li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li>
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<p style="display:none;" id="bibtex-filename">Collections-AFP</p><pre id="copy-text">@article{Collections-AFP,
author = {Peter Lammich},
title = {Collections Framework},
journal = {Archive of Formal Proofs},
month = {November},
year = {2009},
note = {\url{https://isa-afp.org/entries/Collections.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Collections-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Collections-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Collections-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Collections-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Collections-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Collections-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Collections-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Collections-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2011-10-12.tar.gz">Oct 12, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2009-12-13.tar.gz">Dec 13, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Collections-2009-11-29.tar.gz">Nov 29, 2009</a>: Isabelle2009
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Combinable_Wands.html b/web/entries/Combinable_Wands.html
--- a/web/entries/Combinable_Wands.html
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<h1 >
<span class='first'>A</span> <span class='first'>R</span>estricted <span class='first'>D</span>efinition of the <span class='first'>M</span>agic <span class='first'>W</span>and to <span class='first'>S</span>oundly <span class='first'>C</span>ombine <span class='first'>F</span>ractions of a <span class='first'>W</span>and</h1>
<div>
<p><a href="../authors/dardinier">Thibault Dardinier</a> <a href="https://dardinier.me/">🌐</a>
</p>
<p class="date">May 30, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Many separation logics support <em>fractional
permissions</em> to distinguish between read and write access to
a heap location, for instance, to allow concurrent reads while
enforcing exclusive writes. The concept has been generalized to
fractional assertions. $A^p$ (where $A$ is a separation logic
assertion and $p$ a fraction between $0$ and $1$) represents a
fraction $p$ of $A$. $A^p$ holds in a state $\sigma$ iff there exists
a state $\sigma_A$ in which $A$ holds and $\sigma$ is obtained from
$\sigma_A$ by multiplying all permission amounts held by $p$. While
$A^{p + q}$ can always be split into $A^p * A^q$, recombining $A^p *
A^q$ into $A^{p+q}$ is not always sound. We say that $A$ is
<em>combinable</em> iff the entailment $A^p * A^q \models
A^{p+q}$ holds for any two positive fractions $p$ and $q$ such that $p
+ q \le 1$. Combinable assertions are particularly useful to reason
about concurrent programs, for instance, to combine the postconditions
of parallel branches when they terminate. Unfortunately, the magic
wand assertion $A \mathbin{-\!\!*} B$, commonly used to specify properties of
partial data structures, is typically <em>not</em>
combinable. In this entry, we formalize a novel, restricted
definition of the magic wand, described in <a
href="https://arxiv.org/abs/2205.11325">a paper at CAV
22</a>, which we call the <em>combinable wand</em>.
We prove some key properties of the combinable wand; in particular, a
combinable wand is combinable if its right-hand side is combinable.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Combinable_Wands</h3>
<ul>
<li><a href="../theories/combinable_wands/#PosRat">PosRat</a></li>
<li><a href="../theories/combinable_wands/#Mask">Mask</a></li>
<li><a href="../theories/combinable_wands/#PartialHeapSA">PartialHeapSA</a></li>
<li><a href="../theories/combinable_wands/#CombinableWands">CombinableWands</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Package_logic.html">Formalization of a Framework for the Sound Automation of Magic Wands</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Separation_Logic_Unbounded.html">Unbounded Separation Logic</a></li>
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<p style="display:none;" id="bibtex-filename">Combinable_Wands-AFP</p><pre id="copy-text">@article{Combinable_Wands-AFP,
author = {Thibault Dardinier},
title = {A Restricted Definition of the Magic Wand to Soundly Combine Fractions of a Wand},
journal = {Archive of Formal Proofs},
month = {May},
year = {2022},
note = {\url{https://isa-afp.org/entries/Combinable_Wands.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>C</span>ombinatorics on <span class='first'>W</span>ords <span class='first'>B</span>asics</h1>
<div>
<p><a href="../authors/holub">Štěpán Holub</a> <a href="https://www2.karlin.mff.cuni.cz/~holub/">🌐</a>, <a href="../authors/raska">Martin Raška</a> and <a href="../authors/starosta">Štěpán Starosta</a> <a href="https://users.fit.cvut.cz/~staroste/">🌐</a>
</p>
<p class="date">May 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize basics of Combinatorics on Words. This is an extension of
existing theories on lists. We provide additional properties related
to prefix, suffix, factor, length and rotation. The topics include
prefix and suffix comparability, mismatch, word power, total and
reversed morphisms, border, periods, primitivity and roots. We also
formalize basic, mostly folklore results related to word equations:
equidivisibility, commutation and conjugation. Slightly advanced
properties include the Periodicity lemma (often cited as the Fine and
Wilf theorem) and the variant of the Lyndon-Schützenberger theorem for
words, including its full parametric solution. We support the algebraic point of view which sees words as generators of submonoids of a free monoid. This leads to the concepts of the (free) hull, the (free) basis (or code). We also provide relevant proof methods and a tool to generate reverse-symmetric claims.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>August 24, 2022</dt>
<dd>Many updates and additions. New theories: Border_Array, Morphisms, Equations_Basic, and Binary_Code_Morphisms.
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Holub, Š., &amp; Starosta, Š. (2021). Formalization of Basic Combinatorics on Words. <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.ITP.2021.22
</li><li>
<a href="https://arxiv.org/abs/2104.11622">Producing symmetrical facts for lists induced by the list reversal mapping in Isabelle/HOL</a>
</li><li>
<a href="https://gitlab.com/formalcow/combinatorics-on-words-formalized">Development repository</a>
</li></ul>
<h3>Session Combinatorics_Words</h3>
<ul>
<li><a href="../theories/combinatorics_words/#Arithmetical_Hints">Arithmetical_Hints</a></li>
<li><a href="../theories/combinatorics_words/#Reverse_Symmetry">Reverse_Symmetry</a></li>
<li><a href="../theories/combinatorics_words/#CoWBasic">CoWBasic</a></li>
<li><a href="../theories/combinatorics_words/#Border_Array">Border_Array</a></li>
<li><a href="../theories/combinatorics_words/#Submonoids">Submonoids</a></li>
<li><a href="../theories/combinatorics_words/#Morphisms">Morphisms</a></li>
<li><a href="../theories/combinatorics_words/#Periodicity_Lemma">Periodicity_Lemma</a></li>
<li><a href="../theories/combinatorics_words/#Lyndon_Schutzenberger">Lyndon_Schutzenberger</a></li>
<li><a href="../theories/combinatorics_words/#Binary_Code_Morphisms">Binary_Code_Morphisms</a></li>
<li><a href="../theories/combinatorics_words/#Equations_Basic">Equations_Basic</a></li>
<li><a href="../theories/combinatorics_words/#CoWAll">CoWAll</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Combinatorics_Words_Graph_Lemma.html">Graph Lemma</a></li><li><a href="../entries/Combinatorics_Words_Lyndon.html">Lyndon words</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Combinatorics_Words-AFP</p><pre id="copy-text">@article{Combinatorics_Words-AFP,
author = {Štěpán Holub and Martin Raška and Štěpán Starosta},
title = {Combinatorics on Words Basics},
journal = {Archive of Formal Proofs},
month = {May},
year = {2021},
note = {\url{https://isa-afp.org/entries/Combinatorics_Words.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2021-05-26.tar.gz">May 26, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>G</span>raph <span class='first'>L</span>emma</h1>
<div>
<p><a href="../authors/holub">Štěpán Holub</a> <a href="https://www2.karlin.mff.cuni.cz/~holub/">🌐</a> and <a href="../authors/starosta">Štěpán Starosta</a> <a href="https://users.fit.cvut.cz/~staroste/">🌐</a>
</p>
<p class="date">May 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Graph lemma quantifies the defect effect of a system of word
equations. That is, it provides an upper bound on the rank of the
system. We formalize the proof based on the decomposition of a
solution into its free basis. A direct application is an alternative
proof of the fact that two noncommuting words form a code.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>August 24, 2022</dt>
<dd>Reworked version. Added theory Glued_Codes.
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
<a href="https://gitlab.com/formalcow/combinatorics-on-words-formalized">Development repository</a>
</li></ul>
<h3>Session Combinatorics_Words_Graph_Lemma</h3>
<ul>
<li><a href="../theories/combinatorics_words_graph_lemma/#Glued_Codes">Glued_Codes</a></li>
<li><a href="../theories/combinatorics_words_graph_lemma/#Graph_Lemma">Graph_Lemma</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Combinatorics_Words.html">Combinatorics on Words Basics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Combinatorics_Words_Graph_Lemma-AFP</p><pre id="copy-text">@article{Combinatorics_Words_Graph_Lemma-AFP,
author = {Štěpán Holub and Štěpán Starosta},
title = {Graph Lemma},
journal = {Archive of Formal Proofs},
month = {May},
year = {2021},
note = {\url{https://isa-afp.org/entries/Combinatorics_Words_Graph_Lemma.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words_Graph_Lemma-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words_Graph_Lemma-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words_Graph_Lemma-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Combinatorics_Words_Graph_Lemma-2021-05-26.tar.gz">May 26, 2021</a>: Isabelle2021
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diff --git a/web/entries/Combinatorics_Words_Lyndon.html b/web/entries/Combinatorics_Words_Lyndon.html
--- a/web/entries/Combinatorics_Words_Lyndon.html
+++ b/web/entries/Combinatorics_Words_Lyndon.html
@@ -1,178 +1,180 @@
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<h1 >
<span class='first'>L</span>yndon <span class='first'>W</span>ords</h1>
<div>
<p><a href="../authors/holub">Štěpán Holub</a> <a href="https://www2.karlin.mff.cuni.cz/~holub/">🌐</a> and <a href="../authors/starosta">Štěpán Starosta</a> <a href="https://users.fit.cvut.cz/~staroste/">🌐</a>
</p>
<p class="date">May 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Lyndon words are words lexicographically minimal in their conjugacy
class. We formalize their basic properties and characterizations, in
particular the concepts of the longest Lyndon suffix and the Lyndon
factorization. Most of the work assumes a fixed lexicographical order.
Nevertheless we also define the smallest relation guaranteeing
lexicographical minimality of a given word (in its conjugacy class).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Holub, Š., & Starosta, Š. (2021). Lyndon Words Formalized in Isabelle/HOL. Lecture Notes in Computer Science, 217–228. <a href="https://doi.org/10.1007/978-3-030-81508-0_18">https://doi.org/10.1007/978-3-030-81508-0_18</a>
</li><li>
<a href="https://gitlab.com/formalcow/combinatorics-on-words-formalized">Development repository</a>
</li></ul>
<h3>Session Combinatorics_Words_Lyndon</h3>
<ul>
<li><a href="../theories/combinatorics_words_lyndon/#Lyndon">Lyndon</a></li>
<li><a href="../theories/combinatorics_words_lyndon/#Lyndon_Addition">Lyndon_Addition</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Combinatorics_Words.html">Combinatorics on Words Basics</a></li><li><a href="../entries/Szpilrajn.html">Order Extension and Szpilrajn&rsquo;s Extension Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Combinatorics_Words_Lyndon-AFP</p><pre id="copy-text">@article{Combinatorics_Words_Lyndon-AFP,
author = {Štěpán Holub and Štěpán Starosta},
title = {Lyndon words},
journal = {Archive of Formal Proofs},
month = {May},
year = {2021},
note = {\url{https://isa-afp.org/entries/Combinatorics_Words_Lyndon.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>imultaneous <span class='first'>D</span>iagonalization of <span class='first'>P</span>airwise <span class='first'>C</span>ommuting <span class='first'>H</span>ermitian <span class='first'>M</span>atrices</h1>
<div>
<p><a href="../authors/echenim">Mnacho Echenim</a> <a href="https://lig-membres.imag.fr/mechenim/">🌐</a>
</p>
<p class="date">July 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A Hermitian matrix is a square complex matrix that is equal to its
conjugate transpose. The (finite-dimensional) spectral theorem states
that any such matrix can be decomposed into a product of a unitary
matrix and a diagonal matrix containing only real elements. We
formalize the generalization of this result, which states that any
finite set of Hermitian and pairwise commuting matrices can be
decomposed as previously, using the same unitary matrix; in other
words, they are simultaneously diagonalizable. Sets of pairwise
commuting Hermitian matrices are called <em>Complete Sets of
Commuting Observables</em> in Quantum Mechanics, where they represent
physical quantities that can be simultaneously measured to uniquely
distinguish quantum states.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Commuting_Hermitian</h3>
<ul>
<li><a href="../theories/commuting_hermitian/#Commuting_Hermitian_Misc">Commuting_Hermitian_Misc</a></li>
<li><a href="../theories/commuting_hermitian/#Spectral_Theory_Complements">Spectral_Theory_Complements</a></li>
<li><a href="../theories/commuting_hermitian/#Commuting_Hermitian">Commuting_Hermitian</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Projective_Measurements.html">Quantum projective measurements and the CHSH inequality</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Commuting_Hermitian-AFP</p><pre id="copy-text">@article{Commuting_Hermitian-AFP,
author = {Mnacho Echenim},
title = {Simultaneous diagonalization of pairwise commuting Hermitian matrices},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/Commuting_Hermitian.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-Commuting_Hermitian-2022-08-16.tar.gz">Aug 16, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Comparison_Sort_Lower_Bound.html b/web/entries/Comparison_Sort_Lower_Bound.html
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<h1 >
<span class='first'>L</span>ower <span class='first'>B</span>ound on <span class='first'>C</span>omparison-<span class='first'>B</span>ased <span class='first'>S</span>orting <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 15, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article contains a formal proof of the well-known fact
that number of comparisons that a comparison-based sorting algorithm
needs to perform to sort a list of length <em>n</em> is at
least <em>log<sub>2</sub>&nbsp;(n!)</em>
in the worst case, i.&thinsp;e.&nbsp;<em>Ω(n log
n)</em>.</p> <p>For this purpose, a shallow
embedding for comparison-based sorting algorithms is defined: a
sorting algorithm is a recursive datatype containing either a HOL
function or a query of a comparison oracle with a continuation
containing the remaining computation. This makes it possible to force
the algorithm to use only comparisons and to track the number of
comparisons made.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Comparison_Sort_Lower_Bound</h3>
<ul>
<li><a href="../theories/comparison_sort_lower_bound/#Linorder_Relations">Linorder_Relations</a></li>
<li><a href="../theories/comparison_sort_lower_bound/#Comparison_Sort_Lower_Bound">Comparison_Sort_Lower_Bound</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Treaps.html">Treaps</a></li><li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Comparison_Sort_Lower_Bound-AFP</p><pre id="copy-text">@article{Comparison_Sort_Lower_Bound-AFP,
author = {Manuel Eberl},
title = {Lower bound on comparison-based sorting algorithms},
journal = {Archive of Formal Proofs},
month = {March},
year = {2017},
note = {\url{https://isa-afp.org/entries/Comparison_Sort_Lower_Bound.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>ompiling <span class='first'>E</span>xceptions <span class='first'>C</span>orrectly</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">July 9, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">An exception compilation scheme that dynamically creates and removes exception handler entries on the stack. A formalization of an article of the same name by <a href="http://www.cs.nott.ac.uk/~gmh/">Hutton</a> and Wright.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul><h3>Related publications</h3>
<ul><li>
Hutton, G., & Wright, J. (2004). Compiling Exceptions Correctly. Mathematics of Program Construction, 211–227. <a href="https://doi.org/10.1007/978-3-540-27764-4_12">https://doi.org/10.1007/978-3-540-27764-4_12</a>
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<p style="display:none;" id="bibtex-filename">Compiling-Exceptions-Correctly-AFP</p><pre id="copy-text">@article{Compiling-Exceptions-Correctly-AFP,
author = {Tobias Nipkow},
title = {Compiling Exceptions Correctly},
journal = {Archive of Formal Proofs},
month = {July},
year = {2004},
note = {\url{https://isa-afp.org/entries/Compiling-Exceptions-Correctly.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Complete_Non_Orders.html b/web/entries/Complete_Non_Orders.html
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@@ -1,182 +1,184 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Complete Non-Orders and Fixed Points - Archive of Formal Proofs</title><meta name="description" content="We develop an Isabelle/HOL library of order-theoretic concepts, such
as various completeness conditions and fixed-point theorems. We keep
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<h1 >
<span class='first'>C</span>omplete <span class='first'>N</span>on-<span class='first'>O</span>rders and <span class='first'>F</span>ixed <span class='first'>P</span>oints</h1>
<div>
<p><a href="../authors/yamada">Akihisa Yamada</a> <a href="http://group-mmm.org/~ayamada/">🌐</a> and <a href="../authors/dubut">Jérémy Dubut</a> <a href="http://group-mmm.org/~dubut/">🌐</a>
</p>
<p class="date">June 27, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop an Isabelle/HOL library of order-theoretic concepts, such
as various completeness conditions and fixed-point theorems. We keep
our formalization as general as possible: we reprove several
well-known results about complete orders, often without any properties
of ordering, thus complete non-orders. In particular, we generalize
the Knaster–Tarski theorem so that we ensure the existence of a
quasi-fixed point of monotone maps over complete non-orders, and show
that the set of quasi-fixed points is complete under a mild
condition—attractivity—which is implied by either antisymmetry or
transitivity. This result generalizes and strengthens a result by
Stauti and Maaden. Finally, we recover Kleene’s fixed-point theorem
for omega-complete non-orders, again using attractivity to prove that
Kleene’s fixed points are least quasi-fixed points.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session Complete_Non_Orders</h3>
<ul>
<li><a href="../theories/complete_non_orders/#Binary_Relations">Binary_Relations</a></li>
<li><a href="../theories/complete_non_orders/#Complete_Relations">Complete_Relations</a></li>
<li><a href="../theories/complete_non_orders/#Fixed_Points">Fixed_Points</a></li>
<li><a href="../theories/complete_non_orders/#Kleene_Fixed_Point">Kleene_Fixed_Point</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Complete_Non_Orders-AFP</p><pre id="copy-text">@article{Complete_Non_Orders-AFP,
author = {Akihisa Yamada and Jérémy Dubut},
title = {Complete Non-Orders and Fixed Points},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Complete_Non_Orders.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Completeness.html b/web/entries/Completeness.html
--- a/web/entries/Completeness.html
+++ b/web/entries/Completeness.html
@@ -1,215 +1,217 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Completeness theorem - Archive of Formal Proofs</title><meta name="description" content="The completeness of first-order logic is proved, following the first five pages of Wainer and Wallen&#39;s chapter of the book Proof Theory by Aczel et al.,..."><meta property="og:title" content="Completeness theorem" />
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<h1 >
<span class='first'>C</span>ompleteness <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/margetson">James Margetson</a> and <a href="../authors/ridge">Tom Ridge</a>
</p>
<p class="date">September 20, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The completeness of first-order logic is proved, following the first five pages of Wainer and Wallen's chapter of the book <i>Proof Theory</i> by Aczel et al., CUP, 1992. Their presentation of formulas allows the proofs to use symmetry arguments. Margetson formalized this theorem by early 2000. The Isar conversion is thanks to Tom Ridge. A paper describing the formalization is available <a href="Completeness-paper.pdf">[pdf]</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Completeness</h3>
<ul>
<li><a href="../theories/completeness/#PermutationLemmas">PermutationLemmas</a></li>
<li><a href="../theories/completeness/#Base">Base</a></li>
<li><a href="../theories/completeness/#Formula">Formula</a></li>
<li><a href="../theories/completeness/#Sequents">Sequents</a></li>
<li><a href="../theories/completeness/#Tree">Tree</a></li>
<li><a href="../theories/completeness/#Completeness">Completeness</a></li>
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<p style="display:none;" id="bibtex-filename">Completeness-AFP</p><pre id="copy-text">@article{Completeness-AFP,
author = {James Margetson and Tom Ridge},
title = {Completeness theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2004},
note = {\url{https://isa-afp.org/entries/Completeness.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Completeness-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2005-07-22.tar.gz">Jul 22, 2005</a>: Isabelle2004
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2004-09-21.tar.gz">Sep 21, 2004</a>: Isabelle2004
</li><li>
<a href="https://www.isa-afp.org/release/afp-Completeness-2004-09-20.tar.gz">Sep 20, 2004</a>: Isabelle2004
</li></ul>
</div>
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\ No newline at end of file
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<h1 >
<span class='first'>C</span>omplex <span class='first'>B</span>ounded <span class='first'>O</span>perators</h1>
<div>
<p><a href="../authors/caballero">José Manuel Rodríguez Caballero</a> <a href="https://josephcmac.github.io/">🌐</a> and <a href="../authors/unruh">Dominique Unruh</a> <a href="https://www.ut.ee/~unruh/">🌐</a>
</p>
<p class="date">September 18, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of bounded operators on complex vector
spaces. Our formalization contains material on complex vector spaces
(normed spaces, Banach spaces, Hilbert spaces) that complements and
goes beyond the developments of real vectors spaces in the
Isabelle/HOL standard library. We define the type of bounded
operators between complex vector spaces
(<em>cblinfun</em>) and develop the theory of unitaries,
projectors, extension of bounded linear functions (BLT theorem),
adjoints, Loewner order, closed subspaces and more. For the
finite-dimensional case, we provide code generation support by
identifying finite-dimensional operators with matrices as formalized
in the <a href="Jordan_Normal_Form.html">Jordan_Normal_Form</a> AFP entry.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Complex_Bounded_Operators</h3>
<ul>
<li><a href="../theories/complex_bounded_operators/#Extra_General">Extra_General</a></li>
<li><a href="../theories/complex_bounded_operators/#Extra_Vector_Spaces">Extra_Vector_Spaces</a></li>
<li><a href="../theories/complex_bounded_operators/#Extra_Ordered_Fields">Extra_Ordered_Fields</a></li>
<li><a href="../theories/complex_bounded_operators/#Extra_Operator_Norm">Extra_Operator_Norm</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Vector_Spaces0">Complex_Vector_Spaces0</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Vector_Spaces">Complex_Vector_Spaces</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Inner_Product0">Complex_Inner_Product0</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Inner_Product">Complex_Inner_Product</a></li>
<li><a href="../theories/complex_bounded_operators/#One_Dimensional_Spaces">One_Dimensional_Spaces</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Euclidean_Space0">Complex_Euclidean_Space0</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Bounded_Linear_Function0">Complex_Bounded_Linear_Function0</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_Bounded_Linear_Function">Complex_Bounded_Linear_Function</a></li>
<li><a href="../theories/complex_bounded_operators/#Complex_L2">Complex_L2</a></li>
<li><a href="../theories/complex_bounded_operators/#Extra_Jordan_Normal_Form">Extra_Jordan_Normal_Form</a></li>
<li><a href="../theories/complex_bounded_operators/#Cblinfun_Matrix">Cblinfun_Matrix</a></li>
<li><a href="../theories/complex_bounded_operators/#Cblinfun_Code">Cblinfun_Code</a></li>
<li><a href="../theories/complex_bounded_operators/#Extra_Pretty_Code_Examples">Extra_Pretty_Code_Examples</a></li>
<li><a href="../theories/complex_bounded_operators/#Cblinfun_Code_Examples">Cblinfun_Code_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Banach_Steinhaus.html">Banach-Steinhaus Theorem</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Registers.html">Quantum and Classical Registers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Complex_Bounded_Operators-AFP</p><pre id="copy-text">@article{Complex_Bounded_Operators-AFP,
author = {José Manuel Rodríguez Caballero and Dominique Unruh},
title = {Complex Bounded Operators},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Complex_Bounded_Operators.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Complex_Bounded_Operators-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Complex_Bounded_Operators-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complex_Bounded_Operators-2021-09-20.tar.gz">Sep 20, 2021</a>: Isabelle2021
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diff --git a/web/entries/Complex_Geometry.html b/web/entries/Complex_Geometry.html
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@@ -1,195 +1,197 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Complex Geometry - Archive of Formal Proofs</title><meta name="description" content="A formalization of geometry of complex numbers is presented.
Fundamental objects that are investigated are the complex plane
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<h1 >
<span class='first'>C</span>omplex <span class='first'>G</span>eometry</h1>
<div>
<p><a href="../authors/maricf">Filip Marić</a> <a href="http://www.matf.bg.ac.rs/~filip">🌐</a> and <a href="../authors/simic">Danijela Simić</a> <a href="http://poincare.matf.bg.ac.rs/~danijela">🌐</a>
</p>
<p class="date">December 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A formalization of geometry of complex numbers is presented.
Fundamental objects that are investigated are the complex plane
extended by a single infinite point, its objects (points, lines and
circles), and groups of transformations that act on them (e.g.,
inversions and Möbius transformations). Most objects are defined
algebraically, but correspondence with classical geometric definitions
is shown.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Complex_Geometry</h3>
<ul>
<li><a href="../theories/complex_geometry/#More_Transcendental">More_Transcendental</a></li>
<li><a href="../theories/complex_geometry/#Canonical_Angle">Canonical_Angle</a></li>
<li><a href="../theories/complex_geometry/#More_Complex">More_Complex</a></li>
<li><a href="../theories/complex_geometry/#Angles">Angles</a></li>
<li><a href="../theories/complex_geometry/#More_Set">More_Set</a></li>
<li><a href="../theories/complex_geometry/#Linear_Systems">Linear_Systems</a></li>
<li><a href="../theories/complex_geometry/#Quadratic">Quadratic</a></li>
<li><a href="../theories/complex_geometry/#Matrices">Matrices</a></li>
<li><a href="../theories/complex_geometry/#Unitary_Matrices">Unitary_Matrices</a></li>
<li><a href="../theories/complex_geometry/#Unitary11_Matrices">Unitary11_Matrices</a></li>
<li><a href="../theories/complex_geometry/#Hermitean_Matrices">Hermitean_Matrices</a></li>
<li><a href="../theories/complex_geometry/#Elementary_Complex_Geometry">Elementary_Complex_Geometry</a></li>
<li><a href="../theories/complex_geometry/#Homogeneous_Coordinates">Homogeneous_Coordinates</a></li>
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<li><a href="../theories/complex_geometry/#Circlines">Circlines</a></li>
<li><a href="../theories/complex_geometry/#Oriented_Circlines">Oriented_Circlines</a></li>
<li><a href="../theories/complex_geometry/#Circlines_Angle">Circlines_Angle</a></li>
<li><a href="../theories/complex_geometry/#Unit_Circle_Preserving_Moebius">Unit_Circle_Preserving_Moebius</a></li>
<li><a href="../theories/complex_geometry/#Riemann_Sphere">Riemann_Sphere</a></li>
<li><a href="../theories/complex_geometry/#Chordal_Metric">Chordal_Metric</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Cubic_Quartic_Equations.html">Solving Cubic and Quartic Equations</a></li><li><a href="../entries/Poincare_Disc.html">Poincaré Disc Model</a></li></ul>
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document</a>
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<p style="display:none;" id="bibtex-filename">Complex_Geometry-AFP</p><pre id="copy-text">@article{Complex_Geometry-AFP,
author = {Filip Marić and Danijela Simić},
title = {Complex Geometry},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Complex_Geometry.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complex_Geometry-2020-01-17.tar.gz">Jan 17, 2020</a>: Isabelle2019
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<h1 >
<span class='first'>C</span><span class='first'>O</span><span class='first'>M</span><span class='first'>P</span><span class='first'>L</span><span class='first'>X</span>: <span class='first'>A</span> <span class='first'>V</span>erification <span class='first'>F</span>ramework for <span class='first'>C</span>oncurrent <span class='first'>I</span>mperative <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/amani">Sidney Amani</a>, <a href="../authors/andronick">June Andronick</a>, <a href="../authors/bortin">Maksym Bortin</a>, <a href="../authors/lewis">Corey Lewis</a>, <a href="../authors/rizkallah">Christine Rizkallah</a> and <a href="../authors/tuongj">Joseph Tuong</a>
</p>
<p class="date">November 29, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We propose a concurrency reasoning framework for imperative programs,
based on the Owicki-Gries (OG) foundational shared-variable
concurrency method. Our framework combines the approaches of
Hoare-Parallel, a formalisation of OG in Isabelle/HOL for a simple
while-language, and Simpl, a generic imperative language embedded in
Isabelle/HOL, allowing formal reasoning on C programs. We define the
Complx language, extending the syntax and semantics of Simpl with
support for parallel composition and synchronisation. We additionally
define an OG logic, which we prove sound w.r.t. the semantics, and a
verification condition generator, both supporting involved low-level
imperative constructs such as function calls and abrupt termination.
We illustrate our framework on an example that features exceptions,
guards and function calls. We aim to then target concurrent operating
systems, such as the interruptible eChronos embedded operating system
for which we already have a model-level OG proof using Hoare-Parallel.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 13, 2017</dt>
<dd>Improve VCG for nested parallels and sequential sections
(revision 30739dbc3dcb)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session Complx</h3>
<ul>
<li><a href="../theories/complx/#Language">Language</a></li>
<li><a href="../theories/complx/#SmallStep">SmallStep</a></li>
<li><a href="../theories/complx/#OG_Annotations">OG_Annotations</a></li>
<li><a href="../theories/complx/#OG_Hoare">OG_Hoare</a></li>
<li><a href="../theories/complx/#SeqCatch_decomp">SeqCatch_decomp</a></li>
<li><a href="../theories/complx/#OG_Soundness">OG_Soundness</a></li>
<li><a href="../theories/complx/#Cache_Tactics">Cache_Tactics</a></li>
<li><a href="../theories/complx/#OG_Tactics">OG_Tactics</a></li>
<li><a href="../theories/complx/#OG_Syntax">OG_Syntax</a></li>
<li><a href="../theories/complx/#Examples">Examples</a></li>
<li><a href="../theories/complx/#SumArr">SumArr</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/IMP2.html">IMP2 – Simple Program Verification in Isabelle/HOL</a></li>
<li><a href="../entries/Auto2_Imperative_HOL.html">Verifying Imperative Programs using Auto2</a></li>
<li><a href="../entries/Hoare_Time.html">Hoare Logics for Time Bounds</a></li>
<li><a href="../entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></li>
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<p style="display:none;" id="bibtex-filename">Complx-AFP</p><pre id="copy-text">@article{Complx-AFP,
author = {Sidney Amani and June Andronick and Maksym Bortin and Corey Lewis and Christine Rizkallah and Joseph Tuong},
title = {COMPLX: A Verification Framework for Concurrent Imperative Programs},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Complx.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Complx-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Complx-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Complx-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Complx-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Complx-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Complx-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complx-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complx-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complx-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Complx-2016-11-29.tar.gz">Nov 29, 2016</a>: Isabelle2016
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diff --git a/web/entries/ComponentDependencies.html b/web/entries/ComponentDependencies.html
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<h1 >
<span class='first'>F</span>ormalisation and <span class='first'>A</span>nalysis of <span class='first'>C</span>omponent <span class='first'>D</span>ependencies</h1>
<div>
<p><a href="../authors/spichkova">Maria Spichkova</a> <a class="obfuscated" data="eyJob3N0IjpbInJtaXQiLCJlZHUiLCJhdSJdLCJ1c2VyIjpbIm1hcmlhIiwic3BpY2hrb3ZhIl19">📧</a>
</p>
<p class="date">April 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This set of theories presents a formalisation in Isabelle/HOL of data dependencies between components. The approach allows to analyse system structure oriented towards efficient checking of system: it aims at elaborating for a concrete system, which parts of the system are necessary to check a given property.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session ComponentDependencies</h3>
<ul>
<li><a href="../theories/componentdependencies/#DataDependenciesConcreteValues">DataDependenciesConcreteValues</a></li>
<li><a href="../theories/componentdependencies/#DataDependencies">DataDependencies</a></li>
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<p style="display:none;" id="bibtex-filename">ComponentDependencies-AFP</p><pre id="copy-text">@article{ComponentDependencies-AFP,
author = {Maria Spichkova},
title = {Formalisation and Analysis of Component Dependencies},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/ComponentDependencies.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-ComponentDependencies-2014-04-29.tar.gz">Apr 29, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/ConcurrentGC.html b/web/entries/ConcurrentGC.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO - Archive of Formal Proofs</title><meta name="description" content=" We use ConcurrentIMP to model Schism, a state-of-the-art real-time garbage collection scheme for weak memory, and show that it is safe on x86-TSO.
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<h1 >
<span class='first'>R</span>elaxing <span class='first'>S</span>afely: <span class='first'>V</span>erified <span class='first'>O</span>n-the-<span class='first'>F</span>ly <span class='first'>G</span>arbage <span class='first'>C</span>ollection for <span class='first'>X</span>86-<span class='first'>T</span><span class='first'>S</span><span class='first'>O</span></h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>, <a href="../authors/hosking">Tony Hosking</a> <a href="https://www.cs.purdue.edu/homes/hosking/">🌐</a> and <a href="../authors/engelhardt">Kai Engelhardt</a>
</p>
<p class="date">April 13, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
We use ConcurrentIMP to model Schism, a state-of-the-art real-time
garbage collection scheme for weak memory, and show that it is safe
on x86-TSO.</p>
<p>
This development accompanies the PLDI 2015 paper of the same name.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/concurrent">Computer science/Algorithms/Concurrent</a></li></ul>
<h3>Session ConcurrentGC</h3>
<ul>
<li><a href="../theories/concurrentgc/#Model">Model</a></li>
<li><a href="../theories/concurrentgc/#Proofs_Basis">Proofs_Basis</a></li>
<li><a href="../theories/concurrentgc/#Global_Invariants">Global_Invariants</a></li>
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<li><a href="../theories/concurrentgc/#Global_Invariants_Lemmas">Global_Invariants_Lemmas</a></li>
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<li><a href="../theories/concurrentgc/#Initial_Conditions">Initial_Conditions</a></li>
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<li><a href="../theories/concurrentgc/#MarkObject">MarkObject</a></li>
<li><a href="../theories/concurrentgc/#Phases">Phases</a></li>
<li><a href="../theories/concurrentgc/#StrongTricolour">StrongTricolour</a></li>
<li><a href="../theories/concurrentgc/#TSO">TSO</a></li>
<li><a href="../theories/concurrentgc/#Valid_Refs">Valid_Refs</a></li>
<li><a href="../theories/concurrentgc/#Worklists">Worklists</a></li>
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<p style="display:none;" id="bibtex-filename">ConcurrentGC-AFP</p><pre id="copy-text">@article{ConcurrentGC-AFP,
author = {Peter Gammie and Tony Hosking and Kai Engelhardt},
title = {Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO},
journal = {Archive of Formal Proofs},
month = {April},
year = {2015},
note = {\url{https://isa-afp.org/entries/ConcurrentGC.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/ConcurrentIMP.html b/web/entries/ConcurrentIMP.html
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<h1 >
<span class='first'>C</span>oncurrent <span class='first'>I</span><span class='first'>M</span><span class='first'>P</span></h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">April 13, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">ConcurrentIMP extends the small imperative language IMP with control
non-determinism and constructs for synchronous message passing.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session ConcurrentIMP</h3>
<ul>
<li><a href="../theories/concurrentimp/#CIMP_pred">CIMP_pred</a></li>
<li><a href="../theories/concurrentimp/#Infinite_Sequences">Infinite_Sequences</a></li>
<li><a href="../theories/concurrentimp/#LTL">LTL</a></li>
<li><a href="../theories/concurrentimp/#CIMP_lang">CIMP_lang</a></li>
<li><a href="../theories/concurrentimp/#CIMP_vcg">CIMP_vcg</a></li>
<li><a href="../theories/concurrentimp/#CIMP_vcg_rules">CIMP_vcg_rules</a></li>
<li><a href="../theories/concurrentimp/#CIMP">CIMP</a></li>
<li><a href="../theories/concurrentimp/#CIMP_locales">CIMP_locales</a></li>
<li><a href="../theories/concurrentimp/#CIMP_one_place_buffer">CIMP_one_place_buffer</a></li>
<li><a href="../theories/concurrentimp/#CIMP_unbounded_buffer">CIMP_unbounded_buffer</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/ConcurrentGC.html">Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO</a></li></ul>
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<p style="display:none;" id="bibtex-filename">ConcurrentIMP-AFP</p><pre id="copy-text">@article{ConcurrentIMP-AFP,
author = {Peter Gammie},
title = {Concurrent IMP},
journal = {Archive of Formal Proofs},
month = {April},
year = {2015},
note = {\url{https://isa-afp.org/entries/ConcurrentIMP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Concurrent_Ref_Alg.html b/web/entries/Concurrent_Ref_Alg.html
--- a/web/entries/Concurrent_Ref_Alg.html
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<h1 >
<span class='first'>C</span>oncurrent <span class='first'>R</span>efinement <span class='first'>A</span>lgebra and <span class='first'>R</span>ely <span class='first'>Q</span>uotients</h1>
<div>
<p><a href="../authors/fell">Julian Fell</a> <a class="obfuscated" data="eyJob3N0IjpbInVxIiwibmV0IiwiYXUiXSwidXNlciI6WyJqdWxpYW4iLCJmZWxsIl19">📧</a>, <a href="../authors/hayes">Ian J. Hayes</a> <a class="obfuscated" data="eyJob3N0IjpbIml0ZWUiLCJ1cSIsImVkdSIsImF1Il0sInVzZXIiOlsiaWFuIiwiaGF5ZXMiXX0=">📧</a> and <a href="../authors/velykis">Andrius Velykis</a> <a href="http://andrius.velykis.lt">🌐</a>
</p>
<p class="date">December 30, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The concurrent refinement algebra developed here is designed to
provide a foundation for rely/guarantee reasoning about concurrent
programs. The algebra builds on a complete lattice of commands by
providing sequential composition, parallel composition and a novel
weak conjunction operator. The weak conjunction operator coincides
with the lattice supremum providing its arguments are non-aborting,
but aborts if either of its arguments do. Weak conjunction provides an
abstract version of a guarantee condition as a guarantee process. We
distinguish between models that distribute sequential composition over
non-deterministic choice from the left (referred to as being
conjunctive in the refinement calculus literature) and those that
don't. Least and greatest fixed points of monotone functions are
provided to allow recursion and iteration operators to be added to the
language. Additional iteration laws are available for conjunctive
models. The rely quotient of processes <i>c</i> and
<i>i</i> is the process that, if executed in parallel with
<i>i</i> implements <i>c</i>. It represents an
abstract version of a rely condition generalised to a process.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li></ul>
<h3>Session Concurrent_Ref_Alg</h3>
<ul>
<li><a href="../theories/concurrent_ref_alg/#Refinement_Lattice">Refinement_Lattice</a></li>
<li><a href="../theories/concurrent_ref_alg/#Sequential">Sequential</a></li>
<li><a href="../theories/concurrent_ref_alg/#Parallel">Parallel</a></li>
<li><a href="../theories/concurrent_ref_alg/#Conjunction">Conjunction</a></li>
<li><a href="../theories/concurrent_ref_alg/#CRA">CRA</a></li>
<li><a href="../theories/concurrent_ref_alg/#Galois_Connections">Galois_Connections</a></li>
<li><a href="../theories/concurrent_ref_alg/#Iteration">Iteration</a></li>
<li><a href="../theories/concurrent_ref_alg/#Conjunctive_Sequential">Conjunctive_Sequential</a></li>
<li><a href="../theories/concurrent_ref_alg/#Infimum_Nat">Infimum_Nat</a></li>
<li><a href="../theories/concurrent_ref_alg/#Conjunctive_Iteration">Conjunctive_Iteration</a></li>
<li><a href="../theories/concurrent_ref_alg/#Rely_Quotient">Rely_Quotient</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Concurrent_Ref_Alg-AFP</p><pre id="copy-text">@article{Concurrent_Ref_Alg-AFP,
author = {Julian Fell and Ian J. Hayes and Andrius Velykis},
title = {Concurrent Refinement Algebra and Rely Quotients},
journal = {Archive of Formal Proofs},
month = {December},
year = {2016},
note = {\url{https://isa-afp.org/entries/Concurrent_Ref_Alg.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Concurrent_Ref_Alg-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Concurrent_Ref_Alg-2017-01-04.tar.gz">Jan 4, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Concurrent_Revisions.html b/web/entries/Concurrent_Revisions.html
--- a/web/entries/Concurrent_Revisions.html
+++ b/web/entries/Concurrent_Revisions.html
@@ -1,181 +1,183 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Concurrent Revisions - Archive of Formal Proofs</title><meta name="description" content="Concurrent revisions is a concurrency control model developed by Microsoft Research. It has many interesting properties that distinguish it from other..."><meta property="og:title" content="Formalization of Concurrent Revisions" />
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>C</span>oncurrent <span class='first'>R</span>evisions</h1>
<div>
<p><a href="../authors/overbeek">Roy Overbeek</a> <a class="obfuscated" data="eyJob3N0IjpbImN3aSIsIm5sIl0sInVzZXIiOlsiUm95IiwiT3ZlcmJlZWsiXX0=">📧</a>
</p>
<p class="date">December 25, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Concurrent revisions is a concurrency control model developed by
Microsoft Research. It has many interesting properties that
distinguish it from other well-known models such as transactional
memory. One of these properties is <em>determinacy</em>:
programs written within the model always produce the same outcome,
independent of scheduling activity. The concurrent revisions model has
an operational semantics, with an informal proof of determinacy. This
document contains an Isabelle/HOL formalization of this semantics and
the proof of determinacy.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li></ul>
<h3>Session Concurrent_Revisions</h3>
<ul>
<li><a href="../theories/concurrent_revisions/#Data">Data</a></li>
<li><a href="../theories/concurrent_revisions/#Occurrences">Occurrences</a></li>
<li><a href="../theories/concurrent_revisions/#Renaming">Renaming</a></li>
<li><a href="../theories/concurrent_revisions/#Substitution">Substitution</a></li>
<li><a href="../theories/concurrent_revisions/#OperationalSemantics">OperationalSemantics</a></li>
<li><a href="../theories/concurrent_revisions/#Executions">Executions</a></li>
<li><a href="../theories/concurrent_revisions/#Determinacy">Determinacy</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Concurrent_Revisions-AFP</p><pre id="copy-text">@article{Concurrent_Revisions-AFP,
author = {Roy Overbeek},
title = {Formalization of Concurrent Revisions},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Concurrent_Revisions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Concurrent_Revisions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Concurrent_Revisions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Concurrent_Revisions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Concurrent_Revisions-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Concurrent_Revisions-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<h1 >
<span class='first'>C</span>onditional <span class='first'>S</span>implification</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The article provides a collection of experimental general-purpose
proof methods for the object logic Isabelle/HOL of the formal proof
assistant Isabelle. The methods in the collection offer functionality
that is similar to certain aspects of the functionality provided by
the standard proof methods of Isabelle that combine classical
reasoning and rewriting, such as the method <i>auto</i>,
but use a different approach for rewriting. More specifically, these
methods allow for the side conditions of the rewrite rules to be
solved via intro-resolution.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 7, 2022</dt>
<dd>added a switch for backtracking (revision 241da1cdeabf)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Conditional_Simplification</h3>
<ul>
<li><a href="../theories/conditional_simplification/#CS_Tools">CS_Tools</a></li>
<li><a href="../theories/conditional_simplification/#IHOL_CS">IHOL_CS</a></li>
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<li><a href="../theories/conditional_simplification/#CS_Reference">CS_Reference</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Conditional_Simplification-AFP</p><pre id="copy-text">@article{Conditional_Simplification-AFP,
author = {Mihails Milehins},
title = {Conditional Simplification},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Conditional_Simplification.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Conditional_Simplification-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Conditional_Simplification-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>C</span>onditional <span class='first'>T</span>ransfer <span class='first'>R</span>ule</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article provides a collection of experimental utilities for
unoverloading of definitions and synthesis of conditional transfer
rules for the object logic Isabelle/HOL of the formal proof assistant
Isabelle written in Isabelle/ML.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Conditional_Transfer_Rule</h3>
<ul>
<li><a href="../theories/conditional_transfer_rule/#CTR_Tools">CTR_Tools</a></li>
<li><a href="../theories/conditional_transfer_rule/#IML_UT">IML_UT</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/SpecCheck.html">SpecCheck - Specification-Based Testing for Isabelle/ML</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Types_To_Sets_Extension.html">Extension of Types-To-Sets</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li>
<li><a href="../entries/CZH_Elementary_Categories.html">Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</a></li>
<li><a href="../entries/CZH_Universal_Constructions.html">Category Theory for ZFC in HOL III: Universal Constructions</a></li>
<li><a href="../entries/Conditional_Simplification.html">Conditional Simplification</a></li>
<li><a href="../entries/Intro_Dest_Elim.html">IDE: Introduction, Destruction, Elimination</a></li>
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<p style="display:none;" id="bibtex-filename">Conditional_Transfer_Rule-AFP</p><pre id="copy-text">@article{Conditional_Transfer_Rule-AFP,
author = {Mihails Milehins},
title = {Conditional Transfer Rule},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Conditional_Transfer_Rule.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Conditional_Transfer_Rule-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>C</span>onsensus <span class='first'>R</span>efined</h1>
<div>
<p><a href="../authors/maric">Ognjen Marić</a> and <a href="../authors/sprenger">Christoph Sprenger</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInNwcmVuZ2VyIl19">📧</a>
</p>
<p class="date">March 18, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Algorithms for solving the consensus problem are fundamental to
distributed computing. Despite their brevity, their
ability to operate in concurrent, asynchronous and failure-prone
environments comes at the cost of complex and subtle
behaviors. Accordingly, understanding how they work and proving
their correctness is a non-trivial endeavor where abstraction
is immensely helpful.
Moreover, research on consensus has yielded a large number of
algorithms, many of which appear to share common algorithmic
ideas. A natural question is whether and how these similarities can
be distilled and described in a precise, unified way.
In this work, we combine stepwise refinement and
lockstep models to provide an abstract and unified
view of a sizeable family of consensus algorithms. Our models
provide insights into the design choices underlying the different
algorithms, and classify them based on those choices.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Consensus_Refined</h3>
<ul>
<li><a href="../theories/consensus_refined/#Infra">Infra</a></li>
<li><a href="../theories/consensus_refined/#Consensus_Types">Consensus_Types</a></li>
<li><a href="../theories/consensus_refined/#Quorums">Quorums</a></li>
<li><a href="../theories/consensus_refined/#Consensus_Misc">Consensus_Misc</a></li>
<li><a href="../theories/consensus_refined/#Two_Steps">Two_Steps</a></li>
<li><a href="../theories/consensus_refined/#Three_Steps">Three_Steps</a></li>
<li><a href="../theories/consensus_refined/#Refinement">Refinement</a></li>
<li><a href="../theories/consensus_refined/#HO_Transition_System">HO_Transition_System</a></li>
<li><a href="../theories/consensus_refined/#Voting">Voting</a></li>
<li><a href="../theories/consensus_refined/#Voting_Opt">Voting_Opt</a></li>
<li><a href="../theories/consensus_refined/#OneThirdRule_Defs">OneThirdRule_Defs</a></li>
<li><a href="../theories/consensus_refined/#OneThirdRule_Proofs">OneThirdRule_Proofs</a></li>
<li><a href="../theories/consensus_refined/#Ate_Defs">Ate_Defs</a></li>
<li><a href="../theories/consensus_refined/#Ate_Proofs">Ate_Proofs</a></li>
<li><a href="../theories/consensus_refined/#Same_Vote">Same_Vote</a></li>
<li><a href="../theories/consensus_refined/#Observing_Quorums">Observing_Quorums</a></li>
<li><a href="../theories/consensus_refined/#Observing_Quorums_Opt">Observing_Quorums_Opt</a></li>
<li><a href="../theories/consensus_refined/#Two_Step_Observing">Two_Step_Observing</a></li>
<li><a href="../theories/consensus_refined/#Uv_Defs">Uv_Defs</a></li>
<li><a href="../theories/consensus_refined/#Uv_Proofs">Uv_Proofs</a></li>
<li><a href="../theories/consensus_refined/#BenOr_Defs">BenOr_Defs</a></li>
<li><a href="../theories/consensus_refined/#BenOr_Proofs">BenOr_Proofs</a></li>
<li><a href="../theories/consensus_refined/#MRU_Vote">MRU_Vote</a></li>
<li><a href="../theories/consensus_refined/#MRU_Vote_Opt">MRU_Vote_Opt</a></li>
<li><a href="../theories/consensus_refined/#Three_Step_MRU">Three_Step_MRU</a></li>
<li><a href="../theories/consensus_refined/#New_Algorithm_Defs">New_Algorithm_Defs</a></li>
<li><a href="../theories/consensus_refined/#New_Algorithm_Proofs">New_Algorithm_Proofs</a></li>
<li><a href="../theories/consensus_refined/#Paxos_Defs">Paxos_Defs</a></li>
<li><a href="../theories/consensus_refined/#Paxos_Proofs">Paxos_Proofs</a></li>
<li><a href="../theories/consensus_refined/#CT_Defs">CT_Defs</a></li>
<li><a href="../theories/consensus_refined/#CT_Proofs">CT_Proofs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Heard_Of.html">Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</a></li><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Consensus_Refined-AFP</p><pre id="copy-text">@article{Consensus_Refined-AFP,
author = {Ognjen Marić and Christoph Sprenger},
title = {Consensus Refined},
journal = {Archive of Formal Proofs},
month = {March},
year = {2015},
note = {\url{https://isa-afp.org/entries/Consensus_Refined.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>onstructive <span class='first'>C</span>ryptography in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/sefidgar">S. Reza Sefidgar</a>
</p>
<p class="date">December 17, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Inspired by Abstract Cryptography, we extend CryptHOL, a framework for
formalizing game-based proofs, with an abstract model of Random
Systems and provide proof rules about their composition and equality.
This foundation facilitates the formalization of Constructive
Cryptography proofs, where the security of a cryptographic scheme is
realized as a special form of construction in which a complex random
system is built from simpler ones. This is a first step towards a
fully-featured compositional framework, similar to Universal
Composability framework, that supports formalization of
simulation-based proofs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Constructive_Cryptography</h3>
<ul>
<li><a href="../theories/constructive_cryptography/#Resource">Resource</a></li>
<li><a href="../theories/constructive_cryptography/#Converter">Converter</a></li>
<li><a href="../theories/constructive_cryptography/#Converter_Rewrite">Converter_Rewrite</a></li>
<li><a href="../theories/constructive_cryptography/#Random_System">Random_System</a></li>
<li><a href="../theories/constructive_cryptography/#Distinguisher">Distinguisher</a></li>
<li><a href="../theories/constructive_cryptography/#Wiring">Wiring</a></li>
<li><a href="../theories/constructive_cryptography/#Constructive_Cryptography">Constructive_Cryptography</a></li>
<li><a href="../theories/constructive_cryptography/#System_Construction">System_Construction</a></li>
<li><a href="../theories/constructive_cryptography/#One_Time_Pad">One_Time_Pad</a></li>
<li><a href="../theories/constructive_cryptography/#Message_Authentication_Code">Message_Authentication_Code</a></li>
<li><a href="../theories/constructive_cryptography/#Secure_Channel">Secure_Channel</a></li>
<li><a href="../theories/constructive_cryptography/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CryptHOL.html">CryptHOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Constructive_Cryptography_CM.html">Constructive Cryptography in HOL: the Communication Modeling Aspect</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Constructive_Cryptography-AFP</p><pre id="copy-text">@article{Constructive_Cryptography-AFP,
author = {Andreas Lochbihler and S. Reza Sefidgar},
title = {Constructive Cryptography in HOL},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Constructive_Cryptography.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>onstructive <span class='first'>C</span>ryptography in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span>: <span class='first'>T</span>he <span class='first'>C</span>ommunication <span class='first'>M</span>odeling <span class='first'>A</span>spect</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/sefidgar">S. Reza Sefidgar</a>
</p>
<p class="date">March 17, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Constructive Cryptography (CC) [<a
href="https://conference.iiis.tsinghua.edu.cn/ICS2011/content/papers/14.html">ICS
2011</a>, <a
href="https://doi.org/10.1007/978-3-642-27375-9_3">TOSCA
2011</a>, <a
href="https://doi.org/10.1007/978-3-662-53641-4_1">TCC
2016</a>] introduces an abstract approach to composable security
statements that allows one to focus on a particular aspect of security
proofs at a time. Instead of proving the properties of concrete
systems, CC studies system classes, i.e., the shared behavior of
similar systems, and their transformations. Modeling of systems
communication plays a crucial role in composability and reusability of
security statements; yet, this aspect has not been studied in any of
the existing CC results. We extend our previous CC formalization
[<a href="https://isa-afp.org/entries/Constructive_Cryptography.html">Constructive_Cryptography</a>,
<a href="https://doi.org/10.1109/CSF.2019.00018">CSF
2019</a>] with a new semantic domain called Fused Resource
Templates (FRT) that abstracts over the systems communication patterns
in CC proofs. This widens the scope of cryptography proof
formalizations in the CryptHOL library [<a
href="https://isa-afp.org/entries/CryptHOL.html">CryptHOL</a>,
<a
href="https://doi.org/10.1007/978-3-662-49498-1_20">ESOP
2016</a>, <a
href="https://doi.org/10.1007/s00145-019-09341-z">J
Cryptol 2020</a>]. This formalization is described in <a
href="http://www.andreas-lochbihler.de/pub/basin2021.pdf">Abstract
Modeling of Systems Communication in Constructive Cryptography using
CryptHOL</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Constructive_Cryptography_CM</h3>
<ul>
<li><a href="../theories/constructive_cryptography_cm/#More_CC">More_CC</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Observe_Failure">Observe_Failure</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Fold_Spmf">Fold_Spmf</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Fused_Resource">Fused_Resource</a></li>
<li><a href="../theories/constructive_cryptography_cm/#State_Isomorphism">State_Isomorphism</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Construction_Utility">Construction_Utility</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Concrete_Security">Concrete_Security</a></li>
<li><a href="../theories/constructive_cryptography_cm/#Asymptotic_Security">Asymptotic_Security</a></li>
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<li><a href="../theories/constructive_cryptography_cm/#Diffie_Hellman_CC">Diffie_Hellman_CC</a></li>
<li><a href="../theories/constructive_cryptography_cm/#DH_OTP">DH_OTP</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Constructive_Cryptography.html">Constructive Cryptography in HOL</a></li><li><a href="../entries/Game_Based_Crypto.html">Game-based cryptography in HOL</a></li><li><a href="../entries/Sigma_Commit_Crypto.html">Sigma Protocols and Commitment Schemes</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Constructive_Cryptography_CM-AFP</p><pre id="copy-text">@article{Constructive_Cryptography_CM-AFP,
author = {Andreas Lochbihler and S. Reza Sefidgar},
title = {Constructive Cryptography in HOL: the Communication Modeling Aspect},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Constructive_Cryptography_CM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Constructive_Cryptography_CM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>C</span>onstructor <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">April 19, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle's code generator performs various adaptations for target
languages. Among others, constructor applications have to be fully
saturated. That means that for constructor calls occuring as arguments
to higher-order functions, synthetic lambdas have to be inserted. This
entry provides tooling to avoid this construction altogether by
introducing constructor functions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Constructor_Funs</h3>
<ul>
<li><a href="../theories/constructor_funs/#Constructor_Funs">Constructor_Funs</a></li>
<li><a href="../theories/constructor_funs/#Test_Constructor_Funs">Test_Constructor_Funs</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Constructor_Funs-AFP</p><pre id="copy-text">@article{Constructor_Funs-AFP,
author = {Lars Hupel},
title = {Constructor Functions},
journal = {Archive of Formal Proofs},
month = {April},
year = {2017},
note = {\url{https://isa-afp.org/entries/Constructor_Funs.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Constructor_Funs-2017-04-20.tar.gz">Apr 20, 2017</a>: Isabelle2016-1
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<h1 >
<span class='first'>L</span>ight-<span class='first'>W</span>eight <span class='first'>C</span>ontainers</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
with contributions from <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">April 15, 2013</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a framework for container types like sets and maps such that generated code implements these containers with different (efficient) data structures.
Thanks to type classes and refinement during code generation, this light-weight approach can seamlessly replace Isabelle's default setup for code generation.
Heuristics automatically pick one of the available data structures depending on the type of elements to be stored, but users can also choose on their own.
The extensible design permits to add more implementations at any time.
<p>
To support arbitrary nesting of sets, we define a linear order on sets based on a linear order of the elements and provide efficient implementations.
It even allows to compare complements with non-complements.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 5, 2018</dt>
<dd>add two application examples: depth-first search and 2SAT (revision e5e1a1da2411)</dd><dt>July 8, 2014</dt>
<dd>add support for going from partial functions to mappings (revision 7a6fc957e8ed)<br></dd><dt>September 20, 2013</dt>
<dd>provide generators for canonical type class instantiations
(revision 159f4401f4a8 by René Thiemann)<br>
</dd><dt>July 11, 2013</dt>
<dd>add pretty printing for sets (revision 7f3f52c5f5fa)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Containers</h3>
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<li><a href="../theories/containers/#Containers_Auxiliary">Containers_Auxiliary</a></li>
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<li><a href="../theories/containers/#List_Fusion">List_Fusion</a></li>
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<li><a href="../theories/containers/#Extend_Partial_Order">Extend_Partial_Order</a></li>
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<li><a href="../theories/containers/#Collection_Enum">Collection_Enum</a></li>
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<li><a href="../theories/containers/#RBT_ext">RBT_ext</a></li>
<li><a href="../theories/containers/#RBT_Mapping2">RBT_Mapping2</a></li>
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<li><a href="../theories/containers/#Map_To_Mapping">Map_To_Mapping</a></li>
<li><a href="../theories/containers/#Containers">Containers</a></li>
<li><a href="../theories/containers/#Compatibility_Containers_Regular_Sets">Compatibility_Containers_Regular_Sets</a></li>
<li><a href="../theories/containers/#Containers_Userguide">Containers_Userguide</a></li>
<li><a href="../theories/containers/#Card_Datatype_Ex">Card_Datatype_Ex</a></li>
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<h3>Session Containers-Benchmarks</h3>
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<li><a href="../theories/containers-benchmarks/#Benchmark_Bool">Benchmark_Bool</a></li>
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<li><a href="../theories/containers-benchmarks/#Benchmark_LC">Benchmark_LC</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_Default">Benchmark_Default</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_ICF">Benchmark_ICF</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_RBT">Benchmark_RBT</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_Set">Benchmark_Set</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_Set_Default">Benchmark_Set_Default</a></li>
<li><a href="../theories/containers-benchmarks/#Benchmark_Set_LC">Benchmark_Set_LC</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Finger-Trees.html">Finger Trees</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Trie.html">Trie</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/FSM_Tests.html">Verified Complete Test Strategies for Finite State Machines</a></li><li><a href="../entries/Eval_FO.html">First-Order Query Evaluation</a></li><li><a href="../entries/VYDRA_MDL.html">Multi-Head Monitoring of Metric Dynamic Logic</a></li><li><a href="../entries/AI_Planning_Languages_Semantics.html">AI Planning Languages Semantics</a></li><li><a href="../entries/MFOTL_Monitor.html">Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li>
<li><a href="../entries/XML.html">XML</a></li>
<li><a href="../entries/Imperative_Insertion_Sort.html">Imperative Insertion Sort</a></li>
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<p style="display:none;" id="bibtex-filename">Containers-AFP</p><pre id="copy-text">@article{Containers-AFP,
author = {Andreas Lochbihler},
title = {Light-weight Containers},
journal = {Archive of Formal Proofs},
month = {April},
year = {2013},
note = {\url{https://isa-afp.org/entries/Containers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/CoreC++.html b/web/entries/CoreC++.html
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<h1 >
<span class='first'>C</span>ore<span class='first'>C</span>++</h1>
<div>
<p><a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">May 15, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an operational semantics and type safety proof for multiple inheritance in C++. The semantics models the behavior of method calls, field accesses, and two forms of casts in C++ class hierarchies. For explanations see the OOPSLA 2006 paper by Wasserrab, Nipkow, Snelting and Tip.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session CoreC&#43;&#43;</h3>
<ul>
<li><a href="../theories/corec&#43;&#43;/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/corec&#43;&#43;/#Type">Type</a></li>
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<li><a href="../theories/corec&#43;&#43;/#Expr">Expr</a></li>
<li><a href="../theories/corec&#43;&#43;/#Decl">Decl</a></li>
<li><a href="../theories/corec&#43;&#43;/#ClassRel">ClassRel</a></li>
<li><a href="../theories/corec&#43;&#43;/#SubObj">SubObj</a></li>
<li><a href="../theories/corec&#43;&#43;/#Objects">Objects</a></li>
<li><a href="../theories/corec&#43;&#43;/#Exceptions">Exceptions</a></li>
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<li><a href="../theories/corec&#43;&#43;/#BigStep">BigStep</a></li>
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<p style="display:none;" id="bibtex-filename">CoreC&#43;&#43;-AFP</p><pre id="copy-text">@article{CoreC&#43;&#43;-AFP,
author = {Daniel Wasserrab},
title = {CoreC&#43;&#43;},
journal = {Archive of Formal Proofs},
month = {May},
year = {2006},
note = {\url{https://isa-afp.org/entries/CoreC&#43;&#43;.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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</li><li>
<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
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<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
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<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
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<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
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<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
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<a href="https://www.isa-afp.org/release/afp-CoreC&#43;&#43;-2006-05-16.tar.gz">May 16, 2006</a>: Isabelle2005
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel of the <span class='first'>D</span>ocument <span class='first'>O</span>bject <span class='first'>M</span>odel</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">December 26, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we formalize the core of the Document Object Model
(DOM). At its core, the DOM defines a tree-like data structure for
representing documents in general and HTML documents in particular. It
is the heart of any modern web browser. Formalizing the key concepts
of the DOM is a prerequisite for the formal reasoning over client-side
JavaScript programs and for the analysis of security concepts in
modern web browsers. We present a formalization of the core DOM, with
focus on the node-tree and the operations defined on node-trees, in
Isabelle/HOL. We use the formalization to verify the functional
correctness of the most important functions defined in the DOM
standard. Moreover, our formalization is 1) extensible, i.e., can be
extended without the need of re-proving already proven properties and
2) executable, i.e., we can generate executable code from our
specification.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Core_DOM</h3>
<ul>
<li><a href="../theories/core_dom/#Hiding_Type_Variables">Hiding_Type_Variables</a></li>
<li><a href="../theories/core_dom/#Ref">Ref</a></li>
<li><a href="../theories/core_dom/#Core_DOM_Basic_Datatypes">Core_DOM_Basic_Datatypes</a></li>
<li><a href="../theories/core_dom/#BaseClass">BaseClass</a></li>
<li><a href="../theories/core_dom/#Heap_Error_Monad">Heap_Error_Monad</a></li>
<li><a href="../theories/core_dom/#BaseMonad">BaseMonad</a></li>
<li><a href="../theories/core_dom/#ObjectPointer">ObjectPointer</a></li>
<li><a href="../theories/core_dom/#ObjectClass">ObjectClass</a></li>
<li><a href="../theories/core_dom/#ObjectMonad">ObjectMonad</a></li>
<li><a href="../theories/core_dom/#NodePointer">NodePointer</a></li>
<li><a href="../theories/core_dom/#NodeClass">NodeClass</a></li>
<li><a href="../theories/core_dom/#NodeMonad">NodeMonad</a></li>
<li><a href="../theories/core_dom/#ElementPointer">ElementPointer</a></li>
<li><a href="../theories/core_dom/#CharacterDataPointer">CharacterDataPointer</a></li>
<li><a href="../theories/core_dom/#DocumentPointer">DocumentPointer</a></li>
<li><a href="../theories/core_dom/#ShadowRootPointer">ShadowRootPointer</a></li>
<li><a href="../theories/core_dom/#ElementClass">ElementClass</a></li>
<li><a href="../theories/core_dom/#ElementMonad">ElementMonad</a></li>
<li><a href="../theories/core_dom/#CharacterDataClass">CharacterDataClass</a></li>
<li><a href="../theories/core_dom/#CharacterDataMonad">CharacterDataMonad</a></li>
<li><a href="../theories/core_dom/#DocumentClass">DocumentClass</a></li>
<li><a href="../theories/core_dom/#DocumentMonad">DocumentMonad</a></li>
<li><a href="../theories/core_dom/#Core_DOM_Functions">Core_DOM_Functions</a></li>
<li><a href="../theories/core_dom/#Core_DOM_Heap_WF">Core_DOM_Heap_WF</a></li>
<li><a href="../theories/core_dom/#Core_DOM">Core_DOM</a></li>
<li><a href="../theories/core_dom/#Testing_Utils">Testing_Utils</a></li>
<li><a href="../theories/core_dom/#Core_DOM_BaseTest">Core_DOM_BaseTest</a></li>
<li><a href="../theories/core_dom/#Document_adoptNode">Document_adoptNode</a></li>
<li><a href="../theories/core_dom/#Document_getElementById">Document_getElementById</a></li>
<li><a href="../theories/core_dom/#Node_insertBefore">Node_insertBefore</a></li>
<li><a href="../theories/core_dom/#Node_removeChild">Node_removeChild</a></li>
<li><a href="../theories/core_dom/#Core_DOM_Tests">Core_DOM_Tests</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Shadow_DOM.html">A Formal Model of the Document Object Model with Shadow Roots</a></li></ul>
</div>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Core_DOM/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Core_DOM/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Core_DOM-AFP</p><pre id="copy-text">@article{Core_DOM-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {A Formal Model of the Document Object Model},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Core_DOM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Core_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Core_DOM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Core_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_DOM-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_DOM-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_DOM-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_DOM-2019-01-07.tar.gz">Jan 7, 2019</a>: Isabelle2018
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diff --git a/web/entries/Core_SC_DOM.html b/web/entries/Core_SC_DOM.html
--- a/web/entries/Core_SC_DOM.html
+++ b/web/entries/Core_SC_DOM.html
@@ -1,212 +1,214 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Safely Composable DOM - Archive of Formal Proofs</title><meta name="description" content="In this AFP entry, we formalize the core of the Safely Composable
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>afely <span class='first'>C</span>omposable <span class='first'>D</span><span class='first'>O</span><span class='first'>M</span></h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">September 28, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we formalize the core of the Safely Composable
Document Object Model (SC DOM). The SC DOM improve the standard DOM
(as formalized in the AFP entry "Core DOM") by strengthening
the tree boundaries set by shadow roots: in the SC DOM, the shadow
root is a sub-class of the document class (instead of a base class).
This modifications also results in changes to some API methods (e.g.,
getOwnerDocument) to return the nearest shadow root rather than the
document root. As a result, many API methods that, when called on a
node inside a shadow tree, would previously ``break out''
and return or modify nodes that are possibly outside the shadow tree,
now stay within its boundaries. This change in behavior makes programs
that operate on shadow trees more predictable for the developer and
allows them to make more assumptions about other code accessing the
DOM.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Core_SC_DOM</h3>
<ul>
<li><a href="../theories/core_sc_dom/#Hiding_Type_Variables">Hiding_Type_Variables</a></li>
<li><a href="../theories/core_sc_dom/#Ref">Ref</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM_Basic_Datatypes">Core_DOM_Basic_Datatypes</a></li>
<li><a href="../theories/core_sc_dom/#BaseClass">BaseClass</a></li>
<li><a href="../theories/core_sc_dom/#Heap_Error_Monad">Heap_Error_Monad</a></li>
<li><a href="../theories/core_sc_dom/#BaseMonad">BaseMonad</a></li>
<li><a href="../theories/core_sc_dom/#ObjectPointer">ObjectPointer</a></li>
<li><a href="../theories/core_sc_dom/#ObjectClass">ObjectClass</a></li>
<li><a href="../theories/core_sc_dom/#ObjectMonad">ObjectMonad</a></li>
<li><a href="../theories/core_sc_dom/#NodePointer">NodePointer</a></li>
<li><a href="../theories/core_sc_dom/#NodeClass">NodeClass</a></li>
<li><a href="../theories/core_sc_dom/#NodeMonad">NodeMonad</a></li>
<li><a href="../theories/core_sc_dom/#ElementPointer">ElementPointer</a></li>
<li><a href="../theories/core_sc_dom/#CharacterDataPointer">CharacterDataPointer</a></li>
<li><a href="../theories/core_sc_dom/#DocumentPointer">DocumentPointer</a></li>
<li><a href="../theories/core_sc_dom/#ShadowRootPointer">ShadowRootPointer</a></li>
<li><a href="../theories/core_sc_dom/#ElementClass">ElementClass</a></li>
<li><a href="../theories/core_sc_dom/#ElementMonad">ElementMonad</a></li>
<li><a href="../theories/core_sc_dom/#CharacterDataClass">CharacterDataClass</a></li>
<li><a href="../theories/core_sc_dom/#CharacterDataMonad">CharacterDataMonad</a></li>
<li><a href="../theories/core_sc_dom/#DocumentClass">DocumentClass</a></li>
<li><a href="../theories/core_sc_dom/#DocumentMonad">DocumentMonad</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM_Functions">Core_DOM_Functions</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM_Heap_WF">Core_DOM_Heap_WF</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM">Core_DOM</a></li>
<li><a href="../theories/core_sc_dom/#Testing_Utils">Testing_Utils</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM_BaseTest">Core_DOM_BaseTest</a></li>
<li><a href="../theories/core_sc_dom/#Document_adoptNode">Document_adoptNode</a></li>
<li><a href="../theories/core_sc_dom/#Document_getElementById">Document_getElementById</a></li>
<li><a href="../theories/core_sc_dom/#Node_insertBefore">Node_insertBefore</a></li>
<li><a href="../theories/core_sc_dom/#Node_removeChild">Node_removeChild</a></li>
<li><a href="../theories/core_sc_dom/#Core_DOM_Tests">Core_DOM_Tests</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Shadow_SC_DOM.html">A Formal Model of the Safely Composable Document Object Model with Shadow Roots</a></li></ul>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Core_SC_DOM/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Core_SC_DOM-AFP</p><pre id="copy-text">@article{Core_SC_DOM-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {The Safely Composable DOM},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Core_SC_DOM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Core_SC_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Core_SC_DOM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Core_SC_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_SC_DOM-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Core_SC_DOM-2020-11-26.tar.gz">Nov 26, 2020</a>: Isabelle2020
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diff --git a/web/entries/Correctness_Algebras.html b/web/entries/Correctness_Algebras.html
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@@ -1,212 +1,214 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations - Archive of Formal Proofs</title><meta name="description" content="We study models of state-based non-deterministic sequential
computations and describe them using algebras. We propose algebras
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<h1 >
<span class='first'>A</span>lgebras for <span class='first'>I</span>teration, <span class='first'>I</span>nfinite <span class='first'>E</span>xecutions and <span class='first'>C</span>orrectness of <span class='first'>S</span>equential <span class='first'>C</span>omputations</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">October 12, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We study models of state-based non-deterministic sequential
computations and describe them using algebras. We propose algebras
that describe iteration for strict and non-strict computations. They
unify computation models which differ in the fixpoints used to
represent iteration. We propose algebras that describe the infinite
executions of a computation. They lead to a unified approximation
order and results that connect fixpoints in the approximation and
refinement orders. This unifies the semantics of recursion for a range
of computation models. We propose algebras that describe preconditions
and the effect of while-programs under postconditions. They unify
correctness statements in two dimensions: one statement applies in
various computation models to various correctness claims.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Correctness_Algebras</h3>
<ul>
<li><a href="../theories/correctness_algebras/#Base">Base</a></li>
<li><a href="../theories/correctness_algebras/#Omega_Algebras">Omega_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#Capped_Omega_Algebras">Capped_Omega_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#General_Refinement_Algebras">General_Refinement_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#Lattice_Ordered_Semirings">Lattice_Ordered_Semirings</a></li>
<li><a href="../theories/correctness_algebras/#Boolean_Semirings">Boolean_Semirings</a></li>
<li><a href="../theories/correctness_algebras/#Binary_Iterings">Binary_Iterings</a></li>
<li><a href="../theories/correctness_algebras/#Binary_Iterings_Strict">Binary_Iterings_Strict</a></li>
<li><a href="../theories/correctness_algebras/#Binary_Iterings_Nonstrict">Binary_Iterings_Nonstrict</a></li>
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<li><a href="../theories/correctness_algebras/#N_Semirings_Boolean">N_Semirings_Boolean</a></li>
<li><a href="../theories/correctness_algebras/#N_Semirings_Modal">N_Semirings_Modal</a></li>
<li><a href="../theories/correctness_algebras/#Approximation">Approximation</a></li>
<li><a href="../theories/correctness_algebras/#Recursion_Strict">Recursion_Strict</a></li>
<li><a href="../theories/correctness_algebras/#N_Algebras">N_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#Recursion">Recursion</a></li>
<li><a href="../theories/correctness_algebras/#N_Omega_Algebras">N_Omega_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#N_Omega_Binary_Iterings">N_Omega_Binary_Iterings</a></li>
<li><a href="../theories/correctness_algebras/#N_Relation_Algebras">N_Relation_Algebras</a></li>
<li><a href="../theories/correctness_algebras/#Domain">Domain</a></li>
<li><a href="../theories/correctness_algebras/#Domain_Iterings">Domain_Iterings</a></li>
<li><a href="../theories/correctness_algebras/#Domain_Recursion">Domain_Recursion</a></li>
<li><a href="../theories/correctness_algebras/#Extended_Designs">Extended_Designs</a></li>
<li><a href="../theories/correctness_algebras/#Relative_Domain">Relative_Domain</a></li>
<li><a href="../theories/correctness_algebras/#Relative_Modal">Relative_Modal</a></li>
<li><a href="../theories/correctness_algebras/#Complete_Tests">Complete_Tests</a></li>
<li><a href="../theories/correctness_algebras/#Complete_Domain">Complete_Domain</a></li>
<li><a href="../theories/correctness_algebras/#Preconditions">Preconditions</a></li>
<li><a href="../theories/correctness_algebras/#Hoare">Hoare</a></li>
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<li><a href="../theories/correctness_algebras/#Monotonic_Boolean_Transformers">Monotonic_Boolean_Transformers</a></li>
<li><a href="../theories/correctness_algebras/#Monotonic_Boolean_Transformers_Instances">Monotonic_Boolean_Transformers_Instances</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></li><li><a href="../entries/Stone_Kleene_Relation_Algebras.html">Stone-Kleene Relation Algebras</a></li><li><a href="../entries/Subset_Boolean_Algebras.html">A Hierarchy of Algebras for Boolean Subsets</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Correctness_Algebras-AFP</p><pre id="copy-text">@article{Correctness_Algebras-AFP,
author = {Walter Guttmann},
title = {Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations},
journal = {Archive of Formal Proofs},
month = {October},
year = {2021},
note = {\url{https://isa-afp.org/entries/Correctness_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent - Archive of Formal Proofs</title><meta name="description" content="In this article, I formalise a proof from THE BOOK; namely a formula that was called ‘one of the most beautiful formulas involving elementary functions’:..."><meta property="og:title" content="A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent" />
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<h1 >
<span class='first'>A</span> <span class='first'>P</span>roof <span class='first'>F</span>rom the <span class='first'>B</span><span class='first'>O</span><span class='first'>O</span><span class='first'>K</span>: <span class='first'>T</span>he <span class='first'>P</span>artial <span class='first'>F</span>raction <span class='first'>E</span>xpansion of the <span class='first'>C</span>otangent</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 15, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>In this article, I formalise a proof from <a
href="https://dx.doi.org/10.1007/978-3-662-57265-8">THE
BOOK</a>; namely a formula that was called ‘one of the most
beautiful formulas involving elementary functions’:</p> \[\pi
\cot(\pi z) = \frac{1}{z} + \sum_{n=1}^\infty\left(\frac{1}{z+n} +
\frac{1}{z-n}\right)\] <p>The proof uses Herglotz's trick
to show the real case and analytic continuation for the complex
case.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Cotangent_PFD_Formula</h3>
<ul>
<li><a href="../theories/cotangent_pfd_formula/#Cotangent_PFD_Formula">Cotangent_PFD_Formula</a></li></ul><div class="flex-wrap">
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Cotangent_PFD_Formula/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Cotangent_PFD_Formula-AFP</p><pre id="copy-text">@article{Cotangent_PFD_Formula-AFP,
author = {Manuel Eberl},
title = {A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/Cotangent_PFD_Formula.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Count_Complex_Roots.html b/web/entries/Count_Complex_Roots.html
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<h1 >
<span class='first'>C</span>ount the <span class='first'>N</span>umber of <span class='first'>C</span>omplex <span class='first'>R</span>oots</h1>
<div>
<p><a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">October 17, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Based on evaluating Cauchy indices through remainder sequences, this
entry provides an effective procedure to count the number of complex
roots (with multiplicity) of a polynomial within various shapes (e.g., rectangle,
circle and half-plane). Potential applications of this entry include certified
complex root isolation (of a polynomial) and testing the Routh-Hurwitz
stability criterion (i.e., to check whether all the roots of some
characteristic polynomial have negative real parts).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>October 26, 2021</dt>
<dd>resolved the roots-on-the-border problem in the rectangular case (revision 82a159e398cf).</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Count_Complex_Roots</h3>
<ul>
<li><a href="../theories/count_complex_roots/#CC_Polynomials_Extra">CC_Polynomials_Extra</a></li>
<li><a href="../theories/count_complex_roots/#Extended_Sturm">Extended_Sturm</a></li>
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<li><a href="../theories/count_complex_roots/#Count_Half_Plane">Count_Half_Plane</a></li>
<li><a href="../theories/count_complex_roots/#Count_Circle">Count_Circle</a></li>
<li><a href="../theories/count_complex_roots/#Count_Rectangle">Count_Rectangle</a></li>
<li><a href="../theories/count_complex_roots/#Count_Complex_Roots">Count_Complex_Roots</a></li>
<li><a href="../theories/count_complex_roots/#Count_Complex_Roots_Examples">Count_Complex_Roots_Examples</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li><li><a href="../entries/Sturm_Tarski.html">The Sturm-Tarski Theorem</a></li><li><a href="../entries/Winding_Number_Eval.html">Evaluate Winding Numbers through Cauchy Indices</a></li></ul>
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Count_Complex_Roots-AFP</p><pre id="copy-text">@article{Count_Complex_Roots-AFP,
author = {Wenda Li},
title = {Count the Number of Complex Roots},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Count_Complex_Roots.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Count_Complex_Roots-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Count_Complex_Roots-2017-10-18.tar.gz">Oct 18, 2017</a>: Isabelle2017
</li></ul>
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diff --git a/web/entries/CryptHOL.html b/web/entries/CryptHOL.html
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<h1 >
<span class='first'>C</span>rypt<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 5, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>CryptHOL provides a framework for formalising cryptographic arguments
in Isabelle/HOL. It shallowly embeds a probabilistic functional
programming language in higher order logic. The language features
monadic sequencing, recursion, random sampling, failures and failure
handling, and black-box access to oracles. Oracles are probabilistic
functions which maintain hidden state between different invocations.
All operators are defined in the new semantic domain of
generative probabilistic values, a codatatype. We derive proof rules for
the operators and establish a connection with the theory of relational
parametricity. Thus, the resuting proofs are trustworthy and
comprehensible, and the framework is extensible and widely applicable.
</p><p>
The framework is used in the accompanying AFP entry "Game-based
Cryptography in HOL". There, we show-case our framework by formalizing
different game-based proofs from the literature. This formalisation
continues the work described in the author's ESOP 2016 paper.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session CryptHOL</h3>
<ul>
<li><a href="../theories/crypthol/#Misc_CryptHOL">Misc_CryptHOL</a></li>
<li><a href="../theories/crypthol/#Set_Applicative">Set_Applicative</a></li>
<li><a href="../theories/crypthol/#SPMF_Applicative">SPMF_Applicative</a></li>
<li><a href="../theories/crypthol/#List_Bits">List_Bits</a></li>
<li><a href="../theories/crypthol/#Environment_Functor">Environment_Functor</a></li>
<li><a href="../theories/crypthol/#Partial_Function_Set">Partial_Function_Set</a></li>
<li><a href="../theories/crypthol/#Negligible">Negligible</a></li>
<li><a href="../theories/crypthol/#Resumption">Resumption</a></li>
<li><a href="../theories/crypthol/#Generat">Generat</a></li>
<li><a href="../theories/crypthol/#Generative_Probabilistic_Value">Generative_Probabilistic_Value</a></li>
<li><a href="../theories/crypthol/#Computational_Model">Computational_Model</a></li>
<li><a href="../theories/crypthol/#GPV_Expectation">GPV_Expectation</a></li>
<li><a href="../theories/crypthol/#GPV_Bisim">GPV_Bisim</a></li>
<li><a href="../theories/crypthol/#GPV_Applicative">GPV_Applicative</a></li>
<li><a href="../theories/crypthol/#Cyclic_Group">Cyclic_Group</a></li>
<li><a href="../theories/crypthol/#Cyclic_Group_SPMF">Cyclic_Group_SPMF</a></li>
<li><a href="../theories/crypthol/#CryptHOL">CryptHOL</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Applicative_Lifting.html">Applicative Lifting</a></li><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/Monad_Normalisation.html">Monad normalisation</a></li><li><a href="../entries/Monomorphic_Monad.html">Effect polymorphism in higher-order logic</a></li><li><a href="../entries/Probabilistic_While.html">Probabilistic while loop</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Sigma_Commit_Crypto.html">Sigma Protocols and Commitment Schemes</a></li><li><a href="../entries/Constructive_Cryptography.html">Constructive Cryptography in HOL</a></li><li><a href="../entries/Game_Based_Crypto.html">Game-based cryptography in HOL</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Attack_Trees.html">Attack Trees in Isabelle for GDPR compliance of IoT healthcare systems</a></li>
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<p style="display:none;" id="bibtex-filename">CryptHOL-AFP</p><pre id="copy-text">@article{CryptHOL-AFP,
author = {Andreas Lochbihler},
title = {CryptHOL},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/CryptHOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-CryptHOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CryptHOL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CryptHOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptHOL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptHOL-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptHOL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-CryptHOL-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptHOL-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptHOL-2017-05-11.tar.gz">May 11, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/CryptoBasedCompositionalProperties.html b/web/entries/CryptoBasedCompositionalProperties.html
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<h1 >
<span class='first'>C</span>ompositional <span class='first'>P</span>roperties of <span class='first'>C</span>rypto-<span class='first'>B</span>ased <span class='first'>C</span>omponents</h1>
<div>
<p><a href="../authors/spichkova">Maria Spichkova</a> <a class="obfuscated" data="eyJob3N0IjpbInJtaXQiLCJlZHUiLCJhdSJdLCJ1c2VyIjpbIm1hcmlhIiwic3BpY2hrb3ZhIl19">📧</a>
</p>
<p class="date">January 11, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This paper presents an Isabelle/HOL set of theories which allows the specification of crypto-based components and the verification of their composition properties wrt. cryptographic aspects. We introduce a formalisation of the security property of data secrecy, the corresponding definitions and proofs. Please note that here we import the Isabelle/HOL theory ListExtras.thy, presented in the AFP entry FocusStreamsCaseStudies-AFP.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session CryptoBasedCompositionalProperties</h3>
<ul>
<li><a href="../theories/cryptobasedcompositionalproperties/#ListExtras">ListExtras</a></li>
<li><a href="../theories/cryptobasedcompositionalproperties/#Secrecy_types">Secrecy_types</a></li>
<li><a href="../theories/cryptobasedcompositionalproperties/#inout">inout</a></li>
<li><a href="../theories/cryptobasedcompositionalproperties/#Secrecy">Secrecy</a></li>
<li><a href="../theories/cryptobasedcompositionalproperties/#CompLocalSecrets">CompLocalSecrets</a></li>
<li><a href="../theories/cryptobasedcompositionalproperties/#KnowledgeKeysSecrets">KnowledgeKeysSecrets</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">CryptoBasedCompositionalProperties-AFP</p><pre id="copy-text">@article{CryptoBasedCompositionalProperties-AFP,
author = {Maria Spichkova},
title = {Compositional Properties of Crypto-Based Components},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/CryptoBasedCompositionalProperties.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2014-01-14.tar.gz">Jan 14, 2014</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-CryptoBasedCompositionalProperties-2014-01-11.tar.gz">Jan 11, 2014</a>: Isabelle2013-2
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<h1 >
<span class='first'>S</span>olving <span class='first'>C</span>ubic and <span class='first'>Q</span>uartic <span class='first'>E</span>quations</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">September 3, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We formalize Cardano's formula to solve a cubic equation
$$ax^3 + bx^2 + cx + d = 0,$$ as well as Ferrari's formula to
solve a quartic equation. We further turn both formulas into
executable algorithms based on the algebraic number implementation in
the AFP. To this end we also slightly extended this library, namely by
making the minimal polynomial of an algebraic number executable, and
by defining and implementing $n$-th roots of complex
numbers.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Cubic_Quartic_Equations</h3>
<ul>
<li><a href="../theories/cubic_quartic_equations/#Ferraris_Formula">Ferraris_Formula</a></li>
<li><a href="../theories/cubic_quartic_equations/#Cardanos_Formula">Cardanos_Formula</a></li>
<li><a href="../theories/cubic_quartic_equations/#Complex_Roots">Complex_Roots</a></li>
<li><a href="../theories/cubic_quartic_equations/#Cubic_Polynomials">Cubic_Polynomials</a></li>
<li><a href="../theories/cubic_quartic_equations/#Quartic_Polynomials">Quartic_Polynomials</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Complex_Geometry.html">Complex Geometry</a></li><li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Cubic_Quartic_Equations-AFP</p><pre id="copy-text">@article{Cubic_Quartic_Equations-AFP,
author = {René Thiemann},
title = {Solving Cubic and Quartic Equations},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Cubic_Quartic_Equations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Cubic_Quartic_Equations-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Cubic_Quartic_Equations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ramework for <span class='first'>V</span>erifying <span class='first'>D</span>epth-<span class='first'>F</span>irst <span class='first'>S</span>earch <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/neumann">René Neumann</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJyZW5lIiwibmV1bWFubiJdfQ==">📧</a>
</p>
<p class="date">July 5, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
This entry presents a framework for the modular verification of
DFS-based algorithms, which is described in our [CPP-2015] paper. It
provides a generic DFS algorithm framework, that can be parameterized
with user-defined actions on certain events (e.g. discovery of new
node). It comes with an extensible library of invariants, which can
be used to derive invariants of a specific parameterization. Using
refinement techniques, efficient implementations of the algorithms can
easily be derived. Here, the framework comes with templates for a
recursive and a tail-recursive implementation, and also with several
templates for implementing the data structures required by the DFS
algorithm. Finally, this entry contains a set of re-usable DFS-based
algorithms, which illustrate the application of the framework.
</p><p>
[CPP-2015] Peter Lammich, René Neumann: A Framework for Verifying
Depth-First Search Algorithms. CPP 2015: 137-146</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session DFS_Framework</h3>
<ul>
<li><a href="../theories/dfs_framework/#DFS_Framework_Misc">DFS_Framework_Misc</a></li>
<li><a href="../theories/dfs_framework/#DFS_Framework_Refine_Aux">DFS_Framework_Refine_Aux</a></li>
<li><a href="../theories/dfs_framework/#Impl_Rev_Array_Stack">Impl_Rev_Array_Stack</a></li>
<li><a href="../theories/dfs_framework/#On_Stack">On_Stack</a></li>
<li><a href="../theories/dfs_framework/#DFS_Chapter_Framework">DFS_Chapter_Framework</a></li>
<li><a href="../theories/dfs_framework/#Param_DFS">Param_DFS</a></li>
<li><a href="../theories/dfs_framework/#DFS_Invars_Basic">DFS_Invars_Basic</a></li>
<li><a href="../theories/dfs_framework/#DFS_Invars_SCC">DFS_Invars_SCC</a></li>
<li><a href="../theories/dfs_framework/#General_DFS_Structure">General_DFS_Structure</a></li>
<li><a href="../theories/dfs_framework/#Tailrec_Impl">Tailrec_Impl</a></li>
<li><a href="../theories/dfs_framework/#Rec_Impl">Rec_Impl</a></li>
<li><a href="../theories/dfs_framework/#Simple_Impl">Simple_Impl</a></li>
<li><a href="../theories/dfs_framework/#Restr_Impl">Restr_Impl</a></li>
<li><a href="../theories/dfs_framework/#DFS_Framework">DFS_Framework</a></li>
<li><a href="../theories/dfs_framework/#DFS_Chapter_Examples">DFS_Chapter_Examples</a></li>
<li><a href="../theories/dfs_framework/#Cyc_Check">Cyc_Check</a></li>
<li><a href="../theories/dfs_framework/#DFS_Find_Path">DFS_Find_Path</a></li>
<li><a href="../theories/dfs_framework/#Reachable_Nodes">Reachable_Nodes</a></li>
<li><a href="../theories/dfs_framework/#Feedback_Arcs">Feedback_Arcs</a></li>
<li><a href="../theories/dfs_framework/#Nested_DFS">Nested_DFS</a></li>
<li><a href="../theories/dfs_framework/#Tarjan_LowLink">Tarjan_LowLink</a></li>
<li><a href="../theories/dfs_framework/#Tarjan">Tarjan</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li></ul>
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<p style="display:none;" id="bibtex-filename">DFS_Framework-AFP</p><pre id="copy-text">@article{DFS_Framework-AFP,
author = {Peter Lammich and René Neumann},
title = {A Framework for Verifying Depth-First Search Algorithms},
journal = {Archive of Formal Proofs},
month = {July},
year = {2016},
note = {\url{https://isa-afp.org/entries/DFS_Framework.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-DFS_Framework-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-DFS_Framework-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DFS_Framework-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-DFS_Framework-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-DFS_Framework-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-DFS_Framework-2016-07-05.tar.gz">Jul 5, 2016</a>: Isabelle2016
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+++ b/web/entries/DOM_Components.html
@@ -1,188 +1,190 @@
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>W</span>eb <span class='first'>C</span>omponents</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">September 28, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">While the DOM with shadow trees provide the technical basis for
defining web components, the DOM standard neither defines the concept
of web components nor specifies the safety properties that web
components should guarantee. Consequently, the standard also does not
discuss how or even if the methods for modifying the DOM respect
component boundaries. In AFP entry, we present a formally verified
model of web components and define safety properties which ensure that
different web components can only interact with each other using
well-defined interfaces. Moreover, our verification of the application
programming interface (API) of the DOM revealed numerous invariants
that implementations of the DOM API need to preserve to ensure the
integrity of components.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session DOM_Components</h3>
<ul>
<li><a href="../theories/dom_components/#Core_DOM_Components">Core_DOM_Components</a></li>
<li><a href="../theories/dom_components/#Shadow_DOM_Components">Shadow_DOM_Components</a></li>
<li><a href="../theories/dom_components/#fancy_tabs">fancy_tabs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Shadow_DOM.html">A Formal Model of the Document Object Model with Shadow Roots</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/SC_DOM_Components.html">A Formalization of Safely Composable Web Components</a></li>
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<p style="display:none;" id="bibtex-filename">DOM_Components-AFP</p><pre id="copy-text">@article{DOM_Components-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {A Formalization of Web Components},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/DOM_Components.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-DOM_Components-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-DOM_Components-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-DOM_Components-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DOM_Components-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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\ No newline at end of file
diff --git a/web/entries/DPRM_Theorem.html b/web/entries/DPRM_Theorem.html
--- a/web/entries/DPRM_Theorem.html
+++ b/web/entries/DPRM_Theorem.html
@@ -1,215 +1,220 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Diophantine Equations and the DPRM Theorem - Archive of Formal Proofs</title><meta name="description" content="We present a formalization of Matiyasevich&#39;s proof of the DPRM
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<h1 >
<span class='first'>D</span>iophantine <span class='first'>E</span>quations and the <span class='first'>D</span><span class='first'>P</span><span class='first'>R</span><span class='first'>M</span> <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bayer">Jonas Bayer</a>, <a href="../authors/david">Marco David</a>, <a href="../authors/stock">Benedikt Stock</a>, <a href="../authors/pal">Abhik Pal</a>, <a href="../authors/matiyasevich">Yuri Matiyasevich</a> and <a href="../authors/schleicher">Dierk Schleicher</a>
</p>
<p class="date">June 6, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of Matiyasevich's proof of the DPRM
theorem, which states that every recursively enumerable set of natural
numbers is Diophantine. This result from 1970 yields a negative
solution to Hilbert's 10th problem over the integers. To
represent recursively enumerable sets in equations, we implement and
arithmetize register machines. We formalize a general theory of
Diophantine sets and relations to reason about them abstractly. Using
several number-theoretic lemmas, we prove that exponentiation has a
Diophantine representation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session DPRM_Theorem</h3>
<ul>
<li><a href="../theories/dprm_theorem/#Parametric_Polynomials">Parametric_Polynomials</a></li>
<li><a href="../theories/dprm_theorem/#Assignments">Assignments</a></li>
<li><a href="../theories/dprm_theorem/#Diophantine_Relations">Diophantine_Relations</a></li>
<li><a href="../theories/dprm_theorem/#Existential_Quantifier">Existential_Quantifier</a></li>
<li><a href="../theories/dprm_theorem/#Modulo_Divisibility">Modulo_Divisibility</a></li>
<li><a href="../theories/dprm_theorem/#Exponentiation">Exponentiation</a></li>
<li><a href="../theories/dprm_theorem/#Alpha_Sequence">Alpha_Sequence</a></li>
<li><a href="../theories/dprm_theorem/#Exponential_Relation">Exponential_Relation</a></li>
<li><a href="../theories/dprm_theorem/#Digit_Function">Digit_Function</a></li>
<li><a href="../theories/dprm_theorem/#Binomial_Coefficient">Binomial_Coefficient</a></li>
<li><a href="../theories/dprm_theorem/#Binary_Orthogonal">Binary_Orthogonal</a></li>
<li><a href="../theories/dprm_theorem/#Binary_Masking">Binary_Masking</a></li>
<li><a href="../theories/dprm_theorem/#Binary_And">Binary_And</a></li>
<li><a href="../theories/dprm_theorem/#RegisterMachineSpecification">RegisterMachineSpecification</a></li>
<li><a href="../theories/dprm_theorem/#RegisterMachineProperties">RegisterMachineProperties</a></li>
<li><a href="../theories/dprm_theorem/#RegisterMachineSimulation">RegisterMachineSimulation</a></li>
<li><a href="../theories/dprm_theorem/#SingleStepRegister">SingleStepRegister</a></li>
<li><a href="../theories/dprm_theorem/#SingleStepState">SingleStepState</a></li>
<li><a href="../theories/dprm_theorem/#MultipleStepRegister">MultipleStepRegister</a></li>
<li><a href="../theories/dprm_theorem/#MultipleStepState">MultipleStepState</a></li>
<li><a href="../theories/dprm_theorem/#MachineMasking">MachineMasking</a></li>
<li><a href="../theories/dprm_theorem/#MachineEquations">MachineEquations</a></li>
<li><a href="../theories/dprm_theorem/#CommutationRelations">CommutationRelations</a></li>
<li><a href="../theories/dprm_theorem/#MultipleToSingleSteps">MultipleToSingleSteps</a></li>
<li><a href="../theories/dprm_theorem/#Equation_Setup">Equation_Setup</a></li>
<li><a href="../theories/dprm_theorem/#Register_Machine_Sums">Register_Machine_Sums</a></li>
<li><a href="../theories/dprm_theorem/#RM_Sums_Diophantine">RM_Sums_Diophantine</a></li>
<li><a href="../theories/dprm_theorem/#Register_Equations">Register_Equations</a></li>
<li><a href="../theories/dprm_theorem/#State_0_Equation">State_0_Equation</a></li>
<li><a href="../theories/dprm_theorem/#State_d_Equation">State_d_Equation</a></li>
<li><a href="../theories/dprm_theorem/#State_Unique_Equations">State_Unique_Equations</a></li>
<li><a href="../theories/dprm_theorem/#All_State_Equations">All_State_Equations</a></li>
<li><a href="../theories/dprm_theorem/#Mask_Equations">Mask_Equations</a></li>
<li><a href="../theories/dprm_theorem/#Constants_Equations">Constants_Equations</a></li>
<li><a href="../theories/dprm_theorem/#All_Equations_Invariance">All_Equations_Invariance</a></li>
<li><a href="../theories/dprm_theorem/#All_Equations">All_Equations</a></li>
<li><a href="../theories/dprm_theorem/#Machine_Equation_Equivalence">Machine_Equation_Equivalence</a></li>
<li><a href="../theories/dprm_theorem/#DPRM">DPRM</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Digit_Expansions.html">Digit Expansions</a></li><li><a href="../entries/Lucas_Theorem.html">Lucas&rsquo;s Theorem</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Padic_Field.html">p-adic Fields and p-adic Semialgebraic Sets</a></li>
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outline</a>
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<p style="display:none;" id="bibtex-filename">DPRM_Theorem-AFP</p><pre id="copy-text">@article{DPRM_Theorem-AFP,
author = {Jonas Bayer and Marco David and Benedikt Stock and Abhik Pal and Yuri Matiyasevich and Dierk Schleicher},
title = {Diophantine Equations and the DPRM Theorem},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/DPRM_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-DPRM_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-DPRM_Theorem-2022-06-07.tar.gz">Jun 7, 2022</a>: Isabelle2021-1
+ </li></ul>
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\ No newline at end of file
diff --git a/web/entries/DPT-SAT-Solver.html b/web/entries/DPT-SAT-Solver.html
--- a/web/entries/DPT-SAT-Solver.html
+++ b/web/entries/DPT-SAT-Solver.html
@@ -1,196 +1,198 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Fast SAT Solver for Isabelle in Standard ML - Archive of Formal Proofs</title><meta name="description" content="This contribution contains a fast SAT solver for Isabelle written in Standard ML. By loading the theory DPT_SAT_Solver, the SAT solver installs itself..."><meta property="og:title" content="A Fast SAT Solver for Isabelle in Standard ML" />
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ast <span class='first'>S</span><span class='first'>A</span><span class='first'>T</span> <span class='first'>S</span>olver for <span class='first'>I</span>sabelle in <span class='first'>S</span>tandard <span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/heller">Armin Heller</a>
</p>
<p class="date">December 9, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This contribution contains a fast SAT solver for Isabelle written in Standard ML. By loading the theory <tt>DPT_SAT_Solver</tt>, the SAT solver installs itself (under the name ``dptsat'') and certain Isabelle tools like Refute will start using it automatically. This is a port of the DPT (Decision Procedure Toolkit) SAT Solver written in OCaml.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session DPT-SAT-Solver</h3>
<ul>
<li><a href="../theories/dpt-sat-solver/#DPT_SAT_Solver">DPT_SAT_Solver</a></li>
<li><a href="../theories/dpt-sat-solver/#DPT_SAT_Tests">DPT_SAT_Tests</a></li></ul><div class="flex-wrap">
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/DPT-SAT-Solver/document.pdf">Proof
document</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/DPT-SAT-Solver/session_graph.pdf">Dependencies</a></nav>
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<div>
<p style="display:none;" id="bibtex-filename">DPT-SAT-Solver-AFP</p><pre id="copy-text">@article{DPT-SAT-Solver-AFP,
author = {Armin Heller},
title = {A Fast SAT Solver for Isabelle in Standard ML},
journal = {Archive of Formal Proofs},
month = {December},
year = {2009},
note = {\url{https://isa-afp.org/entries/DPT-SAT-Solver.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-DPT-SAT-Solver-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2015-07-27.tar.gz">Jul 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
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<a href="https://www.isa-afp.org/release/afp-DPT-SAT-Solver-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
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<h1 >
<span class='first'>S</span>emantics and <span class='first'>D</span>ata <span class='first'>R</span>efinement of <span class='first'>I</span>nvariant <span class='first'>B</span>ased <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/preoteasa">Viorel Preoteasa</a> <a href="http://users.abo.fi/vpreotea/">🌐</a> and <a href="../authors/back">Ralph-Johan Back</a> <a href="http://users.abo.fi/Ralph-Johan.Back/">🌐</a>
</p>
<p class="date">May 28, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The invariant based programming is a technique of constructing correct programs by first identifying the basic situations (pre- and post-conditions and invariants) that can occur during the execution of the program, and then defining the transitions and proving that they preserve the invariants. Data refinement is a technique of building correct programs working on concrete datatypes as refinements of more abstract programs. In the theories presented here we formalize the predicate transformer semantics for invariant based programs and their data refinement.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 5, 2012</dt>
<dd>Moved some general complete lattice properties to the AFP entry Lattice Properties.
Changed the definition of the data refinement relation to be more general and updated all corresponding theorems.
Added new syntax for demonic and angelic update statements.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session DataRefinementIBP</h3>
<ul>
<li><a href="../theories/datarefinementibp/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/datarefinementibp/#Statements">Statements</a></li>
<li><a href="../theories/datarefinementibp/#Hoare">Hoare</a></li>
<li><a href="../theories/datarefinementibp/#Diagram">Diagram</a></li>
<li><a href="../theories/datarefinementibp/#DataRefinement">DataRefinement</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/LatticeProperties.html">Lattice Properties</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/GraphMarkingIBP.html">Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</a></li></ul>
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<p style="display:none;" id="bibtex-filename">DataRefinementIBP-AFP</p><pre id="copy-text">@article{DataRefinementIBP-AFP,
author = {Viorel Preoteasa and Ralph-Johan Back},
title = {Semantics and Data Refinement of Invariant Based Programs},
journal = {Archive of Formal Proofs},
month = {May},
year = {2010},
note = {\url{https://isa-afp.org/entries/DataRefinementIBP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-DataRefinementIBP-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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<a href="https://www.isa-afp.org/release/afp-DataRefinementIBP-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
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<a href="https://www.isa-afp.org/release/afp-DataRefinementIBP-2010-05-28.tar.gz">May 28, 2010</a>: Isabelle2009-1
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diff --git a/web/entries/Datatype_Order_Generator.html b/web/entries/Datatype_Order_Generator.html
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<h1 >
<span class='first'>G</span>enerating <span class='first'>L</span>inear <span class='first'>O</span>rders for <span class='first'>D</span>atatypes</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">August 7, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a framework for registering automatic methods to derive
class instances of datatypes, as it is possible using Haskell's ``deriving Ord, Show, ...'' feature.
<p>
We further implemented such automatic methods to derive (linear) orders or hash-functions which are
required in the Isabelle Collection Framework. Moreover, for the tactic of Huffman and Krauss to show that a
datatype is countable, we implemented a wrapper so that this tactic becomes accessible in our framework.
<p>
Our formalization was performed as part of the <a href="http://cl-informatik.uibk.ac.at/software/ceta">IsaFoR/CeTA</a> project.
With our new tactic we could completely remove
tedious proofs for linear orders of two datatypes.
<p>
This development is aimed at datatypes generated by the "old_datatype"
command.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Datatype_Order_Generator</h3>
<ul>
<li><a href="../theories/datatype_order_generator/#Derive_Aux">Derive_Aux</a></li>
<li><a href="../theories/datatype_order_generator/#Order_Generator">Order_Generator</a></li>
<li><a href="../theories/datatype_order_generator/#Hash_Generator">Hash_Generator</a></li>
<li><a href="../theories/datatype_order_generator/#Derive">Derive</a></li>
<li><a href="../theories/datatype_order_generator/#Derive_Examples">Derive_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li></ul>
</div><div>
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<ul class="horizontal-list"><li><a href="../entries/FSM_Tests.html">Verified Complete Test Strategies for Finite State Machines</a></li><li><a href="../entries/WOOT_Strong_Eventual_Consistency.html">Strong Eventual Consistency of the Collaborative Editing Framework WOOT</a></li><li><a href="../entries/Higher_Order_Terms.html">An Algebra for Higher-Order Terms</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Datatype_Order_Generator-AFP</p><pre id="copy-text">@article{Datatype_Order_Generator-AFP,
author = {René Thiemann},
title = {Generating linear orders for datatypes},
journal = {Archive of Formal Proofs},
month = {August},
year = {2012},
note = {\url{https://isa-afp.org/entries/Datatype_Order_Generator.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Datatype_Order_Generator-2012-08-07.tar.gz">Aug 7, 2012</a>: Isabelle2012
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<h1 >
<span class='first'>D</span>eclarative <span class='first'>S</span>emantics for <span class='first'>F</span>unctional <span class='first'>L</span>anguages</h1>
<div>
<p><a href="../authors/siek">Jeremy Siek</a> <a href="http://homes.soic.indiana.edu/jsiek/">🌐</a>
</p>
<p class="date">July 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a semantics for an applied call-by-value lambda-calculus
that is compositional, extensional, and elementary. We present four
different views of the semantics: 1) as a relational (big-step)
semantics that is not operational but instead declarative, 2) as a
denotational semantics that does not use domain theory, 3) as a
non-deterministic interpreter, and 4) as a variant of the intersection
type systems of the Torino group. We prove that the semantics is
correct by showing that it is sound and complete with respect to
operational semantics on programs and that is sound with respect to
contextual equivalence. We have not yet investigated whether it is
fully abstract. We demonstrate that this approach to semantics is
useful with three case studies. First, we use the semantics to prove
correctness of a compiler optimization that inlines function
application. Second, we adapt the semantics to the polymorphic
lambda-calculus extended with general recursion and prove semantic
type soundness. Third, we adapt the semantics to the call-by-value
lambda-calculus with mutable references.
<br>
The paper that accompanies these Isabelle theories is <a href="https://arxiv.org/abs/1707.03762">available on arXiv</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages">Computer science/Programming languages</a></li></ul>
<h3>Session Decl_Sem_Fun_PL</h3>
<ul>
<li><a href="../theories/decl_sem_fun_pl/#Lambda">Lambda</a></li>
<li><a href="../theories/decl_sem_fun_pl/#SmallStepLam">SmallStepLam</a></li>
<li><a href="../theories/decl_sem_fun_pl/#BigStepLam">BigStepLam</a></li>
<li><a href="../theories/decl_sem_fun_pl/#ValuesFSet">ValuesFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#ValuesFSetProps">ValuesFSetProps</a></li>
<li><a href="../theories/decl_sem_fun_pl/#RelationalSemFSet">RelationalSemFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DeclSemAsDenotFSet">DeclSemAsDenotFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#EquivRelationalDenotFSet">EquivRelationalDenotFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#ChangeEnv">ChangeEnv</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DeclSemAsNDInterpFSet">DeclSemAsNDInterpFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#InterTypeSystem">InterTypeSystem</a></li>
<li><a href="../theories/decl_sem_fun_pl/#Values">Values</a></li>
<li><a href="../theories/decl_sem_fun_pl/#ValueProps">ValueProps</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DeclSemAsDenot">DeclSemAsDenot</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DenotLam5">DenotLam5</a></li>
<li><a href="../theories/decl_sem_fun_pl/#EquivDenotInterTypes">EquivDenotInterTypes</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DenotSoundFSet">DenotSoundFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DenotCompleteFSet">DenotCompleteFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DenotCongruenceFSet">DenotCongruenceFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#DenotEqualitiesFSet">DenotEqualitiesFSet</a></li>
<li><a href="../theories/decl_sem_fun_pl/#Optimizer">Optimizer</a></li>
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<p style="display:none;" id="bibtex-filename">Decl_Sem_Fun_PL-AFP</p><pre id="copy-text">@article{Decl_Sem_Fun_PL-AFP,
author = {Jeremy Siek},
title = {Declarative Semantics for Functional Languages},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/Decl_Sem_Fun_PL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>D</span>ecreasing <span class='first'>D</span>iagrams <span class='first'>I</span><span class='first'>I</span></h1>
<div>
<p><a href="../authors/felgenhauer">Bertram Felgenhauer</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYmVydHJhbSIsImZlbGdlbmhhdWVyIl19">📧</a>
</p>
<p class="date">August 20, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory formalizes the commutation version of decreasing diagrams for Church-Rosser modulo. The proof follows Felgenhauer and van Oostrom (RTA 2013). The theory also provides important specializations, in particular van Oostrom’s conversion version (TCS 2008) of decreasing diagrams.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Decreasing-Diagrams-II</h3>
<ul>
<li><a href="../theories/decreasing-diagrams-ii/#Decreasing_Diagrams_II_Aux">Decreasing_Diagrams_II_Aux</a></li>
<li><a href="../theories/decreasing-diagrams-ii/#Decreasing_Diagrams_II">Decreasing_Diagrams_II</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Open_Induction.html">Open Induction</a></li><li><a href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Decreasing-Diagrams.html">Decreasing Diagrams</a></li>
<li><a href="../entries/Rewriting_Z.html">The Z Property</a></li>
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<p style="display:none;" id="bibtex-filename">Decreasing-Diagrams-II-AFP</p><pre id="copy-text">@article{Decreasing-Diagrams-II-AFP,
author = {Bertram Felgenhauer},
title = {Decreasing Diagrams II},
journal = {Archive of Formal Proofs},
month = {August},
year = {2015},
note = {\url{https://isa-afp.org/entries/Decreasing-Diagrams-II.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-II-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Decreasing-Diagrams.html b/web/entries/Decreasing-Diagrams.html
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<h1 >
<span class='first'>D</span>ecreasing <span class='first'>D</span>iagrams</h1>
<div>
<p><a href="../authors/zankl">Harald Zankl</a> <a href="http://cl-informatik.uibk.ac.at/users/hzankl">🌐</a>
</p>
<p class="date">November 1, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory contains a formalization of decreasing diagrams showing that any locally decreasing abstract rewrite system is confluent. We consider the valley (van Oostrom, TCS 1994) and the conversion version (van Oostrom, RTA 2008) and closely follow the original proofs. As an application we prove Newman's lemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Decreasing-Diagrams</h3>
<ul>
<li><a href="../theories/decreasing-diagrams/#Decreasing_Diagrams">Decreasing_Diagrams</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Decreasing-Diagrams-II.html">Decreasing Diagrams II</a></li>
<li><a href="../entries/Stewart_Apollonius.html">Stewart&rsquo;s Theorem and Apollonius' Theorem</a></li>
<li><a href="../entries/Rewriting_Z.html">The Z Property</a></li>
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<p style="display:none;" id="bibtex-filename">Decreasing-Diagrams-AFP</p><pre id="copy-text">@article{Decreasing-Diagrams-AFP,
author = {Harald Zankl},
title = {Decreasing Diagrams},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/Decreasing-Diagrams.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2013-12-02.tar.gz">Dec 2, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Decreasing-Diagrams-2013-11-18.tar.gz">Nov 18, 2013</a>: Isabelle2013-1
</li></ul>
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diff --git a/web/entries/Dedekind_Real.html b/web/entries/Dedekind_Real.html
--- a/web/entries/Dedekind_Real.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Constructing the Reals as Dedekind Cuts of Rationals - Archive of Formal Proofs</title><meta name="description" content="The type of real numbers is constructed from the positive rationals
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<h1 >
<span class='first'>C</span>onstructing the <span class='first'>R</span>eals as <span class='first'>D</span>edekind <span class='first'>C</span>uts of <span class='first'>R</span>ationals</h1>
<div>
<p><a href="../authors/fleuriot">Jacques D. Fleuriot</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
</p>
<p class="date">March 24, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The type of real numbers is constructed from the positive rationals
using the method of Dedekind cuts. This development, briefly described
in papers by the authors, follows the textbook presentation by
Gleason. It's notable that the first formalisation of a
significant piece of mathematics, by Jutting in 1977, involved a
similar construction.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Dedekind_Real</h3>
<ul>
<li><a href="../theories/dedekind_real/#Dedekind_Real">Dedekind_Real</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Dedekind_Real-AFP</p><pre id="copy-text">@article{Dedekind_Real-AFP,
author = {Jacques D. Fleuriot and Lawrence C. Paulson},
title = {Constructing the Reals as Dedekind Cuts of Rationals},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/Dedekind_Real.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Dedekind_Real-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Dedekind_Real-2022-03-29.tar.gz">Mar 29, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Deep_Learning.html b/web/entries/Deep_Learning.html
--- a/web/entries/Deep_Learning.html
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@@ -1,214 +1,216 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Expressiveness of Deep Learning - Archive of Formal Proofs</title><meta name="description" content="Deep learning has had a profound impact on computer science in recent years, with applications to search engines, image recognition and language..."><meta property="og:title" content="Expressiveness of Deep Learning" />
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<h1 >
<span class='first'>E</span>xpressiveness of <span class='first'>D</span>eep <span class='first'>L</span>earning</h1>
<div>
<p><a href="../authors/bentkamp">Alexander Bentkamp</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYmVudGthbXAiXX0=">📧</a>
</p>
<p class="date">November 10, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Deep learning has had a profound impact on computer science in recent years, with applications to search engines, image recognition and language processing, bioinformatics, and more. Recently, Cohen et al. provided theoretical evidence for the superiority of deep learning over shallow learning. This formalization of their work simplifies and generalizes the original proof, while working around the limitations of the Isabelle type system. To support the formalization, I developed reusable libraries of formalized mathematics, including results about the matrix rank, the Lebesgue measure, and multivariate polynomials, as well as a library for tensor analysis.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/machine-learning">Computer science/Machine learning</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Deep_Learning</h3>
<ul>
<li><a href="../theories/deep_learning/#Tensor">Tensor</a></li>
<li><a href="../theories/deep_learning/#Tensor_Subtensor">Tensor_Subtensor</a></li>
<li><a href="../theories/deep_learning/#Tensor_Plus">Tensor_Plus</a></li>
<li><a href="../theories/deep_learning/#Tensor_Scalar_Mult">Tensor_Scalar_Mult</a></li>
<li><a href="../theories/deep_learning/#Tensor_Product">Tensor_Product</a></li>
<li><a href="../theories/deep_learning/#Tensor_Unit_Vec">Tensor_Unit_Vec</a></li>
<li><a href="../theories/deep_learning/#Tensor_Rank">Tensor_Rank</a></li>
<li><a href="../theories/deep_learning/#Tensor_Matricization">Tensor_Matricization</a></li>
<li><a href="../theories/deep_learning/#DL_Rank_CP_Rank">DL_Rank_CP_Rank</a></li>
<li><a href="../theories/deep_learning/#DL_Flatten_Matrix">DL_Flatten_Matrix</a></li>
<li><a href="../theories/deep_learning/#DL_Network">DL_Network</a></li>
<li><a href="../theories/deep_learning/#DL_Concrete_Matrices">DL_Concrete_Matrices</a></li>
<li><a href="../theories/deep_learning/#DL_Missing_Finite_Set">DL_Missing_Finite_Set</a></li>
<li><a href="../theories/deep_learning/#DL_Deep_Model">DL_Deep_Model</a></li>
<li><a href="../theories/deep_learning/#DL_Deep_Model_Poly">DL_Deep_Model_Poly</a></li>
<li><a href="../theories/deep_learning/#Lebesgue_Functional">Lebesgue_Functional</a></li>
<li><a href="../theories/deep_learning/#Lebesgue_Zero_Set">Lebesgue_Zero_Set</a></li>
<li><a href="../theories/deep_learning/#DL_Shallow_Model">DL_Shallow_Model</a></li>
<li><a href="../theories/deep_learning/#DL_Fundamental_Theorem_Network_Capacity">DL_Fundamental_Theorem_Network_Capacity</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li><li><a href="../entries/VectorSpace.html">Vector Spaces</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/QHLProver.html">Quantum Hoare Logic</a></li></ul>
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<li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
<li><a href="../entries/Physical_Quantities.html">A Sound Type System for Physical Quantities, Units, and Measurements</a></li>
<li><a href="../entries/WebAssembly.html">WebAssembly</a></li>
<li><a href="../entries/Minkowskis_Theorem.html">Minkowski&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Deep_Learning-AFP</p><pre id="copy-text">@article{Deep_Learning-AFP,
author = {Alexander Bentkamp},
title = {Expressiveness of Deep Learning},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Deep_Learning.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Deep_Learning-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Deep_Learning-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Deep_Learning-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Deep_Learning-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Deep_Learning-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Deep_Learning-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Deep_Learning-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Deep_Learning-2016-11-10.tar.gz">Nov 10, 2016</a>: Isabelle2016
</li></ul>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Cofinality and the Delta System Lemma - Archive of Formal Proofs</title><meta name="description" content="We formalize the basic results on cofinality of linearly ordered sets
and ordinals and Šanin’s Lemma for uncountable families of finite
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<h1 >
<span class='first'>C</span>ofinality and the <span class='first'>D</span>elta <span class='first'>S</span>ystem <span class='first'>L</span>emma</h1>
<div>
<p><a href="../authors/terraf">Pedro Sánchez Terraf</a> <a href="https://cs.famaf.unc.edu.ar/~pedro/home_en.html">🌐</a>
</p>
<p class="date">December 27, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the basic results on cofinality of linearly ordered sets
and ordinals and Šanin’s Lemma for uncountable families of finite
sets. This last result is used to prove the countable chain condition
for Cohen posets. We work in the set theory framework of Isabelle/ZF,
using the Axiom of Choice as needed.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Delta_System_Lemma</h3>
<ul>
<li><a href="../theories/delta_system_lemma/#ZF_Library">ZF_Library</a></li>
<li><a href="../theories/delta_system_lemma/#Cofinality">Cofinality</a></li>
<li><a href="../theories/delta_system_lemma/#Cardinal_Library">Cardinal_Library</a></li>
<li><a href="../theories/delta_system_lemma/#Konig">Konig</a></li>
<li><a href="../theories/delta_system_lemma/#Delta_System">Delta_System</a></li>
<li><a href="../theories/delta_system_lemma/#Cohen_Posets">Cohen_Posets</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Transitive_Models.html">Transitive Models of Fragments of ZFC</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Delta_System_Lemma-AFP</p><pre id="copy-text">@article{Delta_System_Lemma-AFP,
author = {Pedro Sánchez Terraf},
title = {Cofinality and the Delta System Lemma},
journal = {Archive of Formal Proofs},
month = {December},
year = {2020},
note = {\url{https://isa-afp.org/entries/Delta_System_Lemma.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Delta_System_Lemma-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Delta_System_Lemma-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Delta_System_Lemma-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Delta_System_Lemma-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Delta_System_Lemma-2020-12-28.tar.gz">Dec 28, 2020</a>: Isabelle2020
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diff --git a/web/entries/Density_Compiler.html b/web/entries/Density_Compiler.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Verified Compiler for Probability Density Functions - Archive of Formal Proofs</title><meta name="description" content="Bhat et al. [TACAS 2013] developed an inductive compiler that computes density functions for probability spaces described by programs in a probabilistic..."><meta property="og:title" content="A Verified Compiler for Probability Density Functions" />
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>C</span>ompiler for <span class='first'>P</span>robability <span class='first'>D</span>ensity <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>, <a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">October 9, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><a href="https://doi.org/10.1007/978-3-642-36742-7_35">Bhat et al. [TACAS 2013]</a> developed an inductive compiler that computes
density functions for probability spaces described by programs in a
probabilistic functional language. In this work, we implement such a
compiler for a modified version of this language within the theorem prover
Isabelle and give a formal proof of its soundness w.r.t. the semantics of
the source and target language. Together with Isabelle's code generation
for inductive predicates, this yields a fully verified, executable density
compiler. The proof is done in two steps: First, an abstract compiler
working with abstract functions modelled directly in the theorem prover's
logic is defined and proved sound. Then, this compiler is refined to a
concrete version that returns a target-language expression.
<p>
An article with the same title and authors is published in the proceedings
of ESOP 2015.
A detailed presentation of this work can be found in the first author's
master's thesis with the same title.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul><h3>Related publications</h3>
<ul><li>
Eberl, M., Hölzl, J., & Nipkow, T. (2015). A Verified Compiler for Probability Density Functions. Lecture Notes in Computer Science, 80–104. <a href="https://doi.org/10.1007/978-3-662-46669-8_4">https://doi.org/10.1007/978-3-662-46669-8_4</a>
</li><li>
<a href="https://arxiv.org/abs/1707.06901">arxiv</a>
</li></ul>
<h3>Session Density_Compiler</h3>
<ul>
<li><a href="../theories/density_compiler/#Density_Predicates">Density_Predicates</a></li>
<li><a href="../theories/density_compiler/#PDF_Transformations">PDF_Transformations</a></li>
<li><a href="../theories/density_compiler/#PDF_Values">PDF_Values</a></li>
<li><a href="../theories/density_compiler/#PDF_Semantics">PDF_Semantics</a></li>
<li><a href="../theories/density_compiler/#PDF_Density_Contexts">PDF_Density_Contexts</a></li>
<li><a href="../theories/density_compiler/#PDF_Compiler_Pred">PDF_Compiler_Pred</a></li>
<li><a href="../theories/density_compiler/#PDF_Target_Semantics">PDF_Target_Semantics</a></li>
<li><a href="../theories/density_compiler/#PDF_Target_Density_Contexts">PDF_Target_Density_Contexts</a></li>
<li><a href="../theories/density_compiler/#PDF_Compiler">PDF_Compiler</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Density_Compiler-AFP</p><pre id="copy-text">@article{Density_Compiler-AFP,
author = {Manuel Eberl and Johannes Hölzl and Tobias Nipkow},
title = {A Verified Compiler for Probability Density Functions},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/Density_Compiler.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Density_Compiler-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Density_Compiler-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Density_Compiler-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2014-12-22.tar.gz">Dec 22, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Density_Compiler-2014-10-09.tar.gz">Oct 9, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>C</span>ompositional <span class='first'>S</span>ecurity-<span class='first'>P</span>reserving <span class='first'>R</span>efinement for <span class='first'>C</span>oncurrent <span class='first'>I</span>mperative <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/murray">Toby Murray</a> <a href="https://people.eng.unimelb.edu.au/tobym/">🌐</a>, <a href="../authors/sison">Robert Sison</a>, <a href="../authors/pierzchalski">Edward Pierzchalski</a> and <a href="../authors/rizkallah">Christine Rizkallah</a> <a href="https://www.mpi-inf.mpg.de/~crizkall/">🌐</a>
</p>
<p class="date">June 28, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The paper "Compositional Verification and Refinement of Concurrent
Value-Dependent Noninterference" by Murray et. al. (CSF 2016) presents
a compositional theory of refinement for a value-dependent
noninterference property, defined in (Murray, PLAS 2015), for
concurrent programs. This development formalises that refinement
theory, and demonstrates its application on some small examples.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 2, 2016</dt>
<dd>TobyM extended "simple" refinement theory to be usable for all bisimulations.
(revision 547f31c25f60)</dd><dt>August 19, 2016</dt>
<dd>Removed unused "stop" parameters from the sifum_refinement locale.
(revision dbc482d36372)
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Dependent_SIFUM_Refinement</h3>
<ul>
<li><a href="../theories/dependent_sifum_refinement/#CompositionalRefinement">CompositionalRefinement</a></li>
<li><a href="../theories/dependent_sifum_refinement/#Eg1">Eg1</a></li>
<li><a href="../theories/dependent_sifum_refinement/#Eg1RefinementTrivial">Eg1RefinementTrivial</a></li>
<li><a href="../theories/dependent_sifum_refinement/#Eg2">Eg2</a></li>
<li><a href="../theories/dependent_sifum_refinement/#Eg1Eg2">Eg1Eg2</a></li>
<li><a href="../theories/dependent_sifum_refinement/#Eg1Eg2RefinementSimple">Eg1Eg2RefinementSimple</a></li>
<li><a href="../theories/dependent_sifum_refinement/#EgHighBranchRevC">EgHighBranchRevC</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Dependent_SIFUM_Type_Systems.html">A Dependent Security Type System for Concurrent Imperative Programs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Dependent_SIFUM_Refinement-AFP</p><pre id="copy-text">@article{Dependent_SIFUM_Refinement-AFP,
author = {Toby Murray and Robert Sison and Edward Pierzchalski and Christine Rizkallah},
title = {Compositional Security-Preserving Refinement for Concurrent Imperative Programs},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Dependent_SIFUM_Refinement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Dependent_SIFUM_Refinement-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span> <span class='first'>D</span>ependent <span class='first'>S</span>ecurity <span class='first'>T</span>ype <span class='first'>S</span>ystem for <span class='first'>C</span>oncurrent <span class='first'>I</span>mperative <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/murray">Toby Murray</a> <a href="https://people.eng.unimelb.edu.au/tobym/">🌐</a>, <a href="../authors/sison">Robert Sison</a>, <a href="../authors/pierzchalski">Edward Pierzchalski</a> and <a href="../authors/rizkallah">Christine Rizkallah</a> <a href="https://www.mpi-inf.mpg.de/~crizkall/">🌐</a>
</p>
<p class="date">June 25, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The paper "Compositional Verification and Refinement of Concurrent
Value-Dependent Noninterference" by Murray et. al. (CSF 2016) presents
a dependent security type system for compositionally verifying a
value-dependent noninterference property, defined in (Murray, PLAS
2015), for concurrent programs. This development formalises that
security definition, the type system and its soundness proof, and
demonstrates its application on some small examples. It was derived
from the SIFUM_Type_Systems AFP entry, by Sylvia Grewe, Heiko Mantel
and Daniel Schoepe, and whose structure it inherits.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 27, 2016</dt>
<dd>Added security locale support for the imposition of requirements on the initial memory.
(revision cce4ceb74ddb)</dd><dt>August 19, 2016</dt>
<dd>Removed unused "stop" parameter and "stop_no_eval" assumption from the sifum_security locale.
(revision dbc482d36372)
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session Dependent_SIFUM_Type_Systems</h3>
<ul>
<li><a href="../theories/dependent_sifum_type_systems/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Security">Security</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Compositionality">Compositionality</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Language">Language</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#TypeSystem">TypeSystem</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#LocallySoundModeUse">LocallySoundModeUse</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Example">Example</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#TypeSystemTactics">TypeSystemTactics</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Example_TypeSystem">Example_TypeSystem</a></li>
<li><a href="../theories/dependent_sifum_type_systems/#Example_Swap_Add">Example_Swap_Add</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Dependent_SIFUM_Refinement.html">Compositional Security-Preserving Refinement for Concurrent Imperative Programs</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Dependent_SIFUM_Type_Systems-AFP</p><pre id="copy-text">@article{Dependent_SIFUM_Type_Systems-AFP,
author = {Toby Murray and Robert Sison and Edward Pierzchalski and Christine Rizkallah},
title = {A Dependent Security Type System for Concurrent Imperative Programs},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Dependent_SIFUM_Type_Systems.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Dependent_SIFUM_Type_Systems-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Dependent_SIFUM_Type_Systems-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>D</span>epth <span class='first'>F</span>irst <span class='first'>S</span>earch</h1>
<div>
<p><a href="../authors/nishihara">Toshiaki Nishihara</a> and <a href="../authors/minamide">Yasuhiko Minamide</a>
</p>
<p class="date">June 24, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Depth-first search of a graph is formalized with recdef. It is shown that it visits all of the reachable nodes from a given list of nodes. Executable ML code of depth-first search is obtained using the code generation feature of Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Depth-First-Search</h3>
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author = {Toshiaki Nishihara and Yasuhiko Minamide},
title = {Depth First Search},
journal = {Archive of Formal Proofs},
month = {June},
year = {2004},
note = {\url{https://isa-afp.org/entries/Depth-First-Search.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>D</span>erangements <span class='first'>F</span>ormula</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">June 27, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Derangements Formula describes the number of fixpoint-free permutations
as a closed formula. This theorem is the 88th theorem in a list of the
``<a href="http://www.cs.ru.nl/~freek/100/">Top 100 Mathematical Theorems</a>''.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Derangements</h3>
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<li><a href="../theories/derangements/#Derangements">Derangements</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Derangements-AFP</p><pre id="copy-text">@article{Derangements-AFP,
author = {Lukas Bulwahn},
title = {Derangements Formula},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/Derangements.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Derangements-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>D</span>eriving <span class='first'>C</span>lass <span class='first'>I</span>nstances for <span class='first'>D</span>atatypes</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
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<p class="date">March 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We provide a framework for registering automatic methods
to derive class instances of datatypes,
as it is possible using Haskell's ``deriving Ord, Show, ...'' feature.</p>
<p>We further implemented such automatic methods to derive comparators, linear orders, parametrizable equality functions,
and hash-functions which are required in the
Isabelle Collection Framework and the Container Framework.
Moreover, for the tactic of Blanchette to show that a datatype is countable, we implemented a
wrapper so that this tactic becomes accessible in our framework. All of the generators are based on
the infrastructure that is provided by the BNF-based datatype package.</p>
<p>Our formalization was performed as part of the <a href="http://cl-informatik.uibk.ac.at/software/ceta">IsaFoR/CeTA</a> project.
With our new tactics we could remove
several tedious proofs for (conditional) linear orders, and conditional equality operators
within IsaFoR and the Container Framework.</p></div>
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<ul class="horizontal-list"><li><a href="../entries/Safe_Range_RC.html">Making Arbitrary Relational Calculus Queries Safe-Range</a></li><li><a href="../entries/Van_Emde_Boas_Trees.html">van Emde Boas Trees</a></li><li><a href="../entries/LTL_Master_Theorem.html">A Compositional and Unified Translation of LTL into ω-Automata</a></li><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/MSO_Regex_Equivalence.html">Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</a></li><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></li><li><a href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li>
<li><a href="../entries/Certification_Monads.html">Certification Monads</a></li>
<li><a href="../entries/XML.html">XML</a></li>
<li><a href="../entries/Transitive-Closure-II.html">Executable Transitive Closures</a></li>
<li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li>
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<p style="display:none;" id="bibtex-filename">Deriving-AFP</p><pre id="copy-text">@article{Deriving-AFP,
author = {Christian Sternagel and René Thiemann},
title = {Deriving class instances for datatypes},
journal = {Archive of Formal Proofs},
month = {March},
year = {2015},
note = {\url{https://isa-afp.org/entries/Deriving.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>D</span>escartes' <span class='first'>R</span>ule of <span class='first'>S</span>igns</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Descartes' Rule of Signs relates the number of positive real roots of a
polynomial with the number of sign changes in its coefficient sequence.
</p><p>
Our proof follows the simple inductive proof given by Rob Arthan, which was also
used by John Harrison in his HOL Light formalisation. We proved most of the
lemmas for arbitrary linearly-ordered integrity domains (e.g. integers,
rationals, reals); the main result, however, requires the intermediate value
theorem and was therefore only proven for real polynomials.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Descartes_Sign_Rule</h3>
<ul>
<li><a href="../theories/descartes_sign_rule/#Descartes_Sign_Rule">Descartes_Sign_Rule</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Descartes_Sign_Rule-AFP</p><pre id="copy-text">@article{Descartes_Sign_Rule-AFP,
author = {Manuel Eberl},
title = {Descartes&#39; Rule of Signs},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Descartes_Sign_Rule.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Design_Theory.html b/web/entries/Design_Theory.html
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<h1 >
<span class='first'>C</span>ombinatorial <span class='first'>D</span>esign <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">August 13, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Combinatorial design theory studies incidence set systems with certain
balance and symmetry properties. It is closely related to hypergraph
theory. This formalisation presents a general library for formal
reasoning on incidence set systems, designs and their applications,
including formal definitions and proofs for many key properties,
operations, and theorems on the construction and existence of designs.
Notably, this includes formalising t-designs, balanced incomplete
block designs (BIBD), group divisible designs (GDD), pairwise balanced
designs (PBD), design isomorphisms, and the relationship between
graphs and designs. A locale-centric approach has been used to manage
the relationships between the many different types of designs.
Theorems of particular interest include the necessary conditions for
existence of a BIBD, Wilson's construction on GDDs, and
Bose's inequality on resolvable designs. Parts of this
formalisation are explored in the paper "A Modular First
Formalisation of Combinatorial Design Theory", presented at CICM 2021.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Design_Theory</h3>
<ul>
<li><a href="../theories/design_theory/#Multisets_Extras">Multisets_Extras</a></li>
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<li><a href="../theories/design_theory/#Block_Designs">Block_Designs</a></li>
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<li><a href="../theories/design_theory/#Resolvable_Designs">Resolvable_Designs</a></li>
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<li><a href="../theories/design_theory/#Designs_And_Graphs">Designs_And_Graphs</a></li>
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<li><a href="../theories/design_theory/#Design_Theory_Root">Design_Theory_Root</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Card_Partitions.html">Cardinality of Set Partitions</a></li><li><a href="../entries/Graph_Theory.html">Graph Theory</a></li><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Undirected_Graph_Theory.html">Undirected Graph Theory</a></li><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Design_Theory-AFP</p><pre id="copy-text">@article{Design_Theory-AFP,
author = {Chelsea Edmonds and Lawrence C. Paulson},
title = {Combinatorial Design Theory},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/Design_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Dict_Construction.html b/web/entries/Dict_Construction.html
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@@ -1,189 +1,191 @@
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<h1 >
<span class='first'>D</span>ictionary <span class='first'>C</span>onstruction</h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">May 24, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle's code generator natively supports type classes. For
targets that do not have language support for classes and instances,
it performs the well-known dictionary translation, as described by
Haftmann and Nipkow. This translation happens outside the logic, i.e.,
there is no guarantee that it is correct, besides the pen-and-paper
proof. This work implements a certified dictionary translation that
produces new class-free constants and derives equality theorems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Dict_Construction</h3>
<ul>
<li><a href="../theories/dict_construction/#Introduction">Introduction</a></li>
<li><a href="../theories/dict_construction/#Impossibility">Impossibility</a></li>
<li><a href="../theories/dict_construction/#Dict_Construction">Dict_Construction</a></li>
<li><a href="../theories/dict_construction/#Termination">Termination</a></li>
<li><a href="../theories/dict_construction/#Test_Dict_Construction">Test_Dict_Construction</a></li>
<li><a href="../theories/dict_construction/#Test_Side_Conditions">Test_Side_Conditions</a></li>
<li><a href="../theories/dict_construction/#Test_Lazy_Case">Test_Lazy_Case</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Lazy_Case.html">Lazifying case constants</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li></ul>
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document</a>
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<p style="display:none;" id="bibtex-filename">Dict_Construction-AFP</p><pre id="copy-text">@article{Dict_Construction-AFP,
author = {Lars Hupel},
title = {Dictionary Construction},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Dict_Construction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Dict_Construction-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Dict_Construction-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Dict_Construction-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dict_Construction-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dict_Construction-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dict_Construction-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dict_Construction-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dict_Construction-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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\ No newline at end of file
diff --git a/web/entries/Differential_Dynamic_Logic.html b/web/entries/Differential_Dynamic_Logic.html
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<h1 >
<span class='first'>D</span>ifferential <span class='first'>D</span>ynamic <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/bohrer">Rose Bohrer</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicm9zZSIsImJvaHJlciIsImNzIl19">📧</a>
</p>
<p class="date">February 13, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize differential dynamic logic, a logic for proving
properties of hybrid systems. The proof calculus in this formalization
is based on the uniform substitution principle. We show it is sound
with respect to our denotational semantics, which provides increased
confidence in the correctness of the KeYmaera X theorem prover based
on this calculus. As an application, we include a proof term checker
embedded in Isabelle/HOL with several example proofs. Published in:
Rose Bohrer, Vincent Rahli, Ivana Vukotic, Marcus Völp, André
Platzer: Formally verified differential dynamic logic. CPP 2017.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Differential_Dynamic_Logic</h3>
<ul>
<li><a href="../theories/differential_dynamic_logic/#Ids">Ids</a></li>
<li><a href="../theories/differential_dynamic_logic/#Lib">Lib</a></li>
<li><a href="../theories/differential_dynamic_logic/#Syntax">Syntax</a></li>
<li><a href="../theories/differential_dynamic_logic/#Denotational_Semantics">Denotational_Semantics</a></li>
<li><a href="../theories/differential_dynamic_logic/#Axioms">Axioms</a></li>
<li><a href="../theories/differential_dynamic_logic/#Frechet_Correctness">Frechet_Correctness</a></li>
<li><a href="../theories/differential_dynamic_logic/#Static_Semantics">Static_Semantics</a></li>
<li><a href="../theories/differential_dynamic_logic/#Coincidence">Coincidence</a></li>
<li><a href="../theories/differential_dynamic_logic/#Bound_Effect">Bound_Effect</a></li>
<li><a href="../theories/differential_dynamic_logic/#Differential_Axioms">Differential_Axioms</a></li>
<li><a href="../theories/differential_dynamic_logic/#USubst">USubst</a></li>
<li><a href="../theories/differential_dynamic_logic/#USubst_Lemma">USubst_Lemma</a></li>
<li><a href="../theories/differential_dynamic_logic/#Uniform_Renaming">Uniform_Renaming</a></li>
<li><a href="../theories/differential_dynamic_logic/#Pretty_Printer">Pretty_Printer</a></li>
<li><a href="../theories/differential_dynamic_logic/#Proof_Checker">Proof_Checker</a></li>
<li><a href="../theories/differential_dynamic_logic/#Differential_Dynamic_Logic">Differential_Dynamic_Logic</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Abs_Int_ITP2012.html">Abstract Interpretation of Annotated Commands</a></li>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Differential_Dynamic_Logic/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Differential_Dynamic_Logic-AFP</p><pre id="copy-text">@article{Differential_Dynamic_Logic-AFP,
author = {Rose Bohrer},
title = {Differential Dynamic Logic},
journal = {Archive of Formal Proofs},
month = {February},
year = {2017},
note = {\url{https://isa-afp.org/entries/Differential_Dynamic_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Dynamic_Logic-2017-02-14.tar.gz">Feb 14, 2017</a>: Isabelle2016-1
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Differential_Game_Logic.html b/web/entries/Differential_Game_Logic.html
--- a/web/entries/Differential_Game_Logic.html
+++ b/web/entries/Differential_Game_Logic.html
@@ -1,188 +1,190 @@
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<h1 >
<span class='first'>D</span>ifferential <span class='first'>G</span>ame <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/platzer">André Platzer</a> <a href="https://www.cs.cmu.edu/~aplatzer/">🌐</a>
</p>
<p class="date">June 3, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalization provides differential game logic (dGL), a logic for
proving properties of hybrid game. In addition to the syntax and
semantics, it formalizes a uniform substitution calculus for dGL.
Church's uniform substitutions substitute a term or formula for a
function or predicate symbol everywhere. The uniform substitutions for
dGL also substitute hybrid games for a game symbol everywhere. We
prove soundness of one-pass uniform substitutions and the axioms of
differential game logic with respect to their denotational semantics.
One-pass uniform substitutions are faster by postponing
soundness-critical admissibility checks with a linear pass homomorphic
application and regain soundness by a variable condition at the
replacements. The formalization is based on prior non-mechanized
soundness proofs for dGL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Differential_Game_Logic</h3>
<ul>
<li><a href="../theories/differential_game_logic/#Lib">Lib</a></li>
<li><a href="../theories/differential_game_logic/#Identifiers">Identifiers</a></li>
<li><a href="../theories/differential_game_logic/#Syntax">Syntax</a></li>
<li><a href="../theories/differential_game_logic/#Denotational_Semantics">Denotational_Semantics</a></li>
<li><a href="../theories/differential_game_logic/#Static_Semantics">Static_Semantics</a></li>
<li><a href="../theories/differential_game_logic/#Coincidence">Coincidence</a></li>
<li><a href="../theories/differential_game_logic/#USubst">USubst</a></li>
<li><a href="../theories/differential_game_logic/#Ids">Ids</a></li>
<li><a href="../theories/differential_game_logic/#Axioms">Axioms</a></li>
<li><a href="../theories/differential_game_logic/#Differential_Game_Logic">Differential_Game_Logic</a></li></ul><div class="flex-wrap">
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Differential_Game_Logic/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">Differential_Game_Logic-AFP</p><pre id="copy-text">@article{Differential_Game_Logic-AFP,
author = {André Platzer},
title = {Differential Game Logic},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Differential_Game_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Differential_Game_Logic-2019-06-24.tar.gz">Jun 24, 2019</a>: Isabelle2019
</li></ul>
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diff --git a/web/entries/Digit_Expansions.html b/web/entries/Digit_Expansions.html
--- a/web/entries/Digit_Expansions.html
+++ b/web/entries/Digit_Expansions.html
@@ -1,169 +1,176 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Digit Expansions - Archive of Formal Proofs</title><meta name="description" content="We formalize how a natural number can be expanded into its digits in
some base and prove properties about functions that operate on digit
expansions. This..."><meta property="og:title" content="Digit Expansions" />
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<h1 >
<span class='first'>D</span>igit <span class='first'>E</span>xpansions</h1>
<div>
<p><a href="../authors/bayer">Jonas Bayer</a>, <a href="../authors/david">Marco David</a>, <a href="../authors/pal">Abhik Pal</a> and <a href="../authors/stock">Benedikt Stock</a>
</p>
<p class="date">April 20, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize how a natural number can be expanded into its digits in
some base and prove properties about functions that operate on digit
expansions. This includes the formalization of concepts such as digit
shifts and carries. For a base that is a power of 2 we formalize the
binary AND, binary orthogonality and binary masking of two natural
numbers. This library on digit expansions builds the basis for the
formalization of the DPRM theorem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Digit_Expansions</h3>
<ul>
<li><a href="../theories/digit_expansions/#Bits_Digits">Bits_Digits</a></li>
<li><a href="../theories/digit_expansions/#Carries">Carries</a></li>
<li><a href="../theories/digit_expansions/#Binary_Operations">Binary_Operations</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/DPRM_Theorem.html">Diophantine Equations and the DPRM Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Digit_Expansions-AFP</p><pre id="copy-text">@article{Digit_Expansions-AFP,
author = {Jonas Bayer and Marco David and Abhik Pal and Benedikt Stock},
title = {Digit Expansions},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Digit_Expansions.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/Dijkstra_Shortest_Path.html b/web/entries/Dijkstra_Shortest_Path.html
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<h1 >
<span class='first'>D</span>ijkstra's <span class='first'>S</span>hortest <span class='first'>P</span>ath <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/nordhoff">Benedikt Nordhoff</a> <a class="obfuscated" data="eyJob3N0IjpbInd3dSIsImRlIl0sInVzZXIiOlsiYiIsIm4iXX0=">📧</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">January 30, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implement and prove correct Dijkstra's algorithm for the
single source shortest path problem, conceived in 1956 by E. Dijkstra.
The algorithm is implemented using the data refinement framework for monadic,
nondeterministic programs. An efficient implementation is derived using data
structures from the Isabelle Collection Framework.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
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<li><a href="../theories/dijkstra_shortest_path/#Introduction">Introduction</a></li>
<li><a href="../theories/dijkstra_shortest_path/#Dijkstra_Misc">Dijkstra_Misc</a></li>
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<li><a href="../theories/dijkstra_shortest_path/#Weight">Weight</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/Formal_SSA.html">Verified Construction of Static Single Assignment Form</a></li><li><a href="../entries/Koenigsberg_Friendship.html">The Königsberg Bridge Problem and the Friendship Theorem</a></li></ul>
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<li><a href="../entries/Van_Emde_Boas_Trees.html">van Emde Boas Trees</a></li>
<li><a href="../entries/Diophantine_Eqns_Lin_Hom.html">Homogeneous Linear Diophantine Equations</a></li>
<li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li>
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<p style="display:none;" id="bibtex-filename">Dijkstra_Shortest_Path-AFP</p><pre id="copy-text">@article{Dijkstra_Shortest_Path-AFP,
author = {Benedikt Nordhoff and Peter Lammich},
title = {Dijkstra&#39;s Shortest Path Algorithm},
journal = {Archive of Formal Proofs},
month = {January},
year = {2012},
note = {\url{https://isa-afp.org/entries/Dijkstra_Shortest_Path.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Diophantine_Eqns_Lin_Hom.html b/web/entries/Diophantine_Eqns_Lin_Hom.html
--- a/web/entries/Diophantine_Eqns_Lin_Hom.html
+++ b/web/entries/Diophantine_Eqns_Lin_Hom.html
@@ -1,186 +1,188 @@
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<h1 >
<span class='first'>H</span>omogeneous <span class='first'>L</span>inear <span class='first'>D</span>iophantine <span class='first'>E</span>quations</h1>
<div>
<p><a href="../authors/messner">Florian Messner</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiZmxvcmlhbiIsImciLCJtZXNzbmVyIl19">📧</a>, <a href="../authors/parsert">Julian Parsert</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsianVsaWFuIiwicGFyc2VydCJdfQ==">📧</a>, <a href="../authors/schoepf">Jonas Schöpf</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiam9uYXMiLCJzY2hvZXBmIl19">📧</a> and <a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">October 14, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the theory of homogeneous linear diophantine equations,
focusing on two main results: (1) an abstract characterization of
minimal complete sets of solutions, and (2) an algorithm computing
them. Both, the characterization and the algorithm are based on
previous work by Huet. Our starting point is a simple but inefficient
variant of Huet's lexicographic algorithm incorporating improved
bounds due to Clausen and Fortenbacher. We proceed by proving its
soundness and completeness. Finally, we employ code equations to
obtain a reasonably efficient implementation. Thus, we provide a
formally verified solver for homogeneous linear diophantine equations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Diophantine_Eqns_Lin_Hom</h3>
<ul>
<li><a href="../theories/diophantine_eqns_lin_hom/#List_Vector">List_Vector</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Linear_Diophantine_Equations">Linear_Diophantine_Equations</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Sorted_Wrt">Sorted_Wrt</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Minimize_Wrt">Minimize_Wrt</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Simple_Algorithm">Simple_Algorithm</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Algorithm">Algorithm</a></li>
<li><a href="../theories/diophantine_eqns_lin_hom/#Solver_Code">Solver_Code</a></li></ul><div class="flex-wrap">
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Diophantine_Eqns_Lin_Hom/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Diophantine_Eqns_Lin_Hom/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Diophantine_Eqns_Lin_Hom-AFP</p><pre id="copy-text">@article{Diophantine_Eqns_Lin_Hom-AFP,
author = {Florian Messner and Julian Parsert and Jonas Schöpf and Christian Sternagel},
title = {Homogeneous Linear Diophantine Equations},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Diophantine_Eqns_Lin_Hom.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Diophantine_Eqns_Lin_Hom-2017-10-15.tar.gz">Oct 15, 2017</a>: Isabelle2017
</li></ul>
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diff --git a/web/entries/Dirichlet_L.html b/web/entries/Dirichlet_L.html
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<h1 >
<span class='first'>D</span>irichlet <span class='first'>L</span>-<span class='first'>F</span>unctions and <span class='first'>D</span>irichlet's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of Dirichlet characters
and Dirichlet <em>L</em>-functions including proofs of
their basic properties &ndash; most notably their analyticity,
their areas of convergence, and their non-vanishing for &Re;(s)
&ge; 1. All of this is built in a very high-level style using
Dirichlet series. The proof of the non-vanishing follows a very short
and elegant proof by Newman, which we attempt to reproduce faithfully
in a similar level of abstraction in Isabelle.</p> <p>This
also leads to a relatively short proof of Dirichlet’s Theorem, which
states that, if <em>h</em> and <em>n</em> are
coprime, there are infinitely many primes <em>p</em> with
<em>p</em> &equiv; <em>h</em> (mod
<em>n</em>).</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Dirichlet_L</h3>
<ul>
<li><a href="../theories/dirichlet_l/#Multiplicative_Characters">Multiplicative_Characters</a></li>
<li><a href="../theories/dirichlet_l/#Dirichlet_Characters">Dirichlet_Characters</a></li>
<li><a href="../theories/dirichlet_l/#Dirichlet_L_Functions">Dirichlet_L_Functions</a></li>
<li><a href="../theories/dirichlet_l/#Dirichlet_Theorem">Dirichlet_Theorem</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bertrands_Postulate.html">Bertrand&rsquo;s postulate</a></li><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li><li><a href="../entries/Finitely_Generated_Abelian_Groups.html">Finitely Generated Abelian Groups</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Gauss_Sums.html">Gauss Sums and the Pólya–Vinogradov Inequality</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Mason_Stothers.html">The Mason–Stothers Theorem</a></li>
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document</a>
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<p style="display:none;" id="bibtex-filename">Dirichlet_L-AFP</p><pre id="copy-text">@article{Dirichlet_L-AFP,
author = {Manuel Eberl},
title = {Dirichlet L-Functions and Dirichlet&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/Dirichlet_L.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-Dirichlet_L-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dirichlet_L-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Dirichlet_Series.html b/web/entries/Dirichlet_Series.html
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@@ -1,220 +1,222 @@
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<h1 >
<span class='first'>D</span>irichlet <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">October 12, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry is a formalisation of much of Chapters 2, 3, and 11 of
Apostol's &ldquo;Introduction to Analytic Number
Theory&rdquo;. This includes: <ul> <li>Definitions and
basic properties for several number-theoretic functions (Euler's
&phi;, M&ouml;bius &mu;, Liouville's &lambda;,
the divisor function &sigma;, von Mangoldt's
&Lambda;)</li> <li>Executable code for most of these
functions, the most efficient implementations using the factoring
algorithm by Thiemann <i>et al.</i></li>
<li>Dirichlet products and formal Dirichlet series</li>
<li>Analytic results connecting convergent formal Dirichlet
series to complex functions</li> <li>Euler product
expansions</li> <li>Asymptotic estimates of
number-theoretic functions including the density of squarefree
integers and the average number of divisors of a natural
number</li> </ul> These results are useful as a basis for
developing more number-theoretic results, such as the Prime Number
Theorem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Dirichlet_Series</h3>
<ul>
<li><a href="../theories/dirichlet_series/#Dirichlet_Misc">Dirichlet_Misc</a></li>
<li><a href="../theories/dirichlet_series/#Multiplicative_Function">Multiplicative_Function</a></li>
<li><a href="../theories/dirichlet_series/#Dirichlet_Product">Dirichlet_Product</a></li>
<li><a href="../theories/dirichlet_series/#Dirichlet_Series">Dirichlet_Series</a></li>
<li><a href="../theories/dirichlet_series/#Moebius_Mu">Moebius_Mu</a></li>
<li><a href="../theories/dirichlet_series/#More_Totient">More_Totient</a></li>
<li><a href="../theories/dirichlet_series/#Liouville_Lambda">Liouville_Lambda</a></li>
<li><a href="../theories/dirichlet_series/#Divisor_Count">Divisor_Count</a></li>
<li><a href="../theories/dirichlet_series/#Arithmetic_Summatory">Arithmetic_Summatory</a></li>
<li><a href="../theories/dirichlet_series/#Partial_Summation">Partial_Summation</a></li>
<li><a href="../theories/dirichlet_series/#Euler_Products">Euler_Products</a></li>
<li><a href="../theories/dirichlet_series/#Dirichlet_Series_Analysis">Dirichlet_Series_Analysis</a></li>
<li><a href="../theories/dirichlet_series/#Arithmetic_Summatory_Asymptotics">Arithmetic_Summatory_Asymptotics</a></li>
<li><a href="../theories/dirichlet_series/#Dirichlet_Efficient_Code">Dirichlet_Efficient_Code</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Euler_MacLaurin.html">The Euler–MacLaurin Formula</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Finite_Fields.html">Finite Fields</a></li><li><a href="../entries/Gauss_Sums.html">Gauss Sums and the Pólya–Vinogradov Inequality</a></li><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Digit_Expansions.html">Digit Expansions</a></li>
<li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li>
<li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li>
<li><a href="../entries/SumSquares.html">Sums of Two and Four Squares</a></li>
</ul>
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outline</a>
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author = {Manuel Eberl},
title = {Dirichlet Series},
journal = {Archive of Formal Proofs},
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year = {2017},
note = {\url{https://isa-afp.org/entries/Dirichlet_Series.html},
Formal proof development},
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diff --git a/web/entries/DiscretePricing.html b/web/entries/DiscretePricing.html
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<h1 >
<span class='first'>P</span>ricing in <span class='first'>D</span>iscrete <span class='first'>F</span>inancial <span class='first'>M</span>odels</h1>
<div>
<p><a href="../authors/echenim">Mnacho Echenim</a> <a href="https://lig-membres.imag.fr/mechenim/">🌐</a>
</p>
<p class="date">July 16, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We have formalized the computation of fair prices for derivative
products in discrete financial models. As an application, we derive a
way to compute fair prices of derivative products in the
Cox-Ross-Rubinstein model of a financial market, thus completing the
work that was presented in this <a
href="https://hal.archives-ouvertes.fr/hal-01562944">paper</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 12, 2019</dt>
<dd>Renamed discr_mkt predicate to stk_strict_subs and got rid of predicate A for a more natural definition of the type discrete_market;
renamed basic quantity processes for coherent notation;
renamed value_process into val_process and closing_value_process to cls_val_process;
relaxed hypothesis of lemma CRR_market_fair_price.
Added functions to price some basic options.
(revision 0b813a1a833f)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session DiscretePricing</h3>
<ul>
<li><a href="../theories/discretepricing/#Generated_Subalgebra">Generated_Subalgebra</a></li>
<li><a href="../theories/discretepricing/#Filtration">Filtration</a></li>
<li><a href="../theories/discretepricing/#Martingale">Martingale</a></li>
<li><a href="../theories/discretepricing/#Disc_Cond_Expect">Disc_Cond_Expect</a></li>
<li><a href="../theories/discretepricing/#Infinite_Coin_Toss_Space">Infinite_Coin_Toss_Space</a></li>
<li><a href="../theories/discretepricing/#Geometric_Random_Walk">Geometric_Random_Walk</a></li>
<li><a href="../theories/discretepricing/#Fair_Price">Fair_Price</a></li>
<li><a href="../theories/discretepricing/#CRR_Model">CRR_Model</a></li>
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<p style="display:none;" id="bibtex-filename">DiscretePricing-AFP</p><pre id="copy-text">@article{DiscretePricing-AFP,
author = {Mnacho Echenim},
title = {Pricing in discrete financial models},
journal = {Archive of Formal Proofs},
month = {July},
year = {2018},
note = {\url{https://isa-afp.org/entries/DiscretePricing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>D</span>iscrete <span class='first'>S</span>ummation</h1>
<div>
<p><a href="../authors/haftmann">Florian Haftmann</a> <a href="http://isabelle.in.tum.de/~haftmann">🌐</a>
with contributions from <a href="../authors/chaieb">Amine Chaieb</a>
</p>
<p class="date">April 13, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories introduce basic concepts and proofs about discrete summation: shifts, formal summation, falling factorials and stirling numbers. As proof of concept, a simple summation conversion is provided.</div>
<h3>License</h3>
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<li><a href="../theories/discrete_summation/#Factorials">Factorials</a></li>
<li><a href="../theories/discrete_summation/#Discrete_Summation">Discrete_Summation</a></li>
<li><a href="../theories/discrete_summation/#Summation_Conversion">Summation_Conversion</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Falling_Factorial_Sum.html">The Falling Factorial of a Sum</a></li><li><a href="../entries/Card_Partitions.html">Cardinality of Set Partitions</a></li></ul>
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author = {Florian Haftmann},
title = {Discrete Summation},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/Discrete_Summation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>P</span>roving the <span class='first'>C</span>orrectness of <span class='first'>D</span>isk <span class='first'>P</span>axos</h1>
<div>
<p><a href="../authors/jaskelioff">Mauro Jaskelioff</a> <a href="http://www.fceia.unr.edu.ar/~mauro/">🌐</a> and <a href="../authors/merz">Stephan Merz</a> <a href="http://www.loria.fr/~merz">🌐</a>
</p>
<p class="date">June 22, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Disk Paxos is an algorithm for building arbitrary fault-tolerant distributed systems. The specification of Disk Paxos has been proved correct informally and tested using the TLC model checker, but up to now, it has never been fully formally verified. In this work we have formally verified its correctness using the Isabelle theorem prover and the HOL logic system, showing that Isabelle is a practical tool for verifying properties of TLA+ specifications.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session DiskPaxos</h3>
<ul>
<li><a href="../theories/diskpaxos/#DiskPaxos_Model">DiskPaxos_Model</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv1">DiskPaxos_Inv1</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv2">DiskPaxos_Inv2</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv3">DiskPaxos_Inv3</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv4">DiskPaxos_Inv4</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv5">DiskPaxos_Inv5</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Chosen">DiskPaxos_Chosen</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Inv6">DiskPaxos_Inv6</a></li>
<li><a href="../theories/diskpaxos/#DiskPaxos_Invariant">DiskPaxos_Invariant</a></li>
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<p style="display:none;" id="bibtex-filename">DiskPaxos-AFP</p><pre id="copy-text">@article{DiskPaxos-AFP,
author = {Mauro Jaskelioff and Stephan Merz},
title = {Proving the Correctness of Disk Paxos},
journal = {Archive of Formal Proofs},
month = {June},
year = {2005},
note = {\url{https://isa-afp.org/entries/DiskPaxos.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-DiskPaxos-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-DiskPaxos-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-DiskPaxos-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-DiskPaxos-2005-06-22.tar.gz">Jun 22, 2005</a>: Isabelle2004
</li></ul>
</div>
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</html>
\ No newline at end of file
diff --git a/web/entries/Dominance_CHK.html b/web/entries/Dominance_CHK.html
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<h1 >
<span class='first'>A</span> <span class='first'>D</span>ata <span class='first'>F</span>low <span class='first'>A</span>nalysis <span class='first'>A</span>lgorithm for <span class='first'>C</span>omputing <span class='first'>D</span>ominators</h1>
<div>
<p><a href="../authors/jiang">Nan Jiang</a>
</p>
<p class="date">September 5, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalises the fast iterative algorithm for computing dominators
due to Cooper, Harvey and Kennedy. It gives a specification of computing
dominators on a control
flow graph where each node refers to its reverse post order number. A
semilattice of reversed-ordered list which represents dominators is
built and a Kildall-style algorithm on the semilattice is defined for
computing dominators. Finally the soundness and completeness of the
algorithm are proved w.r.t. the specification.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Dominance_CHK</h3>
<ul>
<li><a href="../theories/dominance_chk/#Cfg">Cfg</a></li>
<li><a href="../theories/dominance_chk/#Sorted_Less2">Sorted_Less2</a></li>
<li><a href="../theories/dominance_chk/#Sorted_List_Operations2">Sorted_List_Operations2</a></li>
<li><a href="../theories/dominance_chk/#Dom_Semi_List">Dom_Semi_List</a></li>
<li><a href="../theories/dominance_chk/#Dom_Kildall">Dom_Kildall</a></li>
<li><a href="../theories/dominance_chk/#Dom_Kildall_Property">Dom_Kildall_Property</a></li>
<li><a href="../theories/dominance_chk/#Dom_Kildall_Correct">Dom_Kildall_Correct</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jinja.html">Jinja is not Java</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Shivers-CFA.html">Shivers' Control Flow Analysis</a></li>
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<p style="display:none;" id="bibtex-filename">Dominance_CHK-AFP</p><pre id="copy-text">@article{Dominance_CHK-AFP,
author = {Nan Jiang},
title = {A data flow analysis algorithm for computing dominators},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Dominance_CHK.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Dominance_CHK-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Dominance_CHK-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Dominance_CHK-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Dominance_CHK-2021-09-07.tar.gz">Sep 7, 2021</a>: Isabelle2021
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diff --git a/web/entries/DynamicArchitectures.html b/web/entries/DynamicArchitectures.html
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<h1 >
<span class='first'>D</span>ynamic <span class='first'>A</span>rchitectures</h1>
<div>
<p><a href="../authors/marmsoler">Diego Marmsoler</a> <a href="http://marmsoler.com">🌐</a>
</p>
<p class="date">July 28, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The architecture of a system describes the system's overall
organization into components and connections between those components.
With the emergence of mobile computing, dynamic architectures have
become increasingly important. In such architectures, components may
appear or disappear, and connections may change over time. In the
following we mechanize a theory of dynamic architectures and verify
the soundness of a corresponding calculus. Therefore, we first
formalize the notion of configuration traces as a model for dynamic
architectures. Then, the behavior of single components is formalized
in terms of behavior traces and an operator is introduced and studied
to extract the behavior of a single component out of a given
configuration trace. Then, behavior trace assertions are introduced as
a temporal specification technique to specify behavior of components.
Reasoning about component behavior in a dynamic context is formalized
in terms of a calculus for dynamic architectures. Finally, the
soundness of the calculus is verified by introducing an alternative
interpretation for behavior trace assertions over configuration traces
and proving the rules of the calculus. Since projection may lead to
finite as well as infinite behavior traces, they are formalized in
terms of coinductive lists. Thus, our theory is based on
Lochbihler's formalization of coinductive lists. The theory may
be applied to verify properties for dynamic architectures.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 7, 2018</dt>
<dd>adding logical operators to specify configuration traces (revision 09178f08f050)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session DynamicArchitectures</h3>
<ul>
<li><a href="../theories/dynamicarchitectures/#Configuration_Traces">Configuration_Traces</a></li>
<li><a href="../theories/dynamicarchitectures/#Dynamic_Architecture_Calculus">Dynamic_Architecture_Calculus</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Architectural_Design_Patterns.html">A Theory of Architectural Design Patterns</a></li></ul>
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<p style="display:none;" id="bibtex-filename">DynamicArchitectures-AFP</p><pre id="copy-text">@article{DynamicArchitectures-AFP,
author = {Diego Marmsoler},
title = {Dynamic Architectures},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/DynamicArchitectures.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Dynamic_Tables.html b/web/entries/Dynamic_Tables.html
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@@ -1,186 +1,188 @@
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<h1 >
<span class='first'>P</span>arameterized <span class='first'>D</span>ynamic <span class='first'>T</span>ables</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 7, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes the amortized analysis of dynamic tables
parameterized with their minimal and maximal load factors and the
expansion and contraction factors.
<P>
A full description is found in a
<a href="http://www21.in.tum.de/~nipkow/pubs">companion paper</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Dynamic_Tables</h3>
<ul>
<li><a href="../theories/dynamic_tables/#Tables_real">Tables_real</a></li>
<li><a href="../theories/dynamic_tables/#Tables_nat">Tables_nat</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Amortized_Complexity.html">Amortized Complexity Verified</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Dynamic_Tables-AFP</p><pre id="copy-text">@article{Dynamic_Tables-AFP,
author = {Tobias Nipkow},
title = {Parameterized Dynamic Tables},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/Dynamic_Tables.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/E_Transcendental.html b/web/entries/E_Transcendental.html
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>ranscendence of <span class='first'>E</span></h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">January 12, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This work contains a proof that Euler's number e is transcendental. The
proof follows the standard approach of assuming that e is algebraic and
then using a specific integer polynomial to derive two inconsistent bounds,
leading to a contradiction.</p> <p>This kind of approach can be found in
many different sources; this formalisation mostly follows a <a href="http://planetmath.org/proofoflindemannweierstrasstheoremandthateandpiaretranscendental">PlanetMath article</a> by Roger Lipsett.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session E_Transcendental</h3>
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<li><a href="../theories/e_transcendental/#E_Transcendental">E_Transcendental</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Zeta_3_Irrational.html">The Irrationality of ζ(3)</a></li><li><a href="../entries/Pi_Transcendental.html">The Transcendence of π</a></li></ul>
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<p style="display:none;" id="bibtex-filename">E_Transcendental-AFP</p><pre id="copy-text">@article{E_Transcendental-AFP,
author = {Manuel Eberl},
title = {The Transcendence of e},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/E_Transcendental.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Echelon_Form.html b/web/entries/Echelon_Form.html
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@@ -1,203 +1,205 @@
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<h1 >
<span class='first'>E</span>chelon <span class='first'>F</span>orm</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>
</p>
<p class="date">February 12, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize an algorithm to compute the Echelon Form of a matrix. We have proved its existence over Bézout domains and made it executable over Euclidean domains, such as the integer ring and the univariate polynomials over a field. This allows us to compute determinants, inverses and characteristic polynomials of matrices. The work is based on the HOL-Multivariate Analysis library, and on both the Gauss-Jordan and Cayley-Hamilton AFP entries. As a by-product, some algebraic structures have been implemented (principal ideal domains, Bézout domains...). The algorithm has been refined to immutable arrays and code can be generated to functional languages as well.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Echelon_Form</h3>
<ul>
<li><a href="../theories/echelon_form/#Rings2">Rings2</a></li>
<li><a href="../theories/echelon_form/#Cayley_Hamilton_Compatible">Cayley_Hamilton_Compatible</a></li>
<li><a href="../theories/echelon_form/#Code_Cayley_Hamilton">Code_Cayley_Hamilton</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form">Echelon_Form</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form_Det">Echelon_Form_Det</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form_Inverse">Echelon_Form_Inverse</a></li>
<li><a href="../theories/echelon_form/#Examples_Echelon_Form_Abstract">Examples_Echelon_Form_Abstract</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form_IArrays">Echelon_Form_IArrays</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form_Det_IArrays">Echelon_Form_Det_IArrays</a></li>
<li><a href="../theories/echelon_form/#Code_Cayley_Hamilton_IArrays">Code_Cayley_Hamilton_IArrays</a></li>
<li><a href="../theories/echelon_form/#Echelon_Form_Inverse_IArrays">Echelon_Form_Inverse_IArrays</a></li>
<li><a href="../theories/echelon_form/#Examples_Echelon_Form_IArrays">Examples_Echelon_Form_IArrays</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Cayley_Hamilton.html">The Cayley-Hamilton Theorem</a></li><li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li><li><a href="../entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hermite.html">Hermite Normal Form</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/QR_Decomposition.html">QR Decomposition</a></li>
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<p style="display:none;" id="bibtex-filename">Echelon_Form-AFP</p><pre id="copy-text">@article{Echelon_Form-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {Echelon Form},
journal = {Archive of Formal Proofs},
month = {February},
year = {2015},
note = {\url{https://isa-afp.org/entries/Echelon_Form.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Echelon_Form-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Echelon_Form-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Echelon_Form-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Echelon_Form-2015-02-12.tar.gz">Feb 12, 2015</a>: Isabelle2014
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/EdmondsKarp_Maxflow.html b/web/entries/EdmondsKarp_Maxflow.html
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<h1 >
<span class='first'>F</span>ormalizing the <span class='first'>E</span>dmonds-<span class='first'>K</span>arp <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJsYW1taWNoIl19">📧</a> and <a href="../authors/sefidgar">S. Reza Sefidgar</a>
</p>
<p class="date">August 12, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of the Ford-Fulkerson method for computing
the maximum flow in a network. Our formal proof closely follows a
standard textbook proof, and is accessible even without being an
expert in Isabelle/HOL--- the interactive theorem prover used for the
formalization. We then use stepwise refinement to obtain the
Edmonds-Karp algorithm, and formally prove a bound on its complexity.
Further refinement yields a verified implementation, whose execution
time compares well to an unverified reference implementation in Java.
This entry is based on our ITP-2016 paper with the same title.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session EdmondsKarp_Maxflow</h3>
<ul>
<li><a href="../theories/edmondskarp_maxflow/#FordFulkerson_Algo">FordFulkerson_Algo</a></li>
<li><a href="../theories/edmondskarp_maxflow/#EdmondsKarp_Termination_Abstract">EdmondsKarp_Termination_Abstract</a></li>
<li><a href="../theories/edmondskarp_maxflow/#EdmondsKarp_Algo">EdmondsKarp_Algo</a></li>
<li><a href="../theories/edmondskarp_maxflow/#Augmenting_Path_BFS">Augmenting_Path_BFS</a></li>
<li><a href="../theories/edmondskarp_maxflow/#EdmondsKarp_Impl">EdmondsKarp_Impl</a></li>
<li><a href="../theories/edmondskarp_maxflow/#Edka_Checked_Impl">Edka_Checked_Impl</a></li>
<li><a href="../theories/edmondskarp_maxflow/#Edka_Benchmark_Export">Edka_Benchmark_Export</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MFMC_Countable.html">A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Prpu_Maxflow.html">Formalizing Push-Relabel Algorithms</a></li>
<li><a href="../entries/Solidity.html">Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</a></li>
<li><a href="../entries/BTree.html">A Verified Imperative Implementation of B-Trees</a></li>
<li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li>
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<p style="display:none;" id="bibtex-filename">EdmondsKarp_Maxflow-AFP</p><pre id="copy-text">@article{EdmondsKarp_Maxflow-AFP,
author = {Peter Lammich and S. Reza Sefidgar},
title = {Formalizing the Edmonds-Karp Algorithm},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/EdmondsKarp_Maxflow.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-EdmondsKarp_Maxflow-2016-08-12.tar.gz">Aug 12, 2016</a>: Isabelle2016
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diff --git a/web/entries/Efficient-Mergesort.html b/web/entries/Efficient-Mergesort.html
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+++ b/web/entries/Efficient-Mergesort.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Efficient Mergesort - Archive of Formal Proofs</title><meta name="description" content="We provide a formalization of the mergesort algorithm as used in GHC&#39;s Data.List module, proving correctness and stability. Furthermore, experimental data..."><meta property="og:title" content="Efficient Mergesort" />
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<h1 >
<span class='first'>E</span>fficient <span class='first'>M</span>ergesort</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">November 9, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a formalization of the mergesort algorithm as used in GHC's Data.List module, proving correctness and stability. Furthermore, experimental data suggests that generated (Haskell-)code for this algorithm is much faster than for previous algorithms available in the Isabelle distribution.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>November 20, 2020</dt>
<dd>Additional theory Natural_Mergesort that developes an efficient mergesort
algorithm without key-functions for educational purposes.</dd><dt>September 19, 2018</dt>
<dd>Theory Efficient_Mergesort replaces theory Efficient_Sort but keeping the old
name Efficient_Sort.
</dd><dt>September 17, 2018</dt>
<dd>Added theory Efficient_Mergesort that works exclusively with the mutual
induction schemas generated by the function package.<br>
</dd><dt>October 24, 2012</dt>
<dd>Added reference to journal article.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Efficient-Mergesort</h3>
<ul>
<li><a href="../theories/efficient-mergesort/#Efficient_Sort">Efficient_Sort</a></li>
<li><a href="../theories/efficient-mergesort/#Mergesort_Complexity">Mergesort_Complexity</a></li>
<li><a href="../theories/efficient-mergesort/#Natural_Mergesort">Natural_Mergesort</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Efficient-Mergesort-AFP</p><pre id="copy-text">@article{Efficient-Mergesort-AFP,
author = {Christian Sternagel},
title = {Efficient Mergesort},
journal = {Archive of Formal Proofs},
month = {November},
year = {2011},
note = {\url{https://isa-afp.org/entries/Efficient-Mergesort.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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fields of characteristic greater than 2. In addition to affine
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<h1 >
<span class='first'>T</span>he <span class='first'>G</span>roup <span class='first'>L</span>aw for <span class='first'>E</span>lliptic <span class='first'>C</span>urves</h1>
<div>
<p><a href="../authors/berghofer">Stefan Berghofer</a> <a href="http://www.in.tum.de/~berghofe">🌐</a>
</p>
<p class="date">February 28, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We prove the group law for elliptic curves in Weierstrass form over
fields of characteristic greater than 2. In addition to affine
coordinates, we also formalize projective coordinates, which allow for
more efficient computations. By specializing the abstract
formalization to prime fields, we can apply the curve operations to
parameters used in standard security protocols.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li></ul>
<h3>Session Elliptic_Curves_Group_Law</h3>
<ul>
<li><a href="../theories/elliptic_curves_group_law/#Elliptic_Axclass">Elliptic_Axclass</a></li>
<li><a href="../theories/elliptic_curves_group_law/#Elliptic_Locale">Elliptic_Locale</a></li>
<li><a href="../theories/elliptic_curves_group_law/#Elliptic_Test">Elliptic_Test</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Elliptic_Curves_Group_Law-AFP</p><pre id="copy-text">@article{Elliptic_Curves_Group_Law-AFP,
author = {Stefan Berghofer},
title = {The Group Law for Elliptic Curves},
journal = {Archive of Formal Proofs},
month = {February},
year = {2017},
note = {\url{https://isa-afp.org/entries/Elliptic_Curves_Group_Law.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Encodability_Process_Calculi.html b/web/entries/Encodability_Process_Calculi.html
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<h1 >
<span class='first'>A</span>nalysing and <span class='first'>C</span>omparing <span class='first'>E</span>ncodability <span class='first'>C</span>riteria for <span class='first'>P</span>rocess <span class='first'>C</span>alculi</h1>
<div>
<p><a href="../authors/peters">Kirstin Peters</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsia2lyc3RpbiIsInBldGVycyJdfQ==">📧</a> and <a href="../authors/glabbeek">Rob van Glabbeek</a> <a href="http://theory.stanford.edu/~rvg/">🌐</a>
</p>
<p class="date">August 10, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Encodings or the proof of their absence are the main way to
compare process calculi. To analyse the quality of encodings and to rule out
trivial or meaningless encodings, they are augmented with quality
criteria. There exists a bunch of different criteria and different variants
of criteria in order to reason in different settings. This leads to
incomparable results. Moreover it is not always clear whether the criteria
used to obtain a result in a particular setting do indeed fit to this
setting. We show how to formally reason about and compare encodability
criteria by mapping them on requirements on a relation between source and
target terms that is induced by the encoding function. In particular we
analyse the common criteria full abstraction, operational correspondence,
divergence reflection, success sensitiveness, and respect of barbs; e.g. we
analyse the exact nature of the simulation relation (coupled simulation
versus bisimulation) that is induced by different variants of operational
correspondence. This way we reduce the problem of analysing or comparing
encodability criteria to the better understood problem of comparing
relations on processes.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session Encodability_Process_Calculi</h3>
<ul>
<li><a href="../theories/encodability_process_calculi/#Relations">Relations</a></li>
<li><a href="../theories/encodability_process_calculi/#ProcessCalculi">ProcessCalculi</a></li>
<li><a href="../theories/encodability_process_calculi/#SimulationRelations">SimulationRelations</a></li>
<li><a href="../theories/encodability_process_calculi/#Encodings">Encodings</a></li>
<li><a href="../theories/encodability_process_calculi/#SourceTargetRelation">SourceTargetRelation</a></li>
<li><a href="../theories/encodability_process_calculi/#SuccessSensitiveness">SuccessSensitiveness</a></li>
<li><a href="../theories/encodability_process_calculi/#DivergenceReflection">DivergenceReflection</a></li>
<li><a href="../theories/encodability_process_calculi/#OperationalCorrespondence">OperationalCorrespondence</a></li>
<li><a href="../theories/encodability_process_calculi/#FullAbstraction">FullAbstraction</a></li>
<li><a href="../theories/encodability_process_calculi/#CombinedCriteria">CombinedCriteria</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Encodability_Process_Calculi-AFP</p><pre id="copy-text">@article{Encodability_Process_Calculi-AFP,
author = {Kirstin Peters and Rob van Glabbeek},
title = {Analysing and Comparing Encodability Criteria for Process Calculi},
journal = {Archive of Formal Proofs},
month = {August},
year = {2015},
note = {\url{https://isa-afp.org/entries/Encodability_Process_Calculi.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>pistemic <span class='first'>L</span>ogic: <span class='first'>C</span>ompleteness of <span class='first'>M</span>odal <span class='first'>L</span>ogics</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">October 29, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of epistemic logic with countably many
agents. It includes proofs of soundness and completeness for the axiom
system K. The completeness proof is based on the textbook
"Reasoning About Knowledge" by Fagin, Halpern, Moses and
Vardi (MIT Press 1995).
The extensions of system K (T, KB, K4, S4, S5) and their completeness proofs
are based on the textbook "Modal Logic" by Blackburn, de Rijke and Venema
(Cambridge University Press 2001).
Papers: <a href="https://doi.org/10.1007/978-3-030-88853-4_1">doi.org/10.1007/978-3-030-88853-4_1</a>, <a href="https://doi.org/10.1007/978-3-030-90138-7_2">doi.org/10.1007/978-3-030-90138-7_2</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 15, 2021</dt>
<dd>Added completeness of modal logics T, KB, K4, S4 and S5.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session Epistemic_Logic</h3>
<ul>
<li><a href="../theories/epistemic_logic/#Epistemic_Logic">Epistemic_Logic</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Stalnaker_Logic.html">Stalnaker&rsquo;s Epistemic Logic</a></li><li><a href="../entries/Public_Announcement_Logic.html">Public Announcement Logic</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Epistemic_Logic-AFP</p><pre id="copy-text">@article{Epistemic_Logic-AFP,
author = {Asta Halkjær From},
title = {Epistemic Logic: Completeness of Modal Logics},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/Epistemic_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Equivalence_Relation_Enumeration.html b/web/entries/Equivalence_Relation_Enumeration.html
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<h1 >
<span class='first'>E</span>numeration of <span class='first'>E</span>quivalence <span class='first'>R</span>elations</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">February 4, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry contains a formalization of an algorithm
enumerating all equivalence relations on an initial segment of the
natural numbers. The approach follows the method described by Stanton
and White <a
href="https://doi.org/10.1007/978-1-4612-4968-9">[5,§
1.5]</a> using restricted growth functions.</p>
<p>The algorithm internally enumerates restricted growth
functions (as lists), whose equivalence kernels then form the
equivalence relations. This has the advantage that the representation
is compact and lookup of the relation reduces to a list lookup
operation.</p> <p>The algorithm can also be used within a
proof and an example application is included, where a sequence of
variables is split by the possible partitions they can form.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Equivalence_Relation_Enumeration</h3>
<ul>
<li><a href="../theories/equivalence_relation_enumeration/#Equivalence_Relation_Enumeration">Equivalence_Relation_Enumeration</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Card_Equiv_Relations.html">Cardinality of Equivalence Relations</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Equivalence_Relation_Enumeration-AFP</p><pre id="copy-text">@article{Equivalence_Relation_Enumeration-AFP,
author = {Emin Karayel},
title = {Enumeration of Equivalence Relations},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/Equivalence_Relation_Enumeration.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>rgodic <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/gouezel">Sebastien Gouezel</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaXYtcmVubmVzMSIsImZyIl0sInVzZXIiOlsic2ViYXN0aWVuIiwiZ291ZXplbCJdfQ==">📧</a>
with contributions from <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 1, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Ergodic theory is the branch of mathematics that studies the behaviour of measure preserving transformations, in finite or infinite measure. It interacts both with probability theory (mainly through measure theory) and with geometry as a lot of interesting examples are from geometric origin. We implement the first definitions and theorems of ergodic theory, including notably Poicaré recurrence theorem for finite measure preserving systems (together with the notion of conservativity in general), induced maps, Kac's theorem, Birkhoff theorem (arguably the most important theorem in ergodic theory), and variations around it such as conservativity of the corresponding skew product, or Atkinson lemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Ergodic_Theory</h3>
<ul>
<li><a href="../theories/ergodic_theory/#SG_Library_Complement">SG_Library_Complement</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Roth_Arithmetic_Progressions.html">Roth&rsquo;s Theorem on Arithmetic Progressions</a></li><li><a href="../entries/Laws_of_Large_Numbers.html">The Laws of Large Numbers</a></li><li><a href="../entries/Gromov_Hyperbolicity.html">Gromov Hyperbolicity</a></li><li><a href="../entries/Lp.html">Lp spaces</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Ergodic_Theory-AFP</p><pre id="copy-text">@article{Ergodic_Theory-AFP,
author = {Sebastien Gouezel},
title = {Ergodic Theory},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Ergodic_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Error_Function.html b/web/entries/Error_Function.html
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<h1 >
<span class='first'>T</span>he <span class='first'>E</span>rror <span class='first'>F</span>unction</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 6, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> This entry provides the definitions and basic properties of
the complex and real error function erf and the complementary error
function erfc. Additionally, it gives their full asymptotic
expansions. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Error_Function</h3>
<ul>
<li><a href="../theories/error_function/#Error_Function">Error_Function</a></li>
<li><a href="../theories/error_function/#Error_Function_Asymptotics">Error_Function_Asymptotics</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<p style="display:none;" id="bibtex-filename">Error_Function-AFP</p><pre id="copy-text">@article{Error_Function-AFP,
author = {Manuel Eberl},
title = {The Error Function},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/Error_Function.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Euler_MacLaurin.html b/web/entries/Euler_MacLaurin.html
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<h1 >
<span class='first'>T</span>he <span class='first'>E</span>uler–<span class='first'>M</span>ac<span class='first'>L</span>aurin <span class='first'>F</span>ormula</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 10, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The Euler-MacLaurin formula relates the value of a
discrete sum to that of the corresponding integral in terms of the
derivatives at the borders of the summation and a remainder term.
Since the remainder term is often very small as the summation bounds
grow, this can be used to compute asymptotic expansions for
sums.</p> <p>This entry contains a proof of this formula
for functions from the reals to an arbitrary Banach space. Two
variants of the formula are given: the standard textbook version and a
variant outlined in <em>Concrete Mathematics</em> that is
more useful for deriving asymptotic estimates.</p> <p>As
example applications, we use that formula to derive the full
asymptotic expansion of the harmonic numbers and the sum of inverse
squares.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Euler_MacLaurin</h3>
<ul>
<li><a href="../theories/euler_maclaurin/#Euler_MacLaurin">Euler_MacLaurin</a></li>
<li><a href="../theories/euler_maclaurin/#Euler_MacLaurin_Landau">Euler_MacLaurin_Landau</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bernoulli.html">Bernoulli Numbers</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li></ul>
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Euler_MacLaurin-AFP</p><pre id="copy-text">@article{Euler_MacLaurin-AFP,
author = {Manuel Eberl},
title = {The Euler–MacLaurin Formula},
journal = {Archive of Formal Proofs},
month = {March},
year = {2017},
note = {\url{https://isa-afp.org/entries/Euler_MacLaurin.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Euler_Partition.html b/web/entries/Euler_Partition.html
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<h1 >
<span class='first'>E</span>uler's <span class='first'>P</span>artition <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">November 19, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Euler's Partition Theorem states that the number of partitions with only
distinct parts is equal to the number of partitions with only odd parts.
The combinatorial proof follows John Harrison's HOL Light formalization.
This theorem is the 45th theorem of the Top 100 Theorems list.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Euler_Partition</h3>
<ul>
<li><a href="../theories/euler_partition/#Euler_Partition">Euler_Partition</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Card_Number_Partitions.html">Cardinality of Number Partitions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Ptolemys_Theorem.html">Ptolemy&rsquo;s Theorem</a></li>
<li><a href="../entries/Bertrands_Postulate.html">Bertrand&rsquo;s postulate</a></li>
<li><a href="../entries/Chord_Segments.html">Intersecting Chords Theorem</a></li>
<li><a href="../entries/Triangle.html">Basic Geometric Properties of Triangles</a></li>
<li><a href="../entries/Descartes_Sign_Rule.html">Descartes' Rule of Signs</a></li>
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<p style="display:none;" id="bibtex-filename">Euler_Partition-AFP</p><pre id="copy-text">@article{Euler_Partition-AFP,
author = {Lukas Bulwahn},
title = {Euler&#39;s Partition Theorem},
journal = {Archive of Formal Proofs},
month = {November},
year = {2015},
note = {\url{https://isa-afp.org/entries/Euler_Partition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Euler_Partition-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Eval_FO.html b/web/entries/Eval_FO.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>First-Order Query Evaluation - Archive of Formal Proofs</title><meta name="description" content="We formalize first-order query evaluation over an infinite domain with equality. We first define the syntax and semantics of first-order logic with..."><meta property="og:title" content="First-Order Query Evaluation" />
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<h1 >
<span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>Q</span>uery <span class='first'>E</span>valuation</h1>
<div>
<p><a href="../authors/raszyk">Martin Raszyk</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbIm1hcnRpbiIsInJhc3p5ayJdfQ==">📧</a>
</p>
<p class="date">February 15, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize first-order query evaluation over an infinite domain with
equality. We first define the syntax and semantics of first-order
logic with equality. Next we define a locale
<i>eval&lowbar;fo</i> abstracting a representation of
a potentially infinite set of tuples satisfying a first-order query
over finite relations. Inside the locale, we define a function
<i>eval</i> checking if the set of tuples satisfying a
first-order query over a database (an interpretation of the
query's predicates) is finite (i.e., deciding <i>relative
safety</i>) and computing the set of satisfying tuples if it is
finite. Altogether the function <i>eval</i> solves
<i>capturability</i> (Avron and Hirshfeld, 1991) of
first-order logic with equality. We also use the function
<i>eval</i> to prove a code equation for the semantics of
first-order logic, i.e., the function checking if a first-order query
over a database is satisfied by a variable assignment.<br/> We provide an
interpretation of the locale <i>eval&lowbar;fo</i>
based on the approach by Ailamazyan et al. A core notion in the
interpretation is the active domain of a query and a database that
contains all domain elements that occur in the database or interpret
the query's constants. We prove the main theorem of Ailamazyan et
al. relating the satisfaction of a first-order query over an infinite
domain to the satisfaction of this query over a finite domain
consisting of the active domain and a few additional domain elements
(outside the active domain) whose number only depends on the query. In
our interpretation of the locale
<i>eval&lowbar;fo</i>, we use a potentially higher
number of the additional domain elements, but their number still only
depends on the query and thus has no effect on the data complexity
(Vardi, 1982) of query evaluation. Our interpretation yields an
<i>executable</i> function <i>eval</i>. The
time complexity of <i>eval</i> on a query is linear in the
total number of tuples in the intermediate relations for the
subqueries. Specifically, we build a database index to evaluate a
conjunction. We also optimize the case of a negated subquery in a
conjunction. Finally, we export code for the infinite domain of
natural numbers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-management-systems">Computer science/Data management systems</a></li><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li></ul>
<h3>Session Eval_FO</h3>
<ul>
<li><a href="../theories/eval_fo/#Infinite">Infinite</a></li>
<li><a href="../theories/eval_fo/#FO">FO</a></li>
<li><a href="../theories/eval_fo/#Eval_FO">Eval_FO</a></li>
<li><a href="../theories/eval_fo/#Mapping_Code">Mapping_Code</a></li>
<li><a href="../theories/eval_fo/#Cluster">Cluster</a></li>
<li><a href="../theories/eval_fo/#Ailamazyan">Ailamazyan</a></li>
<li><a href="../theories/eval_fo/#Ailamazyan_Code">Ailamazyan_Code</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Containers.html">Light-weight Containers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Eval_FO-AFP</p><pre id="copy-text">@article{Eval_FO-AFP,
author = {Martin Raszyk},
title = {First-Order Query Evaluation},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/Eval_FO.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Extended_Finite_State_Machine_Inference.html b/web/entries/Extended_Finite_State_Machine_Inference.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Inference of Extended Finite State Machines - Archive of Formal Proofs</title><meta name="description" content="In this AFP entry, we provide a formal implementation of a
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<h1 >
<span class='first'>I</span>nference of <span class='first'>E</span>xtended <span class='first'>F</span>inite <span class='first'>S</span>tate <span class='first'>M</span>achines</h1>
<div>
<p><a href="../authors/foster">Michael Foster</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJtIiwiZm9zdGVyIl19">📧</a>, <a href="../authors/brucker">Achim D. Brucker</a> <a class="obfuscated" data="eyJob3N0IjpbImV4ZXRlciIsImFjIiwidWsiXSwidXNlciI6WyJhIiwiYnJ1Y2tlciJdfQ==">📧</a>, <a href="../authors/taylor">Ramsay G. Taylor</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJyIiwiZyIsInRheWxvciJdfQ==">📧</a> and <a href="../authors/derrick">John Derrick</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJqIiwiZGVycmljayJdfQ==">📧</a>
</p>
<p class="date">September 7, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we provide a formal implementation of a
state-merging technique to infer extended finite state machines
(EFSMs), complete with output and update functions, from black-box
traces. In particular, we define the subsumption in context relation
as a means of determining whether one transition is able to account
for the behaviour of another. Building on this, we define the direct
subsumption relation, which lifts the subsumption in context relation
to EFSM level such that we can use it to determine whether it is safe
to merge a given pair of transitions. Key proofs include the
conditions necessary for subsumption to occur and that subsumption
and direct subsumption are preorder relations. We also provide a
number of different heuristics which can be used to abstract away
concrete values into registers so that more states and transitions can
be merged and provide proofs of the various conditions which must hold
for these abstractions to subsume their ungeneralised counterparts. A
Code Generator setup to create executable Scala code is also defined.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Extended_Finite_State_Machine_Inference</h3>
<ul>
<li><a href="../theories/extended_finite_state_machine_inference/#Subsumption">Subsumption</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Drinks_Subsumption">Drinks_Subsumption</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Inference">Inference</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#SelectionStrategies">SelectionStrategies</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Store_Reuse">Store_Reuse</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Store_Reuse_Subsumption">Store_Reuse_Subsumption</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Increment_Reset">Increment_Reset</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Same_Register">Same_Register</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Least_Upper_Bound">Least_Upper_Bound</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Distinguishing_Guards">Distinguishing_Guards</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Weak_Subsumption">Weak_Subsumption</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Group_By">Group_By</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#PTA_Generalisation">PTA_Generalisation</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#EFSM_Dot">EFSM_Dot</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#efsm2sal">efsm2sal</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Code_Target_List">Code_Target_List</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Code_Target_Set">Code_Target_Set</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Code_Target_FSet">Code_Target_FSet</a></li>
<li><a href="../theories/extended_finite_state_machine_inference/#Code_Generation">Code_Generation</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Extended_Finite_State_Machines.html">A Formal Model of Extended Finite State Machines</a></li></ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Extended_Finite_State_Machine_Inference/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Extended_Finite_State_Machine_Inference-AFP</p><pre id="copy-text">@article{Extended_Finite_State_Machine_Inference-AFP,
author = {Michael Foster and Achim D. Brucker and Ramsay G. Taylor and John Derrick},
title = {Inference of Extended Finite State Machines},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Extended_Finite_State_Machine_Inference.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel of <span class='first'>E</span>xtended <span class='first'>F</span>inite <span class='first'>S</span>tate <span class='first'>M</span>achines</h1>
<div>
<p><a href="../authors/foster">Michael Foster</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJtIiwiZm9zdGVyIl19">📧</a>, <a href="../authors/brucker">Achim D. Brucker</a> <a class="obfuscated" data="eyJob3N0IjpbImV4ZXRlciIsImFjIiwidWsiXSwidXNlciI6WyJhIiwiYnJ1Y2tlciJdfQ==">📧</a>, <a href="../authors/taylor">Ramsay G. Taylor</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJyIiwiZyIsInRheWxvciJdfQ==">📧</a> and <a href="../authors/derrick">John Derrick</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJqIiwiZGVycmljayJdfQ==">📧</a>
</p>
<p class="date">September 7, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we provide a formalisation of extended finite state
machines (EFSMs) where models are represented as finite sets of
transitions between states. EFSMs execute traces to produce observable
outputs. We also define various simulation and equality metrics for
EFSMs in terms of traces and prove their strengths in relation to each
other. Another key contribution is a framework of function definitions
such that LTL properties can be phrased over EFSMs. Finally, we
provide a simple example case study in the form of a drinks machine.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Extended_Finite_State_Machines</h3>
<ul>
<li><a href="../theories/extended_finite_state_machines/#Trilean">Trilean</a></li>
<li><a href="../theories/extended_finite_state_machines/#Value">Value</a></li>
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<li><a href="../theories/extended_finite_state_machines/#Value_Lexorder">Value_Lexorder</a></li>
<li><a href="../theories/extended_finite_state_machines/#AExp">AExp</a></li>
<li><a href="../theories/extended_finite_state_machines/#AExp_Lexorder">AExp_Lexorder</a></li>
<li><a href="../theories/extended_finite_state_machines/#GExp">GExp</a></li>
<li><a href="../theories/extended_finite_state_machines/#GExp_Lexorder">GExp_Lexorder</a></li>
<li><a href="../theories/extended_finite_state_machines/#FSet_Utils">FSet_Utils</a></li>
<li><a href="../theories/extended_finite_state_machines/#Transition">Transition</a></li>
<li><a href="../theories/extended_finite_state_machines/#Transition_Lexorder">Transition_Lexorder</a></li>
<li><a href="../theories/extended_finite_state_machines/#EFSM">EFSM</a></li>
<li><a href="../theories/extended_finite_state_machines/#EFSM_LTL">EFSM_LTL</a></li>
<li><a href="../theories/extended_finite_state_machines/#Drinks_Machine">Drinks_Machine</a></li>
<li><a href="../theories/extended_finite_state_machines/#Drinks_Machine_2">Drinks_Machine_2</a></li>
<li><a href="../theories/extended_finite_state_machines/#Drinks_Machine_LTL">Drinks_Machine_LTL</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/FinFun.html">Code Generation for Functions as Data</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Extended_Finite_State_Machine_Inference.html">Inference of Extended Finite State Machines</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Paraconsistency.html">Paraconsistency</a></li>
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<p style="display:none;" id="bibtex-filename">Extended_Finite_State_Machines-AFP</p><pre id="copy-text">@article{Extended_Finite_State_Machines-AFP,
author = {Michael Foster and Achim D. Brucker and Ramsay G. Taylor and John Derrick},
title = {A Formal Model of Extended Finite State Machines},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Extended_Finite_State_Machines.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/FFT.html b/web/entries/FFT.html
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<h1 >
<span class='first'>F</span>ast <span class='first'>F</span>ourier <span class='first'>T</span>ransform</h1>
<div>
<p><a href="../authors/ballarin">Clemens Ballarin</a> <a href="http://www21.in.tum.de/~ballarin/">🌐</a>
</p>
<p class="date">October 12, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise a functional implementation of the FFT algorithm over the complex numbers, and its inverse. Both are shown equivalent to the usual definitions of these operations through Vandermonde matrices. They are also shown to be inverse to each other, more precisely, that composition of the inverse and the transformation yield the identity up to a scalar.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session FFT</h3>
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<p style="display:none;" id="bibtex-filename">FFT-AFP</p><pre id="copy-text">@article{FFT-AFP,
author = {Clemens Ballarin},
title = {Fast Fourier Transform},
journal = {Archive of Formal Proofs},
month = {October},
year = {2005},
note = {\url{https://isa-afp.org/entries/FFT.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FFT-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/FLP.html b/web/entries/FLP.html
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>onstructive <span class='first'>P</span>roof for <span class='first'>F</span><span class='first'>L</span><span class='first'>P</span></h1>
<div>
<p><a href="../authors/bisping">Benjamin Bisping</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbXB1cyIsInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsiYmVuamFtaW4iLCJiaXNwaW5nIl19">📧</a>, <a href="../authors/brodmann">Paul-David Brodmann</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsicCIsImJyb2RtYW5uIl19">📧</a>, <a href="../authors/jungnickel">Tim Jungnickel</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsidGltIiwianVuZ25pY2tlbCJdfQ==">📧</a>, <a href="../authors/rickmann">Christina Rickmann</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsiYyIsInJpY2ttYW5uIl19">📧</a>, <a href="../authors/seidler">Henning Seidler</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haWxib3giLCJ0dS1iZXJsaW4iLCJkZSJdLCJ1c2VyIjpbImhlbm5pbmciLCJzZWlkbGVyIl19">📧</a>, <a href="../authors/stueber">Anke Stüber</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbXB1cyIsInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsiYW5rZSIsInN0dWViZXIiXX0=">📧</a>, <a href="../authors/weidner">Arno Wilhelm-Weidner</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsiYXJubyIsIndpbGhlbG0td2VpZG5lciJdfQ==">📧</a>, <a href="../authors/peters">Kirstin Peters</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsia2lyc3RpbiIsInBldGVycyJdfQ==">📧</a> and <a href="../authors/nestmann">Uwe Nestmann</a> <a href="https://www.mtv.tu-berlin.de/nestmann/">🌐</a>
</p>
<p class="date">May 18, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The impossibility of distributed consensus with one faulty process is
a result with important consequences for real world distributed
systems e.g., commits in replicated databases. Since proofs are not
immune to faults and even plausible proofs with a profound formalism
can conclude wrong results, we validate the fundamental result named
FLP after Fischer, Lynch and Paterson.
We present a formalization of distributed systems
and the aforementioned consensus problem. Our proof is based on Hagen
Völzer's paper "A constructive proof for FLP". In addition to the
enhanced confidence in the validity of Völzer's proof, we contribute
the missing gaps to show the correctness in Isabelle/HOL. We clarify
the proof details and even prove fairness of the infinite execution
that contradicts consensus. Our Isabelle formalization can also be
reused for further proofs of properties of distributed systems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li></ul>
<h3>Session FLP</h3>
<ul>
<li><a href="../theories/flp/#Multiset">Multiset</a></li>
<li><a href="../theories/flp/#AsynchronousSystem">AsynchronousSystem</a></li>
<li><a href="../theories/flp/#ListUtilities">ListUtilities</a></li>
<li><a href="../theories/flp/#Execution">Execution</a></li>
<li><a href="../theories/flp/#FLPSystem">FLPSystem</a></li>
<li><a href="../theories/flp/#FLPTheorem">FLPTheorem</a></li>
<li><a href="../theories/flp/#FLPExistingSystem">FLPExistingSystem</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">FLP-AFP</p><pre id="copy-text">@article{FLP-AFP,
author = {Benjamin Bisping and Paul-David Brodmann and Tim Jungnickel and Christina Rickmann and Henning Seidler and Anke Stüber and Arno Wilhelm-Weidner and Kirstin Peters and Uwe Nestmann},
title = {A Constructive Proof for FLP},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/FLP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-FLP-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FLP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FLP-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-FLP-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<h1 >
<span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic <span class='first'>A</span>ccording to <span class='first'>F</span>itting</h1>
<div>
<p><a href="../authors/berghofer">Stefan Berghofer</a> <a href="http://www.in.tum.de/~berghofe">🌐</a>
with contributions from <a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">August 2, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of parts of Melvin Fitting's book "First-Order Logic and Automated Theorem Proving". The formalization covers the syntax of first-order logic, its semantics, the model existence theorem, a natural deduction proof calculus together with a proof of correctness and completeness, as well as the Löwenheim-Skolem theorem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 21, 2018</dt>
<dd>Proved completeness theorem for open formulas. Proofs are now written in the declarative style. Enumeration of pairs and datatypes is automated using the Countable theory.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li></ul>
<h3>Session FOL-Fitting</h3>
<ul>
<li><a href="../theories/fol-fitting/#FOL_Fitting">FOL_Fitting</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/FO_Theory_Rewriting.html">First-Order Theory of Rewriting</a></li><li><a href="../entries/FOL_Seq_Calc1.html">A Sequent Calculus for First-Order Logic</a></li></ul>
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<div>
<p style="display:none;" id="bibtex-filename">FOL-Fitting-AFP</p><pre id="copy-text">@article{FOL-Fitting-AFP,
author = {Stefan Berghofer},
title = {First-Order Logic According to Fitting},
journal = {Archive of Formal Proofs},
month = {August},
year = {2007},
note = {\url{https://isa-afp.org/entries/FOL-Fitting.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-FOL-Fitting-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/FOL_Axiomatic.html b/web/entries/FOL_Axiomatic.html
--- a/web/entries/FOL_Axiomatic.html
+++ b/web/entries/FOL_Axiomatic.html
@@ -1,171 +1,173 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Soundness and Completeness of an Axiomatic System for First-Order Logic - Archive of Formal Proofs</title><meta name="description" content="This work is a formalization of the soundness and completeness of an axiomatic system for first-order logic. The proof system is based on System Q1 by..."><meta property="og:title" content="Soundness and Completeness of an Axiomatic System for First-Order Logic" />
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<h1 >
<span class='first'>S</span>oundness and <span class='first'>C</span>ompleteness of an <span class='first'>A</span>xiomatic <span class='first'>S</span>ystem for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">September 24, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of the soundness and completeness of an
axiomatic system for first-order logic. The proof system is based on
System Q1 by Smullyan and the completeness proof follows his textbook
"First-Order Logic" (Springer-Verlag 1968). The completeness
proof is in the Henkin style where a consistent set is extended to a
maximal consistent set using Lindenbaum's construction and Henkin
witnesses are added during the construction to ensure saturation as
well. The resulting set is a Hintikka set which, by the model
existence theorem, is satisfiable in the Herbrand universe.
Paper: <a href="https://doi.org/10.4230/LIPIcs.TYPES.2021.8">doi.org/10.4230/LIPIcs.TYPES.2021.8</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session FOL_Axiomatic</h3>
<ul>
<li><a href="../theories/fol_axiomatic/#FOL_Axiomatic">FOL_Axiomatic</a></li>
<li><a href="../theories/fol_axiomatic/#FOL_Axiomatic_Variant">FOL_Axiomatic_Variant</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">FOL_Axiomatic-AFP</p><pre id="copy-text">@article{FOL_Axiomatic-AFP,
author = {Asta Halkjær From},
title = {Soundness and Completeness of an Axiomatic System for First-Order Logic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/FOL_Axiomatic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic <span class='first'>A</span>ccording to <span class='first'>H</span>arrison</h1>
<div>
<p><a href="../authors/jensen">Alexander Birch Jensen</a> <a href="https://people.compute.dtu.dk/aleje/">🌐</a>, <a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a> and <a href="../authors/villadsen">Jørgen Villadsen</a> <a href="https://people.compute.dtu.dk/jovi/">🌐</a>
</p>
<p class="date">January 1, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We present a certified declarative first-order prover with equality
based on John Harrison's Handbook of Practical Logic and
Automated Reasoning, Cambridge University Press, 2009. ML code
reflection is used such that the entire prover can be executed within
Isabelle as a very simple interactive proof assistant. As examples we
consider Pelletier's problems 1-46.</p>
<p>Reference: Programming and Verifying a Declarative First-Order
Prover in Isabelle/HOL. Alexander Birch Jensen, John Bruntse Larsen,
Anders Schlichtkrull & Jørgen Villadsen. AI Communications 31:281-299
2018. <a href="https://content.iospress.com/articles/ai-communications/aic764">
https://content.iospress.com/articles/ai-communications/aic764</a></p>
<p>See also: Students' Proof Assistant (SPA).
<a href=https://github.com/logic-tools/spa>
https://github.com/logic-tools/spa</a></p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 21, 2018</dt>
<dd>Proof of Pelletier's problem 34 (Andrews's Challenge) thanks to Asta Halkjær From.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session FOL_Harrison</h3>
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<li><a href="../theories/fol_harrison/#FOL_Harrison">FOL_Harrison</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">FOL_Harrison-AFP</p><pre id="copy-text">@article{FOL_Harrison-AFP,
author = {Alexander Birch Jensen and Anders Schlichtkrull and Jørgen Villadsen},
title = {First-Order Logic According to Harrison},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/FOL_Harrison.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>equent <span class='first'>C</span>alculus for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
with contributions from <a href="../authors/jensen">Alexander Birch Jensen</a> <a href="https://people.compute.dtu.dk/aleje/">🌐</a>, <a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a> and <a href="../authors/villadsen">Jørgen Villadsen</a> <a href="https://people.compute.dtu.dk/jovi/">🌐</a>
</p>
<p class="date">July 18, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work formalizes soundness and completeness of a one-sided sequent
calculus for first-order logic. The completeness is shown via a
translation from a complete semantic tableau calculus, the proof of
which is based on the First-Order Logic According to Fitting theory.
The calculi and proof techniques are taken from Ben-Ari's
Mathematical Logic for Computer Science.
Paper: <a href="http://ceur-ws.org/Vol-3002/paper7.pdf">ceur-ws.org/Vol-3002/paper7.pdf</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session FOL_Seq_Calc1</h3>
<ul>
<li><a href="../theories/fol_seq_calc1/#Common">Common</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/FOL_Seq_Calc2.html">A Sequent Calculus Prover for First-Order Logic with Functions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/FOL_Axiomatic.html">Soundness and Completeness of an Axiomatic System for First-Order Logic</a></li>
<li><a href="../entries/Relational_Paths.html">Relational Characterisations of Paths</a></li>
<li><a href="../entries/Abstract_Soundness.html">Abstract Soundness</a></li>
<li><a href="../entries/Completeness.html">Completeness theorem</a></li>
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<p style="display:none;" id="bibtex-filename">FOL_Seq_Calc1-AFP</p><pre id="copy-text">@article{FOL_Seq_Calc1-AFP,
author = {Asta Halkjær From},
title = {A Sequent Calculus for First-Order Logic},
journal = {Archive of Formal Proofs},
month = {July},
year = {2019},
note = {\url{https://isa-afp.org/entries/FOL_Seq_Calc1.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc1-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc1-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>equent <span class='first'>C</span>alculus <span class='first'>P</span>rover for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic <span class='first'>W</span>ith <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a> and <a href="../authors/jacobsen">Frederik Krogsdal Jacobsen</a> <a href="http://people.compute.dtu.dk/fkjac/">🌐</a>
</p>
<p class="date">January 31, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize an automated theorem prover for first-order logic with
functions. The proof search procedure is based on sequent calculus and
we verify its soundness and completeness using the Abstract Soundness
and Abstract Completeness theories. Our analytic completeness proof
covers both open and closed formulas. Since our deterministic prover
considers only the subset of terms relevant to proving a given
sequent, we do so as well when building a countermodel from a failed
proof. We formally connect our prover with the proof system and
semantics of the existing SeCaV system. In particular, the
prover's output can be post-processed in Haskell to generate
human-readable SeCaV proofs which are also machine-verifiable proof
certificates.
Paper: <a href="https://doi.org/10.4230/LIPIcs.ITP.2022.13">doi.org/10.4230/LIPIcs.ITP.2022.13</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session FOL_Seq_Calc2</h3>
<ul>
<li><a href="../theories/fol_seq_calc2/#SeCaV">SeCaV</a></li>
<li><a href="../theories/fol_seq_calc2/#Sequent1">Sequent1</a></li>
<li><a href="../theories/fol_seq_calc2/#Sequent_Calculus_Verifier">Sequent_Calculus_Verifier</a></li>
<li><a href="../theories/fol_seq_calc2/#Prover">Prover</a></li>
<li><a href="../theories/fol_seq_calc2/#Export">Export</a></li>
<li><a href="../theories/fol_seq_calc2/#ProverLemmas">ProverLemmas</a></li>
<li><a href="../theories/fol_seq_calc2/#Hintikka">Hintikka</a></li>
<li><a href="../theories/fol_seq_calc2/#EPathHintikka">EPathHintikka</a></li>
<li><a href="../theories/fol_seq_calc2/#Usemantics">Usemantics</a></li>
<li><a href="../theories/fol_seq_calc2/#Countermodel">Countermodel</a></li>
<li><a href="../theories/fol_seq_calc2/#Soundness">Soundness</a></li>
<li><a href="../theories/fol_seq_calc2/#Completeness">Completeness</a></li>
<li><a href="../theories/fol_seq_calc2/#Results">Results</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract_Completeness.html">Abstract Completeness</a></li><li><a href="../entries/Abstract_Soundness.html">Abstract Soundness</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/FOL_Seq_Calc1.html">A Sequent Calculus for First-Order Logic</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Pratt_Certificate.html">Pratt&rsquo;s Primality Certificates</a></li>
<li><a href="../entries/Separata.html">Separata: Isabelle tactics for Separation Algebra</a></li>
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<p style="display:none;" id="bibtex-filename">FOL_Seq_Calc2-AFP</p><pre id="copy-text">@article{FOL_Seq_Calc2-AFP,
author = {Asta Halkjær From and Frederik Krogsdal Jacobsen},
title = {A Sequent Calculus Prover for First-Order Logic with Functions},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/FOL_Seq_Calc2.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc2-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc2-2022-02-02.tar.gz">Feb 2, 2022</a>: Isabelle2021-1
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Naive Prover for First-Order Logic - Archive of Formal Proofs</title><meta name="description" content=" The AFP entry Abstract Completeness by Blanchette, Popescu and Traytel formalizes the core of Beth/Hintikka-style completeness proofs for first-order..."><meta property="og:title" content="A Naive Prover for First-Order Logic" />
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<h1 >
<span class='first'>A</span> <span class='first'>N</span>aive <span class='first'>P</span>rover for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">March 22, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> The AFP entry <a
href="https://www.isa-afp.org/entries/Abstract_Completeness.html">Abstract
Completeness</a> by Blanchette, Popescu and Traytel formalizes
the core of Beth/Hintikka-style completeness proofs for first-order
logic and can be used to formalize executable sequent calculus
provers. In the Journal of Automated Reasoning, the authors
instantiate the framework with a sequent calculus for first-order
logic and prove its completeness. Their use of an infinite set of
proof rules indexed by formulas yields very direct arguments. A fair
stream of these rules controls the prover, making its definition
remarkably simple. The AFP entry, however, only contains a toy example
for propositional logic. The AFP entry <a
href="https://www.isa-afp.org/entries/FOL_Seq_Calc2.html">A
Sequent Calculus Prover for First-Order Logic with Functions</a>
by From and Jacobsen also uses the framework, but uses a finite set of
generic rules resulting in a more sophisticated prover with more
complicated proofs. </p> <p> This entry contains an
executable sequent calculus prover for first-order logic with
functions in the style presented by Blanchette et al. The prover can
be exported to Haskell and this entry includes formalized proofs of
its soundness and completeness. The proofs are simpler than those for
the prover by From and Jacobsen but the performance of the prover is
significantly worse. </p> <p> The included theory
<em>Fair-Stream</em> first proves that the sequence of
natural numbers 0, 0, 1, 0, 1, 2, etc. is fair. It then proves that
mapping any surjective function across the sequence preserves
fairness. This method of obtaining a fair stream of rules is similar
to the one given by Blanchette et al. The concrete functions from
natural numbers to terms, formulas and rules are defined using the
<em>Nat-Bijection</em> theory in the HOL-Library.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session FOL_Seq_Calc3</h3>
<ul>
<li><a href="../theories/fol_seq_calc3/#List_Syntax">List_Syntax</a></li>
<li><a href="../theories/fol_seq_calc3/#Fair_Stream">Fair_Stream</a></li>
<li><a href="../theories/fol_seq_calc3/#Syntax">Syntax</a></li>
<li><a href="../theories/fol_seq_calc3/#Semantics">Semantics</a></li>
<li><a href="../theories/fol_seq_calc3/#Encoding">Encoding</a></li>
<li><a href="../theories/fol_seq_calc3/#Prover">Prover</a></li>
<li><a href="../theories/fol_seq_calc3/#Export">Export</a></li>
<li><a href="../theories/fol_seq_calc3/#Soundness">Soundness</a></li>
<li><a href="../theories/fol_seq_calc3/#Completeness">Completeness</a></li>
<li><a href="../theories/fol_seq_calc3/#Result">Result</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract_Completeness.html">Abstract Completeness</a></li><li><a href="../entries/Abstract_Soundness.html">Abstract Soundness</a></li></ul>
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<p style="display:none;" id="bibtex-filename">FOL_Seq_Calc3-AFP</p><pre id="copy-text">@article{FOL_Seq_Calc3-AFP,
author = {Asta Halkjær From},
title = {A Naive Prover for First-Order Logic},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/FOL_Seq_Calc3.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc3-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FOL_Seq_Calc3-2022-03-29.tar.gz">Mar 29, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/FO_Theory_Rewriting.html b/web/entries/FO_Theory_Rewriting.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>First-Order Theory of Rewriting - Archive of Formal Proofs</title><meta name="description" content="The first-order theory of rewriting (FORT) is a decidable theory for
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<h1 >
<span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>T</span>heory of <span class='first'>R</span>ewriting</h1>
<div>
<p><a href="../authors/lochmann">Alexander Lochmann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWxleGFuZGVyIiwibG9jaG1hbm4iXX0=">📧</a> and <a href="../authors/felgenhauer">Bertram Felgenhauer</a>
</p>
<p class="date">February 2, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The first-order theory of rewriting (FORT) is a decidable theory for
linear variable-separated rewrite systems. The decision procedure is
based on tree automata technique and an inference system presented in
"Certifying Proofs in the First-Order Theory of Rewriting".
This AFP entry provides a formalization of the underlying decision
procedure. Moreover it allows to generate a function that can verify
each inference step via the code generation facility of Isabelle/HOL.
Additionally it contains the specification of a certificate language
(that allows to state proofs in FORT) and a formalized function that
allows to verify the validity of the proof. This gives software tool
authors, that implement the decision procedure, the possibility to
verify their output.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session FO_Theory_Rewriting</h3>
<ul>
<li><a href="../theories/fo_theory_rewriting/#Utils">Utils</a></li>
<li><a href="../theories/fo_theory_rewriting/#Multihole_Context">Multihole_Context</a></li>
<li><a href="../theories/fo_theory_rewriting/#Ground_MCtxt">Ground_MCtxt</a></li>
<li><a href="../theories/fo_theory_rewriting/#Bot_Terms">Bot_Terms</a></li>
<li><a href="../theories/fo_theory_rewriting/#Saturation">Saturation</a></li>
<li><a href="../theories/fo_theory_rewriting/#Rewriting">Rewriting</a></li>
<li><a href="../theories/fo_theory_rewriting/#LV_to_GTT">LV_to_GTT</a></li>
<li><a href="../theories/fo_theory_rewriting/#NF">NF</a></li>
<li><a href="../theories/fo_theory_rewriting/#Tree_Automata_Derivation_Split">Tree_Automata_Derivation_Split</a></li>
<li><a href="../theories/fo_theory_rewriting/#TA_Clousure_Const">TA_Clousure_Const</a></li>
<li><a href="../theories/fo_theory_rewriting/#Type_Instances_Impl">Type_Instances_Impl</a></li>
<li><a href="../theories/fo_theory_rewriting/#NF_Impl">NF_Impl</a></li>
<li><a href="../theories/fo_theory_rewriting/#Context_Extensions">Context_Extensions</a></li>
<li><a href="../theories/fo_theory_rewriting/#FOR_Certificate">FOR_Certificate</a></li>
<li><a href="../theories/fo_theory_rewriting/#Lift_Root_Step">Lift_Root_Step</a></li>
<li><a href="../theories/fo_theory_rewriting/#Context_RR2">Context_RR2</a></li>
<li><a href="../theories/fo_theory_rewriting/#GTT_RRn">GTT_RRn</a></li>
<li><a href="../theories/fo_theory_rewriting/#FOL_Extra">FOL_Extra</a></li>
<li><a href="../theories/fo_theory_rewriting/#FOR_Semantics">FOR_Semantics</a></li>
<li><a href="../theories/fo_theory_rewriting/#FOR_Check">FOR_Check</a></li>
<li><a href="../theories/fo_theory_rewriting/#FOR_Check_Impl">FOR_Check_Impl</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></li><li><a href="../entries/Regular_Tree_Relations.html">Regular Tree Relations</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/FO_Theory_Rewriting/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/FO_Theory_Rewriting/document.pdf">Proof
document</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/FO_Theory_Rewriting/session_graph.pdf">Dependencies</a></nav>
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<p style="display:none;" id="bibtex-filename">FO_Theory_Rewriting-AFP</p><pre id="copy-text">@article{FO_Theory_Rewriting-AFP,
author = {Alexander Lochmann and Bertram Felgenhauer},
title = {First-Order Theory of Rewriting},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/FO_Theory_Rewriting.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a class="close" href="#">&times;</a>
<a href="https://www.isa-afp.org/release//afp-FO_Theory_Rewriting-current.tar.gz" download>Download latest</a>
-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-FO_Theory_Rewriting-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FO_Theory_Rewriting-2022-02-10.tar.gz">Feb 10, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/FSM_Tests.html b/web/entries/FSM_Tests.html
--- a/web/entries/FSM_Tests.html
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@@ -1,223 +1,228 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verified Complete Test Strategies for Finite State Machines - Archive of Formal Proofs</title><meta name="description" content="This entry provides executable formalisations of complete test generation algorithms for finite state machines. It covers testing for the..."><meta property="og:title" content="Verified Complete Test Strategies for Finite State Machines" />
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<h1 >
<span class='first'>V</span>erified <span class='first'>C</span>omplete <span class='first'>T</span>est <span class='first'>S</span>trategies for <span class='first'>F</span>inite <span class='first'>S</span>tate <span class='first'>M</span>achines</h1>
<div>
<p><a href="../authors/sachtleben">Robert Sachtleben</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1icmVtZW4iLCJkZSJdLCJ1c2VyIjpbInJvYl9zYWMiXX0=">📧</a>
</p>
<p class="date">August 9, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides executable formalisations of complete test
generation algorithms for finite state machines. It covers testing for
the language-equivalence and reduction conformance relations,
supporting the former via the W, Wp, HSI, H, SPY and SPYH-methods, and
the latter via adaptive state counting. The test strategies are
implemented using generic frameworks, allowing for reuse of shared
components between related strategies. This work is described in the
author&#x27;s <a href="https://doi.org/10.26092/elib/1665">doctoral
thesis</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session FSM_Tests</h3>
<ul>
<li><a href="../theories/fsm_tests/#Util">Util</a></li>
<li><a href="../theories/fsm_tests/#Util_Refined">Util_Refined</a></li>
<li><a href="../theories/fsm_tests/#FSM_Impl">FSM_Impl</a></li>
<li><a href="../theories/fsm_tests/#FSM">FSM</a></li>
<li><a href="../theories/fsm_tests/#Product_FSM">Product_FSM</a></li>
<li><a href="../theories/fsm_tests/#Minimisation">Minimisation</a></li>
<li><a href="../theories/fsm_tests/#Distinguishability">Distinguishability</a></li>
<li><a href="../theories/fsm_tests/#IO_Sequence_Set">IO_Sequence_Set</a></li>
<li><a href="../theories/fsm_tests/#Observability">Observability</a></li>
<li><a href="../theories/fsm_tests/#Prefix_Tree">Prefix_Tree</a></li>
<li><a href="../theories/fsm_tests/#Prefix_Tree_Refined">Prefix_Tree_Refined</a></li>
<li><a href="../theories/fsm_tests/#State_Cover">State_Cover</a></li>
<li><a href="../theories/fsm_tests/#OFSM_Tables_Refined">OFSM_Tables_Refined</a></li>
<li><a href="../theories/fsm_tests/#Prime_Transformation">Prime_Transformation</a></li>
<li><a href="../theories/fsm_tests/#Convergence">Convergence</a></li>
<li><a href="../theories/fsm_tests/#Convergence_Graph">Convergence_Graph</a></li>
<li><a href="../theories/fsm_tests/#Empty_Convergence_Graph">Empty_Convergence_Graph</a></li>
<li><a href="../theories/fsm_tests/#H_Framework">H_Framework</a></li>
<li><a href="../theories/fsm_tests/#SPY_Framework">SPY_Framework</a></li>
<li><a href="../theories/fsm_tests/#Pair_Framework">Pair_Framework</a></li>
<li><a href="../theories/fsm_tests/#Intermediate_Implementations">Intermediate_Implementations</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_Representations">Test_Suite_Representations</a></li>
<li><a href="../theories/fsm_tests/#Simple_Convergence_Graph">Simple_Convergence_Graph</a></li>
<li><a href="../theories/fsm_tests/#Intermediate_Frameworks">Intermediate_Frameworks</a></li>
<li><a href="../theories/fsm_tests/#H_Method_Implementations">H_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#HSI_Method_Implementations">HSI_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#Partial_S_Method_Implementations">Partial_S_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#SPY_Method_Implementations">SPY_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#SPYH_Method_Implementations">SPYH_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_Representations_Refined">Test_Suite_Representations_Refined</a></li>
<li><a href="../theories/fsm_tests/#W_Method_Implementations">W_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#Wp_Method_Implementations">Wp_Method_Implementations</a></li>
<li><a href="../theories/fsm_tests/#Backwards_Reachability_Analysis">Backwards_Reachability_Analysis</a></li>
<li><a href="../theories/fsm_tests/#State_Separator">State_Separator</a></li>
<li><a href="../theories/fsm_tests/#Adaptive_Test_Case">Adaptive_Test_Case</a></li>
<li><a href="../theories/fsm_tests/#State_Preamble">State_Preamble</a></li>
<li><a href="../theories/fsm_tests/#Helper_Algorithms">Helper_Algorithms</a></li>
<li><a href="../theories/fsm_tests/#Maximal_Path_Trie">Maximal_Path_Trie</a></li>
<li><a href="../theories/fsm_tests/#R_Distinguishability">R_Distinguishability</a></li>
<li><a href="../theories/fsm_tests/#Traversal_Set">Traversal_Set</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite">Test_Suite</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_IO">Test_Suite_IO</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_Calculation">Test_Suite_Calculation</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_Calculation_Refined">Test_Suite_Calculation_Refined</a></li>
<li><a href="../theories/fsm_tests/#FSM_Code_Datatype">FSM_Code_Datatype</a></li>
<li><a href="../theories/fsm_tests/#Test_Suite_Generator_Code_Export">Test_Suite_Generator_Code_Export</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Adaptive_State_Counting.html">Formalisation of an Adaptive State Counting Algorithm</a></li>
<li><a href="../entries/JinjaDCI.html">JinjaDCI: a Java semantics with dynamic class initialization</a></li>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/FSM_Tests/document.pdf">Proof
document</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/FSM_Tests/session_graph.pdf">Dependencies</a></nav>
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<p style="display:none;" id="bibtex-filename">FSM_Tests-AFP</p><pre id="copy-text">@article{FSM_Tests-AFP,
author = {Robert Sachtleben},
title = {Verified Complete Test Strategies for Finite State Machines},
journal = {Archive of Formal Proofs},
month = {August},
year = {2022},
note = {\url{https://isa-afp.org/entries/FSM_Tests.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-FSM_Tests-current.tar.gz" download>Download latest</a>
-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-FSM_Tests-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FSM_Tests-2022-08-11.tar.gz">Aug 11, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Factor_Algebraic_Polynomial.html b/web/entries/Factor_Algebraic_Polynomial.html
--- a/web/entries/Factor_Algebraic_Polynomial.html
+++ b/web/entries/Factor_Algebraic_Polynomial.html
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<h1 >
<span class='first'>F</span>actorization of <span class='first'>P</span>olynomials <span class='first'>W</span>ith <span class='first'>A</span>lgebraic <span class='first'>C</span>oefficients</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">November 8, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The AFP already contains a verified implementation of algebraic
numbers. However, it is has a severe limitation in its factorization
algorithm of real and complex polynomials: the factorization is only
guaranteed to succeed if the coefficients of the polynomial are
rational numbers. In this work, we verify an algorithm to factor all
real and complex polynomials whose coefficients are algebraic. The
existence of such an algorithm proves in a constructive way that the
set of complex algebraic numbers is algebraically closed. Internally,
the algorithm is based on resultants of multivariate polynomials and
an approximation algorithm using interval arithmetic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Factor_Algebraic_Polynomial</h3>
<ul>
<li><a href="../theories/factor_algebraic_polynomial/#Poly_Connection">Poly_Connection</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#MPoly_Divide">MPoly_Divide</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#MPoly_Divide_Code">MPoly_Divide_Code</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#MPoly_Container">MPoly_Container</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Multivariate_Resultant">Multivariate_Resultant</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Is_Int_To_Int">Is_Int_To_Int</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Roots_of_Algebraic_Poly">Roots_of_Algebraic_Poly</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Roots_of_Algebraic_Poly_Impl">Roots_of_Algebraic_Poly_Impl</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Roots_via_IA">Roots_via_IA</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Roots_of_Real_Complex_Poly">Roots_of_Real_Complex_Poly</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Factor_Complex_Poly">Factor_Complex_Poly</a></li>
<li><a href="../theories/factor_algebraic_polynomial/#Factor_Real_Poly">Factor_Real_Poly</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Cubic_Quartic_Equations.html">Solving Cubic and Quartic Equations</a></li><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Interval_Arithmetic_Word32.html">Interval Arithmetic on 32-bit Words</a></li>
<li><a href="../entries/Transcendence_Series_Hancl_Rucki.html">The Transcendence of Certain Infinite Series</a></li>
<li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li>
<li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li>
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<p style="display:none;" id="bibtex-filename">Factor_Algebraic_Polynomial-AFP</p><pre id="copy-text">@article{Factor_Algebraic_Polynomial-AFP,
author = {Manuel Eberl and René Thiemann},
title = {Factorization of Polynomials with Algebraic Coefficients},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Factor_Algebraic_Polynomial.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>U</span>pper <span class='first'>B</span>ounding <span class='first'>D</span>iameters of <span class='first'>S</span>tate <span class='first'>S</span>paces of <span class='first'>F</span>actored <span class='first'>T</span>ransition <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/kurz">Friedrich Kurz</a> and <a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a href="http://home.in.tum.de/~mansour/">🌐</a>
</p>
<p class="date">October 12, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A completeness threshold is required to guarantee the completeness of
planning as satisfiability, and bounded model checking of safety
properties. One valid completeness threshold is the diameter of the
underlying transition system. The diameter is the maximum element in
the set of lengths of all shortest paths between pairs of states. The
diameter is not calculated exactly in our setting, where the
transition system is succinctly described using a (propositionally)
factored representation. Rather, an upper bound on the diameter is
calculated compositionally, by bounding the diameters of small
abstract subsystems, and then composing those. We port a HOL4
formalisation of a compositional algorithm for computing a relatively
tight upper bound on the system diameter. This compositional algorithm
exploits acyclicity in the state space to achieve compositionality,
and it was introduced by Abdulaziz et. al. The formalisation that we
port is described as a part of another paper by Abdulaziz et. al. As a
part of this porting we developed a libray about transition systems,
which shall be of use in future related mechanisation efforts.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Factored_Transition_System_Bounding</h3>
<ul>
<li><a href="../theories/factored_transition_system_bounding/#FactoredSystemLib">FactoredSystemLib</a></li>
<li><a href="../theories/factored_transition_system_bounding/#ListUtils">ListUtils</a></li>
<li><a href="../theories/factored_transition_system_bounding/#FSSublist">FSSublist</a></li>
<li><a href="../theories/factored_transition_system_bounding/#HoArithUtils">HoArithUtils</a></li>
<li><a href="../theories/factored_transition_system_bounding/#FmapUtils">FmapUtils</a></li>
<li><a href="../theories/factored_transition_system_bounding/#FactoredSystem">FactoredSystem</a></li>
<li><a href="../theories/factored_transition_system_bounding/#ActionSeqProcess">ActionSeqProcess</a></li>
<li><a href="../theories/factored_transition_system_bounding/#RelUtils">RelUtils</a></li>
<li><a href="../theories/factored_transition_system_bounding/#Dependency">Dependency</a></li>
<li><a href="../theories/factored_transition_system_bounding/#Invariants">Invariants</a></li>
<li><a href="../theories/factored_transition_system_bounding/#SetUtils">SetUtils</a></li>
<li><a href="../theories/factored_transition_system_bounding/#TopologicalProps">TopologicalProps</a></li>
<li><a href="../theories/factored_transition_system_bounding/#SystemAbstraction">SystemAbstraction</a></li>
<li><a href="../theories/factored_transition_system_bounding/#Acyclicity">Acyclicity</a></li>
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<p style="display:none;" id="bibtex-filename">Factored_Transition_System_Bounding-AFP</p><pre id="copy-text">@article{Factored_Transition_System_Bounding-AFP,
author = {Friedrich Kurz and Mohammad Abdulaziz},
title = {Upper Bounding Diameters of State Spaces of Factored Transition Systems},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/Factored_Transition_System_Bounding.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Factored_Transition_System_Bounding-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>T</span>he <span class='first'>F</span>alling <span class='first'>F</span>actorial of a <span class='first'>S</span>um</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">December 22, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry shows that the falling factorial of a sum can be computed
with an expression using binomial coefficients and the falling
factorial of its summands. The entry provides three different proofs:
a combinatorial proof, an induction proof and an algebraic proof using
the Vandermonde identity. The three formalizations try to follow
their informal presentations from a Mathematics Stack Exchange page as
close as possible. The induction and algebraic formalization end up to
be very close to their informal presentation, whereas the
combinatorial proof first requires the introduction of list
interleavings, and significant more detail than its informal
presentation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Falling_Factorial_Sum</h3>
<ul>
<li><a href="../theories/falling_factorial_sum/#Falling_Factorial_Sum_Combinatorics">Falling_Factorial_Sum_Combinatorics</a></li>
<li><a href="../theories/falling_factorial_sum/#Falling_Factorial_Sum_Induction">Falling_Factorial_Sum_Induction</a></li>
<li><a href="../theories/falling_factorial_sum/#Falling_Factorial_Sum_Vandermonde">Falling_Factorial_Sum_Vandermonde</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Card_Partitions.html">Cardinality of Set Partitions</a></li><li><a href="../entries/Discrete_Summation.html">Discrete Summation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Falling_Factorial_Sum-AFP</p><pre id="copy-text">@article{Falling_Factorial_Sum-AFP,
author = {Lukas Bulwahn},
title = {The Falling Factorial of a Sum},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/Falling_Factorial_Sum.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Falling_Factorial_Sum-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Falling_Factorial_Sum-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Falling_Factorial_Sum-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>F</span>arkas' <span class='first'>L</span>emma and <span class='first'>M</span>otzkin's <span class='first'>T</span>ransposition <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bottesch">Ralph Bottesch</a> <a href="http://cl-informatik.uibk.ac.at/users/bottesch/">🌐</a>, <a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">January 17, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a proof of Motzkin's transposition theorem and
Farkas' lemma in Isabelle/HOL. Our proof is based on the
formalization of the simplex algorithm which, given a set of linear
constraints, either returns a satisfying assignment to the problem or
detects unsatisfiability. By reusing facts about the simplex algorithm
we show that a set of linear constraints is unsatisfiable if and only
if there is a linear combination of the constraints which evaluates to
a trivially unsatisfiable inequality.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Farkas</h3>
<ul>
<li><a href="../theories/farkas/#Farkas">Farkas</a></li>
<li><a href="../theories/farkas/#Matrix_Farkas">Matrix_Farkas</a></li>
<li><a href="../theories/farkas/#Simplex_for_Reals">Simplex_for_Reals</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Simplex.html">An Incremental Simplex Algorithm with Unsatisfiable Core Generation</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Linear_Programming.html">Linear Programming</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Farkas-AFP</p><pre id="copy-text">@article{Farkas-AFP,
author = {Ralph Bottesch and Max W. Haslbeck and René Thiemann},
title = {Farkas&#39; Lemma and Motzkin&#39;s Transposition Theorem},
journal = {Archive of Formal Proofs},
month = {January},
year = {2019},
note = {\url{https://isa-afp.org/entries/Farkas.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Farkas-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Farkas-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Farkas-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Farkas-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Farkas-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Farkas-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Farkas-2019-01-21.tar.gz">Jan 21, 2019</a>: Isabelle2018
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diff --git a/web/entries/FeatherweightJava.html b/web/entries/FeatherweightJava.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Theory of Featherweight Java in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content="We formalize the type system, small-step operational semantics, and type soundness proof for Featherweight Java, a simple object calculus, in Isabelle/HOL."><meta property="og:title" content="A Theory of Featherweight Java in Isabelle/HOL" />
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<h1 >
<span class='first'>A</span> <span class='first'>T</span>heory of <span class='first'>F</span>eatherweight <span class='first'>J</span>ava in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/fosterj">J. Nathan Foster</a> <a href="http://www.cs.cornell.edu/~jnfoster/">🌐</a> and <a href="../authors/vytiniotis">Dimitrios Vytiniotis</a> <a href="http://research.microsoft.com/en-us/people/dimitris/">🌐</a>
</p>
<p class="date">March 31, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the type system, small-step operational semantics, and type soundness proof for Featherweight Java, a simple object calculus, in Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session FeatherweightJava</h3>
<ul>
<li><a href="../theories/featherweightjava/#FJDefs">FJDefs</a></li>
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<p style="display:none;" id="bibtex-filename">FeatherweightJava-AFP</p><pre id="copy-text">@article{FeatherweightJava-AFP,
author = {J. Nathan Foster and Dimitrios Vytiniotis},
title = {A Theory of Featherweight Java in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {March},
year = {2006},
note = {\url{https://isa-afp.org/entries/FeatherweightJava.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2006-04-06.tar.gz">Apr 6, 2006</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-FeatherweightJava-2006-04-05.tar.gz">Apr 5, 2006</a>: Isabelle2005
</li></ul>
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<h1 >
<span class='first'>F</span>eatherweight <span class='first'>O</span><span class='first'>C</span><span class='first'>L</span>: <span class='first'>A</span> <span class='first'>P</span>roposal for a <span class='first'>M</span>achine-<span class='first'>C</span>hecked <span class='first'>F</span>ormal <span class='first'>S</span>emantics for <span class='first'>O</span><span class='first'>C</span><span class='first'>L</span> 2.5</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a class="obfuscated" data="eyJob3N0IjpbInNwYW1mZW5jZSIsIm5ldCJdLCJ1c2VyIjpbImJydWNrZXIiXX0=">📧</a>, <a href="../authors/tuong">Frédéric Tuong</a> <a class="obfuscated" data="eyJob3N0IjpbInVzZXJzIiwiZ2ZvcmdlIiwiaW5yaWEiLCJmciJdLCJ1c2VyIjpbInR1b25nIl19">📧</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">January 16, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Unified Modeling Language (UML) is one of the few
modeling languages that is widely used in industry. While
UML is mostly known as diagrammatic modeling language
(e.g., visualizing class models), it is complemented by a
textual language, called Object Constraint Language
(OCL). The current version of OCL is based on a four-valued
logic that turns UML into a formal language. Any type
comprises the elements "invalid" and "null" which are
propagated as strict and non-strict, respectively.
Unfortunately, the former semi-formal semantics of this
specification language, captured in the "Annex A" of the
OCL standard, leads to different interpretations of corner
cases. We formalize the core of OCL: denotational
definitions, a logical calculus and operational rules that
allow for the execution of OCL expressions by a mixture of
term rewriting and code compilation. Our formalization
reveals several inconsistencies and contradictions in the
current version of the OCL standard. Overall, this document
is intended to provide the basis for a machine-checked text
"Annex A" of the OCL standard targeting at tool
implementors.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>October 13, 2015</dt>
<dd><a href="https://foss.heptapod.net/isa-afp/afp-devel/-/commit/e68e1996d5d4926397c9244e786446e99ab17e63">afp-devel@ea3b38fc54d6</a> and
<a href="https://projects.brucker.ch/hol-testgen/log/trunk?rev=12148">hol-testgen@12148</a><br>
&nbsp;&nbsp;&nbsp;Update of Featherweight OCL including a change in the abstract.<br>
</dd><dt>January 16, 2014</dt>
<dd><a href="https://foss.heptapod.net/isa-afp/afp-devel/-/commit/6217cc5b29c560f24ecc64c81047778becb69f51">afp-devel@9091ce05cb20</a> and
<a href="https://projects.brucker.ch/hol-testgen/log/trunk?rev=10241">hol-testgen@10241</a><br>
&nbsp;&nbsp;&nbsp;New Entry: Featherweight OCL</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session Featherweight_OCL</h3>
<ul>
<li><a href="../theories/featherweight_ocl/#UML_Types">UML_Types</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Logic">UML_Logic</a></li>
<li><a href="../theories/featherweight_ocl/#UML_PropertyProfiles">UML_PropertyProfiles</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Boolean">UML_Boolean</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Void">UML_Void</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Integer">UML_Integer</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Real">UML_Real</a></li>
<li><a href="../theories/featherweight_ocl/#UML_String">UML_String</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Pair">UML_Pair</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Bag">UML_Bag</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Set">UML_Set</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Sequence">UML_Sequence</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Library">UML_Library</a></li>
<li><a href="../theories/featherweight_ocl/#UML_State">UML_State</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Contracts">UML_Contracts</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Tools">UML_Tools</a></li>
<li><a href="../theories/featherweight_ocl/#UML_Main">UML_Main</a></li>
<li><a href="../theories/featherweight_ocl/#Analysis_UML">Analysis_UML</a></li>
<li><a href="../theories/featherweight_ocl/#Analysis_OCL">Analysis_OCL</a></li>
<li><a href="../theories/featherweight_ocl/#Design_UML">Design_UML</a></li>
<li><a href="../theories/featherweight_ocl/#Design_OCL">Design_OCL</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Featherweight_OCL-AFP</p><pre id="copy-text">@article{Featherweight_OCL-AFP,
author = {Achim D. Brucker and Frédéric Tuong and Burkhart Wolff},
title = {Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/Featherweight_OCL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ermat's <span class='first'>L</span>ast <span class='first'>T</span>heorem for <span class='first'>E</span>xponents 3 and 4 and the <span class='first'>P</span>arametrisation of <span class='first'>P</span>ythagorean <span class='first'>T</span>riples</h1>
<div>
<p><a href="../authors/oosterhuis">Roelof Oosterhuis</a>
</p>
<p class="date">August 12, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document presents the mechanised proofs of<ul><li>Fermat's Last Theorem for exponents 3 and 4 and</li><li>the parametrisation of Pythagorean Triples.</li></ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Fermat3_4</h3>
<ul>
<li><a href="../theories/fermat3_4/#Fermat4">Fermat4</a></li>
<li><a href="../theories/fermat3_4/#Quad_Form">Quad_Form</a></li>
<li><a href="../theories/fermat3_4/#Fermat3">Fermat3</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Fermat3_4-AFP</p><pre id="copy-text">@article{Fermat3_4-AFP,
author = {Roelof Oosterhuis},
title = {Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples},
journal = {Archive of Formal Proofs},
month = {August},
year = {2007},
note = {\url{https://isa-afp.org/entries/Fermat3_4.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ile <span class='first'>R</span>efinement</h1>
<div>
<p><a href="../authors/zee">Karen Zee</a> <a href="http://www.mit.edu/~kkz/">🌐</a> and <a href="../authors/kuncak">Viktor Kuncak</a> <a href="http://lara.epfl.ch/~kuncak/">🌐</a>
</p>
<p class="date">December 9, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories illustrates the verification of basic file operations (file creation, file read and file write) in the Isabelle theorem prover. We describe a file at two levels of abstraction: an abstract file represented as a resizable array, and a concrete file represented using data blocks.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session FileRefinement</h3>
<ul>
<li><a href="../theories/filerefinement/#CArrays">CArrays</a></li>
<li><a href="../theories/filerefinement/#ResizableArrays">ResizableArrays</a></li>
<li><a href="../theories/filerefinement/#FileRefinement">FileRefinement</a></li></ul><div class="flex-wrap">
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<a href="https://www.isa-afp.org/browser_info/current/AFP/FileRefinement/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">FileRefinement-AFP</p><pre id="copy-text">@article{FileRefinement-AFP,
author = {Karen Zee and Viktor Kuncak},
title = {File Refinement},
journal = {Archive of Formal Proofs},
month = {December},
year = {2004},
note = {\url{https://isa-afp.org/entries/FileRefinement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-FileRefinement-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-FileRefinement-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FileRefinement-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-FileRefinement-2004-12-15.tar.gz">Dec 15, 2004</a>: Isabelle2004
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/FinFun.html b/web/entries/FinFun.html
--- a/web/entries/FinFun.html
+++ b/web/entries/FinFun.html
@@ -1,210 +1,212 @@
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<h1 >
<span class='first'>C</span>ode <span class='first'>G</span>eneration for <span class='first'>F</span>unctions as <span class='first'>D</span>ata</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 6, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">FinFuns are total functions that are constant except for a finite set of points, i.e. a generalisation of finite maps. They are formalised as a new type in Isabelle/HOL such that the code generator can handle equality tests and quantification on FinFuns. On the code output level, FinFuns are explicitly represented by constant functions and pointwise updates, similarly to associative lists. Inside the logic, they behave like ordinary functions with extensionality. Via the update/constant pattern, a recursion combinator and an induction rule for FinFuns allow for defining and reasoning about operators on FinFun that are also executable.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 7, 2012</dt>
<dd>replace sets as FinFuns by predicates as FinFuns because the set type constructor has been reintroduced
(revision b7aa87989f3a)</dd><dt>November 4, 2010</dt>
<dd>new conversion function from FinFun to list of elements in the domain
(revision 0c167102e6ed)<br>
</dd><dt>August 13, 2010</dt>
<dd>new concept domain of a FinFun as a FinFun
(revision 34b3517cbc09)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session FinFun</h3>
<ul>
<li><a href="../theories/finfun/#FinFun">FinFun</a></li>
<li><a href="../theories/finfun/#FinFunPred">FinFunPred</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Extended_Finite_State_Machines.html">A Formal Model of Extended Finite State Machines</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li><li><a href="../entries/Launchbury.html">The Correctness of Launchbury&rsquo;s Natural Semantics for Lazy Evaluation</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">FinFun-AFP</p><pre id="copy-text">@article{FinFun-AFP,
author = {Andreas Lochbihler},
title = {Code Generation for Functions as Data},
journal = {Archive of Formal Proofs},
month = {May},
year = {2009},
note = {\url{https://isa-afp.org/entries/FinFun.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-FinFun-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-FinFun-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FinFun-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FinFun-2009-05-25.tar.gz">May 25, 2009</a>: Isabelle2009
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Finger-Trees.html b/web/entries/Finger-Trees.html
--- a/web/entries/Finger-Trees.html
+++ b/web/entries/Finger-Trees.html
@@ -1,206 +1,208 @@
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<h1 >
<span class='first'>F</span>inger <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/nordhoff">Benedikt Nordhoff</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1tdWVuc3RlciIsImRlIl0sInVzZXIiOlsiYl9ub3JkMDEiXX0=">📧</a>, <a href="../authors/koerner">Stefan Körner</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1tdWVuc3RlciIsImRlIl0sInVzZXIiOlsic19rb2VyMDMiXX0=">📧</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">October 28, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implement and prove correct 2-3 finger trees.
Finger trees are a general purpose data structure, that can be used to
efficiently implement other data structures, such as priority queues.
Intuitively, a finger tree is an annotated sequence, where the annotations are
elements of a monoid. Apart from operations to access the ends of the sequence,
the main operation is to split the sequence at the point where a
<em>monotone predicate</em> over the sum of the left part of the sequence
becomes true for the first time.
The implementation follows the paper of Hinze and Paterson.
The code generator can be used to get efficient, verified code.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Finger-Trees</h3>
<ul>
<li><a href="../theories/finger-trees/#FingerTree">FingerTree</a></li>
<li><a href="../theories/finger-trees/#Test">Test</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Finger-Trees-AFP</p><pre id="copy-text">@article{Finger-Trees-AFP,
author = {Benedikt Nordhoff and Stefan Körner and Peter Lammich},
title = {Finger Trees},
journal = {Archive of Formal Proofs},
month = {October},
year = {2010},
note = {\url{https://isa-afp.org/entries/Finger-Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Finger-Trees-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Finger-Trees-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Finger-Trees-2010-10-28.tar.gz">Oct 28, 2010</a>: Isabelle2009-2
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diff --git a/web/entries/Finite-Map-Extras.html b/web/entries/Finite-Map-Extras.html
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<h1 >
<span class='first'>F</span>inite <span class='first'>M</span>ap <span class='first'>E</span>xtras</h1>
<div>
<p><a href="../authors/diaz">Javier Díaz</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamF2aWVyIiwiZGlheiIsIm1hbnppIl19">📧</a>
</p>
<p class="date">October 12, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry includes useful syntactic sugar, new operators and functions, and
their associated lemmas for finite maps which currently are not
present in the standard Finite_Map theory.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Finite-Map-Extras</h3>
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<li><a href="../theories/finite-map-extras/#Finite_Map_Extras">Finite_Map_Extras</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Finite-Map-Extras-AFP</p><pre id="copy-text">@article{Finite-Map-Extras-AFP,
author = {Javier Díaz},
title = {Finite Map Extras},
journal = {Archive of Formal Proofs},
month = {October},
year = {2020},
note = {\url{https://isa-afp.org/entries/Finite-Map-Extras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Finite_Automata_HF.html b/web/entries/Finite_Automata_HF.html
--- a/web/entries/Finite_Automata_HF.html
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@@ -1,194 +1,196 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Finite Automata in Hereditarily Finite Set Theory - Archive of Formal Proofs</title><meta name="description" content="Finite Automata, both deterministic and non-deterministic, for regular languages.
The Myhill-Nerode Theorem. Closure under intersection, concatenation,..."><meta property="og:title" content="Finite Automata in Hereditarily Finite Set Theory" />
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<h1 >
<span class='first'>F</span>inite <span class='first'>A</span>utomata in <span class='first'>H</span>ereditarily <span class='first'>F</span>inite <span class='first'>S</span>et <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">February 5, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Finite Automata, both deterministic and non-deterministic, for regular languages.
The Myhill-Nerode Theorem. Closure under intersection, concatenation, etc.
Regular expressions define regular languages. Closure under reversal;
the powerset construction mapping NFAs to DFAs. Left and right languages; minimal DFAs.
Brzozowski's minimization algorithm. Uniqueness up to isomorphism of minimal DFAs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Finite_Automata_HF</h3>
<ul>
<li><a href="../theories/finite_automata_hf/#Finite_Automata_HF">Finite_Automata_HF</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li>
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<p style="display:none;" id="bibtex-filename">Finite_Automata_HF-AFP</p><pre id="copy-text">@article{Finite_Automata_HF-AFP,
author = {Lawrence C. Paulson},
title = {Finite Automata in Hereditarily Finite Set Theory},
journal = {Archive of Formal Proofs},
month = {February},
year = {2015},
note = {\url{https://isa-afp.org/entries/Finite_Automata_HF.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Finite_Automata_HF-2015-02-05.tar.gz">Feb 5, 2015</a>: Isabelle2014
</li></ul>
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diff --git a/web/entries/Finite_Fields.html b/web/entries/Finite_Fields.html
--- a/web/entries/Finite_Fields.html
+++ b/web/entries/Finite_Fields.html
@@ -1,192 +1,197 @@
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<h1 >
<span class='first'>F</span>inite <span class='first'>F</span>ields</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">June 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes the classification of the finite fields (also
called Galois fields): For each prime power $p^n$ there exists exactly
one (up to isomorphisms) finite field of that size and there are no
other finite fields. The derivation includes a formalization of the
characteristic of rings, the Frobenius endomorphism, formal
differentiation for polynomials in HOL-Algebra and Gauss' formula
for the number of monic irreducible polynomials over finite fields: \[
\frac{1}{n} \sum_{d | n} \mu(d) p^{n/d} \textrm{.} \] The proofs are
based on the books from <a
href="https://doi.org/10.1007/978-1-4757-2103-4">Ireland
and Rosen</a>, as well as, <a
href="https://doi.org/10.1017/CBO9781139172769">Lidl and
Niederreiter</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Finite_Fields</h3>
<ul>
<li><a href="../theories/finite_fields/#Finite_Fields_Preliminary_Results">Finite_Fields_Preliminary_Results</a></li>
<li><a href="../theories/finite_fields/#Finite_Fields_Factorization_Ext">Finite_Fields_Factorization_Ext</a></li>
<li><a href="../theories/finite_fields/#Ring_Characteristic">Ring_Characteristic</a></li>
<li><a href="../theories/finite_fields/#Formal_Polynomial_Derivatives">Formal_Polynomial_Derivatives</a></li>
<li><a href="../theories/finite_fields/#Monic_Polynomial_Factorization">Monic_Polynomial_Factorization</a></li>
<li><a href="../theories/finite_fields/#Card_Irreducible_Polynomials_Aux">Card_Irreducible_Polynomials_Aux</a></li>
<li><a href="../theories/finite_fields/#Card_Irreducible_Polynomials">Card_Irreducible_Polynomials</a></li>
<li><a href="../theories/finite_fields/#Finite_Fields_Isomorphic">Finite_Fields_Isomorphic</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Universal_Hash_Families.html">Universal Hash Families</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Universal_Hash_Families.html">Universal Hash Families</a></li>
<li><a href="../entries/Lehmer.html">Lehmer&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Finite_Fields-AFP</p><pre id="copy-text">@article{Finite_Fields-AFP,
author = {Emin Karayel},
title = {Finite Fields},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/Finite_Fields.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Finite_Fields-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Finite_Fields-2022-06-16.tar.gz">Jun 16, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Finitely_Generated_Abelian_Groups.html b/web/entries/Finitely_Generated_Abelian_Groups.html
--- a/web/entries/Finitely_Generated_Abelian_Groups.html
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results including the fundamental theorem of finitely generated
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<h1 >
<span class='first'>F</span>initely <span class='first'>G</span>enerated <span class='first'>A</span>belian <span class='first'>G</span>roups</h1>
<div>
<p><a href="../authors/thommes">Joseph Thommes</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">July 7, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article deals with the formalisation of some group-theoretic
results including the fundamental theorem of finitely generated
abelian groups characterising the structure of these groups as a
uniquely determined product of cyclic groups. Both the invariant
factor decomposition and the primary decomposition are covered.
Additional work includes results about the direct product, the
internal direct product and more group-theoretic lemmas.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Finitely_Generated_Abelian_Groups</h3>
<ul>
<li><a href="../theories/finitely_generated_abelian_groups/#Set_Multiplication">Set_Multiplication</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Miscellaneous_Groups">Miscellaneous_Groups</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Generated_Groups_Extend">Generated_Groups_Extend</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#General_Auxiliary">General_Auxiliary</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#IDirProds">IDirProds</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Finite_Product_Extend">Finite_Product_Extend</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Group_Hom">Group_Hom</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Finite_And_Cyclic_Groups">Finite_And_Cyclic_Groups</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#DirProds">DirProds</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Group_Relations">Group_Relations</a></li>
<li><a href="../theories/finitely_generated_abelian_groups/#Finitely_Generated_Abelian_Groups">Finitely_Generated_Abelian_Groups</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Finitely_Generated_Abelian_Groups-AFP</p><pre id="copy-text">@article{Finitely_Generated_Abelian_Groups-AFP,
author = {Joseph Thommes and Manuel Eberl},
title = {Finitely Generated Abelian Groups},
journal = {Archive of Formal Proofs},
month = {July},
year = {2021},
note = {\url{https://isa-afp.org/entries/Finitely_Generated_Abelian_Groups.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Finitely_Generated_Abelian_Groups-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Finitely_Generated_Abelian_Groups-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Finitely_Generated_Abelian_Groups-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Finitely_Generated_Abelian_Groups-2021-07-13.tar.gz">Jul 13, 2021</a>: Isabelle2021
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diff --git a/web/entries/First_Order_Terms.html b/web/entries/First_Order_Terms.html
--- a/web/entries/First_Order_Terms.html
+++ b/web/entries/First_Order_Terms.html
@@ -1,196 +1,198 @@
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<h1 >
<span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">February 6, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize basic results on first-order terms, including matching and a
first-order unification algorithm, as well as well-foundedness of the
subsumption order. This entry is part of the <i>Isabelle
Formalization of Rewriting</i> <a
href="http://cl-informatik.uibk.ac.at/isafor">IsaFoR</a>,
where first-order terms are omni-present: the unification algorithm is
used to certify several confluence and termination techniques, like
critical-pair computation and dependency graph approximations; and the
subsumption order is a crucial ingredient for completion.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session First_Order_Terms</h3>
<ul>
<li><a href="../theories/first_order_terms/#Transitive_Closure_More">Transitive_Closure_More</a></li>
<li><a href="../theories/first_order_terms/#Seq_More">Seq_More</a></li>
<li><a href="../theories/first_order_terms/#Fun_More">Fun_More</a></li>
<li><a href="../theories/first_order_terms/#Option_Monad">Option_Monad</a></li>
<li><a href="../theories/first_order_terms/#Term">Term</a></li>
<li><a href="../theories/first_order_terms/#Term_Pair_Multiset">Term_Pair_Multiset</a></li>
<li><a href="../theories/first_order_terms/#Abstract_Matching">Abstract_Matching</a></li>
<li><a href="../theories/first_order_terms/#Unifiers">Unifiers</a></li>
<li><a href="../theories/first_order_terms/#Abstract_Unification">Abstract_Unification</a></li>
<li><a href="../theories/first_order_terms/#Unification">Unification</a></li>
<li><a href="../theories/first_order_terms/#Matching">Matching</a></li>
<li><a href="../theories/first_order_terms/#Subsumption">Subsumption</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li><li><a href="../entries/Stateful_Protocol_Composition_and_Typing.html">Stateful Protocol Composition and Typing</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Resolution_FOL.html">The Resolution Calculus for First-Order Logic</a></li></ul>
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<p style="display:none;" id="bibtex-filename">First_Order_Terms-AFP</p><pre id="copy-text">@article{First_Order_Terms-AFP,
author = {Christian Sternagel and René Thiemann},
title = {First-Order Terms},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/First_Order_Terms.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2018-02-07.tar.gz">Feb 7, 2018</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Order_Terms-2018-02-06.tar.gz">Feb 6, 2018</a>: Isabelle2017
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diff --git a/web/entries/First_Welfare_Theorem.html b/web/entries/First_Welfare_Theorem.html
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<h1 >
<span class='first'>M</span>icroeconomics and the <span class='first'>F</span>irst <span class='first'>W</span>elfare <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/parsert">Julian Parsert</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsianVsaWFuIiwicGFyc2VydCJdfQ==">📧</a> and <a href="../authors/kaliszyk">Cezary Kaliszyk</a> <a href="http://cl-informatik.uibk.ac.at/users/cek/">🌐</a>
</p>
<p class="date">September 1, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Economic activity has always been a fundamental part of society. Due
to modern day politics, economic theory has gained even more influence
on our lives. Thus we want models and theories to be as precise as
possible. This can be achieved using certification with the help of
formal proof technology. Hence we will use Isabelle/HOL to construct
two economic models, that of the the pure exchange economy and a
version of the Arrow-Debreu Model. We will prove that the
<i>First Theorem of Welfare Economics</i> holds within
both. The theorem is the mathematical formulation of Adam Smith's
famous <i>invisible hand</i> and states that a group of
self-interested and rational actors will eventually achieve an
efficient allocation of goods and services.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>June 17, 2018</dt>
<dd>Added some lemmas and a theory file, also introduced Microeconomics folder.
<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session First_Welfare_Theorem</h3>
<ul>
<li><a href="../theories/first_welfare_theorem/#Syntax">Syntax</a></li>
<li><a href="../theories/first_welfare_theorem/#Argmax">Argmax</a></li>
<li><a href="../theories/first_welfare_theorem/#Preferences">Preferences</a></li>
<li><a href="../theories/first_welfare_theorem/#Utility_Functions">Utility_Functions</a></li>
<li><a href="../theories/first_welfare_theorem/#Consumers">Consumers</a></li>
<li><a href="../theories/first_welfare_theorem/#Common">Common</a></li>
<li><a href="../theories/first_welfare_theorem/#Exchange_Economy">Exchange_Economy</a></li>
<li><a href="../theories/first_welfare_theorem/#Private_Ownership_Economy">Private_Ownership_Economy</a></li>
<li><a href="../theories/first_welfare_theorem/#Arrow_Debreu_Model">Arrow_Debreu_Model</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Neumann_Morgenstern_Utility.html">Von-Neumann-Morgenstern Utility Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">First_Welfare_Theorem-AFP</p><pre id="copy-text">@article{First_Welfare_Theorem-AFP,
author = {Julian Parsert and Cezary Kaliszyk},
title = {Microeconomics and the First Welfare Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2017},
note = {\url{https://isa-afp.org/entries/First_Welfare_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2017-09-05.tar.gz">Sep 5, 2017</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-First_Welfare_Theorem-2017-09-04.tar.gz">Sep 4, 2017</a>: Isabelle2016-1
</li></ul>
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diff --git a/web/entries/Fishburn_Impossibility.html b/web/entries/Fishburn_Impossibility.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency - Archive of Formal Proofs</title><meta name="description" content="This formalisation contains the proof that there is no anonymous Social Choice Function for at least three agents and alternatives that fulfils both..."><meta property="og:title" content="The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency" />
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>ncompatibility of <span class='first'>F</span>ishburn-<span class='first'>S</span>trategyproofness and <span class='first'>P</span>areto-<span class='first'>E</span>fficiency</h1>
<div>
<p><a href="../authors/brandt">Felix Brandt</a> <a href="http://dss.in.tum.de/staff/brandt.html">🌐</a>, <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>, <a href="../authors/saile">Christian Saile</a> <a href="http://dss.in.tum.de/staff/christian-saile.html">🌐</a> and <a href="../authors/stricker">Christian Stricker</a> <a href="http://dss.in.tum.de/staff/christian-stricker.html">🌐</a>
</p>
<p class="date">March 22, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This formalisation contains the proof that there is no
anonymous Social Choice Function for at least three agents and
alternatives that fulfils both Pareto-Efficiency and
Fishburn-Strategyproofness. It was derived from a proof of <a
href="http://dss.in.tum.de/files/brandt-research/stratset.pdf">Brandt
<em>et al.</em></a>, which relies on an unverified
translation of a fixed finite instance of the original problem to SAT.
This Isabelle proof contains a machine-checked version of both the
statement for exactly three agents and alternatives and the lifting to
the general case.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Fishburn_Impossibility</h3>
<ul>
<li><a href="../theories/fishburn_impossibility/#Social_Choice_Functions">Social_Choice_Functions</a></li>
<li><a href="../theories/fishburn_impossibility/#Fishburn_Impossibility">Fishburn_Impossibility</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Randomised_Social_Choice.html">Randomised Social Choice Theory</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/SDS_Impossibility.html">The Incompatibility of SD-Efficiency and SD-Strategy-Proofness</a></li>
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<p style="display:none;" id="bibtex-filename">Fishburn_Impossibility-AFP</p><pre id="copy-text">@article{Fishburn_Impossibility-AFP,
author = {Felix Brandt and Manuel Eberl and Christian Saile and Christian Stricker},
title = {The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency},
journal = {Archive of Formal Proofs},
month = {March},
year = {2018},
note = {\url{https://isa-afp.org/entries/Fishburn_Impossibility.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2018-06-10.tar.gz">Jun 10, 2018</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fishburn_Impossibility-2018-03-23.tar.gz">Mar 23, 2018</a>: Isabelle2017
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<h1 >
<span class='first'>F</span>isher–<span class='first'>Y</span>ates <span class='first'>S</span>huffle</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">September 30, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This work defines and proves the correctness of the Fisher–Yates
algorithm for shuffling – i.e. producing a random permutation – of a
list. The algorithm proceeds by traversing the list and in
each step swapping the current element with a random element from the
remaining list.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Fisher_Yates</h3>
<ul>
<li><a href="../theories/fisher_yates/#Fisher_Yates">Fisher_Yates</a></li></ul><div class="flex-wrap">
</div>
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<p style="display:none;" id="bibtex-filename">Fisher_Yates-AFP</p><pre id="copy-text">@article{Fisher_Yates-AFP,
author = {Manuel Eberl},
title = {Fisher–Yates shuffle},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Fisher_Yates.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Fisher_Yates-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Fisher_Yates-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Fisher_Yates-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Fisher_Yates-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Fisher_Yates-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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</li><li>
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diff --git a/web/entries/Fishers_Inequality.html b/web/entries/Fishers_Inequality.html
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<h1 >
<span class='first'>F</span>isher's <span class='first'>I</span>nequality: <span class='first'>L</span>inear <span class='first'>A</span>lgebraic <span class='first'>P</span>roof <span class='first'>T</span>echniques for <span class='first'>C</span>ombinatorics</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
</p>
<p class="date">April 21, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Linear algebraic techniques are powerful, yet often underrated tools
in combinatorial proofs. This formalisation provides a library
including matrix representations of incidence set systems, general
formal proof techniques for the rank argument and linear bound
argument, and finally a formalisation of a number of variations of the
well-known Fisher's inequality. We build on our prior work
formalising combinatorial design theory using a locale-centric
approach, including extensions such as constant intersect designs and
dual incidence systems. In addition to Fisher's inequality, we
also formalise proofs on other incidence system properties using the
incidence matrix representation, such as design existence, dual system
relationships and incidence system isomorphisms. This formalisation is
presented in the paper "Formalising Fisher's Inequality:
Formal Linear Algebraic Techniques in Combinatorics", accepted to
ITP 2022.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Fishers_Inequality</h3>
<ul>
<li><a href="../theories/fishers_inequality/#Set_Multiset_Extras">Set_Multiset_Extras</a></li>
<li><a href="../theories/fishers_inequality/#Matrix_Vector_Extras">Matrix_Vector_Extras</a></li>
<li><a href="../theories/fishers_inequality/#Design_Extras">Design_Extras</a></li>
<li><a href="../theories/fishers_inequality/#Incidence_Matrices">Incidence_Matrices</a></li>
<li><a href="../theories/fishers_inequality/#Dual_Systems">Dual_Systems</a></li>
<li><a href="../theories/fishers_inequality/#Rank_Argument_General">Rank_Argument_General</a></li>
<li><a href="../theories/fishers_inequality/#Linear_Bound_Argument">Linear_Bound_Argument</a></li>
<li><a href="../theories/fishers_inequality/#Fishers_Inequality">Fishers_Inequality</a></li>
<li><a href="../theories/fishers_inequality/#Vector_Matrix_Mod">Vector_Matrix_Mod</a></li>
<li><a href="../theories/fishers_inequality/#Fishers_Inequality_Variations">Fishers_Inequality_Variations</a></li>
<li><a href="../theories/fishers_inequality/#Fishers_Inequality_Root">Fishers_Inequality_Root</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/BenOr_Kozen_Reif.html">The BKR Decision Procedure for Univariate Real Arithmetic</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Design_Theory.html">Combinatorial Design Theory</a></li><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Fishers_Inequality-AFP</p><pre id="copy-text">@article{Fishers_Inequality-AFP,
author = {Chelsea Edmonds and Lawrence C. Paulson},
title = {Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Fishers_Inequality.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Fishers_Inequality-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Fishers_Inequality-2022-06-19.tar.gz">Jun 19, 2022</a>: Isabelle2021-1
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Fishers_Inequality-2022-04-29.tar.gz">Apr 29, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Flow_Networks.html b/web/entries/Flow_Networks.html
--- a/web/entries/Flow_Networks.html
+++ b/web/entries/Flow_Networks.html
@@ -1,212 +1,214 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Flow Networks and the Min-Cut-Max-Flow Theorem - Archive of Formal Proofs</title><meta name="description" content="We present a formalization of flow networks and the Min-Cut-Max-Flow
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<h1 >
<span class='first'>F</span>low <span class='first'>N</span>etworks and the <span class='first'>M</span>in-<span class='first'>C</span>ut-<span class='first'>M</span>ax-<span class='first'>F</span>low <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/sefidgar">S. Reza Sefidgar</a>
</p>
<p class="date">June 1, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of flow networks and the Min-Cut-Max-Flow
theorem. Our formal proof closely follows a standard textbook proof,
and is accessible even without being an expert in Isabelle/HOL, the
interactive theorem prover used for the formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Flow_Networks</h3>
<ul>
<li><a href="../theories/flow_networks/#Fofu_Abs_Base">Fofu_Abs_Base</a></li>
<li><a href="../theories/flow_networks/#Fofu_Impl_Base">Fofu_Impl_Base</a></li>
<li><a href="../theories/flow_networks/#Refine_Add_Fofu">Refine_Add_Fofu</a></li>
<li><a href="../theories/flow_networks/#Graph">Graph</a></li>
<li><a href="../theories/flow_networks/#Network">Network</a></li>
<li><a href="../theories/flow_networks/#Residual_Graph">Residual_Graph</a></li>
<li><a href="../theories/flow_networks/#Augmenting_Flow">Augmenting_Flow</a></li>
<li><a href="../theories/flow_networks/#Augmenting_Path">Augmenting_Path</a></li>
<li><a href="../theories/flow_networks/#Ford_Fulkerson">Ford_Fulkerson</a></li>
<li><a href="../theories/flow_networks/#Graph_Impl">Graph_Impl</a></li>
<li><a href="../theories/flow_networks/#Network_Impl">Network_Impl</a></li>
<li><a href="../theories/flow_networks/#NetCheck">NetCheck</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/DFS_Framework.html">A Framework for Verifying Depth-First Search Algorithms</a></li><li><a href="../entries/Program-Conflict-Analysis.html">Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Prpu_Maxflow.html">Formalizing Push-Relabel Algorithms</a></li><li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li>
<li><a href="../entries/Prpu_Maxflow.html">Formalizing Push-Relabel Algorithms</a></li>
<li><a href="../entries/Solidity.html">Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</a></li>
<li><a href="../entries/BTree.html">A Verified Imperative Implementation of B-Trees</a></li>
<li><a href="../entries/Pop_Refinement.html">Pop-Refinement</a></li>
</ul>
</div>
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<p style="display:none;" id="bibtex-filename">Flow_Networks-AFP</p><pre id="copy-text">@article{Flow_Networks-AFP,
author = {Peter Lammich and S. Reza Sefidgar},
title = {Flow Networks and the Min-Cut-Max-Flow Theorem},
journal = {Archive of Formal Proofs},
month = {June},
year = {2017},
note = {\url{https://isa-afp.org/entries/Flow_Networks.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Flow_Networks-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
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diff --git a/web/entries/Floyd_Warshall.html b/web/entries/Floyd_Warshall.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Floyd-Warshall Algorithm for Shortest Paths - Archive of Formal Proofs</title><meta name="description" content="The Floyd-Warshall algorithm [Flo62, Roy59, War62] is a classic
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<h1 >
<span class='first'>T</span>he <span class='first'>F</span>loyd-<span class='first'>W</span>arshall <span class='first'>A</span>lgorithm for <span class='first'>S</span>hortest <span class='first'>P</span>aths</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">May 8, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Floyd-Warshall algorithm [Flo62, Roy59, War62] is a classic
dynamic programming algorithm to compute the length of all shortest
paths between any two vertices in a graph (i.e. to solve the all-pairs
shortest path problem, or APSP for short). Given a representation of
the graph as a matrix of weights M, it computes another matrix M'
which represents a graph with the same path lengths and contains the
length of the shortest path between any two vertices i and j. This is
only possible if the graph does not contain any negative cycles.
However, in this case the Floyd-Warshall algorithm will detect the
situation by calculating a negative diagonal entry. This entry
includes a formalization of the algorithm and of these key properties.
The algorithm is refined to an efficient imperative version using the
Imperative Refinement Framework.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Floyd_Warshall</h3>
<ul>
<li><a href="../theories/floyd_warshall/#Floyd_Warshall">Floyd_Warshall</a></li>
<li><a href="../theories/floyd_warshall/#Recursion_Combinators">Recursion_Combinators</a></li>
<li><a href="../theories/floyd_warshall/#FW_Code">FW_Code</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Floyd_Warshall-AFP</p><pre id="copy-text">@article{Floyd_Warshall-AFP,
author = {Simon Wimmer and Peter Lammich},
title = {The Floyd-Warshall Algorithm for Shortest Paths},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Floyd_Warshall.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Flyspeck-Tame.html b/web/entries/Flyspeck-Tame.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Flyspeck I: Tame Graphs - Archive of Formal Proofs</title><meta name="description" content="These theories present the verified enumeration of tame plane graphs as defined by Thomas C. Hales in his proof of the Kepler Conjecture in his book Dense..."><meta property="og:title" content="Flyspeck I: Tame Graphs" />
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<h1 >
<span class='first'>F</span>lyspeck <span class='first'>I</span>: <span class='first'>T</span>ame <span class='first'>G</span>raphs</h1>
<div>
<p><a href="../authors/bauer">Gertrud Bauer</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">May 22, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories present the verified enumeration of <i>tame</i> plane graphs
as defined by Thomas C. Hales in his proof of the Kepler Conjecture in his
book <i>Dense Sphere Packings. A Blueprint for Formal Proofs.</i> [CUP 2012].
The values of the constants in the definition of tameness are identical to
those in the <a href="https://code.google.com/p/flyspeck/">Flyspeck project</a>.
The <a href="http://www21.in.tum.de/~nipkow/pubs/Flyspeck/">IJCAR 2006 paper by Nipkow, Bauer and Schultz</a> refers to the original version of Hales' proof,
the <a href="http://www21.in.tum.de/~nipkow/pubs/itp11.html">ITP 2011 paper by Nipkow</a> refers to the Blueprint version of the proof.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 3, 2014</dt>
<dd>modified constants in def of tameness and Archive according to the final state of the Flyspeck proof.</dd><dt>November 2, 2010</dt>
<dd>modified theories to reflect the modified definition of tameness in Hales' revised proof.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T., Bauer, G., & Schultz, P. (2006). Flyspeck I: Tame Graphs. Lecture Notes in Computer Science, 21–35. <a href="https://doi.org/10.1007/11814771_4">https://doi.org/10.1007/11814771_4</a>
</li><li>
Nipkow, T. (2011). Verified Efficient Enumeration of Plane Graphs Modulo Isomorphism. Lecture Notes in Computer Science, 281–296. <a href="https://doi.org/10.1007/978-3-642-22863-6_21">https://doi.org/10.1007/978-3-642-22863-6_21</a>
</li><li>
Hales, T. C., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., & Zumkeller, R. (2009). A Revision of the Proof of the Kepler Conjecture. Discrete &amp; Computational Geometry, 44(1), 1–34. <a href="https://doi.org/10.1007/s00454-009-9148-4">https://doi.org/10.1007/s00454-009-9148-4</a>
</li><li>
HALES, T., ADAMS, M., BAUER, G., DANG, T. D., HARRISON, J., HOANG, L. T., KALISZYK, C., MAGRON, V., MCLAUGHLIN, S., NGUYEN, T. T., NGUYEN, Q. T., NIPKOW, T., OBUA, S., PLESO, J., RUTE, J., SOLOVYEV, A., TA, T. H. A., TRAN, N. T., TRIEU, T. D., … ZUMKELLER, R. (2017). A FORMAL PROOF OF THE KEPLER CONJECTURE. Forum of Mathematics, Pi, 5. <a href="https://doi.org/10.1017/fmp.2017.1">https://doi.org/10.1017/fmp.2017.1</a>
</li></ul>
<h3>Session Flyspeck-Tame</h3>
<ul>
<li><a href="../theories/flyspeck-tame/#ListAux">ListAux</a></li>
<li><a href="../theories/flyspeck-tame/#Quasi_Order">Quasi_Order</a></li>
<li><a href="../theories/flyspeck-tame/#PlaneGraphIso">PlaneGraphIso</a></li>
<li><a href="../theories/flyspeck-tame/#Rotation">Rotation</a></li>
<li><a href="../theories/flyspeck-tame/#Graph">Graph</a></li>
<li><a href="../theories/flyspeck-tame/#IArray_Syntax">IArray_Syntax</a></li>
<li><a href="../theories/flyspeck-tame/#Enumerator">Enumerator</a></li>
<li><a href="../theories/flyspeck-tame/#FaceDivision">FaceDivision</a></li>
<li><a href="../theories/flyspeck-tame/#RTranCl">RTranCl</a></li>
<li><a href="../theories/flyspeck-tame/#Plane">Plane</a></li>
<li><a href="../theories/flyspeck-tame/#Plane1">Plane1</a></li>
<li><a href="../theories/flyspeck-tame/#GraphProps">GraphProps</a></li>
<li><a href="../theories/flyspeck-tame/#EnumeratorProps">EnumeratorProps</a></li>
<li><a href="../theories/flyspeck-tame/#FaceDivisionProps">FaceDivisionProps</a></li>
<li><a href="../theories/flyspeck-tame/#Invariants">Invariants</a></li>
<li><a href="../theories/flyspeck-tame/#PlaneProps">PlaneProps</a></li>
<li><a href="../theories/flyspeck-tame/#ListSum">ListSum</a></li>
<li><a href="../theories/flyspeck-tame/#Tame">Tame</a></li>
<li><a href="../theories/flyspeck-tame/#Plane1Props">Plane1Props</a></li>
<li><a href="../theories/flyspeck-tame/#Generator">Generator</a></li>
<li><a href="../theories/flyspeck-tame/#TameProps">TameProps</a></li>
<li><a href="../theories/flyspeck-tame/#TameEnum">TameEnum</a></li>
<li><a href="../theories/flyspeck-tame/#ScoreProps">ScoreProps</a></li>
<li><a href="../theories/flyspeck-tame/#LowerBound">LowerBound</a></li>
<li><a href="../theories/flyspeck-tame/#GeneratorProps">GeneratorProps</a></li>
<li><a href="../theories/flyspeck-tame/#TameEnumProps">TameEnumProps</a></li>
<li><a href="../theories/flyspeck-tame/#Worklist">Worklist</a></li>
<li><a href="../theories/flyspeck-tame/#Maps">Maps</a></li>
<li><a href="../theories/flyspeck-tame/#Arch">Arch</a></li>
<li><a href="../theories/flyspeck-tame/#ArchCompAux">ArchCompAux</a></li>
<li><a href="../theories/flyspeck-tame/#ArchCompProps">ArchCompProps</a></li>
<li><a href="../theories/flyspeck-tame/#Relative_Completeness">Relative_Completeness</a></li></ul>
<h3>Session Flyspeck-Tame-Computation</h3>
<ul>
<li><a href="../theories/flyspeck-tame-computation/#ArchComp">ArchComp</a></li>
<li><a href="../theories/flyspeck-tame-computation/#Completeness">Completeness</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Trie.html">Trie</a></li><li><a href="../entries/Flyspeck-Tame.html">Flyspeck I: Tame Graphs</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Flyspeck-Tame.html">Flyspeck I: Tame Graphs</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Flyspeck-Tame-AFP</p><pre id="copy-text">@article{Flyspeck-Tame-AFP,
author = {Gertrud Bauer and Tobias Nipkow},
title = {Flyspeck I: Tame Graphs},
journal = {Archive of Formal Proofs},
month = {May},
year = {2006},
note = {\url{https://isa-afp.org/entries/Flyspeck-Tame.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2018-08-17.tar.gz">Aug 17, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2012-05-25.tar.gz">May 25, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2010-06-30.tar.gz">Jun 30, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2008-01-04.tar.gz">Jan 4, 2008</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-Flyspeck-Tame-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/FocusStreamsCaseStudies.html b/web/entries/FocusStreamsCaseStudies.html
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+++ b/web/entries/FocusStreamsCaseStudies.html
@@ -1,205 +1,207 @@
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<h1 >
<span class='first'>S</span>tream <span class='first'>P</span>rocessing <span class='first'>C</span>omponents: <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>F</span>ormalisation and <span class='first'>C</span>ase <span class='first'>S</span>tudies</h1>
<div>
<p><a href="../authors/spichkova">Maria Spichkova</a> <a class="obfuscated" data="eyJob3N0IjpbInJtaXQiLCJlZHUiLCJhdSJdLCJ1c2VyIjpbIm1hcmlhIiwic3BpY2hrb3ZhIl19">📧</a>
</p>
<p class="date">November 14, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This set of theories presents an Isabelle/HOL formalisation of stream processing components introduced
in Focus,
a framework for formal specification and development of interactive systems.
This is an extended and updated version of the formalisation, which was
elaborated within the methodology "Focus on Isabelle".
In addition, we also applied the formalisation on three case studies
that cover different application areas: process control (Steam Boiler System),
data transmission (FlexRay communication protocol),
memory and processing components (Automotive-Gateway System).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session FocusStreamsCaseStudies</h3>
<ul>
<li><a href="../theories/focusstreamscasestudies/#ArithExtras">ArithExtras</a></li>
<li><a href="../theories/focusstreamscasestudies/#ListExtras">ListExtras</a></li>
<li><a href="../theories/focusstreamscasestudies/#arith_hints">arith_hints</a></li>
<li><a href="../theories/focusstreamscasestudies/#stream">stream</a></li>
<li><a href="../theories/focusstreamscasestudies/#BitBoolTS">BitBoolTS</a></li>
<li><a href="../theories/focusstreamscasestudies/#JoinSplitTime">JoinSplitTime</a></li>
<li><a href="../theories/focusstreamscasestudies/#SteamBoiler">SteamBoiler</a></li>
<li><a href="../theories/focusstreamscasestudies/#SteamBoiler_proof">SteamBoiler_proof</a></li>
<li><a href="../theories/focusstreamscasestudies/#FR_types">FR_types</a></li>
<li><a href="../theories/focusstreamscasestudies/#FR">FR</a></li>
<li><a href="../theories/focusstreamscasestudies/#FR_proof">FR_proof</a></li>
<li><a href="../theories/focusstreamscasestudies/#Gateway_types">Gateway_types</a></li>
<li><a href="../theories/focusstreamscasestudies/#Gateway">Gateway</a></li>
<li><a href="../theories/focusstreamscasestudies/#Gateway_proof_aux">Gateway_proof_aux</a></li>
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<p style="display:none;" id="bibtex-filename">FocusStreamsCaseStudies-AFP</p><pre id="copy-text">@article{FocusStreamsCaseStudies-AFP,
author = {Maria Spichkova},
title = {Stream Processing Components: Isabelle/HOL Formalisation and Case Studies},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/FocusStreamsCaseStudies.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-FocusStreamsCaseStudies-2013-11-18.tar.gz">Nov 18, 2013</a>: Isabelle2013-1
</li></ul>
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diff --git a/web/entries/Forcing.html b/web/entries/Forcing.html
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@@ -1,203 +1,205 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Forcing in Isabelle/ZF - Archive of Formal Proofs</title><meta name="description" content="We formalize the theory of forcing in the set theory framework of
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>F</span>orcing in <span class='first'>I</span>sabelle/<span class='first'>Z</span><span class='first'>F</span></h1>
<div>
<p><a href="../authors/gunther">Emmanuel Gunther</a> <a class="obfuscated" data="eyJob3N0IjpbImZhbWFmIiwidW5jIiwiZWR1IiwiYXIiXSwidXNlciI6WyJndW50aGVyIl19">📧</a>, <a href="../authors/pagano">Miguel Pagano</a> <a href="https://cs.famaf.unc.edu.ar/~mpagano/">🌐</a> and <a href="../authors/terraf">Pedro Sánchez Terraf</a> <a href="https://cs.famaf.unc.edu.ar/~pedro/home_en.html">🌐</a>
</p>
<p class="date">May 6, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the theory of forcing in the set theory framework of
Isabelle/ZF. Under the assumption of the existence of a countable
transitive model of ZFC, we construct a proper generic extension and
show that the latter also satisfies ZFC.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Forcing</h3>
<ul>
<li><a href="../theories/forcing/#Utils">Utils</a></li>
<li><a href="../theories/forcing/#Forcing_Notions">Forcing_Notions</a></li>
<li><a href="../theories/forcing/#Pointed_DC">Pointed_DC</a></li>
<li><a href="../theories/forcing/#Rasiowa_Sikorski">Rasiowa_Sikorski</a></li>
<li><a href="../theories/forcing/#Nat_Miscellanea">Nat_Miscellanea</a></li>
<li><a href="../theories/forcing/#Internalizations">Internalizations</a></li>
<li><a href="../theories/forcing/#Recursion_Thms">Recursion_Thms</a></li>
<li><a href="../theories/forcing/#Relative_Univ">Relative_Univ</a></li>
<li><a href="../theories/forcing/#Synthetic_Definition">Synthetic_Definition</a></li>
<li><a href="../theories/forcing/#Interface">Interface</a></li>
<li><a href="../theories/forcing/#Forcing_Data">Forcing_Data</a></li>
<li><a href="../theories/forcing/#Internal_ZFC_Axioms">Internal_ZFC_Axioms</a></li>
<li><a href="../theories/forcing/#Renaming">Renaming</a></li>
<li><a href="../theories/forcing/#Renaming_Auto">Renaming_Auto</a></li>
<li><a href="../theories/forcing/#Names">Names</a></li>
<li><a href="../theories/forcing/#FrecR">FrecR</a></li>
<li><a href="../theories/forcing/#Arities">Arities</a></li>
<li><a href="../theories/forcing/#Forces_Definition">Forces_Definition</a></li>
<li><a href="../theories/forcing/#Forcing_Theorems">Forcing_Theorems</a></li>
<li><a href="../theories/forcing/#Separation_Rename">Separation_Rename</a></li>
<li><a href="../theories/forcing/#Separation_Axiom">Separation_Axiom</a></li>
<li><a href="../theories/forcing/#Pairing_Axiom">Pairing_Axiom</a></li>
<li><a href="../theories/forcing/#Union_Axiom">Union_Axiom</a></li>
<li><a href="../theories/forcing/#Powerset_Axiom">Powerset_Axiom</a></li>
<li><a href="../theories/forcing/#Extensionality_Axiom">Extensionality_Axiom</a></li>
<li><a href="../theories/forcing/#Foundation_Axiom">Foundation_Axiom</a></li>
<li><a href="../theories/forcing/#Least">Least</a></li>
<li><a href="../theories/forcing/#Replacement_Axiom">Replacement_Axiom</a></li>
<li><a href="../theories/forcing/#Infinity_Axiom">Infinity_Axiom</a></li>
<li><a href="../theories/forcing/#Choice_Axiom">Choice_Axiom</a></li>
<li><a href="../theories/forcing/#Ordinals_In_MG">Ordinals_In_MG</a></li>
<li><a href="../theories/forcing/#Proper_Extension">Proper_Extension</a></li>
<li><a href="../theories/forcing/#Succession_Poset">Succession_Poset</a></li>
<li><a href="../theories/forcing/#Forcing_Main">Forcing_Main</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Forcing-AFP</p><pre id="copy-text">@article{Forcing-AFP,
author = {Emmanuel Gunther and Miguel Pagano and Pedro Sánchez Terraf},
title = {Formalization of Forcing in Isabelle/ZF},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Forcing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Forcing-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Forcing-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Forcing-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Forcing-2020-05-07.tar.gz">May 7, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Forcing-2020-05-06.tar.gz">May 6, 2020</a>: Isabelle2020
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<h1 >
<span class='first'>F</span>ormal <span class='first'>P</span>uiseux <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 17, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Formal Puiseux series are generalisations of formal power
series and formal Laurent series that also allow for fractional
exponents. They have the following general form: \[\sum_{i=N}^\infty
a_{i/d} X^{i/d}\] where <em>N</em> is an integer and
<em>d</em> is a positive integer.</p> <p>This
entry defines these series including their basic algebraic properties.
Furthermore, it proves the Newton–Puiseux Theorem, namely that the
Puiseux series over an algebraically closed field of characteristic 0
are also algebraically closed.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Formal_Puiseux_Series</h3>
<ul>
<li><a href="../theories/formal_puiseux_series/#Puiseux_Polynomial_Library">Puiseux_Polynomial_Library</a></li>
<li><a href="../theories/formal_puiseux_series/#Puiseux_Laurent_Library">Puiseux_Laurent_Library</a></li>
<li><a href="../theories/formal_puiseux_series/#FPS_Hensel">FPS_Hensel</a></li>
<li><a href="../theories/formal_puiseux_series/#Formal_Puiseux_Series">Formal_Puiseux_Series</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Nullstellensatz.html">Hilbert&rsquo;s Nullstellensatz</a></li>
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<p style="display:none;" id="bibtex-filename">Formal_Puiseux_Series-AFP</p><pre id="copy-text">@article{Formal_Puiseux_Series-AFP,
author = {Manuel Eberl},
title = {Formal Puiseux Series},
journal = {Archive of Formal Proofs},
month = {February},
year = {2021},
note = {\url{https://isa-afp.org/entries/Formal_Puiseux_Series.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Formal_Puiseux_Series-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Formal_Puiseux_Series-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Formal_Puiseux_Series-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Formal_Puiseux_Series-2021-02-24.tar.gz">Feb 24, 2021</a>: Isabelle2021
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diff --git a/web/entries/Formal_SSA.html b/web/entries/Formal_SSA.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verified Construction of Static Single Assignment Form - Archive of Formal Proofs</title><meta name="description" content=" We define a functional variant of the static single assignment (SSA) form construction algorithm described by Braun et al., which combines simplicity and..."><meta property="og:title" content="Verified Construction of Static Single Assignment Form" />
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<h1 >
<span class='first'>V</span>erified <span class='first'>C</span>onstruction of <span class='first'>S</span>tatic <span class='first'>S</span>ingle <span class='first'>A</span>ssignment <span class='first'>F</span>orm</h1>
<div>
<p><a href="../authors/ullrich">Sebastian Ullrich</a> <a class="obfuscated" data="eyJob3N0IjpbIm51bGxyaSIsImNoIl0sInVzZXIiOlsic2ViYXN0aSJdfQ==">📧</a> and <a href="../authors/lohner">Denis Lohner</a> <a href="http://pp.ipd.kit.edu/person.php?id=88">🌐</a>
</p>
<p class="date">February 5, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
We define a functional variant of the static single assignment (SSA)
form construction algorithm described by <a
href="https://doi.org/10.1007/978-3-642-37051-9_6">Braun et al.</a>,
which combines simplicity and efficiency. The definition is based on a
general, abstract control flow graph representation using Isabelle locales.
</p>
<p>
We prove that the algorithm's output is semantically equivalent to the
input according to a small-step semantics, and that it is in minimal SSA
form for the common special case of reducible inputs. We then show the
satisfiability of the locale assumptions by giving instantiations for a
simple While language.
</p>
<p>
Furthermore, we use a generic instantiation based on typedefs in order
to extract OCaml code and replace the unverified SSA construction
algorithm of the <a href="https://doi.org/10.1145/2579080">CompCertSSA
project</a> with it.
</p>
<p>
A more detailed description of the verified SSA construction can be found
in the paper <a href="https://doi.org/10.1145/2892208.2892211">Verified
Construction of Static Single Assignment Form</a>, CC 2016.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul>
<h3>Session Formal_SSA</h3>
<ul>
<li><a href="../theories/formal_ssa/#FormalSSA_Misc">FormalSSA_Misc</a></li>
<li><a href="../theories/formal_ssa/#Serial_Rel">Serial_Rel</a></li>
<li><a href="../theories/formal_ssa/#Mapping_Exts">Mapping_Exts</a></li>
<li><a href="../theories/formal_ssa/#RBT_Mapping_Exts">RBT_Mapping_Exts</a></li>
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<li><a href="../theories/formal_ssa/#SSA_CFG">SSA_CFG</a></li>
<li><a href="../theories/formal_ssa/#Minimality">Minimality</a></li>
<li><a href="../theories/formal_ssa/#Construct_SSA">Construct_SSA</a></li>
<li><a href="../theories/formal_ssa/#Construct_SSA_notriv">Construct_SSA_notriv</a></li>
<li><a href="../theories/formal_ssa/#SSA_Semantics">SSA_Semantics</a></li>
<li><a href="../theories/formal_ssa/#While_Combinator_Exts">While_Combinator_Exts</a></li>
<li><a href="../theories/formal_ssa/#SSA_CFG_code">SSA_CFG_code</a></li>
<li><a href="../theories/formal_ssa/#Construct_SSA_code">Construct_SSA_code</a></li>
<li><a href="../theories/formal_ssa/#SSA_Transfer_Rules">SSA_Transfer_Rules</a></li>
<li><a href="../theories/formal_ssa/#Construct_SSA_notriv_code">Construct_SSA_notriv_code</a></li>
<li><a href="../theories/formal_ssa/#Generic_Interpretation">Generic_Interpretation</a></li>
<li><a href="../theories/formal_ssa/#Generic_Extract">Generic_Extract</a></li>
<li><a href="../theories/formal_ssa/#Disjoin_Transform">Disjoin_Transform</a></li>
<li><a href="../theories/formal_ssa/#WhileGraphSSA">WhileGraphSSA</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Dijkstra_Shortest_Path.html">Dijkstra&rsquo;s Shortest Path Algorithm</a></li><li><a href="../entries/Slicing.html">Towards Certified Slicing</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Minimal_SSA.html">Minimal Static Single Assignment Form</a></li></ul>
</div>
<div>
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<p style="display:none;" id="bibtex-filename">Formal_SSA-AFP</p><pre id="copy-text">@article{Formal_SSA-AFP,
author = {Sebastian Ullrich and Denis Lohner},
title = {Verified Construction of Static Single Assignment Form},
journal = {Archive of Formal Proofs},
month = {February},
year = {2016},
note = {\url{https://isa-afp.org/entries/Formal_SSA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Formal_SSA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Formal_SSA-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Formal_SSA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Formal_SSA-2016-02-08.tar.gz">Feb 8, 2016</a>: Isabelle2015
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diff --git a/web/entries/Formula_Derivatives.html b/web/entries/Formula_Derivatives.html
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+++ b/web/entries/Formula_Derivatives.html
@@ -1,211 +1,213 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Derivatives of Logical Formulas - Archive of Formal Proofs</title><meta name="description" content="We formalize new decision procedures for WS1S, M2L(Str), and Presburger Arithmetics. Formulas of these logics denote regular languages. Unlike traditional..."><meta property="og:title" content="Derivatives of Logical Formulas" />
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<h1 >
<span class='first'>D</span>erivatives of <span class='first'>L</span>ogical <span class='first'>F</span>ormulas</h1>
<div>
<p><a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">May 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize new decision procedures for WS1S, M2L(Str), and Presburger
Arithmetics. Formulas of these logics denote regular languages. Unlike
traditional decision procedures, we do <em>not</em> translate formulas into automata
(nor into regular expressions), at least not explicitly. Instead we devise
notions of derivatives (inspired by Brzozowski derivatives for regular
expressions) that operate on formulas directly and compute a syntactic
bisimulation using these derivatives. The treatment of Boolean connectives and
quantifiers is uniform for all mentioned logics and is abstracted into a
locale. This locale is then instantiated by different atomic formulas and their
derivatives (which may differ even for the same logic under different encodings
of interpretations as formal words).
<p>
The WS1S instance is described in the draft paper <a
href="https://people.inf.ethz.ch/trayteld/papers/csl15-ws1s_derivatives/index.html">A
Coalgebraic Decision Procedure for WS1S</a> by the author.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/logic/general-logic/decidability-of-theories">Logic/General logic/Decidability of theories</a></li></ul>
<h3>Session Formula_Derivatives</h3>
<ul>
<li><a href="../theories/formula_derivatives/#While_Default">While_Default</a></li>
<li><a href="../theories/formula_derivatives/#FSet_More">FSet_More</a></li>
<li><a href="../theories/formula_derivatives/#Automaton">Automaton</a></li>
<li><a href="../theories/formula_derivatives/#Abstract_Formula">Abstract_Formula</a></li>
<li><a href="../theories/formula_derivatives/#WS1S_Prelim">WS1S_Prelim</a></li>
<li><a href="../theories/formula_derivatives/#WS1S_Formula">WS1S_Formula</a></li>
<li><a href="../theories/formula_derivatives/#WS1S_Alt_Formula">WS1S_Alt_Formula</a></li>
<li><a href="../theories/formula_derivatives/#Presburger_Formula">Presburger_Formula</a></li>
<li><a href="../theories/formula_derivatives/#WS1S_Presburger_Equivalence">WS1S_Presburger_Equivalence</a></li>
<li><a href="../theories/formula_derivatives/#WS1S_Nameful">WS1S_Nameful</a></li></ul>
<h3>Session Formula_Derivatives-Examples</h3>
<ul>
<li><a href="../theories/formula_derivatives-examples/#WS1S_Examples">WS1S_Examples</a></li>
<li><a href="../theories/formula_derivatives-examples/#WS1S_Alt_Examples">WS1S_Alt_Examples</a></li>
<li><a href="../theories/formula_derivatives-examples/#Presburger_Examples">Presburger_Examples</a></li>
<li><a href="../theories/formula_derivatives-examples/#WS1S_Presburger_Examples">WS1S_Presburger_Examples</a></li>
<li><a href="../theories/formula_derivatives-examples/#WS1S_Nameful_Examples">WS1S_Nameful_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive_Languages.html">A Codatatype of Formal Languages</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Formula_Derivatives-AFP</p><pre id="copy-text">@article{Formula_Derivatives-AFP,
author = {Dmitriy Traytel},
title = {Derivatives of Logical Formulas},
journal = {Archive of Formal Proofs},
month = {May},
year = {2015},
note = {\url{https://isa-afp.org/entries/Formula_Derivatives.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>oundation of <span class='first'>G</span>eometry in <span class='first'>P</span>lanes, and <span class='first'>S</span>ome <span class='first'>C</span>omplements: <span class='first'>E</span>xcluding the <span class='first'>P</span>arallel <span class='first'>A</span>xioms</h1>
<div>
<p><a href="../authors/iwama">Fumiya Iwama</a>
</p>
<p class="date">November 22, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">"Foundations of Geometry" is a mathematical book written by
Hilbert in 1899. This entry is a complete formalization of
"Incidence" (excluding cubic axioms), "Order" and
"Congruence" (excluding point sequences) of the axioms
constructed in this book. In addition, the theorem of the problem
about the part that is treated implicitly and is not clearly stated in
it is being carried out in parallel.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Foundation_of_geometry</h3>
<ul>
<li><a href="../theories/foundation_of_geometry/#Incidence">Incidence</a></li>
<li><a href="../theories/foundation_of_geometry/#Order">Order</a></li>
<li><a href="../theories/foundation_of_geometry/#Congruence">Congruence</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Foundation_of_geometry-AFP</p><pre id="copy-text">@article{Foundation_of_geometry-AFP,
author = {Fumiya Iwama},
title = {Foundation of geometry in planes, and some complements: Excluding the parallel axioms},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Foundation_of_geometry.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ourier <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">September 6, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development formalises the square integrable functions over the
reals and the basics of Fourier series. It culminates with a proof
that every well-behaved periodic function can be approximated by a
Fourier series. The material is ported from HOL Light:
https://github.com/jrh13/hol-light/blob/master/100/fourier.ml</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Fourier</h3>
<ul>
<li><a href="../theories/fourier/#Periodic">Periodic</a></li>
<li><a href="../theories/fourier/#Lspace">Lspace</a></li>
<li><a href="../theories/fourier/#Square_Integrable">Square_Integrable</a></li>
<li><a href="../theories/fourier/#Confine">Confine</a></li>
<li><a href="../theories/fourier/#Fourier_Aux2">Fourier_Aux2</a></li>
<li><a href="../theories/fourier/#Fourier">Fourier</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Lp.html">Lp spaces</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Cartan_FP.html">The Cartan Fixed Point Theorems</a></li>
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<p style="display:none;" id="bibtex-filename">Fourier-AFP</p><pre id="copy-text">@article{Fourier-AFP,
author = {Lawrence C. Paulson},
title = {Fourier Series},
journal = {Archive of Formal Proofs},
month = {September},
year = {2019},
note = {\url{https://isa-afp.org/entries/Fourier.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ree <span class='first'>B</span>oolean <span class='first'>A</span>lgebra</h1>
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<p><a href="../authors/huffman">Brian Huffman</a> <a href="http://cs.pdx.edu/~brianh/">🌐</a>
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<p class="date">March 29, 2010</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)<i>formula</i> represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type.</div>
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<ul><li><a href="../topics/logic/general-logic/classical-propositional-logic">Logic/General logic/Classical propositional logic</a></li></ul>
<h3>Session Free-Boolean-Algebra</h3>
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<p style="display:none;" id="bibtex-filename">Free-Boolean-Algebra-AFP</p><pre id="copy-text">@article{Free-Boolean-Algebra-AFP,
author = {Brian Huffman},
title = {Free Boolean Algebra},
journal = {Archive of Formal Proofs},
month = {March},
year = {2010},
note = {\url{https://isa-afp.org/entries/Free-Boolean-Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Free-Groups.html b/web/entries/Free-Groups.html
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<h1 >
<span class='first'>F</span>ree <span class='first'>G</span>roups</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a class="obfuscated" data="eyJob3N0IjpbImpvYWNoaW0tYnJlaXRuZXIiLCJkZSJdLCJ1c2VyIjpbIm1haWwiXX0=">📧</a>
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<p class="date">June 24, 2010</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Free Groups are, in a sense, the most generic kind of group. They
are defined over a set of generators with no additional relations in between
them. They play an important role in the definition of group presentations
and in other fields. This theory provides the definition of Free Group as
the set of fully canceled words in the generators. The universal property is
proven, as well as some isomorphisms results about Free Groups.</div>
<h3>License</h3>
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<dl><dt>December 11, 2011</dt>
<dd>Added the Ping Pong Lemma.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Free-Groups</h3>
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<li><a href="../theories/free-groups/#Cancelation">Cancelation</a></li>
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<li><a href="../theories/free-groups/#UnitGroup">UnitGroup</a></li>
<li><a href="../theories/free-groups/#C2">C2</a></li>
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<p style="display:none;" id="bibtex-filename">Free-Groups-AFP</p><pre id="copy-text">@article{Free-Groups-AFP,
author = {Joachim Breitner},
title = {Free Groups},
journal = {Archive of Formal Proofs},
month = {June},
year = {2010},
note = {\url{https://isa-afp.org/entries/Free-Groups.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>R</span>andomized <span class='first'>A</span>pproximation <span class='first'>A</span>lgorithms for <span class='first'>F</span>requency <span class='first'>M</span>oments</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">April 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1999 Alon et. al. introduced the still active research topic of
approximating the frequency moments of a data stream using randomized
algorithms with minimal space usage. This includes the problem of
estimating the cardinality of the stream elements - the zeroth
frequency moment. But, also higher-order frequency moments that
provide information about the skew of the data stream. (The
<i>k</i>-th frequency moment of a data stream is the sum
of the <i>k</i>-th powers of the occurrence counts of each
element in the stream.) This entry formalizes three randomized
algorithms for the approximation of
<i>F<sub>0</sub></i>,
<i>F<sub>2</sub></i> and
<i>F<sub>k</sub></i> for <i>k ≥
3</i> based on [<a
href="https://doi.org/10.1006/jcss.1997.1545">1</a>,
<a
href="https://doi.org/10.1007/3-540-45726-7_1">2</a>]
and verifies their expected accuracy, success probability and space
usage.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/approximation">Computer science/Algorithms/Approximation</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul><h3>Related publications</h3>
<ul><li>
Karayel, E. (2022). Formalization of Randomized Approximation Algorithms for Frequency Moments. <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.ITP.2022.21
</li></ul>
<h3>Session Frequency_Moments</h3>
<ul>
<li><a href="../theories/frequency_moments/#Frequency_Moments_Preliminary_Results">Frequency_Moments_Preliminary_Results</a></li>
<li><a href="../theories/frequency_moments/#Frequency_Moments">Frequency_Moments</a></li>
<li><a href="../theories/frequency_moments/#K_Smallest">K_Smallest</a></li>
<li><a href="../theories/frequency_moments/#Landau_Ext">Landau_Ext</a></li>
<li><a href="../theories/frequency_moments/#Probability_Ext">Probability_Ext</a></li>
<li><a href="../theories/frequency_moments/#Product_PMF_Ext">Product_PMF_Ext</a></li>
<li><a href="../theories/frequency_moments/#Frequency_Moment_0">Frequency_Moment_0</a></li>
<li><a href="../theories/frequency_moments/#Frequency_Moment_2">Frequency_Moment_2</a></li>
<li><a href="../theories/frequency_moments/#Frequency_Moment_k">Frequency_Moment_k</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bertrands_Postulate.html">Bertrand&rsquo;s postulate</a></li><li><a href="../entries/Equivalence_Relation_Enumeration.html">Enumeration of Equivalence Relations</a></li><li><a href="../entries/Interpolation_Polynomials_HOL_Algebra.html">Interpolation Polynomials (in HOL-Algebra)</a></li><li><a href="../entries/Lp.html">Lp spaces</a></li><li><a href="../entries/Median_Method.html">Median Method</a></li><li><a href="../entries/Prefix_Free_Code_Combinators.html">A Combinator Library for Prefix-Free Codes</a></li><li><a href="../entries/Universal_Hash_Families.html">Universal Hash Families</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Frequency_Moments-AFP</p><pre id="copy-text">@article{Frequency_Moments-AFP,
author = {Emin Karayel},
title = {Formalization of Randomized Approximation Algorithms for Frequency Moments},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Frequency_Moments.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Fresh_Identifiers.html b/web/entries/Fresh_Identifiers.html
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<h1 >
<span class='first'>F</span>resh <span class='first'>I</span>dentifiers</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/bauereiss">Thomas Bauereiss</a> <a class="obfuscated" data="eyJob3N0IjpbImJhdWVyZWlzcyIsIm5hbWUiXSwidXNlciI6WyJ0aG9tYXMiXX0=">📧</a>
</p>
<p class="date">August 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry defines a type class with an operator returning a fresh
identifier, given a set of already used identifiers and a preferred
identifier. The entry provides a default instantiation for any
infinite type, as well as executable instantiations for natural
numbers and strings.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Fresh_Identifiers</h3>
<ul>
<li><a href="../theories/fresh_identifiers/#Fresh">Fresh</a></li>
<li><a href="../theories/fresh_identifiers/#Fresh_Nat">Fresh_Nat</a></li>
<li><a href="../theories/fresh_identifiers/#Fresh_String">Fresh_String</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CoCon.html">CoCon: A Confidentiality-Verified Conference Management System</a></li><li><a href="../entries/CoSMed.html">CoSMed: A confidentiality-verified social media platform</a></li><li><a href="../entries/CoSMeDis.html">CoSMeDis: A confidentiality-verified distributed social media platform</a></li></ul>
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author = {Andrei Popescu and Thomas Bauereiss},
title = {Fresh identifiers},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/Fresh_Identifiers.html},
Formal proof development},
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diff --git a/web/entries/FunWithFunctions.html b/web/entries/FunWithFunctions.html
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@@ -1,195 +1,197 @@
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<h1 >
<span class='first'>F</span>un <span class='first'>W</span>ith <span class='first'>F</span>unctions</h1>
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<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
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<p class="date">August 26, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a collection of cute puzzles of the form ``Show that if a function satisfies the following constraints, it must be ...'' Please add further examples to this collection!</div>
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author = {Tobias Nipkow},
title = {Fun With Functions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2008},
note = {\url{https://isa-afp.org/entries/FunWithFunctions.html},
Formal proof development},
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diff --git a/web/entries/FunWithTilings.html b/web/entries/FunWithTilings.html
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<h1 >
<span class='first'>F</span>un <span class='first'>W</span>ith <span class='first'>T</span>ilings</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
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<p class="date">November 7, 2008</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Tilings are defined inductively. It is shown that one form of mutilated chess board cannot be tiled with dominoes, while another one can be tiled with L-shaped tiles. Please add further fun examples of this kind!</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
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<h3>Session FunWithTilings</h3>
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<p style="display:none;" id="bibtex-filename">FunWithTilings-AFP</p><pre id="copy-text">@article{FunWithTilings-AFP,
author = {Tobias Nipkow and Lawrence C. Paulson},
title = {Fun With Tilings},
journal = {Archive of Formal Proofs},
month = {November},
year = {2008},
note = {\url{https://isa-afp.org/entries/FunWithTilings.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Functional-Automata.html b/web/entries/Functional-Automata.html
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+++ b/web/entries/Functional-Automata.html
@@ -1,225 +1,227 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Functional Automata - Archive of Formal Proofs</title><meta name="description" content="This theory defines deterministic and nondeterministic automata in a functional representation: the transition function/relation and the finality predicate..."><meta property="og:title" content="Functional Automata" />
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<h1 >
<span class='first'>F</span>unctional <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">March 30, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory defines deterministic and nondeterministic automata in a functional representation: the transition function/relation and the finality predicate are just functions. Hence the state space may be infinite. It is shown how to convert regular expressions into such automata. A scanner (generator) is implemented with the help of functional automata: the scanner chops the input up into longest recognized substrings. Finally we also show how to convert a certain subclass of functional automata (essentially the finite deterministic ones) into regular sets.</div>
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<h3>Session Functional-Automata</h3>
<ul>
<li><a href="../theories/functional-automata/#AutoProj">AutoProj</a></li>
<li><a href="../theories/functional-automata/#DA">DA</a></li>
<li><a href="../theories/functional-automata/#NA">NA</a></li>
<li><a href="../theories/functional-automata/#NAe">NAe</a></li>
<li><a href="../theories/functional-automata/#Automata">Automata</a></li>
<li><a href="../theories/functional-automata/#RegExp2NA">RegExp2NA</a></li>
<li><a href="../theories/functional-automata/#RegExp2NAe">RegExp2NAe</a></li>
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<p style="display:none;" id="bibtex-filename">Functional-Automata-AFP</p><pre id="copy-text">@article{Functional-Automata-AFP,
author = {Tobias Nipkow},
title = {Functional Automata},
journal = {Archive of Formal Proofs},
month = {March},
year = {2004},
note = {\url{https://isa-afp.org/entries/Functional-Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Functional_Ordered_Resolution_Prover.html b/web/entries/Functional_Ordered_Resolution_Prover.html
--- a/web/entries/Functional_Ordered_Resolution_Prover.html
+++ b/web/entries/Functional_Ordered_Resolution_Prover.html
@@ -1,178 +1,180 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover - Archive of Formal Proofs</title><meta name="description" content="This Isabelle/HOL formalization refines the abstract ordered resolution prover presented in Section 4.3 of Bachmair and Ganzinger&#39;s &#34;Resolution Theorem..."><meta property="og:title" content="A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover" />
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>F</span>unctional <span class='first'>I</span>mplementation of <span class='first'>B</span>achmair and <span class='first'>G</span>anzinger's <span class='first'>O</span>rdered <span class='first'>R</span>esolution <span class='first'>P</span>rover</h1>
<div>
<p><a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a>, <a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbInZ1IiwibmwiXSwidXNlciI6WyJqIiwiYyIsImJsYW5jaGV0dGUiXX0=">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">November 23, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization refines the abstract ordered
resolution prover presented in Section 4.3 of Bachmair and
Ganzinger's "Resolution Theorem Proving" chapter in the
<i>Handbook of Automated Reasoning</i>. The result is a
functional implementation of a first-order prover.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Functional_Ordered_Resolution_Prover</h3>
<ul>
<li><a href="../theories/functional_ordered_resolution_prover/#Weighted_FO_Ordered_Resolution_Prover">Weighted_FO_Ordered_Resolution_Prover</a></li>
<li><a href="../theories/functional_ordered_resolution_prover/#Deterministic_FO_Ordered_Resolution_Prover">Deterministic_FO_Ordered_Resolution_Prover</a></li>
<li><a href="../theories/functional_ordered_resolution_prover/#IsaFoR_Term">IsaFoR_Term</a></li>
<li><a href="../theories/functional_ordered_resolution_prover/#Executable_Subsumption">Executable_Subsumption</a></li>
<li><a href="../theories/functional_ordered_resolution_prover/#Executable_FO_Ordered_Resolution_Prover">Executable_FO_Ordered_Resolution_Prover</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Order_Terms.html">First-Order Terms</a></li><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li><li><a href="../entries/Open_Induction.html">Open Induction</a></li><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Functional_Ordered_Resolution_Prover-AFP</p><pre id="copy-text">@article{Functional_Ordered_Resolution_Prover-AFP,
author = {Anders Schlichtkrull and Jasmin Christian Blanchette and Dmitriy Traytel},
title = {A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover},
journal = {Archive of Formal Proofs},
month = {November},
year = {2018},
note = {\url{https://isa-afp.org/entries/Functional_Ordered_Resolution_Prover.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>urstenberg's <span class='first'>T</span>opology and <span class='first'>H</span>is <span class='first'>P</span>roof of the <span class='first'>I</span>nfinitude of <span class='first'>P</span>rimes</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 22, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article gives a formal version of Furstenberg's
topological proof of the infinitude of primes. He defines a topology
on the integers based on arithmetic progressions (or, equivalently,
residue classes). Using some fairly obvious properties of this
topology, the infinitude of primes is then easily obtained.</p>
<p>Apart from this, this topology is also fairly ‘nice’ in
general: it is second countable, metrizable, and perfect. All of these
(well-known) facts are formally proven, including an explicit metric
for the topology given by Zulfeqarr.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Furstenberg_Topology</h3>
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<li><a href="../theories/furstenberg_topology/#Furstenberg_Topology">Furstenberg_Topology</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Furstenberg_Topology-AFP</p><pre id="copy-text">@article{Furstenberg_Topology-AFP,
author = {Manuel Eberl},
title = {Furstenberg&#39;s topology and his proof of the infinitude of primes},
journal = {Archive of Formal Proofs},
month = {March},
year = {2020},
note = {\url{https://isa-afp.org/entries/Furstenberg_Topology.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Furstenberg_Topology-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Furstenberg_Topology-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>S</span>yntax and <span class='first'>S</span>emantics of a <span class='first'>G</span><span class='first'>P</span><span class='first'>U</span> <span class='first'>K</span>ernel <span class='first'>P</span>rogramming <span class='first'>L</span>anguage</h1>
<div>
<p><a href="../authors/wickerson">John Wickerson</a> <a href="http://www.doc.ic.ac.uk/~jpw48">🌐</a>
</p>
<p class="date">April 3, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document accompanies the article "The Design and
Implementation of a Verification Technique for GPU Kernels"
by Adam Betts, Nathan Chong, Alastair F. Donaldson, Jeroen
Ketema, Shaz Qadeer, Paul Thomson and John Wickerson. It
formalises all of the definitions provided in Sections 3
and 4 of the article.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session GPU_Kernel_PL</h3>
<ul>
<li><a href="../theories/gpu_kernel_pl/#Misc">Misc</a></li>
<li><a href="../theories/gpu_kernel_pl/#KPL_syntax">KPL_syntax</a></li>
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<p style="display:none;" id="bibtex-filename">GPU_Kernel_PL-AFP</p><pre id="copy-text">@article{GPU_Kernel_PL-AFP,
author = {John Wickerson},
title = {Syntax and semantics of a GPU kernel programming language},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/GPU_Kernel_PL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-GPU_Kernel_PL-2014-04-06.tar.gz">Apr 6, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/Gabow_SCC.html b/web/entries/Gabow_SCC.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verified Efficient Implementation of Gabow&#39;s Strongly Connected Components Algorithm - Archive of Formal Proofs</title><meta name="description" content="We present an Isabelle/HOL formalization of Gabow&#39;s algorithm for
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<h1 >
<span class='first'>V</span>erified <span class='first'>E</span>fficient <span class='first'>I</span>mplementation of <span class='first'>G</span>abow's <span class='first'>S</span>trongly <span class='first'>C</span>onnected <span class='first'>C</span>omponents <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">May 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an Isabelle/HOL formalization of Gabow's algorithm for
finding the strongly connected components of a directed graph.
Using data refinement techniques, we extract efficient code that
performs comparable to a reference implementation in Java.
Our style of formalization allows for re-using large parts of the proofs
when defining variants of the algorithm. We demonstrate this by
verifying an algorithm for the emptiness check of generalized Büchi
automata, re-using most of the existing proofs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Gabow_SCC</h3>
<ul>
<li><a href="../theories/gabow_scc/#Gabow_Skeleton">Gabow_Skeleton</a></li>
<li><a href="../theories/gabow_scc/#Gabow_SCC">Gabow_SCC</a></li>
<li><a href="../theories/gabow_scc/#Find_Path">Find_Path</a></li>
<li><a href="../theories/gabow_scc/#Gabow_GBG">Gabow_GBG</a></li>
<li><a href="../theories/gabow_scc/#Gabow_Skeleton_Code">Gabow_Skeleton_Code</a></li>
<li><a href="../theories/gabow_scc/#Gabow_SCC_Code">Gabow_SCC_Code</a></li>
<li><a href="../theories/gabow_scc/#Find_Path_Impl">Find_Path_Impl</a></li>
<li><a href="../theories/gabow_scc/#Gabow_GBG_Code">Gabow_GBG_Code</a></li>
<li><a href="../theories/gabow_scc/#All_Of_Gabow_SCC">All_Of_Gabow_SCC</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Collections.html">Collections Framework</a></li>
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outline</a>
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<p style="display:none;" id="bibtex-filename">Gabow_SCC-AFP</p><pre id="copy-text">@article{Gabow_SCC-AFP,
author = {Peter Lammich},
title = {Verified Efficient Implementation of Gabow&#39;s Strongly Connected Components Algorithm},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/Gabow_SCC.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gabow_SCC-2014-05-29.tar.gz">May 29, 2014</a>: Isabelle2013-2
</li></ul>
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diff --git a/web/entries/GaleStewart_Games.html b/web/entries/GaleStewart_Games.html
--- a/web/entries/GaleStewart_Games.html
+++ b/web/entries/GaleStewart_Games.html
@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>G</span>ale-<span class='first'>S</span>tewart <span class='first'>G</span>ames</h1>
<div>
<p><a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a href="https://sjcjoosten.nl/">🌐</a>
</p>
<p class="date">April 23, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalisation of the main result of Gale and Stewart from
1953, showing that closed finite games are determined. This property
is now known as the Gale Stewart Theorem. While the original paper
shows some additional theorems as well, we only formalize this main
result, but do so in a somewhat general way. We formalize games of a
fixed arbitrary length, including infinite length, using co-inductive
lists, and show that defensive strategies exist unless the other
player is winning. For closed games, defensive strategies are winning
for the closed player, proving that such games are determined. For
finite games, which are a special case in our formalisation, all games
are closed.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session GaleStewart_Games</h3>
<ul>
<li><a href="../theories/galestewart_games/#MoreCoinductiveList2">MoreCoinductiveList2</a></li>
<li><a href="../theories/galestewart_games/#MoreENat">MoreENat</a></li>
<li><a href="../theories/galestewart_games/#MorePrefix">MorePrefix</a></li>
<li><a href="../theories/galestewart_games/#AlternatingLists">AlternatingLists</a></li>
<li><a href="../theories/galestewart_games/#GaleStewartGames">GaleStewartGames</a></li>
<li><a href="../theories/galestewart_games/#GaleStewartDefensiveStrategies">GaleStewartDefensiveStrategies</a></li>
<li><a href="../theories/galestewart_games/#GaleStewartDeterminedGames">GaleStewartDeterminedGames</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Parity_Game.html">Positional Determinacy of Parity Games</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/LocalLexing.html">Local Lexing</a></li>
<li><a href="../entries/Menger.html">Menger&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">GaleStewart_Games-AFP</p><pre id="copy-text">@article{GaleStewart_Games-AFP,
author = {Sebastiaan J. C. Joosten},
title = {Gale-Stewart Games},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/GaleStewart_Games.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-GaleStewart_Games-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-GaleStewart_Games-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-GaleStewart_Games-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GaleStewart_Games-2021-04-28.tar.gz">Apr 28, 2021</a>: Isabelle2021
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diff --git a/web/entries/Gale_Shapley.html b/web/entries/Gale_Shapley.html
--- a/web/entries/Gale_Shapley.html
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<h1 >
<span class='first'>G</span>ale-<span class='first'>S</span>hapley <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">December 29, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a stepwise refinement and proof of the Gale-Shapley stable
matching (or marriage) algorithm down to executable code. Both a
purely functional implementation based on lists and a functional
implementation based on efficient arrays (provided by the Collections
Framework in the AFP) are developed. The latter implementation runs in
time <i>O(n<sup>2</sup>)</i> where
<i>n</i> is the cardinality of the two sets to be matched.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul><h3>Related publications</h3>
<ul><li>
<a href="https://en.wikipedia.org/wiki/Stable_marriage_problem">Wikipedia</a>
</li></ul>
<h3>Session Gale_Shapley</h3>
<ul>
<li><a href="../theories/gale_shapley/#Gale_Shapley1">Gale_Shapley1</a></li>
<li><a href="../theories/gale_shapley/#Gale_Shapley2">Gale_Shapley2</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Buchi_Complementation.html">Büchi Complementation</a></li>
<li><a href="../entries/Tree-Automata.html">Tree Automata</a></li>
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<p style="display:none;" id="bibtex-filename">Gale_Shapley-AFP</p><pre id="copy-text">@article{Gale_Shapley-AFP,
author = {Tobias Nipkow},
title = {Gale-Shapley Algorithm},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/Gale_Shapley.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Gale_Shapley-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Gale_Shapley-2022-01-03.tar.gz">Jan 3, 2022</a>: Isabelle2021-1
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Game-based cryptography in HOL - Archive of Formal Proofs</title><meta name="description" content="In this AFP entry, we show how to specify game-based cryptographic security notions and formally prove secure several cryptographic constructions from the..."><meta property="og:title" content="Game-based cryptography in HOL" />
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<h1 >
<span class='first'>G</span>ame-<span class='first'>B</span>ased <span class='first'>C</span>ryptography in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>, <a href="../authors/sefidgar">S. Reza Sefidgar</a> and <a href="../authors/bhatt">Bhargav Bhatt</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbImJoYXJnYXYiLCJiaGF0dCJdfQ==">📧</a>
</p>
<p class="date">May 5, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>In this AFP entry, we show how to specify game-based cryptographic
security notions and formally prove secure several cryptographic
constructions from the literature using the CryptHOL framework. Among
others, we formalise the notions of a random oracle, a pseudo-random
function, an unpredictable function, and of encryption schemes that are
indistinguishable under chosen plaintext and/or ciphertext attacks. We
prove the random-permutation/random-function switching lemma, security
of the Elgamal and hashed Elgamal public-key encryption scheme and
correctness and security of several constructions with pseudo-random
functions.
</p><p>Our proofs follow the game-hopping style advocated by
Shoup and Bellare and Rogaway, from which most of the examples have
been taken. We generalise some of their results such that they can be
reused in other proofs. Thanks to CryptHOL's integration with
Isabelle's parametricity infrastructure, many simple hops are easily
justified using the theory of representation independence.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 28, 2018</dt>
<dd>added the CryptHOL tutorial for game-based cryptography
(revision 489a395764ae)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li></ul>
<h3>Session Game_Based_Crypto</h3>
<ul>
<li><a href="../theories/game_based_crypto/#Diffie_Hellman">Diffie_Hellman</a></li>
<li><a href="../theories/game_based_crypto/#IND_CCA2">IND_CCA2</a></li>
<li><a href="../theories/game_based_crypto/#IND_CCA2_sym">IND_CCA2_sym</a></li>
<li><a href="../theories/game_based_crypto/#IND_CPA">IND_CPA</a></li>
<li><a href="../theories/game_based_crypto/#IND_CPA_PK">IND_CPA_PK</a></li>
<li><a href="../theories/game_based_crypto/#IND_CPA_PK_Single">IND_CPA_PK_Single</a></li>
<li><a href="../theories/game_based_crypto/#SUF_CMA">SUF_CMA</a></li>
<li><a href="../theories/game_based_crypto/#Pseudo_Random_Function">Pseudo_Random_Function</a></li>
<li><a href="../theories/game_based_crypto/#Pseudo_Random_Permutation">Pseudo_Random_Permutation</a></li>
<li><a href="../theories/game_based_crypto/#Guessing_Many_One">Guessing_Many_One</a></li>
<li><a href="../theories/game_based_crypto/#Unpredictable_Function">Unpredictable_Function</a></li>
<li><a href="../theories/game_based_crypto/#Security_Spec">Security_Spec</a></li>
<li><a href="../theories/game_based_crypto/#Elgamal">Elgamal</a></li>
<li><a href="../theories/game_based_crypto/#Hashed_Elgamal">Hashed_Elgamal</a></li>
<li><a href="../theories/game_based_crypto/#RP_RF">RP_RF</a></li>
<li><a href="../theories/game_based_crypto/#PRF_UHF">PRF_UHF</a></li>
<li><a href="../theories/game_based_crypto/#PRF_IND_CPA">PRF_IND_CPA</a></li>
<li><a href="../theories/game_based_crypto/#PRF_UPF_IND_CCA">PRF_UPF_IND_CCA</a></li>
<li><a href="../theories/game_based_crypto/#Cryptographic_Constructions">Cryptographic_Constructions</a></li>
<li><a href="../theories/game_based_crypto/#Game_Based_Crypto">Game_Based_Crypto</a></li>
<li><a href="../theories/game_based_crypto/#CryptHOL_Tutorial">CryptHOL_Tutorial</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CryptHOL.html">CryptHOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Constructive_Cryptography_CM.html">Constructive Cryptography in HOL: the Communication Modeling Aspect</a></li><li><a href="../entries/Multi_Party_Computation.html">Multi-Party Computation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Game_Based_Crypto-AFP</p><pre id="copy-text">@article{Game_Based_Crypto-AFP,
author = {Andreas Lochbihler and S. Reza Sefidgar and Bhargav Bhatt},
title = {Game-based cryptography in HOL},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Game_Based_Crypto.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Game_Based_Crypto-2017-05-11.tar.gz">May 11, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Gauss-Jordan-Elim-Fun.html b/web/entries/Gauss-Jordan-Elim-Fun.html
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<h1 >
<span class='first'>G</span>auss-<span class='first'>J</span>ordan <span class='first'>E</span>limination for <span class='first'>M</span>atrices <span class='first'>R</span>epresented as <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">August 19, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory provides a compact formulation of Gauss-Jordan elimination for matrices represented as functions. Its distinctive feature is succinctness. It is not meant for large computations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Gauss-Jordan-Elim-Fun</h3>
<ul>
<li><a href="../theories/gauss-jordan-elim-fun/#Gauss_Jordan_Elim_Fun">Gauss_Jordan_Elim_Fun</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Markov_Models.html">Markov Models</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Gauss-Jordan-Elim-Fun-AFP</p><pre id="copy-text">@article{Gauss-Jordan-Elim-Fun-AFP,
author = {Tobias Nipkow},
title = {Gauss-Jordan Elimination for Matrices Represented as Functions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2011},
note = {\url{https://isa-afp.org/entries/Gauss-Jordan-Elim-Fun.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>G</span>auss-<span class='first'>J</span>ordan <span class='first'>A</span>lgorithm and <span class='first'>I</span>ts <span class='first'>A</span>pplications</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>
</p>
<p class="date">September 3, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Gauss-Jordan algorithm states that any matrix over a field can be transformed by means of elementary row operations to a matrix in reduced row echelon form. The formalization is based on the Rank Nullity Theorem entry of the AFP and on the HOL-Multivariate-Analysis session of Isabelle, where matrices are represented as functions over finite types. We have set up the code generator to make this representation executable. In order to improve the performance, a refinement to immutable arrays has been carried out. We have formalized some of the applications of the Gauss-Jordan algorithm. Thanks to this development, the following facts can be computed over matrices whose elements belong to a field: Ranks, Determinants, Inverses, Bases and dimensions and Solutions of systems of linear equations. Code can be exported to SML and Haskell.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Gauss_Jordan</h3>
<ul>
<li><a href="../theories/gauss_jordan/#Rref">Rref</a></li>
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<li><a href="../theories/gauss_jordan/#Elementary_Operations">Elementary_Operations</a></li>
<li><a href="../theories/gauss_jordan/#Rank">Rank</a></li>
<li><a href="../theories/gauss_jordan/#Gauss_Jordan">Gauss_Jordan</a></li>
<li><a href="../theories/gauss_jordan/#Linear_Maps">Linear_Maps</a></li>
<li><a href="../theories/gauss_jordan/#Gauss_Jordan_PA">Gauss_Jordan_PA</a></li>
<li><a href="../theories/gauss_jordan/#Determinants2">Determinants2</a></li>
<li><a href="../theories/gauss_jordan/#Inverse">Inverse</a></li>
<li><a href="../theories/gauss_jordan/#Bases_Of_Fundamental_Subspaces">Bases_Of_Fundamental_Subspaces</a></li>
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<li><a href="../theories/gauss_jordan/#Code_Z2">Code_Z2</a></li>
<li><a href="../theories/gauss_jordan/#Examples_Gauss_Jordan_Abstract">Examples_Gauss_Jordan_Abstract</a></li>
<li><a href="../theories/gauss_jordan/#IArray_Addenda">IArray_Addenda</a></li>
<li><a href="../theories/gauss_jordan/#Matrix_To_IArray">Matrix_To_IArray</a></li>
<li><a href="../theories/gauss_jordan/#Gauss_Jordan_IArrays">Gauss_Jordan_IArrays</a></li>
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<li><a href="../theories/gauss_jordan/#Inverse_IArrays">Inverse_IArrays</a></li>
<li><a href="../theories/gauss_jordan/#Examples_Gauss_Jordan_IArrays">Examples_Gauss_Jordan_IArrays</a></li>
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<li><a href="../theories/gauss_jordan/#Code_Rational">Code_Rational</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MDP-Algorithms.html">Verified Algorithms for Solving Markov Decision Processes</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Echelon_Form.html">Echelon Form</a></li><li><a href="../entries/QR_Decomposition.html">QR Decomposition</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Gauss_Jordan-AFP</p><pre id="copy-text">@article{Gauss_Jordan-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {Gauss-Jordan Algorithm and Its Applications},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Gauss_Jordan.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Gauss_Jordan-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Gauss_Jordan-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Gauss_Jordan-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Gauss Sums and the Pólya–Vinogradov Inequality - Archive of Formal Proofs</title><meta name="description" content="This article provides a full formalisation of Chapter 8 of Apostol&#39;s Introduction to Analytic Number Theory. Subjects that are covered are:
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<h1 >
<span class='first'>G</span>auss <span class='first'>S</span>ums and the <span class='first'>P</span>ólya–<span class='first'>V</span>inogradov <span class='first'>I</span>nequality</h1>
<div>
<p><a href="../authors/raya">Rodrigo Raya</a> <a href="https://people.epfl.ch/rodrigo.raya">🌐</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 10, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a full formalisation of Chapter 8 of
Apostol's <em><a
href="https://www.springer.com/de/book/9780387901633">Introduction
to Analytic Number Theory</a></em>. Subjects that are
covered are:</p> <ul> <li>periodic arithmetic
functions and their finite Fourier series</li>
<li>(generalised) Ramanujan sums</li> <li>Gauss sums
and separable characters</li> <li>induced moduli and
primitive characters</li> <li>the
Pólya&mdash;Vinogradov inequality</li> </ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Gauss_Sums</h3>
<ul>
<li><a href="../theories/gauss_sums/#Gauss_Sums_Auxiliary">Gauss_Sums_Auxiliary</a></li>
<li><a href="../theories/gauss_sums/#Periodic_Arithmetic">Periodic_Arithmetic</a></li>
<li><a href="../theories/gauss_sums/#Complex_Roots_Of_Unity">Complex_Roots_Of_Unity</a></li>
<li><a href="../theories/gauss_sums/#Finite_Fourier_Series">Finite_Fourier_Series</a></li>
<li><a href="../theories/gauss_sums/#Ramanujan_Sums">Ramanujan_Sums</a></li>
<li><a href="../theories/gauss_sums/#Gauss_Sums">Gauss_Sums</a></li>
<li><a href="../theories/gauss_sums/#Polya_Vinogradov">Polya_Vinogradov</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Gauss_Sums-AFP</p><pre id="copy-text">@article{Gauss_Sums-AFP,
author = {Rodrigo Raya and Manuel Eberl},
title = {Gauss Sums and the Pólya–Vinogradov Inequality},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Gauss_Sums.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Gauss_Sums-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Gauss_Sums-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gauss_Sums-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Gauss_Sums-2020-01-10.tar.gz">Jan 10, 2020</a>: Isabelle2019
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<h1 >
<span class='first'>G</span>aussian <span class='first'>I</span>ntegers</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">April 24, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The Gaussian integers are the subring &#8484;[i] of the
complex numbers, i. e. the ring of all complex numbers with integral
real and imaginary part. This article provides a definition of this
ring as well as proofs of various basic properties, such as that they
form a Euclidean ring and a full classification of their primes. An
executable (albeit not very efficient) factorisation algorithm is also
provided.</p> <p>Lastly, this Gaussian integer
formalisation is used in two short applications:</p> <ol>
<li> The characterisation of all positive integers that can be
written as sums of two squares</li> <li> Euclid's
formula for primitive Pythagorean triples</li> </ol>
<p>While elementary proofs for both of these are already
available in the AFP, the theory of Gaussian integers provides more
concise proofs and a more high-level view.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Gaussian_Integers</h3>
<ul>
<li><a href="../theories/gaussian_integers/#Gaussian_Integers">Gaussian_Integers</a></li>
<li><a href="../theories/gaussian_integers/#Gaussian_Integers_Test">Gaussian_Integers_Test</a></li>
<li><a href="../theories/gaussian_integers/#Gaussian_Integers_Sums_Of_Two_Squares">Gaussian_Integers_Sums_Of_Two_Squares</a></li>
<li><a href="../theories/gaussian_integers/#Gaussian_Integers_Pythagorean_Triples">Gaussian_Integers_Pythagorean_Triples</a></li>
<li><a href="../theories/gaussian_integers/#Gaussian_Integers_Everything">Gaussian_Integers_Everything</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Gaussian_Integers-AFP</p><pre id="copy-text">@article{Gaussian_Integers-AFP,
author = {Manuel Eberl},
title = {Gaussian Integers},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Gaussian_Integers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Gaussian_Integers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Gaussian_Integers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Gaussian_Integers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gaussian_Integers-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Gaussian_Integers-2020-04-30.tar.gz">Apr 30, 2020</a>: Isabelle2020
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diff --git a/web/entries/GenClock.html b/web/entries/GenClock.html
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@@ -1,203 +1,205 @@
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<h1 >
<span class='first'>F</span>ormalization of a <span class='first'>G</span>eneralized <span class='first'>P</span>rotocol for <span class='first'>C</span>lock <span class='first'>S</span>ynchronization</h1>
<div>
<p><a href="../authors/tiu">Alwen Tiu</a> <a href="http://users.cecs.anu.edu.au/~tiu/">🌐</a>
</p>
<p class="date">June 24, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the generalized Byzantine fault-tolerant clock synchronization protocol of Schneider. This protocol abstracts from particular algorithms or implementations for clock synchronization. This abstraction includes several assumptions on the behaviors of physical clocks and on general properties of concrete algorithms/implementations. Based on these assumptions the correctness of the protocol is proved by Schneider. His proof was later verified by Shankar using the theorem prover EHDM (precursor to PVS). Our formalization in Isabelle/HOL is based on Shankar's formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session GenClock</h3>
<ul>
<li><a href="../theories/genclock/#GenClock">GenClock</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">GenClock-AFP</p><pre id="copy-text">@article{GenClock-AFP,
author = {Alwen Tiu},
title = {Formalization of a Generalized Protocol for Clock Synchronization},
journal = {Archive of Formal Proofs},
month = {June},
year = {2005},
note = {\url{https://isa-afp.org/entries/GenClock.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-GenClock-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-GenClock-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-GenClock-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-GenClock-2005-06-24.tar.gz">Jun 24, 2005</a>: Isabelle2004
</li></ul>
</div>
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diff --git a/web/entries/General-Triangle.html b/web/entries/General-Triangle.html
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<h1 >
<span class='first'>T</span>he <span class='first'>G</span>eneral <span class='first'>T</span>riangle <span class='first'>I</span>s <span class='first'>U</span>nique</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a class="obfuscated" data="eyJob3N0IjpbImpvYWNoaW0tYnJlaXRuZXIiLCJkZSJdLCJ1c2VyIjpbIm1haWwiXX0=">📧</a>
</p>
<p class="date">April 1, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Some acute-angled triangles are special, e.g. right-angled or isoscele triangles. Some are not of this kind, but, without measuring angles, look as if they were. In that sense, there is exactly one general triangle. This well-known fact is proven here formally.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session General-Triangle</h3>
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<li><a href="../theories/general-triangle/#GeneralTriangle">GeneralTriangle</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">General-Triangle-AFP</p><pre id="copy-text">@article{General-Triangle-AFP,
author = {Joachim Breitner},
title = {The General Triangle Is Unique},
journal = {Archive of Formal Proofs},
month = {April},
year = {2011},
note = {\url{https://isa-afp.org/entries/General-Triangle.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Generalized_Counting_Sort.html b/web/entries/Generalized_Counting_Sort.html
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<h1 >
<span class='first'>A</span>n <span class='first'>E</span>fficient <span class='first'>G</span>eneralization of <span class='first'>C</span>ounting <span class='first'>S</span>ort for <span class='first'>L</span>arge, <span class='first'>P</span>ossibly <span class='first'>I</span>nfinite <span class='first'>K</span>ey <span class='first'>R</span>anges</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">December 4, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Counting sort is a well-known algorithm that sorts objects of any kind
mapped to integer keys, or else to keys in one-to-one correspondence
with some subset of the integers (e.g. alphabet letters). However, it
is suitable for direct use, viz. not just as a subroutine of another
sorting algorithm (e.g. radix sort), only if the key range is not
significantly larger than the number of the objects to be sorted.
This paper describes a tail-recursive generalization of counting sort
making use of a bounded number of counters, suitable for direct use in
case of a large, or even infinite key range of any kind, subject to
the only constraint of being a subset of an arbitrary linear order.
After performing a pen-and-paper analysis of how such algorithm has to
be designed to maximize its efficiency, this paper formalizes the
resulting generalized counting sort (GCsort) algorithm and then
formally proves its correctness properties, namely that (a) the
counters' number is maximized never exceeding the fixed upper
bound, (b) objects are conserved, (c) objects get sorted, and (d) the
algorithm is stable.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Generalized_Counting_Sort</h3>
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<li><a href="../theories/generalized_counting_sort/#Algorithm">Algorithm</a></li>
<li><a href="../theories/generalized_counting_sort/#Conservation">Conservation</a></li>
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<p style="display:none;" id="bibtex-filename">Generalized_Counting_Sort-AFP</p><pre id="copy-text">@article{Generalized_Counting_Sort-AFP,
author = {Pasquale Noce},
title = {An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Generalized_Counting_Sort.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Generalized_Counting_Sort-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Generic_Deriving.html b/web/entries/Generic_Deriving.html
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<h1 >
<span class='first'>D</span>eriving <span class='first'>G</span>eneric <span class='first'>C</span>lass <span class='first'>I</span>nstances for <span class='first'>D</span>atatypes</h1>
<div>
<p><a href="../authors/raedle">Jonas Rädle</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiam9uYXMiLCJyYWVkbGUiXX0=">📧</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">November 6, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We provide a framework for automatically deriving instances for
generic type classes. Our approach is inspired by Haskell's
<i>generic-deriving</i> package and Scala's
<i>shapeless</i> library. In addition to generating the
code for type class functions, we also attempt to automatically prove
type class laws for these instances. As of now, however, some manual
proofs are still required for recursive datatypes.</p>
<p>Note: There are already articles in the AFP that provide
automatic instantiation for a number of classes. Concretely, <a href="https://www.isa-afp.org/entries/Deriving.html">Deriving</a> allows the automatic instantiation of comparators, linear orders, equality, and hashing. <a href="https://www.isa-afp.org/entries/Show.html">Show</a> instantiates a Haskell-style <i>show</i> class.</p><p>Our approach works for arbitrary classes (with some Isabelle/HOL overhead for each class), but a smaller set of datatypes.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Generic_Deriving-AFP</p><pre id="copy-text">@article{Generic_Deriving-AFP,
author = {Jonas Rädle and Lars Hupel},
title = {Deriving generic class instances for datatypes},
journal = {Archive of Formal Proofs},
month = {November},
year = {2018},
note = {\url{https://isa-afp.org/entries/Generic_Deriving.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Deriving-2018-11-21.tar.gz">Nov 21, 2018</a>: Isabelle2018
</li></ul>
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\ No newline at end of file
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>M</span>ultiway-<span class='first'>J</span>oin <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/dardinier">Thibault Dardinier</a>
</p>
<p class="date">September 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Worst-case optimal multiway-join algorithms are recent seminal
achievement of the database community. These algorithms compute the
natural join of multiple relational databases and improve in the worst
case over traditional query plan optimizations of nested binary joins.
In 2014, <a
href="https://doi.org/10.1145/2590989.2590991">Ngo, Ré,
and Rudra</a> gave a unified presentation of different multi-way
join algorithms. We formalized and proved correct their "Generic
Join" algorithm and extended it to support negative joins.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-management-systems">Computer science/Data management systems</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Generic_Join</h3>
<ul>
<li><a href="../theories/generic_join/#Generic_Join">Generic_Join</a></li>
<li><a href="../theories/generic_join/#Generic_Join_Correctness">Generic_Join_Correctness</a></li>
<li><a href="../theories/generic_join/#Examples_Join">Examples_Join</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/MFOTL_Monitor.html">Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MFODL_Monitor_Optimized.html">Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Generic_Join-AFP</p><pre id="copy-text">@article{Generic_Join-AFP,
author = {Thibault Dardinier},
title = {Formalization of Multiway-Join Algorithms},
journal = {Archive of Formal Proofs},
month = {September},
year = {2019},
note = {\url{https://isa-afp.org/entries/Generic_Join.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Generic_Join-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Generic_Join-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Generic_Join-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Join-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Join-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Generic_Join-2019-09-18.tar.gz">Sep 18, 2019</a>: Isabelle2019
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diff --git a/web/entries/GewirthPGCProof.html b/web/entries/GewirthPGCProof.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalisation and Evaluation of Alan Gewirth&#39;s Proof for the Principle of Generic Consistency in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content="An ambitious ethical theory ---Alan Gewirth&#39;s &#34;Principle of
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<h1 >
<span class='first'>F</span>ormalisation and <span class='first'>E</span>valuation of <span class='first'>A</span>lan <span class='first'>G</span>ewirth's <span class='first'>P</span>roof for the <span class='first'>P</span>rinciple of <span class='first'>G</span>eneric <span class='first'>C</span>onsistency in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/fuenmayor">David Fuenmayor</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZGF2ZnVlbm1heW9yIl19">📧</a> and <a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a>
</p>
<p class="date">October 30, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">An ambitious ethical theory ---Alan Gewirth's "Principle of
Generic Consistency"--- is encoded and analysed in Isabelle/HOL.
Gewirth's theory has stirred much attention in philosophy and
ethics and has been proposed as a potential means to bound the impact
of artificial general intelligence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 9, 2019</dt>
<dd>added proof for a stronger variant of the PGC and examplary inferences
(revision 88182cb0a2f6)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session GewirthPGCProof</h3>
<ul>
<li><a href="../theories/gewirthpgcproof/#CJDDLplus">CJDDLplus</a></li>
<li><a href="../theories/gewirthpgcproof/#ExtendedDDL">ExtendedDDL</a></li>
<li><a href="../theories/gewirthpgcproof/#GewirthArgument">GewirthArgument</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">GewirthPGCProof-AFP</p><pre id="copy-text">@article{GewirthPGCProof-AFP,
author = {David Fuenmayor and Christoph Benzmüller},
title = {Formalisation and Evaluation of Alan Gewirth&#39;s Proof for the Principle of Generic Consistency in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/GewirthPGCProof.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-GewirthPGCProof-2018-10-31.tar.gz">Oct 31, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Girth_Chromatic.html b/web/entries/Girth_Chromatic.html
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<h1 >
<span class='first'>A</span> <span class='first'>P</span>robabilistic <span class='first'>P</span>roof of the <span class='first'>G</span>irth-<span class='first'>C</span>hromatic <span class='first'>N</span>umber <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">February 6, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This works presents a formalization of the Girth-Chromatic number theorem in graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. The proof uses the theory of Random Graphs to prove the existence with probabilistic arguments.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Girth_Chromatic</h3>
<ul>
<li><a href="../theories/girth_chromatic/#Girth_Chromatic_Misc">Girth_Chromatic_Misc</a></li>
<li><a href="../theories/girth_chromatic/#Ugraphs">Ugraphs</a></li>
<li><a href="../theories/girth_chromatic/#Girth_Chromatic">Girth_Chromatic</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Undirected_Graph_Theory.html">Undirected Graph Theory</a></li><li><a href="../entries/Roth_Arithmetic_Progressions.html">Roth&rsquo;s Theorem on Arithmetic Progressions</a></li><li><a href="../entries/Szemeredi_Regularity.html">Szemerédi&rsquo;s Regularity Lemma</a></li><li><a href="../entries/Random_Graph_Subgraph_Threshold.html">Properties of Random Graphs &ndash; Subgraph Containment</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Girth_Chromatic-AFP</p><pre id="copy-text">@article{Girth_Chromatic-AFP,
author = {Lars Noschinski},
title = {A Probabilistic Proof of the Girth-Chromatic Number Theorem},
journal = {Archive of Formal Proofs},
month = {February},
year = {2012},
note = {\url{https://isa-afp.org/entries/Girth_Chromatic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Girth_Chromatic-2012-02-06.tar.gz">Feb 6, 2012</a>: Isabelle2011-1
</li></ul>
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diff --git a/web/entries/GoedelGod.html b/web/entries/GoedelGod.html
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<h1 >
<span class='first'>G</span>ödel's <span class='first'>G</span>od in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://page.mi.fu-berlin.de/cbenzmueller/">🌐</a> and <a href="../authors/paleo">Bruno Woltzenlogel Paleo</a> <a href="http://www.logic.at/staff/bruno/">🌐</a>
</p>
<p class="date">November 12, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Dana Scott's version of Gödel's proof of God's existence is formalized in quantified
modal logic KB (QML KB).
QML KB is modeled as a fragment of classical higher-order logic (HOL);
thus, the formalization is essentially a formalization in HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session GoedelGod</h3>
<ul>
<li><a href="../theories/goedelgod/#GoedelGod">GoedelGod</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">GoedelGod-AFP</p><pre id="copy-text">@article{GoedelGod-AFP,
author = {Christoph Benzmüller and Bruno Woltzenlogel Paleo},
title = {Gödel&#39;s God in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/GoedelGod.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-GoedelGod-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-GoedelGod-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-GoedelGod-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-GoedelGod-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-GoedelGod-2013-11-18.tar.gz">Nov 18, 2013</a>: Isabelle2013-1
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diff --git a/web/entries/Goedel_HFSet_Semantic.html b/web/entries/Goedel_HFSet_Semantic.html
--- a/web/entries/Goedel_HFSet_Semantic.html
+++ b/web/entries/Goedel_HFSet_Semantic.html
@@ -1,193 +1,195 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>From Abstract to Concrete G&ouml;del&#39;s Incompleteness Theorems&mdash;Part I - Archive of Formal Proofs</title><meta name="description" content="We validate an abstract formulation of G&amp;ouml;del&#39;s First and Second Incompleteness Theorems from a separate AFP entry by instantiating them to the case of..."><meta property="og:title" content="From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part I" />
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<h1 >
<span class='first'>F</span>rom <span class='first'>A</span>bstract to <span class='first'>C</span>oncrete <span class='first'>G</span>&ouml;del's <span class='first'>I</span>ncompleteness <span class='first'>T</span>heorems&mdash;<span class='first'>P</span>art <span class='first'>I</span></h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We validate an abstract formulation of G&ouml;del's First and
Second Incompleteness Theorems from a <a
href="https://www.isa-afp.org/entries/Goedel_Incompleteness.html">separate
AFP entry</a> by instantiating them to the case of
<i>finite sound extensions of the Hereditarily Finite (HF) Set
theory</i>, i.e., FOL theories extending the HF Set theory with
a finite set of axioms that are sound in the standard model. The
concrete results had been previously formalised in an <a
href="https://www.isa-afp.org/entries/Incompleteness.html">AFP
entry by Larry Paulson</a>; our instantiation reuses the
infrastructure developed in that entry.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Goedel_HFSet_Semantic</h3>
<ul>
<li><a href="../theories/goedel_hfset_semantic/#Instance">Instance</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_Incompleteness.html">An Abstract Formalization of Gödel&rsquo;s Incompleteness Theorems</a></li><li><a href="../entries/Incompleteness.html">Gödel&rsquo;s Incompleteness Theorems</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li>
<li><a href="../entries/Hales_Jewett.html">The Hales–Jewett Theorem</a></li>
<li><a href="../entries/Irrationals_From_THEBOOK.html">Irrational numbers from THE BOOK</a></li>
<li><a href="../entries/CoSMeDis.html">CoSMeDis: A confidentiality-verified distributed social media platform</a></li>
<li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li>
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<p style="display:none;" id="bibtex-filename">Goedel_HFSet_Semantic-AFP</p><pre id="copy-text">@article{Goedel_HFSet_Semantic-AFP,
author = {Andrei Popescu and Dmitriy Traytel},
title = {From Abstract to Concrete Gödel&#39;s Incompleteness Theorems—Part I},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Goedel_HFSet_Semantic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Goedel_HFSet_Semantic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Goedel_HFSet_Semantic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Goedel_HFSet_Semantic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Goedel_HFSet_Semanticless.html b/web/entries/Goedel_HFSet_Semanticless.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>From Abstract to Concrete G&ouml;del&#39;s Incompleteness Theorems&mdash;Part II - Archive of Formal Proofs</title><meta name="description" content="We validate an abstract formulation of G&amp;ouml;del&#39;s Second Incompleteness Theorem from a separate AFP entry by instantiating it to the case of finite..."><meta property="og:title" content="From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part II" />
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<h1 >
<span class='first'>F</span>rom <span class='first'>A</span>bstract to <span class='first'>C</span>oncrete <span class='first'>G</span>&ouml;del's <span class='first'>I</span>ncompleteness <span class='first'>T</span>heorems&mdash;<span class='first'>P</span>art <span class='first'>I</span><span class='first'>I</span></h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We validate an abstract formulation of G&ouml;del's Second
Incompleteness Theorem from a <a
href="https://www.isa-afp.org/entries/Goedel_Incompleteness.html">separate
AFP entry</a> by instantiating it to the case of <i>finite
consistent extensions of the Hereditarily Finite (HF) Set
theory</i>, i.e., consistent FOL theories extending the HF Set
theory with a finite set of axioms. The instantiation draws heavily
on infrastructure previously developed by Larry Paulson in his <a
href="https://www.isa-afp.org/entries/Incompleteness.html">direct
formalisation of the concrete result</a>. It strengthens
Paulson's formalization of G&ouml;del's Second from that
entry by <i>not</i> assuming soundness, and in fact not
relying on any notion of model or semantic interpretation. The
strengthening was obtained by first replacing some of Paulson’s
semantic arguments with proofs within his HF calculus, and then
plugging in some of Paulson's (modified) lemmas to instantiate
our soundness-free G&ouml;del's Second locale.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Goedel_HFSet_Semanticless</h3>
<ul>
<li><a href="../theories/goedel_hfset_semanticless/#SyntaxN">SyntaxN</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Coding">Coding</a></li>
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<li><a href="../theories/goedel_hfset_semanticless/#Sigma">Sigma</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Coding_Predicates">Coding_Predicates</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Pf_Predicates">Pf_Predicates</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#II_Prelims">II_Prelims</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Pseudo_Coding">Pseudo_Coding</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Quote">Quote</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Functions">Functions</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Goedel_I">Goedel_I</a></li>
<li><a href="../theories/goedel_hfset_semanticless/#Instance">Instance</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_Incompleteness.html">An Abstract Formalization of Gödel&rsquo;s Incompleteness Theorems</a></li><li><a href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
<li><a href="../entries/CoSMeDis.html">CoSMeDis: A confidentiality-verified distributed social media platform</a></li>
<li><a href="../entries/Binding_Syntax_Theory.html">A General Theory of Syntax with Bindings</a></li>
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<p style="display:none;" id="bibtex-filename">Goedel_HFSet_Semanticless-AFP</p><pre id="copy-text">@article{Goedel_HFSet_Semanticless-AFP,
author = {Andrei Popescu and Dmitriy Traytel},
title = {From Abstract to Concrete Gödel&#39;s Incompleteness Theorems—Part II},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Goedel_HFSet_Semanticless.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span>n <span class='first'>A</span>bstract <span class='first'>F</span>ormalization of <span class='first'>G</span>&ouml;del's <span class='first'>I</span>ncompleteness <span class='first'>T</span>heorems</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an abstract formalization of G&ouml;del's
incompleteness theorems. We analyze sufficient conditions for the
theorems' applicability to a partially specified logic. Our
abstract perspective enables a comparison between alternative
approaches from the literature. These include Rosser's variation
of the first theorem, Jeroslow's variation of the second theorem,
and the Swierczkowski&ndash;Paulson semantics-based approach. This
AFP entry is the main entry point to the results described in our
CADE-27 paper <a
href="https://dx.doi.org/10.1007/978-3-030-29436-6_26">A
Formally Verified Abstract Account of Gödel's Incompleteness
Theorems</a>. As part of our abstract formalization's
validation, we instantiate our locales twice in the separate AFP
entries <a
href="https://www.isa-afp.org/entries/Goedel_HFSet_Semantic.html">Goedel_HFSet_Semantic</a>
and <a
href="https://www.isa-afp.org/entries/Goedel_HFSet_Semanticless.html">Goedel_HFSet_Semanticless</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Goedel_Incompleteness</h3>
<ul>
<li><a href="../theories/goedel_incompleteness/#Deduction2">Deduction2</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_Encoding">Abstract_Encoding</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_Representability">Abstract_Representability</a></li>
<li><a href="../theories/goedel_incompleteness/#Diagonalization">Diagonalization</a></li>
<li><a href="../theories/goedel_incompleteness/#Derivability_Conditions">Derivability_Conditions</a></li>
<li><a href="../theories/goedel_incompleteness/#Goedel_Formula">Goedel_Formula</a></li>
<li><a href="../theories/goedel_incompleteness/#Standard_Model_More">Standard_Model_More</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_First_Goedel">Abstract_First_Goedel</a></li>
<li><a href="../theories/goedel_incompleteness/#Rosser_Formula">Rosser_Formula</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_First_Goedel_Rosser">Abstract_First_Goedel_Rosser</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_Second_Goedel">Abstract_Second_Goedel</a></li>
<li><a href="../theories/goedel_incompleteness/#Abstract_Jeroslow_Encoding">Abstract_Jeroslow_Encoding</a></li>
<li><a href="../theories/goedel_incompleteness/#Jeroslow_Original">Jeroslow_Original</a></li>
<li><a href="../theories/goedel_incompleteness/#Jeroslow_Simplified">Jeroslow_Simplified</a></li>
<li><a href="../theories/goedel_incompleteness/#Loeb_Formula">Loeb_Formula</a></li>
<li><a href="../theories/goedel_incompleteness/#Loeb">Loeb</a></li>
<li><a href="../theories/goedel_incompleteness/#Tarski">Tarski</a></li>
<li><a href="../theories/goedel_incompleteness/#All_Abstract">All_Abstract</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Syntax_Independent_Logic.html">Syntax-Independent Logic Infrastructure</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li><li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li></ul>
</div>
<div>
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<ul class="horizontal-list">
<li><a href="../entries/Hales_Jewett.html">The Hales–Jewett Theorem</a></li>
<li><a href="../entries/Irrationals_From_THEBOOK.html">Irrational numbers from THE BOOK</a></li>
<li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li>
<li><a href="../entries/Core_SC_DOM.html">The Safely Composable DOM</a></li>
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
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<p style="display:none;" id="bibtex-filename">Goedel_Incompleteness-AFP</p><pre id="copy-text">@article{Goedel_Incompleteness-AFP,
author = {Andrei Popescu and Dmitriy Traytel},
title = {An Abstract Formalization of Gödel&#39;s Incompleteness Theorems},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Goedel_Incompleteness.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>I</span>mplementing the <span class='first'>G</span>oodstein <span class='first'>F</span>unction in &<span class='first'>L</span>ambda;-<span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/felgenhauer">Bertram Felgenhauer</a> <a class="obfuscated" data="eyJob3N0IjpbImdteCIsImRlIl0sInVzZXIiOlsiaW50LWUiXX0=">📧</a>
</p>
<p class="date">February 21, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this formalization, we develop an implementation of the Goodstein
function G in plain &lambda;-calculus, linked to a concise, self-contained
specification. The implementation works on a Church-encoded
representation of countable ordinals. The initial conversion to
hereditary base 2 is not covered, but the material is sufficient to
compute the particular value G(16), and easily extends to other fixed
arguments.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Goodstein_Lambda</h3>
<ul>
<li><a href="../theories/goodstein_lambda/#Goodstein_Lambda">Goodstein_Lambda</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Goodstein_Lambda-AFP</p><pre id="copy-text">@article{Goodstein_Lambda-AFP,
author = {Bertram Felgenhauer},
title = {Implementing the Goodstein Function in λ-Calculus},
journal = {Archive of Formal Proofs},
month = {February},
year = {2020},
note = {\url{https://isa-afp.org/entries/Goodstein_Lambda.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>V</span>erification of the <span class='first'>D</span>eutsch-<span class='first'>S</span>chorr-<span class='first'>W</span>aite <span class='first'>G</span>raph <span class='first'>M</span>arking <span class='first'>A</span>lgorithm <span class='first'>U</span>sing <span class='first'>D</span>ata <span class='first'>R</span>efinement</h1>
<div>
<p><a href="../authors/preoteasa">Viorel Preoteasa</a> <a href="http://users.abo.fi/vpreotea/">🌐</a> and <a href="../authors/back">Ralph-Johan Back</a> <a href="http://users.abo.fi/Ralph-Johan.Back/">🌐</a>
</p>
<p class="date">May 28, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The verification of the Deutsch-Schorr-Waite graph marking algorithm is used as a benchmark in many formalizations of pointer programs. The main purpose of this mechanization is to show how data refinement of invariant based programs can be used in verifying practical algorithms. The verification starts with an abstract algorithm working on a graph given by a relation <i>next</i> on nodes. Gradually the abstract program is refined into Deutsch-Schorr-Waite graph marking algorithm where only one bit per graph node of additional memory is used for marking.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 5, 2012</dt>
<dd>Updated for the new definition of data refinement and the new syntax for demonic and angelic update statements</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session GraphMarkingIBP</h3>
<ul>
<li><a href="../theories/graphmarkingibp/#Graph">Graph</a></li>
<li><a href="../theories/graphmarkingibp/#SetMark">SetMark</a></li>
<li><a href="../theories/graphmarkingibp/#StackMark">StackMark</a></li>
<li><a href="../theories/graphmarkingibp/#LinkMark">LinkMark</a></li>
<li><a href="../theories/graphmarkingibp/#DSWMark">DSWMark</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">GraphMarkingIBP-AFP</p><pre id="copy-text">@article{GraphMarkingIBP-AFP,
author = {Viorel Preoteasa and Ralph-Johan Back},
title = {Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement},
journal = {Archive of Formal Proofs},
month = {May},
year = {2010},
note = {\url{https://isa-afp.org/entries/GraphMarkingIBP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Graph_Saturation.html b/web/entries/Graph_Saturation.html
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<h1 >
<span class='first'>G</span>raph <span class='first'>S</span>aturation</h1>
<div>
<p><a href="../authors/joosten">Sebastiaan J. C. Joosten</a>
</p>
<p class="date">November 23, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is an Isabelle/HOL formalisation of graph saturation, closely
following a <a href="https://doi.org/10.1016/j.jlamp.2018.06.005">paper by the author</a> on graph saturation.
Nine out of ten lemmas of the original paper are proven in this
formalisation. The formalisation additionally includes two theorems
that show the main premise of the paper: that consistency and
entailment are decided through graph saturation. This formalisation
does not give executable code, and it did not implement any of the
optimisations suggested in the paper.</div>
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<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Graph_Saturation-AFP</p><pre id="copy-text">@article{Graph_Saturation-AFP,
author = {Sebastiaan J. C. Joosten},
title = {Graph Saturation},
journal = {Archive of Formal Proofs},
month = {November},
year = {2018},
note = {\url{https://isa-afp.org/entries/Graph_Saturation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Saturation-2018-11-28.tar.gz">Nov 28, 2018</a>: Isabelle2018
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diff --git a/web/entries/Graph_Theory.html b/web/entries/Graph_Theory.html
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<h1 >
<span class='first'>G</span>raph <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">April 28, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a formalization of directed graphs, supporting (labelled) multi-edges and infinite graphs. A polymorphic edge type allows edges to be treated as pairs of vertices, if multi-edges are not required. Formalized properties are i.a. walks (and related concepts), connectedness and subgraphs and basic properties of isomorphisms.
<p>
This formalization is used to prove characterizations of Euler Trails, Shortest Paths and Kuratowski subgraphs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Graph_Theory</h3>
<ul>
<li><a href="../theories/graph_theory/#Rtrancl_On">Rtrancl_On</a></li>
<li><a href="../theories/graph_theory/#Stuff">Stuff</a></li>
<li><a href="../theories/graph_theory/#Digraph">Digraph</a></li>
<li><a href="../theories/graph_theory/#Bidirected_Digraph">Bidirected_Digraph</a></li>
<li><a href="../theories/graph_theory/#Arc_Walk">Arc_Walk</a></li>
<li><a href="../theories/graph_theory/#Pair_Digraph">Pair_Digraph</a></li>
<li><a href="../theories/graph_theory/#Digraph_Component">Digraph_Component</a></li>
<li><a href="../theories/graph_theory/#Vertex_Walk">Vertex_Walk</a></li>
<li><a href="../theories/graph_theory/#Digraph_Component_Vwalk">Digraph_Component_Vwalk</a></li>
<li><a href="../theories/graph_theory/#Digraph_Isomorphism">Digraph_Isomorphism</a></li>
<li><a href="../theories/graph_theory/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/graph_theory/#Subdivision">Subdivision</a></li>
<li><a href="../theories/graph_theory/#Euler">Euler</a></li>
<li><a href="../theories/graph_theory/#Kuratowski">Kuratowski</a></li>
<li><a href="../theories/graph_theory/#Weighted_Graph">Weighted_Graph</a></li>
<li><a href="../theories/graph_theory/#Shortest_Path">Shortest_Path</a></li>
<li><a href="../theories/graph_theory/#Graph_Theory">Graph_Theory</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Query_Optimization.html">Verification of Query Optimization Algorithms</a></li><li><a href="../entries/Design_Theory.html">Combinatorial Design Theory</a></li><li><a href="../entries/Planarity_Certificates.html">Planarity Certificates</a></li><li><a href="../entries/Parity_Game.html">Positional Determinacy of Parity Games</a></li><li><a href="../entries/ShortestPath.html">An Axiomatic Characterization of the Single-Source Shortest Path Problem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Graph_Theory-AFP</p><pre id="copy-text">@article{Graph_Theory-AFP,
author = {Lars Noschinski},
title = {Graph Theory},
journal = {Archive of Formal Proofs},
month = {April},
year = {2013},
note = {\url{https://isa-afp.org/entries/Graph_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Graph_Theory-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Graph_Theory-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Graph_Theory-2013-05-02.tar.gz">May 2, 2013</a>: Isabelle2013
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diff --git a/web/entries/Green.html b/web/entries/Green.html
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@@ -1,186 +1,188 @@
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<h1 >
<span class='first'>A</span>n <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>F</span>ormalisation of <span class='first'>G</span>reen's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a href="http://home.in.tum.de/~mansour/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">January 11, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise a statement of Green’s theorem—the first formalisation to
our knowledge—in Isabelle/HOL. The theorem statement that we formalise
is enough for most applications, especially in physics and
engineering. Our formalisation is made possible by a novel proof that
avoids the ubiquitous line integral cancellation argument. This
eliminates the need to formalise orientations and region boundaries
explicitly with respect to the outwards-pointing normal vector.
Instead we appeal to a homological argument about equivalences between
paths.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Green</h3>
<ul>
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<li><a href="../theories/green/#Derivs">Derivs</a></li>
<li><a href="../theories/green/#Integrals">Integrals</a></li>
<li><a href="../theories/green/#Paths">Paths</a></li>
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<li><a href="../theories/green/#CircExample">CircExample</a></li>
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<p style="display:none;" id="bibtex-filename">Green-AFP</p><pre id="copy-text">@article{Green-AFP,
author = {Mohammad Abdulaziz and Lawrence C. Paulson},
title = {An Isabelle/HOL formalisation of Green&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {January},
year = {2018},
note = {\url{https://isa-afp.org/entries/Green.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Green-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Green-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Green-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>G</span>röbner <span class='first'>B</span>ases <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a> and <a href="../authors/maletzky">Alexander Maletzky</a> <a href="https://risc.jku.at/m/alexander-maletzky/">🌐</a>
</p>
<p class="date">May 2, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalization is concerned with the theory of Gröbner bases in
(commutative) multivariate polynomial rings over fields, originally
developed by Buchberger in his 1965 PhD thesis. Apart from the
statement and proof of the main theorem of the theory, the
formalization also implements Buchberger's algorithm for actually
computing Gröbner bases as a tail-recursive function, thus allowing to
effectively decide ideal membership in finitely generated polynomial
ideals. Furthermore, all functions can be executed on a concrete
representation of multivariate polynomials as association lists.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 18, 2019</dt>
<dd>Specialized Gröbner bases to less abstract representation of polynomials, where
power-products are represented as polynomial mappings.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Groebner_Bases</h3>
<ul>
<li><a href="../theories/groebner_bases/#General">General</a></li>
<li><a href="../theories/groebner_bases/#Confluence">Confluence</a></li>
<li><a href="../theories/groebner_bases/#Reduction">Reduction</a></li>
<li><a href="../theories/groebner_bases/#Groebner_Bases">Groebner_Bases</a></li>
<li><a href="../theories/groebner_bases/#Algorithm_Schema">Algorithm_Schema</a></li>
<li><a href="../theories/groebner_bases/#Buchberger">Buchberger</a></li>
<li><a href="../theories/groebner_bases/#Benchmarks">Benchmarks</a></li>
<li><a href="../theories/groebner_bases/#Algorithm_Schema_Impl">Algorithm_Schema_Impl</a></li>
<li><a href="../theories/groebner_bases/#Code_Target_Rat">Code_Target_Rat</a></li>
<li><a href="../theories/groebner_bases/#Buchberger_Examples">Buchberger_Examples</a></li>
<li><a href="../theories/groebner_bases/#More_MPoly_Type_Class">More_MPoly_Type_Class</a></li>
<li><a href="../theories/groebner_bases/#Auto_Reduction">Auto_Reduction</a></li>
<li><a href="../theories/groebner_bases/#Reduced_GB">Reduced_GB</a></li>
<li><a href="../theories/groebner_bases/#Reduced_GB_Examples">Reduced_GB_Examples</a></li>
<li><a href="../theories/groebner_bases/#Macaulay_Matrix">Macaulay_Matrix</a></li>
<li><a href="../theories/groebner_bases/#F4">F4</a></li>
<li><a href="../theories/groebner_bases/#F4_Examples">F4_Examples</a></li>
<li><a href="../theories/groebner_bases/#Syzygy">Syzygy</a></li>
<li><a href="../theories/groebner_bases/#Syzygy_Examples">Syzygy_Examples</a></li>
<li><a href="../theories/groebner_bases/#Groebner_PM">Groebner_PM</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li><li><a href="../entries/Nullstellensatz.html">Hilbert&rsquo;s Nullstellensatz</a></li><li><a href="../entries/Groebner_Macaulay.html">Gröbner Bases, Macaulay Matrices and Dubé&rsquo;s Degree Bounds</a></li><li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Groebner_Macaulay.html">Gröbner Bases, Macaulay Matrices and Dubé&rsquo;s Degree Bounds</a></li>
<li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
<li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li>
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<p style="display:none;" id="bibtex-filename">Groebner_Bases-AFP</p><pre id="copy-text">@article{Groebner_Bases-AFP,
author = {Fabian Immler and Alexander Maletzky},
title = {Gröbner Bases Theory},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Groebner_Bases.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>G</span>röbner <span class='first'>B</span>ases, <span class='first'>M</span>acaulay <span class='first'>M</span>atrices and <span class='first'>D</span>ubé's <span class='first'>D</span>egree <span class='first'>B</span>ounds</h1>
<div>
<p><a href="../authors/maletzky">Alexander Maletzky</a> <a href="https://risc.jku.at/m/alexander-maletzky/">🌐</a>
</p>
<p class="date">June 15, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes the connection between Gröbner bases and
Macaulay matrices (sometimes also referred to as `generalized
Sylvester matrices'). In particular, it contains a method for
computing Gröbner bases, which proceeds by first constructing some
Macaulay matrix of the initial set of polynomials, then row-reducing
this matrix, and finally converting the result back into a set of
polynomials. The output is shown to be a Gröbner basis if the Macaulay
matrix constructed in the first step is sufficiently large. In order
to obtain concrete upper bounds on the size of the matrix (and hence
turn the method into an effectively executable algorithm), Dubé's
degree bounds on Gröbner bases are utilized; consequently, they are
also part of the formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Groebner_Macaulay</h3>
<ul>
<li><a href="../theories/groebner_macaulay/#Degree_Section">Degree_Section</a></li>
<li><a href="../theories/groebner_macaulay/#Degree_Bound_Utils">Degree_Bound_Utils</a></li>
<li><a href="../theories/groebner_macaulay/#Groebner_Macaulay">Groebner_Macaulay</a></li>
<li><a href="../theories/groebner_macaulay/#Binomial_Int">Binomial_Int</a></li>
<li><a href="../theories/groebner_macaulay/#Poly_Fun">Poly_Fun</a></li>
<li><a href="../theories/groebner_macaulay/#Monomial_Module">Monomial_Module</a></li>
<li><a href="../theories/groebner_macaulay/#Dube_Prelims">Dube_Prelims</a></li>
<li><a href="../theories/groebner_macaulay/#Hilbert_Function">Hilbert_Function</a></li>
<li><a href="../theories/groebner_macaulay/#Cone_Decomposition">Cone_Decomposition</a></li>
<li><a href="../theories/groebner_macaulay/#Dube_Bound">Dube_Bound</a></li>
<li><a href="../theories/groebner_macaulay/#Groebner_Macaulay_Examples">Groebner_Macaulay_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Groebner_Macaulay-AFP</p><pre id="copy-text">@article{Groebner_Macaulay-AFP,
author = {Alexander Maletzky},
title = {Gröbner Bases, Macaulay Matrices and Dubé&#39;s Degree Bounds},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Groebner_Macaulay.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Gromov_Hyperbolicity.html b/web/entries/Gromov_Hyperbolicity.html
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<h1 >
<span class='first'>G</span>romov <span class='first'>H</span>yperbolicity</h1>
<div>
<p><a href="../authors/gouezel">Sebastien Gouezel</a>
</p>
<p class="date">January 16, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A geodesic metric space is Gromov hyperbolic if all its geodesic
triangles are thin, i.e., every side is contained in a fixed
thickening of the two other sides. While this definition looks
innocuous, it has proved extremely important and versatile in modern
geometry since its introduction by Gromov. We formalize the basic
classical properties of Gromov hyperbolic spaces, notably the Morse
lemma asserting that quasigeodesics are close to geodesics, the
invariance of hyperbolicity under quasi-isometries, we define and
study the Gromov boundary and its associated distance, and prove that
a quasi-isometry between Gromov hyperbolic spaces extends to a
homeomorphism of the boundaries. We also prove a less classical
theorem, by Bonk and Schramm, asserting that a Gromov hyperbolic space
embeds isometrically in a geodesic Gromov-hyperbolic space. As the
original proof uses a transfinite sequence of Cauchy completions, this
is an interesting formalization exercise. Along the way, we introduce
basic material on isometries, quasi-isometries, Lipschitz maps,
geodesic spaces, the Hausdorff distance, the Cauchy completion of a
metric space, and the exponential on extended real numbers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Gromov_Hyperbolicity</h3>
<ul>
<li><a href="../theories/gromov_hyperbolicity/#Library_Complements">Library_Complements</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Eexp_Eln">Eexp_Eln</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Hausdorff_Distance">Hausdorff_Distance</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Isometries">Isometries</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Metric_Completion">Metric_Completion</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Gromov_Hyperbolicity">Gromov_Hyperbolicity</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Morse_Gromov_Theorem">Morse_Gromov_Theorem</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Bonk_Schramm_Extension">Bonk_Schramm_Extension</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Gromov_Boundary">Gromov_Boundary</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Boundary_Extension">Boundary_Extension</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Busemann_Function">Busemann_Function</a></li>
<li><a href="../theories/gromov_hyperbolicity/#Isometries_Classification">Isometries_Classification</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ergodic_Theory.html">Ergodic Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Gromov_Hyperbolicity-AFP</p><pre id="copy-text">@article{Gromov_Hyperbolicity-AFP,
author = {Sebastien Gouezel},
title = {Gromov Hyperbolicity},
journal = {Archive of Formal Proofs},
month = {January},
year = {2018},
note = {\url{https://isa-afp.org/entries/Gromov_Hyperbolicity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Grothendieck_Schemes.html b/web/entries/Grothendieck_Schemes.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Grothendieck&#39;s Schemes in Algebraic Geometry - Archive of Formal Proofs</title><meta name="description" content="We formalize mainstream structures in algebraic geometry culminating
in Grothendieck&#39;s schemes: presheaves of rings, sheaves of rings,
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<h1 >
<span class='first'>G</span>rothendieck's <span class='first'>S</span>chemes in <span class='first'>A</span>lgebraic <span class='first'>G</span>eometry</h1>
<div>
<p><a href="../authors/bordg">Anthony Bordg</a> <a href="https://sites.google.com/site/anthonybordg/">🌐</a>, <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a> and <a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">March 29, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize mainstream structures in algebraic geometry culminating
in Grothendieck's schemes: presheaves of rings, sheaves of rings,
ringed spaces, locally ringed spaces, affine schemes and schemes. We
prove that the spectrum of a ring is a locally ringed space, hence an
affine scheme. Finally, we prove that any affine scheme is a scheme.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Grothendieck_Schemes</h3>
<ul>
<li><a href="../theories/grothendieck_schemes/#Set_Extras">Set_Extras</a></li>
<li><a href="../theories/grothendieck_schemes/#Group_Extras">Group_Extras</a></li>
<li><a href="../theories/grothendieck_schemes/#Topological_Space">Topological_Space</a></li>
<li><a href="../theories/grothendieck_schemes/#Comm_Ring">Comm_Ring</a></li>
<li><a href="../theories/grothendieck_schemes/#Scheme">Scheme</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jacobson_Basic_Algebra.html">A Case Study in Basic Algebra</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Grothendieck_Schemes-AFP</p><pre id="copy-text">@article{Grothendieck_Schemes-AFP,
author = {Anthony Bordg and Lawrence C. Paulson and Wenda Li},
title = {Grothendieck&#39;s Schemes in Algebraic Geometry},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Grothendieck_Schemes.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Group-Ring-Module.html b/web/entries/Group-Ring-Module.html
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@@ -1,220 +1,222 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Groups, Rings and Modules - Archive of Formal Proofs</title><meta name="description" content="The theory of groups, rings and modules is developed to a great depth. Group theory results include Zassenhaus&#39;s theorem and the Jordan-Hoelder theorem...."><meta property="og:title" content="Groups, Rings and Modules" />
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<h1 >
<span class='first'>G</span>roups, <span class='first'>R</span>ings and <span class='first'>M</span>odules</h1>
<div>
<p><a href="../authors/kobayashi">Hidetsune Kobayashi</a>, <a href="../authors/chen">L. Chen</a> and <a href="../authors/murao">H. Murao</a>
</p>
<p class="date">May 18, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory of groups, rings and modules is developed to a great depth. Group theory results include Zassenhaus's theorem and the Jordan-Hoelder theorem. The ring theory development includes ideals, quotient rings and the Chinese remainder theorem. The module development includes the Nakayama lemma, exact sequences and Tensor products.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Group-Ring-Module</h3>
<ul>
<li><a href="../theories/group-ring-module/#Algebra1">Algebra1</a></li>
<li><a href="../theories/group-ring-module/#Algebra2">Algebra2</a></li>
<li><a href="../theories/group-ring-module/#Algebra3">Algebra3</a></li>
<li><a href="../theories/group-ring-module/#Algebra4">Algebra4</a></li>
<li><a href="../theories/group-ring-module/#Algebra5">Algebra5</a></li>
<li><a href="../theories/group-ring-module/#Algebra6">Algebra6</a></li>
<li><a href="../theories/group-ring-module/#Algebra7">Algebra7</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Valuation.html">Fundamental Properties of Valuation Theory and Hensel&rsquo;s Lemma</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Group-Ring-Module-AFP</p><pre id="copy-text">@article{Group-Ring-Module-AFP,
author = {Hidetsune Kobayashi and L. Chen and H. Murao},
title = {Groups, Rings and Modules},
journal = {Archive of Formal Proofs},
month = {May},
year = {2004},
note = {\url{https://isa-afp.org/entries/Group-Ring-Module.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2009-04-30.tar.gz">Apr 30, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2004-05-20.tar.gz">May 20, 2004</a>: Isabelle2004
</li><li>
<a href="https://www.isa-afp.org/release/afp-Group-Ring-Module-2004-05-19.tar.gz">May 19, 2004</a>: Isabelle2004
</li></ul>
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<h1 >
<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span>-<span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>V</span>ersion 2.0</h1>
<div>
<p><a href="../authors/taha">Safouan Taha</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsic2Fmb3VhbiIsInRhaGEiXX0=">📧</a>, <a href="../authors/ye">Lina Ye</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsibGluYSIsInllIl19">📧</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">April 26, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a complete formalization of the work of Hoare and Roscoe on
the denotational semantics of the Failure/Divergence Model of CSP. It
follows essentially the presentation of CSP in Roscoe’s Book ”Theory
and Practice of Concurrency” [8] and the semantic details in a joint
Paper of Roscoe and Brooks ”An improved failures model for
communicating processes". The present work is based on a prior
formalization attempt, called HOL-CSP 1.0, done in 1997 by H. Tej and
B. Wolff with the Isabelle proof technology available at that time.
This work revealed minor, but omnipresent foundational errors in key
concepts like the process invariant. The present version HOL-CSP
profits from substantially improved libraries (notably HOLCF),
improved automated proof techniques, and structured proof techniques
in Isar and is substantially shorter but more complete.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session HOL-CSP</h3>
<ul>
<li><a href="../theories/hol-csp/#Introduction">Introduction</a></li>
<li><a href="../theories/hol-csp/#Process">Process</a></li>
<li><a href="../theories/hol-csp/#Bot">Bot</a></li>
<li><a href="../theories/hol-csp/#Skip">Skip</a></li>
<li><a href="../theories/hol-csp/#Stop">Stop</a></li>
<li><a href="../theories/hol-csp/#Mprefix">Mprefix</a></li>
<li><a href="../theories/hol-csp/#Det">Det</a></li>
<li><a href="../theories/hol-csp/#Ndet">Ndet</a></li>
<li><a href="../theories/hol-csp/#Seq">Seq</a></li>
<li><a href="../theories/hol-csp/#Hide">Hide</a></li>
<li><a href="../theories/hol-csp/#Sync">Sync</a></li>
<li><a href="../theories/hol-csp/#Mndet">Mndet</a></li>
<li><a href="../theories/hol-csp/#CSP">CSP</a></li>
<li><a href="../theories/hol-csp/#Assertions">Assertions</a></li>
<li><a href="../theories/hol-csp/#Conclusion">Conclusion</a></li>
<li><a href="../theories/hol-csp/#CopyBuffer">CopyBuffer</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CSP_RefTK.html">The HOL-CSP Refinement Toolkit</a></li></ul>
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<h4>PDFs</h4>
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outline</a>
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<p style="display:none;" id="bibtex-filename">HOL-CSP-AFP</p><pre id="copy-text">@article{HOL-CSP-AFP,
author = {Safouan Taha and Lina Ye and Burkhart Wolff},
title = {HOL-CSP Version 2.0},
journal = {Archive of Formal Proofs},
month = {April},
year = {2019},
note = {\url{https://isa-afp.org/entries/HOL-CSP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-HOL-CSP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-HOL-CSP-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-HOL-CSP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOL-CSP-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOL-CSP-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOL-CSP-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOL-CSP-2019-04-29.tar.gz">Apr 29, 2019</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/HOLCF-Prelude.html b/web/entries/HOLCF-Prelude.html
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<h1 >
<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span><span class='first'>C</span><span class='first'>F</span>-<span class='first'>P</span>relude</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a class="obfuscated" data="eyJob3N0IjpbImNpcyIsInVwZW5uIiwiZWR1Il0sInVzZXIiOlsiam9hY2hpbSJdfQ==">📧</a>, <a href="../authors/huffman">Brian Huffman</a>, <a href="../authors/mitchell">Neil Mitchell</a> and <a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">July 15, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Isabelle/HOLCF-Prelude is a formalization of a large part of
Haskell's standard prelude in Isabelle/HOLCF. We use it to prove
the correctness of the Eratosthenes' Sieve, in its
self-referential implementation commonly used to showcase
Haskell's laziness; prove correctness of GHC's
"fold/build" rule and related rewrite rules; and certify a
number of hints suggested by HLint.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session HOLCF-Prelude</h3>
<ul>
<li><a href="../theories/holcf-prelude/#HOLCF_Main">HOLCF_Main</a></li>
<li><a href="../theories/holcf-prelude/#Type_Classes">Type_Classes</a></li>
<li><a href="../theories/holcf-prelude/#Numeral_Cpo">Numeral_Cpo</a></li>
<li><a href="../theories/holcf-prelude/#Data_Function">Data_Function</a></li>
<li><a href="../theories/holcf-prelude/#Data_Bool">Data_Bool</a></li>
<li><a href="../theories/holcf-prelude/#Data_Tuple">Data_Tuple</a></li>
<li><a href="../theories/holcf-prelude/#Data_Integer">Data_Integer</a></li>
<li><a href="../theories/holcf-prelude/#Data_List">Data_List</a></li>
<li><a href="../theories/holcf-prelude/#Data_Maybe">Data_Maybe</a></li>
<li><a href="../theories/holcf-prelude/#Definedness">Definedness</a></li>
<li><a href="../theories/holcf-prelude/#List_Comprehension">List_Comprehension</a></li>
<li><a href="../theories/holcf-prelude/#Num_Class">Num_Class</a></li>
<li><a href="../theories/holcf-prelude/#HOLCF_Prelude">HOLCF_Prelude</a></li>
<li><a href="../theories/holcf-prelude/#Fibs">Fibs</a></li>
<li><a href="../theories/holcf-prelude/#Sieve_Primes">Sieve_Primes</a></li>
<li><a href="../theories/holcf-prelude/#GHC_Rewrite_Rules">GHC_Rewrite_Rules</a></li>
<li><a href="../theories/holcf-prelude/#HLint">HLint</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/BirdKMP.html">Putting the `K' into Bird&rsquo;s derivation of Knuth-Morris-Pratt string matching</a></li></ul>
</div>
</div>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/HOLCF-Prelude/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">HOLCF-Prelude-AFP</p><pre id="copy-text">@article{HOLCF-Prelude-AFP,
author = {Joachim Breitner and Brian Huffman and Neil Mitchell and Christian Sternagel},
title = {HOLCF-Prelude},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/HOLCF-Prelude.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-HOLCF-Prelude-2017-07-15.tar.gz">Jul 15, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/HRB-Slicing.html b/web/entries/HRB-Slicing.html
--- a/web/entries/HRB-Slicing.html
+++ b/web/entries/HRB-Slicing.html
@@ -1,232 +1,234 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer - Archive of Formal Proofs</title><meta name="description" content="After verifying dynamic and static interprocedural slicing, we present a modular framework for static interprocedural slicing. To this end, we formalized..."><meta property="og:title" content="Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer" />
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<h1 >
<span class='first'>B</span>acking <span class='first'>U</span>p <span class='first'>S</span>licing: <span class='first'>V</span>erifying the <span class='first'>I</span>nterprocedural <span class='first'>T</span>wo-<span class='first'>P</span>hase <span class='first'>H</span>orwitz-<span class='first'>R</span>eps-<span class='first'>B</span>inkley <span class='first'>S</span>licer</h1>
<div>
<p><a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">November 13, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">After verifying <a href="Slicing.html">dynamic and static interprocedural slicing</a>, we present a modular framework for static interprocedural slicing. To this end, we formalized the standard two-phase slicer from Horwitz, Reps and Binkley (see their TOPLAS 12(1) 1990 paper) together with summary edges as presented by Reps et al. (see FSE 1994). The framework is again modular in the programming language by using an abstract CFG, defined via structural and well-formedness properties. Using a weak simulation between the original and sliced graph, we were able to prove the correctness of static interprocedural slicing. We also instantiate our framework with a simple While language with procedures. This shows that the chosen abstractions are indeed valid.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session HRB-Slicing</h3>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jinja.html">Jinja is not Java</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/InformationFlowSlicing_Inter.html">Inter-Procedural Information Flow Noninterference via Slicing</a></li></ul>
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<p style="display:none;" id="bibtex-filename">HRB-Slicing-AFP</p><pre id="copy-text">@article{HRB-Slicing-AFP,
author = {Daniel Wasserrab},
title = {Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer},
journal = {Archive of Formal Proofs},
month = {November},
year = {2009},
note = {\url{https://isa-afp.org/entries/HRB-Slicing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span>ahn and <span class='first'>J</span>ordan <span class='first'>D</span>ecomposition <span class='first'>T</span>heorems</h1>
<div>
<p><a href="../authors/cousin">Marie Cousin</a> <a class="obfuscated" data="eyJob3N0IjpbImdyZW5vYmxlLWlucCIsIm9yZyJdLCJ1c2VyIjpbIm1hcmllIiwiY291c2luIl19">📧</a>, <a href="../authors/echenim">Mnacho Echenim</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaXYtZ3Jlbm9ibGUtYWxwZXMiLCJmciJdLCJ1c2VyIjpbIm1uYWNobyIsImVjaGVuaW0iXX0=">📧</a> and <a href="../authors/guiol">Hervé Guiol</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaXYtZ3Jlbm9ibGUtYWxwZXMiLCJmciJdLCJ1c2VyIjpbImhlcnZlIiwiZ3Vpb2wiXX0=">📧</a>
</p>
<p class="date">November 19, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work we formalize the Hahn decomposition theorem for signed
measures, namely that any measure space for a signed measure can be
decomposed into a positive and a negative set, where every measurable
subset of the positive one has a positive measure, and every
measurable subset of the negative one has a negative measure. We also
formalize the Jordan decomposition theorem as a corollary, which
states that the signed measure under consideration admits a unique
decomposition into a difference of two positive measures, at least one
of which is finite.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/measure-and-integration">Mathematics/Measure and integration</a></li></ul>
<h3>Session Hahn_Jordan_Decomposition</h3>
<ul>
<li><a href="../theories/hahn_jordan_decomposition/#Extended_Reals_Sums_Compl">Extended_Reals_Sums_Compl</a></li>
<li><a href="../theories/hahn_jordan_decomposition/#Hahn_Jordan_Prelims">Hahn_Jordan_Prelims</a></li>
<li><a href="../theories/hahn_jordan_decomposition/#Hahn_Jordan_Decomposition">Hahn_Jordan_Decomposition</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Hahn_Jordan_Decomposition-AFP</p><pre id="copy-text">@article{Hahn_Jordan_Decomposition-AFP,
author = {Marie Cousin and Mnacho Echenim and Hervé Guiol},
title = {The Hahn and Jordan Decomposition Theorems},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Hahn_Jordan_Decomposition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span>ales–<span class='first'>J</span>ewett <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/sulejmani">Ujkan Sulejmani</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsidWprYW4iLCJzdWxlam1hbmkiXX0=">📧</a>, <a href="../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsibWFudWVsIiwiZWJlcmwiXX0=">📧</a> and <a href="../authors/kreuzer">Katharina Kreuzer</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiayIsImtyZXV6ZXIiXX0=">📧</a>
</p>
<p class="date">September 2, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article is a formalisation of a proof of the
Hales–Jewett theorem presented in the textbook <em>Ramsey
Theory</em> by Graham et al.</p>
<p>The Hales–Jewett theorem is a result in Ramsey Theory which
states that, for any non-negative integers $r$ and $t$, there exists a
minimal dimension $N$, such that any $r$-coloured
$N'$-dimensional cube over $t$ elements (with $N' \geq N$)
contains a monochromatic line. This theorem generalises Van der
Waerden's Theorem, which has already been formalised in another
<a
href="https://www.isa-afp.org/entries/Van_der_Waerden.html">AFP
entry</a>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Hales_Jewett</h3>
<ul>
<li><a href="../theories/hales_jewett/#Hales_Jewett">Hales_Jewett</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Hales_Jewett-AFP</p><pre id="copy-text">@article{Hales_Jewett-AFP,
author = {Ujkan Sulejmani and Manuel Eberl and Katharina Kreuzer},
title = {The Hales–Jewett Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Hales_Jewett.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Hales_Jewett-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hales_Jewett-2022-09-07.tar.gz">Sep 7, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Heard_Of.html b/web/entries/Heard_Of.html
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<h1 >
<span class='first'>V</span>erifying <span class='first'>F</span>ault-<span class='first'>T</span>olerant <span class='first'>D</span>istributed <span class='first'>A</span>lgorithms in the <span class='first'>H</span>eard-of <span class='first'>M</span>odel</h1>
<div>
<p><a href="../authors/debrat">Henri Debrat</a> <a class="obfuscated" data="eyJob3N0IjpbImxvcmlhIiwiZnIiXSwidXNlciI6WyJoZW5yaSIsImRlYnJhdCJdfQ==">📧</a> and <a href="../authors/merz">Stephan Merz</a> <a href="http://www.loria.fr/~merz">🌐</a>
</p>
<p class="date">July 27, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Distributed computing is inherently based on replication, promising
increased tolerance to failures of individual computing nodes or
communication channels. Realizing this promise, however, involves
quite subtle algorithmic mechanisms, and requires precise statements
about the kinds and numbers of faults that an algorithm tolerates (such
as process crashes, communication faults or corrupted values). The
landmark theorem due to Fischer, Lynch, and Paterson shows that it is
impossible to achieve Consensus among N asynchronously communicating
nodes in the presence of even a single permanent failure. Existing
solutions must rely on assumptions of "partial synchrony".
<p>
Indeed, there have been numerous misunderstandings on what exactly a given
algorithm is supposed to realize in what kinds of environments. Moreover, the
abundance of subtly different computational models complicates comparisons
between different algorithms. Charron-Bost and Schiper introduced the Heard-Of
model for representing algorithms and failure assumptions in a uniform
framework, simplifying comparisons between algorithms.
<p>
In this contribution, we represent the Heard-Of model in Isabelle/HOL. We define
two semantics of runs of algorithms with different unit of atomicity and relate
these through a reduction theorem that allows us to verify algorithms in the
coarse-grained semantics (where proofs are easier) and infer their correctness
for the fine-grained one (which corresponds to actual executions). We
instantiate the framework by verifying six Consensus algorithms that differ in
the underlying algorithmic mechanisms and the kinds of faults they tolerate.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Heard_Of</h3>
<ul>
<li><a href="../theories/heard_of/#HOModel">HOModel</a></li>
<li><a href="../theories/heard_of/#Reduction">Reduction</a></li>
<li><a href="../theories/heard_of/#Majorities">Majorities</a></li>
<li><a href="../theories/heard_of/#OneThirdRuleDefs">OneThirdRuleDefs</a></li>
<li><a href="../theories/heard_of/#OneThirdRuleProof">OneThirdRuleProof</a></li>
<li><a href="../theories/heard_of/#UvDefs">UvDefs</a></li>
<li><a href="../theories/heard_of/#UvProof">UvProof</a></li>
<li><a href="../theories/heard_of/#LastVotingDefs">LastVotingDefs</a></li>
<li><a href="../theories/heard_of/#LastVotingProof">LastVotingProof</a></li>
<li><a href="../theories/heard_of/#UteDefs">UteDefs</a></li>
<li><a href="../theories/heard_of/#UteProof">UteProof</a></li>
<li><a href="../theories/heard_of/#AteDefs">AteDefs</a></li>
<li><a href="../theories/heard_of/#AteProof">AteProof</a></li>
<li><a href="../theories/heard_of/#EigbyzDefs">EigbyzDefs</a></li>
<li><a href="../theories/heard_of/#EigbyzProof">EigbyzProof</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Consensus_Refined.html">Consensus Refined</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Heard_Of-AFP</p><pre id="copy-text">@article{Heard_Of-AFP,
author = {Henri Debrat and Stephan Merz},
title = {Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model},
journal = {Archive of Formal Proofs},
month = {July},
year = {2012},
note = {\url{https://isa-afp.org/entries/Heard_Of.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Heard_Of-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Heard_Of-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Heard_Of-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Heard_Of-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Heard_Of-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Heard_Of-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Heard_Of-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Heard_Of-2012-07-30.tar.gz">Jul 30, 2012</a>: Isabelle2012
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diff --git a/web/entries/Hello_World.html b/web/entries/Hello_World.html
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@@ -1,175 +1,177 @@
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<h1 >
<span class='first'>H</span>ello <span class='first'>W</span>orld</h1>
<div>
<p><a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">March 7, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this article, we present a formalization of the well-known
"Hello, World!" code, including a formal framework for
reasoning about IO. Our model is inspired by the handling of IO in
Haskell. We start by formalizing the 🌍 and embrace the IO monad
afterwards. Then we present a sample main :: IO (), followed by its
proof of correctness.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Hello_World</h3>
<ul>
<li><a href="../theories/hello_world/#IO">IO</a></li>
<li><a href="../theories/hello_world/#HelloWorld">HelloWorld</a></li>
<li><a href="../theories/hello_world/#HelloWorld_Proof">HelloWorld_Proof</a></li>
<li><a href="../theories/hello_world/#RunningCodeFromIsabelle">RunningCodeFromIsabelle</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Hello_World-AFP</p><pre id="copy-text">@article{Hello_World-AFP,
author = {Cornelius Diekmann and Lars Hupel},
title = {Hello World},
journal = {Archive of Formal Proofs},
month = {March},
year = {2020},
note = {\url{https://isa-afp.org/entries/Hello_World.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Hello_World-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Hello_World-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hello_World-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Hello_World-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Hello_World-2020-03-23.tar.gz">Mar 23, 2020</a>: Isabelle2019
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diff --git a/web/entries/HereditarilyFinite.html b/web/entries/HereditarilyFinite.html
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span>ereditarily <span class='first'>F</span>inite <span class='first'>S</span>ets</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">November 17, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory of hereditarily finite sets is formalised, following
the <a href="http://journals.impan.gov.pl/dm/Inf/422-0-1.html">development</a> of Swierczkowski.
An HF set is a finite collection of other HF sets; they enjoy an induction principle
and satisfy all the axioms of ZF set theory apart from the axiom of infinity, which is negated.
All constructions that are possible in ZF set theory (Cartesian products, disjoint sums, natural numbers,
functions) without using infinite sets are possible here.
The definition of addition for the HF sets follows Kirby.
This development forms the foundation for the Isabelle proof of Gödel's incompleteness theorems,
which has been <a href="Incompleteness.html">formalised separately</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>February 23, 2015</dt>
<dd>Added the theory "Finitary" defining the class of types that can be embedded in hf, including int, char, option, list, etc.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session HereditarilyFinite</h3>
<ul>
<li><a href="../theories/hereditarilyfinite/#HF">HF</a></li>
<li><a href="../theories/hereditarilyfinite/#Ordinal">Ordinal</a></li>
<li><a href="../theories/hereditarilyfinite/#Rank">Rank</a></li>
<li><a href="../theories/hereditarilyfinite/#Finite_Automata">Finite_Automata</a></li>
<li><a href="../theories/hereditarilyfinite/#Finitary">Finitary</a></li>
<li><a href="../theories/hereditarilyfinite/#OrdArith">OrdArith</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li><li><a href="../entries/Category3.html">Category Theory with Adjunctions and Limits</a></li><li><a href="../entries/Finite_Automata_HF.html">Finite Automata in Hereditarily Finite Set Theory</a></li><li><a href="../entries/Incompleteness.html">Gödel&rsquo;s Incompleteness Theorems</a></li></ul>
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<p style="display:none;" id="bibtex-filename">HereditarilyFinite-AFP</p><pre id="copy-text">@article{HereditarilyFinite-AFP,
author = {Lawrence C. Paulson},
title = {The Hereditarily Finite Sets},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/HereditarilyFinite.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-HereditarilyFinite-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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diff --git a/web/entries/Hermite.html b/web/entries/Hermite.html
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<h1 >
<span class='first'>H</span>ermite <span class='first'>N</span>ormal <span class='first'>F</span>orm</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>
</p>
<p class="date">July 7, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Hermite Normal Form is a canonical matrix analogue of Reduced Echelon Form, but involving matrices over more general rings. In this work we formalise an algorithm to compute the Hermite Normal Form of a matrix by means of elementary row operations, taking advantage of the Echelon Form AFP entry. We have proven the correctness of such an algorithm and refined it to immutable arrays. Furthermore, we have also formalised the uniqueness of the Hermite Normal Form of a matrix. Code can be exported and some examples of execution involving integer matrices and polynomial matrices are presented as well.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Hermite</h3>
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<li><a href="../theories/hermite/#Hermite">Hermite</a></li>
<li><a href="../theories/hermite/#Hermite_IArrays">Hermite_IArrays</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Echelon_Form.html">Echelon Form</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li><li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li></ul>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li>
<li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li>
<li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li>
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<p style="display:none;" id="bibtex-filename">Hermite-AFP</p><pre id="copy-text">@article{Hermite-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {Hermite Normal Form},
journal = {Archive of Formal Proofs},
month = {July},
year = {2015},
note = {\url{https://isa-afp.org/entries/Hermite.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Hermite-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Hermite-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hermite-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Hermite-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Hermite-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Hermite-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Hermite-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Hermite-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Hermite-2015-07-07.tar.gz">Jul 7, 2015</a>: Isabelle2015
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diff --git a/web/entries/Hermite_Lindemann.html b/web/entries/Hermite_Lindemann.html
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@@ -1,209 +1,211 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span>ermite–<span class='first'>L</span>indemann–<span class='first'>W</span>eierstraß <span class='first'>T</span>ranscendence <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 3, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of the
Hermite-Lindemann-Weierstraß Theorem (also known as simply
Hermite-Lindemann or Lindemann-Weierstraß). This theorem is one of the
crowning achievements of 19th century number theory.</p>
<p>The theorem states that if $\alpha_1, \ldots,
\alpha_n\in\mathbb{C}$ are algebraic numbers that are linearly
independent over $\mathbb{Z}$, then $e^{\alpha_1},\ldots,e^{\alpha_n}$
are algebraically independent over $\mathbb{Q}$.</p>
<p>Like the <a
href="https://doi.org/10.1007/978-3-319-66107-0_5">previous
formalisation in Coq by Bernard</a>, I proceeded by formalising
<a
href="https://doi.org/10.1017/CBO9780511565977">Baker's
version of the theorem and proof</a> and then deriving the
original one from that. Baker's version states that for any
algebraic numbers $\beta_1, \ldots, \beta_n\in\mathbb{C}$ and distinct
algebraic numbers $\alpha_i, \ldots, \alpha_n\in\mathbb{C}$, we have
$\beta_1 e^{\alpha_1} + \ldots + \beta_n e^{\alpha_n} = 0$ if and only
if all the $\beta_i$ are zero.</p> <p>This has a number of
direct corollaries, e.g.:</p> <ul> <li>$e$ and $\pi$
are transcendental</li> <li>$e^z$, $\sin z$, $\tan z$,
etc. are transcendental for algebraic
$z\in\mathbb{C}\setminus\{0\}$</li> <li>$\ln z$ is
transcendental for algebraic $z\in\mathbb{C}\setminus\{0,
1\}$</li> </ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Hermite_Lindemann</h3>
<ul>
<li><a href="../theories/hermite_lindemann/#Algebraic_Integer_Divisibility">Algebraic_Integer_Divisibility</a></li>
<li><a href="../theories/hermite_lindemann/#More_Polynomial_HLW">More_Polynomial_HLW</a></li>
<li><a href="../theories/hermite_lindemann/#More_Min_Int_Poly">More_Min_Int_Poly</a></li>
<li><a href="../theories/hermite_lindemann/#Complex_Lexorder">Complex_Lexorder</a></li>
<li><a href="../theories/hermite_lindemann/#More_Multivariate_Polynomial_HLW">More_Multivariate_Polynomial_HLW</a></li>
<li><a href="../theories/hermite_lindemann/#More_Algebraic_Numbers_HLW">More_Algebraic_Numbers_HLW</a></li>
<li><a href="../theories/hermite_lindemann/#Misc_HLW">Misc_HLW</a></li>
<li><a href="../theories/hermite_lindemann/#Hermite_Lindemann">Hermite_Lindemann</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Pi_Transcendental.html">The Transcendence of π</a></li><li><a href="../entries/Power_Sum_Polynomials.html">Power Sum Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li></ul>
</div>
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<li><a href="../entries/Transcendence_Series_Hancl_Rucki.html">The Transcendence of Certain Infinite Series</a></li>
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<p style="display:none;" id="bibtex-filename">Hermite_Lindemann-AFP</p><pre id="copy-text">@article{Hermite_Lindemann-AFP,
author = {Manuel Eberl},
title = {The Hermite–Lindemann–Weierstraß Transcendence Theorem},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Hermite_Lindemann.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>H</span>idden <span class='first'>M</span>arkov <span class='first'>M</span>odels</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>
</p>
<p class="date">May 25, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains a formalization of hidden Markov models [3] based
on Johannes Hölzl's formalization of discrete time Markov chains
[1]. The basic definitions are provided and the correctness of two
main (dynamic programming) algorithms for hidden Markov models is
proved: the forward algorithm for computing the likelihood of an
observed sequence, and the Viterbi algorithm for decoding the most
probable hidden state sequence. The Viterbi algorithm is made
executable including memoization. Hidden markov models have various
applications in natural language processing. For an introduction see
Jurafsky and Martin [2].</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Hidden_Markov_Models</h3>
<ul>
<li><a href="../theories/hidden_markov_models/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/hidden_markov_models/#Hidden_Markov_Model">Hidden_Markov_Model</a></li>
<li><a href="../theories/hidden_markov_models/#HMM_Implementation">HMM_Implementation</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Markov_Models.html">Markov Models</a></li><li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Hidden_Markov_Models-AFP</p><pre id="copy-text">@article{Hidden_Markov_Models-AFP,
author = {Simon Wimmer},
title = {Hidden Markov Models},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Hidden_Markov_Models.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Hidden_Markov_Models-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span>n <span class='first'>A</span>lgebra for <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
with contributions from <a href="../authors/zhang">Yu Zhang</a>
</p>
<p class="date">January 15, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this formalization, I introduce a higher-order term algebra,
generalizing the notions of free variables, matching, and
substitution. The need arose from the work on a <a
href="http://dx.doi.org/10.1007/978-3-319-89884-1_35">verified
compiler from Isabelle to CakeML</a>. Terms can be thought of as
consisting of a generic (free variables, constants, application) and
a specific part. As example applications, this entry provides
instantiations for de-Bruijn terms, terms with named variables, and
<a
href="https://www.isa-afp.org/entries/Lambda_Free_RPOs.html">Blanchette’s
&lambda;-free higher-order terms</a>. Furthermore, I
implement translation functions between de-Bruijn terms and named
terms and prove their correctness.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session Higher_Order_Terms</h3>
<ul>
<li><a href="../theories/higher_order_terms/#Term_Utils">Term_Utils</a></li>
<li><a href="../theories/higher_order_terms/#Find_First">Find_First</a></li>
<li><a href="../theories/higher_order_terms/#Name">Name</a></li>
<li><a href="../theories/higher_order_terms/#Fresh_Monad">Fresh_Monad</a></li>
<li><a href="../theories/higher_order_terms/#Fresh_Class">Fresh_Class</a></li>
<li><a href="../theories/higher_order_terms/#Term_Class">Term_Class</a></li>
<li><a href="../theories/higher_order_terms/#Term">Term</a></li>
<li><a href="../theories/higher_order_terms/#Pats">Pats</a></li>
<li><a href="../theories/higher_order_terms/#Nterm">Nterm</a></li>
<li><a href="../theories/higher_order_terms/#Term_to_Nterm">Term_to_Nterm</a></li>
<li><a href="../theories/higher_order_terms/#Unification_Compat">Unification_Compat</a></li>
<li><a href="../theories/higher_order_terms/#Lambda_Free_Compat">Lambda_Free_Compat</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Higher_Order_Terms-AFP</p><pre id="copy-text">@article{Higher_Order_Terms-AFP,
author = {Lars Hupel},
title = {An Algebra for Higher-Order Terms},
journal = {Archive of Formal Proofs},
month = {January},
year = {2019},
note = {\url{https://isa-afp.org/entries/Higher_Order_Terms.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
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<a href="https://www.isa-afp.org/release/afp-Higher_Order_Terms-2019-01-15.tar.gz">Jan 15, 2019</a>: Isabelle2018
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diff --git a/web/entries/Hoare_Time.html b/web/entries/Hoare_Time.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Hoare Logics for Time Bounds - Archive of Formal Proofs</title><meta name="description" content="We study three different Hoare logics for reasoning about time bounds of imperative programs and formalize them in Isabelle/HOL: a classical Hoare like..."><meta property="og:title" content="Hoare Logics for Time Bounds" />
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<h1 >
<span class='first'>H</span>oare <span class='first'>L</span>ogics for <span class='first'>T</span>ime <span class='first'>B</span>ounds</h1>
<div>
<p><a href="../authors/haslbeckm">Maximilian P. L. Haslbeck</a> <a href="http://in.tum.de/~haslbema/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">February 26, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We study three different Hoare logics for reasoning about time bounds
of imperative programs and formalize them in Isabelle/HOL: a classical
Hoare like logic due to Nielson, a logic with potentials due to
Carbonneaux <i>et al.</i> and a <i>separation
logic</i> following work by Atkey, Chaguérand and Pottier.
These logics are formally shown to be sound and complete. Verification
condition generators are developed and are shown sound and complete
too. We also consider variants of the systems where we abstract from
multiplicative constants in the running time bounds, thus supporting a
big-O style of reasoning. Finally we compare the expressive power of
the three systems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Hoare_Time</h3>
<ul>
<li><a href="../theories/hoare_time/#AExp">AExp</a></li>
<li><a href="../theories/hoare_time/#BExp">BExp</a></li>
<li><a href="../theories/hoare_time/#Com">Com</a></li>
<li><a href="../theories/hoare_time/#Big_Step">Big_Step</a></li>
<li><a href="../theories/hoare_time/#Big_StepT">Big_StepT</a></li>
<li><a href="../theories/hoare_time/#Nielson_Hoare">Nielson_Hoare</a></li>
<li><a href="../theories/hoare_time/#Nielson_VCG">Nielson_VCG</a></li>
<li><a href="../theories/hoare_time/#Vars">Vars</a></li>
<li><a href="../theories/hoare_time/#Nielson_VCGi">Nielson_VCGi</a></li>
<li><a href="../theories/hoare_time/#Nielson_VCGi_complete">Nielson_VCGi_complete</a></li>
<li><a href="../theories/hoare_time/#Nielson_Examples">Nielson_Examples</a></li>
<li><a href="../theories/hoare_time/#Nielson_Sqrt">Nielson_Sqrt</a></li>
<li><a href="../theories/hoare_time/#Quant_Hoare">Quant_Hoare</a></li>
<li><a href="../theories/hoare_time/#Quant_VCG">Quant_VCG</a></li>
<li><a href="../theories/hoare_time/#Quant_Examples">Quant_Examples</a></li>
<li><a href="../theories/hoare_time/#QuantK_Hoare">QuantK_Hoare</a></li>
<li><a href="../theories/hoare_time/#QuantK_VCG">QuantK_VCG</a></li>
<li><a href="../theories/hoare_time/#QuantK_Examples">QuantK_Examples</a></li>
<li><a href="../theories/hoare_time/#QuantK_Sqrt">QuantK_Sqrt</a></li>
<li><a href="../theories/hoare_time/#Partial_Evaluation">Partial_Evaluation</a></li>
<li><a href="../theories/hoare_time/#Product_Separation_Algebra">Product_Separation_Algebra</a></li>
<li><a href="../theories/hoare_time/#Sep_Algebra_Add">Sep_Algebra_Add</a></li>
<li><a href="../theories/hoare_time/#Big_StepT_Partial">Big_StepT_Partial</a></li>
<li><a href="../theories/hoare_time/#SepLog_Hoare">SepLog_Hoare</a></li>
<li><a href="../theories/hoare_time/#SepLog_Examples">SepLog_Examples</a></li>
<li><a href="../theories/hoare_time/#SepLogK_Hoare">SepLogK_Hoare</a></li>
<li><a href="../theories/hoare_time/#SepLogK_VCG">SepLogK_VCG</a></li>
<li><a href="../theories/hoare_time/#Discussion">Discussion</a></li>
<li><a href="../theories/hoare_time/#DiscussionO">DiscussionO</a></li>
<li><a href="../theories/hoare_time/#Hoare_Time">Hoare_Time</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Separation_Algebra.html">Separation Algebra</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Auto2_Imperative_HOL.html">Verifying Imperative Programs using Auto2</a></li>
<li><a href="../entries/Complx.html">COMPLX: A Verification Framework for Concurrent Imperative Programs</a></li>
<li><a href="../entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></li>
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<p style="display:none;" id="bibtex-filename">Hoare_Time-AFP</p><pre id="copy-text">@article{Hoare_Time-AFP,
author = {Maximilian P. L. Haslbeck and Tobias Nipkow},
title = {Hoare Logics for Time Bounds},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/Hoare_Time.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Hoare_Time-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hoare_Time-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Hoare_Time-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Hood_Melville_Queue.html b/web/entries/Hood_Melville_Queue.html
--- a/web/entries/Hood_Melville_Queue.html
+++ b/web/entries/Hood_Melville_Queue.html
@@ -1,171 +1,173 @@
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<h1 >
<span class='first'>H</span>ood-<span class='first'>M</span>elville <span class='first'>Q</span>ueue</h1>
<div>
<p><a href="../authors/londono">Alejandro Gómez-Londoño</a> <a class="obfuscated" data="eyJob3N0IjpbImNoYWxtZXJzIiwic2UiXSwidXNlciI6WyJhbGVqYW5kcm8iLCJnb21leiJdfQ==">📧</a>
</p>
<p class="date">January 18, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a verified implementation of a constant time queue. The
original design is due to <a
href="https://doi.org/10.1016/0020-0190(81)90030-2">Hood
and Melville</a>. This formalization follows the presentation in
<em>Purely Functional Data Structures</em>by Okasaki.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Hood, R., & Melville, R. (1981). Real-time queue operations in pure LISP. Information Processing Letters, 13(2), 50–54. <a href="https://doi.org/10.1016/0020-0190(81)90030-2">https://doi.org/10.1016/0020-0190(81)90030-2</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Queue_(abstract_data_type)">Wikipedia</a>
</li></ul>
<h3>Session Hood_Melville_Queue</h3>
<ul>
<li><a href="../theories/hood_melville_queue/#Hood_Melville_Queue">Hood_Melville_Queue</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Hood_Melville_Queue-AFP</p><pre id="copy-text">@article{Hood_Melville_Queue-AFP,
author = {Alejandro Gómez-Londoño},
title = {Hood-Melville Queue},
journal = {Archive of Formal Proofs},
month = {January},
year = {2021},
note = {\url{https://isa-afp.org/entries/Hood_Melville_Queue.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Hood_Melville_Queue-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Hood_Melville_Queue-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hood_Melville_Queue-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Hood_Melville_Queue-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/HotelKeyCards.html b/web/entries/HotelKeyCards.html
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@@ -1,210 +1,212 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Hotel Key Card System - Archive of Formal Proofs</title><meta name="description" content="Two models of an electronic hotel key card system are contrasted: a state based and a trace based one. Both are defined, verified, and proved equivalent in..."><meta property="og:title" content="Hotel Key Card System" />
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<h1 >
<span class='first'>H</span>otel <span class='first'>K</span>ey <span class='first'>C</span>ard <span class='first'>S</span>ystem</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">September 9, 2006</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Two models of an electronic hotel key card system are contrasted: a state based and a trace based one. Both are defined, verified, and proved equivalent in the theorem prover Isabelle/HOL. It is shown that if a guest follows a certain safety policy regarding her key cards, she can be sure that nobody but her can enter her room.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T. (2006). Verifying a Hotel Key Card System. Theoretical Aspects of Computing - ICTAC 2006, 1–14. <a href="https://doi.org/10.1007/11921240_1">https://doi.org/10.1007/11921240_1</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/ictac06.html">Open access</a>
</li></ul>
<h3>Session HotelKeyCards</h3>
<ul>
<li><a href="../theories/hotelkeycards/#Notation">Notation</a></li>
<li><a href="../theories/hotelkeycards/#Basis">Basis</a></li>
<li><a href="../theories/hotelkeycards/#State">State</a></li>
<li><a href="../theories/hotelkeycards/#NewCard">NewCard</a></li>
<li><a href="../theories/hotelkeycards/#Trace">Trace</a></li>
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<p style="display:none;" id="bibtex-filename">HotelKeyCards-AFP</p><pre id="copy-text">@article{HotelKeyCards-AFP,
author = {Tobias Nipkow},
title = {Hotel Key Card System},
journal = {Archive of Formal Proofs},
month = {September},
year = {2006},
note = {\url{https://isa-afp.org/entries/HotelKeyCards.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-HotelKeyCards-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li></ul>
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>extbook <span class='first'>P</span>roof of <span class='first'>H</span>uffman's <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a href="http://www21.in.tum.de/~blanchet">🌐</a>
</p>
<p class="date">October 15, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Huffman's algorithm is a procedure for constructing a binary tree with minimum weighted path length. This report presents a formal proof of the correctness of Huffman's algorithm written using Isabelle/HOL. Our proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom induction rules to help Isabelle's automatic tactics, leading to very short proofs for most of the lemmas.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Huffman</h3>
<ul>
<li><a href="../theories/huffman/#Huffman">Huffman</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Huffman-AFP</p><pre id="copy-text">@article{Huffman-AFP,
author = {Jasmin Christian Blanchette},
title = {The Textbook Proof of Huffman&#39;s Algorithm},
journal = {Archive of Formal Proofs},
month = {October},
year = {2008},
note = {\url{https://isa-afp.org/entries/Huffman.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Huffman-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Huffman-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Huffman-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Huffman-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2008-10-21.tar.gz">Oct 21, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Huffman-2008-10-15.tar.gz">Oct 15, 2008</a>: Isabelle2008
</li></ul>
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<h1 >
<span class='first'>F</span>ormalizing a <span class='first'>S</span>eligman-<span class='first'>S</span>tyle <span class='first'>T</span>ableau <span class='first'>S</span>ystem for <span class='first'>H</span>ybrid <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">December 20, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of soundness and completeness proofs
for a Seligman-style tableau system for hybrid logic. The completeness
result is obtained via a synthetic approach using maximally
consistent sets of tableau blocks. The formalization differs from
previous work in a few ways. First, to avoid the need to backtrack in
the construction of a tableau, the formalized system has no unnamed
initial segment, and therefore no Name rule. Second, I show that the
full Bridge rule is admissible in the system. Third, I start from rules
restricted to only extend the branch with new formulas, including only
witnessing diamonds that are not already witnessed, and show that
the unrestricted rules are admissible. Similarly, I start from simpler
versions of the @-rules and show that these are sufficient.
The GoTo rule is restricted using a notion of potential such that each
application consumes potential and potential is earned through applications of
the remaining rules. I show that if a branch can be closed then it can
be closed starting from a single unit. Finally, Nom is restricted by
a fixed set of allowed nominals. The resulting system should be terminating.
Paper: <a href="https://doi.org/10.4230/LIPIcs.TYPES.2020.5">doi.org/10.4230/LIPIcs.TYPES.2020.5</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 3, 2020</dt>
<dd>The fully restricted system has been shown complete by updating the synthetic completeness proof.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li></ul>
<h3>Session Hybrid_Logic</h3>
<ul>
<li><a href="../theories/hybrid_logic/#Hybrid_Logic">Hybrid_Logic</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Hybrid_Logic-AFP</p><pre id="copy-text">@article{Hybrid_Logic-AFP,
author = {Asta Halkjær From},
title = {Formalizing a Seligman-Style Tableau System for Hybrid Logic},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Hybrid_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Hybrid_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>H</span>ybrid <span class='first'>M</span>ulti-<span class='first'>L</span>ane <span class='first'>S</span>patial <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/linker">Sven Linker</a> <a class="obfuscated" data="eyJob3N0IjpbImxpdmVycG9vbCIsImFjIiwidWsiXSwidXNlciI6WyJzIiwibGlua2VyIl19">📧</a>
</p>
<p class="date">November 6, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a semantic embedding of a spatio-temporal multi-modal
logic, specifically defined to reason about motorway traffic, into
Isabelle/HOL. The semantic model is an abstraction of a motorway,
emphasising local spatial properties, and parameterised by the types
of sensors deployed in the vehicles. We use the logic to define
controller constraints to ensure safety, i.e., the absence of
collisions on the motorway. After proving safety with a restrictive
definition of sensors, we relax these assumptions and show how to
amend the controller constraints to still guarantee safety.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li></ul>
<h3>Session Hybrid_Multi_Lane_Spatial_Logic</h3>
<ul>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#NatInt">NatInt</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#RealInt">RealInt</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Cars">Cars</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Traffic">Traffic</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Views">Views</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Restriction">Restriction</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Move">Move</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Sensors">Sensors</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Length">Length</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#HMLSL">HMLSL</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Perfect_Sensors">Perfect_Sensors</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#HMLSL_Perfect">HMLSL_Perfect</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Safety_Perfect">Safety_Perfect</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Regular_Sensors">Regular_Sensors</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#HMLSL_Regular">HMLSL_Regular</a></li>
<li><a href="../theories/hybrid_multi_lane_spatial_logic/#Safety_Regular">Safety_Regular</a></li></ul><div class="flex-wrap">
</div>
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<p style="display:none;" id="bibtex-filename">Hybrid_Multi_Lane_Spatial_Logic-AFP</p><pre id="copy-text">@article{Hybrid_Multi_Lane_Spatial_Logic-AFP,
author = {Sven Linker},
title = {Hybrid Multi-Lane Spatial Logic},
journal = {Archive of Formal Proofs},
month = {November},
year = {2017},
note = {\url{https://isa-afp.org/entries/Hybrid_Multi_Lane_Spatial_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Hybrid_Multi_Lane_Spatial_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Hybrid_Multi_Lane_Spatial_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Hybrid_Systems_VCs.html b/web/entries/Hybrid_Systems_VCs.html
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<h1 >
<span class='first'>V</span>erification <span class='first'>C</span>omponents for <span class='first'>H</span>ybrid <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/munive">Jonathan Julian Huerta y Munive</a>
</p>
<p class="date">September 10, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These components formalise a semantic framework for the deductive
verification of hybrid systems. They support reasoning about
continuous evolutions of hybrid programs in the style of differential
dynamics logic. Vector fields or flows model these evolutions, and
their verification is done with invariants for the former or orbits
for the latter. Laws of modal Kleene algebra or categorical predicate
transformers implement the verification condition generation. Examples
show the approach at work.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>December 13, 2020</dt>
<dd>added components based on Kleene algebras with tests. These implement differential Hoare logic (dH) and a Morgan-style differential refinement calculus (dR) for verification of hybrid programs.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Hybrid_Systems_VCs</h3>
<ul>
<li><a href="../theories/hybrid_systems_vcs/#HS_Preliminaries">HS_Preliminaries</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_ODEs">HS_ODEs</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_Spartan">HS_VC_Spartan</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_Examples">HS_VC_Examples</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_PT">HS_VC_PT</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_PT_Examples">HS_VC_PT_Examples</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_MKA">HS_VC_MKA</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KA_rel">HS_VC_KA_rel</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_MKA_rel">HS_VC_MKA_rel</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_MKA_Examples_rel">HS_VC_MKA_Examples_rel</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KA_ndfun">HS_VC_KA_ndfun</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_MKA_ndfun">HS_VC_MKA_ndfun</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_MKA_Examples_ndfun">HS_VC_MKA_Examples_ndfun</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KAT">HS_VC_KAT</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KAT_rel">HS_VC_KAT_rel</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KAT_Examples_rel">HS_VC_KAT_Examples_rel</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KAT_ndfun">HS_VC_KAT_ndfun</a></li>
<li><a href="../theories/hybrid_systems_vcs/#HS_VC_KAT_Examples_ndfun">HS_VC_KAT_Examples_ndfun</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li><li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li><li><a href="../entries/Transformer_Semantics.html">Transformer Semantics</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Matrices_for_ODEs.html">Matrices for ODEs</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li>
<li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li>
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<p style="display:none;" id="bibtex-filename">Hybrid_Systems_VCs-AFP</p><pre id="copy-text">@article{Hybrid_Systems_VCs-AFP,
author = {Jonathan Julian Huerta y Munive},
title = {Verification Components for Hybrid Systems},
journal = {Archive of Formal Proofs},
month = {September},
year = {2019},
note = {\url{https://isa-afp.org/entries/Hybrid_Systems_VCs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>hallow <span class='first'>E</span>mbedding of <span class='first'>H</span>yper<span class='first'>C</span><span class='first'>T</span><span class='first'>L</span>*</h1>
<div>
<p><a href="../authors/rabe">Markus N. Rabe</a> <a href="http://www.react.uni-saarland.de/people/rabe.html">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">April 16, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize HyperCTL*, a temporal logic for expressing security properties. We
first define a shallow embedding of HyperCTL*, within which we prove inductive and coinductive
rules for the operators. Then we show that a HyperCTL* formula captures Goguen-Meseguer
noninterference, a landmark information flow property. We also define a deep embedding and
connect it to the shallow embedding by a denotational semantics, for which we prove sanity w.r.t.
dependence on the free variables. Finally, we show that under some finiteness assumptions about
the model, noninterference is given by a (finitary) syntactic formula.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li></ul>
<h3>Session HyperCTL</h3>
<ul>
<li><a href="../theories/hyperctl/#Prelim">Prelim</a></li>
<li><a href="../theories/hyperctl/#Shallow">Shallow</a></li>
<li><a href="../theories/hyperctl/#Noninterference">Noninterference</a></li>
<li><a href="../theories/hyperctl/#Deep">Deep</a></li>
<li><a href="../theories/hyperctl/#Finite_Noninterference">Finite_Noninterference</a></li>
<li><a href="../theories/hyperctl/#HyperCTL">HyperCTL</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">HyperCTL-AFP</p><pre id="copy-text">@article{HyperCTL-AFP,
author = {Markus N. Rabe and Peter Lammich and Andrei Popescu},
title = {A shallow embedding of HyperCTL*},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/HyperCTL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Hyperdual.html b/web/entries/Hyperdual.html
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<h1 >
<span class='first'>H</span>yperdual <span class='first'>N</span>umbers and <span class='first'>F</span>orward <span class='first'>D</span>ifferentiation</h1>
<div>
<p><a href="../authors/smola">Filip Smola</a> and <a href="../authors/fleuriot">Jacques D. Fleuriot</a> <a href="https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html">🌐</a>
</p>
<p class="date">December 31, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Hyperdual numbers are ones with a real component and a number
of infinitesimal components, usually written as $a_0 + a_1 \cdot
\epsilon_1 + a_2 \cdot \epsilon_2 + a_3 \cdot \epsilon_1\epsilon_2$.
They have been proposed by <a
href="https://doi.org/10.2514/6.2011-886">Fike and
Alonso</a> in an approach to automatic
differentiation.</p> <p>In this entry we formalise
hyperdual numbers and their application to forward differentiation. We
show them to be an instance of multiple algebraic structures and then,
along with facts about twice-differentiability, we define what we call
the hyperdual extensions of functions on real-normed fields. This
extension formally represents the proposed way that the first and
second derivatives of a function can be automatically calculated. We
demonstrate it on the standard logistic function $f(x) = \frac{1}{1 +
e^{-x}}$ and also reproduce the example analytic function $f(x) =
\frac{e^x}{\sqrt{sin(x)^3 + cos(x)^3}}$ used for demonstration by Fike
and Alonso.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Hyperdual</h3>
<ul>
<li><a href="../theories/hyperdual/#Hyperdual">Hyperdual</a></li>
<li><a href="../theories/hyperdual/#TwiceFieldDifferentiable">TwiceFieldDifferentiable</a></li>
<li><a href="../theories/hyperdual/#HyperdualFunctionExtension">HyperdualFunctionExtension</a></li>
<li><a href="../theories/hyperdual/#LogisticFunction">LogisticFunction</a></li>
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<p style="display:none;" id="bibtex-filename">Hyperdual-AFP</p><pre id="copy-text">@article{Hyperdual-AFP,
author = {Filip Smola and Jacques D. Fleuriot},
title = {Hyperdual Numbers and Forward Differentiation},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/Hyperdual.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel of <span class='first'>I</span><span class='first'>E</span><span class='first'>E</span><span class='first'>E</span> <span class='first'>F</span>loating <span class='first'>P</span>oint <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/yu">Lei Yu</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJseTI3MSJdfQ==">📧</a>
with contributions from <a href="../authors/hellauer">Fabian Hellauer</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJoZWxsYXVlciJdfQ==">📧</a> and <a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>
</p>
<p class="date">July 27, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a formal model of IEEE-754 floating-point arithmetic. This formalization, including formal specification of the standard and proofs of important properties of floating-point arithmetic, forms the foundation for verifying programs with floating-point computation. There is also a code generation setup for floats so that we can execute programs using this formalization in functional programming languages.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>February 5, 2018</dt>
<dd>'Modernized' representation following the formalization in HOL4:
former "float_format" and predicate "is_valid" is now encoded in a type "('e, 'f) float" where
'e and 'f encode the size of exponent and fraction.</dd><dt>September 25, 2017</dt>
<dd>Added conversions from and to software floating point numbers
(by Fabian Hellauer and Fabian Immler).<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session IEEE_Floating_Point</h3>
<ul>
<li><a href="../theories/ieee_floating_point/#IEEE">IEEE</a></li>
<li><a href="../theories/ieee_floating_point/#IEEE_Properties">IEEE_Properties</a></li>
<li><a href="../theories/ieee_floating_point/#FP64">FP64</a></li>
<li><a href="../theories/ieee_floating_point/#Conversion_IEEE_Float">Conversion_IEEE_Float</a></li>
<li><a href="../theories/ieee_floating_point/#Double">Double</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MFODL_Monitor_Optimized.html">Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</a></li><li><a href="../entries/CakeML.html">CakeML</a></li></ul>
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outline</a>
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<p style="display:none;" id="bibtex-filename">IEEE_Floating_Point-AFP</p><pre id="copy-text">@article{IEEE_Floating_Point-AFP,
author = {Lei Yu},
title = {A Formal Model of IEEE Floating Point Arithmetic},
journal = {Archive of Formal Proofs},
month = {July},
year = {2013},
note = {\url{https://isa-afp.org/entries/IEEE_Floating_Point.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-IEEE_Floating_Point-2013-07-28.tar.gz">Jul 28, 2013</a>: Isabelle2013
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/IFC_Tracking.html b/web/entries/IFC_Tracking.html
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<h1 >
<span class='first'>I</span>nformation <span class='first'>F</span>low <span class='first'>C</span>ontrol via <span class='first'>D</span>ependency <span class='first'>T</span>racking</h1>
<div>
<p><a href="../authors/nordhoff">Benedikt Nordhoff</a> <a class="obfuscated" data="eyJob3N0IjpbInd3dSIsImRlIl0sInVzZXIiOlsiYiIsIm4iXX0=">📧</a>
</p>
<p class="date">April 1, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a characterisation of how information is propagated by
program executions based on the tracking data and control dependencies
within executions themselves. The characterisation might be used for
deriving approximative safety properties to be targeted by static
analyses or checked at runtime. We utilise a simple yet versatile
control flow graph model as a program representation. As our model is
not assumed to be finite it can be instantiated for a broad class of
programs. The targeted security property is indistinguishable
security where executions produce sequences of observations and only
non-terminating executions are allowed to drop a tail of those. A
very crude approximation of our characterisation is slicing based on
program dependence graphs, which we use as a minimal example and
derive a corresponding soundness result. For further details and
applications refer to the authors upcoming dissertation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session IFC_Tracking</h3>
<ul>
<li><a href="../theories/ifc_tracking/#IFC">IFC</a></li>
<li><a href="../theories/ifc_tracking/#PDG">PDG</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">IFC_Tracking-AFP</p><pre id="copy-text">@article{IFC_Tracking-AFP,
author = {Benedikt Nordhoff},
title = {Information Flow Control via Dependency Tracking},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/IFC_Tracking.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-IFC_Tracking-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-IFC_Tracking-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IFC_Tracking-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-IFC_Tracking-2021-04-01.tar.gz">Apr 1, 2021</a>: Isabelle2021
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/IMAP-CRDT.html b/web/entries/IMAP-CRDT.html
--- a/web/entries/IMAP-CRDT.html
+++ b/web/entries/IMAP-CRDT.html
@@ -1,188 +1,190 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The IMAP CmRDT - Archive of Formal Proofs</title><meta name="description" content="We provide our Isabelle/HOL formalization of a Conflict-free
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We show that Strong..."><meta property="og:title" content="The IMAP CmRDT" />
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span><span class='first'>M</span><span class='first'>A</span><span class='first'>P</span> <span class='first'>C</span>m<span class='first'>R</span><span class='first'>D</span><span class='first'>T</span></h1>
<div>
<p><a href="../authors/jungnickel">Tim Jungnickel</a> <a class="obfuscated" data="eyJob3N0IjpbInR1LWJlcmxpbiIsImRlIl0sInVzZXIiOlsidGltIiwianVuZ25pY2tlbCJdfQ==">📧</a>, <a href="../authors/oldenburg">Lennart Oldenburg</a> and <a href="../authors/loibl">Matthias Loibl</a>
</p>
<p class="date">November 9, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide our Isabelle/HOL formalization of a Conflict-free
Replicated Datatype for Internet Message Access Protocol commands.
We show that Strong Eventual Consistency (SEC) is guaranteed
by proving the commutativity of concurrent operations. We base our
formalization on the recently proposed "framework for
establishing Strong Eventual Consistency for Conflict-free Replicated
Datatypes" (AFP.CRDT) from Gomes et al. Hence, we provide an
additional example of how the recently proposed framework can be used
to design and prove CRDTs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session IMAP-CRDT</h3>
<ul>
<li><a href="../theories/imap-crdt/#IMAP-def">IMAP-def</a></li>
<li><a href="../theories/imap-crdt/#IMAP-proof-commute">IMAP-proof-commute</a></li>
<li><a href="../theories/imap-crdt/#IMAP-proof-helpers">IMAP-proof-helpers</a></li>
<li><a href="../theories/imap-crdt/#IMAP-proof-independent">IMAP-proof-independent</a></li>
<li><a href="../theories/imap-crdt/#IMAP-proof">IMAP-proof</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CRDT.html">A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">IMAP-CRDT-AFP</p><pre id="copy-text">@article{IMAP-CRDT-AFP,
author = {Tim Jungnickel and Lennart Oldenburg and Matthias Loibl},
title = {The IMAP CmRDT},
journal = {Archive of Formal Proofs},
month = {November},
year = {2017},
note = {\url{https://isa-afp.org/entries/IMAP-CRDT.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2020-01-14.tar.gz">Jan 14, 2020</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-IMAP-CRDT-2017-11-10.tar.gz">Nov 10, 2017</a>: Isabelle2017
</li></ul>
</div>
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diff --git a/web/entries/IMO2019.html b/web/entries/IMO2019.html
--- a/web/entries/IMO2019.html
+++ b/web/entries/IMO2019.html
@@ -1,178 +1,180 @@
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<h1 >
<span class='first'>S</span>elected <span class='first'>P</span>roblems <span class='first'>F</span>rom the <span class='first'>I</span>nternational <span class='first'>M</span>athematical <span class='first'>O</span>lympiad 2019</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">August 5, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry contains formalisations of the answers to three of
the six problem of the International Mathematical Olympiad 2019,
namely Q1, Q4, and Q5.</p> <p>The reason why these
problems were chosen is that they are particularly amenable to
formalisation: they can be solved with minimal use of libraries. The
remaining three concern geometry and graph theory, which, in the
author's opinion, are more difficult to formalise resp. require a
more complex library.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/misc">Mathematics/Misc</a></li></ul>
<h3>Session IMO2019</h3>
<ul>
<li><a href="../theories/imo2019/#IMO2019_Q1">IMO2019_Q1</a></li>
<li><a href="../theories/imo2019/#IMO2019_Q4">IMO2019_Q4</a></li>
<li><a href="../theories/imo2019/#IMO2019_Q5">IMO2019_Q5</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li></ul>
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<p style="display:none;" id="bibtex-filename">IMO2019-AFP</p><pre id="copy-text">@article{IMO2019-AFP,
author = {Manuel Eberl},
title = {Selected Problems from the International Mathematical Olympiad 2019},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/IMO2019.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-IMO2019-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-IMO2019-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IMO2019-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>I</span><span class='first'>M</span><span class='first'>P</span>2 – <span class='first'>S</span>imple <span class='first'>P</span>rogram <span class='first'>V</span>erification in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>
</p>
<p class="date">January 15, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">IMP2 is a simple imperative language together with Isabelle tooling to
create a program verification environment in Isabelle/HOL. The tools
include a C-like syntax, a verification condition generator, and
Isabelle commands for the specification of programs. The framework is
modular, i.e., it allows easy reuse of already proved programs within
larger programs. This entry comes with a quickstart guide and a large
collection of examples, spanning basic algorithms with simple proofs
to more advanced algorithms and proof techniques like data refinement.
Some highlights from the examples are: <ul> <li>Bisection
Square Root, </li> <li>Extended Euclid, </li>
<li>Exponentiation by Squaring, </li> <li>Binary
Search, </li> <li>Insertion Sort, </li>
<li>Quicksort, </li> <li>Depth First Search.
</li> </ul> The abstract syntax and semantics are very
simple and well-documented. They are suitable to be used in a course,
as extension to the IMP language which comes with the Isabelle
distribution. While this entry is limited to a simple imperative
language, the ideas could be extended to more sophisticated languages.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session IMP2</h3>
<ul>
<li><a href="../theories/imp2/#IMP2_Aux_Lemmas">IMP2_Aux_Lemmas</a></li>
<li><a href="../theories/imp2/#IMP2_Utils">IMP2_Utils</a></li>
<li><a href="../theories/imp2/#Named_Simpsets">Named_Simpsets</a></li>
<li><a href="../theories/imp2/#Subgoal_Focus_Some">Subgoal_Focus_Some</a></li>
<li><a href="../theories/imp2/#Syntax">Syntax</a></li>
<li><a href="../theories/imp2/#Semantics">Semantics</a></li>
<li><a href="../theories/imp2/#Annotated_Syntax">Annotated_Syntax</a></li>
<li><a href="../theories/imp2/#IMP2_Basic_Simpset">IMP2_Basic_Simpset</a></li>
<li><a href="../theories/imp2/#Parser">Parser</a></li>
<li><a href="../theories/imp2/#IMP2_Basic_Decls">IMP2_Basic_Decls</a></li>
<li><a href="../theories/imp2/#IMP2_Program_Analysis">IMP2_Program_Analysis</a></li>
<li><a href="../theories/imp2/#IMP2_Var_Postprocessor">IMP2_Var_Postprocessor</a></li>
<li><a href="../theories/imp2/#IMP2_Var_Abs">IMP2_Var_Abs</a></li>
<li><a href="../theories/imp2/#IMP2_VCG">IMP2_VCG</a></li>
<li><a href="../theories/imp2/#IMP2_Specification">IMP2_Specification</a></li>
<li><a href="../theories/imp2/#IMP2">IMP2</a></li>
<li><a href="../theories/imp2/#Quickstart_Guide">Quickstart_Guide</a></li>
<li><a href="../theories/imp2/#IMP2_from_IMP">IMP2_from_IMP</a></li>
<li><a href="../theories/imp2/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/IMP2_Binary_Heap.html">Binary Heaps for IMP2</a></li></ul>
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<p style="display:none;" id="bibtex-filename">IMP2-AFP</p><pre id="copy-text">@article{IMP2-AFP,
author = {Peter Lammich and Simon Wimmer},
title = {IMP2 – Simple Program Verification in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {January},
year = {2019},
note = {\url{https://isa-afp.org/entries/IMP2.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IMP2-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/IMP2_Binary_Heap.html b/web/entries/IMP2_Binary_Heap.html
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<h1 >
<span class='first'>B</span>inary <span class='first'>H</span>eaps for <span class='first'>I</span><span class='first'>M</span><span class='first'>P</span>2</h1>
<div>
<p><a href="../authors/griebel">Simon Griebel</a>
</p>
<p class="date">June 13, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this submission array-based binary minimum heaps are formalized.
The correctness of the following heap operations is proved: insert,
get-min, delete-min and make-heap. These are then used to verify an
in-place heapsort. The formalization is based on IMP2, an imperative
program verification framework implemented in Isabelle/HOL. The
verified heap functions are iterative versions of the partly recursive
functions found in "Algorithms and Data Structures – The Basic
Toolbox" by K. Mehlhorn and P. Sanders and "Introduction to
Algorithms" by T. H. Cormen, C. E. Leiserson, R. L. Rivest and C.
Stein.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session IMP2_Binary_Heap</h3>
<ul>
<li><a href="../theories/imp2_binary_heap/#IMP2_Binary_Heap">IMP2_Binary_Heap</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/IMP2.html">IMP2 – Simple Program Verification in Isabelle/HOL</a></li></ul>
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<p style="display:none;" id="bibtex-filename">IMP2_Binary_Heap-AFP</p><pre id="copy-text">@article{IMP2_Binary_Heap-AFP,
author = {Simon Griebel},
title = {Binary Heaps for IMP2},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/IMP2_Binary_Heap.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-IMP2_Binary_Heap-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>horter <span class='first'>C</span>ompiler <span class='first'>C</span>orrectness <span class='first'>P</span>roof for <span class='first'>L</span>anguage <span class='first'>I</span><span class='first'>M</span><span class='first'>P</span></h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">June 4, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This paper presents a compiler correctness proof for the didactic
imperative programming language IMP, introduced in Nipkow and
Klein's book on formal programming language semantics (version of
March 2021), whose size is just two thirds of the book's proof in
the number of formal text lines. As such, it promises to constitute a
further enhanced reference for the formal verification of compilers
meant for larger, real-world programming languages. The presented
proof does not depend on language determinism, so that the proposed
approach can be applied to non-deterministic languages as well. As a
confirmation, this paper extends IMP with an additional
non-deterministic choice command, and proves compiler correctness,
viz. the simulation of compiled code execution by source code, for
such extended language.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul>
<h3>Session IMP_Compiler</h3>
<ul>
<li><a href="../theories/imp_compiler/#Compiler">Compiler</a></li>
<li><a href="../theories/imp_compiler/#Compiler2">Compiler2</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">IMP_Compiler-AFP</p><pre id="copy-text">@article{IMP_Compiler-AFP,
author = {Pasquale Noce},
title = {A Shorter Compiler Correctness Proof for Language IMP},
journal = {Archive of Formal Proofs},
month = {June},
year = {2021},
note = {\url{https://isa-afp.org/entries/IMP_Compiler.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-IMP_Compiler-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IMP_Compiler-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>A</span> <span class='first'>R</span>euse-<span class='first'>B</span>ased <span class='first'>M</span>ulti-<span class='first'>S</span>tage <span class='first'>C</span>ompiler <span class='first'>V</span>erification for <span class='first'>L</span>anguage <span class='first'>I</span><span class='first'>M</span><span class='first'>P</span></h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">July 10, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">After introducing the didactic imperative programming language IMP,
Nipkow and Klein's book on formal programming language semantics
(version of March 2021) specifies compilation of IMP commands into a
lower-level language based on a stack machine, and expounds a formal
verification of that compiler. Exercise 8.4 asks the reader to adjust
such proof for a new compilation target, consisting of a machine
language that (i) accesses memory locations through their addresses
instead of variable names, and (ii) maintains a stack in memory via a
stack pointer rather than relying upon a built-in stack. A natural
strategy to maximize reuse of the original proof is keeping the
original language as an assembly one and splitting compilation into
multiple steps, namely a source-to-assembly step matching the original
compilation process followed by an assembly-to-machine step. In this
way, proving assembly code-machine code equivalence is the only extant
task. A previous paper by the present author introduces a reasoning
toolbox that allows for a compiler correctness proof shorter than the
book's one, as such promising to constitute a further enhanced
reference for the formal verification of real-world compilers. This
paper in turn shows that such toolbox can be reused to accomplish the
aforesaid task as well, which demonstrates that the proposed approach
also promotes proof reuse in multi-stage compiler verifications.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul>
<h3>Session IMP_Compiler_Reuse</h3>
<ul>
<li><a href="../theories/imp_compiler_reuse/#Compiler">Compiler</a></li>
<li><a href="../theories/imp_compiler_reuse/#Compiler2">Compiler2</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">IMP_Compiler_Reuse-AFP</p><pre id="copy-text">@article{IMP_Compiler_Reuse-AFP,
author = {Pasquale Noce},
title = {A Reuse-Based Multi-Stage Compiler Verification for Language IMP},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/IMP_Compiler_Reuse.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-IMP_Compiler_Reuse-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IMP_Compiler_Reuse-2022-07-11.tar.gz">Jul 11, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/IP_Addresses.html b/web/entries/IP_Addresses.html
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@@ -1,216 +1,218 @@
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<h1 >
<span class='first'>I</span><span class='first'>P</span> <span class='first'>A</span>ddresses</h1>
<div>
<p><a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>, <a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">June 28, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains a definition of IP addresses and a library to work
with them. Generic IP addresses are modeled as machine words of
arbitrary length. Derived from this generic definition, IPv4 addresses
are 32bit machine words, IPv6 addresses are 128bit words.
Additionally, IPv4 addresses can be represented in dot-decimal
notation and IPv6 addresses in (compressed) colon-separated notation.
We support toString functions and parsers for both notations. Sets of
IP addresses can be represented with a netmask (e.g.
192.168.0.0/255.255.0.0) or in CIDR notation (e.g. 192.168.0.0/16). To
provide executable code for set operations on IP address ranges, the
library includes a datatype to work on arbitrary intervals of machine
words.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session IP_Addresses</h3>
<ul>
<li><a href="../theories/ip_addresses/#NumberWang_IPv4">NumberWang_IPv4</a></li>
<li><a href="../theories/ip_addresses/#NumberWang_IPv6">NumberWang_IPv6</a></li>
<li><a href="../theories/ip_addresses/#WordInterval">WordInterval</a></li>
<li><a href="../theories/ip_addresses/#Hs_Compat">Hs_Compat</a></li>
<li><a href="../theories/ip_addresses/#IP_Address">IP_Address</a></li>
<li><a href="../theories/ip_addresses/#IPv4">IPv4</a></li>
<li><a href="../theories/ip_addresses/#IPv6">IPv6</a></li>
<li><a href="../theories/ip_addresses/#Prefix_Match">Prefix_Match</a></li>
<li><a href="../theories/ip_addresses/#CIDR_Split">CIDR_Split</a></li>
<li><a href="../theories/ip_addresses/#WordInterval_Sorted">WordInterval_Sorted</a></li>
<li><a href="../theories/ip_addresses/#IP_Address_Parser">IP_Address_Parser</a></li>
<li><a href="../theories/ip_addresses/#Lib_Numbers_toString">Lib_Numbers_toString</a></li>
<li><a href="../theories/ip_addresses/#Lib_Word_toString">Lib_Word_toString</a></li>
<li><a href="../theories/ip_addresses/#Lib_List_toString">Lib_List_toString</a></li>
<li><a href="../theories/ip_addresses/#IP_Address_toString">IP_Address_toString</a></li>
<li><a href="../theories/ip_addresses/#Prefix_Match_toString">Prefix_Match_toString</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Simple_Firewall.html">Simple Firewall</a></li></ul>
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author = {Cornelius Diekmann and Julius Michaelis and Lars Hupel},
title = {IP Addresses},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/IP_Addresses.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-IP_Addresses-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Imperative_Insertion_Sort.html b/web/entries/Imperative_Insertion_Sort.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Imperative Insertion Sort - Archive of Formal Proofs</title><meta name="description" content="The insertion sort algorithm of Cormen et al. (Introduction to Algorithms) is expressed in Imperative HOL and proved to be correct and terminating. For..."><meta property="og:title" content="Imperative Insertion Sort" />
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<h1 >
<span class='first'>I</span>mperative <span class='first'>I</span>nsertion <span class='first'>S</span>ort</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">September 25, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The insertion sort algorithm of Cormen et al. (Introduction to Algorithms) is expressed in Imperative HOL and proved to be correct and terminating. For this purpose we also provide a theory about imperative loop constructs with accompanying induction/invariant rules for proving partial and total correctness. Furthermore, the formalized algorithm is fit for code generation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Imperative_Insertion_Sort</h3>
<ul>
<li><a href="../theories/imperative_insertion_sort/#Imperative_Loops">Imperative_Loops</a></li>
<li><a href="../theories/imperative_insertion_sort/#Imperative_Insertion_Sort">Imperative_Insertion_Sort</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Imperative_Insertion_Sort-AFP</p><pre id="copy-text">@article{Imperative_Insertion_Sort-AFP,
author = {Christian Sternagel},
title = {Imperative Insertion Sort},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Imperative_Insertion_Sort.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Imperative_Insertion_Sort-2014-09-25.tar.gz">Sep 25, 2014</a>: Isabelle2014
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diff --git a/web/entries/Implicational_Logic.html b/web/entries/Implicational_Logic.html
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<h1 >
<span class='first'>S</span>oundness and <span class='first'>C</span>ompleteness of <span class='first'>I</span>mplicational <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a> and <a href="../authors/villadsen">Jørgen Villadsen</a> <a href="https://people.compute.dtu.dk/jovi/">🌐</a>
</p>
<p class="date">September 13, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of soundness and completeness of the Bernays-Tarski
axiom system for classical implicational logic. The completeness proof is
constructive following the approach by László Kalmár, Elliott Mendelson and
others. The result can be extended to full classical propositional logic by
uncommenting a few lines for falsehood.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/classical-propositional-logic">Logic/General logic/Classical propositional logic</a></li><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Implicational_Logic</h3>
<ul>
<li><a href="../theories/implicational_logic/#Implicational_Logic">Implicational_Logic</a></li>
<li><a href="../theories/implicational_logic/#Implicational_Logic_Appendix">Implicational_Logic_Appendix</a></li></ul><div class="flex-wrap">
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author = {Asta Halkjær From and Jørgen Villadsen},
title = {Soundness and Completeness of Implicational Logic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Implicational_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>P</span>roving the <span class='first'>I</span>mpossibility of <span class='first'>T</span>risecting an <span class='first'>A</span>ngle and <span class='first'>D</span>oubling the <span class='first'>C</span>ube</h1>
<div>
<p><a href="../authors/romanos">Ralph Romanos</a> <a class="obfuscated" data="eyJob3N0IjpbInN0dWRlbnQiLCJlY3AiLCJmciJdLCJ1c2VyIjpbInJhbHBoIiwicm9tYW5vcyJdfQ==">📧</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">August 5, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Squaring the circle, doubling the cube and trisecting an angle, using a compass and straightedge alone, are classic unsolved problems first posed by the ancient Greeks. All three problems were proved to be impossible in the 19th century. The following document presents the proof of the impossibility of solving the latter two problems using Isabelle/HOL, following a proof by Carrega. The proof uses elementary methods: no Galois theory or field extensions. The set of points constructible using a compass and straightedge is defined inductively. Radical expressions, which involve only square roots and arithmetic of rational numbers, are defined, and we find that all constructive points have radical coordinates. Finally, doubling the cube and trisecting certain angles requires solving certain cubic equations that can be proved to have no rational roots. The Isabelle proofs require a great many detailed calculations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Impossible_Geometry</h3>
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<li><a href="../theories/impossible_geometry/#Impossible_Geometry">Impossible_Geometry</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Impossible_Geometry-AFP</p><pre id="copy-text">@article{Impossible_Geometry-AFP,
author = {Ralph Romanos and Lawrence C. Paulson},
title = {Proving the Impossibility of Trisecting an Angle and Doubling the Cube},
journal = {Archive of Formal Proofs},
month = {August},
year = {2012},
note = {\url{https://isa-afp.org/entries/Impossible_Geometry.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Impossible_Geometry-2012-08-06.tar.gz">Aug 6, 2012</a>: Isabelle2012
</li></ul>
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<h1 >
<span class='first'>G</span>ödel's <span class='first'>I</span>ncompleteness <span class='first'>T</span>heorems</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">November 17, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Gödel's two incompleteness theorems are formalised, following a careful <a href="http://journals.impan.gov.pl/dm/Inf/422-0-1.html">presentation</a> by Swierczkowski, in the theory of <a href="HereditarilyFinite.html">hereditarily finite sets</a>. This represents the first ever machine-assisted proof of the second incompleteness theorem. Compared with traditional formalisations using Peano arithmetic (see e.g. Boolos), coding is simpler, with no need to formalise the notion
of multiplication (let alone that of a prime number)
in the formalised calculus upon which the theorem is based.
However, other technical problems had to be solved in order to complete the argument.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Incompleteness</h3>
<ul>
<li><a href="../theories/incompleteness/#SyntaxN">SyntaxN</a></li>
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<li><a href="../theories/incompleteness/#Coding_Predicates">Coding_Predicates</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li><li><a href="../entries/Surprise_Paradox.html">Surprise Paradox</a></li></ul>
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<li><a href="../entries/Recursion-Addition.html">Recursion Theorem in ZF</a></li>
<li><a href="../entries/Probabilistic_Prime_Tests.html">Probabilistic Primality Testing</a></li>
<li><a href="../entries/Bertrands_Postulate.html">Bertrand&rsquo;s postulate</a></li>
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<p style="display:none;" id="bibtex-filename">Incompleteness-AFP</p><pre id="copy-text">@article{Incompleteness-AFP,
author = {Lawrence C. Paulson},
title = {Gödel&#39;s Incompleteness Theorems},
journal = {Archive of Formal Proofs},
month = {November},
year = {2013},
note = {\url{https://isa-afp.org/entries/Incompleteness.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Incompleteness-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Incompleteness-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Incompleteness-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Incompleteness-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<h1 >
<span class='first'>T</span>he <span class='first'>M</span>eta <span class='first'>T</span>heory of the <span class='first'>I</span>ncredible <span class='first'>P</span>roof <span class='first'>M</span>achine</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a href="http://pp.ipd.kit.edu/~breitner">🌐</a> and <a href="../authors/lohner">Denis Lohner</a> <a href="http://pp.ipd.kit.edu/person.php?id=88">🌐</a>
</p>
<p class="date">May 20, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The <a href="http://incredible.pm">Incredible Proof Machine</a> is an
interactive visual theorem prover which represents proofs as port
graphs. We model this proof representation in Isabelle, and prove that
it is just as powerful as natural deduction.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Incredible_Proof_Machine</h3>
<ul>
<li><a href="../theories/incredible_proof_machine/#Indexed_FSet">Indexed_FSet</a></li>
<li><a href="../theories/incredible_proof_machine/#Abstract_Formula">Abstract_Formula</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Signatures">Incredible_Signatures</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Deduction">Incredible_Deduction</a></li>
<li><a href="../theories/incredible_proof_machine/#Abstract_Rules">Abstract_Rules</a></li>
<li><a href="../theories/incredible_proof_machine/#Abstract_Rules_To_Incredible">Abstract_Rules_To_Incredible</a></li>
<li><a href="../theories/incredible_proof_machine/#Entailment">Entailment</a></li>
<li><a href="../theories/incredible_proof_machine/#Natural_Deduction">Natural_Deduction</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Correctness">Incredible_Correctness</a></li>
<li><a href="../theories/incredible_proof_machine/#Rose_Tree">Rose_Tree</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Trees">Incredible_Trees</a></li>
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<li><a href="../theories/incredible_proof_machine/#Incredible_Completeness">Incredible_Completeness</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Everything">Incredible_Everything</a></li>
<li><a href="../theories/incredible_proof_machine/#Propositional_Formulas">Propositional_Formulas</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Propositional">Incredible_Propositional</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Propositional_Tasks">Incredible_Propositional_Tasks</a></li>
<li><a href="../theories/incredible_proof_machine/#Predicate_Formulas">Predicate_Formulas</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Predicate">Incredible_Predicate</a></li>
<li><a href="../theories/incredible_proof_machine/#Incredible_Predicate_Tasks">Incredible_Predicate_Tasks</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<p style="display:none;" id="bibtex-filename">Incredible_Proof_Machine-AFP</p><pre id="copy-text">@article{Incredible_Proof_Machine-AFP,
author = {Joachim Breitner and Denis Lohner},
title = {The meta theory of the Incredible Proof Machine},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Incredible_Proof_Machine.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Incredible_Proof_Machine-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Independence_CH.html b/web/entries/Independence_CH.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Independence of the Continuum Hypothesis in Isabelle/ZF - Archive of Formal Proofs</title><meta name="description" content="We redeveloped our formalization of forcing in the set theory
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>ndependence of the <span class='first'>C</span>ontinuum <span class='first'>H</span>ypothesis in <span class='first'>I</span>sabelle/<span class='first'>Z</span><span class='first'>F</span></h1>
<div>
<p><a href="../authors/gunther">Emmanuel Gunther</a> <a class="obfuscated" data="eyJob3N0IjpbImZhbWFmIiwidW5jIiwiZWR1IiwiYXIiXSwidXNlciI6WyJndW50aGVyIl19">📧</a>, <a href="../authors/pagano">Miguel Pagano</a> <a href="https://cs.famaf.unc.edu.ar/~mpagano/">🌐</a>, <a href="../authors/terraf">Pedro Sánchez Terraf</a> <a href="https://cs.famaf.unc.edu.ar/~pedro/home_en.html">🌐</a> and <a href="../authors/steinberg">Matías Steinberg</a> <a class="obfuscated" data="eyJob3N0IjpbIm1pIiwidW5jIiwiZWR1IiwiYXIiXSwidXNlciI6WyJtYXRpYXMiLCJzdGVpbmJlcmciXX0=">📧</a>
</p>
<p class="date">March 6, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We redeveloped our formalization of forcing in the set theory
framework of Isabelle/ZF. Under the assumption of the existence of a
countable transitive model of ZFC, we construct proper generic
extensions that satisfy the Continuum Hypothesis and its negation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Independence_CH</h3>
<ul>
<li><a href="../theories/independence_ch/#Forcing_Notions">Forcing_Notions</a></li>
<li><a href="../theories/independence_ch/#Cohen_Posets_Relative">Cohen_Posets_Relative</a></li>
<li><a href="../theories/independence_ch/#Edrel">Edrel</a></li>
<li><a href="../theories/independence_ch/#FrecR">FrecR</a></li>
<li><a href="../theories/independence_ch/#FrecR_Arities">FrecR_Arities</a></li>
<li><a href="../theories/independence_ch/#Fm_Definitions">Fm_Definitions</a></li>
<li><a href="../theories/independence_ch/#Internal_ZFC_Axioms">Internal_ZFC_Axioms</a></li>
<li><a href="../theories/independence_ch/#Interface">Interface</a></li>
<li><a href="../theories/independence_ch/#Separation_Instances">Separation_Instances</a></li>
<li><a href="../theories/independence_ch/#Replacement_Instances">Replacement_Instances</a></li>
<li><a href="../theories/independence_ch/#ZF_Trans_Interpretations">ZF_Trans_Interpretations</a></li>
<li><a href="../theories/independence_ch/#Forcing_Data">Forcing_Data</a></li>
<li><a href="../theories/independence_ch/#Forces_Definition">Forces_Definition</a></li>
<li><a href="../theories/independence_ch/#Names">Names</a></li>
<li><a href="../theories/independence_ch/#Forcing_Theorems">Forcing_Theorems</a></li>
<li><a href="../theories/independence_ch/#Ordinals_In_MG">Ordinals_In_MG</a></li>
<li><a href="../theories/independence_ch/#Separation_Rename">Separation_Rename</a></li>
<li><a href="../theories/independence_ch/#Separation_Axiom">Separation_Axiom</a></li>
<li><a href="../theories/independence_ch/#Pairing_Axiom">Pairing_Axiom</a></li>
<li><a href="../theories/independence_ch/#Union_Axiom">Union_Axiom</a></li>
<li><a href="../theories/independence_ch/#Powerset_Axiom">Powerset_Axiom</a></li>
<li><a href="../theories/independence_ch/#Extensionality_Axiom">Extensionality_Axiom</a></li>
<li><a href="../theories/independence_ch/#Foundation_Axiom">Foundation_Axiom</a></li>
<li><a href="../theories/independence_ch/#Replacement_Axiom">Replacement_Axiom</a></li>
<li><a href="../theories/independence_ch/#Infinity_Axiom">Infinity_Axiom</a></li>
<li><a href="../theories/independence_ch/#Choice_Axiom">Choice_Axiom</a></li>
<li><a href="../theories/independence_ch/#Proper_Extension">Proper_Extension</a></li>
<li><a href="../theories/independence_ch/#Succession_Poset">Succession_Poset</a></li>
<li><a href="../theories/independence_ch/#Forcing_Main">Forcing_Main</a></li>
<li><a href="../theories/independence_ch/#Cardinal_Preservation">Cardinal_Preservation</a></li>
<li><a href="../theories/independence_ch/#Not_CH">Not_CH</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Transitive_Models.html">Transitive Models of Fragments of ZFC</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Forcing.html">Formalization of Forcing in Isabelle/ZF</a></li>
<li><a href="../entries/Delta_System_Lemma.html">Cofinality and the Delta System Lemma</a></li>
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<p style="display:none;" id="bibtex-filename">Independence_CH-AFP</p><pre id="copy-text">@article{Independence_CH-AFP,
author = {Emmanuel Gunther and Miguel Pagano and Pedro Sánchez Terraf and Matías Steinberg},
title = {The Independence of the Continuum Hypothesis in Isabelle/ZF},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/Independence_CH.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Independence_CH-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Independence_CH-2022-03-07.tar.gz">Mar 7, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Inductive_Confidentiality.html b/web/entries/Inductive_Confidentiality.html
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<h1 >
<span class='first'>I</span>nductive <span class='first'>S</span>tudy of <span class='first'>C</span>onfidentiality</h1>
<div>
<p><a href="../authors/bella">Giampaolo Bella</a> <a href="http://www.dmi.unict.it/~giamp/">🌐</a>
</p>
<p class="date">May 2, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains the full theory files accompanying article <i>Inductive Study of Confidentiality --- for Everyone</i> in <i>Formal Aspects of Computing</i>. They aim at an illustrative and didactic presentation of the Inductive Method of protocol analysis, focusing on the treatment of one of the main goals of security protocols: confidentiality against a threat model. The treatment of confidentiality, which in fact forms a key aspect of all protocol analysis tools, has been found cryptic by many learners of the Inductive Method, hence the motivation for this work. The theory files in this document guide the reader step by step towards design and proof of significant confidentiality theorems. These are developed against two threat models, the standard Dolev-Yao and a more audacious one, the General Attacker, which turns out to be particularly useful also for teaching purposes.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Inductive_Confidentiality</h3>
<ul>
<li><a href="../theories/inductive_confidentiality/#Message">Message</a></li>
<li><a href="../theories/inductive_confidentiality/#Event">Event</a></li>
<li><a href="../theories/inductive_confidentiality/#Public">Public</a></li>
<li><a href="../theories/inductive_confidentiality/#NS_Public_Bad">NS_Public_Bad</a></li>
<li><a href="../theories/inductive_confidentiality/#ConfidentialityDY">ConfidentialityDY</a></li>
<li><a href="../theories/inductive_confidentiality/#MessageGA">MessageGA</a></li>
<li><a href="../theories/inductive_confidentiality/#EventGA">EventGA</a></li>
<li><a href="../theories/inductive_confidentiality/#PublicGA">PublicGA</a></li>
<li><a href="../theories/inductive_confidentiality/#NS_Public_Bad_GA">NS_Public_Bad_GA</a></li>
<li><a href="../theories/inductive_confidentiality/#ConfidentialityGA">ConfidentialityGA</a></li>
<li><a href="../theories/inductive_confidentiality/#Knowledge">Knowledge</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Inductive_Confidentiality-AFP</p><pre id="copy-text">@article{Inductive_Confidentiality-AFP,
author = {Giampaolo Bella},
title = {Inductive Study of Confidentiality},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Inductive_Confidentiality.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>ome <span class='first'>C</span>lassical <span class='first'>R</span>esults in <span class='first'>I</span>nductive <span class='first'>I</span>nference of <span class='first'>R</span>ecursive <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/balbach">Frank J. Balbach</a> <a class="obfuscated" data="eyJob3N0IjpbImdteCIsImRlIl0sInVzZXIiOlsiZnJhbmstYmFsYmFjaCJdfQ==">📧</a>
</p>
<p class="date">August 31, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> This entry formalizes some classical concepts and results
from inductive inference of recursive functions. In the basic setting
a partial recursive function ("strategy") must identify
("learn") all functions from a set ("class") of
recursive functions. To that end the strategy receives more and more
values $f(0), f(1), f(2), \ldots$ of some function $f$ from the given
class and in turn outputs descriptions of partial recursive functions,
for example, Gödel numbers. The strategy is considered successful if
the sequence of outputs ("hypotheses") converges to a
description of $f$. A class of functions learnable in this sense is
called "learnable in the limit". The set of all these
classes is denoted by LIM. </p> <p> Other types of
inference considered are finite learning (FIN), behaviorally correct
learning in the limit (BC), and some variants of LIM with restrictions
on the hypotheses: total learning (TOTAL), consistent learning (CONS),
and class-preserving learning (CP). The main results formalized are
the proper inclusions $\mathrm{FIN} \subset \mathrm{CP} \subset
\mathrm{TOTAL} \subset \mathrm{CONS} \subset \mathrm{LIM} \subset
\mathrm{BC} \subset 2^{\mathcal{R}}$, where $\mathcal{R}$ is the set
of all total recursive functions. Further results show that for all
these inference types except CONS, strategies can be assumed to be
total recursive functions; that all inference types but CP are closed
under the subset relation between classes; and that no inference type
is closed under the union of classes. </p> <p> The above
is based on a formalization of recursive functions heavily inspired by
the <a
href="https://www.isa-afp.org/entries/Universal_Turing_Machine.html">Universal
Turing Machine</a> entry by Xu et al., but different in that it
models partial functions with codomain <em>nat
option</em>. The formalization contains a construction of a
universal partial recursive function, without resorting to Turing
machines, introduces decidability and recursive enumerability, and
proves some standard results: existence of a Kleene normal form, the
<em>s-m-n</em> theorem, Rice's theorem, and assorted
fixed-point theorems (recursion theorems) by Kleene, Rogers, and
Smullyan. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li><li><a href="../topics/computer-science/machine-learning">Computer science/Machine learning</a></li></ul>
<h3>Session Inductive_Inference</h3>
<ul>
<li><a href="../theories/inductive_inference/#Partial_Recursive">Partial_Recursive</a></li>
<li><a href="../theories/inductive_inference/#Universal">Universal</a></li>
<li><a href="../theories/inductive_inference/#Standard_Results">Standard_Results</a></li>
<li><a href="../theories/inductive_inference/#Inductive_Inference_Basics">Inductive_Inference_Basics</a></li>
<li><a href="../theories/inductive_inference/#CP_FIN_NUM">CP_FIN_NUM</a></li>
<li><a href="../theories/inductive_inference/#CONS_LIM">CONS_LIM</a></li>
<li><a href="../theories/inductive_inference/#Lemma_R">Lemma_R</a></li>
<li><a href="../theories/inductive_inference/#LIM_BC">LIM_BC</a></li>
<li><a href="../theories/inductive_inference/#TOTAL_CONS">TOTAL_CONS</a></li>
<li><a href="../theories/inductive_inference/#R1_BC">R1_BC</a></li>
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<p style="display:none;" id="bibtex-filename">Inductive_Inference-AFP</p><pre id="copy-text">@article{Inductive_Inference-AFP,
author = {Frank J. Balbach},
title = {Some classical results in inductive inference of recursive functions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/Inductive_Inference.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>I</span>nfeasible <span class='first'>P</span>aths <span class='first'>E</span>limination by <span class='first'>S</span>ymbolic <span class='first'>E</span>xecution <span class='first'>T</span>echniques: <span class='first'>P</span>roof of <span class='first'>C</span>orrectness and <span class='first'>P</span>reservation of <span class='first'>P</span>aths</h1>
<div>
<p><a href="../authors/aissat">Romain Aissat</a>, <a href="../authors/voisin">Frederic Voisin</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">August 18, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">TRACER is a tool for verifying safety properties of sequential C
programs. TRACER attempts at building a finite symbolic execution
graph which over-approximates the set of all concrete reachable states
and the set of feasible paths. We present an abstract framework for
TRACER and similar CEGAR-like systems. The framework provides 1) a
graph- transformation based method for reducing the feasible paths in
control-flow graphs, 2) a model for symbolic execution, subsumption,
predicate abstraction and invariant generation. In this framework we
formally prove two key properties: correct construction of the
symbolic states and preservation of feasible paths. The framework
focuses on core operations, leaving to concrete prototypes to “fit in”
heuristics for combining them. The accompanying paper (published in
ITP 2016) can be found at
https://www.lri.fr/∼wolff/papers/conf/2016-itp-InfPathsNSE.pdf.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session InfPathElimination</h3>
<ul>
<li><a href="../theories/infpathelimination/#Graph">Graph</a></li>
<li><a href="../theories/infpathelimination/#Aexp">Aexp</a></li>
<li><a href="../theories/infpathelimination/#Bexp">Bexp</a></li>
<li><a href="../theories/infpathelimination/#Labels">Labels</a></li>
<li><a href="../theories/infpathelimination/#Store">Store</a></li>
<li><a href="../theories/infpathelimination/#Conf">Conf</a></li>
<li><a href="../theories/infpathelimination/#SymExec">SymExec</a></li>
<li><a href="../theories/infpathelimination/#LTS">LTS</a></li>
<li><a href="../theories/infpathelimination/#SubRel">SubRel</a></li>
<li><a href="../theories/infpathelimination/#ArcExt">ArcExt</a></li>
<li><a href="../theories/infpathelimination/#SubExt">SubExt</a></li>
<li><a href="../theories/infpathelimination/#RB">RB</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">InfPathElimination-AFP</p><pre id="copy-text">@article{InfPathElimination-AFP,
author = {Romain Aissat and Frederic Voisin and Burkhart Wolff},
title = {Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/InfPathElimination.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Information Flow Noninterference via Slicing - Archive of Formal Proofs</title><meta name="description" content=" In this contribution, we show how correctness proofs for intra- and interprocedural slicing can be used to prove that slicing is able to guarantee..."><meta property="og:title" content="Information Flow Noninterference via Slicing" />
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<h1 >
<span class='first'>I</span>nformation <span class='first'>F</span>low <span class='first'>N</span>oninterference via <span class='first'>S</span>licing</h1>
<div>
<p><a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">March 23, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
In this contribution, we show how correctness proofs for <a
href="Slicing.html">intra-</a> and <a
href="HRB-Slicing.html">interprocedural slicing</a> can be used to prove
that slicing is able to guarantee information flow noninterference.
Moreover, we also illustrate how to lift the control flow graphs of the
respective frameworks such that they fulfil the additional assumptions
needed in the noninterference proofs. A detailed description of the
intraprocedural proof and its interplay with the slicing framework can be
found in the PLAS'09 paper by Wasserrab et al.
</p>
<p>
This entry contains the part for intra-procedural slicing. See entry
<a href="InformationFlowSlicing_Inter.html">InformationFlowSlicing_Inter</a>
for the inter-procedural part.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 10, 2016</dt>
<dd>The original entry <a
href="InformationFlowSlicing.html">InformationFlowSlicing</a> contained both
the <a href="InformationFlowSlicing_Inter.html">inter-</a> and <a
href="InformationFlowSlicing.html">intra-procedural</a> case was split into
two for easier maintenance.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session InformationFlowSlicing</h3>
<ul>
<li><a href="../theories/informationflowslicing/#NonInterferenceIntra">NonInterferenceIntra</a></li>
<li><a href="../theories/informationflowslicing/#LiftingIntra">LiftingIntra</a></li>
<li><a href="../theories/informationflowslicing/#NonInterferenceWhile">NonInterferenceWhile</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Slicing.html">Towards Certified Slicing</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/InformationFlowSlicing_Inter.html">Inter-Procedural Information Flow Noninterference via Slicing</a></li>
<li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li>
<li><a href="../entries/Simple_Firewall.html">Simple Firewall</a></li>
<li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li>
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<p style="display:none;" id="bibtex-filename">InformationFlowSlicing-AFP</p><pre id="copy-text">@article{InformationFlowSlicing-AFP,
author = {Daniel Wasserrab},
title = {Information Flow Noninterference via Slicing},
journal = {Archive of Formal Proofs},
month = {March},
year = {2010},
note = {\url{https://isa-afp.org/entries/InformationFlowSlicing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-InformationFlowSlicing-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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</li><li>
<a href="https://www.isa-afp.org/release/afp-InformationFlowSlicing-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-InformationFlowSlicing-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-InformationFlowSlicing-2010-03-23.tar.gz">Mar 23, 2010</a>: Isabelle2009-1
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--- a/web/entries/InformationFlowSlicing_Inter.html
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@@ -1,211 +1,213 @@
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<h1 >
<span class='first'>I</span>nter-<span class='first'>P</span>rocedural <span class='first'>I</span>nformation <span class='first'>F</span>low <span class='first'>N</span>oninterference via <span class='first'>S</span>licing</h1>
<div>
<p><a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">March 23, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
In this contribution, we show how correctness proofs for <a
href="Slicing.html">intra-</a> and <a
href="HRB-Slicing.html">interprocedural slicing</a> can be used to prove
that slicing is able to guarantee information flow noninterference.
Moreover, we also illustrate how to lift the control flow graphs of the
respective frameworks such that they fulfil the additional assumptions
needed in the noninterference proofs. A detailed description of the
intraprocedural proof and its interplay with the slicing framework can be
found in the PLAS'09 paper by Wasserrab et al.
</p>
<p>
This entry contains the part for inter-procedural slicing. See entry
<a href="InformationFlowSlicing.html">InformationFlowSlicing</a>
for the intra-procedural part.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 10, 2016</dt>
<dd>The original entry <a
href="InformationFlowSlicing.html">InformationFlowSlicing</a> contained both
the <a href="InformationFlowSlicing_Inter.html">inter-</a> and <a
href="InformationFlowSlicing.html">intra-procedural</a> case was split into
two for easier maintenance.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session InformationFlowSlicing_Inter</h3>
<ul>
<li><a href="../theories/informationflowslicing_inter/#NonInterferenceInter">NonInterferenceInter</a></li>
<li><a href="../theories/informationflowslicing_inter/#LiftingInter">LiftingInter</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/HRB-Slicing.html">Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></li>
<li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li>
<li><a href="../entries/Simple_Firewall.html">Simple Firewall</a></li>
<li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li>
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<p style="display:none;" id="bibtex-filename">InformationFlowSlicing_Inter-AFP</p><pre id="copy-text">@article{InformationFlowSlicing_Inter-AFP,
author = {Daniel Wasserrab},
title = {Inter-Procedural Information Flow Noninterference via Slicing},
journal = {Archive of Formal Proofs},
month = {March},
year = {2010},
note = {\url{https://isa-afp.org/entries/InformationFlowSlicing_Inter.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-InformationFlowSlicing_Inter-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>I</span>ntegration <span class='first'>T</span>heory and <span class='first'>R</span>andom <span class='first'>V</span>ariables</h1>
<div>
<p><a href="../authors/richter">Stefan Richter</a> <a href="http://www-lti.informatik.rwth-aachen.de/~richter/">🌐</a>
</p>
<p class="date">November 19, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Lebesgue-style integration plays a major role in advanced probability. We formalize concepts of elementary measure theory, real-valued random variables as Borel-measurable functions, and a stepwise inductive definition of the integral itself. All proofs are carried out in human readable style using the Isar language.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><p><em>This article is of historical interest only. Lebesgue-style integration and probability theory are now available as part of the Isabelle/HOL distribution (directory Probability).</em></p><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Integration</h3>
<ul>
<li><a href="../theories/integration/#Sigma_Algebra">Sigma_Algebra</a></li>
<li><a href="../theories/integration/#MonConv">MonConv</a></li>
<li><a href="../theories/integration/#Measure">Measure</a></li>
<li><a href="../theories/integration/#RealRandVar">RealRandVar</a></li>
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<p style="display:none;" id="bibtex-filename">Integration-AFP</p><pre id="copy-text">@article{Integration-AFP,
author = {Stefan Richter},
title = {Integration theory and random variables},
journal = {Archive of Formal Proofs},
month = {November},
year = {2004},
note = {\url{https://isa-afp.org/entries/Integration.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>I</span>nterpolation <span class='first'>P</span>olynomials (<span class='first'>I</span>n <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span>-<span class='first'>A</span>lgebra)</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">January 29, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>A well known result from algebra is that, on any field, there
is exactly one polynomial of degree less than n interpolating n points
[<a
href="https://doi.org/10.1017/CBO9780511814549">1</a>,
§7].</p> <p>This entry contains a formalization of the
above result, as well as the following generalization in the case of
finite fields <i>F</i>: There are
<i>|F|<sup>m-n</sup></i> polynomials of degree
less than <i>m ≥ n</i> interpolating the same n points,
where <i>|F|</i> denotes the size of the domain of the
field. To establish the result the entry also includes a formalization
of Lagrange interpolation, which might be of independent
interest.</p> <p>The formalized results are defined on the
algebraic structures from HOL-Algebra, which are distinct from the
type-class based structures defined in HOL. Note that there is an
existing formalization for polynomial interpolation and, in
particular, Lagrange interpolation by Thiemann and Yamada [<a
href="https://www.isa-afp.org/entries/Polynomial_Interpolation.html">2</a>]
on the type-class based structures in HOL.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Interpolation_Polynomials_HOL_Algebra</h3>
<ul>
<li><a href="../theories/interpolation_polynomials_hol_algebra/#Bounded_Degree_Polynomials">Bounded_Degree_Polynomials</a></li>
<li><a href="../theories/interpolation_polynomials_hol_algebra/#Lagrange_Interpolation">Lagrange_Interpolation</a></li>
<li><a href="../theories/interpolation_polynomials_hol_algebra/#Interpolation_Polynomial_Cardinalities">Interpolation_Polynomial_Cardinalities</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li><li><a href="../entries/Universal_Hash_Families.html">Universal Hash Families</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Interpolation_Polynomials_HOL_Algebra-AFP</p><pre id="copy-text">@article{Interpolation_Polynomials_HOL_Algebra-AFP,
author = {Emin Karayel},
title = {Interpolation Polynomials (in HOL-Algebra)},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Interpolation_Polynomials_HOL_Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Interpolation_Polynomials_HOL_Algebra-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>I</span>nline <span class='first'>C</span>aching and <span class='first'>U</span>nboxing <span class='first'>O</span>ptimization for <span class='first'>I</span>nterpreters</h1>
<div>
<p><a href="../authors/desharnais">Martin Desharnais</a> <a href="https://martin.desharnais.me">🌐</a>
</p>
<p class="date">December 7, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization builds on the
<em>VeriComp</em> entry of the <em>Archive of Formal
Proofs</em> to provide the following contributions: <ul>
<li>an operational semantics for a realistic virtual machine
(Std) for dynamically typed programming languages;</li>
<li>the formalization of an inline caching optimization (Inca),
a proof of bisimulation with (Std), and a compilation
function;</li> <li>the formalization of an unboxing
optimization (Ubx), a proof of bisimulation with (Inca), and a simple
compilation function.</li> </ul> This formalization was
described in the CPP 2021 paper <em>Towards Efficient and
Verified Virtual Machines for Dynamic Languages</em></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 25, 2021</dt>
<dd>proved conditional completeness of compilation<br></dd><dt>June 14, 2021</dt>
<dd>refactored function definitions to contain explicit basic blocks<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/misc">Computer science/Programming languages/Misc</a></li></ul>
<h3>Session Interpreter_Optimizations</h3>
<ul>
<li><a href="../theories/interpreter_optimizations/#Env">Env</a></li>
<li><a href="../theories/interpreter_optimizations/#Env_list">Env_list</a></li>
<li><a href="../theories/interpreter_optimizations/#List_util">List_util</a></li>
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<li><a href="../theories/interpreter_optimizations/#Option_Extra">Option_Extra</a></li>
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<li><a href="../theories/interpreter_optimizations/#Op">Op</a></li>
<li><a href="../theories/interpreter_optimizations/#OpInl">OpInl</a></li>
<li><a href="../theories/interpreter_optimizations/#Dynamic">Dynamic</a></li>
<li><a href="../theories/interpreter_optimizations/#Inca">Inca</a></li>
<li><a href="../theories/interpreter_optimizations/#Unboxed">Unboxed</a></li>
<li><a href="../theories/interpreter_optimizations/#OpUbx">OpUbx</a></li>
<li><a href="../theories/interpreter_optimizations/#Ubx">Ubx</a></li>
<li><a href="../theories/interpreter_optimizations/#Ubx_Verification">Ubx_Verification</a></li>
<li><a href="../theories/interpreter_optimizations/#Unboxed_lemmas">Unboxed_lemmas</a></li>
<li><a href="../theories/interpreter_optimizations/#Inca_to_Ubx_simulation">Inca_to_Ubx_simulation</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/VeriComp.html">A Generic Framework for Verified Compilers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Interpreter_Optimizations-AFP</p><pre id="copy-text">@article{Interpreter_Optimizations-AFP,
author = {Martin Desharnais},
title = {Inline Caching and Unboxing Optimization for Interpreters},
journal = {Archive of Formal Proofs},
month = {December},
year = {2020},
note = {\url{https://isa-afp.org/entries/Interpreter_Optimizations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Interpreter_Optimizations-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Interpreter_Optimizations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Interval_Arithmetic_Word32.html b/web/entries/Interval_Arithmetic_Word32.html
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<h1 >
<span class='first'>I</span>nterval <span class='first'>A</span>rithmetic on 32-<span class='first'>B</span>it <span class='first'>W</span>ords</h1>
<div>
<p><a href="../authors/bohrer">Rose Bohrer</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicm9zZSIsImJvaHJlciIsImNzIl19">📧</a>
</p>
<p class="date">November 27, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Interval_Arithmetic implements conservative interval arithmetic
computations, then uses this interval arithmetic to implement a simple
programming language where all terms have 32-bit signed word values,
with explicit infinities for terms outside the representable bounds.
Our target use case is interpreters for languages that must have a
well-understood low-level behavior. We include a formalization of
bounded-length strings which are used for the identifiers of our
language. Bounded-length identifiers are useful in some applications,
for example the <a href="https://www.isa-afp.org/entries/Differential_Dynamic_Logic.html">Differential_Dynamic_Logic</a> article,
where a Euclidean space indexed by identifiers demands that identifiers
are finitely many.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Interval_Arithmetic_Word32</h3>
<ul>
<li><a href="../theories/interval_arithmetic_word32/#Interval_Word32">Interval_Word32</a></li>
<li><a href="../theories/interval_arithmetic_word32/#Finite_String">Finite_String</a></li>
<li><a href="../theories/interval_arithmetic_word32/#Interpreter">Interpreter</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
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<p style="display:none;" id="bibtex-filename">Interval_Arithmetic_Word32-AFP</p><pre id="copy-text">@article{Interval_Arithmetic_Word32-AFP,
author = {Rose Bohrer},
title = {Interval Arithmetic on 32-bit Words},
journal = {Archive of Formal Proofs},
month = {November},
year = {2019},
note = {\url{https://isa-afp.org/entries/Interval_Arithmetic_Word32.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Interval_Arithmetic_Word32-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Interval_Arithmetic_Word32-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Interval_Arithmetic_Word32-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Interval_Arithmetic_Word32-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Interval_Arithmetic_Word32-2019-11-28.tar.gz">Nov 28, 2019</a>: Isabelle2019
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<h1 >
<span class='first'>I</span><span class='first'>D</span><span class='first'>E</span>: <span class='first'>I</span>ntroduction, <span class='first'>D</span>estruction, <span class='first'>E</span>limination</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The article provides the command <b>mk_ide</b> for the
object logic Isabelle/HOL of the formal proof assistant Isabelle. The
command <b>mk_ide</b> enables the automated synthesis of
the introduction, destruction and elimination rules from arbitrary
definitions of constant predicates stated in Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Intro_Dest_Elim</h3>
<ul>
<li><a href="../theories/intro_dest_elim/#IDE_Tools">IDE_Tools</a></li>
<li><a href="../theories/intro_dest_elim/#IHOL_IDE">IHOL_IDE</a></li>
<li><a href="../theories/intro_dest_elim/#Reference_Prerequisites">Reference_Prerequisites</a></li>
<li><a href="../theories/intro_dest_elim/#IDE_Reference">IDE_Reference</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Intro_Dest_Elim-AFP</p><pre id="copy-text">@article{Intro_Dest_Elim-AFP,
author = {Mihails Milehins},
title = {IDE: Introduction, Destruction, Elimination},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Intro_Dest_Elim.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Intro_Dest_Elim-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Intro_Dest_Elim-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Intro_Dest_Elim-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Intro_Dest_Elim-2021-09-14.tar.gz">Sep 14, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>F</span>rom the <span class='first'>B</span><span class='first'>O</span><span class='first'>O</span><span class='first'>K</span>: <span class='first'>T</span>wo <span class='first'>S</span>quares via <span class='first'>I</span>nvolutions</h1>
<div>
<p><a href="../authors/bortin">Maksym Bortin</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWJvcnRpbiJdfQ==">📧</a>
</p>
<p class="date">August 15, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory contains the involution-based proof of the two squares
theorem from <a
href="https://dx.doi.org/10.1007/978-3-662-57265-8">THE
BOOK</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Involutions2Squares</h3>
<ul>
<li><a href="../theories/involutions2squares/#Involutions2Squares">Involutions2Squares</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Involutions2Squares-AFP</p><pre id="copy-text">@article{Involutions2Squares-AFP,
author = {Maksym Bortin},
title = {From THE BOOK: Two Squares via Involutions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2022},
note = {\url{https://isa-afp.org/entries/Involutions2Squares.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Iptables_Semantics.html b/web/entries/Iptables_Semantics.html
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<h1 >
<span class='first'>I</span>ptables <span class='first'>S</span>emantics</h1>
<div>
<p><a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">September 9, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a big step semantics of the filtering behavior of the
Linux/netfilter iptables firewall. We provide algorithms to simplify
complex iptables rulests to a simple firewall model (c.f. AFP entry <a
href="https://www.isa-afp.org/entries/Simple_Firewall.html">Simple_Firewall</a>)
and to verify spoofing protection of a ruleset.
Internally, we embed our semantics into ternary logic, ultimately
supporting every iptables match condition by abstracting over
unknowns. Using this AFP entry and all entries it depends on, we
created an easy-to-use, stand-alone haskell tool called <a
href="http://iptables.isabelle.systems">fffuu</a>. The tool does not
require any input &mdash;except for the <tt>iptables-save</tt> dump of
the analyzed firewall&mdash; and presents interesting results about
the user's ruleset. Real-Word firewall errors have been uncovered, and
the correctness of rulesets has been proved, with the help of
our tool.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session Iptables_Semantics</h3>
<ul>
<li><a href="../theories/iptables_semantics/#List_Misc">List_Misc</a></li>
<li><a href="../theories/iptables_semantics/#Negation_Type">Negation_Type</a></li>
<li><a href="../theories/iptables_semantics/#WordInterval_Lists">WordInterval_Lists</a></li>
<li><a href="../theories/iptables_semantics/#Repeat_Stabilize">Repeat_Stabilize</a></li>
<li><a href="../theories/iptables_semantics/#Firewall_Common">Firewall_Common</a></li>
<li><a href="../theories/iptables_semantics/#Semantics">Semantics</a></li>
<li><a href="../theories/iptables_semantics/#Matching">Matching</a></li>
<li><a href="../theories/iptables_semantics/#Ruleset_Update">Ruleset_Update</a></li>
<li><a href="../theories/iptables_semantics/#Call_Return_Unfolding">Call_Return_Unfolding</a></li>
<li><a href="../theories/iptables_semantics/#Ternary">Ternary</a></li>
<li><a href="../theories/iptables_semantics/#Matching_Ternary">Matching_Ternary</a></li>
<li><a href="../theories/iptables_semantics/#Semantics_Ternary">Semantics_Ternary</a></li>
<li><a href="../theories/iptables_semantics/#Datatype_Selectors">Datatype_Selectors</a></li>
<li><a href="../theories/iptables_semantics/#IpAddresses">IpAddresses</a></li>
<li><a href="../theories/iptables_semantics/#L4_Protocol_Flags">L4_Protocol_Flags</a></li>
<li><a href="../theories/iptables_semantics/#Ports">Ports</a></li>
<li><a href="../theories/iptables_semantics/#Conntrack_State">Conntrack_State</a></li>
<li><a href="../theories/iptables_semantics/#Tagged_Packet">Tagged_Packet</a></li>
<li><a href="../theories/iptables_semantics/#Common_Primitive_Syntax">Common_Primitive_Syntax</a></li>
<li><a href="../theories/iptables_semantics/#Unknown_Match_Tacs">Unknown_Match_Tacs</a></li>
<li><a href="../theories/iptables_semantics/#Common_Primitive_Matcher_Generic">Common_Primitive_Matcher_Generic</a></li>
<li><a href="../theories/iptables_semantics/#Common_Primitive_Matcher">Common_Primitive_Matcher</a></li>
<li><a href="../theories/iptables_semantics/#Example_Semantics">Example_Semantics</a></li>
<li><a href="../theories/iptables_semantics/#Alternative_Semantics">Alternative_Semantics</a></li>
<li><a href="../theories/iptables_semantics/#Semantics_Stateful">Semantics_Stateful</a></li>
<li><a href="../theories/iptables_semantics/#Semantics_Goto">Semantics_Goto</a></li>
<li><a href="../theories/iptables_semantics/#Negation_Type_DNF">Negation_Type_DNF</a></li>
<li><a href="../theories/iptables_semantics/#Matching_Embeddings">Matching_Embeddings</a></li>
<li><a href="../theories/iptables_semantics/#Fixed_Action">Fixed_Action</a></li>
<li><a href="../theories/iptables_semantics/#Normalized_Matches">Normalized_Matches</a></li>
<li><a href="../theories/iptables_semantics/#Negation_Type_Matching">Negation_Type_Matching</a></li>
<li><a href="../theories/iptables_semantics/#Primitive_Normalization">Primitive_Normalization</a></li>
<li><a href="../theories/iptables_semantics/#MatchExpr_Fold">MatchExpr_Fold</a></li>
<li><a href="../theories/iptables_semantics/#Common_Primitive_Lemmas">Common_Primitive_Lemmas</a></li>
<li><a href="../theories/iptables_semantics/#Ports_Normalize">Ports_Normalize</a></li>
<li><a href="../theories/iptables_semantics/#IpAddresses_Normalize">IpAddresses_Normalize</a></li>
<li><a href="../theories/iptables_semantics/#Interfaces_Normalize">Interfaces_Normalize</a></li>
<li><a href="../theories/iptables_semantics/#Word_Upto">Word_Upto</a></li>
<li><a href="../theories/iptables_semantics/#Protocols_Normalize">Protocols_Normalize</a></li>
<li><a href="../theories/iptables_semantics/#Remdups_Rev">Remdups_Rev</a></li>
<li><a href="../theories/iptables_semantics/#Ipassmt">Ipassmt</a></li>
<li><a href="../theories/iptables_semantics/#No_Spoof">No_Spoof</a></li>
<li><a href="../theories/iptables_semantics/#Common_Primitive_toString">Common_Primitive_toString</a></li>
<li><a href="../theories/iptables_semantics/#Routing_IpAssmt">Routing_IpAssmt</a></li>
<li><a href="../theories/iptables_semantics/#Output_Interface_Replace">Output_Interface_Replace</a></li>
<li><a href="../theories/iptables_semantics/#Interface_Replace">Interface_Replace</a></li>
<li><a href="../theories/iptables_semantics/#Optimizing">Optimizing</a></li>
<li><a href="../theories/iptables_semantics/#Transform">Transform</a></li>
<li><a href="../theories/iptables_semantics/#Conntrack_State_Transform">Conntrack_State_Transform</a></li>
<li><a href="../theories/iptables_semantics/#Primitive_Abstract">Primitive_Abstract</a></li>
<li><a href="../theories/iptables_semantics/#SimpleFw_Compliance">SimpleFw_Compliance</a></li>
<li><a href="../theories/iptables_semantics/#Semantics_Embeddings">Semantics_Embeddings</a></li>
<li><a href="../theories/iptables_semantics/#Iptables_Semantics">Iptables_Semantics</a></li>
<li><a href="../theories/iptables_semantics/#Code_Interface">Code_Interface</a></li>
<li><a href="../theories/iptables_semantics/#Parser6">Parser6</a></li>
<li><a href="../theories/iptables_semantics/#No_Spoof_Embeddings">No_Spoof_Embeddings</a></li>
<li><a href="../theories/iptables_semantics/#Parser">Parser</a></li>
<li><a href="../theories/iptables_semantics/#Code_haskell">Code_haskell</a></li>
<li><a href="../theories/iptables_semantics/#Access_Matrix_Embeddings">Access_Matrix_Embeddings</a></li>
<li><a href="../theories/iptables_semantics/#Documentation">Documentation</a></li></ul>
<h3>Session Iptables_Semantics_Examples</h3>
<ul>
<li><a href="../theories/iptables_semantics_examples/#Parser_Test">Parser_Test</a></li>
<li><a href="../theories/iptables_semantics_examples/#Parser6_Test">Parser6_Test</a></li>
<li><a href="../theories/iptables_semantics_examples/#Small_Examples">Small_Examples</a></li>
<li><a href="../theories/iptables_semantics_examples/#Ports_Fail">Ports_Fail</a></li>
<li><a href="../theories/iptables_semantics_examples/#Contrived_Example">Contrived_Example</a></li>
<li><a href="../theories/iptables_semantics_examples/#iptables_Ln_tuned_parsed">iptables_Ln_tuned_parsed</a></li>
<li><a href="../theories/iptables_semantics_examples/#Analyze_Synology_Diskstation">Analyze_Synology_Diskstation</a></li>
<li><a href="../theories/iptables_semantics_examples/#Analyze_Ringofsaturn_com">Analyze_Ringofsaturn_com</a></li>
<li><a href="../theories/iptables_semantics_examples/#Analyze_SQRL_Shorewall">Analyze_SQRL_Shorewall</a></li>
<li><a href="../theories/iptables_semantics_examples/#SQRL_2015_nospoof">SQRL_2015_nospoof</a></li>
<li><a href="../theories/iptables_semantics_examples/#SNS_IAS_Eduroam_Spoofing">SNS_IAS_Eduroam_Spoofing</a></li>
<li><a href="../theories/iptables_semantics_examples/#Analyze_medium_sized_company">Analyze_medium_sized_company</a></li></ul>
<h3>Session Iptables_Semantics_Examples_Big</h3>
<ul>
<li><a href="../theories/iptables_semantics_examples_big/#Analyze_topos_generated">Analyze_topos_generated</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#IP_Address_Space_Examples_All_Small">IP_Address_Space_Examples_All_Small</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#Analyze_TUM_Net_Firewall">Analyze_TUM_Net_Firewall</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#Analyze_Containern">Analyze_Containern</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#TUM_Spoofing_new3">TUM_Spoofing_new3</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#TUM_Simple_FW">TUM_Simple_FW</a></li>
<li><a href="../theories/iptables_semantics_examples_big/#IP_Address_Space_Examples_All_Large">IP_Address_Space_Examples_All_Large</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/Routing.html">Routing</a></li><li><a href="../entries/Iptables_Semantics.html">Iptables Semantics</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LOFT.html">LOFT — Verified Migration of Linux Firewalls to SDN</a></li><li><a href="../entries/Iptables_Semantics.html">Iptables Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Iptables_Semantics-AFP</p><pre id="copy-text">@article{Iptables_Semantics-AFP,
author = {Cornelius Diekmann and Lars Hupel},
title = {Iptables Semantics},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Iptables_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Iptables_Semantics-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Irrational_Series_Erdos_Straus.html b/web/entries/Irrational_Series_Erdos_Straus.html
--- a/web/entries/Irrational_Series_Erdos_Straus.html
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@@ -1,174 +1,176 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Irrationality Criteria for Series by Erdős and Straus - Archive of Formal Proofs</title><meta name="description" content="We formalise certain irrationality criteria for infinite series of the form: \[\sum_{n=1}^\infty \frac{b_n}{\prod_{i=1}^n a_i} \] where $\{b_n\}$ is a..."><meta property="og:title" content="Irrationality Criteria for Series by Erdős and Straus" />
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<h1 >
<span class='first'>I</span>rrationality <span class='first'>C</span>riteria for <span class='first'>S</span>eries by <span class='first'>E</span>rdős and <span class='first'>S</span>traus</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">May 12, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise certain irrationality criteria for infinite series of the form:
\[\sum_{n=1}^\infty \frac{b_n}{\prod_{i=1}^n a_i} \]
where $\{b_n\}$ is a sequence of integers and $\{a_n\}$ a sequence of positive integers
with $a_n >1$ for all large n. The results are due to P. Erdős and E. G. Straus
<a href="https://projecteuclid.org/euclid.pjm/1102911140">[1]</a>.
In particular, we formalise Theorem 2.1, Corollary 2.10 and Theorem 3.1.
The latter is an application of Theorem 2.1 involving the prime numbers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Irrational_Series_Erdos_Straus</h3>
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<li><a href="../theories/irrational_series_erdos_straus/#Irrational_Series_Erdos_Straus">Irrational_Series_Erdos_Straus</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Irrational_Series_Erdos_Straus-AFP</p><pre id="copy-text">@article{Irrational_Series_Erdos_Straus-AFP,
author = {Angeliki Koutsoukou-Argyraki and Wenda Li},
title = {Irrationality Criteria for Series by Erdős and Straus},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Irrational_Series_Erdos_Straus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Irrational_Series_Erdos_Straus-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-Irrational_Series_Erdos_Straus-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>I</span>rrational <span class='first'>R</span>apidly <span class='first'>C</span>onvergent <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">May 23, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize with Isabelle/HOL a proof of a theorem by J. Hancl asserting the
irrationality of the sum of a series consisting of rational numbers, built up
by sequences that fulfill certain properties. Even though the criterion is a
number theoretic result, the proof makes use only of analytical arguments. We
also formalize a corollary of the theorem for a specific series fulfilling the
assumptions of the theorem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Irrationality_J_Hancl</h3>
<ul>
<li><a href="../theories/irrationality_j_hancl/#Irrationality_J_Hancl">Irrationality_J_Hancl</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Irrationality_J_Hancl-AFP</p><pre id="copy-text">@article{Irrationality_J_Hancl-AFP,
author = {Angeliki Koutsoukou-Argyraki and Wenda Li},
title = {Irrational Rapidly Convergent Series},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Irrationality_J_Hancl.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Irrationality_J_Hancl-2018-05-26.tar.gz">May 26, 2018</a>: Isabelle2017
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diff --git a/web/entries/Irrationals_From_THEBOOK.html b/web/entries/Irrationals_From_THEBOOK.html
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<h1 >
<span class='first'>I</span>rrational <span class='first'>N</span>umbers <span class='first'>F</span>rom the <span class='first'>B</span><span class='first'>O</span><span class='first'>O</span><span class='first'>K</span></h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">January 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">An elementary proof is formalised: that <em>exp r</em> is irrational for
every nonzero rational number <em>r</em>. The mathematical development comes
from the well-known volume <em>Proofs from THE BOOK</em>,
by Aigner and Ziegler, who credit the idea to Hermite. The development
illustrates a number of basic Isabelle techniques: the manipulation of
summations, the calculation of quite complicated derivatives and the
estimation of integrals. We also see how to import another AFP entry (Stirling's formula).
As for the theorem itself, note that a much stronger and more general
result (the Hermite--Lindemann--Weierstraß transcendence theorem) is
already available in the AFP.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Irrationals_From_THEBOOK</h3>
<ul>
<li><a href="../theories/irrationals_from_thebook/#Irrationals_From_THEBOOK">Irrationals_From_THEBOOK</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Hales_Jewett.html">The Hales–Jewett Theorem</a></li>
<li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li>
<li><a href="../entries/Core_SC_DOM.html">The Safely Composable DOM</a></li>
<li><a href="../entries/Goedel_Incompleteness.html">An Abstract Formalization of Gödel&rsquo;s Incompleteness Theorems</a></li>
<li><a href="../entries/Goedel_HFSet_Semantic.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part I</a></li>
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author = {Lawrence C. Paulson},
title = {Irrational numbers from THE BOOK},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Irrationals_From_THEBOOK.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Irrationals_From_THEBOOK-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Irrationals_From_THEBOOK-2022-01-31.tar.gz">Jan 31, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>T</span>arski's <span class='first'>P</span>arallel <span class='first'>P</span>ostulate <span class='first'>I</span>mplies the 5th <span class='first'>P</span>ostulate of <span class='first'>E</span>uclid, the <span class='first'>P</span>ostulate of <span class='first'>P</span>layfair and the <span class='first'>O</span>riginal <span class='first'>P</span>arallel <span class='first'>P</span>ostulate of <span class='first'>E</span>uclid</h1>
<div>
<p><a href="../authors/coghetto">Roland Coghetto</a> <a class="obfuscated" data="eyJob3N0IjpbImhvdG1haWwiLCJjb20iXSwidXNlciI6WyJyb2xhbmRfY29naGV0dG8iXX0=">📧</a>
</p>
<p class="date">January 31, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The <a href="https://geocoq.github.io/GeoCoq/">GeoCoq library</a> contains a formalization
of geometry using the Coq proof assistant. It contains both proofs
about the foundations of geometry and high-level proofs in the same
style as in high school. We port a part of the GeoCoq
2.4.0 library to Isabelle/HOL: more precisely,
the files Chap02.v to Chap13_3.v, suma.v as well as the associated
definitions and some useful files for the demonstration of certain
parallel postulates. The synthetic approach of the demonstrations is directly
inspired by those contained in GeoCoq. The names of the lemmas and
theorems used are kept as far as possible as well as the definitions.
</p>
<p>It should be noted that T.J.M. Makarios has done
<a href="https://www.isa-afp.org/entries/Tarskis_Geometry.html">some proofs in Tarski's Geometry</a>. It uses a definition that does not quite
coincide with the definition used in Geocoq and here.
Furthermore, corresponding definitions in the <a href="https://www.isa-afp.org/entries/Poincare_Disc.html">Poincaré Disc Model
development</a> are not identical to those defined in GeoCoq.
</p>
<p>In the last part, it is
formalized that, in the neutral/absolute space, the axiom of the
parallels of Tarski's system implies the Playfair axiom, the 5th
postulate of Euclid and Euclid's original parallel postulate. These
proofs, which are not constructive, are directly inspired by Pierre
Boutry, Charly Gries, Julien Narboux and Pascal Schreck.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session IsaGeoCoq</h3>
<ul>
<li><a href="../theories/isageocoq/#Tarski_Neutral">Tarski_Neutral</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">IsaGeoCoq-AFP</p><pre id="copy-text">@article{IsaGeoCoq-AFP,
author = {Roland Coghetto},
title = {Tarski&#39;s Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid},
journal = {Archive of Formal Proofs},
month = {January},
year = {2021},
note = {\url{https://isa-afp.org/entries/IsaGeoCoq.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IsaGeoCoq-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>I</span>sa<span class='first'>N</span>et: <span class='first'>F</span>ormalization of a <span class='first'>V</span>erification <span class='first'>F</span>ramework for <span class='first'>S</span>ecure <span class='first'>D</span>ata <span class='first'>P</span>lane <span class='first'>P</span>rotocols</h1>
<div>
<p><a href="../authors/klenze">Tobias Klenze</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInRvYmlhcyIsImtsZW56ZSJdfQ==">📧</a> and <a href="../authors/sprenger">Christoph Sprenger</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInNwcmVuZ2VyIl19">📧</a>
</p>
<p class="date">June 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Today's Internet is built on decades-old networking protocols
that lack scalability, reliability and security. In response, the
networking community has developed <em>path-aware</em> Internet
architectures that solve these issues while simultaneously empowering
end hosts. In these architectures, autonomous systems authorize
forwarding paths in accordance with their routing policies, and
protect paths using cryptographic authenticators. For each packet, the
sending end host selects an authorized path and embeds it and its
authenticators in the packet header. This allows routers to
efficiently determine how to forward the packet. The central security
property of the data plane, i.e., of forwarding, is that packets can
only travel along authorized paths. This property, which we call
<em>path authorization</em>, protects the routing policies of autonomous
systems from malicious senders. The fundamental role of packet
forwarding in the Internet's ecosystem and the complexity of the
authentication mechanisms employed call for a formal analysis. We
develop IsaNet, a parameterized verification framework for data plane
protocols in Isabelle/HOL. We first formulate an abstract model
without an attacker for which we prove path authorization. We then
refine this model by introducing a Dolev--Yao attacker and by
protecting authorized paths using (generic) cryptographic validation
fields. This model is parametrized by the path authorization mechanism
and assumes five simple verification conditions. We propose novel
attacker models and different sets of assumptions on the underlying
routing protocol. We validate our framework by instantiating it with
nine concrete protocols variants and prove that they each satisfy the
verification conditions (and hence path authorization). The invariants
needed for the security proof are proven in the parametrized model
instead of the instance models. Our framework thus supports low-effort
security proofs for data plane protocols. In contrast to what could be
achieved with state-of-the-art automated protocol verifiers, our
results hold for arbitrary network topologies and sets of authorized
paths.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session IsaNet</h3>
<ul>
<li><a href="../theories/isanet/#Event_Systems">Event_Systems</a></li>
<li><a href="../theories/isanet/#Agents">Agents</a></li>
<li><a href="../theories/isanet/#Keys">Keys</a></li>
<li><a href="../theories/isanet/#Message">Message</a></li>
<li><a href="../theories/isanet/#Tools">Tools</a></li>
<li><a href="../theories/isanet/#Take_While">Take_While</a></li>
<li><a href="../theories/isanet/#Take_While_Update">Take_While_Update</a></li>
<li><a href="../theories/isanet/#Network_Model">Network_Model</a></li>
<li><a href="../theories/isanet/#Parametrized_Dataplane_0">Parametrized_Dataplane_0</a></li>
<li><a href="../theories/isanet/#Parametrized_Dataplane_1">Parametrized_Dataplane_1</a></li>
<li><a href="../theories/isanet/#Parametrized_Dataplane_2">Parametrized_Dataplane_2</a></li>
<li><a href="../theories/isanet/#Network_Assumptions">Network_Assumptions</a></li>
<li><a href="../theories/isanet/#Parametrized_Dataplane_3_directed">Parametrized_Dataplane_3_directed</a></li>
<li><a href="../theories/isanet/#Parametrized_Dataplane_3_undirected">Parametrized_Dataplane_3_undirected</a></li>
<li><a href="../theories/isanet/#SCION">SCION</a></li>
<li><a href="../theories/isanet/#SCION_variant">SCION_variant</a></li>
<li><a href="../theories/isanet/#EPIC_L1_BA">EPIC_L1_BA</a></li>
<li><a href="../theories/isanet/#EPIC_L1_SA">EPIC_L1_SA</a></li>
<li><a href="../theories/isanet/#EPIC_L1_SA_Example">EPIC_L1_SA_Example</a></li>
<li><a href="../theories/isanet/#EPIC_L2_SA">EPIC_L2_SA</a></li>
<li><a href="../theories/isanet/#Abstract_XOR">Abstract_XOR</a></li>
<li><a href="../theories/isanet/#Anapaya_SCION">Anapaya_SCION</a></li>
<li><a href="../theories/isanet/#ICING">ICING</a></li>
<li><a href="../theories/isanet/#ICING_variant">ICING_variant</a></li>
<li><a href="../theories/isanet/#ICING_variant2">ICING_variant2</a></li>
<li><a href="../theories/isanet/#All_Protocols">All_Protocols</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">IsaNet-AFP</p><pre id="copy-text">@article{IsaNet-AFP,
author = {Tobias Klenze and Christoph Sprenger},
title = {IsaNet: Formalization of a Verification Framework for Secure Data Plane Protocols},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/IsaNet.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-IsaNet-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-IsaNet-2022-06-24.tar.gz">Jun 24, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>I</span>sabelle/<span class='first'>C</span></h1>
<div>
<p><a href="../authors/tuong">Frédéric Tuong</a> <a href="https://www.lri.fr/~ftuong/">🌐</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a>
</p>
<p class="date">October 22, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a framework for C code in C11 syntax deeply integrated into
the Isabelle/PIDE development environment. Our framework provides an
abstract interface for verification back-ends to be plugged-in
independently. Thus, various techniques such as deductive program
verification or white-box testing can be applied to the same source,
which is part of an integrated PIDE document model. Semantic back-ends
are free to choose the supported C fragment and its semantics. In
particular, they can differ on the chosen memory model or the
specification mechanism for framing conditions. Our framework supports
semantic annotations of C sources in the form of comments. Annotations
serve to locally control back-end settings, and can express the term
focus to which an annotation refers. Both the logical and the
syntactic context are available when semantic annotations are
evaluated. As a consequence, a formula in an annotation can refer both
to HOL or C variables. Our approach demonstrates the degree of
maturity and expressive power the Isabelle/PIDE sub-system has
achieved in recent years. Our integration technique employs Lex and
Yacc style grammars to ensure efficient deterministic parsing. This
is the core-module of Isabelle/C; the AFP package for Clean and
Clean_wrapper as well as AutoCorres and AutoCorres_wrapper (available
via git) are applications of this front-end.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Isabelle_C</h3>
<ul>
<li><a href="../theories/isabelle_c/#C_Lexer_Language">C_Lexer_Language</a></li>
<li><a href="../theories/isabelle_c/#C_Ast">C_Ast</a></li>
<li><a href="../theories/isabelle_c/#C_Environment">C_Environment</a></li>
<li><a href="../theories/isabelle_c/#C_Parser_Language">C_Parser_Language</a></li>
<li><a href="../theories/isabelle_c/#C_Lexer_Annotation">C_Lexer_Annotation</a></li>
<li><a href="../theories/isabelle_c/#C_Parser_Annotation">C_Parser_Annotation</a></li>
<li><a href="../theories/isabelle_c/#C_Eval">C_Eval</a></li>
<li><a href="../theories/isabelle_c/#C_Command">C_Command</a></li>
<li><a href="../theories/isabelle_c/#C_Document">C_Document</a></li>
<li><a href="../theories/isabelle_c/#C_Main">C_Main</a></li>
<li><a href="../theories/isabelle_c/#C0">C0</a></li>
<li><a href="../theories/isabelle_c/#C1">C1</a></li>
<li><a href="../theories/isabelle_c/#C2">C2</a></li>
<li><a href="../theories/isabelle_c/#C_paper">C_paper</a></li>
<li><a href="../theories/isabelle_c/#C_Appendices">C_Appendices</a></li>
<li><a href="../theories/isabelle_c/#README">README</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Isabelle_C-AFP</p><pre id="copy-text">@article{Isabelle_C-AFP,
author = {Frédéric Tuong and Burkhart Wolff},
title = {Isabelle/C},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/Isabelle_C.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Isabelle_C-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Isabelle_C-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Isabelle_C-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Isabelle_C-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Isabelle_C-2019-12-19.tar.gz">Dec 19, 2019</a>: Isabelle2019
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diff --git a/web/entries/Isabelle_Marries_Dirac.html b/web/entries/Isabelle_Marries_Dirac.html
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<h1 >
<span class='first'>I</span>sabelle <span class='first'>M</span>arries <span class='first'>D</span>irac: <span class='first'>A</span> <span class='first'>L</span>ibrary for <span class='first'>Q</span>uantum <span class='first'>C</span>omputation and <span class='first'>Q</span>uantum <span class='first'>I</span>nformation</h1>
<div>
<p><a href="../authors/bordg">Anthony Bordg</a> <a href="https://sites.google.com/site/anthonybordg/">🌐</a>, <a href="../authors/lachnitt">Hanna Lachnitt</a> <a class="obfuscated" data="eyJob3N0IjpbInN0YW5mb3JkIiwiZWR1Il0sInVzZXIiOlsibGFjaG5pdHQiXX0=">📧</a> and <a href="../authors/he">Yijun He</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJ5aDQwMyJdfQ==">📧</a>
</p>
<p class="date">November 22, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is an effort to formalise some quantum algorithms and
results in quantum information theory. Formal methods being critical
for the safety and security of algorithms and protocols, we foresee
their widespread use for quantum computing in the future. We have
developed a large library for quantum computing in Isabelle based on a
matrix representation for quantum circuits, successfully formalising
the no-cloning theorem, quantum teleportation, Deutsch's
algorithm, the Deutsch-Jozsa algorithm and the quantum Prisoner's
Dilemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/quantum-computing">Computer science/Algorithms/Quantum computing</a></li><li><a href="../topics/mathematics/physics/quantum-information">Mathematics/Physics/Quantum information</a></li></ul>
<h3>Session Isabelle_Marries_Dirac</h3>
<ul>
<li><a href="../theories/isabelle_marries_dirac/#Basics">Basics</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Binary_Nat">Binary_Nat</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Quantum">Quantum</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Complex_Vectors">Complex_Vectors</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Tensor">Tensor</a></li>
<li><a href="../theories/isabelle_marries_dirac/#More_Tensor">More_Tensor</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Measurement">Measurement</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Entanglement">Entanglement</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Quantum_Teleportation">Quantum_Teleportation</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Deutsch">Deutsch</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Deutsch_Jozsa">Deutsch_Jozsa</a></li>
<li><a href="../theories/isabelle_marries_dirac/#No_Cloning">No_Cloning</a></li>
<li><a href="../theories/isabelle_marries_dirac/#Quantum_Prisoners_Dilemma">Quantum_Prisoners_Dilemma</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Matrix_Tensor.html">Tensor Product of Matrices</a></li><li><a href="../entries/VectorSpace.html">Vector Spaces</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Projective_Measurements.html">Quantum projective measurements and the CHSH inequality</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Isabelle_Marries_Dirac-AFP</p><pre id="copy-text">@article{Isabelle_Marries_Dirac-AFP,
author = {Anthony Bordg and Hanna Lachnitt and Yijun He},
title = {Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information},
journal = {Archive of Formal Proofs},
month = {November},
year = {2020},
note = {\url{https://isa-afp.org/entries/Isabelle_Marries_Dirac.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Isabelle_Marries_Dirac-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Isabelle_Marries_Dirac-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Isabelle_Marries_Dirac-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Isabelle_Meta_Model.html b/web/entries/Isabelle_Meta_Model.html
--- a/web/entries/Isabelle_Meta_Model.html
+++ b/web/entries/Isabelle_Meta_Model.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Meta-Model for the Isabelle API - Archive of Formal Proofs</title><meta name="description" content="We represent a theory of (a fragment of) Isabelle/HOL in Isabelle/HOL. The purpose of this exercise is to write packages for domain-specific specifications..."><meta property="og:title" content="A Meta-Model for the Isabelle API" />
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<h1 >
<span class='first'>A</span> <span class='first'>M</span>eta-<span class='first'>M</span>odel for the <span class='first'>I</span>sabelle <span class='first'>A</span><span class='first'>P</span><span class='first'>I</span></h1>
<div>
<p><a href="../authors/tuong">Frédéric Tuong</a> <a class="obfuscated" data="eyJob3N0IjpbInVzZXJzIiwiZ2ZvcmdlIiwiaW5yaWEiLCJmciJdLCJ1c2VyIjpbInR1b25nIl19">📧</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a>
</p>
<p class="date">September 16, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We represent a theory <i>of</i> (a fragment of) Isabelle/HOL <i>in</i>
Isabelle/HOL. The purpose of this exercise is to write packages for
domain-specific specifications such as class models, B-machines, ...,
and generally speaking, any domain-specific languages whose
abstract syntax can be defined by a HOL "datatype". On this basis, the
Isabelle code-generator can then be used to generate code for global
context transformations as well as tactic code.
<p>
Consequently the package is geared towards
parsing, printing and code-generation to the Isabelle API.
It is at the moment not sufficiently rich for doing meta theory on
Isabelle itself. Extensions in this direction are possible though.
<p>
Moreover, the chosen fragment is fairly rudimentary. However it should be
easily adapted to one's needs if a package is written on top of it.
The supported API contains types, terms, transformation of
global context like definitions and data-type declarations as well
as infrastructure for Isar-setups.
<p>
This theory is drawn from the
<a href="http://isa-afp.org/entries/Featherweight_OCL.html">Featherweight OCL</a>
project where
it is used to construct a package for object-oriented data-type theories
generated from UML class diagrams. The Featherweight OCL, for example, allows for
both the direct execution of compiled tactic code by the Isabelle API
as well as the generation of ".thy"-files for debugging purposes.
<p>
Gained experience from this project shows that the compiled code is sufficiently
efficient for practical purposes while being based on a formal <i>model</i>
on which properties of the package can be proven such as termination of certain
transformations, correctness, etc.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session Isabelle_Meta_Model</h3>
<ul>
<li><a href="../theories/isabelle_meta_model/#Antiquote_Setup">Antiquote_Setup</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_Cartouche_Examples">Isabelle_Cartouche_Examples</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_Main0">Isabelle_Main0</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_code_target">Isabelle_code_target</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_code_runtime">Isabelle_code_runtime</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_Main1">Isabelle_Main1</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_typedecl">Isabelle_typedecl</a></li>
<li><a href="../theories/isabelle_meta_model/#Isabelle_Main2">Isabelle_Main2</a></li>
<li><a href="../theories/isabelle_meta_model/#Init">Init</a></li>
<li><a href="../theories/isabelle_meta_model/#Meta_Pure">Meta_Pure</a></li>
<li><a href="../theories/isabelle_meta_model/#Parser_init">Parser_init</a></li>
<li><a href="../theories/isabelle_meta_model/#Parser_Pure">Parser_Pure</a></li>
<li><a href="../theories/isabelle_meta_model/#Meta_SML">Meta_SML</a></li>
<li><a href="../theories/isabelle_meta_model/#Meta_Isabelle">Meta_Isabelle</a></li>
<li><a href="../theories/isabelle_meta_model/#Printer_init">Printer_init</a></li>
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<p style="display:none;" id="bibtex-filename">Isabelle_Meta_Model-AFP</p><pre id="copy-text">@article{Isabelle_Meta_Model-AFP,
author = {Frédéric Tuong and Burkhart Wolff},
title = {A Meta-Model for the Isabelle API},
journal = {Archive of Formal Proofs},
month = {September},
year = {2015},
note = {\url{https://isa-afp.org/entries/Isabelle_Meta_Model.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Isabelle_Meta_Model-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>ase <span class='first'>S</span>tudy in <span class='first'>B</span>asic <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/ballarin">Clemens Ballarin</a> <a href="http://www21.in.tum.de/~ballarin/">🌐</a>
</p>
<p class="date">August 30, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The focus of this case study is re-use in abstract algebra. It
contains locale-based formalisations of selected parts of set, group
and ring theory from Jacobson's <i>Basic Algebra</i>
leading to the respective fundamental homomorphism theorems. The
study is not intended as a library base for abstract algebra. It
rather explores an approach towards abstract algebra in Isabelle.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Jacobson_Basic_Algebra</h3>
<ul>
<li><a href="../theories/jacobson_basic_algebra/#Set_Theory">Set_Theory</a></li>
<li><a href="../theories/jacobson_basic_algebra/#Group_Theory">Group_Theory</a></li>
<li><a href="../theories/jacobson_basic_algebra/#Ring_Theory">Ring_Theory</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Khovanskii_Theorem.html">Khovanskii's Theorem</a></li><li><a href="../entries/Pluennecke_Ruzsa_Inequality.html">The Plünnecke-Ruzsa Inequality</a></li><li><a href="../entries/Grothendieck_Schemes.html">Grothendieck&rsquo;s Schemes in Algebraic Geometry</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Jacobson_Basic_Algebra-AFP</p><pre id="copy-text">@article{Jacobson_Basic_Algebra-AFP,
author = {Clemens Ballarin},
title = {A Case Study in Basic Algebra},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/Jacobson_Basic_Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Jacobson_Basic_Algebra-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Jacobson_Basic_Algebra-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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diff --git a/web/entries/Jinja.html b/web/entries/Jinja.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Jinja is not Java - Archive of Formal Proofs</title><meta name="description" content="We introduce Jinja, a Java-like programming language with a formal semantics designed to exhibit core features of the Java language architecture. Jinja is..."><meta property="og:title" content="Jinja is not Java" />
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<h1 >
<span class='first'>J</span>inja <span class='first'>I</span>s <span class='first'>N</span>ot <span class='first'>J</span>ava</h1>
<div>
<p><a href="../authors/klein">Gerwin Klein</a> <a href="http://www.cse.unsw.edu.au/~kleing/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 1, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We introduce Jinja, a Java-like programming language with a formal semantics designed to exhibit core features of the Java language architecture. Jinja is a compromise between realism of the language and tractability and clarity of the formal semantics. The following aspects are formalised: a big and a small step operational semantics for Jinja and a proof of their equivalence; a type system and a definite initialisation analysis; a type safety proof of the small step semantics; a virtual machine (JVM), its operational semantics and its type system; a type safety proof for the JVM; a bytecode verifier, i.e. data flow analyser for the JVM; a correctness proof of the bytecode verifier w.r.t. the type system; a compiler and a proof that it preserves semantics and well-typedness. The emphasis of this work is not on particular language features but on providing a unified model of the source language, the virtual machine and the compiler. The whole development has been carried out in the theorem prover Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul><h3>Related publications</h3>
<ul><li>
Klein, G., & Nipkow, T. (2006). A machine-checked model for a Java-like language, virtual machine, and compiler. ACM Transactions on Programming Languages and Systems, 28(4), 619–695. <a href="https://doi.org/10.1145/1146809.1146811">https://doi.org/10.1145/1146809.1146811</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/Jinja/">Alternate versions</a>
</li></ul>
<h3>Session Jinja</h3>
<ul>
<li><a href="../theories/jinja/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/jinja/#Type">Type</a></li>
<li><a href="../theories/jinja/#Decl">Decl</a></li>
<li><a href="../theories/jinja/#TypeRel">TypeRel</a></li>
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<li><a href="../theories/jinja/#Exceptions">Exceptions</a></li>
<li><a href="../theories/jinja/#Expr">Expr</a></li>
<li><a href="../theories/jinja/#State">State</a></li>
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<li><a href="../theories/jinja/#SmallStep">SmallStep</a></li>
<li><a href="../theories/jinja/#SystemClasses">SystemClasses</a></li>
<li><a href="../theories/jinja/#WellForm">WellForm</a></li>
<li><a href="../theories/jinja/#WWellForm">WWellForm</a></li>
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<li><a href="../theories/jinja/#WellType">WellType</a></li>
<li><a href="../theories/jinja/#WellTypeRT">WellTypeRT</a></li>
<li><a href="../theories/jinja/#DefAss">DefAss</a></li>
<li><a href="../theories/jinja/#Conform">Conform</a></li>
<li><a href="../theories/jinja/#Progress">Progress</a></li>
<li><a href="../theories/jinja/#JWellForm">JWellForm</a></li>
<li><a href="../theories/jinja/#TypeSafe">TypeSafe</a></li>
<li><a href="../theories/jinja/#Annotate">Annotate</a></li>
<li><a href="../theories/jinja/#Examples">Examples</a></li>
<li><a href="../theories/jinja/#execute_Bigstep">execute_Bigstep</a></li>
<li><a href="../theories/jinja/#execute_WellType">execute_WellType</a></li>
<li><a href="../theories/jinja/#JVMState">JVMState</a></li>
<li><a href="../theories/jinja/#JVMInstructions">JVMInstructions</a></li>
<li><a href="../theories/jinja/#JVMExecInstr">JVMExecInstr</a></li>
<li><a href="../theories/jinja/#JVMExceptions">JVMExceptions</a></li>
<li><a href="../theories/jinja/#JVMExec">JVMExec</a></li>
<li><a href="../theories/jinja/#JVMDefensive">JVMDefensive</a></li>
<li><a href="../theories/jinja/#JVMListExample">JVMListExample</a></li>
<li><a href="../theories/jinja/#Semilat">Semilat</a></li>
<li><a href="../theories/jinja/#Err">Err</a></li>
<li><a href="../theories/jinja/#Opt">Opt</a></li>
<li><a href="../theories/jinja/#Product">Product</a></li>
<li><a href="../theories/jinja/#Listn">Listn</a></li>
<li><a href="../theories/jinja/#Semilattices">Semilattices</a></li>
<li><a href="../theories/jinja/#Typing_Framework_1">Typing_Framework_1</a></li>
<li><a href="../theories/jinja/#SemilatAlg">SemilatAlg</a></li>
<li><a href="../theories/jinja/#Typing_Framework_err">Typing_Framework_err</a></li>
<li><a href="../theories/jinja/#Kildall_1">Kildall_1</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Dominance_CHK.html">A data flow analysis algorithm for computing dominators</a></li><li><a href="../entries/JinjaDCI.html">JinjaDCI: a Java semantics with dynamic class initialization</a></li><li><a href="../entries/HRB-Slicing.html">Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</a></li><li><a href="../entries/Slicing.html">Towards Certified Slicing</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Jinja-AFP</p><pre id="copy-text">@article{Jinja-AFP,
author = {Gerwin Klein and Tobias Nipkow},
title = {Jinja is not Java},
journal = {Archive of Formal Proofs},
month = {June},
year = {2005},
note = {\url{https://isa-afp.org/entries/Jinja.html},
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<h1 >
<span class='first'>J</span>inja<span class='first'>D</span><span class='first'>C</span><span class='first'>I</span>: <span class='first'>A</span> <span class='first'>J</span>ava <span class='first'>S</span>emantics <span class='first'>W</span>ith <span class='first'>D</span>ynamic <span class='first'>C</span>lass <span class='first'>I</span>nitialization</h1>
<div>
<p><a href="../authors/mansky">Susannah Mansky</a> <a class="obfuscated" data="eyJob3N0IjpbImlsbGlub2lzIiwiZWR1Il0sInVzZXIiOlsic2pvaG5zbjIiXX0=">📧</a>
</p>
<p class="date">January 11, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We extend Jinja to include static fields, methods, and instructions,
and dynamic class initialization, based on the Java SE 8
specification. This includes extension of definitions and proofs. This
work is partially described in Mansky and Gunter's paper at CPP
2019 and Mansky's doctoral thesis (UIUC, 2020).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session JinjaDCI</h3>
<ul>
<li><a href="../theories/jinjadci/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/jinjadci/#Type">Type</a></li>
<li><a href="../theories/jinjadci/#Decl">Decl</a></li>
<li><a href="../theories/jinjadci/#TypeRel">TypeRel</a></li>
<li><a href="../theories/jinjadci/#Value">Value</a></li>
<li><a href="../theories/jinjadci/#Objects">Objects</a></li>
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<li><a href="../theories/jinjadci/#Expr">Expr</a></li>
<li><a href="../theories/jinjadci/#WellType">WellType</a></li>
<li><a href="../theories/jinjadci/#WellTypeRT">WellTypeRT</a></li>
<li><a href="../theories/jinjadci/#State">State</a></li>
<li><a href="../theories/jinjadci/#SystemClasses">SystemClasses</a></li>
<li><a href="../theories/jinjadci/#WellForm">WellForm</a></li>
<li><a href="../theories/jinjadci/#WWellForm">WWellForm</a></li>
<li><a href="../theories/jinjadci/#BigStep">BigStep</a></li>
<li><a href="../theories/jinjadci/#DefAss">DefAss</a></li>
<li><a href="../theories/jinjadci/#Conform">Conform</a></li>
<li><a href="../theories/jinjadci/#SmallStep">SmallStep</a></li>
<li><a href="../theories/jinjadci/#EConform">EConform</a></li>
<li><a href="../theories/jinjadci/#Progress">Progress</a></li>
<li><a href="../theories/jinjadci/#JWellForm">JWellForm</a></li>
<li><a href="../theories/jinjadci/#TypeSafe">TypeSafe</a></li>
<li><a href="../theories/jinjadci/#Equivalence">Equivalence</a></li>
<li><a href="../theories/jinjadci/#Annotate">Annotate</a></li>
<li><a href="../theories/jinjadci/#JVMState">JVMState</a></li>
<li><a href="../theories/jinjadci/#JVMInstructions">JVMInstructions</a></li>
<li><a href="../theories/jinjadci/#JVMExceptions">JVMExceptions</a></li>
<li><a href="../theories/jinjadci/#JVMExecInstr">JVMExecInstr</a></li>
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<li><a href="../theories/jinjadci/#JVMDefensive">JVMDefensive</a></li>
<li><a href="../theories/jinjadci/#SemiType">SemiType</a></li>
<li><a href="../theories/jinjadci/#JVM_SemiType">JVM_SemiType</a></li>
<li><a href="../theories/jinjadci/#Effect">Effect</a></li>
<li><a href="../theories/jinjadci/#EffectMono">EffectMono</a></li>
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<li><a href="../theories/jinjadci/#Compiler">Compiler</a></li>
<li><a href="../theories/jinjadci/#TypeComp">TypeComp</a></li>
<li><a href="../theories/jinjadci/#JinjaDCI">JinjaDCI</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jinja.html">Jinja is not Java</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<p style="display:none;" id="bibtex-filename">JinjaDCI-AFP</p><pre id="copy-text">@article{JinjaDCI-AFP,
author = {Susannah Mansky},
title = {JinjaDCI: a Java semantics with dynamic class initialization},
journal = {Archive of Formal Proofs},
month = {January},
year = {2021},
note = {\url{https://isa-afp.org/entries/JinjaDCI.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>J</span>inja <span class='first'>W</span>ith <span class='first'>T</span>hreads</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">December 3, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We extend the Jinja source code semantics by Klein and Nipkow with Java-style arrays and threads. Concurrency is captured in a generic framework semantics for adding concurrency through interleaving to a sequential semantics, which features dynamic thread creation, inter-thread communication via shared memory, lock synchronisation and joins. Also, threads can suspend themselves and be notified by others. We instantiate the framework with the adapted versions of both Jinja source and byte code and show type safety for the multithreaded case. Equally, the compiler from source to byte code is extended, for which we prove weak bisimilarity between the source code small step semantics and the defensive Jinja virtual machine. On top of this, we formalise the JMM and show the DRF guarantee and consistency. For description of the different parts, see Lochbihler's papers at FOOL 2008, ESOP 2010, ITP 2011, and ESOP 2012.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>October 20, 2017</dt>
<dd>add an atomic compare-and-swap operation for volatile fields
(revision a6189b1d6b30)<br></dd><dt>May 16, 2013</dt>
<dd>support for non-deterministic memory allocators
(revision cc3344a49ced)<br>
</dd><dt>November 21, 2012</dt>
<dd>type safety proof for the Java memory model,
allow spurious wake-ups
(revision 76063d860ae0)<br>
</dd><dt>February 16, 2012</dt>
<dd>added example programs
(revision bf0b06c8913d)<br>
</dd><dt>July 21, 2011</dt>
<dd>new interruption model,
generalized JMM proof of DRF guarantee,
allow class Object to declare methods and fields,
simplified subtyping relation,
corrected division and modulo implementation
(revision 46e4181ed142)<br>
</dd><dt>February 2, 2011</dt>
<dd>simplified code generator setup
new random scheduler
(revision 3059dafd013f)<br>
</dd><dt>December 16, 2010</dt>
<dd>improved version of the Java memory model, also for bytecode
executable scheduler for source code semantics
(revision 1f41c1842f5a)<br>
</dd><dt>October 15, 2010</dt>
<dd>preliminary version of the Java memory model for source code
(revision 02fee0ef3ca2)<br>
</dd><dt>June 28, 2010</dt>
<dd>new thread interruption model
(revision c0440d0a1177)<br>
</dd><dt>June 8, 2010</dt>
<dd>added thread interruption;
new abstract memory model with sequential consistency as implementation
(revision 0cb9e8dbd78d)<br>
</dd><dt>November 30, 2009</dt>
<dd>extended compiler correctness proof to infinite and deadlocking computations
(revision e50282397435)<br>
</dd><dt>April 27, 2009</dt>
<dd>added verified compiler from source code to bytecode;
encapsulate native methods in separate semantics
(revision e4f26541e58a)<br>
</dd><dt>April 23, 2008</dt>
<dd>added bytecode formalisation with arrays and threads, added thread joins
(revision f74a8be156a7)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session JinjaThreads</h3>
<ul>
<li><a href="../theories/jinjathreads/#Set_without_equal">Set_without_equal</a></li>
<li><a href="../theories/jinjathreads/#Set_Monad">Set_Monad</a></li>
<li><a href="../theories/jinjathreads/#JT_ICF">JT_ICF</a></li>
<li><a href="../theories/jinjathreads/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/jinjathreads/#Basic_Main">Basic_Main</a></li>
<li><a href="../theories/jinjathreads/#FWState">FWState</a></li>
<li><a href="../theories/jinjathreads/#FWLock">FWLock</a></li>
<li><a href="../theories/jinjathreads/#FWLocking">FWLocking</a></li>
<li><a href="../theories/jinjathreads/#FWThread">FWThread</a></li>
<li><a href="../theories/jinjathreads/#FWWait">FWWait</a></li>
<li><a href="../theories/jinjathreads/#FWCondAction">FWCondAction</a></li>
<li><a href="../theories/jinjathreads/#FWWellform">FWWellform</a></li>
<li><a href="../theories/jinjathreads/#FWLockingThread">FWLockingThread</a></li>
<li><a href="../theories/jinjathreads/#FWInterrupt">FWInterrupt</a></li>
<li><a href="../theories/jinjathreads/#FWSemantics">FWSemantics</a></li>
<li><a href="../theories/jinjathreads/#FWProgressAux">FWProgressAux</a></li>
<li><a href="../theories/jinjathreads/#FWDeadlock">FWDeadlock</a></li>
<li><a href="../theories/jinjathreads/#FWProgress">FWProgress</a></li>
<li><a href="../theories/jinjathreads/#FWLifting">FWLifting</a></li>
<li><a href="../theories/jinjathreads/#LTS">LTS</a></li>
<li><a href="../theories/jinjathreads/#FWLTS">FWLTS</a></li>
<li><a href="../theories/jinjathreads/#Bisimulation">Bisimulation</a></li>
<li><a href="../theories/jinjathreads/#FWBisimulation">FWBisimulation</a></li>
<li><a href="../theories/jinjathreads/#FWBisimDeadlock">FWBisimDeadlock</a></li>
<li><a href="../theories/jinjathreads/#FWLiftingSem">FWLiftingSem</a></li>
<li><a href="../theories/jinjathreads/#FWInitFinLift">FWInitFinLift</a></li>
<li><a href="../theories/jinjathreads/#FWBisimLift">FWBisimLift</a></li>
<li><a href="../theories/jinjathreads/#Semilat">Semilat</a></li>
<li><a href="../theories/jinjathreads/#Err">Err</a></li>
<li><a href="../theories/jinjathreads/#Opt">Opt</a></li>
<li><a href="../theories/jinjathreads/#Product">Product</a></li>
<li><a href="../theories/jinjathreads/#Listn">Listn</a></li>
<li><a href="../theories/jinjathreads/#Semilattices">Semilattices</a></li>
<li><a href="../theories/jinjathreads/#Typing_Framework">Typing_Framework</a></li>
<li><a href="../theories/jinjathreads/#SemilatAlg">SemilatAlg</a></li>
<li><a href="../theories/jinjathreads/#Typing_Framework_err">Typing_Framework_err</a></li>
<li><a href="../theories/jinjathreads/#Kildall">Kildall</a></li>
<li><a href="../theories/jinjathreads/#LBVSpec">LBVSpec</a></li>
<li><a href="../theories/jinjathreads/#LBVCorrect">LBVCorrect</a></li>
<li><a href="../theories/jinjathreads/#LBVComplete">LBVComplete</a></li>
<li><a href="../theories/jinjathreads/#Abstract_BV">Abstract_BV</a></li>
<li><a href="../theories/jinjathreads/#Type">Type</a></li>
<li><a href="../theories/jinjathreads/#Decl">Decl</a></li>
<li><a href="../theories/jinjathreads/#TypeRel">TypeRel</a></li>
<li><a href="../theories/jinjathreads/#Value">Value</a></li>
<li><a href="../theories/jinjathreads/#Exceptions">Exceptions</a></li>
<li><a href="../theories/jinjathreads/#SystemClasses">SystemClasses</a></li>
<li><a href="../theories/jinjathreads/#Heap">Heap</a></li>
<li><a href="../theories/jinjathreads/#Observable_Events">Observable_Events</a></li>
<li><a href="../theories/jinjathreads/#StartConfig">StartConfig</a></li>
<li><a href="../theories/jinjathreads/#Conform">Conform</a></li>
<li><a href="../theories/jinjathreads/#ExternalCall">ExternalCall</a></li>
<li><a href="../theories/jinjathreads/#WellForm">WellForm</a></li>
<li><a href="../theories/jinjathreads/#ExternalCallWF">ExternalCallWF</a></li>
<li><a href="../theories/jinjathreads/#ConformThreaded">ConformThreaded</a></li>
<li><a href="../theories/jinjathreads/#BinOp">BinOp</a></li>
<li><a href="../theories/jinjathreads/#SemiType">SemiType</a></li>
<li><a href="../theories/jinjathreads/#Common_Main">Common_Main</a></li>
<li><a href="../theories/jinjathreads/#State">State</a></li>
<li><a href="../theories/jinjathreads/#Expr">Expr</a></li>
<li><a href="../theories/jinjathreads/#JHeap">JHeap</a></li>
<li><a href="../theories/jinjathreads/#SmallStep">SmallStep</a></li>
<li><a href="../theories/jinjathreads/#WWellForm">WWellForm</a></li>
<li><a href="../theories/jinjathreads/#WellType">WellType</a></li>
<li><a href="../theories/jinjathreads/#DefAss">DefAss</a></li>
<li><a href="../theories/jinjathreads/#JWellForm">JWellForm</a></li>
<li><a href="../theories/jinjathreads/#Threaded">Threaded</a></li>
<li><a href="../theories/jinjathreads/#WellTypeRT">WellTypeRT</a></li>
<li><a href="../theories/jinjathreads/#Progress">Progress</a></li>
<li><a href="../theories/jinjathreads/#DefAssPreservation">DefAssPreservation</a></li>
<li><a href="../theories/jinjathreads/#TypeSafe">TypeSafe</a></li>
<li><a href="../theories/jinjathreads/#ProgressThreaded">ProgressThreaded</a></li>
<li><a href="../theories/jinjathreads/#Deadlocked">Deadlocked</a></li>
<li><a href="../theories/jinjathreads/#Annotate">Annotate</a></li>
<li><a href="../theories/jinjathreads/#J_Main">J_Main</a></li>
<li><a href="../theories/jinjathreads/#JVMState">JVMState</a></li>
<li><a href="../theories/jinjathreads/#JVMInstructions">JVMInstructions</a></li>
<li><a href="../theories/jinjathreads/#JVMHeap">JVMHeap</a></li>
<li><a href="../theories/jinjathreads/#JVMExecInstr">JVMExecInstr</a></li>
<li><a href="../theories/jinjathreads/#JVMExceptions">JVMExceptions</a></li>
<li><a href="../theories/jinjathreads/#JVMExec">JVMExec</a></li>
<li><a href="../theories/jinjathreads/#JVMDefensive">JVMDefensive</a></li>
<li><a href="../theories/jinjathreads/#JVMThreaded">JVMThreaded</a></li>
<li><a href="../theories/jinjathreads/#JVM_Main">JVM_Main</a></li>
<li><a href="../theories/jinjathreads/#JVM_SemiType">JVM_SemiType</a></li>
<li><a href="../theories/jinjathreads/#Effect">Effect</a></li>
<li><a href="../theories/jinjathreads/#BVSpec">BVSpec</a></li>
<li><a href="../theories/jinjathreads/#BVConform">BVConform</a></li>
<li><a href="../theories/jinjathreads/#BVSpecTypeSafe">BVSpecTypeSafe</a></li>
<li><a href="../theories/jinjathreads/#BVNoTypeError">BVNoTypeError</a></li>
<li><a href="../theories/jinjathreads/#BVProgressThreaded">BVProgressThreaded</a></li>
<li><a href="../theories/jinjathreads/#JVMDeadlocked">JVMDeadlocked</a></li>
<li><a href="../theories/jinjathreads/#EffectMono">EffectMono</a></li>
<li><a href="../theories/jinjathreads/#TF_JVM">TF_JVM</a></li>
<li><a href="../theories/jinjathreads/#LBVJVM">LBVJVM</a></li>
<li><a href="../theories/jinjathreads/#BVExec">BVExec</a></li>
<li><a href="../theories/jinjathreads/#BCVExec">BCVExec</a></li>
<li><a href="../theories/jinjathreads/#BV_Main">BV_Main</a></li>
<li><a href="../theories/jinjathreads/#CallExpr">CallExpr</a></li>
<li><a href="../theories/jinjathreads/#J0">J0</a></li>
<li><a href="../theories/jinjathreads/#J0Bisim">J0Bisim</a></li>
<li><a href="../theories/jinjathreads/#J1State">J1State</a></li>
<li><a href="../theories/jinjathreads/#J1Heap">J1Heap</a></li>
<li><a href="../theories/jinjathreads/#J1">J1</a></li>
<li><a href="../theories/jinjathreads/#J1Deadlock">J1Deadlock</a></li>
<li><a href="../theories/jinjathreads/#PCompiler">PCompiler</a></li>
<li><a href="../theories/jinjathreads/#Compiler2">Compiler2</a></li>
<li><a href="../theories/jinjathreads/#Exception_Tables">Exception_Tables</a></li>
<li><a href="../theories/jinjathreads/#J1WellType">J1WellType</a></li>
<li><a href="../theories/jinjathreads/#J1WellForm">J1WellForm</a></li>
<li><a href="../theories/jinjathreads/#TypeComp">TypeComp</a></li>
<li><a href="../theories/jinjathreads/#JVMTau">JVMTau</a></li>
<li><a href="../theories/jinjathreads/#Execs">Execs</a></li>
<li><a href="../theories/jinjathreads/#J1JVMBisim">J1JVMBisim</a></li>
<li><a href="../theories/jinjathreads/#J1JVM">J1JVM</a></li>
<li><a href="../theories/jinjathreads/#JVMJ1">JVMJ1</a></li>
<li><a href="../theories/jinjathreads/#Correctness2">Correctness2</a></li>
<li><a href="../theories/jinjathreads/#ListIndex">ListIndex</a></li>
<li><a href="../theories/jinjathreads/#Compiler1">Compiler1</a></li>
<li><a href="../theories/jinjathreads/#J0J1Bisim">J0J1Bisim</a></li>
<li><a href="../theories/jinjathreads/#Correctness1Threaded">Correctness1Threaded</a></li>
<li><a href="../theories/jinjathreads/#Correctness1">Correctness1</a></li>
<li><a href="../theories/jinjathreads/#JJ1WellForm">JJ1WellForm</a></li>
<li><a href="../theories/jinjathreads/#Compiler">Compiler</a></li>
<li><a href="../theories/jinjathreads/#Correctness">Correctness</a></li>
<li><a href="../theories/jinjathreads/#Preprocessor">Preprocessor</a></li>
<li><a href="../theories/jinjathreads/#Compiler_Main">Compiler_Main</a></li>
<li><a href="../theories/jinjathreads/#MM">MM</a></li>
<li><a href="../theories/jinjathreads/#SC">SC</a></li>
<li><a href="../theories/jinjathreads/#SC_Interp">SC_Interp</a></li>
<li><a href="../theories/jinjathreads/#SC_Collections">SC_Collections</a></li>
<li><a href="../theories/jinjathreads/#Orders">Orders</a></li>
<li><a href="../theories/jinjathreads/#JMM_Spec">JMM_Spec</a></li>
<li><a href="../theories/jinjathreads/#JMM_DRF">JMM_DRF</a></li>
<li><a href="../theories/jinjathreads/#SC_Legal">SC_Legal</a></li>
<li><a href="../theories/jinjathreads/#Non_Speculative">Non_Speculative</a></li>
<li><a href="../theories/jinjathreads/#SC_Completion">SC_Completion</a></li>
<li><a href="../theories/jinjathreads/#HB_Completion">HB_Completion</a></li>
<li><a href="../theories/jinjathreads/#JMM_Heap">JMM_Heap</a></li>
<li><a href="../theories/jinjathreads/#JMM_Framework">JMM_Framework</a></li>
<li><a href="../theories/jinjathreads/#JMM_Typesafe">JMM_Typesafe</a></li>
<li><a href="../theories/jinjathreads/#JMM_Common">JMM_Common</a></li>
<li><a href="../theories/jinjathreads/#JMM_J">JMM_J</a></li>
<li><a href="../theories/jinjathreads/#DRF_J">DRF_J</a></li>
<li><a href="../theories/jinjathreads/#JMM_JVM">JMM_JVM</a></li>
<li><a href="../theories/jinjathreads/#DRF_JVM">DRF_JVM</a></li>
<li><a href="../theories/jinjathreads/#JMM_Type">JMM_Type</a></li>
<li><a href="../theories/jinjathreads/#JMM_Compiler">JMM_Compiler</a></li>
<li><a href="../theories/jinjathreads/#JMM_Type2">JMM_Type2</a></li>
<li><a href="../theories/jinjathreads/#JMM_Interp">JMM_Interp</a></li>
<li><a href="../theories/jinjathreads/#JMM_Typesafe2">JMM_Typesafe2</a></li>
<li><a href="../theories/jinjathreads/#JMM_J_Typesafe">JMM_J_Typesafe</a></li>
<li><a href="../theories/jinjathreads/#JMM_JVM_Typesafe">JMM_JVM_Typesafe</a></li>
<li><a href="../theories/jinjathreads/#JMM_Compiler_Type2">JMM_Compiler_Type2</a></li>
<li><a href="../theories/jinjathreads/#JMM">JMM</a></li>
<li><a href="../theories/jinjathreads/#MM_Main">MM_Main</a></li>
<li><a href="../theories/jinjathreads/#State_Refinement">State_Refinement</a></li>
<li><a href="../theories/jinjathreads/#Scheduler">Scheduler</a></li>
<li><a href="../theories/jinjathreads/#Random_Scheduler">Random_Scheduler</a></li>
<li><a href="../theories/jinjathreads/#Round_Robin">Round_Robin</a></li>
<li><a href="../theories/jinjathreads/#SC_Schedulers">SC_Schedulers</a></li>
<li><a href="../theories/jinjathreads/#TypeRelRefine">TypeRelRefine</a></li>
<li><a href="../theories/jinjathreads/#PCompilerRefine">PCompilerRefine</a></li>
<li><a href="../theories/jinjathreads/#J_Execute">J_Execute</a></li>
<li><a href="../theories/jinjathreads/#ExternalCall_Execute">ExternalCall_Execute</a></li>
<li><a href="../theories/jinjathreads/#JVMExec_Execute2">JVMExec_Execute2</a></li>
<li><a href="../theories/jinjathreads/#JVM_Execute2">JVM_Execute2</a></li>
<li><a href="../theories/jinjathreads/#Code_Generation">Code_Generation</a></li>
<li><a href="../theories/jinjathreads/#JVMExec_Execute">JVMExec_Execute</a></li>
<li><a href="../theories/jinjathreads/#JVM_Execute">JVM_Execute</a></li>
<li><a href="../theories/jinjathreads/#ToString">ToString</a></li>
<li><a href="../theories/jinjathreads/#Java2Jinja">Java2Jinja</a></li>
<li><a href="../theories/jinjathreads/#Execute_Main">Execute_Main</a></li>
<li><a href="../theories/jinjathreads/#ApprenticeChallenge">ApprenticeChallenge</a></li>
<li><a href="../theories/jinjathreads/#BufferExample">BufferExample</a></li>
<li><a href="../theories/jinjathreads/#Examples_Main">Examples_Main</a></li>
<li><a href="../theories/jinjathreads/#JinjaThreads">JinjaThreads</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Binomial-Heaps.html">Binomial Heaps and Skew Binomial Heaps</a></li><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/FinFun.html">Code Generation for Functions as Data</a></li><li><a href="../entries/Finger-Trees.html">Finger Trees</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li><li><a href="../entries/Trie.html">Trie</a></li></ul>
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<p style="display:none;" id="bibtex-filename">JinjaThreads-AFP</p><pre id="copy-text">@article{JinjaThreads-AFP,
author = {Andreas Lochbihler},
title = {Jinja with Threads},
journal = {Archive of Formal Proofs},
month = {December},
year = {2007},
note = {\url{https://isa-afp.org/entries/JinjaThreads.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2012-05-26.tar.gz">May 26, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2011-10-12.tar.gz">Oct 12, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2010-07-02.tar.gz">Jul 2, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2009-04-30.tar.gz">Apr 30, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-JinjaThreads-2007-12-03.tar.gz">Dec 3, 2007</a>: Isabelle2007
</li></ul>
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<h1 >
<span class='first'>J</span>ive <span class='first'>D</span>ata and <span class='first'>S</span>tore <span class='first'>M</span>odel</h1>
<div>
<p><a href="../authors/rauch">Nicole Rauch</a> <a class="obfuscated" data="eyJob3N0IjpbImluZm9ybWF0aWsiLCJ1bmkta2wiLCJkZSJdLCJ1c2VyIjpbInJhdWNoIl19">📧</a> and <a href="../authors/schirmer">Norbert Schirmer</a>
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<p class="date">June 20, 2005</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document presents the formalization of an object-oriented data and store model in Isabelle/HOL. This model is being used in the Java Interactive Verification Environment, Jive.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/misc">Computer science/Programming languages/Misc</a></li></ul>
<h3>Session JiveDataStoreModel</h3>
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<li><a href="../theories/jivedatastoremodel/#TypeIds">TypeIds</a></li>
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<li><a href="../theories/jivedatastoremodel/#Value">Value</a></li>
<li><a href="../theories/jivedatastoremodel/#Location">Location</a></li>
<li><a href="../theories/jivedatastoremodel/#Store">Store</a></li>
<li><a href="../theories/jivedatastoremodel/#StoreProperties">StoreProperties</a></li>
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<p style="display:none;" id="bibtex-filename">JiveDataStoreModel-AFP</p><pre id="copy-text">@article{JiveDataStoreModel-AFP,
author = {Nicole Rauch and Norbert Schirmer},
title = {Jive Data and Store Model},
journal = {Archive of Formal Proofs},
month = {June},
year = {2005},
note = {\url{https://isa-afp.org/entries/JiveDataStoreModel.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-JiveDataStoreModel-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Jordan_Hoelder.html b/web/entries/Jordan_Hoelder.html
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<h1 >
<span class='first'>T</span>he <span class='first'>J</span>ordan-<span class='first'>H</span>ölder <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/raumer">Jakob von Raumer</a> <a class="obfuscated" data="eyJob3N0IjpbIm5vdHRpbmdoYW0iLCJhYyIsInVrIl0sInVzZXIiOlsicHN4anY0Il19">📧</a>
</p>
<p class="date">September 9, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This submission contains theories that lead to a formalization of the proof of the Jordan-Hölder theorem about composition series of finite groups. The theories formalize the notions of isomorphism classes of groups, simple groups, normal series, composition series, maximal normal subgroups. Furthermore, they provide proofs of the second isomorphism theorem for groups, the characterization theorem for maximal normal subgroups as well as many useful lemmas about normal subgroups and factor groups. The proof is inspired by course notes of Stuart Rankin.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Jordan_Hoelder</h3>
<ul>
<li><a href="../theories/jordan_hoelder/#SndIsomorphismGrp">SndIsomorphismGrp</a></li>
<li><a href="../theories/jordan_hoelder/#SubgroupsAndNormalSubgroups">SubgroupsAndNormalSubgroups</a></li>
<li><a href="../theories/jordan_hoelder/#SimpleGroups">SimpleGroups</a></li>
<li><a href="../theories/jordan_hoelder/#MaximalNormalSubgroups">MaximalNormalSubgroups</a></li>
<li><a href="../theories/jordan_hoelder/#CompositionSeries">CompositionSeries</a></li>
<li><a href="../theories/jordan_hoelder/#GroupIsoClasses">GroupIsoClasses</a></li>
<li><a href="../theories/jordan_hoelder/#JordanHolder">JordanHolder</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Secondary_Sylow.html">Secondary Sylow Theorems</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Jordan_Hoelder-AFP</p><pre id="copy-text">@article{Jordan_Hoelder-AFP,
author = {Jakob von Raumer},
title = {The Jordan-Hölder Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Jordan_Hoelder.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Jordan_Hoelder-2014-09-11.tar.gz">Sep 11, 2014</a>: Isabelle2014
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diff --git a/web/entries/Jordan_Normal_Form.html b/web/entries/Jordan_Normal_Form.html
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@@ -1,236 +1,238 @@
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<h1 >
<span class='first'>M</span>atrices, <span class='first'>J</span>ordan <span class='first'>N</span>ormal <span class='first'>F</span>orms, and <span class='first'>S</span>pectral <span class='first'>R</span>adius <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
with contributions from <a href="../authors/bentkamp">Alexander Bentkamp</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYmVudGthbXAiXX0=">📧</a>
</p>
<p class="date">August 21, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Matrix interpretations are useful as measure functions in termination proving. In order to use these interpretations also for complexity analysis, the growth rate of matrix powers has to examined. Here, we formalized a central result of spectral radius theory, namely that the growth rate is polynomially bounded if and only if the spectral radius of a matrix is at most one.
</p><p>
To formally prove this result we first studied the growth rates of matrices in Jordan normal form, and prove the result that every complex matrix has a Jordan normal form using a constructive prove via Schur decomposition.
</p><p>
The whole development is based on a new abstract type for matrices, which is also executable by a suitable setup of the code generator. It completely subsumes our former AFP-entry on executable matrices, and its main advantage is its close connection to the HMA-representation which allowed us to easily adapt existing proofs on determinants.
</p><p>
All the results have been applied to improve CeTA, our certifier to validate termination and complexity proof certificates.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 17, 2018</dt>
<dd>Integrated lemmas from deep-learning AFP-entry of Alexander Bentkamp</dd><dt>January 7, 2016</dt>
<dd>Added Schur-decomposition, Gram-Schmidt orthogonalization, uniqueness of Jordan normal forms<br/></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Jordan_Normal_Form</h3>
<ul>
<li><a href="../theories/jordan_normal_form/#Missing_Misc">Missing_Misc</a></li>
<li><a href="../theories/jordan_normal_form/#Missing_Ring">Missing_Ring</a></li>
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<li><a href="../theories/jordan_normal_form/#Jordan_Normal_Form">Jordan_Normal_Form</a></li>
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<li><a href="../theories/jordan_normal_form/#Jordan_Normal_Form_Uniqueness">Jordan_Normal_Form_Uniqueness</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Simplicial_complexes_and_boolean_functions.html">Simplicial Complexes and Boolean functions</a></li><li><a href="../entries/Complex_Bounded_Operators.html">Complex Bounded Operators</a></li><li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li><li><a href="../entries/Isabelle_Marries_Dirac.html">Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</a></li><li><a href="../entries/Linear_Programming.html">Linear Programming</a></li><li><a href="../entries/QHLProver.html">Quantum Hoare Logic</a></li><li><a href="../entries/Farkas.html">Farkas' Lemma and Motzkin&rsquo;s Transposition Theorem</a></li><li><a href="../entries/Stochastic_Matrices.html">Stochastic Matrices and the Perron-Frobenius Theorem</a></li><li><a href="../entries/Subresultants.html">Subresultants</a></li><li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Jordan_Normal_Form-AFP</p><pre id="copy-text">@article{Jordan_Normal_Form-AFP,
author = {René Thiemann and Akihisa Yamada},
title = {Matrices, Jordan Normal Forms, and Spectral Radius Theory},
journal = {Archive of Formal Proofs},
month = {August},
year = {2015},
note = {\url{https://isa-afp.org/entries/Jordan_Normal_Form.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>K</span>leene <span class='first'>A</span>lgebras <span class='first'>W</span>ith <span class='first'>D</span>omain</h1>
<div>
<p><a href="../authors/gomes">Victor B. F. Gomes</a> <a href="http://www.dcs.shef.ac.uk/~victor">🌐</a>, <a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>, <a href="../authors/hoefner">Peter Höfner</a> <a href="http://www.hoefner-online.de/">🌐</a>, <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a> and <a href="../authors/weber">Tjark Weber</a> <a href="http://user.it.uu.se/~tjawe125/">🌐</a>
</p>
<p class="date">April 12, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Kleene algebras with domain are Kleene algebras endowed with an
operation that maps each element of the algebra to its domain of
definition (or its complement) in abstract fashion. They form a simple
algebraic basis for Hoare logics, dynamic logics or predicate
transformer semantics. We formalise a modular hierarchy of algebras
with domain and antidomain (domain complement) operations in
Isabelle/HOL that ranges from domain and antidomain semigroups to
modal Kleene algebras and divergence Kleene algebras. We link these
algebras with models of binary relations and program traces. We
include some examples from modal logics, termination and program
analysis.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
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<ul class="horizontal-list"><li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li><li><a href="../entries/Algebraic_VCs.html">Program Construction and Verification Components Based on Kleene Algebra</a></li></ul>
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<p style="display:none;" id="bibtex-filename">KAD-AFP</p><pre id="copy-text">@article{KAD-AFP,
author = {Victor B. F. Gomes and Walter Guttmann and Peter Höfner and Georg Struth and Tjark Weber},
title = {Kleene Algebras with Domain},
journal = {Archive of Formal Proofs},
month = {April},
year = {2016},
note = {\url{https://isa-afp.org/entries/KAD.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-KAD-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-KAD-2016-04-12.tar.gz">Apr 12, 2016</a>: Isabelle2016
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Kleene Algebra with Tests and Demonic Refinement Algebras - Archive of Formal Proofs</title><meta name="description" content="We formalise Kleene algebra with tests (KAT) and demonic refinement
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<h1 >
<span class='first'>K</span>leene <span class='first'>A</span>lgebra <span class='first'>W</span>ith <span class='first'>T</span>ests and <span class='first'>D</span>emonic <span class='first'>R</span>efinement <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/gomes">Victor B. F. Gomes</a> <a href="http://www.dcs.shef.ac.uk/~victor">🌐</a> and <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">January 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise Kleene algebra with tests (KAT) and demonic refinement
algebra (DRA) in Isabelle/HOL. KAT is relevant for program verification
and correctness proofs in the partial correctness setting. While DRA
targets similar applications in the context of total correctness. Our
formalisation contains the two most important models of these algebras:
binary relations in the case of KAT and predicate transformers in the
case of DRA. In addition, we derive the inference rules for Hoare logic
in KAT and its relational model and present a simple formally verified
program verification tool prototype based on the algebraic approach.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session KAT_and_DRA</h3>
<ul>
<li><a href="../theories/kat_and_dra/#Test_Dioid">Test_Dioid</a></li>
<li><a href="../theories/kat_and_dra/#Conway_Tests">Conway_Tests</a></li>
<li><a href="../theories/kat_and_dra/#KAT">KAT</a></li>
<li><a href="../theories/kat_and_dra/#DRAT">DRAT</a></li>
<li><a href="../theories/kat_and_dra/#DRA_Models">DRA_Models</a></li>
<li><a href="../theories/kat_and_dra/#KAT_Models">KAT_Models</a></li>
<li><a href="../theories/kat_and_dra/#FolkTheorem">FolkTheorem</a></li>
<li><a href="../theories/kat_and_dra/#PHL_KAT">PHL_KAT</a></li>
<li><a href="../theories/kat_and_dra/#PHL_DRAT">PHL_DRAT</a></li>
<li><a href="../theories/kat_and_dra/#KAT2">KAT2</a></li>
<li><a href="../theories/kat_and_dra/#DRAT2">DRAT2</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li><li><a href="../entries/Algebraic_VCs.html">Program Construction and Verification Components Based on Kleene Algebra</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Zeta_3_Irrational.html">The Irrationality of ζ(3)</a></li>
<li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li>
<li><a href="../entries/Imperative_Insertion_Sort.html">Imperative Insertion Sort</a></li>
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<p style="display:none;" id="bibtex-filename">KAT_and_DRA-AFP</p><pre id="copy-text">@article{KAT_and_DRA-AFP,
author = {Alasdair Armstrong and Victor B. F. Gomes and Georg Struth},
title = {Kleene Algebra with Tests and Demonic Refinement Algebras},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/KAT_and_DRA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-KAT_and_DRA-2014-01-29.tar.gz">Jan 29, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/KBPs.html b/web/entries/KBPs.html
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<h1 >
<span class='first'>K</span>nowledge-<span class='first'>B</span>ased <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">May 17, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Knowledge-based programs (KBPs) are a formalism for directly relating agents' knowledge and behaviour. Here we present a general scheme for compiling KBPs to executable automata with a proof of correctness in Isabelle/HOL. We develop the algorithm top-down, using Isabelle's locale mechanism to structure these proofs, and show that two classic examples can be synthesised using Isabelle's code generator.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 6, 2012</dt>
<dd>Add some more views and revive the code generation.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session KBPs</h3>
<ul>
<li><a href="../theories/kbps/#Extra">Extra</a></li>
<li><a href="../theories/kbps/#List_local">List_local</a></li>
<li><a href="../theories/kbps/#Kripke">Kripke</a></li>
<li><a href="../theories/kbps/#Traces">Traces</a></li>
<li><a href="../theories/kbps/#KBPs">KBPs</a></li>
<li><a href="../theories/kbps/#KBPsAuto">KBPsAuto</a></li>
<li><a href="../theories/kbps/#DFS">DFS</a></li>
<li><a href="../theories/kbps/#MapOps">MapOps</a></li>
<li><a href="../theories/kbps/#KBPsAlg">KBPsAlg</a></li>
<li><a href="../theories/kbps/#ODList">ODList</a></li>
<li><a href="../theories/kbps/#Eval">Eval</a></li>
<li><a href="../theories/kbps/#Trie2">Trie2</a></li>
<li><a href="../theories/kbps/#ClockView">ClockView</a></li>
<li><a href="../theories/kbps/#SPRView">SPRView</a></li>
<li><a href="../theories/kbps/#SPRViewDet">SPRViewDet</a></li>
<li><a href="../theories/kbps/#SPRViewNonDet">SPRViewNonDet</a></li>
<li><a href="../theories/kbps/#SPRViewNonDetIndInit">SPRViewNonDetIndInit</a></li>
<li><a href="../theories/kbps/#SPRViewSingle">SPRViewSingle</a></li>
<li><a href="../theories/kbps/#Views">Views</a></li>
<li><a href="../theories/kbps/#MuddyChildren">MuddyChildren</a></li>
<li><a href="../theories/kbps/#Robot">Robot</a></li>
<li><a href="../theories/kbps/#Examples">Examples</a></li>
<li><a href="../theories/kbps/#KBPs_Main">KBPs_Main</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li><li><a href="../entries/Trie.html">Trie</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL_to_DRA.html">Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</a></li></ul>
</div>
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<li><a href="../entries/Lazy_Case.html">Lazifying case constants</a></li>
<li><a href="../entries/Finger-Trees.html">Finger Trees</a></li>
<li><a href="../entries/Presburger-Automata.html">Formalizing the Logic-Automaton Connection</a></li>
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<p style="display:none;" id="bibtex-filename">KBPs-AFP</p><pre id="copy-text">@article{KBPs-AFP,
author = {Peter Gammie},
title = {Knowledge-based programs},
journal = {Archive of Formal Proofs},
month = {May},
year = {2011},
note = {\url{https://isa-afp.org/entries/KBPs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-KBPs-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-KBPs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-KBPs-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-KBPs-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-KBPs-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-KBPs-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-KBPs-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-KBPs-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-KBPs-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-KBPs-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
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</li><li>
<a href="https://www.isa-afp.org/release/afp-KBPs-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-KBPs-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-KBPs-2011-05-19.tar.gz">May 19, 2011</a>: Isabelle2011
</li></ul>
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<h1 >
<span class='first'>M</span>ultidimensional <span class='first'>B</span>inary <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/rau">Martin Rau</a>
</p>
<p class="date">May 30, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a formalization of multidimensional binary trees,
also known as k-d trees. It includes a balanced build algorithm as
well as the nearest neighbor algorithm and the range search algorithm.
It is based on the papers <a
href="https://dl.acm.org/citation.cfm?doid=361002.361007">Multidimensional
binary search trees used for associative searching</a> and <a
href="https://dl.acm.org/citation.cfm?doid=355744.355745">
An Algorithm for Finding Best Matches in Logarithmic Expected
Time</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 15, 2020</dt>
<dd>Change representation of k-dimensional points from 'list' to
HOL-Analysis.Finite_Cartesian_Product 'vec'. Update proofs
to incorporate HOL-Analysis 'dist' and 'cbox' primitives.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session KD_Tree</h3>
<ul>
<li><a href="../theories/kd_tree/#KD_Tree">KD_Tree</a></li>
<li><a href="../theories/kd_tree/#Build">Build</a></li>
<li><a href="../theories/kd_tree/#Range_Search">Range_Search</a></li>
<li><a href="../theories/kd_tree/#Nearest_Neighbors">Nearest_Neighbors</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Median_Of_Medians_Selection.html">The Median-of-Medians Selection Algorithm</a></li></ul>
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<p style="display:none;" id="bibtex-filename">KD_Tree-AFP</p><pre id="copy-text">@article{KD_Tree-AFP,
author = {Martin Rau},
title = {Multidimensional Binary Search Trees},
journal = {Archive of Formal Proofs},
month = {May},
year = {2019},
note = {\url{https://isa-afp.org/entries/KD_Tree.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Key_Agreement_Strong_Adversaries.html b/web/entries/Key_Agreement_Strong_Adversaries.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Refining Authenticated Key Agreement with Strong Adversaries - Archive of Formal Proofs</title><meta name="description" content="We develop a family of key agreement protocols that are correct by
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<h1 >
<span class='first'>R</span>efining <span class='first'>A</span>uthenticated <span class='first'>K</span>ey <span class='first'>A</span>greement <span class='first'>W</span>ith <span class='first'>S</span>trong <span class='first'>A</span>dversaries</h1>
<div>
<p><a href="../authors/lallemand">Joseph Lallemand</a> <a class="obfuscated" data="eyJob3N0IjpbImxvcmlhIiwiZnIiXSwidXNlciI6WyJqb3NlcGgiLCJsYWxsZW1hbmQiXX0=">📧</a> and <a href="../authors/sprenger">Christoph Sprenger</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInNwcmVuZ2VyIl19">📧</a>
</p>
<p class="date">January 31, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop a family of key agreement protocols that are correct by
construction. Our work substantially extends prior work on developing
security protocols by refinement. First, we strengthen the adversary
by allowing him to compromise different resources of protocol
participants, such as their long-term keys or their session keys. This
enables the systematic development of protocols that ensure strong
properties such as perfect forward secrecy. Second, we broaden the
class of protocols supported to include those with non-atomic keys and
equationally defined cryptographic operators. We use these extensions
to develop key agreement protocols including signed Diffie-Hellman and
the core of IKEv1 and SKEME.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Key_Agreement_Strong_Adversaries</h3>
<ul>
<li><a href="../theories/key_agreement_strong_adversaries/#Infra">Infra</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Refinement">Refinement</a></li>
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<li><a href="../theories/key_agreement_strong_adversaries/#IK">IK</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Secrecy">Secrecy</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#AuthenticationN">AuthenticationN</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#AuthenticationI">AuthenticationI</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Runs">Runs</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Channels">Channels</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Payloads">Payloads</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Implem">Implem</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Implem_lemmas">Implem_lemmas</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Implem_symmetric">Implem_symmetric</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#Implem_asymmetric">Implem_asymmetric</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#pfslvl1">pfslvl1</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#pfslvl2">pfslvl2</a></li>
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<li><a href="../theories/key_agreement_strong_adversaries/#sklvl3">sklvl3</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#sklvl3_asymmetric">sklvl3_asymmetric</a></li>
<li><a href="../theories/key_agreement_strong_adversaries/#sklvl3_symmetric">sklvl3_symmetric</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Key_Agreement_Strong_Adversaries-AFP</p><pre id="copy-text">@article{Key_Agreement_Strong_Adversaries-AFP,
author = {Joseph Lallemand and Christoph Sprenger},
title = {Refining Authenticated Key Agreement with Strong Adversaries},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/Key_Agreement_Strong_Adversaries.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Khovanskii_Theorem.html b/web/entries/Khovanskii_Theorem.html
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@@ -1,179 +1,184 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Khovanskii&#x27;s Theorem - Archive of Formal Proofs</title><meta name="description" content="We formalise the proof of an important theorem in additive
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<h1 >
<span class='first'>K</span>hovanskii&#x27;s <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
</p>
<p class="date">September 2, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise the proof of an important theorem in additive
combinatorics due to Khovanskii, attesting that the cardinality of the
set of all sums of $n$ many elements of $A$, where $A$ is a finite
subset of an abelian group, is a polynomial in $n$ for all
sufficiently large $n$. We follow a proof due to Nathanson and Ruzsa
as presented in the notes “Introduction to Additive Combinatorics” by
Timothy Gowers for the University of Cambridge.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Khovanskii_Theorem</h3>
<ul>
<li><a href="../theories/khovanskii_theorem/#FiniteProduct">FiniteProduct</a></li>
<li><a href="../theories/khovanskii_theorem/#Khovanskii">Khovanskii</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bernoulli.html">Bernoulli Numbers</a></li><li><a href="../entries/Jacobson_Basic_Algebra.html">A Case Study in Basic Algebra</a></li><li><a href="../entries/Pluennecke_Ruzsa_Inequality.html">The Plünnecke-Ruzsa Inequality</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Padic_Ints.html">Hensel&rsquo;s Lemma for the p-adic Integers</a></li>
<li><a href="../entries/Banach_Steinhaus.html">Banach-Steinhaus Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Khovanskii_Theorem-AFP</p><pre id="copy-text">@article{Khovanskii_Theorem-AFP,
author = {Angeliki Koutsoukou-Argyraki and Lawrence C. Paulson},
title = {Khovanskii&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Khovanskii_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Khovanskii_Theorem-2022-09-07.tar.gz">Sep 7, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Kleene_Algebra.html b/web/entries/Kleene_Algebra.html
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<h1 >
<span class='first'>K</span>leene <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a> and <a href="../authors/weber">Tjark Weber</a> <a href="http://user.it.uu.se/~tjawe125/">🌐</a>
</p>
<p class="date">January 15, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These files contain a formalisation of variants of Kleene algebras and
their most important models as axiomatic type classes in Isabelle/HOL.
Kleene algebras are foundational structures in computing with
applications ranging from automata and language theory to computational
modeling, program construction and verification.
<p>
We start with formalising dioids, which are additively idempotent
semirings, and expand them by axiomatisations of the Kleene star for
finite iteration and an omega operation for infinite iteration. We
show that powersets over a given monoid, (regular) languages, sets of
paths in a graph, sets of computation traces, binary relations and
formal power series form Kleene algebras, and consider further models
based on lattices, max-plus semirings and min-plus semirings. We also
demonstrate that dioids are closed under the formation of matrices
(proofs for Kleene algebras remain to be completed).
<p>
On the one hand we have aimed at a reference formalisation of variants
of Kleene algebras that covers a wide range of variants and the core
theorems in a structured and modular way and provides readable proofs
at text book level. On the other hand, we intend to use this algebraic
hierarchy and its models as a generic algebraic middle-layer from which
programming applications can quickly be explored, implemented and verified.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Kleene_Algebra</h3>
<ul>
<li><a href="../theories/kleene_algebra/#Signatures">Signatures</a></li>
<li><a href="../theories/kleene_algebra/#Dioid">Dioid</a></li>
<li><a href="../theories/kleene_algebra/#Dioid_Models">Dioid_Models</a></li>
<li><a href="../theories/kleene_algebra/#Matrix">Matrix</a></li>
<li><a href="../theories/kleene_algebra/#Conway">Conway</a></li>
<li><a href="../theories/kleene_algebra/#Kleene_Algebra">Kleene_Algebra</a></li>
<li><a href="../theories/kleene_algebra/#Kleene_Algebra_Models">Kleene_Algebra_Models</a></li>
<li><a href="../theories/kleene_algebra/#Omega_Algebra">Omega_Algebra</a></li>
<li><a href="../theories/kleene_algebra/#Omega_Algebra_Models">Omega_Algebra_Models</a></li>
<li><a href="../theories/kleene_algebra/#DRA">DRA</a></li>
<li><a href="../theories/kleene_algebra/#PHL_KA">PHL_KA</a></li>
<li><a href="../theories/kleene_algebra/#PHL_DRA">PHL_DRA</a></li>
<li><a href="../theories/kleene_algebra/#Finite_Suprema">Finite_Suprema</a></li>
<li><a href="../theories/kleene_algebra/#Formal_Power_Series">Formal_Power_Series</a></li>
<li><a href="../theories/kleene_algebra/#Inf_Matrix">Inf_Matrix</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Quantales.html">Quantales</a></li><li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li><li><a href="../entries/Multirelations.html">Binary Multirelations</a></li><li><a href="../entries/Regular_Algebras.html">Regular Algebras</a></li><li><a href="../entries/Relation_Algebra.html">Relation Algebra</a></li><li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Kleene_Algebra-AFP</p><pre id="copy-text">@article{Kleene_Algebra-AFP,
author = {Alasdair Armstrong and Georg Struth and Tjark Weber},
title = {Kleene Algebra},
journal = {Archive of Formal Proofs},
month = {January},
year = {2013},
note = {\url{https://isa-afp.org/entries/Kleene_Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Kleene_Algebra-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Kleene_Algebra-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Kleene_Algebra-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Knights_Tour.html b/web/entries/Knights_Tour.html
--- a/web/entries/Knights_Tour.html
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@@ -1,167 +1,174 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Knight&#39;s Tour Revisited Revisited - Archive of Formal Proofs</title><meta name="description" content="This is a formalization of the article Knight&#39;s Tour Revisited by Cull and De Curtins where they prove the existence of a Knight&#39;s path for arbitrary n..."><meta property="og:title" content="Knight&#39;s Tour Revisited Revisited" />
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<h1 >
<span class='first'>K</span>night's <span class='first'>T</span>our <span class='first'>R</span>evisited <span class='first'>R</span>evisited</h1>
<div>
<p><a href="../authors/koller">Lukas Koller</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsibHVrYXMiLCJrb2xsZXIiXX0=">📧</a>
</p>
<p class="date">January 4, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalization of the article <i>Knight's Tour Revisited</i> by
Cull and De Curtins where they prove the existence of a Knight's
path for arbitrary <i>n &times; m</i>-boards with <i>min(n,m) &ge;
5</i>. If <i>n &middot; m</i> is even, then there exists a Knight's
circuit. A Knight's Path is a sequence of moves of a Knight on a
chessboard s.t. the Knight visits every square of a chessboard
exactly once. Finding a Knight's path is a an instance of the
Hamiltonian path problem. A Knight's circuit is a Knight's path,
where additionally the Knight can move from the last square to the
first square of the path, forming a loop. During the formalization
two mistakes in the original proof were discovered. These mistakes
are corrected in this formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Knights_Tour</h3>
<ul>
<li><a href="../theories/knights_tour/#KnightsTour">KnightsTour</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Knights_Tour-AFP</p><pre id="copy-text">@article{Knights_Tour-AFP,
author = {Lukas Koller},
title = {Knight&#39;s Tour Revisited Revisited},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Knights_Tour.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Knights_Tour-2022-01-06.tar.gz">Jan 6, 2022</a>: Isabelle2021-1
+ </li><li>
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<h1 >
<span class='first'>K</span>not <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/prathamesh">T.V.H. Prathamesh</a> <a class="obfuscated" data="eyJob3N0IjpbImltc2MiLCJyZXMiLCJpbiJdLCJ1c2VyIjpbInByYXRoYW1lc2giXX0=">📧</a>
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<p class="date">January 20, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work contains a formalization of some topics in knot theory.
The concepts that were formalized include definitions of tangles, links,
framed links and link/tangle equivalence. The formalization is based on a
formulation of links in terms of tangles. We further construct and prove the
invariance of the Bracket polynomial. Bracket polynomial is an invariant of
framed links closely linked to the Jones polynomial. This is perhaps the first
attempt to formalize any aspect of knot theory in an interactive proof assistant.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/topology">Mathematics/Topology</a></li></ul>
<h3>Session Knot_Theory</h3>
<ul>
<li><a href="../theories/knot_theory/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/knot_theory/#Tangles">Tangles</a></li>
<li><a href="../theories/knot_theory/#Tangle_Algebra">Tangle_Algebra</a></li>
<li><a href="../theories/knot_theory/#Tangle_Relation">Tangle_Relation</a></li>
<li><a href="../theories/knot_theory/#Tangle_Moves">Tangle_Moves</a></li>
<li><a href="../theories/knot_theory/#Link_Algebra">Link_Algebra</a></li>
<li><a href="../theories/knot_theory/#Example">Example</a></li>
<li><a href="../theories/knot_theory/#Kauffman_Matrix">Kauffman_Matrix</a></li>
<li><a href="../theories/knot_theory/#Computations">Computations</a></li>
<li><a href="../theories/knot_theory/#Linkrel_Kauffman">Linkrel_Kauffman</a></li>
<li><a href="../theories/knot_theory/#Kauffman_Invariance">Kauffman_Invariance</a></li>
<li><a href="../theories/knot_theory/#Knot_Theory">Knot_Theory</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Matrix_Tensor.html">Tensor Product of Matrices</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Knot_Theory-AFP</p><pre id="copy-text">@article{Knot_Theory-AFP,
author = {T.V.H. Prathamesh},
title = {Knot Theory},
journal = {Archive of Formal Proofs},
month = {January},
year = {2016},
note = {\url{https://isa-afp.org/entries/Knot_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Knuth_Bendix_Order.html b/web/entries/Knuth_Bendix_Order.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>K</span>nuth–<span class='first'>B</span>endix <span class='first'>O</span>rders</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">May 13, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We define a generalized version of Knuth&ndash;Bendix orders,
including subterm coefficient functions. For these orders we formalize
several properties such as strong normalization, the subterm property,
closure properties under substitutions and contexts, as well as ground
totality.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Knuth_Bendix_Order</h3>
<ul>
<li><a href="../theories/knuth_bendix_order/#Order_Pair">Order_Pair</a></li>
<li><a href="../theories/knuth_bendix_order/#Lexicographic_Extension">Lexicographic_Extension</a></li>
<li><a href="../theories/knuth_bendix_order/#Subterm_and_Context">Subterm_and_Context</a></li>
<li><a href="../theories/knuth_bendix_order/#Term_Aux">Term_Aux</a></li>
<li><a href="../theories/knuth_bendix_order/#KBO">KBO</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Order_Terms.html">First-Order Terms</a></li><li><a href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Regular_Tree_Relations.html">Regular Tree Relations</a></li><li><a href="../entries/Weighted_Path_Order.html">A Formalization of Weighted Path Orders and Recursive Path Orders</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Knuth_Bendix_Order-AFP</p><pre id="copy-text">@article{Knuth_Bendix_Order-AFP,
author = {Christian Sternagel and René Thiemann},
title = {A Formalization of Knuth–Bendix Orders},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Knuth_Bendix_Order.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Knuth_Morris_Pratt.html b/web/entries/Knuth_Morris_Pratt.html
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>tring <span class='first'>S</span>earch <span class='first'>A</span>lgorithm by <span class='first'>K</span>nuth, <span class='first'>M</span>orris and <span class='first'>P</span>ratt</h1>
<div>
<p><a href="../authors/hellauer">Fabian Hellauer</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJoZWxsYXVlciJdfQ==">📧</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">December 18, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Knuth-Morris-Pratt algorithm is often used to show that the
problem of finding a string <i>s</i> in a text
<i>t</i> can be solved deterministically in
<i>O(|s| + |t|)</i> time. We use the Isabelle
Refinement Framework to formulate and verify the algorithm. Via
refinement, we apply some optimisations and finally use the
<em>Sepref</em> tool to obtain executable code in
<em>Imperative/HOL</em>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Knuth_Morris_Pratt</h3>
<ul>
<li><a href="../theories/knuth_morris_pratt/#KMP">KMP</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<li><a href="../entries/Imperative_Insertion_Sort.html">Imperative Insertion Sort</a></li>
<li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li>
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<p style="display:none;" id="bibtex-filename">Knuth_Morris_Pratt-AFP</p><pre id="copy-text">@article{Knuth_Morris_Pratt-AFP,
author = {Fabian Hellauer and Peter Lammich},
title = {The string search algorithm by Knuth, Morris and Pratt},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/Knuth_Morris_Pratt.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Knuth_Morris_Pratt-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Knuth_Morris_Pratt-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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<h1 >
<span class='first'>T</span>he <span class='first'>K</span>önigsberg <span class='first'>B</span>ridge <span class='first'>P</span>roblem and the <span class='first'>F</span>riendship <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">July 19, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a formalization of undirected graphs and simple graphs, which are based on Benedikt Nordhoff and Peter Lammich's simple formalization of labelled directed graphs in the archive. Then, with our formalization of graphs, we show both necessary and sufficient conditions for Eulerian trails and circuits as well as the fact that the Königsberg Bridge Problem does not have a solution. In addition, we show the Friendship Theorem in simple graphs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Koenigsberg_Friendship</h3>
<ul>
<li><a href="../theories/koenigsberg_friendship/#MoreGraph">MoreGraph</a></li>
<li><a href="../theories/koenigsberg_friendship/#KoenigsbergBridge">KoenigsbergBridge</a></li>
<li><a href="../theories/koenigsberg_friendship/#FriendshipTheory">FriendshipTheory</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Dijkstra_Shortest_Path.html">Dijkstra&rsquo;s Shortest Path Algorithm</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Koenigsberg_Friendship-AFP</p><pre id="copy-text">@article{Koenigsberg_Friendship-AFP,
author = {Wenda Li},
title = {The Königsberg Bridge Problem and the Friendship Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2013},
note = {\url{https://isa-afp.org/entries/Koenigsberg_Friendship.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Koenigsberg_Friendship-2013-07-26.tar.gz">Jul 26, 2013</a>: Isabelle2013
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diff --git a/web/entries/Kruskal.html b/web/entries/Kruskal.html
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+++ b/web/entries/Kruskal.html
@@ -1,198 +1,200 @@
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<h1 >
<span class='first'>K</span>ruskal's <span class='first'>A</span>lgorithm for <span class='first'>M</span>inimum <span class='first'>S</span>panning <span class='first'>F</span>orest</h1>
<div>
<p><a href="../authors/haslbeckm">Maximilian P. L. Haslbeck</a> <a href="http://in.tum.de/~haslbema/">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/biendarra">Julian Biendarra</a>
</p>
<p class="date">February 14, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization defines a greedy algorithm for finding
a minimum weight basis on a weighted matroid and proves its
correctness. This algorithm is an abstract version of Kruskal's
algorithm. We interpret the abstract algorithm for the cycle matroid
(i.e. forests in a graph) and refine it to imperative executable code
using an efficient union-find data structure. Our formalization can
be instantiated for different graph representations. We provide
instantiations for undirected graphs and symmetric directed graphs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Kruskal</h3>
<ul>
<li><a href="../theories/kruskal/#Kruskal_Misc">Kruskal_Misc</a></li>
<li><a href="../theories/kruskal/#SeprefUF">SeprefUF</a></li>
<li><a href="../theories/kruskal/#MinWeightBasis">MinWeightBasis</a></li>
<li><a href="../theories/kruskal/#Kruskal">Kruskal</a></li>
<li><a href="../theories/kruskal/#Kruskal_Refine">Kruskal_Refine</a></li>
<li><a href="../theories/kruskal/#Kruskal_Impl">Kruskal_Impl</a></li>
<li><a href="../theories/kruskal/#UGraph">UGraph</a></li>
<li><a href="../theories/kruskal/#UGraph_Impl">UGraph_Impl</a></li>
<li><a href="../theories/kruskal/#Graph_Definition">Graph_Definition</a></li>
<li><a href="../theories/kruskal/#Graph_Definition_Aux">Graph_Definition_Aux</a></li>
<li><a href="../theories/kruskal/#Graph_Definition_Impl">Graph_Definition_Impl</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Matroids.html">Matroids</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Kruskal-AFP</p><pre id="copy-text">@article{Kruskal-AFP,
author = {Maximilian P. L. Haslbeck and Peter Lammich and Julian Biendarra},
title = {Kruskal&#39;s Algorithm for Minimum Spanning Forest},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/Kruskal.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>K</span>uratowski <span class='first'>C</span>losure-<span class='first'>C</span>omplement <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a> and <a href="../authors/gioiosa">Gianpaolo Gioiosa</a>
</p>
<p class="date">October 26, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We discuss a topological curiosity discovered by Kuratowski (1922):
the fact that the number of distinct operators on a topological space
generated by compositions of closure and complement never exceeds 14,
and is exactly 14 in the case of R. In addition, we prove a theorem
due to Chagrov (1982) that classifies topological spaces according to
the number of such operators they support.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/topology">Mathematics/Topology</a></li></ul>
<h3>Session Kuratowski_Closure_Complement</h3>
<ul>
<li><a href="../theories/kuratowski_closure_complement/#KuratowskiClosureComplementTheorem">KuratowskiClosureComplementTheorem</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Kuratowski_Closure_Complement-AFP</p><pre id="copy-text">@article{Kuratowski_Closure_Complement-AFP,
author = {Peter Gammie and Gianpaolo Gioiosa},
title = {The Kuratowski Closure-Complement Theorem},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Kuratowski_Closure_Complement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Kuratowski_Closure_Complement-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/LLL_Basis_Reduction.html b/web/entries/LLL_Basis_Reduction.html
--- a/web/entries/LLL_Basis_Reduction.html
+++ b/web/entries/LLL_Basis_Reduction.html
@@ -1,207 +1,209 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A verified LLL algorithm - Archive of Formal Proofs</title><meta name="description" content="The Lenstra-Lenstra-Lovász basis reduction algorithm, also known as
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>L</span><span class='first'>L</span><span class='first'>L</span> <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/bottesch">Ralph Bottesch</a>, <a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a>, <a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a>, <a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a href="https://sjcjoosten.nl/">🌐</a>, <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a> and <a href="../authors/yamada">Akihisa Yamada</a>
</p>
<p class="date">February 2, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Lenstra-Lenstra-Lovász basis reduction algorithm, also known as
LLL algorithm, is an algorithm to find a basis with short, nearly
orthogonal vectors of an integer lattice. Thereby, it can also be seen
as an approximation to solve the shortest vector problem (SVP), which
is an NP-hard problem, where the approximation quality solely depends
on the dimension of the lattice, but not the lattice itself. The
algorithm also possesses many applications in diverse fields of
computer science, from cryptanalysis to number theory, but it is
specially well-known since it was used to implement the first
polynomial-time algorithm to factor polynomials. In this work we
present the first mechanized soundness proof of the LLL algorithm to
compute short vectors in lattices. The formalization follows a
textbook by von zur Gathen and Gerhard.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 25, 2018</dt>
<dd>Integrated much faster LLL implementation based on integer arithmetic (Bottesch, Haslbeck, Thiemann)</dd><dt>April 16, 2018</dt>
<dd>Integrated formal complexity bounds (Haslbeck, Thiemann)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session LLL_Basis_Reduction</h3>
<ul>
<li><a href="../theories/lll_basis_reduction/#Missing_Lemmas">Missing_Lemmas</a></li>
<li><a href="../theories/lll_basis_reduction/#More_IArray">More_IArray</a></li>
<li><a href="../theories/lll_basis_reduction/#Norms">Norms</a></li>
<li><a href="../theories/lll_basis_reduction/#Int_Rat_Operations">Int_Rat_Operations</a></li>
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<li><a href="../theories/lll_basis_reduction/#List_Representation">List_Representation</a></li>
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<li><a href="../theories/lll_basis_reduction/#Gram_Schmidt_Int">Gram_Schmidt_Int</a></li>
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<li><a href="../theories/lll_basis_reduction/#LLL_Complexity">LLL_Complexity</a></li>
<li><a href="../theories/lll_basis_reduction/#LLL_Number_Bounds">LLL_Number_Bounds</a></li>
<li><a href="../theories/lll_basis_reduction/#LLL_Certification">LLL_Certification</a></li>
<li><a href="../theories/lll_basis_reduction/#FPLLL_Solver">FPLLL_Solver</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li><li><a href="../entries/Linear_Inequalities.html">Linear Inequalities</a></li><li><a href="../entries/LLL_Factorization.html">A verified factorization algorithm for integer polynomials with polynomial complexity</a></li></ul>
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<p style="display:none;" id="bibtex-filename">LLL_Basis_Reduction-AFP</p><pre id="copy-text">@article{LLL_Basis_Reduction-AFP,
author = {Ralph Bottesch and Jose Divasón and Max W. Haslbeck and Sebastiaan J. C. Joosten and René Thiemann and Akihisa Yamada},
title = {A verified LLL algorithm},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/LLL_Basis_Reduction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-LLL_Basis_Reduction-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/LLL_Factorization.html b/web/entries/LLL_Factorization.html
--- a/web/entries/LLL_Factorization.html
+++ b/web/entries/LLL_Factorization.html
@@ -1,203 +1,205 @@
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>F</span>actorization <span class='first'>A</span>lgorithm for <span class='first'>I</span>nteger <span class='first'>P</span>olynomials <span class='first'>W</span>ith <span class='first'>P</span>olynomial <span class='first'>C</span>omplexity</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a>, <a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a href="https://sjcjoosten.nl/">🌐</a>, <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInRycyIsImNtIiwiaXMiLCJuYWdveWEtdSIsImFjIiwianAiXSwidXNlciI6WyJheWFtYWRhIl19">📧</a>
</p>
<p class="date">February 6, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Short vectors in lattices and factors of integer polynomials are
related. Each factor of an integer polynomial belongs to a certain
lattice. When factoring polynomials, the condition that we are looking
for an irreducible polynomial means that we must look for a small
element in a lattice, which can be done by a basis reduction
algorithm. In this development we formalize this connection and
thereby one main application of the LLL basis reduction algorithm: an
algorithm to factor square-free integer polynomials which runs in
polynomial time. The work is based on our previous
Berlekamp–Zassenhaus development, where the exponential reconstruction
phase has been replaced by the polynomial-time basis reduction
algorithm. Thanks to this formalization we found a serious flaw in a
textbook.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session LLL_Factorization</h3>
<ul>
<li><a href="../theories/lll_factorization/#Factor_Bound_2">Factor_Bound_2</a></li>
<li><a href="../theories/lll_factorization/#Missing_Dvd_Int_Poly">Missing_Dvd_Int_Poly</a></li>
<li><a href="../theories/lll_factorization/#LLL_Factorization_Impl">LLL_Factorization_Impl</a></li>
<li><a href="../theories/lll_factorization/#LLL_Factorization">LLL_Factorization</a></li>
<li><a href="../theories/lll_factorization/#Sub_Sums">Sub_Sums</a></li>
<li><a href="../theories/lll_factorization/#Factorization_Algorithm_16_22">Factorization_Algorithm_16_22</a></li>
<li><a href="../theories/lll_factorization/#Modern_Computer_Algebra_Problem">Modern_Computer_Algebra_Problem</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/LLL_Basis_Reduction.html">A verified LLL algorithm</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li>
<li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li>
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<p style="display:none;" id="bibtex-filename">LLL_Factorization-AFP</p><pre id="copy-text">@article{LLL_Factorization-AFP,
author = {Jose Divasón and Sebastiaan J. C. Joosten and René Thiemann and Akihisa Yamada},
title = {A verified factorization algorithm for integer polynomials with polynomial complexity},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/LLL_Factorization.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span><span class='first'>O</span><span class='first'>F</span><span class='first'>T</span> — <span class='first'>V</span>erified <span class='first'>M</span>igration of <span class='first'>L</span>inux <span class='first'>F</span>irewalls to <span class='first'>S</span><span class='first'>D</span><span class='first'>N</span></h1>
<div>
<p><a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>
</p>
<p class="date">October 21, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present LOFT — Linux firewall OpenFlow Translator, a system that
transforms the main routing table and FORWARD chain of iptables of a
Linux-based firewall into a set of static OpenFlow rules. Our
implementation is verified against a model of a simplified Linux-based
router and we can directly show how much of the original functionality
is preserved.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session LOFT</h3>
<ul>
<li><a href="../theories/loft/#OpenFlow_Helpers">OpenFlow_Helpers</a></li>
<li><a href="../theories/loft/#Sort_Descending">Sort_Descending</a></li>
<li><a href="../theories/loft/#List_Group">List_Group</a></li>
<li><a href="../theories/loft/#OpenFlow_Matches">OpenFlow_Matches</a></li>
<li><a href="../theories/loft/#OpenFlow_Action">OpenFlow_Action</a></li>
<li><a href="../theories/loft/#Semantics_OpenFlow">Semantics_OpenFlow</a></li>
<li><a href="../theories/loft/#OpenFlow_Serialize">OpenFlow_Serialize</a></li>
<li><a href="../theories/loft/#Featherweight_OpenFlow_Comparison">Featherweight_OpenFlow_Comparison</a></li>
<li><a href="../theories/loft/#LinuxRouter_OpenFlow_Translation">LinuxRouter_OpenFlow_Translation</a></li>
<li><a href="../theories/loft/#OF_conv_test">OF_conv_test</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Iptables_Semantics.html">Iptables Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">LOFT-AFP</p><pre id="copy-text">@article{LOFT-AFP,
author = {Julius Michaelis and Cornelius Diekmann},
title = {LOFT — Verified Migration of Linux Firewalls to SDN},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/LOFT.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>D</span>uality of <span class='first'>L</span>inear <span class='first'>P</span>rogramming</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">February 3, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the weak and strong duality theorems of linear
programming. For the strong duality theorem we provide three
sufficient preconditions: both the primal problem and the dual problem
are satisfiable, the primal problem is satisfiable and bounded, or the
dual problem is satisfiable and bounded. The proofs are based on an
existing formalization of Farkas' Lemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session LP_Duality</h3>
<ul>
<li><a href="../theories/lp_duality/#Minimum_Maximum">Minimum_Maximum</a></li>
<li><a href="../theories/lp_duality/#LP_Duality">LP_Duality</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Linear_Inequalities.html">Linear Inequalities</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
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<p style="display:none;" id="bibtex-filename">LP_Duality-AFP</p><pre id="copy-text">@article{LP_Duality-AFP,
author = {René Thiemann},
title = {Duality of Linear Programming},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/LP_Duality.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LP_Duality-2022-02-06.tar.gz">Feb 6, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>L</span>inear <span class='first'>T</span>emporal <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/sickert">Salomon Sickert</a> <a href="https://www7.in.tum.de/~sickert">🌐</a>
with contributions from <a href="../authors/seidl">Benedikt Seidl</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiYmVuZWRpa3QiLCJzZWlkbCJdfQ==">📧</a>
</p>
<p class="date">March 1, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory provides a formalisation of linear temporal logic (LTL)
and unifies previous formalisations within the AFP. This entry
establishes syntax and semantics for this logic and decouples it from
existing entries, yielding a common environment for theories reasoning
about LTL. Furthermore a parser written in SML and an executable
simplifier are provided.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 12, 2019</dt>
<dd>Support for additional operators, implementation of common equivalence relations,
definition of syntactic fragments of LTL and the minimal disjunctive normal form. <br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session LTL</h3>
<ul>
<li><a href="../theories/ltl/#LTL">LTL</a></li>
<li><a href="../theories/ltl/#Rewriting">Rewriting</a></li>
<li><a href="../theories/ltl/#Equivalence_Relations">Equivalence_Relations</a></li>
<li><a href="../theories/ltl/#Disjunctive_Normal_Form">Disjunctive_Normal_Form</a></li>
<li><a href="../theories/ltl/#Code_Equations">Code_Equations</a></li>
<li><a href="../theories/ltl/#Example">Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Boolean_Expression_Checkers.html">Boolean Expression Checkers</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL_Normal_Form.html">An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation</a></li><li><a href="../entries/LTL_Master_Theorem.html">A Compositional and Unified Translation of LTL into ω-Automata</a></li><li><a href="../entries/LTL_to_DRA.html">Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</a></li><li><a href="../entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></li><li><a href="../entries/Promela.html">Promela Formalization</a></li><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MFOTL_Monitor.html">Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</a></li>
<li><a href="../entries/LTL_Master_Theorem.html">A Compositional and Unified Translation of LTL into ω-Automata</a></li>
<li><a href="../entries/RefinementReactive.html">Formalization of Refinement Calculus for Reactive Systems</a></li>
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<p style="display:none;" id="bibtex-filename">LTL-AFP</p><pre id="copy-text">@article{LTL-AFP,
author = {Salomon Sickert},
title = {Linear Temporal Logic},
journal = {Archive of Formal Proofs},
month = {March},
year = {2016},
note = {\url{https://isa-afp.org/entries/LTL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-LTL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-LTL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LTL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-LTL-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-LTL-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-LTL-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Compositional and Unified Translation of LTL into ω-Automata - Archive of Formal Proofs</title><meta name="description" content="We present a formalisation of the unified translation approach of linear temporal logic (LTL) into ω-automata from [1]. This approach decomposes LTL..."><meta property="og:title" content="A Compositional and Unified Translation of LTL into ω-Automata" />
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>ompositional and <span class='first'>U</span>nified <span class='first'>T</span>ranslation of <span class='first'>L</span><span class='first'>T</span><span class='first'>L</span> <span class='first'>I</span>nto Ω-<span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/seidl">Benedikt Seidl</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiYmVuZWRpa3QiLCJzZWlkbCJdfQ==">📧</a> and <a href="../authors/sickert">Salomon Sickert</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsicyIsInNpY2tlcnQiXX0=">📧</a>
</p>
<p class="date">April 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalisation of the unified translation approach of
linear temporal logic (LTL) into ω-automata from [1]. This approach
decomposes LTL formulas into ``simple'' languages and allows
a clear separation of concerns: first, we formalise the purely logical
result yielding this decomposition; second, we instantiate this
generic theory to obtain a construction for deterministic
(state-based) Rabin automata (DRA). We extract from this particular
instantiation an executable tool translating LTL to DRAs. To the best
of our knowledge this is the first verified translation from LTL to
DRAs that is proven to be double exponential in the worst case which
asymptotically matches the known lower bound.
<p>
[1] Javier Esparza, Jan Kretínský, Salomon Sickert. One Theorem to Rule Them All:
A Unified Translation of LTL into ω-Automata. LICS 2018</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session LTL_Master_Theorem</h3>
<ul>
<li><a href="../theories/ltl_master_theorem/#Syntactic_Fragments_and_Stability">Syntactic_Fragments_and_Stability</a></li>
<li><a href="../theories/ltl_master_theorem/#After">After</a></li>
<li><a href="../theories/ltl_master_theorem/#Advice">Advice</a></li>
<li><a href="../theories/ltl_master_theorem/#Master_Theorem">Master_Theorem</a></li>
<li><a href="../theories/ltl_master_theorem/#Asymmetric_Master_Theorem">Asymmetric_Master_Theorem</a></li>
<li><a href="../theories/ltl_master_theorem/#Restricted_Master_Theorem">Restricted_Master_Theorem</a></li>
<li><a href="../theories/ltl_master_theorem/#Transition_Functions">Transition_Functions</a></li>
<li><a href="../theories/ltl_master_theorem/#Quotient_Type">Quotient_Type</a></li>
<li><a href="../theories/ltl_master_theorem/#Omega_Words_Fun_Stream">Omega_Words_Fun_Stream</a></li>
<li><a href="../theories/ltl_master_theorem/#DRA_Construction">DRA_Construction</a></li>
<li><a href="../theories/ltl_master_theorem/#DRA_Implementation">DRA_Implementation</a></li>
<li><a href="../theories/ltl_master_theorem/#Extra_Equivalence_Relations">Extra_Equivalence_Relations</a></li>
<li><a href="../theories/ltl_master_theorem/#DRA_Instantiation">DRA_Instantiation</a></li>
<li><a href="../theories/ltl_master_theorem/#Code_Export">Code_Export</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL_Normal_Form.html">An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MFOTL_Monitor.html">Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</a></li>
<li><a href="../entries/RefinementReactive.html">Formalization of Refinement Calculus for Reactive Systems</a></li>
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<p style="display:none;" id="bibtex-filename">LTL_Master_Theorem-AFP</p><pre id="copy-text">@article{LTL_Master_Theorem-AFP,
author = {Benedikt Seidl and Salomon Sickert},
title = {A Compositional and Unified Translation of LTL into ω-Automata},
journal = {Archive of Formal Proofs},
month = {April},
year = {2019},
note = {\url{https://isa-afp.org/entries/LTL_Master_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-LTL_Master_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-LTL_Master_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LTL_Master_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_Master_Theorem-2019-04-17.tar.gz">Apr 17, 2019</a>: Isabelle2018
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<h1 >
<span class='first'>A</span>n <span class='first'>E</span>fficient <span class='first'>N</span>ormalisation <span class='first'>P</span>rocedure for <span class='first'>L</span>inear <span class='first'>T</span>emporal <span class='first'>L</span>ogic: <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>F</span>ormalisation</h1>
<div>
<p><a href="../authors/sickert">Salomon Sickert</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsicyIsInNpY2tlcnQiXX0=">📧</a>
</p>
<p class="date">May 8, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical
theorem stating that every formula of Past LTL (the extension of LTL
with past operators) is equivalent to a formula of the form
$\bigwedge_{i=1}^n \mathbf{G}\mathbf{F} \varphi_i \vee
\mathbf{F}\mathbf{G} \psi_i$, where $\varphi_i$ and $\psi_i$ contain
only past operators. Some years later, Chang, Manna, and Pnueli built
on this result to derive a similar normal form for LTL. Both
normalisation procedures have a non-elementary worst-case blow-up, and
follow an involved path from formulas to counter-free automata to
star-free regular expressions and back to formulas. We improve on both
points. We present an executable formalisation of a direct and purely
syntactic normalisation procedure for LTL yielding a normal form,
comparable to the one by Chang, Manna, and Pnueli, that has only a
single exponential blow-up.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li></ul>
<h3>Session LTL_Normal_Form</h3>
<ul>
<li><a href="../theories/ltl_normal_form/#Normal_Form">Normal_Form</a></li>
<li><a href="../theories/ltl_normal_form/#Normal_Form_Complexity">Normal_Form_Complexity</a></li>
<li><a href="../theories/ltl_normal_form/#Normal_Form_Code_Export">Normal_Form_Code_Export</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li><li><a href="../entries/LTL_Master_Theorem.html">A Compositional and Unified Translation of LTL into ω-Automata</a></li></ul>
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<p style="display:none;" id="bibtex-filename">LTL_Normal_Form-AFP</p><pre id="copy-text">@article{LTL_Normal_Form-AFP,
author = {Salomon Sickert},
title = {An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/LTL_Normal_Form.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-LTL_Normal_Form-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LTL_Normal_Form-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/LTL_to_DRA.html b/web/entries/LTL_to_DRA.html
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<h1 >
<span class='first'>C</span>onverting <span class='first'>L</span>inear <span class='first'>T</span>emporal <span class='first'>L</span>ogic to <span class='first'>D</span>eterministic (<span class='first'>G</span>eneralized) <span class='first'>R</span>abin <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/sickert">Salomon Sickert</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsicyIsInNpY2tlcnQiXX0=">📧</a>
</p>
<p class="date">September 4, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Recently, Javier Esparza and Jan Kretinsky proposed a new method directly translating linear temporal logic (LTL) formulas to deterministic (generalized) Rabin automata. Compared to the existing approaches of constructing a non-deterministic Buechi-automaton in the first step and then applying a determinization procedure (e.g. some variant of Safra's construction) in a second step, this new approach preservers a relation between the formula and the states of the resulting automaton. While the old approach produced a monolithic structure, the new method is compositional. Furthermore, in some cases the resulting automata are much smaller than the automata generated by existing approaches. In order to ensure the correctness of the construction, this entry contains a complete formalisation and verification of the translation. Furthermore from this basis executable code is generated.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 24, 2016</dt>
<dd>Make use of the LTL entry and include the simplifier.</dd><dt>September 23, 2015</dt>
<dd>Enable code export for the eager unfolding optimisation and reduce running time of the generated tool. Moreover, add support for the mlton SML compiler.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session LTL_to_DRA</h3>
<ul>
<li><a href="../theories/ltl_to_dra/#Preliminaries2">Preliminaries2</a></li>
<li><a href="../theories/ltl_to_dra/#Map2">Map2</a></li>
<li><a href="../theories/ltl_to_dra/#Mapping2">Mapping2</a></li>
<li><a href="../theories/ltl_to_dra/#DTS">DTS</a></li>
<li><a href="../theories/ltl_to_dra/#Semi_Mojmir">Semi_Mojmir</a></li>
<li><a href="../theories/ltl_to_dra/#Mojmir">Mojmir</a></li>
<li><a href="../theories/ltl_to_dra/#Rabin">Rabin</a></li>
<li><a href="../theories/ltl_to_dra/#List2">List2</a></li>
<li><a href="../theories/ltl_to_dra/#Mojmir_Rabin">Mojmir_Rabin</a></li>
<li><a href="../theories/ltl_to_dra/#LTL_FGXU">LTL_FGXU</a></li>
<li><a href="../theories/ltl_to_dra/#af">af</a></li>
<li><a href="../theories/ltl_to_dra/#Logical_Characterization">Logical_Characterization</a></li>
<li><a href="../theories/ltl_to_dra/#LTL_Rabin">LTL_Rabin</a></li>
<li><a href="../theories/ltl_to_dra/#LTL_Rabin_Unfold_Opt">LTL_Rabin_Unfold_Opt</a></li>
<li><a href="../theories/ltl_to_dra/#LTL_Compat">LTL_Compat</a></li>
<li><a href="../theories/ltl_to_dra/#LTL_Impl">LTL_Impl</a></li>
<li><a href="../theories/ltl_to_dra/#af_Impl">af_Impl</a></li>
<li><a href="../theories/ltl_to_dra/#Mojmir_Rabin_Impl">Mojmir_Rabin_Impl</a></li>
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<li><a href="../theories/ltl_to_dra/#Export_Code">Export_Code</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Boolean_Expression_Checkers.html">Boolean Expression Checkers</a></li><li><a href="../entries/KBPs.html">Knowledge-based programs</a></li><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<p style="display:none;" id="bibtex-filename">LTL_to_DRA-AFP</p><pre id="copy-text">@article{LTL_to_DRA-AFP,
author = {Salomon Sickert},
title = {Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata},
journal = {Archive of Formal Proofs},
month = {September},
year = {2015},
note = {\url{https://isa-afp.org/entries/LTL_to_DRA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/LTL_to_GBA.html b/web/entries/LTL_to_GBA.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Converting Linear-Time Temporal Logic to Generalized Büchi Automata - Archive of Formal Proofs</title><meta name="description" content="We formalize linear-time temporal logic (LTL) and the algorithm by Gerth et al. to convert LTL formulas to generalized Büchi automata. We also formalize..."><meta property="og:title" content="Converting Linear-Time Temporal Logic to Generalized Büchi Automata" />
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<h1 >
<span class='first'>C</span>onverting <span class='first'>L</span>inear-<span class='first'>T</span>ime <span class='first'>T</span>emporal <span class='first'>L</span>ogic to <span class='first'>G</span>eneralized <span class='first'>B</span>üchi <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/schimpf">Alexander Schimpf</a> <a class="obfuscated" data="eyJob3N0IjpbImluZm9ybWF0aWsiLCJ1bmktZnJlaWJ1cmciLCJkZSJdLCJ1c2VyIjpbInNjaGltcGZhIl19">📧</a> and <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">May 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize linear-time temporal logic (LTL) and the algorithm by Gerth
et al. to convert LTL formulas to generalized Büchi automata.
We also formalize some syntactic rewrite rules that can be applied to
optimize the LTL formula before conversion.
Moreover, we integrate the Stuttering Equivalence AFP-Entry by Stefan
Merz, adapting the lemma that next-free LTL formula cannot distinguish
between stuttering equivalent runs to our setting.
<p>
We use the Isabelle Refinement and Collection framework, as well as the
Autoref tool, to obtain a refined version of our algorithm, from which
efficiently executable code can be extracted.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session LTL_to_GBA</h3>
<ul>
<li><a href="../theories/ltl_to_gba/#LTL_to_GBA">LTL_to_GBA</a></li>
<li><a href="../theories/ltl_to_gba/#LTL_to_GBA_impl">LTL_to_GBA_impl</a></li>
<li><a href="../theories/ltl_to_gba/#All_Of_LTL_to_GBA">All_Of_LTL_to_GBA</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_Automata.html">The CAVA Automata Library</a></li><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li>
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<p style="display:none;" id="bibtex-filename">LTL_to_GBA-AFP</p><pre id="copy-text">@article{LTL_to_GBA-AFP,
author = {Alexander Schimpf and Peter Lammich},
title = {Converting Linear-Time Temporal Logic to Generalized Büchi Automata},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/LTL_to_GBA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-LTL_to_GBA-2014-05-29.tar.gz">May 29, 2014</a>: Isabelle2013-2
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\ No newline at end of file
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<h1 >
<span class='first'>S</span>trong <span class='first'>N</span>ormalization of <span class='first'>M</span>oggis's <span class='first'>C</span>omputational <span class='first'>M</span>etalanguage</h1>
<div>
<p><a href="../authors/doczkal">Christian Doczkal</a> <a class="obfuscated" data="eyJob3N0IjpbInBzIiwidW5pLXNhYXJsYW5kIiwiZGUiXSwidXNlciI6WyJkb2N6a2FsIl19">📧</a>
</p>
<p class="date">August 29, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Handling variable binding is one of the main difficulties in formal proofs. In this context, Moggi's computational metalanguage serves as an interesting case study. It features monadic types and a commuting conversion rule that rearranges the binding structure. Lindley and Stark have given an elegant proof of strong normalization for this calculus. The key construction in their proof is a notion of relational TT-lifting, using stacks of elimination contexts to obtain a Girard-Tait style logical relation. I give a formalization of their proof in Isabelle/HOL-Nominal with a particular emphasis on the treatment of bound variables.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session Lam-ml-Normalization</h3>
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<li><a href="../theories/lam-ml-normalization/#Lam_ml">Lam_ml</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lam-ml-Normalization-AFP</p><pre id="copy-text">@article{Lam-ml-Normalization-AFP,
author = {Christian Doczkal},
title = {Strong Normalization of Moggis&#39;s Computational Metalanguage},
journal = {Archive of Formal Proofs},
month = {August},
year = {2010},
note = {\url{https://isa-afp.org/entries/Lam-ml-Normalization.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lam-ml-Normalization-2010-09-01.tar.gz">Sep 1, 2010</a>: Isabelle2009-2
</li></ul>
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diff --git a/web/entries/LambdaAuth.html b/web/entries/LambdaAuth.html
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>G</span>eneric <span class='first'>A</span>uthenticated <span class='first'>D</span>ata <span class='first'>S</span>tructures</h1>
<div>
<p><a href="../authors/brun">Matthias Brun</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">May 14, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Authenticated data structures are a technique for outsourcing data
storage and maintenance to an untrusted server. The server is required
to produce an efficiently checkable and cryptographically secure proof
that it carried out precisely the requested computation. <a
href="https://doi.org/10.1145/2535838.2535851">Miller et
al.</a> introduced &lambda;&bull; (pronounced
<i>lambda auth</i>)&mdash;a functional programming
language with a built-in primitive authentication construct, which
supports a wide range of user-specified authenticated data structures
while guaranteeing certain correctness and security properties for all
well-typed programs. We formalize &lambda;&bull; and prove its
correctness and security properties. With Isabelle's help, we
uncover and repair several mistakes in the informal proofs and lemma
statements. Our findings are summarized in an <a
href="https://doi.org/10.4230/LIPIcs.ITP.2019.10">ITP'19 paper</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session LambdaAuth</h3>
<ul>
<li><a href="../theories/lambdaauth/#Nominal2_Lemmas">Nominal2_Lemmas</a></li>
<li><a href="../theories/lambdaauth/#FMap_Lemmas">FMap_Lemmas</a></li>
<li><a href="../theories/lambdaauth/#Syntax">Syntax</a></li>
<li><a href="../theories/lambdaauth/#Semantics">Semantics</a></li>
<li><a href="../theories/lambdaauth/#Agreement">Agreement</a></li>
<li><a href="../theories/lambdaauth/#Results">Results</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/ADS_Functor.html">Authenticated Data Structures As Functors</a></li>
<li><a href="../entries/CakeML.html">CakeML</a></li>
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<p style="display:none;" id="bibtex-filename">LambdaAuth-AFP</p><pre id="copy-text">@article{LambdaAuth-AFP,
author = {Matthias Brun and Dmitriy Traytel},
title = {Formalization of Generic Authenticated Data Structures},
journal = {Archive of Formal Proofs},
month = {May},
year = {2019},
note = {\url{https://isa-afp.org/entries/LambdaAuth.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-LambdaAuth-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-LambdaAuth-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LambdaAuth-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaAuth-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaAuth-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaAuth-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaAuth-2019-05-15.tar.gz">May 15, 2019</a>: Isabelle2018
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<h1 >
<span class='first'>T</span>he <span class='first'>L</span>ambda<span class='first'>M</span>u-<span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/matache">Cristina Matache</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiY3JpcyIsIm1hdGFjaGUiXX0=">📧</a>, <a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsidmljdG9yYm9yZ2VzZmciXX0=">📧</a> and <a href="../authors/mulligan">Dominic P. Mulligan</a> <a class="obfuscated" data="eyJob3N0IjpbImdvb2dsZW1haWwiLCJjb20iXSwidXNlciI6WyJkb21pbmljIiwicCIsIm11bGxpZ2FuIl19">📧</a>
</p>
<p class="date">August 16, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The propositions-as-types correspondence is ordinarily presented as
linking the metatheory of typed λ-calculi and the proof theory of
intuitionistic logic. Griffin observed that this correspondence could
be extended to classical logic through the use of control operators.
This observation set off a flurry of further research, leading to the
development of Parigots λμ-calculus. In this work, we formalise λμ-
calculus in Isabelle/HOL and prove several metatheoretical properties
such as type preservation and progress.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session LambdaMu</h3>
<ul>
<li><a href="../theories/lambdamu/#Syntax">Syntax</a></li>
<li><a href="../theories/lambdamu/#Types">Types</a></li>
<li><a href="../theories/lambdamu/#DeBruijn">DeBruijn</a></li>
<li><a href="../theories/lambdamu/#Substitution">Substitution</a></li>
<li><a href="../theories/lambdamu/#Reduction">Reduction</a></li>
<li><a href="../theories/lambdamu/#ContextFacts">ContextFacts</a></li>
<li><a href="../theories/lambdamu/#TypePreservation">TypePreservation</a></li>
<li><a href="../theories/lambdamu/#Progress">Progress</a></li>
<li><a href="../theories/lambdamu/#Peirce">Peirce</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">LambdaMu-AFP</p><pre id="copy-text">@article{LambdaMu-AFP,
author = {Cristina Matache and Victor B. F. Gomes and Dominic P. Mulligan},
title = {The LambdaMu-calculus},
journal = {Archive of Formal Proofs},
month = {August},
year = {2017},
note = {\url{https://isa-afp.org/entries/LambdaMu.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-LambdaMu-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LambdaMu-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-LambdaMu-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaMu-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-LambdaMu-2017-08-21.tar.gz">Aug 21, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Lambda_Free_EPO.html b/web/entries/Lambda_Free_EPO.html
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+++ b/web/entries/Lambda_Free_EPO.html
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<h1 >
<span class='first'>F</span>ormalization of the <span class='first'>E</span>mbedding <span class='first'>P</span>ath <span class='first'>O</span>rder for <span class='first'>L</span>ambda-<span class='first'>F</span>ree <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/bentkamp">Alexander Bentkamp</a> <a href="https://www.cs.vu.nl/~abp290/">🌐</a>
</p>
<p class="date">October 19, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization defines the Embedding Path Order (EPO)
for higher-order terms without lambda-abstraction and proves many
useful properties about it. In contrast to the lambda-free recursive
path orders, it does not fully coincide with RPO on first-order terms,
but it is compatible with arbitrary higher-order contexts.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Lambda_Free_EPO</h3>
<ul>
<li><a href="../theories/lambda_free_epo/#Embeddings">Embeddings</a></li>
<li><a href="../theories/lambda_free_epo/#Chop">Chop</a></li>
<li><a href="../theories/lambda_free_epo/#Lambda_Free_EPO">Lambda_Free_EPO</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Lambda_Free_EPO-AFP</p><pre id="copy-text">@article{Lambda_Free_EPO-AFP,
author = {Alexander Bentkamp},
title = {Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/Lambda_Free_EPO.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_EPO-2018-10-21.tar.gz">Oct 21, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Lambda_Free_KBOs.html b/web/entries/Lambda_Free_KBOs.html
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@@ -1,180 +1,182 @@
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>K</span>nuth–<span class='first'>B</span>endix <span class='first'>O</span>rders for <span class='first'>L</span>ambda-<span class='first'>F</span>ree <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/becker">Heiko Becker</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1zd3MiLCJvcmciXSwidXNlciI6WyJoYmVja2VyIl19">📧</a>, <a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamFzbWluIiwiYmxhbmNoZXR0ZSJdfQ==">📧</a>, <a href="../authors/waldmann">Uwe Waldmann</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbIndhbGRtYW5uIl19">📧</a> and <a href="../authors/wand">Daniel Wand</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbImR3YW5kIl19">📧</a>
</p>
<p class="date">November 12, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization defines Knuth–Bendix orders for higher-order terms without lambda-abstraction and proves many useful properties about them. The main order fully coincides with the standard transfinite KBO with subterm coefficients on first-order terms. It appears promising as the basis of a higher-order superposition calculus.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Lambda_Free_KBOs</h3>
<ul>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_KBO_Util">Lambda_Free_KBO_Util</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_KBO_App">Lambda_Free_KBO_App</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_KBO_Std">Lambda_Free_KBO_Std</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_KBO_Basic">Lambda_Free_KBO_Basic</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_TKBO_Coefs">Lambda_Free_TKBO_Coefs</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Encoding_KBO">Lambda_Encoding_KBO</a></li>
<li><a href="../theories/lambda_free_kbos/#Lambda_Free_KBOs">Lambda_Free_KBOs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Lambda_Free_KBOs-AFP</p><pre id="copy-text">@article{Lambda_Free_KBOs-AFP,
author = {Heiko Becker and Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
title = {Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Lambda_Free_KBOs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lambda_Free_KBOs-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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diff --git a/web/entries/Lambda_Free_RPOs.html b/web/entries/Lambda_Free_RPOs.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms - Archive of Formal Proofs</title><meta name="description" content="This Isabelle/HOL formalization defines recursive path orders (RPOs) for higher-order terms without lambda-abstraction and proves many useful properties..."><meta property="og:title" content="Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms" />
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>R</span>ecursive <span class='first'>P</span>ath <span class='first'>O</span>rders for <span class='first'>L</span>ambda-<span class='first'>F</span>ree <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamFzbWluIiwiYmxhbmNoZXR0ZSJdfQ==">📧</a>, <a href="../authors/waldmann">Uwe Waldmann</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbIndhbGRtYW5uIl19">📧</a> and <a href="../authors/wand">Daniel Wand</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbImR3YW5kIl19">📧</a>
</p>
<p class="date">September 23, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization defines recursive path orders (RPOs) for higher-order terms without lambda-abstraction and proves many useful properties about them. The main order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. An optimized variant is formalized as well. It appears promising as the basis of a higher-order superposition calculus.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Lambda_Free_RPOs</h3>
<ul>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_Util">Lambda_Free_Util</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_Term">Lambda_Free_Term</a></li>
<li><a href="../theories/lambda_free_rpos/#Infinite_Chain">Infinite_Chain</a></li>
<li><a href="../theories/lambda_free_rpos/#Extension_Orders">Extension_Orders</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_RPO_App">Lambda_Free_RPO_App</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_RPO_Std">Lambda_Free_RPO_Std</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_RPO_Optim">Lambda_Free_RPO_Optim</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Encoding">Lambda_Encoding</a></li>
<li><a href="../theories/lambda_free_rpos/#Lambda_Free_RPOs">Lambda_Free_RPOs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Saturation_Framework.html">A Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Higher_Order_Terms.html">An Algebra for Higher-Order Terms</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Lambda_Free_EPO.html">Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Lambda_Free_KBOs.html">Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Lambda_Free_KBOs.html">Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</a></li>
<li><a href="../entries/Lambda_Free_EPO.html">Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Lambda_Free_RPOs-AFP</p><pre id="copy-text">@article{Lambda_Free_RPOs-AFP,
author = {Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
title = {Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Lambda_Free_RPOs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Lambda_Free_RPOs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_RPOs-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Lambda_Free_RPOs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Lambert_W.html b/web/entries/Lambert_W.html
--- a/web/entries/Lambert_W.html
+++ b/web/entries/Lambert_W.html
@@ -1,186 +1,188 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>L</span>ambert <span class='first'>W</span> <span class='first'>F</span>unction on the <span class='first'>R</span>eals</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">April 24, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The Lambert <em>W</em> function is a multi-valued
function defined as the inverse function of <em>x</em>
&#x21A6; <em>x</em>
e<sup><em>x</em></sup>. Besides numerous
applications in combinatorics, physics, and engineering, it also
frequently occurs when solving equations containing both
e<sup><em>x</em></sup> and
<em>x</em>, or both <em>x</em> and log
<em>x</em>.</p> <p>This article provides a
definition of the two real-valued branches
<em>W</em><sub>0</sub>(<em>x</em>)
and
<em>W</em><sub>-1</sub>(<em>x</em>)
and proves various properties such as basic identities and
inequalities, monotonicity, differentiability, asymptotic expansions,
and the MacLaurin series of
<em>W</em><sub>0</sub>(<em>x</em>)
at <em>x</em> = 0.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Lambert_W</h3>
<ul>
<li><a href="../theories/lambert_w/#Lambert_W">Lambert_W</a></li>
<li><a href="../theories/lambert_w/#Lambert_W_MacLaurin_Series">Lambert_W_MacLaurin_Series</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bernoulli.html">Bernoulli Numbers</a></li><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Lambert_W-AFP</p><pre id="copy-text">@article{Lambert_W-AFP,
author = {Manuel Eberl},
title = {The Lambert W Function on the Reals},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Lambert_W.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Landau_Symbols.html b/web/entries/Landau_Symbols.html
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<h1 >
<span class='first'>L</span>andau <span class='first'>S</span>ymbols</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">July 14, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides Landau symbols to describe and reason about the asymptotic growth of functions for sufficiently large inputs. A number of simplification procedures are provided for additional convenience: cancelling of dominated terms in sums under a Landau symbol, cancelling of common factors in products, and a decision procedure for Landau expressions containing products of powers of functions like x, ln(x), ln(ln(x)) etc.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Landau_Symbols</h3>
<ul>
<li><a href="../theories/landau_symbols/#Group_Sort">Group_Sort</a></li>
<li><a href="../theories/landau_symbols/#Landau_Real_Products">Landau_Real_Products</a></li>
<li><a href="../theories/landau_symbols/#Landau_Simprocs">Landau_Simprocs</a></li>
<li><a href="../theories/landau_symbols/#Landau_More">Landau_More</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Error_Function.html">The Error Function</a></li><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li><li><a href="../entries/CryptHOL.html">CryptHOL</a></li><li><a href="../entries/Random_BSTs.html">Expected Shape of Random Binary Search Trees</a></li><li><a href="../entries/Comparison_Sort_Lower_Bound.html">Lower bound on comparison-based sorting algorithms</a></li><li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li><li><a href="../entries/Euler_MacLaurin.html">The Euler–MacLaurin Formula</a></li><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li><li><a href="../entries/Catalan_Numbers.html">Catalan Numbers</a></li><li><a href="../entries/Akra_Bazzi.html">The Akra-Bazzi theorem and the Master theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Landau_Symbols-AFP</p><pre id="copy-text">@article{Landau_Symbols-AFP,
author = {Manuel Eberl},
title = {Landau Symbols},
journal = {Archive of Formal Proofs},
month = {July},
year = {2015},
note = {\url{https://isa-afp.org/entries/Landau_Symbols.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Laplace_Transform.html b/web/entries/Laplace_Transform.html
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<h1 >
<span class='first'>L</span>aplace <span class='first'>T</span>ransform</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>
</p>
<p class="date">August 14, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes the Laplace transform and concrete Laplace
transforms for arithmetic functions, frequency shift, integration and
(higher) differentiation in the time domain. It proves Lerch's
lemma and uniqueness of the Laplace transform for continuous
functions. In order to formalize the foundational assumptions, this
entry contains a formalization of piecewise continuous functions and
functions of exponential order.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Laplace_Transform</h3>
<ul>
<li><a href="../theories/laplace_transform/#Laplace_Transform_Library">Laplace_Transform_Library</a></li>
<li><a href="../theories/laplace_transform/#Piecewise_Continuous">Piecewise_Continuous</a></li>
<li><a href="../theories/laplace_transform/#Existence">Existence</a></li>
<li><a href="../theories/laplace_transform/#Lerch_Lemma">Lerch_Lemma</a></li>
<li><a href="../theories/laplace_transform/#Uniqueness">Uniqueness</a></li>
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<p style="display:none;" id="bibtex-filename">Laplace_Transform-AFP</p><pre id="copy-text">@article{Laplace_Transform-AFP,
author = {Fabian Immler},
title = {Laplace Transform},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/Laplace_Transform.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Laplace_Transform-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Laplace_Transform-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Laplace_Transform-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Laplace_Transform-2020-04-18.tar.gz">Apr 18, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Laplace_Transform-2019-08-16.tar.gz">Aug 16, 2019</a>: Isabelle2019
</li></ul>
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diff --git a/web/entries/Latin_Square.html b/web/entries/Latin_Square.html
--- a/web/entries/Latin_Square.html
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@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>L</span>atin <span class='first'>S</span>quare</h1>
<div>
<p><a href="../authors/bentkamp">Alexander Bentkamp</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYmVudGthbXAiXX0=">📧</a>
</p>
<p class="date">December 2, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A Latin Square is a n x n table filled with integers from 1 to n where each number appears exactly once in each row and each column. A Latin Rectangle is a partially filled n x n table with r filled rows and n-r empty rows, such that each number appears at most once in each row and each column. The main result of this theory is that any Latin Rectangle can be completed to a Latin Square.</div>
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<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
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<ul>
<li><a href="../theories/latin_square/#Latin_Square">Latin_Square</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Marriage.html">Hall&rsquo;s Marriage Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Latin_Square-AFP</p><pre id="copy-text">@article{Latin_Square-AFP,
author = {Alexander Bentkamp},
title = {Latin Square},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Latin_Square.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>attice <span class='first'>P</span>roperties</h1>
<div>
<p><a href="../authors/preoteasa">Viorel Preoteasa</a> <a href="http://users.abo.fi/vpreotea/">🌐</a>
</p>
<p class="date">September 22, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalization introduces and collects some algebraic structures based on lattices and complete lattices for use in other developments. The structures introduced are modular, and lattice ordered groups. In addition to the results proved for the new lattices, this formalization also introduces theorems about latices and complete lattices in general.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 5, 2012</dt>
<dd>Removed the theory about distributive complete lattices which is in the standard library now.
Added a theory about well founded and transitive relations and a result about fixpoints in complete lattices and well founded relations.
Moved the results about conjunctive and disjunctive functions to a new theory.
Removed the syntactic classes for inf and sup which are in the standard library now.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session LatticeProperties</h3>
<ul>
<li><a href="../theories/latticeproperties/#WellFoundedTransitive">WellFoundedTransitive</a></li>
<li><a href="../theories/latticeproperties/#Complete_Lattice_Prop">Complete_Lattice_Prop</a></li>
<li><a href="../theories/latticeproperties/#Conj_Disj">Conj_Disj</a></li>
<li><a href="../theories/latticeproperties/#Lattice_Prop">Lattice_Prop</a></li>
<li><a href="../theories/latticeproperties/#Modular_Distrib_Lattice">Modular_Distrib_Lattice</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></li><li><a href="../entries/PseudoHoops.html">Pseudo Hoops</a></li><li><a href="../entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">LatticeProperties-AFP</p><pre id="copy-text">@article{LatticeProperties-AFP,
author = {Viorel Preoteasa},
title = {Lattice Properties},
journal = {Archive of Formal Proofs},
month = {September},
year = {2011},
note = {\url{https://isa-afp.org/entries/LatticeProperties.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Launchbury.html b/web/entries/Launchbury.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation - Archive of Formal Proofs</title><meta name="description" content="In his seminal paper &#34;Natural Semantics for Lazy Evaluation&#34;, John Launchbury proves his semantics correct with respect to a denotational semantics, and..."><meta property="og:title" content="The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation" />
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<h1 >
<span class='first'>T</span>he <span class='first'>C</span>orrectness of <span class='first'>L</span>aunchbury's <span class='first'>N</span>atural <span class='first'>S</span>emantics for <span class='first'>L</span>azy <span class='first'>E</span>valuation</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a href="http://pp.ipd.kit.edu/~breitner">🌐</a>
</p>
<p class="date">January 31, 2013</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In his seminal paper "Natural Semantics for Lazy Evaluation", John Launchbury proves his semantics correct with respect to a denotational semantics, and outlines an adequacy proof. We have formalized both semantics and machine-checked the correctness proof, clarifying some details. Furthermore, we provide a new and more direct adequacy proof that does not require intermediate operational semantics.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 16, 2015</dt>
<dd>Booleans and if-then-else added to syntax and semantics, making this entry suitable to be used by the entry "Call_Arity".</dd><dt>May 24, 2014</dt>
<dd>Added the proof of adequacy, as well as simplified and improved the existing proofs. Adjusted abstract accordingly.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Launchbury</h3>
<ul>
<li><a href="../theories/launchbury/#AList-Utils">AList-Utils</a></li>
<li><a href="../theories/launchbury/#HOLCF-Join">HOLCF-Join</a></li>
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<li><a href="../theories/launchbury/#Env">Env</a></li>
<li><a href="../theories/launchbury/#Pointwise">Pointwise</a></li>
<li><a href="../theories/launchbury/#HOLCF-Utils">HOLCF-Utils</a></li>
<li><a href="../theories/launchbury/#EvalHeap">EvalHeap</a></li>
<li><a href="../theories/launchbury/#Nominal-Utils">Nominal-Utils</a></li>
<li><a href="../theories/launchbury/#AList-Utils-Nominal">AList-Utils-Nominal</a></li>
<li><a href="../theories/launchbury/#Nominal-HOLCF">Nominal-HOLCF</a></li>
<li><a href="../theories/launchbury/#Env-HOLCF">Env-HOLCF</a></li>
<li><a href="../theories/launchbury/#HasESem">HasESem</a></li>
<li><a href="../theories/launchbury/#Iterative">Iterative</a></li>
<li><a href="../theories/launchbury/#Env-Nominal">Env-Nominal</a></li>
<li><a href="../theories/launchbury/#HeapSemantics">HeapSemantics</a></li>
<li><a href="../theories/launchbury/#Vars">Vars</a></li>
<li><a href="../theories/launchbury/#Terms">Terms</a></li>
<li><a href="../theories/launchbury/#AbstractDenotational">AbstractDenotational</a></li>
<li><a href="../theories/launchbury/#Substitution">Substitution</a></li>
<li><a href="../theories/launchbury/#Abstract-Denotational-Props">Abstract-Denotational-Props</a></li>
<li><a href="../theories/launchbury/#Value">Value</a></li>
<li><a href="../theories/launchbury/#Value-Nominal">Value-Nominal</a></li>
<li><a href="../theories/launchbury/#Denotational">Denotational</a></li>
<li><a href="../theories/launchbury/#Launchbury">Launchbury</a></li>
<li><a href="../theories/launchbury/#CorrectnessOriginal">CorrectnessOriginal</a></li>
<li><a href="../theories/launchbury/#Mono-Nat-Fun">Mono-Nat-Fun</a></li>
<li><a href="../theories/launchbury/#C">C</a></li>
<li><a href="../theories/launchbury/#CValue">CValue</a></li>
<li><a href="../theories/launchbury/#CValue-Nominal">CValue-Nominal</a></li>
<li><a href="../theories/launchbury/#HOLCF-Meet">HOLCF-Meet</a></li>
<li><a href="../theories/launchbury/#C-Meet">C-Meet</a></li>
<li><a href="../theories/launchbury/#C-restr">C-restr</a></li>
<li><a href="../theories/launchbury/#ResourcedDenotational">ResourcedDenotational</a></li>
<li><a href="../theories/launchbury/#CorrectnessResourced">CorrectnessResourced</a></li>
<li><a href="../theories/launchbury/#ResourcedAdequacy">ResourcedAdequacy</a></li>
<li><a href="../theories/launchbury/#ValueSimilarity">ValueSimilarity</a></li>
<li><a href="../theories/launchbury/#Denotational-Related">Denotational-Related</a></li>
<li><a href="../theories/launchbury/#Adequacy">Adequacy</a></li>
<li><a href="../theories/launchbury/#EverythingAdequacy">EverythingAdequacy</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/FinFun.html">Code Generation for Functions as Data</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Call_Arity.html">The Safety of Call Arity</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/TESL_Language.html">A Formal Development of a Polychronous Polytimed Coordination Language</a></li>
<li><a href="../entries/QHLProver.html">Quantum Hoare Logic</a></li>
<li><a href="../entries/HyperCTL.html">A shallow embedding of HyperCTL*</a></li>
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<p style="display:none;" id="bibtex-filename">Launchbury-AFP</p><pre id="copy-text">@article{Launchbury-AFP,
author = {Joachim Breitner},
title = {The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation},
journal = {Archive of Formal Proofs},
month = {January},
year = {2013},
note = {\url{https://isa-afp.org/entries/Launchbury.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Laws_of_Large_Numbers.html b/web/entries/Laws_of_Large_Numbers.html
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+++ b/web/entries/Laws_of_Large_Numbers.html
@@ -1,185 +1,187 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>L</span>aws of <span class='first'>L</span>arge <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 10, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The Law of Large Numbers states that, informally, if one
performs a random experiment $X$ many times and takes the average of
the results, that average will be very close to the expected value
$E[X]$.</p> <p> More formally, let
$(X_i)_{i\in\mathbb{N}}$ be a sequence of independently identically
distributed random variables whose expected value $E[X_1]$ exists.
Denote the running average of $X_1, \ldots, X_n$ as $\overline{X}_n$.
Then:</p> <ul> <li>The Weak Law of Large Numbers
states that $\overline{X}_{n} \longrightarrow E[X_1]$ in probability
for $n\to\infty$, i.e. $\mathcal{P}(|\overline{X}_{n} - E[X_1]| >
\varepsilon) \longrightarrow 0$ as $n\to\infty$ for any $\varepsilon
> 0$.</li> <li>The Strong Law of Large Numbers states
that $\overline{X}_{n} \longrightarrow E[X_1]$ almost surely for
$n\to\infty$, i.e. $\mathcal{P}(\overline{X}_{n} \longrightarrow
E[X_1]) = 1$.</li> </ul> <p>In this entry, I
formally prove the strong law and from it the weak law. The approach
used for the proof of the strong law is a particularly quick and slick
one based on ergodic theory, which was formalised by Gouëzel in
another AFP entry.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Laws_of_Large_Numbers</h3>
<ul>
<li><a href="../theories/laws_of_large_numbers/#Laws_of_Large_Numbers">Laws_of_Large_Numbers</a></li>
<li><a href="../theories/laws_of_large_numbers/#Laws_of_Large_Numbers_Example">Laws_of_Large_Numbers_Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ergodic_Theory.html">Ergodic Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Laws_of_Large_Numbers-AFP</p><pre id="copy-text">@article{Laws_of_Large_Numbers-AFP,
author = {Manuel Eberl},
title = {The Laws of Large Numbers},
journal = {Archive of Formal Proofs},
month = {February},
year = {2021},
note = {\url{https://isa-afp.org/entries/Laws_of_Large_Numbers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Lazy-Lists-II.html b/web/entries/Lazy-Lists-II.html
--- a/web/entries/Lazy-Lists-II.html
+++ b/web/entries/Lazy-Lists-II.html
@@ -1,220 +1,222 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Lazy Lists II - Archive of Formal Proofs</title><meta name="description" content="This theory contains some useful extensions to the LList (lazy list) theory by Larry Paulson, including finite, infinite, and positive llists over an..."><meta property="og:title" content="Lazy Lists II" />
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<h1 >
<span class='first'>L</span>azy <span class='first'>L</span>ists <span class='first'>I</span><span class='first'>I</span></h1>
<div>
<p><a href="../authors/friedrich">Stefan Friedrich</a>
</p>
<p class="date">April 26, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory contains some useful extensions to the LList (lazy list) theory by <a href="http://www.cl.cam.ac.uk/~lp15/">Larry Paulson</a>, including finite, infinite, and positive llists over an alphabet, as well as the new constants take and drop and the prefix order of llists. Finally, the notions of safety and liveness in the sense of Alpern and Schneider (1985) are defined.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Lazy-Lists-II</h3>
<ul>
<li><a href="../theories/lazy-lists-ii/#LList2">LList2</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<h3>Used by</h3>
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<h3>Auto-related entries</h3>
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<p style="display:none;" id="bibtex-filename">Lazy-Lists-II-AFP</p><pre id="copy-text">@article{Lazy-Lists-II-AFP,
author = {Stefan Friedrich},
title = {Lazy Lists II},
journal = {Archive of Formal Proofs},
month = {April},
year = {2004},
note = {\url{https://isa-afp.org/entries/Lazy-Lists-II.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>azifying <span class='first'>C</span>ase <span class='first'>C</span>onstants</h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">April 18, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle's code generator performs various adaptations for target
languages. Among others, case statements are printed as match
expressions. Internally, this is a sophisticated procedure, because in
HOL, case statements are represented as nested calls to the case
combinators as generated by the datatype package. Furthermore, the
procedure relies on laziness of match expressions in the target
language, i.e., that branches guarded by patterns that fail to match
are not evaluated. Similarly, <tt>if-then-else</tt> is
printed to the corresponding construct in the target language. This
entry provides tooling to replace these special cases in the code
generator by ignoring these target language features, instead printing
case expressions and <tt>if-then-else</tt> as functions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Lazy_Case</h3>
<ul>
<li><a href="../theories/lazy_case/#Lazy_Case">Lazy_Case</a></li>
<li><a href="../theories/lazy_case/#Test_Lazy_Case">Test_Lazy_Case</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lazy_Case-AFP</p><pre id="copy-text">@article{Lazy_Case-AFP,
author = {Lars Hupel},
title = {Lazifying case constants},
journal = {Archive of Formal Proofs},
month = {April},
year = {2017},
note = {\url{https://isa-afp.org/entries/Lazy_Case.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>ehmer's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsic2ltb24iLCJ3aW1tZXIiXX0=">📧</a> and <a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">July 22, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1927, Lehmer presented criterions for primality, based on the converse of Fermat's litte theorem. This work formalizes the second criterion from Lehmer's paper, a necessary and sufficient condition for primality.
<p>
As a side product we formalize some properties of Euler's phi-function,
the notion of the order of an element of a group, and the cyclicity of the multiplicative group of a finite field.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Lehmer</h3>
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<li><a href="../theories/lehmer/#Lehmer">Lehmer</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lehmer-AFP</p><pre id="copy-text">@article{Lehmer-AFP,
author = {Simon Wimmer and Lars Noschinski},
title = {Lehmer&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2013},
note = {\url{https://isa-afp.org/entries/Lehmer.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Lehmer-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>L</span>ifting <span class='first'>D</span>efinition <span class='first'>O</span>ption</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">October 13, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implemented a command that can be used to easily generate
elements of a restricted type <tt>{x :: 'a. P x}</tt>,
provided the definition is of the form
<tt>f ys = (if check ys then Some(generate ys :: 'a) else None)</tt> where
<tt>ys</tt> is a list of variables <tt>y1 ... yn</tt> and
<tt>check ys ==> P(generate ys)</tt> can be proved.
<p>
In principle, such a definition is also directly possible using the
<tt>lift_definition</tt> command. However, then this definition will not be
suitable for code-generation. To this end, we automated a more complex
construction of Joachim Breitner which is amenable for code-generation, and
where the test <tt>check ys</tt> will only be performed once. In the
automation, one auxiliary type is created, and Isabelle's lifting- and
transfer-package is invoked several times.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Lifting_Definition_Option</h3>
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<li><a href="../theories/lifting_definition_option/#Lifting_Definition_Option_Examples">Lifting_Definition_Option_Examples</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lifting_Definition_Option-AFP</p><pre id="copy-text">@article{Lifting_Definition_Option-AFP,
author = {René Thiemann},
title = {Lifting Definition Option},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/Lifting_Definition_Option.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>ifting the <span class='first'>E</span>xponent</h1>
<div>
<p><a href="../authors/kadzioka">Maya Kądziołka</a> <a class="obfuscated" data="eyJob3N0IjpbImNvbXBpbGVyY3JpbSIsImVzIl0sInVzZXIiOlsiYWZwIl19">📧</a>
</p>
<p class="date">April 27, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the <i>Lifting the Exponent Lemma</i>, which
shows how to find the largest power of $p$ dividing $a^n \pm b^n$, for
a prime $p$ and positive integers $a$ and $b$. The proof follows <a
href="https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/lifting-the-exponent.pdf">Amir Hossein Parvardi's</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Lifting_the_Exponent</h3>
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<li><a href="../theories/lifting_the_exponent/#LTE">LTE</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lifting_the_Exponent-AFP</p><pre id="copy-text">@article{Lifting_the_Exponent-AFP,
author = {Maya Kądziołka},
title = {Lifting the Exponent},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/Lifting_the_Exponent.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/LightweightJava.html b/web/entries/LightweightJava.html
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<h1 >
<span class='first'>L</span>ightweight <span class='first'>J</span>ava</h1>
<div>
<p><a href="../authors/strnisa">Rok Strniša</a> <a href="http://rok.strnisa.com/lj/">🌐</a> and <a href="../authors/parkinson">Matthew Parkinson</a> <a href="http://research.microsoft.com/people/mattpark/">🌐</a>
</p>
<p class="date">February 7, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A fully-formalized and extensible minimal imperative fragment of Java.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session LightweightJava</h3>
<ul>
<li><a href="../theories/lightweightjava/#Lightweight_Java_Definition">Lightweight_Java_Definition</a></li>
<li><a href="../theories/lightweightjava/#Lightweight_Java_Equivalence">Lightweight_Java_Equivalence</a></li>
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author = {Rok Strniša and Matthew Parkinson},
title = {Lightweight Java},
journal = {Archive of Formal Proofs},
month = {February},
year = {2011},
note = {\url{https://isa-afp.org/entries/LightweightJava.html},
Formal proof development},
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Quantifier Elimination for Linear Arithmetic - Archive of Formal Proofs</title><meta name="description" content="This article formalizes quantifier elimination procedures for dense linear orders, linear real arithmetic and Presburger arithmetic. In each case both a..."><meta property="og:title" content="Quantifier Elimination for Linear Arithmetic" />
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<h1 >
<span class='first'>Q</span>uantifier <span class='first'>E</span>limination for <span class='first'>L</span>inear <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">January 11, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes quantifier elimination procedures for dense linear orders, linear real arithmetic and Presburger arithmetic. In each case both a DNF-based non-elementary algorithm and one or more (doubly) exponential NNF-based algorithms are formalized, including the well-known algorithms by Ferrante and Rackoff and by Cooper. The NNF-based algorithms for dense linear orders are new but based on Ferrante and Rackoff and on an algorithm by Loos and Weisspfenning which simulates infenitesimals. All algorithms are directly executable. In particular, they yield reflective quantifier elimination procedures for HOL itself. The formalization makes heavy use of locales and is therefore highly modular.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/decidability-of-theories">Logic/General logic/Decidability of theories</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T. (2010). Linear Quantifier Elimination. Journal of Automated Reasoning, 45(2), 189–212. <a href="https://doi.org/10.1007/s10817-010-9183-0">https://doi.org/10.1007/s10817-010-9183-0</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jar10.html">Open access</a>
</li></ul>
<h3>Session LinearQuantifierElim</h3>
<ul>
<li><a href="../theories/linearquantifierelim/#Logic">Logic</a></li>
<li><a href="../theories/linearquantifierelim/#QE">QE</a></li>
<li><a href="../theories/linearquantifierelim/#DLO">DLO</a></li>
<li><a href="../theories/linearquantifierelim/#QEdlo">QEdlo</a></li>
<li><a href="../theories/linearquantifierelim/#QEdlo_ex">QEdlo_ex</a></li>
<li><a href="../theories/linearquantifierelim/#QEdlo_fr">QEdlo_fr</a></li>
<li><a href="../theories/linearquantifierelim/#QEdlo_inf">QEdlo_inf</a></li>
<li><a href="../theories/linearquantifierelim/#LinArith">LinArith</a></li>
<li><a href="../theories/linearquantifierelim/#QElin">QElin</a></li>
<li><a href="../theories/linearquantifierelim/#QElin_opt">QElin_opt</a></li>
<li><a href="../theories/linearquantifierelim/#FRE">FRE</a></li>
<li><a href="../theories/linearquantifierelim/#QElin_inf">QElin_inf</a></li>
<li><a href="../theories/linearquantifierelim/#PresArith">PresArith</a></li>
<li><a href="../theories/linearquantifierelim/#QEpres">QEpres</a></li>
<li><a href="../theories/linearquantifierelim/#Cooper">Cooper</a></li>
<li><a href="../theories/linearquantifierelim/#CertDlo">CertDlo</a></li>
<li><a href="../theories/linearquantifierelim/#CertLin">CertLin</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">LinearQuantifierElim-AFP</p><pre id="copy-text">@article{LinearQuantifierElim-AFP,
author = {Tobias Nipkow},
title = {Quantifier Elimination for Linear Arithmetic},
journal = {Archive of Formal Proofs},
month = {January},
year = {2008},
note = {\url{https://isa-afp.org/entries/LinearQuantifierElim.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>inear <span class='first'>I</span>nequalities</h1>
<div>
<p><a href="../authors/bottesch">Ralph Bottesch</a> <a href="http://cl-informatik.uibk.ac.at/users/bottesch/">🌐</a>, <a href="../authors/reynaud">Alban Reynaud</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">June 21, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize results about linear inqualities, mainly from
Schrijver's book. The main results are the proof of the
fundamental theorem on linear inequalities, Farkas' lemma,
Carathéodory's theorem, the Farkas-Minkowsky-Weyl theorem, the
decomposition theorem of polyhedra, and Meyer's result that the
integer hull of a polyhedron is a polyhedron itself. Several theorems
include bounds on the appearing numbers, and in particular we provide
an a-priori bound on mixed-integer solutions of linear inequalities.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 3, 2022</dt>
<dd>improved bounds on determinants to get smaller mixed integer solutions (revision 6cf62d8e618e)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Linear_Inequalities</h3>
<ul>
<li><a href="../theories/linear_inequalities/#Missing_Matrix">Missing_Matrix</a></li>
<li><a href="../theories/linear_inequalities/#Missing_VS_Connect">Missing_VS_Connect</a></li>
<li><a href="../theories/linear_inequalities/#Basis_Extension">Basis_Extension</a></li>
<li><a href="../theories/linear_inequalities/#Sum_Vec_Set">Sum_Vec_Set</a></li>
<li><a href="../theories/linear_inequalities/#Integral_Bounded_Vectors">Integral_Bounded_Vectors</a></li>
<li><a href="../theories/linear_inequalities/#Cone">Cone</a></li>
<li><a href="../theories/linear_inequalities/#Convex_Hull">Convex_Hull</a></li>
<li><a href="../theories/linear_inequalities/#Normal_Vector">Normal_Vector</a></li>
<li><a href="../theories/linear_inequalities/#Dim_Span">Dim_Span</a></li>
<li><a href="../theories/linear_inequalities/#Fundamental_Theorem_Linear_Inequalities">Fundamental_Theorem_Linear_Inequalities</a></li>
<li><a href="../theories/linear_inequalities/#Farkas_Lemma">Farkas_Lemma</a></li>
<li><a href="../theories/linear_inequalities/#Farkas_Minkowsky_Weyl">Farkas_Minkowsky_Weyl</a></li>
<li><a href="../theories/linear_inequalities/#Decomposition_Theorem">Decomposition_Theorem</a></li>
<li><a href="../theories/linear_inequalities/#Mixed_Integer_Solutions">Mixed_Integer_Solutions</a></li>
<li><a href="../theories/linear_inequalities/#Integer_Hull">Integer_Hull</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/LLL_Basis_Reduction.html">A verified LLL algorithm</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/LP_Duality.html">Duality of Linear Programming</a></li><li><a href="../entries/Linear_Programming.html">Linear Programming</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Linear_Inequalities-AFP</p><pre id="copy-text">@article{Linear_Inequalities-AFP,
author = {Ralph Bottesch and Alban Reynaud and René Thiemann},
title = {Linear Inequalities},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Linear_Inequalities.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>L</span>inear <span class='first'>P</span>rogramming</h1>
<div>
<p><a href="../authors/parsert">Julian Parsert</a> <a href="http://www.parsert.com/">🌐</a> and <a href="../authors/kaliszyk">Cezary Kaliszyk</a> <a href="http://cl-informatik.uibk.ac.at/users/cek/">🌐</a>
</p>
<p class="date">August 6, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We use the previous formalization of the general simplex algorithm to
formulate an algorithm for solving linear programs. We encode the
linear programs using only linear constraints. Solving these
constraints also solves the original linear program. This algorithm is
proven to be sound by applying the weak duality theorem which is also
part of this formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Linear_Programming</h3>
<ul>
<li><a href="../theories/linear_programming/#More_Jordan_Normal_Forms">More_Jordan_Normal_Forms</a></li>
<li><a href="../theories/linear_programming/#Matrix_LinPoly">Matrix_LinPoly</a></li>
<li><a href="../theories/linear_programming/#LP_Preliminaries">LP_Preliminaries</a></li>
<li><a href="../theories/linear_programming/#Linear_Programming">Linear_Programming</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Farkas.html">Farkas' Lemma and Motzkin&rsquo;s Transposition Theorem</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Linear_Inequalities.html">Linear Inequalities</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Linear_Programming-AFP</p><pre id="copy-text">@article{Linear_Programming-AFP,
author = {Julian Parsert and Cezary Kaliszyk},
title = {Linear Programming},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/Linear_Programming.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Linear_Programming-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Linear_Programming-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Linear_Recurrences.html b/web/entries/Linear_Recurrences.html
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<h1 >
<span class='first'>L</span>inear <span class='first'>R</span>ecurrences</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">October 12, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> Linear recurrences with constant coefficients are an
interesting class of recurrence equations that can be solved
explicitly. The most famous example are certainly the Fibonacci
numbers with the equation <i>f</i>(<i>n</i>) =
<i>f</i>(<i>n</i>-1) +
<i>f</i>(<i>n</i> - 2) and the quite
non-obvious closed form
(<i>&phi;</i><sup><i>n</i></sup>
-
(-<i>&phi;</i>)<sup>-<i>n</i></sup>)
/ &radic;<span style="text-decoration:
overline">5</span> where &phi; is the golden ratio.
</p> <p> In this work, I build on existing tools in
Isabelle &ndash; such as formal power series and polynomial
factorisation algorithms &ndash; to develop a theory of these
recurrences and derive a fully executable solver for them that can be
exported to programming languages like Haskell. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Linear_Recurrences</h3>
<ul>
<li><a href="../theories/linear_recurrences/#RatFPS">RatFPS</a></li>
<li><a href="../theories/linear_recurrences/#Pochhammer_Polynomials">Pochhammer_Polynomials</a></li>
<li><a href="../theories/linear_recurrences/#Linear_Recurrences_Misc">Linear_Recurrences_Misc</a></li>
<li><a href="../theories/linear_recurrences/#Partial_Fraction_Decomposition">Partial_Fraction_Decomposition</a></li>
<li><a href="../theories/linear_recurrences/#Factorizations">Factorizations</a></li>
<li><a href="../theories/linear_recurrences/#Rational_FPS_Solver">Rational_FPS_Solver</a></li>
<li><a href="../theories/linear_recurrences/#Linear_Recurrences_Common">Linear_Recurrences_Common</a></li>
<li><a href="../theories/linear_recurrences/#Linear_Homogenous_Recurrences">Linear_Homogenous_Recurrences</a></li>
<li><a href="../theories/linear_recurrences/#Eulerian_Polynomials">Eulerian_Polynomials</a></li>
<li><a href="../theories/linear_recurrences/#Linear_Inhomogenous_Recurrences">Linear_Inhomogenous_Recurrences</a></li>
<li><a href="../theories/linear_recurrences/#Rational_FPS_Asymptotics">Rational_FPS_Asymptotics</a></li></ul>
<h3>Session Linear_Recurrences_Solver</h3>
<ul>
<li><a href="../theories/linear_recurrences_solver/#Linear_Recurrences_Solver">Linear_Recurrences_Solver</a></li>
<li><a href="../theories/linear_recurrences_solver/#Linear_Recurrences_Pretty">Linear_Recurrences_Pretty</a></li>
<li><a href="../theories/linear_recurrences_solver/#Show_RatFPS">Show_RatFPS</a></li>
<li><a href="../theories/linear_recurrences_solver/#Linear_Recurrences_Test">Linear_Recurrences_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Count_Complex_Roots.html">Count the Number of Complex Roots</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Formal_Puiseux_Series.html">Formal Puiseux Series</a></li>
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<p style="display:none;" id="bibtex-filename">Linear_Recurrences-AFP</p><pre id="copy-text">@article{Linear_Recurrences-AFP,
author = {Manuel Eberl},
title = {Linear Recurrences},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Linear_Recurrences.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Linear_Recurrences-2017-10-17.tar.gz">Oct 17, 2017</a>: Isabelle2017
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diff --git a/web/entries/Liouville_Numbers.html b/web/entries/Liouville_Numbers.html
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+++ b/web/entries/Liouville_Numbers.html
@@ -1,189 +1,191 @@
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<h1 >
<span class='first'>L</span>iouville <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Liouville numbers are a class of transcendental numbers that can be approximated
particularly well with rational numbers. Historically, they were the first
numbers whose transcendence was proven.
</p><p>
In this entry, we define the concept of Liouville numbers as well as the
standard construction to obtain Liouville numbers (including Liouville's
constant) and we prove their most important properties: irrationality and
transcendence.
</p><p>
The proof is very elementary and requires only standard arithmetic, the Mean
Value Theorem for polynomials, and the boundedness of polynomials on compact
intervals.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Liouville_Numbers</h3>
<ul>
<li><a href="../theories/liouville_numbers/#Liouville_Numbers_Misc">Liouville_Numbers_Misc</a></li>
<li><a href="../theories/liouville_numbers/#Liouville_Numbers">Liouville_Numbers</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Liouville_Numbers-AFP</p><pre id="copy-text">@article{Liouville_Numbers-AFP,
author = {Manuel Eberl},
title = {Liouville numbers},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Liouville_Numbers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Liouville_Numbers-2016-01-05.tar.gz">Jan 5, 2016</a>: Isabelle2015
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<h1 >
<span class='first'>L</span>ist <span class='first'>I</span>ndex</h1>
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<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
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<p class="date">February 20, 2010</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory provides functions for finding the index of an element in a list, by predicate and by value.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session List-Index</h3>
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<li><a href="../theories/list-index/#List_Index">List_Index</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Safe_Range_RC.html">Making Arbitrary Relational Calculus Queries Safe-Range</a></li><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li><li><a href="../entries/Gale_Shapley.html">Gale-Shapley Algorithm</a></li><li><a href="../entries/Dominance_CHK.html">A data flow analysis algorithm for computing dominators</a></li><li><a href="../entries/Metalogic_ProofChecker.html">Isabelle&rsquo;s Metalogic: Formalization and Proof Checker</a></li><li><a href="../entries/JinjaDCI.html">JinjaDCI: a Java semantics with dynamic class initialization</a></li><li><a href="../entries/Verified_SAT_Based_AI_Planning.html">Verified SAT-Based AI Planning</a></li><li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li><li><a href="../entries/Higher_Order_Terms.html">An Algebra for Higher-Order Terms</a></li><li><a href="../entries/Comparison_Sort_Lower_Bound.html">Lower bound on comparison-based sorting algorithms</a></li><li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/Randomised_Social_Choice.html">Randomised Social Choice Theory</a></li><li><a href="../entries/List_Update.html">Analysis of List Update Algorithms</a></li><li><a href="../entries/Planarity_Certificates.html">Planarity Certificates</a></li><li><a href="../entries/LTL_to_DRA.html">Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</a></li><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li><li><a href="../entries/MSO_Regex_Equivalence.html">Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</a></li><li><a href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li><li><a href="../entries/Jinja.html">Jinja is not Java</a></li></ul>
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<p style="display:none;" id="bibtex-filename">List-Index-AFP</p><pre id="copy-text">@article{List-Index-AFP,
author = {Tobias Nipkow},
title = {List Index},
journal = {Archive of Formal Proofs},
month = {February},
year = {2010},
note = {\url{https://isa-afp.org/entries/List-Index.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-List-Index-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-List-Index-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-List-Index-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-List-Index-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-List-Index-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-List-Index-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-List-Index-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Index-2010-02-20.tar.gz">Feb 20, 2010</a>: Isabelle2009-1
</li></ul>
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diff --git a/web/entries/List-Infinite.html b/web/entries/List-Infinite.html
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<h1 >
<span class='first'>I</span>nfinite <span class='first'>L</span>ists</h1>
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<p><a href="../authors/trachtenherz">David Trachtenherz</a>
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<p class="date">February 23, 2011</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We introduce a theory of infinite lists in HOL formalized as functions over naturals (folder ListInf, theories ListInf and ListInf_Prefix). It also provides additional results for finite lists (theory ListInf/List2), natural numbers (folder CommonArith, esp. division/modulo, naturals with infinity), sets (folder CommonSet, esp. cutting/truncating sets, traversing sets of naturals).</div>
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<li><a href="../theories/list-infinite/#Util_Set">Util_Set</a></li>
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<li><a href="../theories/list-infinite/#SetInterval2">SetInterval2</a></li>
<li><a href="../theories/list-infinite/#SetIntervalCut">SetIntervalCut</a></li>
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<li><a href="../theories/list-infinite/#List2">List2</a></li>
<li><a href="../theories/list-infinite/#InfiniteSet2">InfiniteSet2</a></li>
<li><a href="../theories/list-infinite/#ListInf">ListInf</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Nat-Interval-Logic.html">Interval Temporal Logic on Natural Numbers</a></li></ul>
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<p style="display:none;" id="bibtex-filename">List-Infinite-AFP</p><pre id="copy-text">@article{List-Infinite-AFP,
author = {David Trachtenherz},
title = {Infinite Lists},
journal = {Archive of Formal Proofs},
month = {February},
year = {2011},
note = {\url{https://isa-afp.org/entries/List-Infinite.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-List-Infinite-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-List-Infinite-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-List-Infinite-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-List-Infinite-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-List-Infinite-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-List-Infinite-2011-02-24.tar.gz">Feb 24, 2011</a>: Isabelle2011
</li></ul>
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\ No newline at end of file
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@@ -1,195 +1,197 @@
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<h1 >
<span class='first'>R</span>easoning <span class='first'>A</span>bout <span class='first'>L</span>ists via <span class='first'>L</span>ist <span class='first'>I</span>nterleaving</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">June 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Among the various mathematical tools introduced in his outstanding work on
Communicating Sequential Processes, Hoare has defined "interleaves" as the
predicate satisfied by any three lists such that the first list may be
split into sublists alternately extracted from the other two ones, whatever
is the criterion for extracting an item from either one list or the other
in each step.
</p><p>
This paper enriches Hoare's definition by identifying such criterion with
the truth value of a predicate taking as inputs the head and the tail of
the first list. This enhanced "interleaves" predicate turns out to permit
the proof of equalities between lists without the need of an induction.
Some rules that allow to infer "interleaves" statements without induction,
particularly applying to the addition or removal of a prefix to the input
lists, are also proven. Finally, a stronger version of the predicate, named
"Interleaves", is shown to fulfil further rules applying to the addition or
removal of a suffix to the input lists.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session List_Interleaving</h3>
<ul>
<li><a href="../theories/list_interleaving/#ListInterleaving">ListInterleaving</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Ipurge_Unwinding.html">The Ipurge Unwinding Theorem for CSP Noninterference Security</a></li></ul>
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<p style="display:none;" id="bibtex-filename">List_Interleaving-AFP</p><pre id="copy-text">@article{List_Interleaving-AFP,
author = {Pasquale Noce},
title = {Reasoning about Lists via List Interleaving},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/List_Interleaving.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/List_Inversions.html b/web/entries/List_Inversions.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Inversions of a List - Archive of Formal Proofs</title><meta name="description" content="This entry defines the set of inversions of a list, i.e. the pairs of indices that violate sortedness. It also proves the correctness of the well-known O(n..."><meta property="og:title" content="The Inversions of a List" />
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>nversions of a <span class='first'>L</span>ist</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 1, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry defines the set of <em>inversions</em>
of a list, i.e. the pairs of indices that violate sortedness. It also
proves the correctness of the well-known
<em>O</em>(<em>n log n</em>)
divide-and-conquer algorithm to compute the number of
inversions.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session List_Inversions</h3>
<ul>
<li><a href="../theories/list_inversions/#List_Inversions">List_Inversions</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">List_Inversions-AFP</p><pre id="copy-text">@article{List_Inversions-AFP,
author = {Manuel Eberl},
title = {The Inversions of a List},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/List_Inversions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/List_Update.html b/web/entries/List_Update.html
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@@ -1,206 +1,208 @@
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<h1 >
<span class='first'>A</span>nalysis of <span class='first'>L</span>ist <span class='first'>U</span>pdate <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/haslbeckm">Maximilian P. L. Haslbeck</a> <a href="http://in.tum.de/~haslbema/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">February 17, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
These theories formalize the quantitative analysis of a number of classical algorithms for the list update problem: 2-competitiveness of move-to-front, the lower bound of 2 for the competitiveness of deterministic list update algorithms and 1.6-competitiveness of the randomized COMB algorithm, the best randomized list update algorithm known to date.
The material is based on the first two chapters of <i>Online Computation
and Competitive Analysis</i> by Borodin and El-Yaniv.
</p>
<p>
For an informal description see the FSTTCS 2016 publication
<a href="http://www21.in.tum.de/~nipkow/pubs/fsttcs16.html">Verified Analysis of List Update Algorithms</a>
by Haslbeck and Nipkow.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/online">Computer science/Algorithms/Online</a></li></ul>
<h3>Session List_Update</h3>
<ul>
<li><a href="../theories/list_update/#Inversion">Inversion</a></li>
<li><a href="../theories/list_update/#Swaps">Swaps</a></li>
<li><a href="../theories/list_update/#On_Off">On_Off</a></li>
<li><a href="../theories/list_update/#Prob_Theory">Prob_Theory</a></li>
<li><a href="../theories/list_update/#Competitive_Analysis">Competitive_Analysis</a></li>
<li><a href="../theories/list_update/#Move_to_Front">Move_to_Front</a></li>
<li><a href="../theories/list_update/#Bit_Strings">Bit_Strings</a></li>
<li><a href="../theories/list_update/#MTF2_Effects">MTF2_Effects</a></li>
<li><a href="../theories/list_update/#BIT">BIT</a></li>
<li><a href="../theories/list_update/#Partial_Cost_Model">Partial_Cost_Model</a></li>
<li><a href="../theories/list_update/#RExp_Var">RExp_Var</a></li>
<li><a href="../theories/list_update/#OPT2">OPT2</a></li>
<li><a href="../theories/list_update/#Phase_Partitioning">Phase_Partitioning</a></li>
<li><a href="../theories/list_update/#List_Factoring">List_Factoring</a></li>
<li><a href="../theories/list_update/#TS">TS</a></li>
<li><a href="../theories/list_update/#BIT_pairwise">BIT_pairwise</a></li>
<li><a href="../theories/list_update/#BIT_2comp_on2">BIT_2comp_on2</a></li>
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<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li></ul>
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<p style="display:none;" id="bibtex-filename">List_Update-AFP</p><pre id="copy-text">@article{List_Update-AFP,
author = {Maximilian P. L. Haslbeck and Tobias Nipkow},
title = {Analysis of List Update Algorithms},
journal = {Archive of Formal Proofs},
month = {February},
year = {2016},
note = {\url{https://isa-afp.org/entries/List_Update.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-List_Update-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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diff --git a/web/entries/LocalLexing.html b/web/entries/LocalLexing.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Local Lexing - Archive of Formal Proofs</title><meta name="description" content="This formalisation accompanies the paper Local Lexing which introduces a novel parsing concept of the same name. The paper also gives a high-level..."><meta property="og:title" content="Local Lexing" />
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<h1 >
<span class='first'>L</span>ocal <span class='first'>L</span>exing</h1>
<div>
<p><a href="../authors/obua">Steven Obua</a> <a class="obfuscated" data="eyJob3N0IjpbInJlY3Vyc2l2ZW1pbmQiLCJjb20iXSwidXNlciI6WyJzdGV2ZW4iXX0=">📧</a>
</p>
<p class="date">April 28, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalisation accompanies the paper <a
href="https://arxiv.org/abs/1702.03277">Local
Lexing</a> which introduces a novel parsing concept of the same
name. The paper also gives a high-level algorithm for local lexing as
an extension of Earley's algorithm. This formalisation proves the
algorithm to be correct with respect to its local lexing semantics. As
a special case, this formalisation thus also contains a proof of the
correctness of Earley's algorithm. The paper contains a short
outline of how this formalisation is organised.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session LocalLexing</h3>
<ul>
<li><a href="../theories/locallexing/#CFG">CFG</a></li>
<li><a href="../theories/locallexing/#LocalLexing">LocalLexing</a></li>
<li><a href="../theories/locallexing/#LLEarleyParsing">LLEarleyParsing</a></li>
<li><a href="../theories/locallexing/#Limit">Limit</a></li>
<li><a href="../theories/locallexing/#LocalLexingLemmas">LocalLexingLemmas</a></li>
<li><a href="../theories/locallexing/#InductRules">InductRules</a></li>
<li><a href="../theories/locallexing/#ListTools">ListTools</a></li>
<li><a href="../theories/locallexing/#Derivations">Derivations</a></li>
<li><a href="../theories/locallexing/#Validity">Validity</a></li>
<li><a href="../theories/locallexing/#TheoremD2">TheoremD2</a></li>
<li><a href="../theories/locallexing/#TheoremD4">TheoremD4</a></li>
<li><a href="../theories/locallexing/#TheoremD5">TheoremD5</a></li>
<li><a href="../theories/locallexing/#TheoremD6">TheoremD6</a></li>
<li><a href="../theories/locallexing/#TheoremD7">TheoremD7</a></li>
<li><a href="../theories/locallexing/#TheoremD8">TheoremD8</a></li>
<li><a href="../theories/locallexing/#TheoremD9">TheoremD9</a></li>
<li><a href="../theories/locallexing/#Ladder">Ladder</a></li>
<li><a href="../theories/locallexing/#TheoremD10">TheoremD10</a></li>
<li><a href="../theories/locallexing/#TheoremD11">TheoremD11</a></li>
<li><a href="../theories/locallexing/#TheoremD12">TheoremD12</a></li>
<li><a href="../theories/locallexing/#TheoremD13">TheoremD13</a></li>
<li><a href="../theories/locallexing/#TheoremD14">TheoremD14</a></li>
<li><a href="../theories/locallexing/#PathLemmas">PathLemmas</a></li>
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<p style="display:none;" id="bibtex-filename">LocalLexing-AFP</p><pre id="copy-text">@article{LocalLexing-AFP,
author = {Steven Obua},
title = {Local Lexing},
journal = {Archive of Formal Proofs},
month = {April},
year = {2017},
note = {\url{https://isa-afp.org/entries/LocalLexing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-LocalLexing-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-LocalLexing-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-LocalLexing-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-LocalLexing-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-LocalLexing-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-LocalLexing-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-LocalLexing-2017-04-28.tar.gz">Apr 28, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Localization_Ring.html b/web/entries/Localization_Ring.html
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@@ -1,178 +1,180 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Localization of a Commutative Ring - Archive of Formal Proofs</title><meta name="description" content="We formalize the localization of a commutative ring R with respect to
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<h1 >
<span class='first'>T</span>he <span class='first'>L</span>ocalization of a <span class='first'>C</span>ommutative <span class='first'>R</span>ing</h1>
<div>
<p><a href="../authors/bordg">Anthony Bordg</a> <a href="https://sites.google.com/site/anthonybordg/">🌐</a>
</p>
<p class="date">June 14, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the localization of a commutative ring R with respect to
a multiplicative subset (i.e. a submonoid of R seen as a
multiplicative monoid). This localization is itself a commutative ring
and we build the natural homomorphism of rings from R to its
localization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Localization_Ring</h3>
<ul>
<li><a href="../theories/localization_ring/#Localization">Localization</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Padic_Field.html">p-adic Fields and p-adic Semialgebraic Sets</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Localization_Ring-AFP</p><pre id="copy-text">@article{Localization_Ring-AFP,
author = {Anthony Bordg},
title = {The Localization of a Commutative Ring},
journal = {Archive of Formal Proofs},
month = {June},
year = {2018},
note = {\url{https://isa-afp.org/entries/Localization_Ring.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Localization_Ring-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Localization_Ring-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Localization_Ring-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Localization_Ring-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Localization_Ring-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Localization_Ring-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Localization_Ring-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Localization_Ring-2018-06-17.tar.gz">Jun 17, 2018</a>: Isabelle2017
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diff --git a/web/entries/Locally-Nameless-Sigma.html b/web/entries/Locally-Nameless-Sigma.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Locally Nameless Sigma Calculus - Archive of Formal Proofs</title><meta name="description" content="We present a Theory of Objects based on the original functional sigma-calculus by Abadi and Cardelli but with an additional parameter to methods. We prove..."><meta property="og:title" content="Locally Nameless Sigma Calculus" />
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<h1 >
<span class='first'>L</span>ocally <span class='first'>N</span>ameless <span class='first'>S</span>igma <span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/henrio">Ludovic Henrio</a> <a class="obfuscated" data="eyJob3N0IjpbInNvcGhpYSIsImlucmlhIiwiZnIiXSwidXNlciI6WyJMdWRvdmljIiwiSGVucmlvIl19">📧</a>, <a href="../authors/kammueller">Florian Kammüller</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtYmVybGluIiwiZGUiXSwidXNlciI6WyJmbG9rYW0iXX0=">📧</a>, <a href="../authors/lutz">Bianca Lutz</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtYmVybGluIiwiZGUiXSwidXNlciI6WyJzb3dpbG8iXX0=">📧</a> and <a href="../authors/sudhof">Henry Sudhof</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtYmVybGluIiwiZGUiXSwidXNlciI6WyJoc3VkaG9mIl19">📧</a>
</p>
<p class="date">April 30, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a Theory of Objects based on the original functional sigma-calculus by Abadi and Cardelli but with an additional parameter to methods. We prove confluence of the operational semantics following the outline of Nipkow's proof of confluence for the lambda-calculus reusing his theory Commutation, a generic diamond lemma reduction. We furthermore formalize a simple type system for our sigma-calculus including a proof of type safety. The entire development uses the concept of Locally Nameless representation for binders. We reuse an earlier proof of confluence for a simpler sigma-calculus based on de Bruijn indices and lists to represent objects.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session Locally-Nameless-Sigma</h3>
<ul>
<li><a href="../theories/locally-nameless-sigma/#ListPre">ListPre</a></li>
<li><a href="../theories/locally-nameless-sigma/#FMap">FMap</a></li>
<li><a href="../theories/locally-nameless-sigma/#Sigma">Sigma</a></li>
<li><a href="../theories/locally-nameless-sigma/#ParRed">ParRed</a></li>
<li><a href="../theories/locally-nameless-sigma/#Environments">Environments</a></li>
<li><a href="../theories/locally-nameless-sigma/#TypedSigma">TypedSigma</a></li>
<li><a href="../theories/locally-nameless-sigma/#Locally_Nameless_Sigma">Locally_Nameless_Sigma</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Applicative_Lifting.html">Applicative Lifting</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Locally-Nameless-Sigma-AFP</p><pre id="copy-text">@article{Locally-Nameless-Sigma-AFP,
author = {Ludovic Henrio and Florian Kammüller and Bianca Lutz and Henry Sudhof},
title = {Locally Nameless Sigma Calculus},
journal = {Archive of Formal Proofs},
month = {April},
year = {2010},
note = {\url{https://isa-afp.org/entries/Locally-Nameless-Sigma.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Locally-Nameless-Sigma-2010-05-03.tar.gz">May 3, 2010</a>: Isabelle2009-1
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Logging_Independent_Anonymity.html b/web/entries/Logging_Independent_Anonymity.html
--- a/web/entries/Logging_Independent_Anonymity.html
+++ b/web/entries/Logging_Independent_Anonymity.html
@@ -1,177 +1,179 @@
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<h1 >
<span class='first'>L</span>ogging-<span class='first'>I</span>ndependent <span class='first'>M</span>essage <span class='first'>A</span>nonymity in the <span class='first'>R</span>elational <span class='first'>M</span>ethod</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">August 26, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In the context of formal cryptographic protocol verification,
logging-independent message anonymity is the property for a given
message to remain anonymous despite the attacker's capability of
mapping messages of that sort to agents based on some intrinsic
feature of such messages, rather than by logging the messages
exchanged by legitimate agents as with logging-dependent message
anonymity.
This paper illustrates how logging-independent message
anonymity can be formalized according to the relational method for
formal protocol verification by considering a real-world protocol,
namely the Restricted Identification one by the BSI. This sample model
is used to verify that the pseudonymous identifiers output by user
identification tokens remain anonymous under the expected conditions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Logging_Independent_Anonymity</h3>
<ul>
<li><a href="../theories/logging_independent_anonymity/#Definitions">Definitions</a></li>
<li><a href="../theories/logging_independent_anonymity/#Anonymity">Anonymity</a></li>
<li><a href="../theories/logging_independent_anonymity/#Possibility">Possibility</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Logging_Independent_Anonymity-AFP</p><pre id="copy-text">@article{Logging_Independent_Anonymity-AFP,
author = {Pasquale Noce},
title = {Logging-independent Message Anonymity in the Relational Method},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/Logging_Independent_Anonymity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Logging_Independent_Anonymity-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Logging_Independent_Anonymity-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Logging_Independent_Anonymity-2021-09-05.tar.gz">Sep 5, 2021</a>: Isabelle2021
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diff --git a/web/entries/Lowe_Ontological_Argument.html b/web/entries/Lowe_Ontological_Argument.html
--- a/web/entries/Lowe_Ontological_Argument.html
+++ b/web/entries/Lowe_Ontological_Argument.html
@@ -1,186 +1,188 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Computer-assisted Reconstruction and Assessment of E. J. Lowe&#39;s Modal Ontological Argument - Archive of Formal Proofs</title><meta name="description" content="Computers may help us to understand --not just verify-- philosophical
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<h1 >
<span class='first'>C</span>omputer-<span class='first'>A</span>ssisted <span class='first'>R</span>econstruction and <span class='first'>A</span>ssessment of <span class='first'>E</span>. <span class='first'>J</span>. <span class='first'>L</span>owe's <span class='first'>M</span>odal <span class='first'>O</span>ntological <span class='first'>A</span>rgument</h1>
<div>
<p><a href="../authors/fuenmayor">David Fuenmayor</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZGF2ZnVlbm1heW9yIl19">📧</a> and <a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a>
</p>
<p class="date">September 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Computers may help us to understand --not just verify-- philosophical
arguments. By utilizing modern proof assistants in an iterative
interpretive process, we can reconstruct and assess an argument by
fully formal means. Through the mechanization of a variant of St.
Anselm's ontological argument by E. J. Lowe, which is a
paradigmatic example of a natural-language argument with strong ties
to metaphysics and religion, we offer an ideal showcase for our
computer-assisted interpretive method.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session Lowe_Ontological_Argument</h3>
<ul>
<li><a href="../theories/lowe_ontological_argument/#Relations">Relations</a></li>
<li><a href="../theories/lowe_ontological_argument/#QML">QML</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_1">LoweOntologicalArgument_1</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_2">LoweOntologicalArgument_2</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_3">LoweOntologicalArgument_3</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_4">LoweOntologicalArgument_4</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_5">LoweOntologicalArgument_5</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_6">LoweOntologicalArgument_6</a></li>
<li><a href="../theories/lowe_ontological_argument/#LoweOntologicalArgument_7">LoweOntologicalArgument_7</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lowe_Ontological_Argument-AFP</p><pre id="copy-text">@article{Lowe_Ontological_Argument-AFP,
author = {David Fuenmayor and Christoph Benzmüller},
title = {Computer-assisted Reconstruction and Assessment of E. J. Lowe&#39;s Modal Ontological Argument},
journal = {Archive of Formal Proofs},
month = {September},
year = {2017},
note = {\url{https://isa-afp.org/entries/Lowe_Ontological_Argument.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lowe_Ontological_Argument-2017-10-16.tar.gz">Oct 16, 2017</a>: Isabelle2017
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Lower Semicontinuous Functions - Archive of Formal Proofs</title><meta name="description" content="We define the notions of lower and upper semicontinuity for functions from a metric space to the extended real line. We prove that a function is both lower..."><meta property="og:title" content="Lower Semicontinuous Functions" />
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<h1 >
<span class='first'>L</span>ower <span class='first'>S</span>emicontinuous <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/grechuk">Bogdan Grechuk</a> <a class="obfuscated" data="eyJob3N0IjpbInlhbmRleCIsInJ1Il0sInVzZXIiOlsiZ3JlY2h1a2JvZ2RhbiJdfQ==">📧</a>
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<p class="date">January 8, 2011</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We define the notions of lower and upper semicontinuity for functions from a metric space to the extended real line. We prove that a function is both lower and upper semicontinuous if and only if it is continuous. We also give several equivalent characterizations of lower semicontinuity. In particular, we prove that a function is lower semicontinuous if and only if its epigraph is a closed set. Also, we introduce the notion of the lower semicontinuous hull of an arbitrary function and prove its basic properties.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Lower_Semicontinuous</h3>
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<li><a href="../theories/lower_semicontinuous/#Lower_Semicontinuous">Lower_Semicontinuous</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Lower_Semicontinuous-AFP</p><pre id="copy-text">@article{Lower_Semicontinuous-AFP,
author = {Bogdan Grechuk},
title = {Lower Semicontinuous Functions},
journal = {Archive of Formal Proofs},
month = {January},
year = {2011},
note = {\url{https://isa-afp.org/entries/Lower_Semicontinuous.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Lower_Semicontinuous-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Lower_Semicontinuous-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li></ul>
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<h1 >
<span class='first'>L</span>p <span class='first'>S</span>paces</h1>
<div>
<p><a href="../authors/gouezel">Sebastien Gouezel</a> <a href="http://www.math.sciences.univ-nantes.fr/~gouezel/">🌐</a>
</p>
<p class="date">October 5, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Lp is the space of functions whose p-th power is integrable. It is one of the most fundamental Banach spaces that is used in analysis and probability. We develop a framework for function spaces, and then implement the Lp spaces in this framework using the existing integration theory in Isabelle/HOL. Our development contains most fundamental properties of Lp spaces, notably the Hölder and Minkowski inequalities, completeness of Lp, duality, stability under almost sure convergence, multiplication of functions in Lp and Lq, stability under conditional expectation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Lp</h3>
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<li><a href="../theories/lp/#Functional_Spaces">Functional_Spaces</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ergodic_Theory.html">Ergodic Theory</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li><li><a href="../entries/Fourier.html">Fourier Series</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Lp-AFP</p><pre id="copy-text">@article{Lp-AFP,
author = {Sebastien Gouezel},
title = {Lp spaces},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Lp.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>L</span>ucas's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a>
</p>
<p class="date">April 7, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work presents a formalisation of a generating function proof for
Lucas's theorem. We first outline extensions to the existing
Formal Power Series (FPS) library, including an equivalence relation
for coefficients modulo <em>n</em>, an alternate binomial theorem statement,
and a formalised proof of the Freshman's dream (mod <em>p</em>) lemma.
The second part of the work presents the formal proof of Lucas's
Theorem. Working backwards, the formalisation first proves a well
known corollary of the theorem which is easier to formalise, and then
applies induction to prove the original theorem statement. The proof
of the corollary aims to provide a good example of a formalised
generating function equivalence proof using the FPS library. The final
theorem statement is intended to be integrated into the formalised
proof of Hilbert's 10th Problem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Lucas_Theorem</h3>
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<p style="display:none;" id="bibtex-filename">Lucas_Theorem-AFP</p><pre id="copy-text">@article{Lucas_Theorem-AFP,
author = {Chelsea Edmonds},
title = {Lucas&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Lucas_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>V</span>erified <span class='first'>A</span>lgorithms for <span class='first'>S</span>olving <span class='first'>M</span>arkov <span class='first'>D</span>ecision <span class='first'>P</span>rocesses</h1>
<div>
<p><a href="../authors/schaeffeler">Maximilian Schäffeler</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJzY2hhZWZmbSJdfQ==">📧</a> and <a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJtb2hhbW1hZCIsImFiZHVsYXppeiJdfQ==">📧</a>
</p>
<p class="date">December 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of algorithms for solving Markov Decision
Processes (MDPs) with formal guarantees on the optimality of their
solutions. In particular we build on our analysis of the Bellman
operator for discounted infinite horizon MDPs. From the iterator rule
on the Bellman operator we directly derive executable value iteration
and policy iteration algorithms to iteratively solve finite MDPs. We
also prove correct optimized versions of value iteration that use
matrix splittings to improve the convergence rate. In particular, we
formally verify Gauss-Seidel value iteration and modified policy
iteration. The algorithms are evaluated on two standard examples from
the literature, namely, inventory management and gridworld. Our
formalization covers most of chapter 6 in Puterman's book
"Markov Decision Processes: Discrete Stochastic Dynamic
Programming".</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session MDP-Algorithms</h3>
<ul>
<li><a href="../theories/mdp-algorithms/#Value_Iteration">Value_Iteration</a></li>
<li><a href="../theories/mdp-algorithms/#Policy_Iteration">Policy_Iteration</a></li>
<li><a href="../theories/mdp-algorithms/#Modified_Policy_Iteration">Modified_Policy_Iteration</a></li>
<li><a href="../theories/mdp-algorithms/#Matrix_Util">Matrix_Util</a></li>
<li><a href="../theories/mdp-algorithms/#Blinfun_Matrix">Blinfun_Matrix</a></li>
<li><a href="../theories/mdp-algorithms/#Splitting_Methods">Splitting_Methods</a></li>
<li><a href="../theories/mdp-algorithms/#Algorithms">Algorithms</a></li>
<li><a href="../theories/mdp-algorithms/#Code_DP">Code_DP</a></li>
<li><a href="../theories/mdp-algorithms/#Code_Mod">Code_Mod</a></li>
<li><a href="../theories/mdp-algorithms/#Code_Inventory">Code_Inventory</a></li>
<li><a href="../theories/mdp-algorithms/#Code_Gridworld">Code_Gridworld</a></li>
<li><a href="../theories/mdp-algorithms/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li><li><a href="../entries/MDP-Rewards.html">Markov Decision Processes with Rewards</a></li></ul>
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<p style="display:none;" id="bibtex-filename">MDP-Algorithms-AFP</p><pre id="copy-text">@article{MDP-Algorithms-AFP,
author = {Maximilian Schäffeler and Mohammad Abdulaziz},
title = {Verified Algorithms for Solving Markov Decision Processes},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/MDP-Algorithms.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-MDP-Algorithms-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MDP-Algorithms-2021-12-28.tar.gz">Dec 28, 2021</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/MDP-Rewards.html b/web/entries/MDP-Rewards.html
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@@ -1,177 +1,182 @@
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In particular we first build on Hölzl&#39;s formalization of MDPs
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<h1 >
<span class='first'>M</span>arkov <span class='first'>D</span>ecision <span class='first'>P</span>rocesses <span class='first'>W</span>ith <span class='first'>R</span>ewards</h1>
<div>
<p><a href="../authors/schaeffeler">Maximilian Schäffeler</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJzY2hhZWZmbSJdfQ==">📧</a> and <a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJtb2hhbW1hZCIsImFiZHVsYXppeiJdfQ==">📧</a>
</p>
<p class="date">December 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of Markov Decision Processes with rewards.
In particular we first build on Hölzl's formalization of MDPs
(AFP entry: Markov_Models) and extend them with rewards. We proceed
with an analysis of the expected total discounted reward criterion for
infinite horizon MDPs. The central result is the construction of the
iteration rule for the Bellman operator. We prove the optimality
equations for this operator and show the existence of an optimal
stationary deterministic solution. The analysis can be used to obtain
dynamic programming algorithms such as value iteration and policy
iteration to solve MDPs with formal guarantees. Our formalization is
based on chapters 5 and 6 in Puterman's book "Markov
Decision Processes: Discrete Stochastic Dynamic Programming".</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session MDP-Rewards</h3>
<ul>
<li><a href="../theories/mdp-rewards/#Bounded_Functions">Bounded_Functions</a></li>
<li><a href="../theories/mdp-rewards/#Blinfun_Util">Blinfun_Util</a></li>
<li><a href="../theories/mdp-rewards/#MDP_reward_Util">MDP_reward_Util</a></li>
<li><a href="../theories/mdp-rewards/#MDP_cont">MDP_cont</a></li>
<li><a href="../theories/mdp-rewards/#MDP_disc">MDP_disc</a></li>
<li><a href="../theories/mdp-rewards/#MDP_reward">MDP_reward</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MDP-Algorithms.html">Verified Algorithms for Solving Markov Decision Processes</a></li></ul>
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<p style="display:none;" id="bibtex-filename">MDP-Rewards-AFP</p><pre id="copy-text">@article{MDP-Rewards-AFP,
author = {Maximilian Schäffeler and Mohammad Abdulaziz},
title = {Markov Decision Processes with Rewards},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/MDP-Rewards.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-MDP-Rewards-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MDP-Rewards-2021-12-28.tar.gz">Dec 28, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>P</span>roof of the <span class='first'>M</span>ax-<span class='first'>F</span>low <span class='first'>M</span>in-<span class='first'>C</span>ut <span class='first'>T</span>heorem for <span class='first'>C</span>ountable <span class='first'>N</span>etworks</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 9, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalises a proof of the maximum-flow minimal-cut
theorem for networks with countably many edges. A network is a
directed graph with non-negative real-valued edge labels and two
dedicated vertices, the source and the sink. A flow in a network
assigns non-negative real numbers to the edges such that for all
vertices except for the source and the sink, the sum of values on
incoming edges equals the sum of values on outgoing edges. A cut is a
subset of the vertices which contains the source, but not the sink.
Our theorem states that in every network, there is a flow and a cut
such that the flow saturates all the edges going out of the cut and is
zero on all the incoming edges. The proof is based on the paper
<emph>The Max-Flow Min-Cut theorem for countable networks</emph> by
Aharoni et al. Additionally, we prove a characterisation of the
lifting operation for relations on discrete probability distributions,
which leads to a concise proof of its distributivity over relation
composition.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>August 13, 2021</dt>
<dd>generalize the derivation of the characterisation for the relator of discrete probability distributions to work for the bounded and unbounded MFMC theorem
(revision 3c85bb52bbe6)<br></dd><dt>December 19, 2020</dt>
<dd>simpler proof of linkability for bounded unhindered bipartite webs, leading to a simpler proof for networks with bounded out-capacities
(revision 93ca33f4d915)<br>
</dd><dt>September 6, 2017</dt>
<dd>derive characterisation for the lifting operation on discrete distributions from finite version of the max-flow min-cut theorem
(revision a7a198f5bab0)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session MFMC_Countable</h3>
<ul>
<li><a href="../theories/mfmc_countable/#MFMC_Misc">MFMC_Misc</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Finite">MFMC_Finite</a></li>
<li><a href="../theories/mfmc_countable/#Matrix_For_Marginals">Matrix_For_Marginals</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Network">MFMC_Network</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Web">MFMC_Web</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Reduction">MFMC_Reduction</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Bounded">MFMC_Bounded</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Flow_Attainability">MFMC_Flow_Attainability</a></li>
<li><a href="../theories/mfmc_countable/#MFMC_Unbounded">MFMC_Unbounded</a></li>
<li><a href="../theories/mfmc_countable/#Max_Flow_Min_Cut_Countable">Max_Flow_Min_Cut_Countable</a></li>
<li><a href="../theories/mfmc_countable/#Rel_PMF_Characterisation">Rel_PMF_Characterisation</a></li>
<li><a href="../theories/mfmc_countable/#Rel_PMF_Characterisation_MFMC">Rel_PMF_Characterisation_MFMC</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Probabilistic_While.html">Probabilistic while loop</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Randomised_BSTs.html">Randomised Binary Search Trees</a></li>
<li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">MFMC_Countable-AFP</p><pre id="copy-text">@article{MFMC_Countable-AFP,
author = {Andreas Lochbihler},
title = {A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/MFMC_Countable.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-MFMC_Countable-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MFMC_Countable-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-MFMC_Countable-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-MFMC_Countable-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-MFMC_Countable-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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diff --git a/web/entries/MFODL_Monitor_Optimized.html b/web/entries/MFODL_Monitor_Optimized.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations - Archive of Formal Proofs</title><meta name="description" content="A monitor is a runtime verification tool that solves the following problem: Given a stream of time-stamped events and a policy formulated in a..."><meta property="og:title" content="Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations" />
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<h1 >
<span class='first'>F</span>ormalization of an <span class='first'>O</span>ptimized <span class='first'>M</span>onitoring <span class='first'>A</span>lgorithm for <span class='first'>M</span>etric <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>D</span>ynamic <span class='first'>L</span>ogic <span class='first'>W</span>ith <span class='first'>A</span>ggregations</h1>
<div>
<p><a href="../authors/dardinier">Thibault Dardinier</a>, <a href="../authors/heimes">Lukas Heimes</a>, <a href="../authors/raszyk">Martin Raszyk</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbIm1hcnRpbiIsInJhc3p5ayJdfQ==">📧</a>, <a href="../authors/schneider">Joshua Schneider</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbImpvc2h1YSIsInNjaG5laWRlciJdfQ==">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">April 9, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A monitor is a runtime verification tool that solves the following
problem: Given a stream of time-stamped events and a policy formulated
in a specification language, decide whether the policy is satisfied at
every point in the stream. We verify the correctness of an executable
monitor for specifications given as formulas in metric first-order
dynamic logic (MFODL), which combines the features of metric
first-order temporal logic (MFOTL) and metric dynamic logic. Thus,
MFODL supports real-time constraints, first-order parameters, and
regular expressions. Additionally, the monitor supports aggregation
operations such as count and sum. This formalization, which is
described in a <a href="http://people.inf.ethz.ch/trayteld/papers/ijcar20-verimonplus/verimonplus.pdf">
forthcoming paper at IJCAR 2020</a>, significantly extends <a
href="https://www.isa-afp.org/entries/MFOTL_Monitor.html">previous
work on a verified monitor</a> for MFOTL. Apart from the
addition of regular expressions and aggregations, we implemented <a
href="https://www.isa-afp.org/entries/Generic_Join.html">multi-way
joins</a> and a specialized sliding window algorithm to further
optimize the monitor.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>October 19, 2021</dt>
<dd>corrected a mistake in the calculation of median aggregations
(reported by Nicolas Kaletsch, revision 02b14c9bf3da)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session MFODL_Monitor_Optimized</h3>
<ul>
<li><a href="../theories/mfodl_monitor_optimized/#Code_Double">Code_Double</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Event_Data">Event_Data</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Regex">Regex</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Formula">Formula</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Optimized_Join">Optimized_Join</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Monitor">Monitor</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Optimized_MTL">Optimized_MTL</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Monitor_Impl">Monitor_Impl</a></li>
<li><a href="../theories/mfodl_monitor_optimized/#Monitor_Code">Monitor_Code</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Generic_Join.html">Formalization of Multiway-Join Algorithms</a></li><li><a href="../entries/IEEE_Floating_Point.html">A Formal Model of IEEE Floating Point Arithmetic</a></li><li><a href="../entries/MFOTL_Monitor.html">Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/VYDRA_MDL.html">Multi-Head Monitoring of Metric Dynamic Logic</a></li>
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<p style="display:none;" id="bibtex-filename">MFODL_Monitor_Optimized-AFP</p><pre id="copy-text">@article{MFODL_Monitor_Optimized-AFP,
author = {Thibault Dardinier and Lukas Heimes and Martin Raszyk and Joshua Schneider and Dmitriy Traytel},
title = {Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/MFODL_Monitor_Optimized.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-MFODL_Monitor_Optimized-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>F</span>ormalization of a <span class='first'>M</span>onitoring <span class='first'>A</span>lgorithm for <span class='first'>M</span>etric <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>T</span>emporal <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/schneider">Joshua Schneider</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbImpvc2h1YSIsInNjaG5laWRlciJdfQ==">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">July 4, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A monitor is a runtime verification tool that solves the following
problem: Given a stream of time-stamped events and a policy formulated
in a specification language, decide whether the policy is satisfied at
every point in the stream. We verify the correctness of an executable
monitor for specifications given as formulas in metric first-order
temporal logic (MFOTL), an expressive extension of linear temporal
logic with real-time constraints and first-order quantification. The
verified monitor implements a simplified variant of the algorithm used
in the efficient MonPoly monitoring tool. The formalization is
presented in a <a href="https://doi.org/10.1007/978-3-030-32079-9_18">RV
2019 paper</a>, which also compares the output of the verified
monitor to that of other monitoring tools on randomly generated
inputs. This case study revealed several errors in the optimized but
unverified tools.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>August 13, 2020</dt>
<dd>added the formalization of the abstract slicing framework and joint data
slicer (revision b1639ed541b7)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session MFOTL_Monitor</h3>
<ul>
<li><a href="../theories/mfotl_monitor/#Trace">Trace</a></li>
<li><a href="../theories/mfotl_monitor/#Table">Table</a></li>
<li><a href="../theories/mfotl_monitor/#Abstract_Monitor">Abstract_Monitor</a></li>
<li><a href="../theories/mfotl_monitor/#Interval">Interval</a></li>
<li><a href="../theories/mfotl_monitor/#MFOTL">MFOTL</a></li>
<li><a href="../theories/mfotl_monitor/#Monitor">Monitor</a></li>
<li><a href="../theories/mfotl_monitor/#Slicing">Slicing</a></li>
<li><a href="../theories/mfotl_monitor/#Monitor_Code">Monitor_Code</a></li>
<li><a href="../theories/mfotl_monitor/#Examples">Examples</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Containers.html">Light-weight Containers</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MFODL_Monitor_Optimized.html">Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</a></li><li><a href="../entries/Generic_Join.html">Formalization of Multiway-Join Algorithms</a></li></ul>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MFODL_Monitor_Optimized.html">Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</a></li>
<li><a href="../entries/LTL_Master_Theorem.html">A Compositional and Unified Translation of LTL into ω-Automata</a></li>
<li><a href="../entries/LTL.html">Linear Temporal Logic</a></li>
<li><a href="../entries/RefinementReactive.html">Formalization of Refinement Calculus for Reactive Systems</a></li>
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<p style="display:none;" id="bibtex-filename">MFOTL_Monitor-AFP</p><pre id="copy-text">@article{MFOTL_Monitor-AFP,
author = {Joshua Schneider and Dmitriy Traytel},
title = {Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic},
journal = {Archive of Formal Proofs},
month = {July},
year = {2019},
note = {\url{https://isa-afp.org/entries/MFOTL_Monitor.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-MFOTL_Monitor-2019-07-05.tar.gz">Jul 5, 2019</a>: Isabelle2019
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diff --git a/web/entries/MSO_Regex_Equivalence.html b/web/entries/MSO_Regex_Equivalence.html
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<h1 >
<span class='first'>D</span>ecision <span class='first'>P</span>rocedures for <span class='first'>M</span><span class='first'>S</span><span class='first'>O</span> on <span class='first'>W</span>ords <span class='first'>B</span>ased on <span class='first'>D</span>erivatives of <span class='first'>R</span>egular <span class='first'>E</span>xpressions</h1>
<div>
<p><a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 12, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Monadic second-order logic on finite words (MSO) is a decidable yet
expressive logic into which many decision problems can be encoded. Since MSO
formulas correspond to regular languages, equivalence of MSO formulas can be
reduced to the equivalence of some regular structures (e.g. automata). We
verify an executable decision procedure for MSO formulas that is not based
on automata but on regular expressions.
<p>
Decision procedures for regular expression equivalence have been formalized
before, usually based on Brzozowski derivatives. Yet, for a straightforward
embedding of MSO formulas into regular expressions an extension of regular
expressions with a projection operation is required. We prove total
correctness and completeness of an equivalence checker for regular
expressions extended in that way. We also define a language-preserving
translation of formulas into regular expressions with respect to two
different semantics of MSO.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/logic/general-logic/decidability-of-theories">Logic/General logic/Decidability of theories</a></li></ul><h3>Related publications</h3>
<ul><li>
TRAYTEL, D., & NIPKOW, T. (2015). Verified decision procedures for MSO on words based on derivatives of regular expressions. Journal of Functional Programming, 25. https://doi.org/10.1017/s0956796815000246
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jfp15.html">Open access</a>
</li></ul>
<h3>Session MSO_Regex_Equivalence</h3>
<ul>
<li><a href="../theories/mso_regex_equivalence/#List_More">List_More</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Regular_Set">Pi_Regular_Set</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Regular_Exp">Pi_Regular_Exp</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Derivatives">Pi_Derivatives</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Regular_Operators">Pi_Regular_Operators</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Regular_Exp_Dual">Pi_Regular_Exp_Dual</a></li>
<li><a href="../theories/mso_regex_equivalence/#Pi_Equivalence_Checking">Pi_Equivalence_Checking</a></li>
<li><a href="../theories/mso_regex_equivalence/#Init_Normalization">Init_Normalization</a></li>
<li><a href="../theories/mso_regex_equivalence/#PNormalization">PNormalization</a></li>
<li><a href="../theories/mso_regex_equivalence/#Formula">Formula</a></li>
<li><a href="../theories/mso_regex_equivalence/#M2L">M2L</a></li>
<li><a href="../theories/mso_regex_equivalence/#M2L_Normalization">M2L_Normalization</a></li>
<li><a href="../theories/mso_regex_equivalence/#M2L_Equivalence_Checking">M2L_Equivalence_Checking</a></li>
<li><a href="../theories/mso_regex_equivalence/#WS1S">WS1S</a></li>
<li><a href="../theories/mso_regex_equivalence/#WS1S_Normalization">WS1S_Normalization</a></li>
<li><a href="../theories/mso_regex_equivalence/#WS1S_Equivalence_Checking">WS1S_Equivalence_Checking</a></li>
<li><a href="../theories/mso_regex_equivalence/#M2L_Examples">M2L_Examples</a></li>
<li><a href="../theories/mso_regex_equivalence/#WS1S_Examples">WS1S_Examples</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></li>
<li><a href="../entries/Coinductive_Languages.html">A Codatatype of Formal Languages</a></li>
<li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li>
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<p style="display:none;" id="bibtex-filename">MSO_Regex_Equivalence-AFP</p><pre id="copy-text">@article{MSO_Regex_Equivalence-AFP,
author = {Dmitriy Traytel and Tobias Nipkow},
title = {Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions},
journal = {Archive of Formal Proofs},
month = {June},
year = {2014},
note = {\url{https://isa-afp.org/entries/MSO_Regex_Equivalence.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-MSO_Regex_Equivalence-2014-06-12.tar.gz">Jun 12, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/Markov_Models.html b/web/entries/Markov_Models.html
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<h1 >
<span class='first'>M</span>arkov <span class='first'>M</span>odels</h1>
<div>
<p><a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">January 3, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalization of Markov models in Isabelle/HOL. It
builds on Isabelle's probability theory. The available models are
currently Discrete-Time Markov Chains and a extensions of them with
rewards.
<p>
As application of these models we formalize probabilistic model
checking of pCTL formulas, analysis of IPv4 address allocation in
ZeroConf and an analysis of the anonymity of the Crowds protocol.
<a href="http://arxiv.org/abs/1212.3870">See here for the corresponding paper.</a></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Hölzl, J. (2016). Markov Chains and Markov Decision Processes in Isabelle/HOL. Journal of Automated Reasoning, 59(3), 345–387. <a href="https://doi.org/10.1007/s10817-016-9401-5">https://doi.org/10.1007/s10817-016-9401-5</a>
</li><li>
Hölzl, J., & Nipkow, T. (2012). Verifying pCTL Model Checking. Lecture Notes in Computer Science, 347–361. <a href="https://doi.org/10.1007/978-3-642-28756-5_24">https://doi.org/10.1007/978-3-642-28756-5_24</a>
</li><li>
<a href="https://arxiv.org/abs/1212.3870v1">Case studies in Proceedings QFM 2012</a>
</li></ul>
<h3>Session Markov_Models</h3>
<ul>
<li><a href="../theories/markov_models/#Markov_Models_Auxiliary">Markov_Models_Auxiliary</a></li>
<li><a href="../theories/markov_models/#Discrete_Time_Markov_Chain">Discrete_Time_Markov_Chain</a></li>
<li><a href="../theories/markov_models/#Trace_Space_Equals_Markov_Processes">Trace_Space_Equals_Markov_Processes</a></li>
<li><a href="../theories/markov_models/#Classifying_Markov_Chain_States">Classifying_Markov_Chain_States</a></li>
<li><a href="../theories/markov_models/#Markov_Decision_Process">Markov_Decision_Process</a></li>
<li><a href="../theories/markov_models/#MDP_Reachability_Problem">MDP_Reachability_Problem</a></li>
<li><a href="../theories/markov_models/#Discrete_Time_Markov_Process">Discrete_Time_Markov_Process</a></li>
<li><a href="../theories/markov_models/#Continuous_Time_Markov_Chain">Continuous_Time_Markov_Chain</a></li>
<li><a href="../theories/markov_models/#Markov_Models">Markov_Models</a></li>
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<li><a href="../theories/markov_models/#Example_B">Example_B</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Gauss-Jordan-Elim-Fun.html">Gauss-Jordan Elimination for Matrices Represented as Functions</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hidden_Markov_Models.html">Hidden Markov Models</a></li><li><a href="../entries/Probabilistic_Timed_Automata.html">Probabilistic Timed Automata</a></li><li><a href="../entries/Stochastic_Matrices.html">Stochastic Matrices and the Perron-Frobenius Theorem</a></li><li><a href="../entries/Probabilistic_Noninterference.html">Probabilistic Noninterference</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Markov_Models-AFP</p><pre id="copy-text">@article{Markov_Models-AFP,
author = {Johannes Hölzl and Tobias Nipkow},
title = {Markov Models},
journal = {Archive of Formal Proofs},
month = {January},
year = {2012},
note = {\url{https://isa-afp.org/entries/Markov_Models.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Marriage.html b/web/entries/Marriage.html
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<h1 >
<span class='first'>H</span>all's <span class='first'>M</span>arriage <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/jiangd">Dongchen Jiang</a> <a class="obfuscated" data="eyJob3N0IjpbImdvb2dsZW1haWwiLCJjb20iXSwidXNlciI6WyJkb25nY2hlbmppYW5nIl19">📧</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">December 17, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Two proofs of Hall's Marriage Theorem: one due to Halmos and Vaughan, one due to Rado.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 9, 2011</dt>
<dd>Added Rado's proof</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul><h3>Related publications</h3>
<ul><li>
Jiang, D., & Nipkow, T. (2011). Proof Pearl: The Marriage Theorem. Lecture Notes in Computer Science, 394–399. <a href="https://doi.org/10.1007/978-3-642-25379-9_28">https://doi.org/10.1007/978-3-642-25379-9_28</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/cpp11.html">Open access</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Hall%27s_marriage_theorem">Wikipedia</a>
</li></ul>
<h3>Session Marriage</h3>
<ul>
<li><a href="../theories/marriage/#Marriage">Marriage</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Latin_Square.html">Latin Square</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Marriage-AFP</p><pre id="copy-text">@article{Marriage-AFP,
author = {Dongchen Jiang and Tobias Nipkow},
title = {Hall&#39;s Marriage Theorem},
journal = {Archive of Formal Proofs},
month = {December},
year = {2010},
note = {\url{https://isa-afp.org/entries/Marriage.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Mason_Stothers.html b/web/entries/Mason_Stothers.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Mason–Stothers Theorem - Archive of Formal Proofs</title><meta name="description" content="This article provides a formalisation of Snyder’s simple and elegant proof of the Mason&amp;ndash;Stothers theorem, which is the polynomial analogue of the..."><meta property="og:title" content="The Mason–Stothers Theorem" />
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<h1 >
<span class='first'>T</span>he <span class='first'>M</span>ason–<span class='first'>S</span>tothers <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of Snyder’s simple and
elegant proof of the Mason&ndash;Stothers theorem, which is the
polynomial analogue of the famous abc Conjecture for integers.
Remarkably, Snyder found this very elegant proof when he was still a
high-school student.</p> <p>In short, the statement of the
theorem is that three non-zero coprime polynomials
<em>A</em>, <em>B</em>, <em>C</em>
over a field which sum to 0 and do not all have vanishing derivatives
fulfil max{deg(<em>A</em>), deg(<em>B</em>),
deg(<em>C</em>)} < deg(rad(<em>ABC</em>))
where the rad(<em>P</em>) denotes the
<em>radical</em> of <em>P</em>,
i.&thinsp;e. the product of all unique irreducible factors of
<em>P</em>.</p> <p>This theorem also implies a
kind of polynomial analogue of Fermat’s Last Theorem for polynomials:
except for trivial cases,
<em>A<sup>n</sup></em> +
<em>B<sup>n</sup></em> +
<em>C<sup>n</sup></em> = 0 implies
n&nbsp;&le;&nbsp;2 for coprime polynomials
<em>A</em>, <em>B</em>, <em>C</em>
over a field.</em></p></div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Mason_Stothers</h3>
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<li><a href="../theories/mason_stothers/#Mason_Stothers">Mason_Stothers</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Mason_Stothers-AFP</p><pre id="copy-text">@article{Mason_Stothers-AFP,
author = {Manuel Eberl},
title = {The Mason–Stothers Theorem},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/Mason_Stothers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>M</span>atrices for <span class='first'>O</span><span class='first'>D</span><span class='first'>E</span>s</h1>
<div>
<p><a href="../authors/munive">Jonathan Julian Huerta y Munive</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJqamh1ZXJ0YXltdW5pdmUxIl19">📧</a>
</p>
<p class="date">April 19, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Our theories formalise various matrix properties that serve to
establish existence, uniqueness and characterisation of the solution
to affine systems of ordinary differential equations (ODEs). In
particular, we formalise the operator and maximum norm of matrices.
Then we use them to prove that square matrices form a Banach space,
and in this setting, we show an instance of Picard-Lindelöf’s
theorem for affine systems of ODEs. Finally, we use this formalisation
to verify three simple hybrid programs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Matrices_for_ODEs</h3>
<ul>
<li><a href="../theories/matrices_for_odes/#MTX_Preliminaries">MTX_Preliminaries</a></li>
<li><a href="../theories/matrices_for_odes/#MTX_Norms">MTX_Norms</a></li>
<li><a href="../theories/matrices_for_odes/#SQ_MTX">SQ_MTX</a></li>
<li><a href="../theories/matrices_for_odes/#MTX_Flows">MTX_Flows</a></li>
<li><a href="../theories/matrices_for_odes/#MTX_Examples">MTX_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Poincare_Bendixson.html">The Poincaré-Bendixson Theorem</a></li>
<li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li>
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<p style="display:none;" id="bibtex-filename">Matrices_for_ODEs-AFP</p><pre id="copy-text">@article{Matrices_for_ODEs-AFP,
author = {Jonathan Julian Huerta y Munive},
title = {Matrices for ODEs},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Matrices_for_ODEs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>xecutable <span class='first'>M</span>atrix <span class='first'>O</span>perations on <span class='first'>M</span>atrices of <span class='first'>A</span>rbitrary <span class='first'>D</span>imensions</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">June 17, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide the operations of matrix addition, multiplication,
transposition, and matrix comparisons as executable functions over
ordered semirings. Moreover, it is proven that strongly normalizing
(monotone) orders can be lifted to strongly normalizing (monotone) orders
over matrices. We further show that the standard semirings over the
naturals, integers, and rationals, as well as the arctic semirings
satisfy the axioms that are required by our matrix theory. Our
formalization is part of the <a
href="http://cl-informatik.uibk.ac.at/software/ceta">CeTA</a> system
which contains several termination techniques. The provided theories have
been essential to formalize matrix-interpretations and arctic
interpretations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>September 17, 2010</dt>
<dd>Moved theory on arbitrary (ordered) semirings to Abstract Rewriting.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Matrix</h3>
<ul>
<li><a href="../theories/matrix/#Utility">Utility</a></li>
<li><a href="../theories/matrix/#Ordered_Semiring">Ordered_Semiring</a></li>
<li><a href="../theories/matrix/#Matrix_Legacy">Matrix_Legacy</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Matrix_Tensor.html">Tensor Product of Matrices</a></li><li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Matrix-AFP</p><pre id="copy-text">@article{Matrix-AFP,
author = {Christian Sternagel and René Thiemann},
title = {Executable Matrix Operations on Matrices of Arbitrary Dimensions},
journal = {Archive of Formal Proofs},
month = {June},
year = {2010},
note = {\url{https://isa-afp.org/entries/Matrix.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>ensor <span class='first'>P</span>roduct of <span class='first'>M</span>atrices</h1>
<div>
<p><a href="../authors/prathamesh">T.V.H. Prathamesh</a> <a class="obfuscated" data="eyJob3N0IjpbImltc2MiLCJyZXMiLCJpbiJdLCJ1c2VyIjpbInByYXRoYW1lc2giXX0=">📧</a>
</p>
<p class="date">January 18, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work, the Kronecker tensor product of matrices and the proofs of
some of its properties are formalized. Properties which have been formalized
include associativity of the tensor product and the mixed-product
property.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Matrix_Tensor</h3>
<ul>
<li><a href="../theories/matrix_tensor/#Matrix_Tensor">Matrix_Tensor</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Isabelle_Marries_Dirac.html">Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</a></li><li><a href="../entries/Knot_Theory.html">Knot Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Matrix_Tensor-AFP</p><pre id="copy-text">@article{Matrix_Tensor-AFP,
author = {T.V.H. Prathamesh},
title = {Tensor Product of Matrices},
journal = {Archive of Formal Proofs},
month = {January},
year = {2016},
note = {\url{https://isa-afp.org/entries/Matrix_Tensor.html},
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<h1 >
<span class='first'>M</span>atroids</h1>
<div>
<p><a href="../authors/keinholz">Jonas Keinholz</a>
</p>
<p class="date">November 16, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article defines the combinatorial structures known as
<em>Independence Systems</em> and
<em>Matroids</em> and provides basic concepts and theorems
related to them. These structures play an important role in
combinatorial optimisation, e. g. greedy algorithms such as
Kruskal's algorithm. The development is based on Oxley's
<a href="http://www.math.lsu.edu/~oxley/survey4.pdf">`What
is a Matroid?'</a>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Matroids</h3>
<ul>
<li><a href="../theories/matroids/#Indep_System">Indep_System</a></li>
<li><a href="../theories/matroids/#Matroid">Matroid</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Kruskal.html">Kruskal&rsquo;s Algorithm for Minimum Spanning Forest</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Matroids-AFP</p><pre id="copy-text">@article{Matroids-AFP,
author = {Jonas Keinholz},
title = {Matroids},
journal = {Archive of Formal Proofs},
month = {November},
year = {2018},
note = {\url{https://isa-afp.org/entries/Matroids.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Max-Card-Matching.html b/web/entries/Max-Card-Matching.html
--- a/web/entries/Max-Card-Matching.html
+++ b/web/entries/Max-Card-Matching.html
@@ -1,207 +1,209 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Maximum Cardinality Matching - Archive of Formal Proofs</title><meta name="description" content=" A matching in a graph G is a subset M of the edges of G such that no two share an endpoint. A matching has maximum cardinality if its cardinality is at..."><meta property="og:title" content="Maximum Cardinality Matching" />
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<h1 >
<span class='first'>M</span>aximum <span class='first'>C</span>ardinality <span class='first'>M</span>atching</h1>
<div>
<p><a href="../authors/rizkallah">Christine Rizkallah</a> <a href="https://www.mpi-inf.mpg.de/~crizkall/">🌐</a>
</p>
<p class="date">July 21, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
A <em>matching</em> in a graph <i>G</i> is a subset <i>M</i> of the
edges of <i>G</i> such that no two share an endpoint. A matching has maximum
cardinality if its cardinality is at least as large as that of any other
matching. An <em>odd-set cover</em> <i>OSC</i> of a graph <i>G</i> is a
labeling of the nodes of <i>G</i> with integers such that every edge of
<i>G</i> is either incident to a node labeled 1 or connects two nodes
labeled with the same number <i>i &ge; 2</i>.
</p><p>
This article proves Edmonds theorem:<br>
Let <i>M</i> be a matching in a graph <i>G</i> and let <i>OSC</i> be an
odd-set cover of <i>G</i>.
For any <i>i &ge; 0</i>, let <var>n(i)</var> be the number of nodes
labeled <i>i</i>. If <i>|M| = n(1) +
&sum;<sub>i &ge; 2</sub>(n(i) div 2)</i>,
then <i>M</i> is a maximum cardinality matching.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Max-Card-Matching</h3>
<ul>
<li><a href="../theories/max-card-matching/#Matching">Matching</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Max-Card-Matching-AFP</p><pre id="copy-text">@article{Max-Card-Matching-AFP,
author = {Christine Rizkallah},
title = {Maximum Cardinality Matching},
journal = {Archive of Formal Proofs},
month = {July},
year = {2011},
note = {\url{https://isa-afp.org/entries/Max-Card-Matching.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>M</span>aximum <span class='first'>S</span>egment <span class='first'>S</span>um</h1>
<div>
<p><a href="../authors/cremer">Nils Cremer</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsibmlscyIsImNyZW1lciJdfQ==">📧</a>
with contributions from <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">September 29, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work we consider the <a
href="https://en.wikipedia.org/wiki/Maximum_subarray_problem">maximum
segment sum</a> problem, that is to compute, given a list of
numbers, the largest of the sums of the contiguous segments of that
list. We assume that the elements of the list are not necessarily
numbers but just elements of some linearly ordered group. Both
a naive algorithm ($\mathcal{O}(n^2)$) and
<a
href="https://en.wikipedia.org/wiki/Maximum_subarray_problem#Kadane's_algorithm">Kadane's
algorithm</a> ($\mathcal{O}(n)$) are given and their correctness
is proved.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Maximum_Segment_Sum</h3>
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<p style="display:none;" id="bibtex-filename">Maximum_Segment_Sum-AFP</p><pre id="copy-text">@article{Maximum_Segment_Sum-AFP,
author = {Nils Cremer},
title = {Maximum Segment Sum},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Maximum_Segment_Sum.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Median_Method.html b/web/entries/Median_Method.html
--- a/web/entries/Median_Method.html
+++ b/web/entries/Median_Method.html
@@ -1,177 +1,182 @@
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<h1 >
<span class='first'>M</span>edian <span class='first'>M</span>ethod</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">January 25, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The median method is an amplification result for randomized
approximation algorithms described in [<a
href="https://doi.org/10.1006/jcss.1997.1545">1</a>].
Given an algorithm whose result is in a desired interval with a
probability larger than <i>1/2</i>, it is possible to
improve the success probability, by running the algorithm multiple
times independently and using the median. In contrast to using the
mean, the amplification of the success probability grows exponentially
with the number of independent runs.</p> <p>This entry
contains a formalization of the underlying theorem: Given a sequence
of n independent random variables, which are in a desired interval
with a probability <i>1/2 + a</i>. Then their median will
be in the desired interval with a probability of <i>1 −
exp(−2a<sup>2</sup> n)</i>. In particular, the
success probability approaches <i>1</i> exponentially with
the number of variables.</p> <p>In addition to that, this
entry also contains a proof that order-statistics of Borel-measurable
random variables are themselves measurable and that generalized
intervals in linearly ordered Borel-spaces are measurable.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Median_Method</h3>
<ul>
<li><a href="../theories/median_method/#Median">Median</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Median_Method-AFP</p><pre id="copy-text">@article{Median_Method-AFP,
author = {Emin Karayel},
title = {Median Method},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Median_Method.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Median_Of_Medians_Selection.html b/web/entries/Median_Of_Medians_Selection.html
--- a/web/entries/Median_Of_Medians_Selection.html
+++ b/web/entries/Median_Of_Medians_Selection.html
@@ -1,177 +1,179 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Median-of-Medians Selection Algorithm - Archive of Formal Proofs</title><meta name="description" content="This entry provides an executable functional implementation of the Median-of-Medians algorithm for selecting the k-th smallest element of an unsorted list..."><meta property="og:title" content="The Median-of-Medians Selection Algorithm" />
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<h1 >
<span class='first'>T</span>he <span class='first'>M</span>edian-of-<span class='first'>M</span>edians <span class='first'>S</span>election <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry provides an executable functional implementation
of the Median-of-Medians algorithm for selecting the
<em>k</em>-th smallest element of an unsorted list
deterministically in linear time. The size bounds for the recursive
call that lead to the linear upper bound on the run-time of the
algorithm are also proven. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Median_Of_Medians_Selection</h3>
<ul>
<li><a href="../theories/median_of_medians_selection/#Median_Of_Medians_Selection">Median_Of_Medians_Selection</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/KD_Tree.html">Multidimensional Binary Search Trees</a></li></ul>
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author = {Manuel Eberl},
title = {The Median-of-Medians Selection Algorithm},
journal = {Archive of Formal Proofs},
month = {December},
year = {2017},
note = {\url{https://isa-afp.org/entries/Median_Of_Medians_Selection.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Median_Of_Medians_Selection-2017-12-22.tar.gz">Dec 22, 2017</a>: Isabelle2017
</li></ul>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Menger&#39;s Theorem - Archive of Formal Proofs</title><meta name="description" content="We present a formalization of Menger&#39;s Theorem for directed and
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<h1 >
<span class='first'>M</span>enger's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/dittmann">Christoph Dittmann</a> <a class="obfuscated" data="eyJob3N0IjpbImNocmlzdG9waC1kIiwiZGUiXSwidXNlciI6WyJpc2FiZWxsZSJdfQ==">📧</a>
</p>
<p class="date">February 26, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of Menger's Theorem for directed and
undirected graphs in Isabelle/HOL. This well-known result shows that
if two non-adjacent distinct vertices u, v in a directed graph have no
separator smaller than n, then there exist n internally
vertex-disjoint paths from u to v. The version for undirected graphs
follows immediately because undirected graphs are a special case of
directed graphs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Menger</h3>
<ul>
<li><a href="../theories/menger/#Helpers">Helpers</a></li>
<li><a href="../theories/menger/#Graph">Graph</a></li>
<li><a href="../theories/menger/#Separations">Separations</a></li>
<li><a href="../theories/menger/#DisjointPaths">DisjointPaths</a></li>
<li><a href="../theories/menger/#MengerInduction">MengerInduction</a></li>
<li><a href="../theories/menger/#Y_eq_new_last">Y_eq_new_last</a></li>
<li><a href="../theories/menger/#Y_neq_new_last">Y_neq_new_last</a></li>
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<p style="display:none;" id="bibtex-filename">Menger-AFP</p><pre id="copy-text">@article{Menger-AFP,
author = {Christoph Dittmann},
title = {Menger&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {February},
year = {2017},
note = {\url{https://isa-afp.org/entries/Menger.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Menger-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Menger-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Menger-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Menger-2017-02-27.tar.gz">Feb 27, 2017</a>: Isabelle2016-1
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<h1 >
<span class='first'>M</span>ereology</h1>
<div>
<p><a href="../authors/blumson">Ben Blumson</a> <a href="https://philpeople.org/profiles/ben-blumson">🌐</a>
</p>
<p class="date">March 1, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We use Isabelle/HOL to verify elementary theorems and alternative
axiomatizations of classical extensional mereology.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session Mereology</h3>
<ul>
<li><a href="../theories/mereology/#PM">PM</a></li>
<li><a href="../theories/mereology/#M">M</a></li>
<li><a href="../theories/mereology/#MM">MM</a></li>
<li><a href="../theories/mereology/#EM">EM</a></li>
<li><a href="../theories/mereology/#CM">CM</a></li>
<li><a href="../theories/mereology/#CEM">CEM</a></li>
<li><a href="../theories/mereology/#GM">GM</a></li>
<li><a href="../theories/mereology/#GMM">GMM</a></li>
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<p style="display:none;" id="bibtex-filename">Mereology-AFP</p><pre id="copy-text">@article{Mereology-AFP,
author = {Ben Blumson},
title = {Mereology},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Mereology.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Mereology-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Mereology-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Mereology-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Mereology-2021-03-05.tar.gz">Mar 5, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>M</span>ersenne <span class='first'>P</span>rimes and the <span class='first'>L</span>ucas–<span class='first'>L</span>ehmer <span class='first'>T</span>est</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">January 17, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides formal proofs of basic properties of
Mersenne numbers, i. e. numbers of the form
2<sup><em>n</em></sup> - 1, and especially of
Mersenne primes.</p> <p>In particular, an efficient,
verified, and executable version of the Lucas&ndash;Lehmer test is
developed. This test decides primality for Mersenne numbers in time
polynomial in <em>n</em>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Mersenne_Primes</h3>
<ul>
<li><a href="../theories/mersenne_primes/#Lucas_Lehmer_Auxiliary">Lucas_Lehmer_Auxiliary</a></li>
<li><a href="../theories/mersenne_primes/#Lucas_Lehmer">Lucas_Lehmer</a></li>
<li><a href="../theories/mersenne_primes/#Lucas_Lehmer_Code">Lucas_Lehmer_Code</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/Pell.html">Pell&rsquo;s Equation</a></li><li><a href="../entries/Probabilistic_Prime_Tests.html">Probabilistic Primality Testing</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Mersenne_Primes-AFP</p><pre id="copy-text">@article{Mersenne_Primes-AFP,
author = {Manuel Eberl},
title = {Mersenne primes and the Lucas–Lehmer test},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Mersenne_Primes.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Mersenne_Primes-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Mersenne_Primes-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Mersenne_Primes-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>I</span>sabelle's <span class='first'>M</span>etalogic: <span class='first'>F</span>ormalization and <span class='first'>P</span>roof <span class='first'>C</span>hecker</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/rosskopf">Simon Roßkopf</a> <a href="http://www21.in.tum.de/~rosskops">🌐</a>
</p>
<p class="date">April 27, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this entry we formalize Isabelle's metalogic in Isabelle/HOL.
Furthermore, we define a language of proof terms and an executable
proof checker and prove its soundness wrt. the metalogic. The
formalization is intentionally kept close to the Isabelle
implementation(for example using de Brujin indices) to enable easy
integration of generated code with the Isabelle system without a
complicated translation layer. The formalization is described in our
<a href="https://arxiv.org/pdf/2104.12224.pdf">CADE 28 paper</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic">Logic/General logic</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T., & Roßkopf, S. (2021). Isabelle’s Metalogic: Formalization and Proof Checker. Lecture Notes in Computer Science, 93–110. <a href="https://doi.org/10.1007/978-3-030-79876-5_6">https://doi.org/10.1007/978-3-030-79876-5_6</a>
</li></ul>
<h3>Session Metalogic_ProofChecker</h3>
<ul>
<li><a href="../theories/metalogic_proofchecker/#Core">Core</a></li>
<li><a href="../theories/metalogic_proofchecker/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/metalogic_proofchecker/#Term">Term</a></li>
<li><a href="../theories/metalogic_proofchecker/#Sorts">Sorts</a></li>
<li><a href="../theories/metalogic_proofchecker/#SortConstants">SortConstants</a></li>
<li><a href="../theories/metalogic_proofchecker/#Theory">Theory</a></li>
<li><a href="../theories/metalogic_proofchecker/#Term_Subst">Term_Subst</a></li>
<li><a href="../theories/metalogic_proofchecker/#Name">Name</a></li>
<li><a href="../theories/metalogic_proofchecker/#BetaNorm">BetaNorm</a></li>
<li><a href="../theories/metalogic_proofchecker/#BetaNormProof">BetaNormProof</a></li>
<li><a href="../theories/metalogic_proofchecker/#EtaNorm">EtaNorm</a></li>
<li><a href="../theories/metalogic_proofchecker/#EtaNormProof">EtaNormProof</a></li>
<li><a href="../theories/metalogic_proofchecker/#Logic">Logic</a></li>
<li><a href="../theories/metalogic_proofchecker/#EqualityProof">EqualityProof</a></li>
<li><a href="../theories/metalogic_proofchecker/#ProofTerm">ProofTerm</a></li>
<li><a href="../theories/metalogic_proofchecker/#SortsExe">SortsExe</a></li>
<li><a href="../theories/metalogic_proofchecker/#Instances">Instances</a></li>
<li><a href="../theories/metalogic_proofchecker/#TheoryExe">TheoryExe</a></li>
<li><a href="../theories/metalogic_proofchecker/#CheckerExe">CheckerExe</a></li>
<li><a href="../theories/metalogic_proofchecker/#CodeGen">CodeGen</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Metalogic_ProofChecker-AFP</p><pre id="copy-text">@article{Metalogic_ProofChecker-AFP,
author = {Tobias Nipkow and Simon Roßkopf},
title = {Isabelle&#39;s Metalogic: Formalization and Proof Checker},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/Metalogic_ProofChecker.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Metalogic_ProofChecker-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Metalogic_ProofChecker-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Metalogic_ProofChecker-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Metalogic_ProofChecker-2021-04-28.tar.gz">Apr 28, 2021</a>: Isabelle2021
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diff --git a/web/entries/MiniML.html b/web/entries/MiniML.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Mini ML - Archive of Formal Proofs</title><meta name="description" content="This theory defines the type inference rules and the type inference algorithm W for MiniML (simply-typed lambda terms with let) due to Milner. It proves..."><meta property="og:title" content="Mini ML" />
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<h1 >
<span class='first'>M</span>ini <span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/naraschewski">Wolfgang Naraschewski</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">March 19, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory defines the type inference rules and the type inference algorithm <i>W</i> for MiniML (simply-typed lambda terms with <tt>let</tt>) due to Milner. It proves the soundness and completeness of <i>W</i> w.r.t. the rules.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul><h3>Related publications</h3>
<ul><li>
Naraschewski, W., & Nipkow, T. (1999). Journal of Automated Reasoning, 23(3), 299–318. https://doi.org/10.1023/a:1006277616879
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jar10.html">Open access</a>
</li></ul>
<h3>Session MiniML</h3>
<ul>
<li><a href="../theories/miniml/#Maybe">Maybe</a></li>
<li><a href="../theories/miniml/#Type">Type</a></li>
<li><a href="../theories/miniml/#Instance">Instance</a></li>
<li><a href="../theories/miniml/#Generalize">Generalize</a></li>
<li><a href="../theories/miniml/#MiniML">MiniML</a></li>
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<p style="display:none;" id="bibtex-filename">MiniML-AFP</p><pre id="copy-text">@article{MiniML-AFP,
author = {Wolfgang Naraschewski and Tobias Nipkow},
title = {Mini ML},
journal = {Archive of Formal Proofs},
month = {March},
year = {2004},
note = {\url{https://isa-afp.org/entries/MiniML.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-MiniML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-MiniML-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-MiniML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2020-05-06.tar.gz">May 6, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2019-04-18.tar.gz">Apr 18, 2019</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2007-11-27.tar.gz">Nov 27, 2007</a>: Isabelle2007
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2005-10-14.tar.gz">Oct 14, 2005</a>: Isabelle2005
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2004-05-21.tar.gz">May 21, 2004</a>: Isabelle2004
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2004-04-20.tar.gz">Apr 20, 2004</a>: Isabelle2004
</li><li>
<a href="https://www.isa-afp.org/release/afp-MiniML-2004-03-23.tar.gz">Mar 23, 2004</a>: Isabelle2003
</li></ul>
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diff --git a/web/entries/MiniSail.html b/web/entries/MiniSail.html
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@@ -1,207 +1,209 @@
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<h1 >
<span class='first'>M</span>ini<span class='first'>S</span>ail - <span class='first'>A</span> <span class='first'>K</span>ernel <span class='first'>L</span>anguage for the <span class='first'>I</span><span class='first'>S</span><span class='first'>A</span> <span class='first'>S</span>pecification <span class='first'>L</span>anguage <span class='first'>S</span><span class='first'>A</span><span class='first'>I</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/wassell">Mark Wassell</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibXB3YXNzZWxsIl19">📧</a>
</p>
<p class="date">June 18, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">MiniSail is a kernel language for Sail, an instruction set
architecture (ISA) specification language. Sail is an imperative
language with a light-weight dependent type system similar to
refinement type systems. From an ISA specification, the Sail compiler
can generate theorem prover code and C (or OCaml) to give an
executable emulator for an architecture. The idea behind MiniSail is
to capture the key and novel features of Sail in terms of their
syntax, typing rules and operational semantics, and to confirm that
they work together by proving progress and preservation lemmas. We use
the Nominal2 library to handle binding.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session MiniSail</h3>
<ul>
<li><a href="../theories/minisail/#Nominal-Utils">Nominal-Utils</a></li>
<li><a href="../theories/minisail/#Syntax">Syntax</a></li>
<li><a href="../theories/minisail/#IVSubst">IVSubst</a></li>
<li><a href="../theories/minisail/#BTVSubst">BTVSubst</a></li>
<li><a href="../theories/minisail/#Wellformed">Wellformed</a></li>
<li><a href="../theories/minisail/#RCLogic">RCLogic</a></li>
<li><a href="../theories/minisail/#SyntaxL">SyntaxL</a></li>
<li><a href="../theories/minisail/#WellformedL">WellformedL</a></li>
<li><a href="../theories/minisail/#Typing">Typing</a></li>
<li><a href="../theories/minisail/#Operational">Operational</a></li>
<li><a href="../theories/minisail/#SubstMethods">SubstMethods</a></li>
<li><a href="../theories/minisail/#RCLogicL">RCLogicL</a></li>
<li><a href="../theories/minisail/#TypingL">TypingL</a></li>
<li><a href="../theories/minisail/#ContextSubtypingL">ContextSubtypingL</a></li>
<li><a href="../theories/minisail/#IVSubstTypingL">IVSubstTypingL</a></li>
<li><a href="../theories/minisail/#BTVSubstTypingL">BTVSubstTypingL</a></li>
<li><a href="../theories/minisail/#Safety">Safety</a></li>
<li><a href="../theories/minisail/#MiniSail">MiniSail</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
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<p style="display:none;" id="bibtex-filename">MiniSail-AFP</p><pre id="copy-text">@article{MiniSail-AFP,
author = {Mark Wassell},
title = {MiniSail - A kernel language for the ISA specification language SAIL},
journal = {Archive of Formal Proofs},
month = {June},
year = {2021},
note = {\url{https://isa-afp.org/entries/MiniSail.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>M</span>inimal <span class='first'>S</span>tatic <span class='first'>S</span>ingle <span class='first'>A</span>ssignment <span class='first'>F</span>orm</h1>
<div>
<p><a href="../authors/wagner">Max Wagner</a> <a class="obfuscated" data="eyJob3N0IjpbInRyb2xsYnUiLCJkZSJdLCJ1c2VyIjpbIm1heCJdfQ==">📧</a> and <a href="../authors/lohner">Denis Lohner</a> <a href="http://pp.ipd.kit.edu/person.php?id=88">🌐</a>
</p>
<p class="date">January 17, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This formalization is an extension to <a
href="https://www.isa-afp.org/entries/Formal_SSA.html">"Verified
Construction of Static Single Assignment Form"</a>. In
their work, the authors have shown that <a
href="https://doi.org/10.1007/978-3-642-37051-9_6">Braun
et al.'s static single assignment (SSA) construction
algorithm</a> produces minimal SSA form for input programs with
a reducible control flow graph (CFG). However Braun et al. also
proposed an extension to their algorithm that they claim produces
minimal SSA form even for irreducible CFGs.<br> In this
formalization we support that claim by giving a mechanized proof.
</p>
<p>As the extension of Braun et al.'s algorithm
aims for removing so-called redundant strongly connected components of
phi functions, we show that this suffices to guarantee minimality
according to <a href="https://doi.org/10.1145/115372.115320">Cytron et
al.</a>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul>
<h3>Session Minimal_SSA</h3>
<ul>
<li><a href="../theories/minimal_ssa/#Irreducible">Irreducible</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Formal_SSA.html">Verified Construction of Static Single Assignment Form</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Minimal_SSA-AFP</p><pre id="copy-text">@article{Minimal_SSA-AFP,
author = {Max Wagner and Denis Lohner},
title = {Minimal Static Single Assignment Form},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/Minimal_SSA.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>M</span>inkowski's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">July 13, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Minkowski's theorem relates a subset of
&#8477;<sup>n</sup>, the Lebesgue measure, and the
integer lattice &#8484;<sup>n</sup>: It states that
any convex subset of &#8477;<sup>n</sup> with volume
greater than 2<sup>n</sup> contains at least one lattice
point from &#8484;<sup>n</sup>\{0}, i.&thinsp;e. a
non-zero point with integer coefficients.</p> <p>A
related theorem which directly implies this is Blichfeldt's
theorem, which states that any subset of
&#8477;<sup>n</sup> with a volume greater than 1
contains two different points whose difference vector has integer
components.</p> <p>The entry contains a proof of both
theorems.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Minkowskis_Theorem</h3>
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<p style="display:none;" id="bibtex-filename">Minkowskis_Theorem-AFP</p><pre id="copy-text">@article{Minkowskis_Theorem-AFP,
author = {Manuel Eberl},
title = {Minkowski&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/Minkowskis_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Minkowskis_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Minkowskis_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Minsky Machines - Archive of Formal Proofs</title><meta name="description" content=" We formalize undecidablity results for Minsky machines. To this end, we also formalize recursive inseparability. We start by proving that Minsky machines..."><meta property="og:title" content="Minsky Machines" />
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<h1 >
<span class='first'>M</span>insky <span class='first'>M</span>achines</h1>
<div>
<p><a href="../authors/felgenhauer">Bertram Felgenhauer</a>
</p>
<p class="date">August 14, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> We formalize undecidablity results for Minsky machines. To
this end, we also formalize recursive inseparability.
</p><p> We start by proving that Minsky machines can
compute arbitrary primitive recursive and recursive functions. We then
show that there is a deterministic Minsky machine with one argument
and two final states such that the set of inputs that are accepted in
one state is recursively inseparable from the set of inputs that are
accepted in the other state. </p><p> As a corollary, the
set of Minsky configurations that reach the first state but not the
second recursively inseparable from the set of Minsky configurations
that reach the second state but not the first. In particular both
these sets are undecidable. </p><p> We do
<em>not</em> prove that recursive functions can simulate
Minsky machines. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li></ul>
<h3>Session Minsky_Machines</h3>
<ul>
<li><a href="../theories/minsky_machines/#Recursive_Inseparability">Recursive_Inseparability</a></li>
<li><a href="../theories/minsky_machines/#Minsky">Minsky</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Recursion-Theory-I.html">Recursion Theory I</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Minsky_Machines-AFP</p><pre id="copy-text">@article{Minsky_Machines-AFP,
author = {Bertram Felgenhauer},
title = {Minsky Machines},
journal = {Archive of Formal Proofs},
month = {August},
year = {2018},
note = {\url{https://isa-afp.org/entries/Minsky_Machines.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Minsky_Machines-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Minsky_Machines-2018-08-14.tar.gz">Aug 14, 2018</a>: Isabelle2017
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diff --git a/web/entries/Modal_Logics_for_NTS.html b/web/entries/Modal_Logics_for_NTS.html
--- a/web/entries/Modal_Logics_for_NTS.html
+++ b/web/entries/Modal_Logics_for_NTS.html
@@ -1,217 +1,219 @@
<!DOCTYPE html>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Modal Logics for Nominal Transition Systems - Archive of Formal Proofs</title><meta name="description" content="We formalize a uniform semantic substrate for a wide variety of
process calculi where states and action labels can be from arbitrary
nominal sets. A..."><meta property="og:title" content="Modal Logics for Nominal Transition Systems" />
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<h1 >
<span class='first'>M</span>odal <span class='first'>L</span>ogics for <span class='first'>N</span>ominal <span class='first'>T</span>ransition <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/weber">Tjark Weber</a> <a class="obfuscated" data="eyJob3N0IjpbIml0IiwidXUiLCJzZSJdLCJ1c2VyIjpbInRqYXJrIiwid2ViZXIiXX0=">📧</a>, <a href="../authors/eriksson">Lars-Henrik Eriksson</a> <a class="obfuscated" data="eyJob3N0IjpbIml0IiwidXUiLCJzZSJdLCJ1c2VyIjpbImxoZSJdfQ==">📧</a>, <a href="../authors/parrow">Joachim Parrow</a> <a class="obfuscated" data="eyJob3N0IjpbIml0IiwidXUiLCJzZSJdLCJ1c2VyIjpbImpvYWNoaW0iLCJwYXJyb3ciXX0=">📧</a>, <a href="../authors/borgstroem">Johannes Borgström</a> <a class="obfuscated" data="eyJob3N0IjpbIml0IiwidXUiLCJzZSJdLCJ1c2VyIjpbImpvaGFubmVzIiwiYm9yZ3N0cm9tIl19">📧</a> and <a href="../authors/gutkovas">Ramunas Gutkovas</a> <a class="obfuscated" data="eyJob3N0IjpbIml0IiwidXUiLCJzZSJdLCJ1c2VyIjpbInJhbXVuYXMiLCJndXRrb3ZhcyJdfQ==">📧</a>
</p>
<p class="date">October 25, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a uniform semantic substrate for a wide variety of
process calculi where states and action labels can be from arbitrary
nominal sets. A Hennessy-Milner logic for these systems is defined,
and proved adequate for bisimulation equivalence. A main novelty is
the construction of an infinitary nominal data type to model formulas
with (finitely supported) infinite conjunctions and actions that may
contain binding names. The logic is generalized to treat different
bisimulation variants such as early, late and open in a systematic
way.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>January 29, 2017</dt>
<dd>Formalization of weak bisimilarity added
(revision c87cc2057d9c)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li></ul>
<h3>Session Modal_Logics_for_NTS</h3>
<ul>
<li><a href="../theories/modal_logics_for_nts/#Nominal_Bounded_Set">Nominal_Bounded_Set</a></li>
<li><a href="../theories/modal_logics_for_nts/#Nominal_Wellfounded">Nominal_Wellfounded</a></li>
<li><a href="../theories/modal_logics_for_nts/#Residual">Residual</a></li>
<li><a href="../theories/modal_logics_for_nts/#Transition_System">Transition_System</a></li>
<li><a href="../theories/modal_logics_for_nts/#Formula">Formula</a></li>
<li><a href="../theories/modal_logics_for_nts/#Validity">Validity</a></li>
<li><a href="../theories/modal_logics_for_nts/#Logical_Equivalence">Logical_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#Bisimilarity_Implies_Equivalence">Bisimilarity_Implies_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#Equivalence_Implies_Bisimilarity">Equivalence_Implies_Bisimilarity</a></li>
<li><a href="../theories/modal_logics_for_nts/#Disjunction">Disjunction</a></li>
<li><a href="../theories/modal_logics_for_nts/#Expressive_Completeness">Expressive_Completeness</a></li>
<li><a href="../theories/modal_logics_for_nts/#FS_Set">FS_Set</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Transition_System">FL_Transition_System</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Formula">FL_Formula</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Validity">FL_Validity</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Logical_Equivalence">FL_Logical_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Bisimilarity_Implies_Equivalence">FL_Bisimilarity_Implies_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#FL_Equivalence_Implies_Bisimilarity">FL_Equivalence_Implies_Bisimilarity</a></li>
<li><a href="../theories/modal_logics_for_nts/#L_Transform">L_Transform</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Transition_System">Weak_Transition_System</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Formula">Weak_Formula</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Validity">Weak_Validity</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Logical_Equivalence">Weak_Logical_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Bisimilarity_Implies_Equivalence">Weak_Bisimilarity_Implies_Equivalence</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Equivalence_Implies_Bisimilarity">Weak_Equivalence_Implies_Bisimilarity</a></li>
<li><a href="../theories/modal_logics_for_nts/#Weak_Expressive_Completeness">Weak_Expressive_Completeness</a></li>
<li><a href="../theories/modal_logics_for_nts/#S_Transform">S_Transform</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Modal_Logics_for_NTS/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Modal_Logics_for_NTS-AFP</p><pre id="copy-text">@article{Modal_Logics_for_NTS-AFP,
author = {Tjark Weber and Lars-Henrik Eriksson and Joachim Parrow and Johannes Borgström and Ramunas Gutkovas},
title = {Modal Logics for Nominal Transition Systems},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Modal_Logics_for_NTS.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2016-10-27.tar.gz">Oct 27, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modal_Logics_for_NTS-2016-10-25.tar.gz">Oct 25, 2016</a>: Isabelle2016
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Modular_Assembly_Kit_Security.html b/web/entries/Modular_Assembly_Kit_Security.html
--- a/web/entries/Modular_Assembly_Kit_Security.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties - Archive of Formal Proofs</title><meta name="description" content="The &#34;Modular Assembly Kit for Security Properties&#34; (MAKS) is
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<h1 >
<span class='first'>A</span>n <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>F</span>ormalization of the <span class='first'>M</span>odular <span class='first'>A</span>ssembly <span class='first'>K</span>it for <span class='first'>S</span>ecurity <span class='first'>P</span>roperties</h1>
<div>
<p><a href="../authors/bracevac">Oliver Bračevac</a> <a class="obfuscated" data="eyJob3N0IjpbInN0IiwiaW5mb3JtYXRpayIsInR1LWRhcm1zdGFkdCIsImRlIl0sInVzZXIiOlsiYnJhY2V2YWMiXX0=">📧</a>, <a href="../authors/gay">Richard Gay</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJnYXkiXX0=">📧</a>, <a href="../authors/grewe">Sylvia Grewe</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJncmV3ZSJdfQ==">📧</a>, <a href="../authors/mantel">Heiko Mantel</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJtYW50ZWwiXX0=">📧</a>, <a href="../authors/sudbrock">Henning Sudbrock</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJzdWRicm9jayJdfQ==">📧</a> and <a href="../authors/tasch">Markus Tasch</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJ0YXNjaCJdfQ==">📧</a>
</p>
<p class="date">May 7, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The "Modular Assembly Kit for Security Properties" (MAKS) is
a framework for both the definition and verification of possibilistic
information-flow security properties at the specification-level. MAKS
supports the uniform representation of a wide range of possibilistic
information-flow properties and provides support for the verification
of such properties via unwinding results and compositionality results.
We provide a formalization of this framework in Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Modular_Assembly_Kit_Security</h3>
<ul>
<li><a href="../theories/modular_assembly_kit_security/#Projection">Projection</a></li>
<li><a href="../theories/modular_assembly_kit_security/#Prefix">Prefix</a></li>
<li><a href="../theories/modular_assembly_kit_security/#EventSystems">EventSystems</a></li>
<li><a href="../theories/modular_assembly_kit_security/#StateEventSystems">StateEventSystems</a></li>
<li><a href="../theories/modular_assembly_kit_security/#Views">Views</a></li>
<li><a href="../theories/modular_assembly_kit_security/#FlowPolicies">FlowPolicies</a></li>
<li><a href="../theories/modular_assembly_kit_security/#BasicSecurityPredicates">BasicSecurityPredicates</a></li>
<li><a href="../theories/modular_assembly_kit_security/#InformationFlowProperties">InformationFlowProperties</a></li>
<li><a href="../theories/modular_assembly_kit_security/#BSPTaxonomy">BSPTaxonomy</a></li>
<li><a href="../theories/modular_assembly_kit_security/#PropertyLibrary">PropertyLibrary</a></li>
<li><a href="../theories/modular_assembly_kit_security/#SecureSystems">SecureSystems</a></li>
<li><a href="../theories/modular_assembly_kit_security/#UnwindingConditions">UnwindingConditions</a></li>
<li><a href="../theories/modular_assembly_kit_security/#AuxiliaryLemmas">AuxiliaryLemmas</a></li>
<li><a href="../theories/modular_assembly_kit_security/#UnwindingResults">UnwindingResults</a></li>
<li><a href="../theories/modular_assembly_kit_security/#CompositionBase">CompositionBase</a></li>
<li><a href="../theories/modular_assembly_kit_security/#CompositionSupport">CompositionSupport</a></li>
<li><a href="../theories/modular_assembly_kit_security/#GeneralizedZippingLemma">GeneralizedZippingLemma</a></li>
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<p style="display:none;" id="bibtex-filename">Modular_Assembly_Kit_Security-AFP</p><pre id="copy-text">@article{Modular_Assembly_Kit_Security-AFP,
author = {Oliver Bračevac and Richard Gay and Sylvia Grewe and Heiko Mantel and Henning Sudbrock and Markus Tasch},
title = {An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Modular_Assembly_Kit_Security.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_Assembly_Kit_Security-2018-05-09.tar.gz">May 9, 2018</a>: Isabelle2017
</li></ul>
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diff --git a/web/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html b/web/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html
--- a/web/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html
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@@ -1,186 +1,188 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation - Archive of Formal Proofs</title><meta name="description" content="We verify two algorithms for which modular arithmetic plays an
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<h1 >
<span class='first'>T</span>wo <span class='first'>A</span>lgorithms <span class='first'>B</span>ased on <span class='first'>M</span>odular <span class='first'>A</span>rithmetic: <span class='first'>L</span>attice <span class='first'>B</span>asis <span class='first'>R</span>eduction and <span class='first'>H</span>ermite <span class='first'>N</span>ormal <span class='first'>F</span>orm <span class='first'>C</span>omputation</h1>
<div>
<p><a href="../authors/bottesch">Ralph Bottesch</a>, <a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">March 12, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We verify two algorithms for which modular arithmetic plays an
essential role: Storjohann's variant of the LLL lattice basis
reduction algorithm and Kopparty's algorithm for computing the
Hermite normal form of a matrix. To do this, we also formalize some
facts about the modulo operation with symmetric range. Our
implementations are based on the original papers, but are otherwise
efficient. For basis reduction we formalize two versions: one that
includes all of the optimizations/heuristics from Storjohann's
paper, and one excluding a heuristic that we observed to often
decrease efficiency. We also provide a fast, self-contained certifier
for basis reduction, based on the efficient Hermite normal form
algorithm.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Modular_arithmetic_LLL_and_HNF_algorithms</h3>
<ul>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Matrix_Change_Row">Matrix_Change_Row</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Signed_Modulo">Signed_Modulo</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Storjohann_Mod_Operation">Storjohann_Mod_Operation</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Storjohann">Storjohann</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Storjohann_Impl">Storjohann_Impl</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Uniqueness_Hermite">Uniqueness_Hermite</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#Uniqueness_Hermite_JNF">Uniqueness_Hermite_JNF</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#HNF_Mod_Det_Algorithm">HNF_Mod_Det_Algorithm</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#HNF_Mod_Det_Soundness">HNF_Mod_Det_Soundness</a></li>
<li><a href="../theories/modular_arithmetic_lll_and_hnf_algorithms/#LLL_Certification_via_HNF">LLL_Certification_via_HNF</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Hermite.html">Hermite Normal Form</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/LLL_Basis_Reduction.html">A verified LLL algorithm</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li></ul>
</div>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Modular_arithmetic_LLL_and_HNF_algorithms/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Modular_arithmetic_LLL_and_HNF_algorithms-AFP</p><pre id="copy-text">@article{Modular_arithmetic_LLL_and_HNF_algorithms-AFP,
author = {Ralph Bottesch and Jose Divasón and René Thiemann},
title = {Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Modular_arithmetic_LLL_and_HNF_algorithms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Modular_arithmetic_LLL_and_HNF_algorithms-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Modular_arithmetic_LLL_and_HNF_algorithms-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Modular_arithmetic_LLL_and_HNF_algorithms-2021-03-14.tar.gz">Mar 14, 2021</a>: Isabelle2021
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Monad_Memo_DP.html b/web/entries/Monad_Memo_DP.html
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<h1 >
<span class='first'>M</span>onadification, <span class='first'>M</span>emoization and <span class='first'>D</span>ynamic <span class='first'>P</span>rogramming</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>, <a href="../authors/hu">Shuwei Hu</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsic2h1d2VpIiwiaHUiXX0=">📧</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">May 22, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a lightweight framework for the automatic verified
(functional or imperative) memoization of recursive functions. Our
tool can turn a pure Isabelle/HOL function definition into a
monadified version in a state monad or the Imperative HOL heap monad,
and prove a correspondence theorem. We provide a variety of memory
implementations for the two types of monads. A number of simple
techniques allow us to achieve bottom-up computation and
space-efficient memoization. The framework’s utility is demonstrated
on a number of representative dynamic programming problems. A detailed
description of our work can be found in the accompanying paper [2].</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Monad_Memo_DP</h3>
<ul>
<li><a href="../theories/monad_memo_dp/#State_Monad_Ext">State_Monad_Ext</a></li>
<li><a href="../theories/monad_memo_dp/#Pure_Monad">Pure_Monad</a></li>
<li><a href="../theories/monad_memo_dp/#DP_CRelVS">DP_CRelVS</a></li>
<li><a href="../theories/monad_memo_dp/#State_Heap_Misc">State_Heap_Misc</a></li>
<li><a href="../theories/monad_memo_dp/#Heap_Monad_Ext">Heap_Monad_Ext</a></li>
<li><a href="../theories/monad_memo_dp/#State_Heap">State_Heap</a></li>
<li><a href="../theories/monad_memo_dp/#DP_CRelVH">DP_CRelVH</a></li>
<li><a href="../theories/monad_memo_dp/#Memory">Memory</a></li>
<li><a href="../theories/monad_memo_dp/#Pair_Memory">Pair_Memory</a></li>
<li><a href="../theories/monad_memo_dp/#Indexing">Indexing</a></li>
<li><a href="../theories/monad_memo_dp/#Memory_Heap">Memory_Heap</a></li>
<li><a href="../theories/monad_memo_dp/#Transform_Cmd">Transform_Cmd</a></li>
<li><a href="../theories/monad_memo_dp/#Bottom_Up_Computation">Bottom_Up_Computation</a></li>
<li><a href="../theories/monad_memo_dp/#Bottom_Up_Computation_Heap">Bottom_Up_Computation_Heap</a></li>
<li><a href="../theories/monad_memo_dp/#Solve_Cong">Solve_Cong</a></li>
<li><a href="../theories/monad_memo_dp/#Heap_Main">Heap_Main</a></li>
<li><a href="../theories/monad_memo_dp/#State_Main">State_Main</a></li>
<li><a href="../theories/monad_memo_dp/#Example_Misc">Example_Misc</a></li>
<li><a href="../theories/monad_memo_dp/#Tracing">Tracing</a></li>
<li><a href="../theories/monad_memo_dp/#Ground_Function">Ground_Function</a></li>
<li><a href="../theories/monad_memo_dp/#Bellman_Ford">Bellman_Ford</a></li>
<li><a href="../theories/monad_memo_dp/#Heap_Default">Heap_Default</a></li>
<li><a href="../theories/monad_memo_dp/#Knapsack">Knapsack</a></li>
<li><a href="../theories/monad_memo_dp/#Counting_Tiles">Counting_Tiles</a></li>
<li><a href="../theories/monad_memo_dp/#CYK">CYK</a></li>
<li><a href="../theories/monad_memo_dp/#Min_Ed_Dist0">Min_Ed_Dist0</a></li>
<li><a href="../theories/monad_memo_dp/#OptBST">OptBST</a></li>
<li><a href="../theories/monad_memo_dp/#Longest_Common_Subsequence">Longest_Common_Subsequence</a></li>
<li><a href="../theories/monad_memo_dp/#All_Examples">All_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Optimal_BST.html">Optimal Binary Search Trees</a></li><li><a href="../entries/Hidden_Markov_Models.html">Hidden Markov Models</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Simple_Firewall.html">Simple Firewall</a></li>
<li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li>
<li><a href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></li>
<li><a href="../entries/InformationFlowSlicing_Inter.html">Inter-Procedural Information Flow Noninterference via Slicing</a></li>
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<p style="display:none;" id="bibtex-filename">Monad_Memo_DP-AFP</p><pre id="copy-text">@article{Monad_Memo_DP-AFP,
author = {Simon Wimmer and Shuwei Hu and Tobias Nipkow},
title = {Monadification, Memoization and Dynamic Programming},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Monad_Memo_DP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2022-02-13.tar.gz">Feb 13, 2022</a>: Isabelle2021-1
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Memo_DP-2018-05-23.tar.gz">May 23, 2018</a>: Isabelle2017
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diff --git a/web/entries/Monad_Normalisation.html b/web/entries/Monad_Normalisation.html
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<h1 >
<span class='first'>M</span>onad <span class='first'>N</span>ormalisation</h1>
<div>
<p><a href="../authors/schneider">Joshua Schneider</a>, <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a> and <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 5, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The usual monad laws can directly be used as rewrite rules for Isabelle’s
simplifier to normalise monadic HOL terms and decide equivalences.
In a commutative monad, however, the commutativity law is a
higher-order permutative rewrite rule that makes the simplifier loop.
This AFP entry implements a simproc that normalises monadic
expressions in commutative monads using ordered rewriting. The
simproc can also permute computations across control operators like if
and case.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Monad_Normalisation</h3>
<ul>
<li><a href="../theories/monad_normalisation/#Monad_Normalisation">Monad_Normalisation</a></li>
<li><a href="../theories/monad_normalisation/#Monad_Normalisation_Test">Monad_Normalisation_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Skip_Lists.html">Skip Lists</a></li><li><a href="../entries/Randomised_BSTs.html">Randomised Binary Search Trees</a></li><li><a href="../entries/CryptHOL.html">CryptHOL</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Monad_Normalisation-AFP</p><pre id="copy-text">@article{Monad_Normalisation-AFP,
author = {Joshua Schneider and Manuel Eberl and Andreas Lochbihler},
title = {Monad normalisation},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Monad_Normalisation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Monad_Normalisation-2017-05-11.tar.gz">May 11, 2017</a>: Isabelle2016-1
</li></ul>
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diff --git a/web/entries/MonoBoolTranAlgebra.html b/web/entries/MonoBoolTranAlgebra.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Algebra of Monotonic Boolean Transformers - Archive of Formal Proofs</title><meta name="description" content="Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure..."><meta property="og:title" content="Algebra of Monotonic Boolean Transformers" />
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<h1 >
<span class='first'>A</span>lgebra of <span class='first'>M</span>onotonic <span class='first'>B</span>oolean <span class='first'>T</span>ransformers</h1>
<div>
<p><a href="../authors/preoteasa">Viorel Preoteasa</a> <a href="http://users.abo.fi/vpreotea/">🌐</a>
</p>
<p class="date">September 22, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure with programs as elements and with program compositions (sequential composition, choice, skip) as algebra operations. Various versions of these algebras were introduced to model partial correctness, total correctness, refinement, demonic choice, and other aspects. We formalize here an algebra which can be used to model total correctness, refinement, demonic and angelic choice. The basic model of this algebra are monotonic Boolean transformers (monotonic functions from a Boolean algebra to itself).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session MonoBoolTranAlgebra</h3>
<ul>
<li><a href="../theories/monobooltranalgebra/#Mono_Bool_Tran">Mono_Bool_Tran</a></li>
<li><a href="../theories/monobooltranalgebra/#Mono_Bool_Tran_Algebra">Mono_Bool_Tran_Algebra</a></li>
<li><a href="../theories/monobooltranalgebra/#Assertion_Algebra">Assertion_Algebra</a></li>
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<h3>Depends on</h3>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Correctness_Algebras.html">Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</a></li></ul>
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<li><a href="../entries/BirdKMP.html">Putting the `K' into Bird&rsquo;s derivation of Knuth-Morris-Pratt string matching</a></li>
<li><a href="../entries/Signature_Groebner.html">Signature-Based Gröbner Basis Algorithms</a></li>
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<p style="display:none;" id="bibtex-filename">MonoBoolTranAlgebra-AFP</p><pre id="copy-text">@article{MonoBoolTranAlgebra-AFP,
author = {Viorel Preoteasa},
title = {Algebra of Monotonic Boolean Transformers},
journal = {Archive of Formal Proofs},
month = {September},
year = {2011},
note = {\url{https://isa-afp.org/entries/MonoBoolTranAlgebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/MonoidalCategory.html b/web/entries/MonoidalCategory.html
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<h1 >
<span class='first'>M</span>onoidal <span class='first'>C</span>ategories</h1>
<div>
<p><a href="../authors/stark">Eugene W. Stark</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwic3Rvbnlicm9vayIsImVkdSJdLCJ1c2VyIjpbInN0YXJrIl19">📧</a>
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<p class="date">May 4, 2017</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Building on the formalization of basic category theory set out in the
author's previous AFP article, the present article formalizes
some basic aspects of the theory of monoidal categories. Among the
notions defined here are monoidal category, monoidal functor, and
equivalence of monoidal categories. The main theorems formalized are
MacLane's coherence theorem and the constructions of the free
monoidal category and free strict monoidal category generated by a
given category. The coherence theorem is proved syntactically, using
a structurally recursive approach to reduction of terms that might
have some novel aspects. We also give proofs of some results given by
Etingof et al, which may prove useful in a formal setting. In
particular, we show that the left and right unitors need not be taken
as given data in the definition of monoidal category, nor does the
definition of monoidal functor need to take as given a specific
isomorphism expressing the preservation of the unit object. Our
definitions of monoidal category and monoidal functor are stated so as
to take advantage of the economy afforded by these facts.
</p><p>
Revisions made subsequent to the first version of this article added
material on cartesian monoidal categories; showing that the underlying
category of a cartesian monoidal category is a cartesian category, and
that every cartesian category extends to a cartesian monoidal
category.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 10, 2020</dt>
<dd>Added new material on cartesian monoidal categories.
(revision 06640f317a79)<br></dd><dt>February 15, 2020</dt>
<dd>Cosmetic improvements.
(revision a51840d36867)<br>
</dd><dt>May 29, 2018</dt>
<dd>Modifications required due to 'Category3' changes. Introduced notation for "in hom".
(revision 8318366d4575)<br>
</dd><dt>May 18, 2017</dt>
<dd>Integrated material from MonoidalCategory/Category3Adapter into Category3/ and deleted adapter.
(revision 015543cdd069)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li></ul>
<h3>Session MonoidalCategory</h3>
<ul>
<li><a href="../theories/monoidalcategory/#MonoidalCategory">MonoidalCategory</a></li>
<li><a href="../theories/monoidalcategory/#MonoidalFunctor">MonoidalFunctor</a></li>
<li><a href="../theories/monoidalcategory/#FreeMonoidalCategory">FreeMonoidalCategory</a></li>
<li><a href="../theories/monoidalcategory/#CartesianMonoidalCategory">CartesianMonoidalCategory</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Category3.html">Category Theory with Adjunctions and Limits</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Bicategory.html">Bicategories</a></li></ul>
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<p style="display:none;" id="bibtex-filename">MonoidalCategory-AFP</p><pre id="copy-text">@article{MonoidalCategory-AFP,
author = {Eugene W. Stark},
title = {Monoidal Categories},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/MonoidalCategory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>ffect <span class='first'>P</span>olymorphism in <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 5, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The notion of a monad cannot be expressed within higher-order logic
(HOL) due to type system restrictions. We show that if a monad is used
with values of only one type, this notion can be formalised in HOL.
Based on this idea, we develop a library of effect specifications and
implementations of monads and monad transformers. Hence, we can
abstract over the concrete monad in HOL definitions and thus use the
same definition for different (combinations of) effects. We illustrate
the usefulness of effect polymorphism with a monadic interpreter for a
simple language.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>February 15, 2018</dt>
<dd>added further specifications and implementations of non-determinism;
more examples
(revision bc5399eea78e)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Monomorphic_Monad</h3>
<ul>
<li><a href="../theories/monomorphic_monad/#Monomorphic_Monad">Monomorphic_Monad</a></li>
<li><a href="../theories/monomorphic_monad/#Monad_Overloading">Monad_Overloading</a></li>
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Monomorphic_Monad-AFP</p><pre id="copy-text">@article{Monomorphic_Monad-AFP,
author = {Andreas Lochbihler},
title = {Effect polymorphism in higher-order logic},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Monomorphic_Monad.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/MuchAdoAboutTwo.html b/web/entries/MuchAdoAboutTwo.html
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<h1 >
<span class='first'>M</span>uch <span class='first'>A</span>do <span class='first'>A</span>bout <span class='first'>T</span>wo</h1>
<div>
<p><a href="../authors/boehme">Sascha Böhme</a> <a href="http://www21.in.tum.de/~boehmes/">🌐</a>
</p>
<p class="date">November 6, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article is an Isabelle formalisation of a paper with the same title. In a similar way as Knuth's 0-1-principle for sorting algorithms, that paper develops a 0-1-2-principle for parallel prefix computations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session MuchAdoAboutTwo</h3>
<ul>
<li><a href="../theories/muchadoabouttwo/#MuchAdoAboutTwo">MuchAdoAboutTwo</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">MuchAdoAboutTwo-AFP</p><pre id="copy-text">@article{MuchAdoAboutTwo-AFP,
author = {Sascha Böhme},
title = {Much Ado About Two},
journal = {Archive of Formal Proofs},
month = {November},
year = {2007},
note = {\url{https://isa-afp.org/entries/MuchAdoAboutTwo.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Multi_Party_Computation.html b/web/entries/Multi_Party_Computation.html
--- a/web/entries/Multi_Party_Computation.html
+++ b/web/entries/Multi_Party_Computation.html
@@ -1,197 +1,199 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Multi-Party Computation - Archive of Formal Proofs</title><meta name="description" content="We use CryptHOL to consider Multi-Party Computation (MPC) protocols.
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<h1 >
<span class='first'>M</span>ulti-<span class='first'>P</span>arty <span class='first'>C</span>omputation</h1>
<div>
<p><a href="../authors/aspinall">David Aspinall</a> <a href="http://homepages.inf.ed.ac.uk/da/">🌐</a> and <a href="../authors/butler">David Butler</a> <a class="obfuscated" data="eyJob3N0IjpbInR1cmluZyIsImFjIiwidWsiXSwidXNlciI6WyJkYnV0bGVyIl19">📧</a>
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<p class="date">May 9, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We use CryptHOL to consider Multi-Party Computation (MPC) protocols.
MPC was first considered by Yao in 1983 and recent advances in
efficiency and an increased demand mean it is now deployed in the real
world. Security is considered using the real/ideal world paradigm. We
first define security in the semi-honest security setting where
parties are assumed not to deviate from the protocol transcript. In
this setting we prove multiple Oblivious Transfer (OT) protocols
secure and then show security for the gates of the GMW protocol. We
then define malicious security, this is a stronger notion of security
where parties are assumed to be fully corrupted by an adversary. In
this setting we again consider OT, as it is a fundamental building
block of almost all MPC protocols.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Multi_Party_Computation</h3>
<ul>
<li><a href="../theories/multi_party_computation/#Cyclic_Group_Ext">Cyclic_Group_Ext</a></li>
<li><a href="../theories/multi_party_computation/#Number_Theory_Aux">Number_Theory_Aux</a></li>
<li><a href="../theories/multi_party_computation/#Uniform_Sampling">Uniform_Sampling</a></li>
<li><a href="../theories/multi_party_computation/#Semi_Honest_Def">Semi_Honest_Def</a></li>
<li><a href="../theories/multi_party_computation/#OT_Functionalities">OT_Functionalities</a></li>
<li><a href="../theories/multi_party_computation/#ETP">ETP</a></li>
<li><a href="../theories/multi_party_computation/#ETP_OT">ETP_OT</a></li>
<li><a href="../theories/multi_party_computation/#ETP_RSA_OT">ETP_RSA_OT</a></li>
<li><a href="../theories/multi_party_computation/#Noar_Pinkas_OT">Noar_Pinkas_OT</a></li>
<li><a href="../theories/multi_party_computation/#OT14">OT14</a></li>
<li><a href="../theories/multi_party_computation/#GMW">GMW</a></li>
<li><a href="../theories/multi_party_computation/#Secure_Multiplication">Secure_Multiplication</a></li>
<li><a href="../theories/multi_party_computation/#DH_Ext">DH_Ext</a></li>
<li><a href="../theories/multi_party_computation/#Malicious_Defs">Malicious_Defs</a></li>
<li><a href="../theories/multi_party_computation/#Malicious_OT">Malicious_OT</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Game_Based_Crypto.html">Game-based cryptography in HOL</a></li></ul>
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author = {David Aspinall and David Butler},
title = {Multi-Party Computation},
journal = {Archive of Formal Proofs},
month = {May},
year = {2019},
note = {\url{https://isa-afp.org/entries/Multi_Party_Computation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Multi_Party_Computation-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>B</span>inary <span class='first'>M</span>ultirelations</h1>
<div>
<p><a href="../authors/furusawa">Hitoshi Furusawa</a> <a href="http://www.sci.kagoshima-u.ac.jp/~furusawa/">🌐</a> and <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">June 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Binary multirelations associate elements of a set with its subsets; hence
they are binary relations from a set to its power set. Applications include
alternating automata, models and logics for games, program semantics with
dual demonic and angelic nondeterministic choices and concurrent dynamic
logics. This proof document supports an arXiv article that formalises the
basic algebra of multirelations and proposes axiom systems for them,
ranging from weak bi-monoids to weak bi-quantales.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Multirelations</h3>
<ul>
<li><a href="../theories/multirelations/#C_Algebras">C_Algebras</a></li>
<li><a href="../theories/multirelations/#Multirelations">Multirelations</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li>
<li><a href="../entries/Relation_Algebra.html">Relation Algebra</a></li>
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<p style="display:none;" id="bibtex-filename">Multirelations-AFP</p><pre id="copy-text">@article{Multirelations-AFP,
author = {Hitoshi Furusawa and Georg Struth},
title = {Binary Multirelations},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/Multirelations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Multiset_Ordering_NPC.html b/web/entries/Multiset_Ordering_NPC.html
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<h1 >
<span class='first'>T</span>he <span class='first'>G</span>eneralized <span class='first'>M</span>ultiset <span class='first'>O</span>rdering <span class='first'>I</span>s <span class='first'>N</span><span class='first'>P</span>-<span class='first'>C</span>omplete</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/schmidinger">Lukas Schmidinger</a>
</p>
<p class="date">April 20, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We consider the problem of comparing two multisets via the generalized
multiset ordering. We show that the corresponding decision problem is
NP-complete. To be more precise, we encode multiset-comparisons into
propositional formulas or into conjunctive normal forms of quadratic
size; we further prove that satisfiability of conjunctive normal forms
can be encoded as multiset-comparison problems of linear size. As a
corollary, we also show that the problem of deciding whether two terms
are related by a recursive path order is NP-hard, provided the
recursive path order is based on the generalized multiset ordering.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Multiset_Ordering_NPC</h3>
<ul>
<li><a href="../theories/multiset_ordering_npc/#Multiset_Ordering_More">Multiset_Ordering_More</a></li>
<li><a href="../theories/multiset_ordering_npc/#Propositional_Formula">Propositional_Formula</a></li>
<li><a href="../theories/multiset_ordering_npc/#Multiset_Ordering_in_NP">Multiset_Ordering_in_NP</a></li>
<li><a href="../theories/multiset_ordering_npc/#Multiset_Ordering_NP_Hard">Multiset_Ordering_NP_Hard</a></li>
<li><a href="../theories/multiset_ordering_npc/#RPO_NP_Hard">RPO_NP_Hard</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Weighted_Path_Order.html">A Formalization of Weighted Path Orders and Recursive Path Orders</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Multiset_Ordering_NPC-AFP</p><pre id="copy-text">@article{Multiset_Ordering_NPC-AFP,
author = {René Thiemann and Lukas Schmidinger},
title = {The Generalized Multiset Ordering is NP-Complete},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Multiset_Ordering_NPC.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/Myhill-Nerode.html b/web/entries/Myhill-Nerode.html
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<h1 >
<span class='first'>T</span>he <span class='first'>M</span>yhill-<span class='first'>N</span>erode <span class='first'>T</span>heorem <span class='first'>B</span>ased on <span class='first'>R</span>egular <span class='first'>E</span>xpressions</h1>
<div>
<p><a href="../authors/wu">Chunhan Wu</a>, <a href="../authors/zhangx">Xingyuan Zhang</a> and <a href="../authors/urban">Christian Urban</a> <a href="https://nms.kcl.ac.uk/christian.urban/">🌐</a>
with contributions from <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">August 26, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">There are many proofs of the Myhill-Nerode theorem using automata. In this library we give a proof entirely based on regular expressions, since regularity of languages can be conveniently defined using regular expressions (it is more painful in HOL to define regularity in terms of automata). We prove the first direction of the Myhill-Nerode theorem by solving equational systems that involve regular expressions. For the second direction we give two proofs: one using tagging-functions and another using partial derivatives. We also establish various closure properties of regular languages. Most details of the theories are described in our ITP 2011 paper.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Myhill-Nerode</h3>
<ul>
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<li><a href="../entries/MSO_Regex_Equivalence.html">Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</a></li>
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<p style="display:none;" id="bibtex-filename">Myhill-Nerode-AFP</p><pre id="copy-text">@article{Myhill-Nerode-AFP,
author = {Chunhan Wu and Xingyuan Zhang and Christian Urban},
title = {The Myhill-Nerode Theorem Based on Regular Expressions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2011},
note = {\url{https://isa-afp.org/entries/Myhill-Nerode.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus - Archive of Formal Proofs</title><meta name="description" content="I formalise a Church-style simply-typed \(\lambda\)-calculus, extended with pairs, a unit value, and projection functions, and show some metatheory of the..."><meta property="og:title" content="Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus" />
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<h1 >
<span class='first'>V</span>erified <span class='first'>M</span>etatheory and <span class='first'>T</span>ype <span class='first'>I</span>nference for a <span class='first'>N</span>ame-<span class='first'>C</span>arrying <span class='first'>S</span>imply-<span class='first'>T</span>yped <span class='first'>L</span>ambda <span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/rawson">Michael Rawson</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWljaGFlbHJhd3Nvbjc2Il19">📧</a>
</p>
<p class="date">July 9, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">I formalise a Church-style simply-typed
\(\lambda\)-calculus, extended with pairs, a unit value, and
projection functions, and show some metatheory of the calculus, such
as the subject reduction property. Particular attention is paid to the
treatment of names in the calculus. A nominal style of binding is
used, but I use a manual approach over Nominal Isabelle in order to
extract an executable type inference algorithm. More information can
be found in my <a
href="http://www.openthesis.org/documents/Verified-Metatheory-Type-Inference-Simply-603182.html">undergraduate
dissertation</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session Name_Carrying_Type_Inference</h3>
<ul>
<li><a href="../theories/name_carrying_type_inference/#Fresh">Fresh</a></li>
<li><a href="../theories/name_carrying_type_inference/#Permutation">Permutation</a></li>
<li><a href="../theories/name_carrying_type_inference/#PreSimplyTyped">PreSimplyTyped</a></li>
<li><a href="../theories/name_carrying_type_inference/#SimplyTyped">SimplyTyped</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Name_Carrying_Type_Inference-AFP</p><pre id="copy-text">@article{Name_Carrying_Type_Inference-AFP,
author = {Michael Rawson},
title = {Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/Name_Carrying_Type_Inference.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Name_Carrying_Type_Inference-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Name_Carrying_Type_Inference-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Name_Carrying_Type_Inference-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Name_Carrying_Type_Inference-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Name_Carrying_Type_Inference-2017-07-15.tar.gz">Jul 15, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Nano_JSON.html b/web/entries/Nano_JSON.html
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+++ b/web/entries/Nano_JSON.html
@@ -1,181 +1,186 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Nano JSON: Working with JSON formatted data in Isabelle/HOL and Isabelle/ML - Archive of Formal Proofs</title><meta name="description" content="JSON (JavaScript Object Notation) is a common format for exchanging
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<h1 >
<span class='first'>N</span>ano <span class='first'>J</span><span class='first'>S</span><span class='first'>O</span><span class='first'>N</span>: <span class='first'>W</span>orking <span class='first'>W</span>ith <span class='first'>J</span><span class='first'>S</span><span class='first'>O</span><span class='first'>N</span> <span class='first'>F</span>ormatted <span class='first'>D</span>ata in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> and <span class='first'>I</span>sabelle/<span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a>
</p>
<p class="date">July 29, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">JSON (JavaScript Object Notation) is a common format for exchanging
data, based on a collection of key/value-pairs (the JSON objects) and
lists. Its syntax is inspired by JavaScript with the aim of being easy
to read and write for humans and easy to parse and generate for
machines. Despite its origin in the JavaScript world, JSON is
language-independent and many programming languages support working
with JSON-encoded data. This makes JSON an interesting format for
exchanging data with Isabelle/HOL. This AFP entry provides a
JSON-like import-expert format for both Isabelle/ML and Isabelle/HOL.
On the one hand, this AFP entry provides means for Isabelle/HOL users
to work with JSON encoded data without the need using Isabelle/ML. On
the other and, the provided Isabelle/ML interfaces allow additional
extensions or integration into Isabelle extensions written in
Isabelle/ML. While format is not fully JSON compliant (e.g., due to
limitations in the range of supported Unicode characters), it works in
most situations: the provided implementation in Isabelle/ML and its
representation in Isabelle/HOL have been used successfully in several
projects for exchanging data sets of several hundredths of megabyte
between Isabelle and external tools.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Nano_JSON</h3>
<ul>
<li><a href="../theories/nano_json/#Nano_JSON">Nano_JSON</a></li>
<li><a href="../theories/nano_json/#Nano_JSON_Query">Nano_JSON_Query</a></li>
<li><a href="../theories/nano_json/#Nano_JSON_Main">Nano_JSON_Main</a></li>
<li><a href="../theories/nano_json/#Nano_JSON_Manual">Nano_JSON_Manual</a></li>
<li><a href="../theories/nano_json/#Example">Example</a></li>
<li><a href="../theories/nano_json/#Example_Real">Example_Real</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Nano_JSON-AFP</p><pre id="copy-text">@article{Nano_JSON-AFP,
author = {Achim D. Brucker},
title = {Nano JSON: Working with JSON formatted data in Isabelle/HOL and Isabelle/ML},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/Nano_JSON.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
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+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Nano_JSON-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Nano_JSON-2022-08-22.tar.gz">Aug 22, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>T</span>he <span class='first'>N</span>ash-<span class='first'>W</span>illiams <span class='first'>P</span>artition <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">May 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1965, Nash-Williams discovered a generalisation of the infinite
form of Ramsey's theorem. Where the latter concerns infinite sets
of n-element sets for some fixed n, the Nash-Williams theorem concerns
infinite sets of finite sets (or lists) subject to a “no initial
segment” condition. The present formalisation follows a
monograph on Ramsey Spaces by Todorčević.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Nash_Williams</h3>
<ul>
<li><a href="../theories/nash_williams/#Nash_Extras">Nash_Extras</a></li>
<li><a href="../theories/nash_williams/#Nash_Williams">Nash_Williams</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Ordinal_Partitions.html">Ordinal Partitions</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Nash_Williams-AFP</p><pre id="copy-text">@article{Nash_Williams-AFP,
author = {Lawrence C. Paulson},
title = {The Nash-Williams Partition Theorem},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Nash_Williams.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Nash_Williams-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Nash_Williams-2020-06-02.tar.gz">Jun 2, 2020</a>: Isabelle2020
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diff --git a/web/entries/Nat-Interval-Logic.html b/web/entries/Nat-Interval-Logic.html
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<h1 >
<span class='first'>I</span>nterval <span class='first'>T</span>emporal <span class='first'>L</span>ogic on <span class='first'>N</span>atural <span class='first'>N</span>umbers</h1>
<div>
<p><a href="../authors/trachtenherz">David Trachtenherz</a>
</p>
<p class="date">February 23, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We introduce a theory of temporal logic operators using sets of natural numbers as time domain, formalized in a shallow embedding manner. The theory comprises special natural intervals (theory IL_Interval: open and closed intervals, continuous and modulo intervals, interval traversing results), operators for shifting intervals to left/right on the number axis as well as expanding/contracting intervals by constant factors (theory IL_IntervalOperators.thy), and ultimately definitions and results for unary and binary temporal operators on arbitrary natural sets (theory IL_TemporalOperators).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/temporal-logic">Logic/General logic/Temporal logic</a></li></ul>
<h3>Session Nat-Interval-Logic</h3>
<ul>
<li><a href="../theories/nat-interval-logic/#IL_Interval">IL_Interval</a></li>
<li><a href="../theories/nat-interval-logic/#IL_IntervalOperators">IL_IntervalOperators</a></li>
<li><a href="../theories/nat-interval-logic/#IL_TemporalOperators">IL_TemporalOperators</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List-Infinite.html">Infinite Lists</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/AutoFocus-Stream.html">AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Nat-Interval-Logic-AFP</p><pre id="copy-text">@article{Nat-Interval-Logic-AFP,
author = {David Trachtenherz},
title = {Interval Temporal Logic on Natural Numbers},
journal = {Archive of Formal Proofs},
month = {February},
year = {2011},
note = {\url{https://isa-afp.org/entries/Nat-Interval-Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nat-Interval-Logic-2011-02-24.tar.gz">Feb 24, 2011</a>: Isabelle2011
</li></ul>
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@@ -1,241 +1,243 @@
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<h1 >
<span class='first'>N</span>ative <span class='first'>W</span>ord</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
with contributions from <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">September 17, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry makes machine words and machine arithmetic available for code generation from Isabelle/HOL. It provides a common abstraction that hides the differences between the different target languages. The code generator maps these operations to the APIs of the target languages. Apart from that, we extend the available bit operations on types int and integer, and map them to the operations in the target languages.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 15, 2018</dt>
<dd>added cast operators for default-size words (revision fc1f1fb8dd30)<br></dd><dt>September 2, 2017</dt>
<dd>added 64-bit words (revision c89f86244e3c)<br></dd><dt>October 6, 2014</dt>
<dd>proper test setup with compilation and execution of tests in all target languages
(revision 5d7a1c9ae047)<br>
</dd><dt>March 31, 2014</dt>
<dd>added words of default size in the target language (by Peter Lammich)
(revision 25caf5065833)<br>
</dd><dt>November 6, 2013</dt>
<dd>added conversion function between native words and characters
(revision fd23d9a7fe3a)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Native_Word</h3>
<ul>
<li><a href="../theories/native_word/#Code_Target_Word_Base">Code_Target_Word_Base</a></li>
<li><a href="../theories/native_word/#Word_Type_Copies">Word_Type_Copies</a></li>
<li><a href="../theories/native_word/#Code_Int_Integer_Conversion">Code_Int_Integer_Conversion</a></li>
<li><a href="../theories/native_word/#Code_Target_Integer_Bit">Code_Target_Integer_Bit</a></li>
<li><a href="../theories/native_word/#Uint64">Uint64</a></li>
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<li><a href="../theories/native_word/#Uint8">Uint8</a></li>
<li><a href="../theories/native_word/#Uint">Uint</a></li>
<li><a href="../theories/native_word/#Native_Cast">Native_Cast</a></li>
<li><a href="../theories/native_word/#Native_Cast_Uint">Native_Cast_Uint</a></li>
<li><a href="../theories/native_word/#Native_Word_Imperative_HOL">Native_Word_Imperative_HOL</a></li>
<li><a href="../theories/native_word/#Native_Word_Test">Native_Word_Test</a></li>
<li><a href="../theories/native_word/#Code_Target_Int_Bit">Code_Target_Int_Bit</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_Emu">Native_Word_Test_Emu</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_PolyML">Native_Word_Test_PolyML</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_PolyML2">Native_Word_Test_PolyML2</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_PolyML64">Native_Word_Test_PolyML64</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_Scala">Native_Word_Test_Scala</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_GHC">Native_Word_Test_GHC</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_MLton">Native_Word_Test_MLton</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_MLton2">Native_Word_Test_MLton2</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_OCaml">Native_Word_Test_OCaml</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_OCaml2">Native_Word_Test_OCaml2</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_SMLNJ">Native_Word_Test_SMLNJ</a></li>
<li><a href="../theories/native_word/#Native_Word_Test_SMLNJ2">Native_Word_Test_SMLNJ2</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
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<ul class="horizontal-list"><li><a href="../entries/FSM_Tests.html">Verified Complete Test Strategies for Finite State Machines</a></li><li><a href="../entries/MiniSail.html">MiniSail - A kernel language for the ISA specification language SAIL</a></li><li><a href="../entries/Mersenne_Primes.html">Mersenne primes and the Lucas–Lehmer test</a></li><li><a href="../entries/WebAssembly.html">WebAssembly</a></li><li><a href="../entries/Iptables_Semantics.html">Iptables Semantics</a></li><li><a href="../entries/ROBDD.html">Algorithms for Reduced Ordered Binary Decision Diagrams</a></li><li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Native_Word-AFP</p><pre id="copy-text">@article{Native_Word-AFP,
author = {Andreas Lochbihler},
title = {Native Word},
journal = {Archive of Formal Proofs},
month = {September},
year = {2013},
note = {\url{https://isa-afp.org/entries/Native_Word.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Native_Word-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Native_Word-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Native_Word-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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diff --git a/web/entries/Nested_Multisets_Ordinals.html b/web/entries/Nested_Multisets_Ordinals.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals - Archive of Formal Proofs</title><meta name="description" content="This Isabelle/HOL formalization introduces a nested multiset datatype and defines Dershowitz and Manna&#39;s nested multiset order. The order is proved well..."><meta property="og:title" content="Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals" />
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>N</span>ested <span class='first'>M</span>ultisets, <span class='first'>H</span>ereditary <span class='first'>M</span>ultisets, and <span class='first'>S</span>yntactic <span class='first'>O</span>rdinals</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamFzbWluIiwiYmxhbmNoZXR0ZSJdfQ==">📧</a>, <a href="../authors/fleury">Mathias Fleury</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbImZsZXVyeSJdfQ==">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">November 12, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization introduces a nested multiset datatype and defines Dershowitz and Manna's nested multiset order. The order is proved well founded and linear. By removing one constructor, we transform the nested multisets into hereditary multisets. These are isomorphic to the syntactic ordinals—the ordinals can be recursively expressed in Cantor normal form. Addition, subtraction, multiplication, and linear orders are provided on this type.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Nested_Multisets_Ordinals</h3>
<ul>
<li><a href="../theories/nested_multisets_ordinals/#Multiset_More">Multiset_More</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Signed_Multiset">Signed_Multiset</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Nested_Multiset">Nested_Multiset</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Hereditary_Multiset">Hereditary_Multiset</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Signed_Hereditary_Multiset">Signed_Hereditary_Multiset</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Syntactic_Ordinal">Syntactic_Ordinal</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Signed_Syntactic_Ordinal">Signed_Syntactic_Ordinal</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Syntactic_Ordinal_Bridge">Syntactic_Ordinal_Bridge</a></li>
<li><a href="../theories/nested_multisets_ordinals/#McCarthy_91">McCarthy_91</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Hydra_Battle">Hydra_Battle</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Goodstein_Sequence">Goodstein_Sequence</a></li>
<li><a href="../theories/nested_multisets_ordinals/#Unary_PCF">Unary_PCF</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Ordinal.html">Countable Ordinals</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Design_Theory.html">Combinatorial Design Theory</a></li><li><a href="../entries/Progress_Tracking.html">Formalization of Timely Dataflow&rsquo;s Progress Tracking Protocol</a></li><li><a href="../entries/PAC_Checker.html">Practical Algebraic Calculus Checker</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Lambda_Free_KBOs.html">Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Clique_and_Monotone_Circuits.html">Clique is not solvable by monotone circuits of polynomial size</a></li>
<li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li>
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<p style="display:none;" id="bibtex-filename">Nested_Multisets_Ordinals-AFP</p><pre id="copy-text">@article{Nested_Multisets_Ordinals-AFP,
author = {Jasmin Christian Blanchette and Mathias Fleury and Dmitriy Traytel},
title = {Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Nested_Multisets_Ordinals.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Nested_Multisets_Ordinals-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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diff --git a/web/entries/Network_Security_Policy_Verification.html b/web/entries/Network_Security_Policy_Verification.html
--- a/web/entries/Network_Security_Policy_Verification.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Network Security Policy Verification - Archive of Formal Proofs</title><meta name="description" content="We present a unified theory for verifying network security policies. A security policy is represented as directed graph. To check high-level security..."><meta property="og:title" content="Network Security Policy Verification" />
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<h1 >
<span class='first'>N</span>etwork <span class='first'>S</span>ecurity <span class='first'>P</span>olicy <span class='first'>V</span>erification</h1>
<div>
<p><a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>
</p>
<p class="date">July 4, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a unified theory for verifying network security policies.
A security policy is represented as directed graph.
To check high-level security goals, security invariants over the policy are
expressed. We cover monotonic security invariants, i.e. prohibiting more does not harm
security. We provide the following contributions for the security invariant theory.
<ul>
<li>Secure auto-completion of scenario-specific knowledge, which eases usability.</li>
<li>Security violations can be repaired by tightening the policy iff the
security invariants hold for the deny-all policy.</li>
<li>An algorithm to compute a security policy.</li>
<li>A formalization of stateful connection semantics in network security mechanisms.</li>
<li>An algorithm to compute a secure stateful implementation of a policy.</li>
<li>An executable implementation of all the theory.</li>
<li>Examples, ranging from an aircraft cabin data network to the analysis
of a large real-world firewall.</li>
<li>More examples: A fully automated translation of high-level security goals to both
firewall and SDN configurations (see Examples/Distributed_WebApp.thy).</li>
</ul>
For a detailed description, see
<ul>
<li>C. Diekmann, A. Korsten, and G. Carle.
<a href="http://www.net.in.tum.de/fileadmin/bibtex/publications/papers/diekmann2015mansdnnfv.pdf">Demonstrating
topoS: Theorem-prover-based synthesis of secure network configurations.</a>
In 2nd International Workshop on Management of SDN and NFV Systems, manSDN/NFV, Barcelona, Spain, November 2015.</li>
<li>C. Diekmann, S.-A. Posselt, H. Niedermayer, H. Kinkelin, O. Hanka, and G. Carle.
<a href="http://www.net.in.tum.de/pub/diekmann/forte14.pdf">Verifying Security Policies using Host Attributes.</a>
In FORTE, 34th IFIP International Conference on Formal Techniques for Distributed Objects,
Components and Systems, Berlin, Germany, June 2014.</li>
<li>C. Diekmann, L. Hupel, and G. Carle. Directed Security Policies:
<a href="http://rvg.web.cse.unsw.edu.au/eptcs/paper.cgi?ESSS2014.3">A Stateful Network Implementation.</a>
In J. Pang and Y. Liu, editors, Engineering Safety and Security Systems,
volume 150 of Electronic Proceedings in Theoretical Computer Science,
pages 20-34, Singapore, May 2014. Open Publishing Association.</li>
</ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>April 14, 2015</dt>
<dd>Added Distributed WebApp example and improved graphviz visualization
(revision 4dde08ca2ab8)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Network_Security_Policy_Verification</h3>
<ul>
<li><a href="../theories/network_security_policy_verification/#ML_GraphViz">ML_GraphViz</a></li>
<li><a href="../theories/network_security_policy_verification/#ML_GraphViz_Disable">ML_GraphViz_Disable</a></li>
<li><a href="../theories/network_security_policy_verification/#FiniteGraph">FiniteGraph</a></li>
<li><a href="../theories/network_security_policy_verification/#FiniteListGraph">FiniteListGraph</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Util">TopoS_Util</a></li>
<li><a href="../theories/network_security_policy_verification/#Efficient_Distinct">Efficient_Distinct</a></li>
<li><a href="../theories/network_security_policy_verification/#FiniteListGraph_Impl">FiniteListGraph_Impl</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Vertices">TopoS_Vertices</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Interface">TopoS_Interface</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_withOffendingFlows">TopoS_withOffendingFlows</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_ENF">TopoS_ENF</a></li>
<li><a href="../theories/network_security_policy_verification/#vertex_example_simps">vertex_example_simps</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Helper">TopoS_Helper</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Subnets2">SINVAR_Subnets2</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_BLPstrict">SINVAR_BLPstrict</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Tainting">SINVAR_Tainting</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_BLPbasic">SINVAR_BLPbasic</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_TaintingTrusted">SINVAR_TaintingTrusted</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_BLPtrusted">SINVAR_BLPtrusted</a></li>
<li><a href="../theories/network_security_policy_verification/#Analysis_Tainting">Analysis_Tainting</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Interface_impl">TopoS_Interface_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_BLPbasic_impl">SINVAR_BLPbasic_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Subnets">SINVAR_Subnets</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Subnets_impl">SINVAR_Subnets_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_DomainHierarchyNG">SINVAR_DomainHierarchyNG</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_DomainHierarchyNG_impl">SINVAR_DomainHierarchyNG_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_BLPtrusted_impl">SINVAR_BLPtrusted_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_SecGwExt">SINVAR_SecGwExt</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_SecGwExt_impl">SINVAR_SecGwExt_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Sink">SINVAR_Sink</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Sink_impl">SINVAR_Sink_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_SubnetsInGW">SINVAR_SubnetsInGW</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_SubnetsInGW_impl">SINVAR_SubnetsInGW_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_CommunicationPartners">SINVAR_CommunicationPartners</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_CommunicationPartners_impl">SINVAR_CommunicationPartners_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_NoRefl">SINVAR_NoRefl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_NoRefl_impl">SINVAR_NoRefl_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Tainting_impl">SINVAR_Tainting_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_TaintingTrusted_impl">SINVAR_TaintingTrusted_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Dependability">SINVAR_Dependability</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Dependability_impl">SINVAR_Dependability_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_NonInterference">SINVAR_NonInterference</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_NonInterference_impl">SINVAR_NonInterference_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_ACLcommunicateWith">SINVAR_ACLcommunicateWith</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_ACLnotCommunicateWith">SINVAR_ACLnotCommunicateWith</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_ACLnotCommunicateWith_impl">SINVAR_ACLnotCommunicateWith_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_ACLcommunicateWith_impl">SINVAR_ACLcommunicateWith_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Dependability_norefl">SINVAR_Dependability_norefl</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Dependability_norefl_impl">SINVAR_Dependability_norefl_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Library">TopoS_Library</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Composition_Theory">TopoS_Composition_Theory</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Stateful_Policy">TopoS_Stateful_Policy</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Composition_Theory_impl">TopoS_Composition_Theory_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Stateful_Policy_Algorithm">TopoS_Stateful_Policy_Algorithm</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Stateful_Policy_impl">TopoS_Stateful_Policy_impl</a></li>
<li><a href="../theories/network_security_policy_verification/#METASINVAR_SystemBoundary">METASINVAR_SystemBoundary</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_Impl">TopoS_Impl</a></li>
<li><a href="../theories/network_security_policy_verification/#Network_Security_Policy_Verification">Network_Security_Policy_Verification</a></li>
<li><a href="../theories/network_security_policy_verification/#Example_BLP">Example_BLP</a></li>
<li><a href="../theories/network_security_policy_verification/#TopoS_generateCode">TopoS_generateCode</a></li>
<li><a href="../theories/network_security_policy_verification/#attic">attic</a></li>
<li><a href="../theories/network_security_policy_verification/#Impl_List_Playground_ChairNetwork">Impl_List_Playground_ChairNetwork</a></li>
<li><a href="../theories/network_security_policy_verification/#Impl_List_Playground_statefulpolicycompliance">Impl_List_Playground_statefulpolicycompliance</a></li>
<li><a href="../theories/network_security_policy_verification/#Example">Example</a></li>
<li><a href="../theories/network_security_policy_verification/#Example_NetModel">Example_NetModel</a></li>
<li><a href="../theories/network_security_policy_verification/#Example_Forte14">Example_Forte14</a></li>
<li><a href="../theories/network_security_policy_verification/#Distributed_WebApp">Distributed_WebApp</a></li>
<li><a href="../theories/network_security_policy_verification/#I8_SSH_Landscape">I8_SSH_Landscape</a></li>
<li><a href="../theories/network_security_policy_verification/#Impl_List_Playground">Impl_List_Playground</a></li>
<li><a href="../theories/network_security_policy_verification/#Impl_List_Playground_ChairNetwork_statefulpolicy_example">Impl_List_Playground_ChairNetwork_statefulpolicy_example</a></li>
<li><a href="../theories/network_security_policy_verification/#CryptoDB">CryptoDB</a></li>
<li><a href="../theories/network_security_policy_verification/#IDEM">IDEM</a></li>
<li><a href="../theories/network_security_policy_verification/#MeasrDroid">MeasrDroid</a></li>
<li><a href="../theories/network_security_policy_verification/#SINVAR_Examples">SINVAR_Examples</a></li>
<li><a href="../theories/network_security_policy_verification/#Imaginary_Factory_Network">Imaginary_Factory_Network</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Network_Security_Policy_Verification-AFP</p><pre id="copy-text">@article{Network_Security_Policy_Verification-AFP,
author = {Cornelius Diekmann},
title = {Network Security Policy Verification},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/Network_Security_Policy_Verification.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>V</span>on-<span class='first'>N</span>eumann-<span class='first'>M</span>orgenstern <span class='first'>U</span>tility <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/parsert">Julian Parsert</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsianVsaWFuIiwicGFyc2VydCJdfQ==">📧</a> and <a href="../authors/kaliszyk">Cezary Kaliszyk</a> <a href="http://cl-informatik.uibk.ac.at/users/cek/">🌐</a>
</p>
<p class="date">July 4, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Utility functions form an essential part of game theory and economics.
In order to guarantee the existence of utility functions most of the
time sufficient properties are assumed in an axiomatic manner. One
famous and very common set of such assumptions is that of expected
utility theory. Here, the rationality, continuity, and independence of
preferences is assumed. The von-Neumann-Morgenstern Utility theorem
shows that these assumptions are necessary and sufficient for an
expected utility function to exists. This theorem was proven by
Neumann and Morgenstern in ``Theory of Games and Economic
Behavior'' which is regarded as one of the most influential
works in game theory. The formalization includes formal definitions of
the underlying concepts including continuity and independence of
preferences.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Neumann_Morgenstern_Utility</h3>
<ul>
<li><a href="../theories/neumann_morgenstern_utility/#PMF_Composition">PMF_Composition</a></li>
<li><a href="../theories/neumann_morgenstern_utility/#Lotteries">Lotteries</a></li>
<li><a href="../theories/neumann_morgenstern_utility/#Neumann_Morgenstern_Utility_Theorem">Neumann_Morgenstern_Utility_Theorem</a></li>
<li><a href="../theories/neumann_morgenstern_utility/#Expected_Utility">Expected_Utility</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Welfare_Theorem.html">Microeconomics and the First Welfare Theorem</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/ArrowImpossibilityGS.html">Arrow and Gibbard-Satterthwaite</a></li>
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<p style="display:none;" id="bibtex-filename">Neumann_Morgenstern_Utility-AFP</p><pre id="copy-text">@article{Neumann_Morgenstern_Utility-AFP,
author = {Julian Parsert and Cezary Kaliszyk},
title = {Von-Neumann-Morgenstern Utility Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2018},
note = {\url{https://isa-afp.org/entries/Neumann_Morgenstern_Utility.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Neumann_Morgenstern_Utility-2018-07-04.tar.gz">Jul 4, 2018</a>: Isabelle2017
</li></ul>
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<h1 >
<span class='first'>N</span>o <span class='first'>F</span>aster-<span class='first'>T</span>han-<span class='first'>L</span>ight <span class='first'>O</span>bservers</h1>
<div>
<p><a href="../authors/stannett">Mike Stannett</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJtIiwic3Rhbm5ldHQiXX0=">📧</a> and <a href="../authors/nemeti">István Németi</a> <a href="http://www.renyi.hu/~nemeti/">🌐</a>
</p>
<p class="date">April 28, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a formal proof within First Order Relativity Theory that no
observer can travel faster than the speed of light. Originally
reported in Stannett & Németi (2014) "Using Isabelle/HOL to verify
first-order relativity theory", Journal of Automated Reasoning 52(4),
pp. 361-378.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/physics">Mathematics/Physics</a></li></ul>
<h3>Session No_FTL_observers</h3>
<ul>
<li><a href="../theories/no_ftl_observers/#SpaceTime">SpaceTime</a></li>
<li><a href="../theories/no_ftl_observers/#SomeFunc">SomeFunc</a></li>
<li><a href="../theories/no_ftl_observers/#Axioms">Axioms</a></li>
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<p style="display:none;" id="bibtex-filename">No_FTL_observers-AFP</p><pre id="copy-text">@article{No_FTL_observers-AFP,
author = {Mike Stannett and István Németi},
title = {No Faster-Than-Light Observers},
journal = {Archive of Formal Proofs},
month = {April},
year = {2016},
note = {\url{https://isa-afp.org/entries/No_FTL_observers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-No_FTL_observers-2016-04-28.tar.gz">Apr 28, 2016</a>: Isabelle2016
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diff --git a/web/entries/Nominal2.html b/web/entries/Nominal2.html
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<h1 >
<span class='first'>N</span>ominal 2</h1>
<div>
<p><a href="../authors/urban">Christian Urban</a> <a href="https://nms.kcl.ac.uk/christian.urban/">🌐</a>, <a href="../authors/berghofer">Stefan Berghofer</a> <a href="http://www.in.tum.de/~berghofe">🌐</a> and <a href="../authors/kaliszyk">Cezary Kaliszyk</a> <a href="http://cl-informatik.uibk.ac.at/users/cek/">🌐</a>
</p>
<p class="date">February 21, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Dealing with binders, renaming of bound variables, capture-avoiding
substitution, etc., is very often a major problem in formal
proofs, especially in proofs by structural and rule
induction. Nominal Isabelle is designed to make such proofs easy to
formalise: it provides an infrastructure for declaring nominal
datatypes (that is alpha-equivalence classes) and for defining
functions over them by structural recursion. It also provides
induction principles that have Barendregt’s variable convention
already built in.
</p><p>
This entry can be used as a more advanced replacement for
HOL/Nominal in the Isabelle distribution.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Nominal2</h3>
<ul>
<li><a href="../theories/nominal2/#Nominal2_Base">Nominal2_Base</a></li>
<li><a href="../theories/nominal2/#Nominal2_Abs">Nominal2_Abs</a></li>
<li><a href="../theories/nominal2/#Nominal2_FCB">Nominal2_FCB</a></li>
<li><a href="../theories/nominal2/#Nominal2">Nominal2</a></li>
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<li><a href="../theories/nominal2/#Eqvt">Eqvt</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/FinFun.html">Code Generation for Functions as Data</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MiniSail.html">MiniSail - A kernel language for the ISA specification language SAIL</a></li><li><a href="../entries/Goedel_HFSet_Semanticless.html">From Abstract to Concrete Gödel&rsquo;s Incompleteness Theorems—Part II</a></li><li><a href="../entries/Robinson_Arithmetic.html">Robinson Arithmetic</a></li><li><a href="../entries/LambdaAuth.html">Formalization of Generic Authenticated Data Structures</a></li><li><a href="../entries/Modal_Logics_for_NTS.html">Modal Logics for Nominal Transition Systems</a></li><li><a href="../entries/Rewriting_Z.html">The Z Property</a></li><li><a href="../entries/Incompleteness.html">Gödel&rsquo;s Incompleteness Theorems</a></li><li><a href="../entries/Launchbury.html">The Correctness of Launchbury&rsquo;s Natural Semantics for Lazy Evaluation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Nominal2-AFP</p><pre id="copy-text">@article{Nominal2-AFP,
author = {Christian Urban and Stefan Berghofer and Cezary Kaliszyk},
title = {Nominal 2},
journal = {Archive of Formal Proofs},
month = {February},
year = {2013},
note = {\url{https://isa-afp.org/entries/Nominal2.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Nominal2-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Nominal2-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Nominal2-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2016-04-24.tar.gz">Apr 24, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Nominal2-2013-02-24.tar.gz">Feb 24, 2013</a>: Isabelle2013
</li></ul>
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diff --git a/web/entries/Noninterference_CSP.html b/web/entries/Noninterference_CSP.html
--- a/web/entries/Noninterference_CSP.html
+++ b/web/entries/Noninterference_CSP.html
@@ -1,208 +1,210 @@
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<h1 >
<span class='first'>N</span>oninterference <span class='first'>S</span>ecurity in <span class='first'>C</span>ommunicating <span class='first'>S</span>equential <span class='first'>P</span>rocesses</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">May 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
An extension of classical noninterference security for deterministic
state machines, as introduced by Goguen and Meseguer and elegantly
formalized by Rushby, to nondeterministic systems should satisfy two
fundamental requirements: it should be based on a mathematically precise
theory of nondeterminism, and should be equivalent to (or at least not
weaker than) the classical notion in the degenerate deterministic case.
</p>
<p>
This paper proposes a definition of noninterference security applying
to Hoare's Communicating Sequential Processes (CSP) in the general case of
a possibly intransitive noninterference policy, and proves the
equivalence of this security property to classical noninterference
security for processes representing deterministic state machines.
</p>
<p>
Furthermore, McCullough's generalized noninterference security is shown
to be weaker than both the proposed notion of CSP noninterference security
for a generic process, and classical noninterference security for processes
representing deterministic state machines. This renders CSP noninterference
security preferable as an extension of classical noninterference security
to nondeterministic systems.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Noninterference_CSP</h3>
<ul>
<li><a href="../theories/noninterference_csp/#CSPNoninterference">CSPNoninterference</a></li>
<li><a href="../theories/noninterference_csp/#ClassicalNoninterference">ClassicalNoninterference</a></li>
<li><a href="../theories/noninterference_csp/#GeneralizedNoninterference">GeneralizedNoninterference</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Ipurge_Unwinding.html">The Ipurge Unwinding Theorem for CSP Noninterference Security</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Noninterference_CSP-AFP</p><pre id="copy-text">@article{Noninterference_CSP-AFP,
author = {Pasquale Noce},
title = {Noninterference Security in Communicating Sequential Processes},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/Noninterference_CSP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>C</span>onservation of <span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>N</span>oninterference <span class='first'>S</span>ecurity <span class='first'>U</span>nder <span class='first'>C</span>oncurrent <span class='first'>C</span>omposition</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">June 13, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>In his outstanding work on Communicating Sequential Processes,
Hoare has defined two fundamental binary operations allowing to
compose the input processes into another, typically more complex,
process: sequential composition and concurrent composition.
Particularly, the output of the latter operation is a process in which
any event not shared by both operands can occur whenever the operand
that admits the event can engage in it, whereas any event shared by
both operands can occur just in case both can engage in it.</p>
<p>This paper formalizes Hoare's definition of concurrent composition
and proves, in the general case of a possibly intransitive policy,
that CSP noninterference security is conserved under this operation.
This result, along with the previous analogous one concerning
sequential composition, enables the construction of more and more
complex processes enforcing noninterference security by composing,
sequentially or concurrently, simpler secure processes, whose security
can in turn be proven using either the definition of security, or
unwinding theorems.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session Noninterference_Concurrent_Composition</h3>
<ul>
<li><a href="../theories/noninterference_concurrent_composition/#ConcurrentComposition">ConcurrentComposition</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Sequential_Composition.html">Conservation of CSP Noninterference Security under Sequential Composition</a></li></ul>
</div>
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<li><a href="../entries/Noninterference_Generic_Unwinding.html">The Generic Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></li>
<li><a href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></li>
<li><a href="../entries/Noninterference_Inductive_Unwinding.html">The Inductive Unwinding Theorem for CSP Noninterference Security</a></li>
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<p style="display:none;" id="bibtex-filename">Noninterference_Concurrent_Composition-AFP</p><pre id="copy-text">@article{Noninterference_Concurrent_Composition-AFP,
author = {Pasquale Noce},
title = {Conservation of CSP Noninterference Security under Concurrent Composition},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Noninterference_Concurrent_Composition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>G</span>eneric <span class='first'>U</span>nwinding <span class='first'>T</span>heorem for <span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>N</span>oninterference <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">June 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
The classical definition of noninterference security for a deterministic state
machine with outputs requires to consider the outputs produced by machine
actions after any trace, i.e. any indefinitely long sequence of actions, of the
machine. In order to render the verification of the security of such a machine
more straightforward, there is a need of some sufficient condition for security
such that just individual actions, rather than unbounded sequences of actions,
have to be considered.
</p><p>
By extending previous results applying to transitive noninterference policies,
Rushby has proven an unwinding theorem that provides a sufficient condition of
this kind in the general case of a possibly intransitive policy. This condition
has to be satisfied by a generic function mapping security domains into
equivalence relations over machine states.
</p><p>
An analogous problem arises for CSP noninterference security, whose definition
requires to consider any possible future, i.e. any indefinitely long sequence of
subsequent events and any indefinitely large set of refused events associated to
that sequence, for each process trace.
</p><p>
This paper provides a sufficient condition for CSP noninterference security,
which indeed requires to just consider individual accepted and refused events
and applies to the general case of a possibly intransitive policy. This
condition follows Rushby's one for classical noninterference security, and has
to be satisfied by a generic function mapping security domains into equivalence
relations over process traces; hence its name, Generic Unwinding Theorem.
Variants of this theorem applying to deterministic processes and trace set
processes are also proven. Finally, the sufficient condition for security
expressed by the theorem is shown not to be a necessary condition as well, viz.
there exists a secure process such that no domain-relation map satisfying the
condition exists.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session Noninterference_Generic_Unwinding</h3>
<ul>
<li><a href="../theories/noninterference_generic_unwinding/#GenericUnwinding">GenericUnwinding</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Ipurge_Unwinding.html">The Ipurge Unwinding Theorem for CSP Noninterference Security</a></li></ul>
</div>
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<li><a href="../entries/Noninterference_Concurrent_Composition.html">Conservation of CSP Noninterference Security under Concurrent Composition</a></li>
<li><a href="../entries/Noninterference_Sequential_Composition.html">Conservation of CSP Noninterference Security under Sequential Composition</a></li>
<li><a href="../entries/Noninterference_Inductive_Unwinding.html">The Inductive Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></li>
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author = {Pasquale Noce},
title = {The Generic Unwinding Theorem for CSP Noninterference Security},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/Noninterference_Generic_Unwinding.html},
Formal proof development},
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>nductive <span class='first'>U</span>nwinding <span class='first'>T</span>heorem for <span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>N</span>oninterference <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">August 18, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
The necessary and sufficient condition for CSP noninterference security stated by the Ipurge Unwinding Theorem is expressed in terms of a pair of event lists varying over the set of process traces. This does not render it suitable for the subsequent application of rule induction in the case of a process defined inductively, since rule induction may rather be applied to a single variable ranging over an inductively defined set.
</p><p>
Starting from the Ipurge Unwinding Theorem, this paper derives a necessary and sufficient condition for CSP noninterference security that involves a single event list varying over the set of process traces, and is thus suitable for rule induction; hence its name, Inductive Unwinding Theorem. Similarly to the Ipurge Unwinding Theorem, the new theorem only requires to consider individual accepted and refused events for each process trace, and applies to the general case of a possibly intransitive noninterference policy. Specific variants of this theorem are additionally proven for deterministic processes and trace set processes.
</p></div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Noninterference_Inductive_Unwinding</h3>
<ul>
<li><a href="../theories/noninterference_inductive_unwinding/#InductiveUnwinding">InductiveUnwinding</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Ipurge_Unwinding.html">The Ipurge Unwinding Theorem for CSP Noninterference Security</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Noninterference_Generic_Unwinding.html">The Generic Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></li>
<li><a href="../entries/Noninterference_Concurrent_Composition.html">Conservation of CSP Noninterference Security under Concurrent Composition</a></li>
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<p style="display:none;" id="bibtex-filename">Noninterference_Inductive_Unwinding-AFP</p><pre id="copy-text">@article{Noninterference_Inductive_Unwinding-AFP,
author = {Pasquale Noce},
title = {The Inductive Unwinding Theorem for CSP Noninterference Security},
journal = {Archive of Formal Proofs},
month = {August},
year = {2015},
note = {\url{https://isa-afp.org/entries/Noninterference_Inductive_Unwinding.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>purge <span class='first'>U</span>nwinding <span class='first'>T</span>heorem for <span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>N</span>oninterference <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">June 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
The definition of noninterference security for Communicating Sequential
Processes requires to consider any possible future, i.e. any indefinitely long
sequence of subsequent events and any indefinitely large set of refused events
associated to that sequence, for each process trace. In order to render the
verification of the security of a process more straightforward, there is a need
of some sufficient condition for security such that just individual accepted and
refused events, rather than unbounded sequences and sets of events, have to be
considered.
</p><p>
Of course, if such a sufficient condition were necessary as well, it would be
even more valuable, since it would permit to prove not only that a process is
secure by verifying that the condition holds, but also that a process is not
secure by verifying that the condition fails to hold.
</p><p>
This paper provides a necessary and sufficient condition for CSP noninterference
security, which indeed requires to just consider individual accepted and refused
events and applies to the general case of a possibly intransitive policy. This
condition follows Rushby's output consistency for deterministic state machines
with outputs, and has to be satisfied by a specific function mapping security
domains into equivalence relations over process traces. The definition of this
function makes use of an intransitive purge function following Rushby's one;
hence the name given to the condition, Ipurge Unwinding Theorem.
</p><p>
Furthermore, in accordance with Hoare's formal definition of deterministic
processes, it is shown that a process is deterministic just in case it is a
trace set process, i.e. it may be identified by means of a trace set alone,
matching the set of its traces, in place of a failures-divergences pair. Then,
variants of the Ipurge Unwinding Theorem are proven for deterministic processes
and trace set processes.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Noninterference_Ipurge_Unwinding</h3>
<ul>
<li><a href="../theories/noninterference_ipurge_unwinding/#IpurgeUnwinding">IpurgeUnwinding</a></li>
<li><a href="../theories/noninterference_ipurge_unwinding/#DeterministicProcesses">DeterministicProcesses</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List_Interleaving.html">Reasoning about Lists via List Interleaving</a></li><li><a href="../entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Sequential_Composition.html">Conservation of CSP Noninterference Security under Sequential Composition</a></li><li><a href="../entries/Noninterference_Inductive_Unwinding.html">The Inductive Unwinding Theorem for CSP Noninterference Security</a></li><li><a href="../entries/Noninterference_Generic_Unwinding.html">The Generic Unwinding Theorem for CSP Noninterference Security</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Noninterference_Inductive_Unwinding.html">The Inductive Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_Generic_Unwinding.html">The Generic Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_Concurrent_Composition.html">Conservation of CSP Noninterference Security under Concurrent Composition</a></li>
<li><a href="../entries/Noninterference_Sequential_Composition.html">Conservation of CSP Noninterference Security under Sequential Composition</a></li>
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<p style="display:none;" id="bibtex-filename">Noninterference_Ipurge_Unwinding-AFP</p><pre id="copy-text">@article{Noninterference_Ipurge_Unwinding-AFP,
author = {Pasquale Noce},
title = {The Ipurge Unwinding Theorem for CSP Noninterference Security},
journal = {Archive of Formal Proofs},
month = {June},
year = {2015},
note = {\url{https://isa-afp.org/entries/Noninterference_Ipurge_Unwinding.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Noninterference_Ipurge_Unwinding-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>C</span>onservation of <span class='first'>C</span><span class='first'>S</span><span class='first'>P</span> <span class='first'>N</span>oninterference <span class='first'>S</span>ecurity <span class='first'>U</span>nder <span class='first'>S</span>equential <span class='first'>C</span>omposition</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">April 26, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>In his outstanding work on Communicating Sequential Processes, Hoare
has defined two fundamental binary operations allowing to compose the
input processes into another, typically more complex, process:
sequential composition and concurrent composition. Particularly, the
output of the former operation is a process that initially behaves
like the first operand, and then like the second operand once the
execution of the first one has terminated successfully, as long as it
does.</p>
<p>This paper formalizes Hoare's definition of sequential
composition and proves, in the general case of a possibly intransitive
policy, that CSP noninterference security is conserved under this
operation, provided that successful termination cannot be affected by
confidential events and cannot occur as an alternative to other events
in the traces of the first operand. Both of these assumptions are
shown, by means of counterexamples, to be necessary for the theorem to
hold.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session Noninterference_Sequential_Composition</h3>
<ul>
<li><a href="../theories/noninterference_sequential_composition/#Propaedeutics">Propaedeutics</a></li>
<li><a href="../theories/noninterference_sequential_composition/#SequentialComposition">SequentialComposition</a></li>
<li><a href="../theories/noninterference_sequential_composition/#Counterexamples">Counterexamples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Ipurge_Unwinding.html">The Ipurge Unwinding Theorem for CSP Noninterference Security</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Noninterference_Concurrent_Composition.html">Conservation of CSP Noninterference Security under Concurrent Composition</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Noninterference_Concurrent_Composition.html">Conservation of CSP Noninterference Security under Concurrent Composition</a></li>
<li><a href="../entries/Noninterference_Generic_Unwinding.html">The Generic Unwinding Theorem for CSP Noninterference Security</a></li>
<li><a href="../entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></li>
<li><a href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></li>
<li><a href="../entries/Noninterference_Inductive_Unwinding.html">The Inductive Unwinding Theorem for CSP Noninterference Security</a></li>
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<p style="display:none;" id="bibtex-filename">Noninterference_Sequential_Composition-AFP</p><pre id="copy-text">@article{Noninterference_Sequential_Composition-AFP,
author = {Pasquale Noce},
title = {Conservation of CSP Noninterference Security under Sequential Composition},
journal = {Archive of Formal Proofs},
month = {April},
year = {2016},
note = {\url{https://isa-afp.org/entries/Noninterference_Sequential_Composition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Noninterference_Sequential_Composition-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/NormByEval.html b/web/entries/NormByEval.html
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<h1 >
<span class='first'>N</span>ormalization by <span class='first'>E</span>valuation</h1>
<div>
<p><a href="../authors/aehlig">Klaus Aehlig</a> <a href="http://www.linta.de/~aehlig/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">February 18, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes normalization by evaluation as implemented in Isabelle. Lambda calculus plus term rewriting is compiled into a functional program with pattern matching. It is proved that the result of a successful evaluation is a) correct, i.e. equivalent to the input, and b) in normal form.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul><h3>Related publications</h3>
<ul><li>
AEHLIG, K., HAFTMANN, F., & NIPKOW, T. (2012). A compiled implementation of normalisation by evaluation. Journal of Functional Programming, 22(1), 9–30. https://doi.org/10.1017/s0956796812000019
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jfp12.html">Open access</a>
</li></ul>
<h3>Session NormByEval</h3>
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<p style="display:none;" id="bibtex-filename">NormByEval-AFP</p><pre id="copy-text">@article{NormByEval-AFP,
author = {Klaus Aehlig and Tobias Nipkow},
title = {Normalization by Evaluation},
journal = {Archive of Formal Proofs},
month = {February},
year = {2008},
note = {\url{https://isa-afp.org/entries/NormByEval.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-NormByEval-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-NormByEval-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-NormByEval-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
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<a href="https://www.isa-afp.org/release/afp-NormByEval-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
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<a href="https://www.isa-afp.org/release/afp-NormByEval-2008-02-22.tar.gz">Feb 22, 2008</a>: Isabelle2007
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<a href="https://www.isa-afp.org/release/afp-NormByEval-2008-02-18.tar.gz">Feb 18, 2008</a>: Isabelle2007
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<h1 >
<span class='first'>H</span>ilbert's <span class='first'>N</span>ullstellensatz</h1>
<div>
<p><a href="../authors/maletzky">Alexander Maletzky</a> <a href="https://risc.jku.at/m/alexander-maletzky/">🌐</a>
</p>
<p class="date">June 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes Hilbert's Nullstellensatz, an important
theorem in algebraic geometry that can be viewed as the generalization
of the Fundamental Theorem of Algebra to multivariate polynomials: If
a set of (multivariate) polynomials over an algebraically closed field
has no common zero, then the ideal it generates is the entire
polynomial ring. The formalization proves several equivalent versions
of this celebrated theorem: the weak Nullstellensatz, the strong
Nullstellensatz (connecting algebraic varieties and radical ideals),
and the field-theoretic Nullstellensatz. The formalization follows
Chapter 4.1. of <a
href="https://link.springer.com/book/10.1007/978-0-387-35651-8">Ideals,
Varieties, and Algorithms</a> by Cox, Little and O'Shea.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Nullstellensatz</h3>
<ul>
<li><a href="../theories/nullstellensatz/#Algebraically_Closed_Fields">Algebraically_Closed_Fields</a></li>
<li><a href="../theories/nullstellensatz/#Lex_Order_PP">Lex_Order_PP</a></li>
<li><a href="../theories/nullstellensatz/#Univariate_PM">Univariate_PM</a></li>
<li><a href="../theories/nullstellensatz/#Nullstellensatz">Nullstellensatz</a></li>
<li><a href="../theories/nullstellensatz/#Nullstellensatz_Field">Nullstellensatz_Field</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Nullstellensatz-AFP</p><pre id="copy-text">@article{Nullstellensatz-AFP,
author = {Alexander Maletzky},
title = {Hilbert&#39;s Nullstellensatz},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Nullstellensatz.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>N</span>umber <span class='first'>T</span>heoretic <span class='first'>T</span>ransform</h1>
<div>
<p><a href="../authors/ammer">Thomas Ammer</a> and <a href="../authors/kreuzer">Katharina Kreuzer</a>
</p>
<p class="date">August 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry contains an Isabelle formalization of the
<em>Number Theoretic Transform (NTT)</em> which is the
analogue to a <em>Discrete Fourier Transform (DFT)</em>
over a finite field. Roots of unity in the complex numbers are
replaced by those in a finite field. </p><p>First, we
define both <em>NTT</em> and the inverse transform
<em>INTT</em> in Isabelle and prove them to be mutually
inverse. </p><p><em>DFT</em> can be
efficiently computed by the recursive <em>Fast Fourier Transform
(FFT)</em>. In our formalization, this algorithm is adapted to
the setting of the <em>NTT</em>: We implement a
<em>Fast Number Theoretic Transform (FNTT)</em> based on
the Butterfly scheme by Cooley and Tukey. Additionally, we provide an
inverse transform <em>IFNTT</em> and prove it mutually
inverse to <em>FNTT</em>. </p><p> Afterwards,
a recursive formalization of the <em>FNTT</em> running
time is examined and the famous $O(n \log n)$ bounds
are proven.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Number_Theoretic_Transform</h3>
<ul>
<li><a href="../theories/number_theoretic_transform/#Preliminary_Lemmas">Preliminary_Lemmas</a></li>
<li><a href="../theories/number_theoretic_transform/#NTT">NTT</a></li>
<li><a href="../theories/number_theoretic_transform/#Butterfly">Butterfly</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CRYSTALS-Kyber.html">CRYSTALS-Kyber</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Number_Theoretic_Transform-AFP</p><pre id="copy-text">@article{Number_Theoretic_Transform-AFP,
author = {Thomas Ammer and Katharina Kreuzer},
title = {Number Theoretic Transform},
journal = {Archive of Formal Proofs},
month = {August},
year = {2022},
note = {\url{https://isa-afp.org/entries/Number_Theoretic_Transform.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Number_Theoretic_Transform-2022-09-07.tar.gz">Sep 7, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Octonions.html b/web/entries/Octonions.html
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+++ b/web/entries/Octonions.html
@@ -1,177 +1,179 @@
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<h1 >
<span class='first'>O</span>ctonions</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a>
</p>
<p class="date">September 14, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop the basic theory of Octonions, including various identities
and properties of the octonions and of the octonionic product, a
description of 7D isometries and representations of orthogonal
transformations. To this end we first develop the theory of the vector
cross product in 7 dimensions. The development of the theory of
Octonions is inspired by that of the theory of Quaternions by Lawrence
Paulson. However, we do not work within the type class real_algebra_1
because the octonionic product is not associative.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Octonions</h3>
<ul>
<li><a href="../theories/octonions/#Cross_Product_7">Cross_Product_7</a></li>
<li><a href="../theories/octonions/#Octonions">Octonions</a></li></ul><div class="flex-wrap">
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author = {Angeliki Koutsoukou-Argyraki},
title = {Octonions},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Octonions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>O</span>p<span class='first'>S</span>ets: <span class='first'>S</span>equential <span class='first'>S</span>pecifications for <span class='first'>R</span>eplicated <span class='first'>D</span>atatypes</h1>
<div>
<p><a href="../authors/kleppmann">Martin Kleppmann</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbIm1hcnRpbiIsImtsZXBwbWFubiJdfQ==">📧</a>, <a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInZpY3RvciIsImdvbWVzIl19">📧</a>, <a href="../authors/mulligan">Dominic P. Mulligan</a> <a class="obfuscated" data="eyJob3N0IjpbImFybSIsImNvbSJdLCJ1c2VyIjpbIkRvbWluaWMiLCJNdWxsaWdhbiJdfQ==">📧</a> and <a href="../authors/beresford">Alastair R. Beresford</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJhcmIzMyJdfQ==">📧</a>
</p>
<p class="date">May 10, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We introduce OpSets, an executable framework for specifying and
reasoning about the semantics of replicated datatypes that provide
eventual consistency in a distributed system, and for mechanically
verifying algorithms that implement these datatypes. Our approach is
simple but expressive, allowing us to succinctly specify a variety of
abstract datatypes, including maps, sets, lists, text, graphs, trees,
and registers. Our datatypes are also composable, enabling the
construction of complex data structures. To demonstrate the utility of
OpSets for analysing replication algorithms, we highlight an important
correctness property for collaborative text editing that has
traditionally been overlooked; algorithms that do not satisfy this
property can exhibit awkward interleaving of text. We use OpSets to
specify this correctness property and prove that although one existing
replication algorithm satisfies this property, several other published
algorithms do not.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session OpSets</h3>
<ul>
<li><a href="../theories/opsets/#OpSet">OpSet</a></li>
<li><a href="../theories/opsets/#Insert_Spec">Insert_Spec</a></li>
<li><a href="../theories/opsets/#List_Spec">List_Spec</a></li>
<li><a href="../theories/opsets/#Interleaving">Interleaving</a></li>
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<p style="display:none;" id="bibtex-filename">OpSets-AFP</p><pre id="copy-text">@article{OpSets-AFP,
author = {Martin Kleppmann and Victor B. F. Gomes and Dominic P. Mulligan and Alastair R. Beresford},
title = {OpSets: Sequential Specifications for Replicated Datatypes},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/OpSets.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/Open_Induction.html b/web/entries/Open_Induction.html
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<h1 >
<span class='first'>O</span>pen <span class='first'>I</span>nduction</h1>
<div>
<p><a href="../authors/ogawa">Mizuhito Ogawa</a> and <a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
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<p class="date">November 2, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A proof of the open induction schema based on J.-C. Raoult, Proving open properties by induction, <i>Information Processing Letters</i> 29, 1988, pp.19-23.
<p>This research was supported by the Austrian Science Fund (FWF): J3202.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Open_Induction</h3>
<ul>
<li><a href="../theories/open_induction/#Restricted_Predicates">Restricted_Predicates</a></li>
<li><a href="../theories/open_induction/#Open_Induction">Open_Induction</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Decreasing-Diagrams-II.html">Decreasing Diagrams II</a></li><li><a href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></li><li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li></ul>
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author = {Mizuhito Ogawa and Christian Sternagel},
title = {Open Induction},
journal = {Archive of Formal Proofs},
month = {November},
year = {2012},
note = {\url{https://isa-afp.org/entries/Open_Induction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>O</span>ptics</h1>
<div>
<p><a href="../authors/fosters">Simon Foster</a> <a class="obfuscated" data="eyJob3N0IjpbInlvcmsiLCJhYyIsInVrIl0sInVzZXIiOlsic2ltb24iLCJmb3N0ZXIiXX0=">📧</a>, <a href="../authors/laursen">Christian Pardillo-Laursen</a> <a class="obfuscated" data="eyJob3N0IjpbInlvcmsiLCJhYyIsInVrIl0sInVzZXIiOlsiY2hyaXN0aWFuIiwibGF1cnNlbiJdfQ==">📧</a> and <a href="../authors/zeyda">Frank Zeyda</a> <a class="obfuscated" data="eyJob3N0IjpbInlvcmsiLCJhYyIsInVrIl0sInVzZXIiOlsiZnJhbmsiLCJ6ZXlkYSJdfQ==">📧</a>
</p>
<p class="date">May 25, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Lenses provide an abstract interface for manipulating data types
through spatially-separated views. They are defined abstractly in
terms of two functions, <em>get</em>, the return a value
from the source type, and <em>put</em> that updates the
value. We mechanise the underlying theory of lenses, in terms of an
algebraic hierarchy of lenses, including well-behaved and very
well-behaved lenses, each lens class being characterised by a set of
lens laws. We also mechanise a lens algebra in Isabelle that enables
their composition and comparison, so as to allow construction of
complex lenses. This is accompanied by a large library of algebraic
laws. Moreover we also show how the lens classes can be applied by
instantiating them with a number of Isabelle data types.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>October 5, 2022</dt>
<dd>Added Scene Spaces, which are used to model variable sets algebraically.
Improvements to the alphabet command, including additional theorems.
Additional prisms and associated laws. (revision 771b88d61c21)<br>
</dd><dt>November 15, 2021</dt>
<dd>Improvement of alphabet and chantype commands to support code generation.
Addition of a tactic rename_alpha_vars that removes the subscript vs in proof goals.
Bug fixes and improvements to alphabet command ML implementation.
Additional laws for scenes. (revisions 9f8bcd71c121 and c061bf9f46f3)<br>
</dd><dt>January 27, 2021</dt>
<dd>Addition of new theorems throughout, particularly for prisms.
New chantype command allows the definition of an algebraic datatype with generated prisms.
New dataspace command allows the definition of a local-based state space, including lenses and prisms.
Addition of various examples for the above.
(revision 89cf045a)<br>
</dd><dt>March 2, 2020</dt>
<dd>Added partial bijective and symmetric lenses.
Improved alphabet command generating additional lenses and results.
Several additional lens relations, including observational equivalence.
Additional theorems throughout.
Adaptations for Isabelle 2020.
(revision 44e2e5c)<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Optics</h3>
<ul>
<li><a href="../theories/optics/#Interp">Interp</a></li>
<li><a href="../theories/optics/#Two">Two</a></li>
<li><a href="../theories/optics/#Lens_Laws">Lens_Laws</a></li>
<li><a href="../theories/optics/#Lens_Algebra">Lens_Algebra</a></li>
<li><a href="../theories/optics/#Lens_Order">Lens_Order</a></li>
<li><a href="../theories/optics/#Lens_Symmetric">Lens_Symmetric</a></li>
<li><a href="../theories/optics/#Scenes">Scenes</a></li>
<li><a href="../theories/optics/#Scene_Spaces">Scene_Spaces</a></li>
<li><a href="../theories/optics/#Lens_Instances">Lens_Instances</a></li>
<li><a href="../theories/optics/#Lenses">Lenses</a></li>
<li><a href="../theories/optics/#Prisms">Prisms</a></li>
<li><a href="../theories/optics/#Channel_Type">Channel_Type</a></li>
<li><a href="../theories/optics/#Dataspace">Dataspace</a></li>
<li><a href="../theories/optics/#Optics">Optics</a></li>
<li><a href="../theories/optics/#Lens_Record_Example">Lens_Record_Example</a></li>
<li><a href="../theories/optics/#Lens_State">Lens_State</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/UTP.html">Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Optics-AFP</p><pre id="copy-text">@article{Optics-AFP,
author = {Simon Foster and Christian Pardillo-Laursen and Frank Zeyda},
title = {Optics},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Optics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Optics-2022-10-05.tar.gz">Oct 5, 2022</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Optics-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
</li><li>
- <a href="https://www.isa-afp.org/release/afp-Optics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Optics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Optics-2017-06-01.tar.gz">Jun 1, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Optimal_BST.html b/web/entries/Optimal_BST.html
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<h1 >
<span class='first'>O</span>ptimal <span class='first'>B</span>inary <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/somogyi">Dániel Somogyi</a>
</p>
<p class="date">May 27, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes recursive algorithms for the construction
of optimal binary search trees given fixed access frequencies.
We follow Knuth (1971), Yao (1980) and Mehlhorn (1984).
The algorithms are memoized with the help of the AFP article
<a href="Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a>,
thus yielding dynamic programming algorithms.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
<a href="https://en.wikipedia.org/wiki/Optimal_binary_search_tree">Wikipedia</a>
</li></ul>
<h3>Session Optimal_BST</h3>
<ul>
<li><a href="../theories/optimal_bst/#Weighted_Path_Length">Weighted_Path_Length</a></li>
<li><a href="../theories/optimal_bst/#Optimal_BST">Optimal_BST</a></li>
<li><a href="../theories/optimal_bst/#Quadrilateral_Inequality">Quadrilateral_Inequality</a></li>
<li><a href="../theories/optimal_bst/#Optimal_BST2">Optimal_BST2</a></li>
<li><a href="../theories/optimal_bst/#Optimal_BST_Examples">Optimal_BST_Examples</a></li>
<li><a href="../theories/optimal_bst/#Optimal_BST_Code">Optimal_BST_Code</a></li>
<li><a href="../theories/optimal_bst/#Optimal_BST_Memo">Optimal_BST_Memo</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Optimal_BST-AFP</p><pre id="copy-text">@article{Optimal_BST-AFP,
author = {Tobias Nipkow and Dániel Somogyi},
title = {Optimal Binary Search Trees},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Optimal_BST.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Optimal_BST-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Optimal_BST-2018-05-29.tar.gz">May 29, 2018</a>: Isabelle2017
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diff --git a/web/entries/Orbit_Stabiliser.html b/web/entries/Orbit_Stabiliser.html
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<h1 >
<span class='first'>O</span>rbit-<span class='first'>S</span>tabiliser <span class='first'>T</span>heorem <span class='first'>W</span>ith <span class='first'>A</span>pplication to <span class='first'>R</span>otational <span class='first'>S</span>ymmetries</h1>
<div>
<p><a href="../authors/raedle">Jonas Rädle</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiam9uYXMiLCJyYWVkbGUiXX0=">📧</a>
</p>
<p class="date">August 20, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Orbit-Stabiliser theorem is a basic result in the algebra of
groups that factors the order of a group into the sizes of its orbits
and stabilisers. We formalize the notion of a group action and the
related concepts of orbits and stabilisers. This allows us to prove
the orbit-stabiliser theorem. In the second part of this work, we
formalize the tetrahedral group and use the orbit-stabiliser theorem
to prove that there are twelve (orientation-preserving) rotations of
the tetrahedron.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Orbit_Stabiliser</h3>
<ul>
<li><a href="../theories/orbit_stabiliser/#Left_Coset">Left_Coset</a></li>
<li><a href="../theories/orbit_stabiliser/#Orbit_Stabiliser">Orbit_Stabiliser</a></li>
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author = {Jonas Rädle},
title = {Orbit-Stabiliser Theorem with Application to Rotational Symmetries},
journal = {Archive of Formal Proofs},
month = {August},
year = {2017},
note = {\url{https://isa-afp.org/entries/Orbit_Stabiliser.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>P</span>roperties of <span class='first'>O</span>rderings and <span class='first'>L</span>attices</h1>
<div>
<p><a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">December 11, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These components add further fundamental order and lattice-theoretic
concepts and properties to Isabelle's libraries. They follow by
and large the introductory sections of the Compendium of Continuous
Lattices, covering directed and filtered sets, down-closed and
up-closed sets, ideals and filters, Galois connections, closure and
co-closure operators. Some emphasis is on duality and morphisms
between structures, as in the Compendium. To this end, three ad-hoc
approaches to duality are compared.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session Order_Lattice_Props</h3>
<ul>
<li><a href="../theories/order_lattice_props/#Sup_Lattice">Sup_Lattice</a></li>
<li><a href="../theories/order_lattice_props/#Order_Duality">Order_Duality</a></li>
<li><a href="../theories/order_lattice_props/#Order_Lattice_Props">Order_Lattice_Props</a></li>
<li><a href="../theories/order_lattice_props/#Representations">Representations</a></li>
<li><a href="../theories/order_lattice_props/#Galois_Connections">Galois_Connections</a></li>
<li><a href="../theories/order_lattice_props/#Fixpoint_Fusion">Fixpoint_Fusion</a></li>
<li><a href="../theories/order_lattice_props/#Closure_Operators">Closure_Operators</a></li>
<li><a href="../theories/order_lattice_props/#Order_Lattice_Props_Loc">Order_Lattice_Props_Loc</a></li>
<li><a href="../theories/order_lattice_props/#Order_Lattice_Props_Wenzel">Order_Lattice_Props_Wenzel</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Quantales.html">Quantales</a></li><li><a href="../entries/Transformer_Semantics.html">Transformer Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Order_Lattice_Props-AFP</p><pre id="copy-text">@article{Order_Lattice_Props-AFP,
author = {Georg Struth},
title = {Properties of Orderings and Lattices},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Order_Lattice_Props.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Order_Lattice_Props-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Order_Lattice_Props-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Order_Lattice_Props-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Order_Lattice_Props-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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diff --git a/web/entries/Ordered_Resolution_Prover.html b/web/entries/Ordered_Resolution_Prover.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover - Archive of Formal Proofs</title><meta name="description" content="This Isabelle/HOL formalization covers Sections 2 to 4 of Bachmair and Ganzinger&#39;s &#34;Resolution Theorem Proving&#34; chapter in the Handbook of Automated..."><meta property="og:title" content="Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover" />
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>B</span>achmair and <span class='first'>G</span>anzinger's <span class='first'>O</span>rdered <span class='first'>R</span>esolution <span class='first'>P</span>rover</h1>
<div>
<p><a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a>, <a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a class="obfuscated" data="eyJob3N0IjpbInZ1IiwibmwiXSwidXNlciI6WyJqIiwiYyIsImJsYW5jaGV0dGUiXX0=">📧</a>, <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a> and <a href="../authors/waldmann">Uwe Waldmann</a> <a class="obfuscated" data="eyJob3N0IjpbIm1waS1pbmYiLCJtcGciLCJkZSJdLCJ1c2VyIjpbIndhbGRtYW5uIl19">📧</a>
</p>
<p class="date">January 18, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization covers Sections 2 to 4 of Bachmair and
Ganzinger's "Resolution Theorem Proving" chapter in the
<em>Handbook of Automated Reasoning</em>. This includes
soundness and completeness of unordered and ordered variants of ground
resolution with and without literal selection, the standard redundancy
criterion, a general framework for refutational theorem proving, and
soundness and completeness of an abstract first-order prover.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Ordered_Resolution_Prover</h3>
<ul>
<li><a href="../theories/ordered_resolution_prover/#Map2">Map2</a></li>
<li><a href="../theories/ordered_resolution_prover/#Lazy_List_Liminf">Lazy_List_Liminf</a></li>
<li><a href="../theories/ordered_resolution_prover/#Lazy_List_Chain">Lazy_List_Chain</a></li>
<li><a href="../theories/ordered_resolution_prover/#Clausal_Logic">Clausal_Logic</a></li>
<li><a href="../theories/ordered_resolution_prover/#Herbrand_Interpretation">Herbrand_Interpretation</a></li>
<li><a href="../theories/ordered_resolution_prover/#Abstract_Substitution">Abstract_Substitution</a></li>
<li><a href="../theories/ordered_resolution_prover/#Inference_System">Inference_System</a></li>
<li><a href="../theories/ordered_resolution_prover/#Ground_Resolution_Model">Ground_Resolution_Model</a></li>
<li><a href="../theories/ordered_resolution_prover/#Unordered_Ground_Resolution">Unordered_Ground_Resolution</a></li>
<li><a href="../theories/ordered_resolution_prover/#Ordered_Ground_Resolution">Ordered_Ground_Resolution</a></li>
<li><a href="../theories/ordered_resolution_prover/#Proving_Process">Proving_Process</a></li>
<li><a href="../theories/ordered_resolution_prover/#Standard_Redundancy">Standard_Redundancy</a></li>
<li><a href="../theories/ordered_resolution_prover/#FO_Ordered_Resolution">FO_Ordered_Resolution</a></li>
<li><a href="../theories/ordered_resolution_prover/#FO_Ordered_Resolution_Prover">FO_Ordered_Resolution_Prover</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Chandy_Lamport.html">A Formal Proof of The Chandy&ndash;Lamport Distributed Snapshot Algorithm</a></li><li><a href="../entries/Saturation_Framework.html">A Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li>
</ul>
</div>
</div>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Ordered_Resolution_Prover/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Ordered_Resolution_Prover-AFP</p><pre id="copy-text">@article{Ordered_Resolution_Prover-AFP,
author = {Anders Schlichtkrull and Jasmin Christian Blanchette and Dmitriy Traytel and Uwe Waldmann},
title = {Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover},
journal = {Archive of Formal Proofs},
month = {January},
year = {2018},
note = {\url{https://isa-afp.org/entries/Ordered_Resolution_Prover.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordered_Resolution_Prover-2018-01-22.tar.gz">Jan 22, 2018</a>: Isabelle2017
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<h1 >
<span class='first'>C</span>ountable <span class='first'>O</span>rdinals</h1>
<div>
<p><a href="../authors/huffman">Brian Huffman</a> <a href="http://cs.pdx.edu/~brianh/">🌐</a>
</p>
<p class="date">November 11, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development defines a well-ordered type of countable ordinals. It includes notions of continuous and normal functions, recursively defined functions over ordinals, least fixed-points, and derivatives. Much of ordinal arithmetic is formalized, including exponentials and logarithms. The development concludes with formalizations of Cantor Normal Form and Veblen hierarchies over normal functions.</div>
<h3>License</h3>
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<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Ordinal</h3>
<ul>
<li><a href="../theories/ordinal/#OrdinalDef">OrdinalDef</a></li>
<li><a href="../theories/ordinal/#OrdinalInduct">OrdinalInduct</a></li>
<li><a href="../theories/ordinal/#OrdinalCont">OrdinalCont</a></li>
<li><a href="../theories/ordinal/#OrdinalRec">OrdinalRec</a></li>
<li><a href="../theories/ordinal/#OrdinalArith">OrdinalArith</a></li>
<li><a href="../theories/ordinal/#OrdinalInverse">OrdinalInverse</a></li>
<li><a href="../theories/ordinal/#OrdinalFix">OrdinalFix</a></li>
<li><a href="../theories/ordinal/#OrdinalOmega">OrdinalOmega</a></li>
<li><a href="../theories/ordinal/#OrdinalVeblen">OrdinalVeblen</a></li>
<li><a href="../theories/ordinal/#Ordinal">Ordinal</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Ordinal-AFP</p><pre id="copy-text">@article{Ordinal-AFP,
author = {Brian Huffman},
title = {Countable Ordinals},
journal = {Archive of Formal Proofs},
month = {November},
year = {2005},
note = {\url{https://isa-afp.org/entries/Ordinal.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Ordinal_Partitions.html b/web/entries/Ordinal_Partitions.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Ordinal Partitions - Archive of Formal Proofs</title><meta name="description" content="The theory of partition relations concerns generalisations of
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<h1 >
<span class='first'>O</span>rdinal <span class='first'>P</span>artitions</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">August 3, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory of partition relations concerns generalisations of
Ramsey's theorem. For any ordinal $\alpha$, write $\alpha \to
(\alpha, m)^2$ if for each function $f$ from unordered pairs of
elements of $\alpha$ into $\{0,1\}$, either there is a subset
$X\subseteq \alpha$ order-isomorphic to $\alpha$ such that
$f\{x,y\}=0$ for all $\{x,y\}\subseteq X$, or there is an $m$ element
set $Y\subseteq \alpha$ such that $f\{x,y\}=1$ for all
$\{x,y\}\subseteq Y$. (In both cases, with $\{x,y\}$ we require
$x\not=y$.) In particular, the infinite Ramsey theorem can be written
in this notation as $\omega \to (\omega, \omega)^2$, or if we
restrict $m$ to the positive integers as above, then $\omega \to
(\omega, m)^2$ for all $m$. This entry formalises Larson's proof
of $\omega^\omega \to (\omega^\omega, m)^2$ along with a similar proof
of a result due to Specker: $\omega^2 \to (\omega^2, m)^2$. Also
proved is a necessary result by Erdős and Milner:
$\omega^{1+\alpha\cdot n} \to (\omega^{1+\alpha}, 2^n)^2$.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Ordinal_Partitions</h3>
<ul>
<li><a href="../theories/ordinal_partitions/#Library_Additions">Library_Additions</a></li>
<li><a href="../theories/ordinal_partitions/#Partitions">Partitions</a></li>
<li><a href="../theories/ordinal_partitions/#Erdos_Milner">Erdos_Milner</a></li>
<li><a href="../theories/ordinal_partitions/#Omega_Omega">Omega_Omega</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nash_Williams.html">The Nash-Williams Partition Theorem</a></li><li><a href="../entries/ZFC_in_HOL.html">Zermelo Fraenkel Set Theory in Higher-Order Logic</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Ordinal_Partitions-AFP</p><pre id="copy-text">@article{Ordinal_Partitions-AFP,
author = {Lawrence C. Paulson},
title = {Ordinal Partitions},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/Ordinal_Partitions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Ordinals_and_Cardinals.html b/web/entries/Ordinals_and_Cardinals.html
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<h1 >
<span class='first'>O</span>rdinals and <span class='first'>C</span>ardinals</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">September 1, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop a basic theory of ordinals and cardinals in Isabelle/HOL, up to the point where some cardinality facts relevant for the ``working mathematician" become available. Unlike in set theory, here we do not have at hand canonical notions of ordinal and cardinal. Therefore, here an ordinal is merely a well-order relation and a cardinal is an ordinal minim w.r.t. order embedding on its field.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 25, 2012</dt>
<dd>This entry has been discontinued because it is now part of the Isabelle distribution.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Ordinals_and_Cardinals</h3>
<ul>
<li><a href="../theories/ordinals_and_cardinals/#Cardinal_Order_Relation_discontinued">Cardinal_Order_Relation_discontinued</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Ordinals_and_Cardinals-AFP</p><pre id="copy-text">@article{Ordinals_and_Cardinals-AFP,
author = {Andrei Popescu},
title = {Ordinals and Cardinals},
journal = {Archive of Formal Proofs},
month = {September},
year = {2009},
note = {\url{https://isa-afp.org/entries/Ordinals_and_Cardinals.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>O</span>rdinary <span class='first'>D</span>ifferential <span class='first'>E</span>quations</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a> and <a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a>
</p>
<p class="date">April 26, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Session Ordinary-Differential-Equations formalizes ordinary differential equations (ODEs) and initial value
problems. This work comprises proofs for local and global existence of unique solutions
(Picard-Lindelöf theorem). Moreover, it contains a formalization of the (continuous or even
differentiable) dependency of the flow on initial conditions as the <i>flow</i> of ODEs.</p>
<p>
Not in the generated document are the following sessions:
<ul>
<li> HOL-ODE-Numerics:
Rigorous numerical algorithms for computing enclosures of solutions based on Runge-Kutta methods
and affine arithmetic. Reachability analysis with splitting and reduction at hyperplanes.</li>
<li> HOL-ODE-Examples:
Applications of the numerical algorithms to concrete systems of ODEs.</li>
<li> Lorenz_C0, Lorenz_C1:
Verified algorithms for checking C1-information according to Tucker's proof,
computation of C0-information.</li>
</ul>
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 20, 2017</dt>
<dd>added Poincare map and propagation of variational equation in
reachability analysis, verified algorithms for C1-information and computations
for C0-information of the Lorenz attractor.</dd><dt>August 3, 2016</dt>
<dd>numerical algorithms for reachability analysis (using second-order Runge-Kutta methods, splitting, and reduction) implemented using Lammich's framework for automatic refinement<br></dd><dt>April 14, 2016</dt>
<dd>added flow and variational equation<br></dd><dt>February 13, 2014</dt>
<dd>added an implementation of the Euler method based on affine arithmetic<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Ordinary_Differential_Equations</h3>
<ul>
<li><a href="../theories/ordinary_differential_equations/#ODE_Auxiliarities">ODE_Auxiliarities</a></li>
<li><a href="../theories/ordinary_differential_equations/#MVT_Ex">MVT_Ex</a></li>
<li><a href="../theories/ordinary_differential_equations/#Vector_Derivative_On">Vector_Derivative_On</a></li>
<li><a href="../theories/ordinary_differential_equations/#Interval_Integral_HK">Interval_Integral_HK</a></li>
<li><a href="../theories/ordinary_differential_equations/#Gronwall">Gronwall</a></li>
<li><a href="../theories/ordinary_differential_equations/#Initial_Value_Problem">Initial_Value_Problem</a></li>
<li><a href="../theories/ordinary_differential_equations/#Picard_Lindeloef_Qualitative">Picard_Lindeloef_Qualitative</a></li>
<li><a href="../theories/ordinary_differential_equations/#Bounded_Linear_Operator">Bounded_Linear_Operator</a></li>
<li><a href="../theories/ordinary_differential_equations/#Multivariate_Taylor">Multivariate_Taylor</a></li>
<li><a href="../theories/ordinary_differential_equations/#Flow">Flow</a></li>
<li><a href="../theories/ordinary_differential_equations/#Upper_Lower_Solution">Upper_Lower_Solution</a></li>
<li><a href="../theories/ordinary_differential_equations/#Poincare_Map">Poincare_Map</a></li>
<li><a href="../theories/ordinary_differential_equations/#Reachability_Analysis">Reachability_Analysis</a></li>
<li><a href="../theories/ordinary_differential_equations/#Flow_Congs">Flow_Congs</a></li>
<li><a href="../theories/ordinary_differential_equations/#Cones">Cones</a></li>
<li><a href="../theories/ordinary_differential_equations/#Linear_ODE">Linear_ODE</a></li>
<li><a href="../theories/ordinary_differential_equations/#ODE_Analysis">ODE_Analysis</a></li></ul>
<h3>Session HOL-ODE-Numerics</h3>
<ul>
<li><a href="../theories/hol-ode-numerics/#GenCF_No_Comp">GenCF_No_Comp</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Dflt_No_Comp">Refine_Dflt_No_Comp</a></li>
<li><a href="../theories/hol-ode-numerics/#Autoref_Misc">Autoref_Misc</a></li>
<li><a href="../theories/hol-ode-numerics/#Weak_Set">Weak_Set</a></li>
<li><a href="../theories/hol-ode-numerics/#Enclosure_Operations">Enclosure_Operations</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Vector_List">Refine_Vector_List</a></li>
<li><a href="../theories/hol-ode-numerics/#Transfer_Analysis">Transfer_Analysis</a></li>
<li><a href="../theories/hol-ode-numerics/#Transfer_ODE">Transfer_ODE</a></li>
<li><a href="../theories/hol-ode-numerics/#Transfer_Euclidean_Space_Vector">Transfer_Euclidean_Space_Vector</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Hyperplane">Refine_Hyperplane</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Unions">Refine_Unions</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Intersection">Refine_Intersection</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Invar">Refine_Invar</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Interval">Refine_Interval</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Info">Refine_Info</a></li>
<li><a href="../theories/hol-ode-numerics/#Abstract_Rigorous_Numerics">Abstract_Rigorous_Numerics</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Rigorous_Numerics">Refine_Rigorous_Numerics</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Rigorous_Numerics_Aform">Refine_Rigorous_Numerics_Aform</a></li>
<li><a href="../theories/hol-ode-numerics/#Concrete_Rigorous_Numerics">Concrete_Rigorous_Numerics</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_String">Refine_String</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Folds">Refine_Folds</a></li>
<li><a href="../theories/hol-ode-numerics/#One_Step_Method">One_Step_Method</a></li>
<li><a href="../theories/hol-ode-numerics/#Runge_Kutta">Runge_Kutta</a></li>
<li><a href="../theories/hol-ode-numerics/#Abstract_Reachability_Analysis">Abstract_Reachability_Analysis</a></li>
<li><a href="../theories/hol-ode-numerics/#Concrete_Reachability_Analysis">Concrete_Reachability_Analysis</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Parallel">Refine_Parallel</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Default">Refine_Default</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Phantom">Refine_Phantom</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_ScaleR2">Refine_ScaleR2</a></li>
<li><a href="../theories/hol-ode-numerics/#Abstract_Reachability_Analysis_C1">Abstract_Reachability_Analysis_C1</a></li>
<li><a href="../theories/hol-ode-numerics/#Concrete_Reachability_Analysis_C1">Concrete_Reachability_Analysis_C1</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Reachability_Analysis">Refine_Reachability_Analysis</a></li>
<li><a href="../theories/hol-ode-numerics/#Refine_Reachability_Analysis_C1">Refine_Reachability_Analysis_C1</a></li>
<li><a href="../theories/hol-ode-numerics/#Init_ODE_Solver">Init_ODE_Solver</a></li>
<li><a href="../theories/hol-ode-numerics/#Example_Utilities">Example_Utilities</a></li>
<li><a href="../theories/hol-ode-numerics/#ODE_Numerics">ODE_Numerics</a></li></ul>
<h3>Session Lorenz_Approximation</h3>
<ul>
<li><a href="../theories/lorenz_approximation/#Result_Elements">Result_Elements</a></li>
<li><a href="../theories/lorenz_approximation/#Result_File_Coarse">Result_File_Coarse</a></li>
<li><a href="../theories/lorenz_approximation/#Lorenz_Approximation">Lorenz_Approximation</a></li></ul>
<h3>Session HOL-ODE-Examples</h3>
<ul>
<li><a href="../theories/hol-ode-examples/#Examples_Integral">Examples_Integral</a></li>
<li><a href="../theories/hol-ode-examples/#Examples_One_Step_Method">Examples_One_Step_Method</a></li>
<li><a href="../theories/hol-ode-examples/#Examples_Poincare_Map">Examples_Poincare_Map</a></li>
<li><a href="../theories/hol-ode-examples/#ODE_Examples">ODE_Examples</a></li></ul>
<h3>Session HOL-ODE-ARCH-COMP</h3>
<ul>
<li><a href="../theories/hol-ode-arch-comp/#Examples_ARCH_COMP">Examples_ARCH_COMP</a></li></ul>
<h3>Session Lorenz_C0</h3>
<ul>
<li><a href="../theories/lorenz_c0/#Lorenz_C0">Lorenz_C0</a></li></ul>
<h3>Session Lorenz_C1</h3>
<ul>
<li><a href="../theories/lorenz_c1/#Lorenz_C1">Lorenz_C1</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Triangle.html">Basic Geometric Properties of Triangles</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li><li><a href="../entries/Differential_Dynamic_Logic.html">Differential Dynamic Logic</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Matrices_for_ODEs.html">Matrices for ODEs</a></li>
<li><a href="../entries/Poincare_Bendixson.html">The Poincaré-Bendixson Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Ordinary_Differential_Equations-AFP</p><pre id="copy-text">@article{Ordinary_Differential_Equations-AFP,
author = {Fabian Immler and Johannes Hölzl},
title = {Ordinary Differential Equations},
journal = {Archive of Formal Proofs},
month = {April},
year = {2012},
note = {\url{https://isa-afp.org/entries/Ordinary_Differential_Equations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Ordinary_Differential_Equations-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Ordinary_Differential_Equations-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Ordinary_Differential_Equations-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Ordinary_Differential_Equations-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
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<h1 >
<span class='first'>P</span>ractical <span class='first'>A</span>lgebraic <span class='first'>C</span>alculus <span class='first'>C</span>hecker</h1>
<div>
<p><a href="../authors/fleury">Mathias Fleury</a> <a href="http://fmv.jku.at/fleury">🌐</a> and <a href="../authors/kaufmann">Daniela Kaufmann</a> <a href="http://fmv.jku.at/kaufmann">🌐</a>
</p>
<p class="date">August 31, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Generating and checking proof certificates is important to increase
the trust in automated reasoning tools. In recent years formal
verification using computer algebra became more important and is
heavily used in automated circuit verification. An existing proof
format which covers algebraic reasoning and allows efficient proof
checking is the practical algebraic calculus (PAC). In this
development, we present the verified checker Pastèque that is obtained
by synthesis via the Refinement Framework. This is the formalization
going with our FMCAD'20 tool presentation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session PAC_Checker</h3>
<ul>
<li><a href="../theories/pac_checker/#PAC_More_Poly">PAC_More_Poly</a></li>
<li><a href="../theories/pac_checker/#Finite_Map_Multiset">Finite_Map_Multiset</a></li>
<li><a href="../theories/pac_checker/#WB_Sort">WB_Sort</a></li>
<li><a href="../theories/pac_checker/#More_Loops">More_Loops</a></li>
<li><a href="../theories/pac_checker/#PAC_Specification">PAC_Specification</a></li>
<li><a href="../theories/pac_checker/#PAC_Map_Rel">PAC_Map_Rel</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker_Specification">PAC_Checker_Specification</a></li>
<li><a href="../theories/pac_checker/#PAC_Polynomials">PAC_Polynomials</a></li>
<li><a href="../theories/pac_checker/#PAC_Polynomials_Term">PAC_Polynomials_Term</a></li>
<li><a href="../theories/pac_checker/#PAC_Polynomials_Operations">PAC_Polynomials_Operations</a></li>
<li><a href="../theories/pac_checker/#PAC_Misc">PAC_Misc</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker">PAC_Checker</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker_Relation">PAC_Checker_Relation</a></li>
<li><a href="../theories/pac_checker/#PAC_Assoc_Map_Rel">PAC_Assoc_Map_Rel</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker_Init">PAC_Checker_Init</a></li>
<li><a href="../theories/pac_checker/#PAC_Version">PAC_Version</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker_Synthesis">PAC_Checker_Synthesis</a></li>
<li><a href="../theories/pac_checker/#PAC_Checker_MLton">PAC_Checker_MLton</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
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<p style="display:none;" id="bibtex-filename">PAC_Checker-AFP</p><pre id="copy-text">@article{PAC_Checker-AFP,
author = {Mathias Fleury and Daniela Kaufmann},
title = {Practical Algebraic Calculus Checker},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/PAC_Checker.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-PAC_Checker-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-PAC_Checker-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-PAC_Checker-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-PAC_Checker-2020-08-31.tar.gz">Aug 31, 2020</a>: Isabelle2020
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diff --git a/web/entries/PAL.html b/web/entries/PAL.html
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<h1 >
<span class='first'>A</span>utomating <span class='first'>P</span>ublic <span class='first'>A</span>nnouncement <span class='first'>L</span>ogic and the <span class='first'>W</span>ise <span class='first'>M</span>en <span class='first'>P</span>uzzle in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a> and <a href="../authors/reiche">Sebastian Reiche</a> <a href="https://www.linkedin.com/in/sebastian-reiche-0b2093178">🌐</a>
</p>
<p class="date">November 8, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a shallow embedding of public announcement logic (PAL) with
relativized general knowledge in HOL. We then use PAL to obtain an
elegant encoding of the wise men puzzle, which we solve automatically
using sledgehammer.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session PAL</h3>
<ul>
<li><a href="../theories/pal/#PAL">PAL</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">PAL-AFP</p><pre id="copy-text">@article{PAL-AFP,
author = {Christoph Benzmüller and Sebastian Reiche},
title = {Automating Public Announcement Logic and the Wise Men Puzzle in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/PAL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-PAL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-PAL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-PAL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-PAL-2021-11-14.tar.gz">Nov 14, 2021</a>: Isabelle2021
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diff --git a/web/entries/PCF.html b/web/entries/PCF.html
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<h1 >
<span class='first'>L</span>ogical <span class='first'>R</span>elations for <span class='first'>P</span><span class='first'>C</span><span class='first'>F</span></h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGV0ZWc0MiJdfQ==">📧</a>
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<p class="date">July 1, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We apply Andy Pitts's methods of defining relations over domains to
several classical results in the literature. We show that the Y
combinator coincides with the domain-theoretic fixpoint operator,
that parallel-or and the Plotkin existential are not definable in
PCF, that the continuation semantics for PCF coincides with the
direct semantics, and that our domain-theoretic semantics for PCF is
adequate for reasoning about contextual equivalence in an
operational semantics. Our version of PCF is untyped and has both
strict and non-strict function abstractions. The development is
carried out in HOLCF.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session PCF</h3>
<ul>
<li><a href="../theories/pcf/#Basis">Basis</a></li>
<li><a href="../theories/pcf/#Logical_Relations">Logical_Relations</a></li>
<li><a href="../theories/pcf/#PCF">PCF</a></li>
<li><a href="../theories/pcf/#OpSem">OpSem</a></li>
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<p style="display:none;" id="bibtex-filename">PCF-AFP</p><pre id="copy-text">@article{PCF-AFP,
author = {Peter Gammie},
title = {Logical Relations for PCF},
journal = {Archive of Formal Proofs},
month = {July},
year = {2012},
note = {\url{https://isa-afp.org/entries/PCF.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-PCF-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-PCF-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-PCF-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-PCF-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-PCF-2012-07-03.tar.gz">Jul 3, 2012</a>: Isabelle2012
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content=" We present an embedding of the second-order fragment of the Theory of Abstract Objects as described in Edward Zalta&#39;s upcoming work Principia..."><meta property="og:title" content="Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL" />
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<h1 >
<span class='first'>R</span>epresentation and <span class='first'>P</span>artial <span class='first'>A</span>utomation of the <span class='first'>P</span>rincipia <span class='first'>L</span>ogico-<span class='first'>M</span>etaphysica in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/kirchner">Daniel Kirchner</a> <a class="obfuscated" data="eyJob3N0IjpbImVrcHlyb24iLCJvcmciXSwidXNlciI6WyJkYW5pZWwiXX0=">📧</a>
</p>
<p class="date">September 17, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> We present an embedding of the second-order fragment of the
Theory of Abstract Objects as described in Edward Zalta's
upcoming work <a
href="https://mally.stanford.edu/principia.pdf">Principia
Logico-Metaphysica (PLM)</a> in the automated reasoning
framework Isabelle/HOL. The Theory of Abstract Objects is a
metaphysical theory that reifies property patterns, as they for
example occur in the abstract reasoning of mathematics, as
<b>abstract objects</b> and provides an axiomatic
framework that allows to reason about these objects. It thereby serves
as a fundamental metaphysical theory that can be used to axiomatize
and describe a wide range of philosophical objects, such as Platonic
forms or Leibniz' concepts, and has the ambition to function as a
foundational theory of mathematics. The target theory of our embedding
as described in chapters 7-9 of PLM employs a modal relational type
theory as logical foundation for which a representation in functional
type theory is <a
href="https://mally.stanford.edu/Papers/rtt.pdf">known to
be challenging</a>. </p> <p> Nevertheless we arrive
at a functioning representation of the theory in the functional logic
of Isabelle/HOL based on a semantical representation of an Aczel-model
of the theory. Based on this representation we construct an
implementation of the deductive system of PLM which allows to
automatically and interactively find and verify theorems of PLM.
</p> <p> Our work thereby supports the concept of shallow
semantical embeddings of logical systems in HOL as a universal tool
for logical reasoning <a
href="http://www.mi.fu-berlin.de/inf/groups/ag-ki/publications/Universal-Reasoning/1703_09620_pd.pdf">as
promoted by Christoph Benzm&uuml;ller</a>. </p>
<p> The most notable result of the presented work is the
discovery of a previously unknown paradox in the formulation of the
Theory of Abstract Objects. The embedding of the theory in
Isabelle/HOL played a vital part in this discovery. Furthermore it was
possible to immediately offer several options to modify the theory to
guarantee its consistency. Thereby our work could provide a
significant contribution to the development of a proper grounding for
object theory. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session PLM</h3>
<ul>
<li><a href="../theories/plm/#TAO_1_Embedding">TAO_1_Embedding</a></li>
<li><a href="../theories/plm/#TAO_2_Semantics">TAO_2_Semantics</a></li>
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<li><a href="../theories/plm/#TAO_4_BasicDefinitions">TAO_4_BasicDefinitions</a></li>
<li><a href="../theories/plm/#TAO_5_MetaSolver">TAO_5_MetaSolver</a></li>
<li><a href="../theories/plm/#TAO_6_Identifiable">TAO_6_Identifiable</a></li>
<li><a href="../theories/plm/#TAO_7_Axioms">TAO_7_Axioms</a></li>
<li><a href="../theories/plm/#TAO_8_Definitions">TAO_8_Definitions</a></li>
<li><a href="../theories/plm/#TAO_9_PLM">TAO_9_PLM</a></li>
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<li><a href="../theories/plm/#TAO_98_ArtificialTheorems">TAO_98_ArtificialTheorems</a></li>
<li><a href="../theories/plm/#TAO_99_SanityTests">TAO_99_SanityTests</a></li>
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<p style="display:none;" id="bibtex-filename">PLM-AFP</p><pre id="copy-text">@article{PLM-AFP,
author = {Daniel Kirchner},
title = {Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {September},
year = {2017},
note = {\url{https://isa-afp.org/entries/PLM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-PLM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-PLM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
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diff --git a/web/entries/POPLmark-deBruijn.html b/web/entries/POPLmark-deBruijn.html
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<h1 >
<span class='first'>P</span><span class='first'>O</span><span class='first'>P</span><span class='first'>L</span>mark <span class='first'>C</span>hallenge via <span class='first'>D</span>e <span class='first'>B</span>ruijn <span class='first'>I</span>ndices</h1>
<div>
<p><a href="../authors/berghofer">Stefan Berghofer</a> <a href="http://www.in.tum.de/~berghofe">🌐</a>
</p>
<p class="date">August 2, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a solution to the POPLmark challenge designed by Aydemir et al., which has as a goal the formalization of the meta-theory of System F<sub>&lt;:</sub>. The formalization is carried out in the theorem prover Isabelle/HOL using an encoding based on de Bruijn indices. We start with a relatively simple formalization covering only the basic features of System F<sub>&lt;:</sub>, and explain how it can be extended to also cover records and more advanced binding constructs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session POPLmark-deBruijn</h3>
<ul>
<li><a href="../theories/poplmark-debruijn/#Basis">Basis</a></li>
<li><a href="../theories/poplmark-debruijn/#POPLmark">POPLmark</a></li>
<li><a href="../theories/poplmark-debruijn/#POPLmarkRecord">POPLmarkRecord</a></li>
<li><a href="../theories/poplmark-debruijn/#POPLmarkRecordCtxt">POPLmarkRecordCtxt</a></li>
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<p style="display:none;" id="bibtex-filename">POPLmark-deBruijn-AFP</p><pre id="copy-text">@article{POPLmark-deBruijn-AFP,
author = {Stefan Berghofer},
title = {POPLmark Challenge Via de Bruijn Indices},
journal = {Archive of Formal Proofs},
month = {August},
year = {2007},
note = {\url{https://isa-afp.org/entries/POPLmark-deBruijn.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-POPLmark-deBruijn-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-POPLmark-deBruijn-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>P</span>artial <span class='first'>S</span>emigroups and <span class='first'>C</span>onvolution <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/dongol">Brijesh Dongol</a> <a class="obfuscated" data="eyJob3N0IjpbImJydW5lbCIsImFjIiwidWsiXSwidXNlciI6WyJicmlqZXNoIiwiZG9uZ29sIl19">📧</a>, <a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInZpY3RvciIsImdvbWVzIl19">📧</a>, <a href="../authors/hayes">Ian J. Hayes</a> <a class="obfuscated" data="eyJob3N0IjpbIml0ZWUiLCJ1cSIsImVkdSIsImF1Il0sInVzZXIiOlsiaWFuIiwiaGF5ZXMiXX0=">📧</a> and <a href="../authors/struth">Georg Struth</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJnIiwic3RydXRoIl19">📧</a>
</p>
<p class="date">June 13, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Partial Semigroups are relevant to the foundations of quantum
mechanics and combinatorics as well as to interval and separation
logics. Convolution algebras can be understood either as algebras of
generalised binary modalities over ternary Kripke frames, in
particular over partial semigroups, or as algebras of quantale-valued
functions which are equipped with a convolution-style operation of
multiplication that is parametrised by a ternary relation. Convolution
algebras provide algebraic semantics for various substructural logics,
including categorial, relevance and linear logics, for separation
logic and for interval logics; they cover quantitative and qualitative
applications. These mathematical components for partial semigroups and
convolution algebras provide uniform foundations from which models of
computation based on relations, program traces or pomsets, and
verification components for separation or interval temporal logics can
be built with little effort.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session PSemigroupsConvolution</h3>
<ul>
<li><a href="../theories/psemigroupsconvolution/#Partial_Semigroups">Partial_Semigroups</a></li>
<li><a href="../theories/psemigroupsconvolution/#Partial_Semigroup_Models">Partial_Semigroup_Models</a></li>
<li><a href="../theories/psemigroupsconvolution/#Quantales">Quantales</a></li>
<li><a href="../theories/psemigroupsconvolution/#Binary_Modalities">Binary_Modalities</a></li>
<li><a href="../theories/psemigroupsconvolution/#Unary_Modalities">Unary_Modalities</a></li>
<li><a href="../theories/psemigroupsconvolution/#Partial_Semigroup_Lifting">Partial_Semigroup_Lifting</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">PSemigroupsConvolution-AFP</p><pre id="copy-text">@article{PSemigroupsConvolution-AFP,
author = {Brijesh Dongol and Victor B. F. Gomes and Ian J. Hayes and Georg Struth},
title = {Partial Semigroups and Convolution Algebras},
journal = {Archive of Formal Proofs},
month = {June},
year = {2017},
note = {\url{https://isa-afp.org/entries/PSemigroupsConvolution.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Package_logic.html b/web/entries/Package_logic.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of a Framework for the Sound Automation of Magic Wands - Archive of Formal Proofs</title><meta name="description" content="The magic wand $\mathbin{-\!\!*}$ (also called separating implication) is a separation logic connective commonly used to specify properties of partial data..."><meta property="og:title" content="Formalization of a Framework for the Sound Automation of Magic Wands" />
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<h1 >
<span class='first'>F</span>ormalization of a <span class='first'>F</span>ramework for the <span class='first'>S</span>ound <span class='first'>A</span>utomation of <span class='first'>M</span>agic <span class='first'>W</span>ands</h1>
<div>
<p><a href="../authors/dardinier">Thibault Dardinier</a> <a href="https://dardinier.me/">🌐</a>
</p>
<p class="date">May 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The magic wand $\mathbin{-\!\!*}$ (also called separating
implication) is a separation logic connective commonly used to specify
properties of partial data structures, for instance during iterative
traversals. A <em>footprint</em> of a magic wand formula
$$A \mathbin{-\!\!*} B$$ is a state that, combined with any state in
which $A$ holds, yields a state in which $B$ holds. The key
challenge of proving a magic wand (also called
<em>packaging</em> a wand) is to find such a footprint.
Existing package algorithms either have a high annotation overhead or
are unsound. In this entry, we formally define a framework for the
sound automation of magic wands, described in an <a href="https://www.cs.ubc.ca/~alexsumm/papers/DardinierParthasarathyWeeksMuellerSummers22.pdf">upcoming
paper at CAV 2022</a>, and prove that it is sound and complete.
This framework, called the <em>package logic</em>,
precisely characterises a wide design space of possible package
algorithms applicable to a large class of separation logics.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Package_logic</h3>
<ul>
<li><a href="../theories/package_logic/#SepAlgebra">SepAlgebra</a></li>
<li><a href="../theories/package_logic/#PackageLogic">PackageLogic</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Combinable_Wands.html">A Restricted Definition of the Magic Wand to Soundly Combine Fractions of a Wand</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Package_logic-AFP</p><pre id="copy-text">@article{Package_logic-AFP,
author = {Thibault Dardinier},
title = {Formalization of a Framework for the Sound Automation of Magic Wands},
journal = {Archive of Formal Proofs},
month = {May},
year = {2022},
note = {\url{https://isa-afp.org/entries/Package_logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
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diff --git a/web/entries/Padic_Field.html b/web/entries/Padic_Field.html
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<h1 >
<span class='first'>P</span>-<span class='first'>A</span>dic <span class='first'>F</span>ields and <span class='first'>P</span>-<span class='first'>A</span>dic <span class='first'>S</span>emialgebraic <span class='first'>S</span>ets</h1>
<div>
<p><a href="../authors/crighton">Aaron Crighton</a>
</p>
<p class="date">September 22, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The field of p-adic numbers for a prime integer p is constructed.
Basic facts about p-adic topology including Hensel's Lemma are
proved, building on a prior submission by the author. The theory of
semialgebraic sets and semialgebraic functions on cartesian powers of
p-adic fields is also developed, following a formalization of these
concepts due to Denef. This is done towards a formalization of
Denef's proof of Macintyre's quantifier elimination theorem
for p-adic fields. Theories developing general multivariable
polynomial rings over a commutative ring are developed, as well as
some general theory of cartesian powers of an arbitrary ring.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Padic_Field</h3>
<ul>
<li><a href="../theories/padic_field/#Fraction_Field">Fraction_Field</a></li>
<li><a href="../theories/padic_field/#Cring_Multivariable_Poly">Cring_Multivariable_Poly</a></li>
<li><a href="../theories/padic_field/#Indices">Indices</a></li>
<li><a href="../theories/padic_field/#Ring_Powers">Ring_Powers</a></li>
<li><a href="../theories/padic_field/#Padic_Fields">Padic_Fields</a></li>
<li><a href="../theories/padic_field/#Padic_Field_Polynomials">Padic_Field_Polynomials</a></li>
<li><a href="../theories/padic_field/#Padic_Field_Topology">Padic_Field_Topology</a></li>
<li><a href="../theories/padic_field/#Generated_Boolean_Algebra">Generated_Boolean_Algebra</a></li>
<li><a href="../theories/padic_field/#Padic_Field_Powers">Padic_Field_Powers</a></li>
<li><a href="../theories/padic_field/#Padic_Semialgebraic_Function_Ring">Padic_Semialgebraic_Function_Ring</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Localization_Ring.html">The Localization of a Commutative Ring</a></li><li><a href="../entries/Padic_Ints.html">Hensel&rsquo;s Lemma for the p-adic Integers</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/DPRM_Theorem.html">Diophantine Equations and the DPRM Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Padic_Field-AFP</p><pre id="copy-text">@article{Padic_Field-AFP,
author = {Aaron Crighton},
title = {p-adic Fields and p-adic Semialgebraic Sets},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Padic_Field.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Padic_Field-2022-09-22.tar.gz">Sep 22, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Padic_Ints.html b/web/entries/Padic_Ints.html
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<h1 >
<span class='first'>H</span>ensel's <span class='first'>L</span>emma for the <span class='first'>P</span>-<span class='first'>A</span>dic <span class='first'>I</span>ntegers</h1>
<div>
<p><a href="../authors/crighton">Aaron Crighton</a> <a class="obfuscated" data="eyJob3N0IjpbIm1jbWFzdGVyIiwiY2EiXSwidXNlciI6WyJjcmlnaHRvYSJdfQ==">📧</a>
</p>
<p class="date">March 23, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the ring of <em>p</em>-adic integers within the framework of the
HOL-Algebra library. The carrier of the ring is formalized as the
inverse limit of quotients of the integers by powers of a fixed prime
<em>p</em>. We define an integer-valued valuation, as well as an
extended-integer valued valuation which sends 0 to the infinite
element. Basic topological facts about the <em>p</em>-adic integers are
formalized, including completeness and sequential compactness. Taylor
expansions of polynomials over a commutative ring are defined,
culminating in the formalization of Hensel's Lemma based on a
proof due to Keith Conrad.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Padic_Ints</h3>
<ul>
<li><a href="../theories/padic_ints/#Function_Ring">Function_Ring</a></li>
<li><a href="../theories/padic_ints/#Cring_Poly">Cring_Poly</a></li>
<li><a href="../theories/padic_ints/#Supplementary_Ring_Facts">Supplementary_Ring_Facts</a></li>
<li><a href="../theories/padic_ints/#Extended_Int">Extended_Int</a></li>
<li><a href="../theories/padic_ints/#Padic_Construction">Padic_Construction</a></li>
<li><a href="../theories/padic_ints/#Padic_Integers">Padic_Integers</a></li>
<li><a href="../theories/padic_ints/#Padic_Int_Topology">Padic_Int_Topology</a></li>
<li><a href="../theories/padic_ints/#Padic_Int_Polynomials">Padic_Int_Polynomials</a></li>
<li><a href="../theories/padic_ints/#Hensels_Lemma">Hensels_Lemma</a></li>
<li><a href="../theories/padic_ints/#Zp_Compact">Zp_Compact</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Padic_Field.html">p-adic Fields and p-adic Semialgebraic Sets</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Padic_Ints-AFP</p><pre id="copy-text">@article{Padic_Ints-AFP,
author = {Aaron Crighton},
title = {Hensel&#39;s Lemma for the p-adic Integers},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Padic_Ints.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Padic_Ints-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Padic_Ints-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Padic_Ints-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Padic_Ints-2021-05-14.tar.gz">May 14, 2021</a>: Isabelle2021
</li></ul>
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diff --git a/web/entries/Pairing_Heap.html b/web/entries/Pairing_Heap.html
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<h1 >
<span class='first'>P</span>airing <span class='first'>H</span>eap</h1>
<div>
<p><a href="../authors/brinkop">Hauke Brinkop</a> <a class="obfuscated" data="eyJob3N0IjpbImdvb2dsZW1haWwiLCJjb20iXSwidXNlciI6WyJoYXVrZSIsImJyaW5rb3AiXX0=">📧</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">July 14, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This library defines three different versions of pairing heaps: a
functional version of the original design based on binary
trees [Fredman et al. 1986], the version by Okasaki [1998] and
a modified version of the latter that is free of structural invariants.
<p>
The amortized complexity of pairing heaps is analyzed in the AFP article
<a href="http://isa-afp.org/entries/Amortized_Complexity.html">Amortized Complexity</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Extra 0</h3>
<p>Origin: This library was extracted from Amortized Complexity and extended.</p><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Pairing Heaps in <a href="https://functional-algorithms-verified.org">Functional Algorithms, Verified!</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Pairing_heap">Wikipedia</a>
</li></ul>
<h3>Session Pairing_Heap</h3>
<ul>
<li><a href="../theories/pairing_heap/#Pairing_Heap_Tree">Pairing_Heap_Tree</a></li>
<li><a href="../theories/pairing_heap/#Pairing_Heap_List1">Pairing_Heap_List1</a></li>
<li><a href="../theories/pairing_heap/#Pairing_Heap_List2">Pairing_Heap_List2</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li><li><a href="../entries/Amortized_Complexity.html">Amortized Complexity Verified</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Pairing_Heap-AFP</p><pre id="copy-text">@article{Pairing_Heap-AFP,
author = {Hauke Brinkop and Tobias Nipkow},
title = {Pairing Heap},
journal = {Archive of Formal Proofs},
month = {July},
year = {2016},
note = {\url{https://isa-afp.org/entries/Pairing_Heap.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Pairing_Heap-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Pairing_Heap-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Pairing_Heap-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Pairing_Heap-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Pairing_Heap-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<h1 >
<span class='first'>P</span>araconsistency</h1>
<div>
<p><a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a> and <a href="../authors/villadsen">Jørgen Villadsen</a> <a href="https://people.compute.dtu.dk/jovi/">🌐</a>
</p>
<p class="date">December 7, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Paraconsistency is about handling inconsistency in a coherent way. In
classical and intuitionistic logic everything follows from an
inconsistent theory. A paraconsistent logic avoids the explosion.
Quite a few applications in computer science and engineering are
discussed in the Intelligent Systems Reference Library Volume 110:
Towards Paraconsistent Engineering (Springer 2016). We formalize a
paraconsistent many-valued logic that we motivated and described in a
special issue on logical approaches to paraconsistency (Journal of
Applied Non-Classical Logics 2005). We limit ourselves to the
propositional fragment of the higher-order logic. The logic is based
on so-called key equalities and has a countably infinite number of
truth values. We prove theorems in the logic using the definition of
validity. We verify truth tables and also counterexamples for
non-theorems. We prove meta-theorems about the logic and finally we
investigate a case study.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/paraconsistent-logics">Logic/General logic/Paraconsistent logics</a></li></ul>
<h3>Session Paraconsistency</h3>
<ul>
<li><a href="../theories/paraconsistency/#Paraconsistency">Paraconsistency</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Paraconsistency-AFP</p><pre id="copy-text">@article{Paraconsistency-AFP,
author = {Anders Schlichtkrull and Jørgen Villadsen},
title = {Paraconsistency},
journal = {Archive of Formal Proofs},
month = {December},
year = {2016},
note = {\url{https://isa-afp.org/entries/Paraconsistency.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>P</span>ositional <span class='first'>D</span>eterminacy of <span class='first'>P</span>arity <span class='first'>G</span>ames</h1>
<div>
<p><a href="../authors/dittmann">Christoph Dittmann</a> <a href="http://logic.las.tu-berlin.de/Members/Dittmann/">🌐</a>
</p>
<p class="date">November 2, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of parity games (a two-player game on
directed graphs) and a proof of their positional determinacy in
Isabelle/HOL. This proof works for both finite and infinite games.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Parity_Game</h3>
<ul>
<li><a href="../theories/parity_game/#MoreCoinductiveList">MoreCoinductiveList</a></li>
<li><a href="../theories/parity_game/#ParityGame">ParityGame</a></li>
<li><a href="../theories/parity_game/#Strategy">Strategy</a></li>
<li><a href="../theories/parity_game/#AttractingStrategy">AttractingStrategy</a></li>
<li><a href="../theories/parity_game/#Attractor">Attractor</a></li>
<li><a href="../theories/parity_game/#WinningStrategy">WinningStrategy</a></li>
<li><a href="../theories/parity_game/#WellOrderedStrategy">WellOrderedStrategy</a></li>
<li><a href="../theories/parity_game/#WinningRegion">WinningRegion</a></li>
<li><a href="../theories/parity_game/#UniformStrategy">UniformStrategy</a></li>
<li><a href="../theories/parity_game/#AttractorStrategy">AttractorStrategy</a></li>
<li><a href="../theories/parity_game/#PositionalDeterminacy">PositionalDeterminacy</a></li>
<li><a href="../theories/parity_game/#AttractorInductive">AttractorInductive</a></li>
<li><a href="../theories/parity_game/#Graph_TheoryCompatibility">Graph_TheoryCompatibility</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Graph_Theory.html">Graph Theory</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/GaleStewart_Games.html">Gale-Stewart Games</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Parity_Game-AFP</p><pre id="copy-text">@article{Parity_Game-AFP,
author = {Christoph Dittmann},
title = {Positional Determinacy of Parity Games},
journal = {Archive of Formal Proofs},
month = {November},
year = {2015},
note = {\url{https://isa-afp.org/entries/Parity_Game.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Partial_Function_MR.html b/web/entries/Partial_Function_MR.html
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+++ b/web/entries/Partial_Function_MR.html
@@ -1,183 +1,185 @@
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<h1 >
<span class='first'>M</span>utually <span class='first'>R</span>ecursive <span class='first'>P</span>artial <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">February 18, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a wrapper around the partial-function command that supports mutual recursion.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Partial_Function_MR</h3>
<ul>
<li><a href="../theories/partial_function_mr/#Partial_Function_MR">Partial_Function_MR</a></li>
<li><a href="../theories/partial_function_mr/#Partial_Function_MR_Examples">Partial_Function_MR_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Certification_Monads.html">Certification Monads</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Partial_Function_MR-AFP</p><pre id="copy-text">@article{Partial_Function_MR-AFP,
author = {René Thiemann},
title = {Mutually Recursive Partial Functions},
journal = {Archive of Formal Proofs},
month = {February},
year = {2014},
note = {\url{https://isa-afp.org/entries/Partial_Function_MR.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Function_MR-2014-02-19.tar.gz">Feb 19, 2014</a>: Isabelle2013-2
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<h1 >
<span class='first'>P</span>artial <span class='first'>O</span>rder <span class='first'>R</span>eduction</h1>
<div>
<p><a href="../authors/brunner">Julian Brunner</a> <a href="http://www21.in.tum.de/~brunnerj/">🌐</a>
</p>
<p class="date">June 5, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a formalization of the abstract theory of ample
set partial order reduction. The formalization includes transition
systems with actions, trace theory, as well as basics on finite,
infinite, and lazy sequences. We also provide a basic framework for
static analysis on concurrent systems with respect to the ample set
condition.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Partial_Order_Reduction</h3>
<ul>
<li><a href="../theories/partial_order_reduction/#List_Prefixes">List_Prefixes</a></li>
<li><a href="../theories/partial_order_reduction/#List_Extensions">List_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Word_Prefixes">Word_Prefixes</a></li>
<li><a href="../theories/partial_order_reduction/#Set_Extensions">Set_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Basic_Extensions">Basic_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Relation_Extensions">Relation_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Transition_System_Extensions">Transition_System_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Traces">Traces</a></li>
<li><a href="../theories/partial_order_reduction/#Transition_System_Traces">Transition_System_Traces</a></li>
<li><a href="../theories/partial_order_reduction/#Functions">Functions</a></li>
<li><a href="../theories/partial_order_reduction/#ENat_Extensions">ENat_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#CCPO_Extensions">CCPO_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#ESet_Extensions">ESet_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#Coinductive_List_Extensions">Coinductive_List_Extensions</a></li>
<li><a href="../theories/partial_order_reduction/#LList_Prefixes">LList_Prefixes</a></li>
<li><a href="../theories/partial_order_reduction/#Stuttering">Stuttering</a></li>
<li><a href="../theories/partial_order_reduction/#Transition_System_Interpreted_Traces">Transition_System_Interpreted_Traces</a></li>
<li><a href="../theories/partial_order_reduction/#Ample_Abstract">Ample_Abstract</a></li>
<li><a href="../theories/partial_order_reduction/#Formula">Formula</a></li>
<li><a href="../theories/partial_order_reduction/#Ample_Correctness">Ample_Correctness</a></li>
<li><a href="../theories/partial_order_reduction/#Ample_Analysis">Ample_Analysis</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></li><li><a href="../entries/Transition_Systems_and_Automata.html">Transition Systems and Automata</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li></ul>
</div>
</div>
</main>
<nav class='links'>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Partial_Order_Reduction/outline.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Partial_Order_Reduction-AFP</p><pre id="copy-text">@article{Partial_Order_Reduction-AFP,
author = {Julian Brunner},
title = {Partial Order Reduction},
journal = {Archive of Formal Proofs},
month = {June},
year = {2018},
note = {\url{https://isa-afp.org/entries/Partial_Order_Reduction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Partial_Order_Reduction-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Partial_Order_Reduction-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Order_Reduction-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Partial_Order_Reduction-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Partial_Order_Reduction-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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diff --git a/web/entries/Password_Authentication_Protocol.html b/web/entries/Password_Authentication_Protocol.html
--- a/web/entries/Password_Authentication_Protocol.html
+++ b/web/entries/Password_Authentication_Protocol.html
@@ -1,186 +1,188 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verification of a Diffie-Hellman Password-based Authentication Protocol by Extending the Inductive Method - Archive of Formal Proofs</title><meta name="description" content="This paper constructs a formal model of a Diffie-Hellman
password-based authentication protocol between a user and a smart
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<h1 >
<span class='first'>V</span>erification of a <span class='first'>D</span>iffie-<span class='first'>H</span>ellman <span class='first'>P</span>assword-<span class='first'>B</span>ased <span class='first'>A</span>uthentication <span class='first'>P</span>rotocol by <span class='first'>E</span>xtending the <span class='first'>I</span>nductive <span class='first'>M</span>ethod</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">January 3, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This paper constructs a formal model of a Diffie-Hellman
password-based authentication protocol between a user and a smart
card, and proves its security. The protocol provides for the dispatch
of the user's password to the smart card on a secure messaging
channel established by means of Password Authenticated Connection
Establishment (PACE), where the mapping method being used is Chip
Authentication Mapping. By applying and suitably extending
Paulson's Inductive Method, this paper proves that the protocol
establishes trustworthy secure messaging channels, preserves the
secrecy of users' passwords, and provides an effective mutual
authentication service. What is more, these security properties turn
out to hold independently of the secrecy of the PACE authentication
key.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Password_Authentication_Protocol</h3>
<ul>
<li><a href="../theories/password_authentication_protocol/#Propaedeutics">Propaedeutics</a></li>
<li><a href="../theories/password_authentication_protocol/#Protocol">Protocol</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Password_Authentication_Protocol-AFP</p><pre id="copy-text">@article{Password_Authentication_Protocol-AFP,
author = {Pasquale Noce},
title = {Verification of a Diffie-Hellman Password-based Authentication Protocol by Extending the Inductive Method},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/Password_Authentication_Protocol.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Password_Authentication_Protocol-2017-01-06.tar.gz">Jan 6, 2017</a>: Isabelle2016-1
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diff --git a/web/entries/Pell.html b/web/entries/Pell.html
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@@ -1,202 +1,204 @@
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<h1 >
<span class='first'>P</span>ell's <span class='first'>E</span>quation</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">June 23, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> This article gives the basic theory of Pell's equation
<em>x</em><sup>2</sup> = 1 +
<em>D</em>&thinsp;<em>y</em><sup>2</sup>,
where
<em>D</em>&thinsp;&isin;&thinsp;&#8469; is
a parameter and <em>x</em>, <em>y</em> are
integer variables. </p> <p> The main result that is proven
is the following: If <em>D</em> is not a perfect square,
then there exists a <em>fundamental solution</em>
(<em>x</em><sub>0</sub>,
<em>y</em><sub>0</sub>) that is not the
trivial solution (1, 0) and which generates all other solutions
(<em>x</em>, <em>y</em>) in the sense that
there exists some
<em>n</em>&thinsp;&isin;&thinsp;&#8469;
such that |<em>x</em>| +
|<em>y</em>|&thinsp;&radic;<span
style="text-decoration:
overline"><em>D</em></span> =
(<em>x</em><sub>0</sub> +
<em>y</em><sub>0</sub>&thinsp;&radic;<span
style="text-decoration:
overline"><em>D</em></span>)<sup><em>n</em></sup>.
This also implies that the set of solutions is infinite, and it gives
us an explicit and executable characterisation of all the solutions.
</p> <p> Based on this, simple executable algorithms for
computing the fundamental solution and the infinite sequence of all
non-negative solutions are also provided. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Pell</h3>
<ul>
<li><a href="../theories/pell/#Efficient_Discrete_Sqrt">Efficient_Discrete_Sqrt</a></li>
<li><a href="../theories/pell/#Pell">Pell</a></li>
<li><a href="../theories/pell/#Pell_Algorithm">Pell_Algorithm</a></li>
<li><a href="../theories/pell/#Pell_Algorithm_Test">Pell_Algorithm_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Mersenne_Primes.html">Mersenne primes and the Lucas–Lehmer test</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Pell-AFP</p><pre id="copy-text">@article{Pell-AFP,
author = {Manuel Eberl},
title = {Pell&#39;s Equation},
journal = {Archive of Formal Proofs},
month = {June},
year = {2018},
note = {\url{https://isa-afp.org/entries/Pell.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Perfect-Number-Thm.html b/web/entries/Perfect-Number-Thm.html
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<h1 >
<span class='first'>P</span>erfect <span class='first'>N</span>umber <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/ijbema">Mark Ijbema</a> <a class="obfuscated" data="eyJob3N0IjpbImZtZiIsIm5sIl0sInVzZXIiOlsiaWpiZW1hIl19">📧</a>
</p>
<p class="date">November 22, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories present the mechanised proof of the Perfect Number Theorem.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Perfect-Number-Thm</h3>
<ul>
<li><a href="../theories/perfect-number-thm/#PerfectBasics">PerfectBasics</a></li>
<li><a href="../theories/perfect-number-thm/#Sigma">Sigma</a></li>
<li><a href="../theories/perfect-number-thm/#Perfect">Perfect</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Perfect-Number-Thm-AFP</p><pre id="copy-text">@article{Perfect-Number-Thm-AFP,
author = {Mark Ijbema},
title = {Perfect Number Theorem},
journal = {Archive of Formal Proofs},
month = {November},
year = {2009},
note = {\url{https://isa-afp.org/entries/Perfect-Number-Thm.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Perron_Frobenius.html b/web/entries/Perron_Frobenius.html
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@@ -1,227 +1,229 @@
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<h1 >
<span class='first'>P</span>erron-<span class='first'>F</span>robenius <span class='first'>T</span>heorem for <span class='first'>S</span>pectral <span class='first'>R</span>adius <span class='first'>A</span>nalysis</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a>, <a href="../authors/kuncar">Ondřej Kunčar</a> <a href="http://www21.in.tum.de/~kuncar/">🌐</a>, <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">May 20, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The spectral radius of a matrix A is the maximum norm of all
eigenvalues of A. In previous work we already formalized that for a
complex matrix A, the values in A<sup>n</sup> grow polynomially in n
if and only if the spectral radius is at most one. One problem with
the above characterization is the determination of all
<em>complex</em> eigenvalues. In case A contains only non-negative
real values, a simplification is possible with the help of the
Perron&ndash;Frobenius theorem, which tells us that it suffices to consider only
the <em>real</em> eigenvalues of A, i.e., applying Sturm's method can
decide the polynomial growth of A<sup>n</sup>. </p><p> We formalize
the Perron&ndash;Frobenius theorem based on a proof via Brouwer's fixpoint
theorem, which is available in the HOL multivariate analysis (HMA)
library. Since the results on the spectral radius is based on matrices
in the Jordan normal form (JNF) library, we further develop a
connection which allows us to easily transfer theorems between HMA and
JNF. With this connection we derive the combined result: if A is a
non-negative real matrix, and no real eigenvalue of A is strictly
larger than one, then A<sup>n</sup> is polynomially bounded in n. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 17, 2018</dt>
<dd>prove conjecture of CPP'18 paper: Jordan blocks of spectral radius have maximum size
(revision ffdb3794e5d5)</dd><dt>October 18, 2017</dt>
<dd>added Perron-Frobenius theorem for irreducible matrices with generalization
(revision bda1f1ce8a1c)<br/>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Perron_Frobenius</h3>
<ul>
<li><a href="../theories/perron_frobenius/#Cancel_Card_Constraint">Cancel_Card_Constraint</a></li>
<li><a href="../theories/perron_frobenius/#Bij_Nat">Bij_Nat</a></li>
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<li><a href="../theories/perron_frobenius/#Perron_Frobenius_Aux">Perron_Frobenius_Aux</a></li>
<li><a href="../theories/perron_frobenius/#Perron_Frobenius">Perron_Frobenius</a></li>
<li><a href="../theories/perron_frobenius/#Roots_Unity">Roots_Unity</a></li>
<li><a href="../theories/perron_frobenius/#Perron_Frobenius_Irreducible">Perron_Frobenius_Irreducible</a></li>
<li><a href="../theories/perron_frobenius/#Perron_Frobenius_General">Perron_Frobenius_General</a></li>
<li><a href="../theories/perron_frobenius/#Spectral_Radius_Theory">Spectral_Radius_Theory</a></li>
<li><a href="../theories/perron_frobenius/#Spectral_Radius_Largest_Jordan_Block">Spectral_Radius_Largest_Jordan_Block</a></li>
<li><a href="../theories/perron_frobenius/#Hom_Gauss_Jordan">Hom_Gauss_Jordan</a></li>
<li><a href="../theories/perron_frobenius/#Spectral_Radius_Theory_2">Spectral_Radius_Theory_2</a></li>
<li><a href="../theories/perron_frobenius/#Check_Matrix_Growth">Check_Matrix_Growth</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></li><li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li><li><a href="../entries/LLL_Factorization.html">A verified factorization algorithm for integer polynomials with polynomial complexity</a></li><li><a href="../entries/Stochastic_Matrices.html">Stochastic Matrices and the Perron-Frobenius Theorem</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Stochastic_Matrices.html">Stochastic Matrices and the Perron-Frobenius Theorem</a></li>
<li><a href="../entries/Cayley_Hamilton.html">The Cayley-Hamilton Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Perron_Frobenius-AFP</p><pre id="copy-text">@article{Perron_Frobenius-AFP,
author = {Jose Divasón and Ondřej Kunčar and René Thiemann and Akihisa Yamada},
title = {Perron-Frobenius Theorem for Spectral Radius Analysis},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Perron_Frobenius.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Physical_Quantities.html b/web/entries/Physical_Quantities.html
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>ound <span class='first'>T</span>ype <span class='first'>S</span>ystem for <span class='first'>P</span>hysical <span class='first'>Q</span>uantities, <span class='first'>U</span>nits, and <span class='first'>M</span>easurements</h1>
<div>
<p><a href="../authors/fosters">Simon Foster</a> <a href="https://www-users.cs.york.ac.uk/~simonf/">🌐</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a>
</p>
<p class="date">October 20, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The present Isabelle theory builds a formal model for both the
International System of Quantities (ISQ) and the International System
of Units (SI), which are both fundamental for physics and engineering.
Both the ISQ and the SI are deeply integrated into Isabelle's
type system. Quantities are parameterised by dimension types, which
correspond to base vectors, and thus only quantities of the same
dimension can be equated. Since the underlying "algebra of
quantities" induces congruences on quantity and SI types,
specific tactic support is developed to capture these. Our
construction is validated by a test-set of known equivalences between
both quantities and SI units. Moreover, the presented theory can be
used for type-safe conversions between the SI system and others, like
the British Imperial System (BIS).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/physics">Mathematics/Physics</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session Physical_Quantities</h3>
<ul>
<li><a href="../theories/physical_quantities/#Power_int">Power_int</a></li>
<li><a href="../theories/physical_quantities/#Enum_extra">Enum_extra</a></li>
<li><a href="../theories/physical_quantities/#Groups_mult">Groups_mult</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Dimensions">ISQ_Dimensions</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Quantities">ISQ_Quantities</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Proof">ISQ_Proof</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Algebra">ISQ_Algebra</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Units">ISQ_Units</a></li>
<li><a href="../theories/physical_quantities/#ISQ_Conversion">ISQ_Conversion</a></li>
<li><a href="../theories/physical_quantities/#ISQ">ISQ</a></li>
<li><a href="../theories/physical_quantities/#SI_Units">SI_Units</a></li>
<li><a href="../theories/physical_quantities/#CGS">CGS</a></li>
<li><a href="../theories/physical_quantities/#SI_Constants">SI_Constants</a></li>
<li><a href="../theories/physical_quantities/#SI_Prefix">SI_Prefix</a></li>
<li><a href="../theories/physical_quantities/#SI_Derived">SI_Derived</a></li>
<li><a href="../theories/physical_quantities/#SI_Accepted">SI_Accepted</a></li>
<li><a href="../theories/physical_quantities/#SI_Imperial">SI_Imperial</a></li>
<li><a href="../theories/physical_quantities/#SI">SI</a></li>
<li><a href="../theories/physical_quantities/#SI_Astronomical">SI_Astronomical</a></li>
<li><a href="../theories/physical_quantities/#SI_Pretty">SI_Pretty</a></li>
<li><a href="../theories/physical_quantities/#BIS">BIS</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Physical_Quantities-AFP</p><pre id="copy-text">@article{Physical_Quantities-AFP,
author = {Simon Foster and Burkhart Wolff},
title = {A Sound Type System for Physical Quantities, Units, and Measurements},
journal = {Archive of Formal Proofs},
month = {October},
year = {2020},
note = {\url{https://isa-afp.org/entries/Physical_Quantities.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Physical_Quantities-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Pi_Calculus.html b/web/entries/Pi_Calculus.html
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<h1 >
<span class='first'>T</span>he <span class='first'>P</span>i-<span class='first'>C</span>alculus in <span class='first'>N</span>ominal <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/bengtson">Jesper Bengtson</a> <a href="http://www.itu.dk/people/jebe">🌐</a>
</p>
<p class="date">May 29, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a uniform manner. We thus provide one of the most extensive formalisations of a the pi-calculus ever done inside a theorem prover.
<p>
A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.
<p>
This entry is described in detail in <a href="http://www.itu.dk/people/jebe/files/thesis.pdf">Bengtson's thesis</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
<h3>Session Pi_Calculus</h3>
<ul>
<li><a href="../theories/pi_calculus/#Agent">Agent</a></li>
<li><a href="../theories/pi_calculus/#Late_Semantics">Late_Semantics</a></li>
<li><a href="../theories/pi_calculus/#Late_Semantics1">Late_Semantics1</a></li>
<li><a href="../theories/pi_calculus/#Rel">Rel</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Sim">Strong_Late_Sim</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim">Strong_Late_Bisim</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim_Subst">Strong_Late_Bisim_Subst</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Sim_Pres">Strong_Late_Sim_Pres</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim_Pres">Strong_Late_Bisim_Pres</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim_Subst_Pres">Strong_Late_Bisim_Subst_Pres</a></li>
<li><a href="../theories/pi_calculus/#Late_Tau_Chain">Late_Tau_Chain</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Step_Semantics">Weak_Late_Step_Semantics</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Semantics">Weak_Late_Semantics</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Sim">Weak_Late_Sim</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Bisim">Weak_Late_Bisim</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Step_Sim">Weak_Late_Step_Sim</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Cong">Weak_Late_Cong</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Bisim_Subst">Weak_Late_Bisim_Subst</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Cong_Subst">Weak_Late_Cong_Subst</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Sim_SC">Strong_Late_Sim_SC</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim_SC">Strong_Late_Bisim_SC</a></li>
<li><a href="../theories/pi_calculus/#Strong_Late_Bisim_Subst_SC">Strong_Late_Bisim_Subst_SC</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Cong_Subst_SC">Weak_Late_Cong_Subst_SC</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Step_Sim_Pres">Weak_Late_Step_Sim_Pres</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Bisim_SC">Weak_Late_Bisim_SC</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Sim_Pres">Weak_Late_Sim_Pres</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Bisim_Pres">Weak_Late_Bisim_Pres</a></li>
<li><a href="../theories/pi_calculus/#Weak_Late_Cong_Pres">Weak_Late_Cong_Pres</a></li>
<li><a href="../theories/pi_calculus/#Early_Semantics">Early_Semantics</a></li>
<li><a href="../theories/pi_calculus/#Strong_Early_Sim">Strong_Early_Sim</a></li>
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<p style="display:none;" id="bibtex-filename">Pi_Calculus-AFP</p><pre id="copy-text">@article{Pi_Calculus-AFP,
author = {Jesper Bengtson},
title = {The pi-calculus in nominal logic},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Pi_Calculus.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>ranscendence of Π</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">September 28, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry shows the transcendence of &pi; based on the
classic proof using the fundamental theorem of symmetric polynomials
first given by von Lindemann in 1882, but the formalisation mostly
follows the version by Niven. The proof reuses much of the machinery
developed in the AFP entry on the transcendence of
<em>e</em>.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Pi_Transcendental</h3>
<ul>
<li><a href="../theories/pi_transcendental/#Pi_Transcendental_Polynomial_Library">Pi_Transcendental_Polynomial_Library</a></li>
<li><a href="../theories/pi_transcendental/#Pi_Transcendental">Pi_Transcendental</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/E_Transcendental.html">The Transcendence of e</a></li><li><a href="../entries/Symmetric_Polynomials.html">Symmetric Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Nullstellensatz.html">Hilbert&rsquo;s Nullstellensatz</a></li>
<li><a href="../entries/Smooth_Manifolds.html">Smooth Manifolds</a></li>
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<p style="display:none;" id="bibtex-filename">Pi_Transcendental-AFP</p><pre id="copy-text">@article{Pi_Transcendental-AFP,
author = {Manuel Eberl},
title = {The Transcendence of π},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Pi_Transcendental.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Planarity_Certificates.html b/web/entries/Planarity_Certificates.html
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@@ -1,206 +1,208 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Planarity Certificates - Archive of Formal Proofs</title><meta name="description" content="This development provides a formalization of planarity based on
combinatorial maps and proves that Kuratowski&#39;s theorem implies
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<h1 >
<span class='first'>P</span>lanarity <span class='first'>C</span>ertificates</h1>
<div>
<p><a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">November 11, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a formalization of planarity based on
combinatorial maps and proves that Kuratowski's theorem implies
combinatorial planarity.
Moreover, it contains verified implementations of programs checking
certificates for planarity (i.e., a combinatorial map) or non-planarity
(i.e., a Kuratowski subgraph).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Planarity_Certificates</h3>
<ul>
<li><a href="../theories/planarity_certificates/#Lib">Lib</a></li>
<li><a href="../theories/planarity_certificates/#OptionMonad">OptionMonad</a></li>
<li><a href="../theories/planarity_certificates/#NonDetMonad">NonDetMonad</a></li>
<li><a href="../theories/planarity_certificates/#NonDetMonadLemmas">NonDetMonadLemmas</a></li>
<li><a href="../theories/planarity_certificates/#OptionMonadND">OptionMonadND</a></li>
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<li><a href="../theories/planarity_certificates/#Planar_Complete">Planar_Complete</a></li>
<li><a href="../theories/planarity_certificates/#Reachablen">Reachablen</a></li>
<li><a href="../theories/planarity_certificates/#Permutations_2">Permutations_2</a></li>
<li><a href="../theories/planarity_certificates/#Planar_Subdivision">Planar_Subdivision</a></li>
<li><a href="../theories/planarity_certificates/#Planar_Subgraph">Planar_Subgraph</a></li>
<li><a href="../theories/planarity_certificates/#Kuratowski_Combinatorial">Kuratowski_Combinatorial</a></li>
<li><a href="../theories/planarity_certificates/#Simpl_Anno">Simpl_Anno</a></li>
<li><a href="../theories/planarity_certificates/#Check_Non_Planarity_Impl">Check_Non_Planarity_Impl</a></li>
<li><a href="../theories/planarity_certificates/#Check_Non_Planarity_Verification">Check_Non_Planarity_Verification</a></li>
<li><a href="../theories/planarity_certificates/#AutoCorres_Misc">AutoCorres_Misc</a></li>
<li><a href="../theories/planarity_certificates/#Setup_AutoCorres">Setup_AutoCorres</a></li>
<li><a href="../theories/planarity_certificates/#Check_Planarity_Verification">Check_Planarity_Verification</a></li>
<li><a href="../theories/planarity_certificates/#Planarity_Certificates">Planarity_Certificates</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Case_Labeling.html">Generating Cases from Labeled Subgoals</a></li><li><a href="../entries/Graph_Theory.html">Graph Theory</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></li><li><a href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Planarity_Certificates-AFP</p><pre id="copy-text">@article{Planarity_Certificates-AFP,
author = {Lars Noschinski},
title = {Planarity Certificates},
journal = {Archive of Formal Proofs},
month = {November},
year = {2015},
note = {\url{https://isa-afp.org/entries/Planarity_Certificates.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Pluennecke_Ruzsa_Inequality.html b/web/entries/Pluennecke_Ruzsa_Inequality.html
--- a/web/entries/Pluennecke_Ruzsa_Inequality.html
+++ b/web/entries/Pluennecke_Ruzsa_Inequality.html
@@ -1,183 +1,188 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Plünnecke-Ruzsa Inequality - Archive of Formal Proofs</title><meta name="description" content="We formalise Plünnecke&#39;s inequality and the Plünnecke-Ruzsa
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<h1 >
<span class='first'>T</span>he <span class='first'>P</span>lünnecke-<span class='first'>R</span>uzsa <span class='first'>I</span>nequality</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
</p>
<p class="date">May 26, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise Plünnecke's inequality and the Plünnecke-Ruzsa
inequality, following the notes by Timothy Gowers: "Introduction
to Additive Combinatorics" (2022) for the University of
Cambridge. To this end, we first introduce basic definitions and prove
elementary facts on sumsets and difference sets. Then, we show two
versions of the Ruzsa triangle inequality. We follow with a proof due
to Petridis.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Pluennecke_Ruzsa_Inequality</h3>
<ul>
<li><a href="../theories/pluennecke_ruzsa_inequality/#Pluennecke_Ruzsa_Inequality">Pluennecke_Ruzsa_Inequality</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jacobson_Basic_Algebra.html">A Case Study in Basic Algebra</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Khovanskii_Theorem.html">Khovanskii's Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Pluennecke_Ruzsa_Inequality-AFP</p><pre id="copy-text">@article{Pluennecke_Ruzsa_Inequality-AFP,
author = {Angeliki Koutsoukou-Argyraki and Lawrence C. Paulson},
title = {The Plünnecke-Ruzsa Inequality},
journal = {Archive of Formal Proofs},
month = {May},
year = {2022},
note = {\url{https://isa-afp.org/entries/Pluennecke_Ruzsa_Inequality.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <ul><li>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Pluennecke_Ruzsa_Inequality-2022-05-30.tar.gz">May 30, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Poincare_Bendixson.html b/web/entries/Poincare_Bendixson.html
--- a/web/entries/Poincare_Bendixson.html
+++ b/web/entries/Poincare_Bendixson.html
@@ -1,198 +1,200 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>P</span>oincaré-<span class='first'>B</span>endixson <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a> and <a href="../authors/tan">Yong Kiam Tan</a> <a href="https://www.cs.cmu.edu/~yongkiat/">🌐</a>
</p>
<p class="date">December 18, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Poincaré-Bendixson theorem is a classical result in the study of
(continuous) dynamical systems. Colloquially, it restricts the
possible behaviors of planar dynamical systems: such systems cannot be
chaotic. In practice, it is a useful tool for proving the existence of
(limiting) periodic behavior in planar systems. The theorem is an
interesting and challenging benchmark for formalized mathematics
because proofs in the literature rely on geometric sketches and only
hint at symmetric cases. It also requires a substantial background of
mathematical theories, e.g., the Jordan curve theorem, real analysis,
ordinary differential equations, and limiting (long-term) behavior of
dynamical systems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Poincare_Bendixson</h3>
<ul>
<li><a href="../theories/poincare_bendixson/#Analysis_Misc">Analysis_Misc</a></li>
<li><a href="../theories/poincare_bendixson/#ODE_Misc">ODE_Misc</a></li>
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<p style="display:none;" id="bibtex-filename">Poincare_Bendixson-AFP</p><pre id="copy-text">@article{Poincare_Bendixson-AFP,
author = {Fabian Immler and Yong Kiam Tan},
title = {The Poincaré-Bendixson Theorem},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Poincare_Bendixson.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Poincare_Bendixson-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Poincare_Disc.html b/web/entries/Poincare_Disc.html
--- a/web/entries/Poincare_Disc.html
+++ b/web/entries/Poincare_Disc.html
@@ -1,189 +1,191 @@
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geometry within the Isabelle/HOL proof assistant. The model is defined
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<h1 >
<span class='first'>P</span>oincaré <span class='first'>D</span>isc <span class='first'>M</span>odel</h1>
<div>
<p><a href="../authors/simic">Danijela Simić</a> <a href="http://poincare.matf.bg.ac.rs/~danijela">🌐</a>, <a href="../authors/maricf">Filip Marić</a> <a href="http://www.matf.bg.ac.rs/~filip">🌐</a> and <a href="../authors/boutry">Pierre Boutry</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaXN0cmEiLCJmciJdLCJ1c2VyIjpbImJvdXRyeSJdfQ==">📧</a>
</p>
<p class="date">December 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We describe formalization of the Poincaré disc model of hyperbolic
geometry within the Isabelle/HOL proof assistant. The model is defined
within the extended complex plane (one dimensional complex projectives
space &#8450;P1), formalized in the AFP entry “Complex Geometry”.
Points, lines, congruence of pairs of points, betweenness of triples
of points, circles, and isometries are defined within the model. It is
shown that the model satisfies all Tarski's axioms except the
Euclid's axiom. It is shown that it satisfies its negation and
the limiting parallels axiom (which proves it to be a model of
hyperbolic geometry).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Poincare_Disc</h3>
<ul>
<li><a href="../theories/poincare_disc/#Hyperbolic_Functions">Hyperbolic_Functions</a></li>
<li><a href="../theories/poincare_disc/#Tarski">Tarski</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Lines">Poincare_Lines</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Lines_Ideal_Points">Poincare_Lines_Ideal_Points</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Distance">Poincare_Distance</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Circles">Poincare_Circles</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Between">Poincare_Between</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Lines_Axis_Intersections">Poincare_Lines_Axis_Intersections</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Perpendicular">Poincare_Perpendicular</a></li>
<li><a href="../theories/poincare_disc/#Poincare">Poincare</a></li>
<li><a href="../theories/poincare_disc/#Poincare_Tarski">Poincare_Tarski</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Complex_Geometry.html">Complex Geometry</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Poincare_Disc-AFP</p><pre id="copy-text">@article{Poincare_Disc-AFP,
author = {Danijela Simić and Filip Marić and Pierre Boutry},
title = {Poincaré Disc Model},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Poincare_Disc.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Poincare_Disc-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Poincare_Disc-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Poincare_Disc-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Poincare_Disc-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Poincare_Disc-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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diff --git a/web/entries/Polynomial_Factorization.html b/web/entries/Polynomial_Factorization.html
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<h1 >
<span class='first'>P</span>olynomial <span class='first'>F</span>actorization</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">January 29, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Based on existing libraries for polynomial interpolation and matrices,
we formalized several factorization algorithms for polynomials, including
Kronecker's algorithm for integer polynomials,
Yun's square-free factorization algorithm for field polynomials, and
Berlekamp's algorithm for polynomials over finite fields.
By combining the last one with Hensel's lifting,
we derive an efficient factorization algorithm for the integer polynomials,
which is then lifted for rational polynomials by mechanizing Gauss' lemma.
Finally, we assembled a combined factorization algorithm for rational polynomials,
which combines all the mentioned algorithms and additionally uses the explicit formula for roots
of quadratic polynomials and a rational root test.
<p>
As side products, we developed division algorithms for polynomials over integral domains,
as well as primality-testing and prime-factorization algorithms for integers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Polynomial_Factorization</h3>
<ul>
<li><a href="../theories/polynomial_factorization/#Missing_List">Missing_List</a></li>
<li><a href="../theories/polynomial_factorization/#Missing_Multiset">Missing_Multiset</a></li>
<li><a href="../theories/polynomial_factorization/#Precomputation">Precomputation</a></li>
<li><a href="../theories/polynomial_factorization/#Order_Polynomial">Order_Polynomial</a></li>
<li><a href="../theories/polynomial_factorization/#Explicit_Roots">Explicit_Roots</a></li>
<li><a href="../theories/polynomial_factorization/#Dvd_Int_Poly">Dvd_Int_Poly</a></li>
<li><a href="../theories/polynomial_factorization/#Missing_Polynomial_Factorial">Missing_Polynomial_Factorial</a></li>
<li><a href="../theories/polynomial_factorization/#Gauss_Lemma">Gauss_Lemma</a></li>
<li><a href="../theories/polynomial_factorization/#Prime_Factorization">Prime_Factorization</a></li>
<li><a href="../theories/polynomial_factorization/#Rational_Root_Test">Rational_Root_Test</a></li>
<li><a href="../theories/polynomial_factorization/#Kronecker_Factorization">Kronecker_Factorization</a></li>
<li><a href="../theories/polynomial_factorization/#Polynomial_Divisibility">Polynomial_Divisibility</a></li>
<li><a href="../theories/polynomial_factorization/#Fundamental_Theorem_Algebra_Factorized">Fundamental_Theorem_Algebra_Factorized</a></li>
<li><a href="../theories/polynomial_factorization/#Square_Free_Factorization">Square_Free_Factorization</a></li>
<li><a href="../theories/polynomial_factorization/#Gcd_Rat_Poly">Gcd_Rat_Poly</a></li>
<li><a href="../theories/polynomial_factorization/#Rational_Factorization">Rational_Factorization</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li><li><a href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></li><li><a href="../entries/Partial_Function_MR.html">Mutually Recursive Partial Functions</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li><li><a href="../entries/VectorSpace.html">Vector Spaces</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></li><li><a href="../entries/Amicable_Numbers.html">Amicable Numbers</a></li><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li><li><a href="../entries/Gaussian_Integers.html">Gaussian Integers</a></li><li><a href="../entries/Power_Sum_Polynomials.html">Power Sum Polynomials</a></li><li><a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li><li><a href="../entries/Linear_Recurrences.html">Linear Recurrences</a></li><li><a href="../entries/Subresultants.html">Subresultants</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li>
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<p style="display:none;" id="bibtex-filename">Polynomial_Factorization-AFP</p><pre id="copy-text">@article{Polynomial_Factorization-AFP,
author = {René Thiemann and Akihisa Yamada},
title = {Polynomial Factorization},
journal = {Archive of Formal Proofs},
month = {January},
year = {2016},
note = {\url{https://isa-afp.org/entries/Polynomial_Factorization.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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diff --git a/web/entries/Polynomial_Interpolation.html b/web/entries/Polynomial_Interpolation.html
--- a/web/entries/Polynomial_Interpolation.html
+++ b/web/entries/Polynomial_Interpolation.html
@@ -1,215 +1,217 @@
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<h1 >
<span class='first'>P</span>olynomial <span class='first'>I</span>nterpolation</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">January 29, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalized three algorithms for polynomial interpolation over arbitrary
fields: Lagrange's explicit expression, the recursive algorithm of Neville
and Aitken, and the Newton interpolation in combination with an efficient
implementation of divided differences. Variants of these algorithms for
integer polynomials are also available, where sometimes the interpolation
can fail; e.g., there is no linear integer polynomial <i>p</i> such that
<i>p(0) = 0</i> and <i>p(2) = 1</i>. Moreover, for the Newton interpolation
for integer polynomials, we proved that all intermediate results that are
computed during the algorithm must be integers. This admits an early
failure detection in the implementation. Finally, we proved the uniqueness
of polynomial interpolation.
<p>
The development also contains improved code equations to speed up the
division of integers in target languages.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Polynomial_Interpolation</h3>
<ul>
<li><a href="../theories/polynomial_interpolation/#Is_Rat_To_Rat">Is_Rat_To_Rat</a></li>
<li><a href="../theories/polynomial_interpolation/#Divmod_Int">Divmod_Int</a></li>
<li><a href="../theories/polynomial_interpolation/#Improved_Code_Equations">Improved_Code_Equations</a></li>
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<li><a href="../theories/polynomial_interpolation/#Newton_Interpolation">Newton_Interpolation</a></li>
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<li><a href="../theories/polynomial_interpolation/#Neville_Aitken_Interpolation">Neville_Aitken_Interpolation</a></li>
<li><a href="../theories/polynomial_interpolation/#Polynomial_Interpolation">Polynomial_Interpolation</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Three_Circles.html">The Theorem of Three Circles</a></li><li><a href="../entries/Formal_Puiseux_Series.html">Formal Puiseux Series</a></li><li><a href="../entries/Gauss_Sums.html">Gauss Sums and the Pólya–Vinogradov Inequality</a></li><li><a href="../entries/Count_Complex_Roots.html">Count the Number of Complex Roots</a></li><li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Interpolation_Polynomials_HOL_Algebra.html">Interpolation Polynomials (in HOL-Algebra)</a></li>
<li><a href="../entries/LLL_Factorization.html">A verified factorization algorithm for integer polynomials with polynomial complexity</a></li>
<li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li>
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<p style="display:none;" id="bibtex-filename">Polynomial_Interpolation-AFP</p><pre id="copy-text">@article{Polynomial_Interpolation-AFP,
author = {René Thiemann and Akihisa Yamada},
title = {Polynomial Interpolation},
journal = {Archive of Formal Proofs},
month = {January},
year = {2016},
note = {\url{https://isa-afp.org/entries/Polynomial_Interpolation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>xecutable <span class='first'>M</span>ultivariate <span class='first'>P</span>olynomials</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>, <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>, <a href="../authors/maletzky">Alexander Maletzky</a> <a href="https://risc.jku.at/m/alexander-maletzky/">🌐</a>, <a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>, <a href="../authors/haftmann">Florian Haftmann</a> <a href="http://isabelle.in.tum.de/~haftmann">🌐</a>, <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/bentkamp">Alexander Bentkamp</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYmVudGthbXAiXX0=">📧</a>
</p>
<p class="date">August 10, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We define multivariate polynomials over arbitrary (ordered) semirings in
combination with (executable) operations like addition, multiplication,
and substitution. We also define (weak) monotonicity of polynomials and
comparison of polynomials where we provide standard estimations like
absolute positiveness or the more recent approach of Neurauter, Zankl,
and Middeldorp. Moreover, it is proven that strongly normalizing
(monotone) orders can be lifted to strongly normalizing (monotone) orders
over polynomials. Our formalization was performed as part of the <a
href="http://cl-informatik.uibk.ac.at/software/ceta">IsaFoR/CeTA-system</a>
which contains several termination techniques. The provided theories have
been essential to formalize polynomial interpretations.
<p>
This formalization also contains an abstract representation as coefficient functions with finite
support and a type of power-products. If this type is ordered by a linear (term) ordering, various
additional notions, such as leading power-product, leading coefficient etc., are introduced as
well. Furthermore, a lot of generic properties of, and functions on, multivariate polynomials are
formalized, including the substitution and evaluation homomorphisms, embeddings of polynomial rings
into larger rings (i.e. with one additional indeterminate), homogenization and dehomogenization of
polynomials, and the canonical isomorphism between R[X,Y] and R[X][Y].</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>April 18, 2019</dt>
<dd>Added material about polynomials whose power-products are represented themselves
by polynomial mappings.</dd><dt>January 23, 2018</dt>
<dd>Added authors Haftmann, Lochbihler after incorporating
their formalization of multivariate polynomials based on Polynomial mappings.
Moved material from Bentkamp's entry "Deep Learning".<br>
</dd><dt>October 28, 2016</dt>
<dd>Added abstract representation of polynomials and authors Maletzky/Immler.<br></dd><dt>September 17, 2010</dt>
<dd>Moved theories on arbitrary (ordered) semirings to Abstract Rewriting.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Polynomials</h3>
<ul>
<li><a href="../theories/polynomials/#Utils">Utils</a></li>
<li><a href="../theories/polynomials/#MPoly_Type">MPoly_Type</a></li>
<li><a href="../theories/polynomials/#More_MPoly_Type">More_MPoly_Type</a></li>
<li><a href="../theories/polynomials/#Power_Products">Power_Products</a></li>
<li><a href="../theories/polynomials/#More_Modules">More_Modules</a></li>
<li><a href="../theories/polynomials/#MPoly_Type_Class">MPoly_Type_Class</a></li>
<li><a href="../theories/polynomials/#MPoly_Type_Class_Ordered">MPoly_Type_Class_Ordered</a></li>
<li><a href="../theories/polynomials/#Poly_Mapping_Finite_Map">Poly_Mapping_Finite_Map</a></li>
<li><a href="../theories/polynomials/#MPoly_Type_Class_FMap">MPoly_Type_Class_FMap</a></li>
<li><a href="../theories/polynomials/#PP_Type">PP_Type</a></li>
<li><a href="../theories/polynomials/#OAlist">OAlist</a></li>
<li><a href="../theories/polynomials/#OAlist_Poly_Mapping">OAlist_Poly_Mapping</a></li>
<li><a href="../theories/polynomials/#Term_Order">Term_Order</a></li>
<li><a href="../theories/polynomials/#MPoly_Type_Class_OAlist">MPoly_Type_Class_OAlist</a></li>
<li><a href="../theories/polynomials/#Quasi_PM_Power_Products">Quasi_PM_Power_Products</a></li>
<li><a href="../theories/polynomials/#MPoly_PM">MPoly_PM</a></li>
<li><a href="../theories/polynomials/#MPoly_Type_Univariate">MPoly_Type_Univariate</a></li>
<li><a href="../theories/polynomials/#Polynomials">Polynomials</a></li>
<li><a href="../theories/polynomials/#Show_Polynomials">Show_Polynomials</a></li>
<li><a href="../theories/polynomials/#NZM">NZM</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li><li><a href="../entries/Virtual_Substitution.html">Verified Quadratic Virtual Substitution for Real Arithmetic</a></li><li><a href="../entries/PAC_Checker.html">Practical Algebraic Calculus Checker</a></li><li><a href="../entries/Symmetric_Polynomials.html">Symmetric Polynomials</a></li><li><a href="../entries/Lambda_Free_KBOs.html">Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Polynomials-AFP</p><pre id="copy-text">@article{Polynomials-AFP,
author = {Christian Sternagel and René Thiemann and Alexander Maletzky and Fabian Immler and Florian Haftmann and Andreas Lochbihler and Alexander Bentkamp},
title = {Executable Multivariate Polynomials},
journal = {Archive of Formal Proofs},
month = {August},
year = {2010},
note = {\url{https://isa-afp.org/entries/Polynomials.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>P</span>op-<span class='first'>R</span>efinement</h1>
<div>
<p><a href="../authors/coglio">Alessandro Coglio</a> <a href="http://www.kestrel.edu/~coglio">🌐</a>
</p>
<p class="date">July 3, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Pop-refinement is an approach to stepwise refinement, carried out inside an interactive theorem prover by constructing a monotonically decreasing sequence of predicates over deeply embedded target programs. The sequence starts with a predicate that characterizes the possible implementations, and ends with a predicate that characterizes a unique program in explicit syntactic form. Pop-refinement enables more requirements (e.g. program-level and non-functional) to be captured in the initial specification and preserved through refinement. Security requirements expressed as hyperproperties (i.e. predicates over sets of traces) are always preserved by pop-refinement, unlike the popular notion of refinement as trace set inclusion. Two simple examples in Isabelle/HOL are presented, featuring program-level requirements, non-functional requirements, and hyperproperties.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/misc">Computer science/Programming languages/Misc</a></li></ul>
<h3>Session Pop_Refinement</h3>
<ul>
<li><a href="../theories/pop_refinement/#Definition">Definition</a></li>
<li><a href="../theories/pop_refinement/#First_Example">First_Example</a></li>
<li><a href="../theories/pop_refinement/#Second_Example">Second_Example</a></li>
<li><a href="../theories/pop_refinement/#General_Remarks">General_Remarks</a></li>
<li><a href="../theories/pop_refinement/#Related_Work">Related_Work</a></li>
<li><a href="../theories/pop_refinement/#Future_Work">Future_Work</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Pop_Refinement-AFP</p><pre id="copy-text">@article{Pop_Refinement-AFP,
author = {Alessandro Coglio},
title = {Pop-Refinement},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/Pop_Refinement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>P</span><span class='first'>O</span><span class='first'>S</span><span class='first'>I</span><span class='first'>X</span> <span class='first'>L</span>exing <span class='first'>W</span>ith <span class='first'>D</span>erivatives of <span class='first'>R</span>egular <span class='first'>E</span>xpressions</h1>
<div>
<p><a href="../authors/ausaf">Fahad Ausaf</a> <a href="http://kcl.academia.edu/FahadAusaf">🌐</a>, <a href="../authors/dyckhoff">Roy Dyckhoff</a> <a href="https://rd.host.cs.st-andrews.ac.uk">🌐</a> and <a href="../authors/urban">Christian Urban</a> <a href="https://nms.kcl.ac.uk/christian.urban/">🌐</a>
</p>
<p class="date">May 24, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Brzozowski introduced the notion of derivatives for regular
expressions. They can be used for a very simple regular
expression matching algorithm. Sulzmann and Lu cleverly
extended this algorithm in order to deal with POSIX matching,
which is the underlying disambiguation strategy for regular
expressions needed in lexers. Their algorithm generates POSIX
values which encode the information of how a regular
expression matches a string--—that is, which part of the string
is matched by which part of the regular expression. In this
paper we give our inductive definition of what a POSIX value
is and show (i) that such a value is unique (for given regular
expression and string being matched) and (ii) that Sulzmann
and Lu’s algorithm always generates such a value (provided
that the regular expression matches the string). This holds
also when optimisations are included. Finally we show that
(iii) our inductive definition of a POSIX value is equivalent
to an alternative definition by Okui and Suzuki which
identifies POSIX values as least elements according to an
ordering of values.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 17, 2022</dt>
<dd>Christian Urban added a theory about the Posix definition by Okui and Suzuki.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Posix-Lexing</h3>
<ul>
<li><a href="../theories/posix-lexing/#Lexer">Lexer</a></li>
<li><a href="../theories/posix-lexing/#LexicalVals">LexicalVals</a></li>
<li><a href="../theories/posix-lexing/#Simplifying">Simplifying</a></li>
<li><a href="../theories/posix-lexing/#Positions">Positions</a></li>
<li><a href="../theories/posix-lexing/#Regular_Exps3">Regular_Exps3</a></li>
<li><a href="../theories/posix-lexing/#Derivatives3">Derivatives3</a></li>
<li><a href="../theories/posix-lexing/#Lexer3">Lexer3</a></li>
<li><a href="../theories/posix-lexing/#LexicalVals3">LexicalVals3</a></li>
<li><a href="../theories/posix-lexing/#Simplifying3">Simplifying3</a></li>
<li><a href="../theories/posix-lexing/#Positions3">Positions3</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<p style="display:none;" id="bibtex-filename">Posix-Lexing-AFP</p><pre id="copy-text">@article{Posix-Lexing-AFP,
author = {Fahad Ausaf and Roy Dyckhoff and Christian Urban},
title = {POSIX Lexing with Derivatives of Regular Expressions},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Posix-Lexing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Possibilistic_Noninterference.html b/web/entries/Possibilistic_Noninterference.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Possibilistic Noninterference - Archive of Formal Proofs</title><meta name="description" content="We formalize a wide variety of Volpano/Smith-style noninterference notions for a while language with parallel composition. We systematize and classify..."><meta property="og:title" content="Possibilistic Noninterference" />
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<h1 >
<span class='first'>P</span>ossibilistic <span class='first'>N</span>oninterference</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/hoelzl">Johannes Hölzl</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJob2VsemwiXX0=">📧</a>
</p>
<p class="date">September 10, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a wide variety of Volpano/Smith-style noninterference
notions for a while language with parallel composition.
We systematize and classify these notions according to
compositionality w.r.t. the language constructs. Compositionality
yields sound syntactic criteria (a.k.a. type systems) in a uniform way.
<p>
An <a href="http://www21.in.tum.de/~nipkow/pubs/cpp12.html">article</a>
about these proofs is published in the proceedings
of the conference Certified Programs and Proofs 2012.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session Possibilistic_Noninterference</h3>
<ul>
<li><a href="../theories/possibilistic_noninterference/#MyTactics">MyTactics</a></li>
<li><a href="../theories/possibilistic_noninterference/#Interface">Interface</a></li>
<li><a href="../theories/possibilistic_noninterference/#Bisim">Bisim</a></li>
<li><a href="../theories/possibilistic_noninterference/#Language_Semantics">Language_Semantics</a></li>
<li><a href="../theories/possibilistic_noninterference/#During_Execution">During_Execution</a></li>
<li><a href="../theories/possibilistic_noninterference/#Compositionality">Compositionality</a></li>
<li><a href="../theories/possibilistic_noninterference/#Syntactic_Criteria">Syntactic_Criteria</a></li>
<li><a href="../theories/possibilistic_noninterference/#After_Execution">After_Execution</a></li>
<li><a href="../theories/possibilistic_noninterference/#Concrete">Concrete</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Possibilistic_Noninterference-AFP</p><pre id="copy-text">@article{Possibilistic_Noninterference-AFP,
author = {Andrei Popescu and Johannes Hölzl},
title = {Possibilistic Noninterference},
journal = {Archive of Formal Proofs},
month = {September},
year = {2012},
note = {\url{https://isa-afp.org/entries/Possibilistic_Noninterference.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Power Sum Polynomials - Archive of Formal Proofs</title><meta name="description" content="This article provides a formalisation of the symmetric multivariate polynomials known as power sum polynomials. These are of the form pn(X1,&amp;hellip;, Xk) =..."><meta property="og:title" content="Power Sum Polynomials" />
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<h1 >
<span class='first'>P</span>ower <span class='first'>S</span>um <span class='first'>P</span>olynomials</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">April 24, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of the symmetric
multivariate polynomials known as <em>power sum
polynomials</em>. These are of the form
p<sub>n</sub>(<em>X</em><sub>1</sub>,&hellip;,
<em>X</em><sub><em>k</em></sub>) =
<em>X</em><sub>1</sub><sup>n</sup>
+ &hellip; +
X<sub><em>k</em></sub><sup>n</sup>.
A formal proof of the Girard–Newton Theorem is also given. This
theorem relates the power sum polynomials to the elementary symmetric
polynomials s<sub><em>k</em></sub> in the form
of a recurrence relation
(-1)<sup><em>k</em></sup>
<em>k</em> s<sub><em>k</em></sub>
=
&sum;<sub>i&isinv;[0,<em>k</em>)</sub>
(-1)<sup>i</sup> s<sub>i</sub>
p<sub><em>k</em>-<em>i</em></sub>&thinsp;.</p>
<p>As an application, this is then used to solve a generalised
form of a puzzle given as an exercise in Dummit and Foote's
<em>Abstract Algebra</em>: For <em>k</em>
complex unknowns <em>x</em><sub>1</sub>,
&hellip;,
<em>x</em><sub><em>k</em></sub>,
define p<sub><em>j</em></sub> :=
<em>x</em><sub>1</sub><sup><em>j</em></sup>
+ &hellip; +
<em>x</em><sub><em>k</em></sub><sup><em>j</em></sup>.
Then for each vector <em>a</em> &isinv;
&#x2102;<sup><em>k</em></sup>, show that
there is exactly one solution to the system p<sub>1</sub>
= a<sub>1</sub>, &hellip;,
p<sub><em>k</em></sub> =
a<sub><em>k</em></sub> up to permutation of
the
<em>x</em><sub><em>i</em></sub>
and determine the value of
p<sub><em>i</em></sub> for
i&gt;k.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Power_Sum_Polynomials</h3>
<ul>
<li><a href="../theories/power_sum_polynomials/#Power_Sum_Polynomials_Library">Power_Sum_Polynomials_Library</a></li>
<li><a href="../theories/power_sum_polynomials/#Power_Sum_Polynomials">Power_Sum_Polynomials</a></li>
<li><a href="../theories/power_sum_polynomials/#Power_Sum_Puzzle">Power_Sum_Puzzle</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Symmetric_Polynomials.html">Symmetric Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Power_Sum_Polynomials-AFP</p><pre id="copy-text">@article{Power_Sum_Polynomials-AFP,
author = {Manuel Eberl},
title = {Power Sum Polynomials},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Power_Sum_Polynomials.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Pratt_Certificate.html b/web/entries/Pratt_Certificate.html
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@@ -1,203 +1,205 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Pratt&#39;s Primality Certificates - Archive of Formal Proofs</title><meta name="description" content="In 1975, Pratt introduced a proof system for certifying primes. He showed that a number p is prime iff a primality certificate for p exists. By showing a..."><meta property="og:title" content="Pratt&#39;s Primality Certificates" />
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<h1 >
<span class='first'>P</span>ratt's <span class='first'>P</span>rimality <span class='first'>C</span>ertificates</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsic2ltb24iLCJ3aW1tZXIiXX0=">📧</a> and <a href="../authors/noschinski">Lars Noschinski</a> <a href="http://www21.in.tum.de/~noschinl/">🌐</a>
</p>
<p class="date">July 22, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1975, Pratt introduced a proof system for certifying primes. He showed that a number <i>p</i> is prime iff a primality certificate for <i>p</i> exists. By showing a logarithmic upper bound on the length of the certificates in size of the prime number, he concluded that the decision problem for prime numbers is in NP. This work formalizes soundness and completeness of Pratt's proof system as well as an upper bound for the size of the certificate.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
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<li><a href="../theories/pratt_certificate/#Pratt_Certificate">Pratt_Certificate</a></li>
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<p style="display:none;" id="bibtex-filename">Pratt_Certificate-AFP</p><pre id="copy-text">@article{Pratt_Certificate-AFP,
author = {Simon Wimmer and Lars Noschinski},
title = {Pratt&#39;s Primality Certificates},
journal = {Archive of Formal Proofs},
month = {July},
year = {2013},
note = {\url{https://isa-afp.org/entries/Pratt_Certificate.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>ombinator <span class='first'>L</span>ibrary for <span class='first'>P</span>refix-<span class='first'>F</span>ree <span class='first'>C</span>odes</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">April 8, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains a set of binary encodings for primitive data
types, such as natural numbers, integers, floating-point numbers as
well as combinators to construct encodings for products, lists, sets
or functions of/between such types. For natural numbers and integers,
the entry contains various encodings, such as Elias-Gamma-Codes and
exponential Golomb Codes, which are efficient variable-length codes in
use by current compression formats. A use-case for this library is
measuring the persisted size of a complex data structure without
having to hand-craft a dedicated encoding for it, independent of
Isabelle's internal representation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Prefix_Free_Code_Combinators</h3>
<ul>
<li><a href="../theories/prefix_free_code_combinators/#Prefix_Free_Code_Combinators">Prefix_Free_Code_Combinators</a></li>
<li><a href="../theories/prefix_free_code_combinators/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Prefix_Free_Code_Combinators-AFP</p><pre id="copy-text">@article{Prefix_Free_Code_Combinators-AFP,
author = {Emin Karayel},
title = {A Combinator Library for Prefix-Free Codes},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Prefix_Free_Code_Combinators.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Prefix_Free_Code_Combinators-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Prefix_Free_Code_Combinators-2022-04-19.tar.gz">Apr 19, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Presburger-Automata.html b/web/entries/Presburger-Automata.html
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<h1 >
<span class='first'>F</span>ormalizing the <span class='first'>L</span>ogic-<span class='first'>A</span>utomaton <span class='first'>C</span>onnection</h1>
<div>
<p><a href="../authors/berghofer">Stefan Berghofer</a> <a href="http://www.in.tum.de/~berghofe">🌐</a> and <a href="../authors/reiter">Markus Reiter</a>
</p>
<p class="date">December 3, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work presents a formalization of a library for automata on bit strings. It forms the basis of a reflection-based decision procedure for Presburger arithmetic, which is efficiently executable thanks to Isabelle's code generator. With this work, we therefore provide a mechanized proof of a well-known connection between logic and automata theory. The formalization is also described in a publication [TPHOLs 2009].</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/logic/general-logic/decidability-of-theories">Logic/General logic/Decidability of theories</a></li></ul><h3>Related publications</h3>
<ul><li>
Berghofer, S., & Reiter, M. (2009). Formalizing the Logic-Automaton Connection. Theorem Proving in Higher Order Logics, 147–163. <a href="https://doi.org/10.1007/978-3-642-03359-9_12">https://doi.org/10.1007/978-3-642-03359-9_12</a>
</li></ul>
<h3>Session Presburger-Automata</h3>
<ul>
<li><a href="../theories/presburger-automata/#DFS">DFS</a></li>
<li><a href="../theories/presburger-automata/#Presburger_Automata">Presburger_Automata</a></li>
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<p style="display:none;" id="bibtex-filename">Presburger-Automata-AFP</p><pre id="copy-text">@article{Presburger-Automata-AFP,
author = {Stefan Berghofer and Markus Reiter},
title = {Formalizing the Logic-Automaton Connection},
journal = {Archive of Formal Proofs},
month = {December},
year = {2009},
note = {\url{https://isa-afp.org/entries/Presburger-Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Presburger-Automata-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li></ul>
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diff --git a/web/entries/Prim_Dijkstra_Simple.html b/web/entries/Prim_Dijkstra_Simple.html
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<h1 >
<span class='first'>P</span>urely <span class='first'>F</span>unctional, <span class='first'>S</span>imple, and <span class='first'>E</span>fficient <span class='first'>I</span>mplementation of <span class='first'>P</span>rim and <span class='first'>D</span>ijkstra</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 25, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We verify purely functional, simple and efficient implementations of
Prim's and Dijkstra's algorithms. This constitutes the first
verification of an executable and even efficient version of
Prim's algorithm. This entry formalizes the second part of our
ITP-2019 proof pearl <em>Purely Functional, Simple and Efficient
Priority Search Trees and Applications to Prim and Dijkstra</em>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Prim_Dijkstra_Simple</h3>
<ul>
<li><a href="../theories/prim_dijkstra_simple/#Common">Common</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Chapter_Prim">Chapter_Prim</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Undirected_Graph">Undirected_Graph</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Undirected_Graph_Specs">Undirected_Graph_Specs</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Prim_Abstract">Prim_Abstract</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Undirected_Graph_Impl">Undirected_Graph_Impl</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Prim_Impl">Prim_Impl</a></li>
<li><a href="../theories/prim_dijkstra_simple/#Chapter_Dijkstra">Chapter_Dijkstra</a></li>
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<p style="display:none;" id="bibtex-filename">Prim_Dijkstra_Simple-AFP</p><pre id="copy-text">@article{Prim_Dijkstra_Simple-AFP,
author = {Peter Lammich and Tobias Nipkow},
title = {Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Prim_Dijkstra_Simple.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>lementary <span class='first'>F</span>acts <span class='first'>A</span>bout the <span class='first'>D</span>istribution of <span class='first'>P</span>rimes</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 21, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry is a formalisation of Chapter 4 (and parts of
Chapter 3) of Apostol's <a
href="https://www.springer.com/de/book/9780387901633"><em>Introduction
to Analytic Number Theory</em></a>. The main topics that
are addressed are properties of the distribution of prime numbers that
can be shown in an elementary way (i.&thinsp;e. without the Prime
Number Theorem), the various equivalent forms of the PNT (which imply
each other in elementary ways), and consequences that follow from the
PNT in elementary ways. The latter include, most notably, asymptotic
bounds for the number of distinct prime factors of
<em>n</em>, the divisor function
<em>d(n)</em>, Euler's totient function
<em>&phi;(n)</em>, and
lcm(1,&hellip;,<em>n</em>).</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Prime_Distribution_Elementary</h3>
<ul>
<li><a href="../theories/prime_distribution_elementary/#Prime_Distribution_Elementary_Library">Prime_Distribution_Elementary_Library</a></li>
<li><a href="../theories/prime_distribution_elementary/#More_Dirichlet_Misc">More_Dirichlet_Misc</a></li>
<li><a href="../theories/prime_distribution_elementary/#Primes_Omega">Primes_Omega</a></li>
<li><a href="../theories/prime_distribution_elementary/#Primorial">Primorial</a></li>
<li><a href="../theories/prime_distribution_elementary/#Lcm_Nat_Upto">Lcm_Nat_Upto</a></li>
<li><a href="../theories/prime_distribution_elementary/#Shapiro_Tauberian">Shapiro_Tauberian</a></li>
<li><a href="../theories/prime_distribution_elementary/#Partial_Zeta_Bounds">Partial_Zeta_Bounds</a></li>
<li><a href="../theories/prime_distribution_elementary/#Moebius_Mu_Sum">Moebius_Mu_Sum</a></li>
<li><a href="../theories/prime_distribution_elementary/#Elementary_Prime_Bounds">Elementary_Prime_Bounds</a></li>
<li><a href="../theories/prime_distribution_elementary/#Summatory_Divisor_Sigma_Bounds">Summatory_Divisor_Sigma_Bounds</a></li>
<li><a href="../theories/prime_distribution_elementary/#Selberg_Asymptotic_Formula">Selberg_Asymptotic_Formula</a></li>
<li><a href="../theories/prime_distribution_elementary/#PNT_Consequences">PNT_Consequences</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Irrational_Series_Erdos_Straus.html">Irrationality Criteria for Series by Erdős and Straus</a></li><li><a href="../entries/Zeta_3_Irrational.html">The Irrationality of ζ(3)</a></li><li><a href="../entries/IMO2019.html">Selected Problems from the International Mathematical Olympiad 2019</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Gauss_Sums.html">Gauss Sums and the Pólya–Vinogradov Inequality</a></li>
<li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li>
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<p style="display:none;" id="bibtex-filename">Prime_Distribution_Elementary-AFP</p><pre id="copy-text">@article{Prime_Distribution_Elementary-AFP,
author = {Manuel Eberl},
title = {Elementary Facts About the Distribution of Primes},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/Prime_Distribution_Elementary.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Prime_Harmonic_Series.html b/web/entries/Prime_Harmonic_Series.html
--- a/web/entries/Prime_Harmonic_Series.html
+++ b/web/entries/Prime_Harmonic_Series.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Divergence of the Prime Harmonic Series - Archive of Formal Proofs</title><meta name="description" content=" In this work, we prove the lower bound ln(H_n) - ln(5/3) for the partial sum of the Prime Harmonic series and, based on this, the divergence of the Prime..."><meta property="og:title" content="The Divergence of the Prime Harmonic Series" />
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<h1 >
<span class='first'>T</span>he <span class='first'>D</span>ivergence of the <span class='first'>P</span>rime <span class='first'>H</span>armonic <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
In this work, we prove the lower bound <span class="nobr">ln(H_n) -
ln(5/3)</span> for the
partial sum of the Prime Harmonic series and, based on this, the divergence of
the Prime Harmonic Series
<span class="nobr">∑[p&thinsp;prime]&thinsp;·&thinsp;1/p.</span>
</p><p>
The proof relies on the unique squarefree decomposition of natural numbers. This
is similar to Euler's original proof (which was highly informal and morally
questionable). Its advantage over proofs by contradiction, like the famous one
by Paul Erdős, is that it provides a relatively good lower bound for the partial
sums.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Prime_Harmonic_Series</h3>
<ul>
<li><a href="../theories/prime_harmonic_series/#Prime_Harmonic_Misc">Prime_Harmonic_Misc</a></li>
<li><a href="../theories/prime_harmonic_series/#Squarefree_Nat">Squarefree_Nat</a></li>
<li><a href="../theories/prime_harmonic_series/#Prime_Harmonic">Prime_Harmonic</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Prime_Harmonic_Series-AFP</p><pre id="copy-text">@article{Prime_Harmonic_Series-AFP,
author = {Manuel Eberl},
title = {The Divergence of the Prime Harmonic Series},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Prime_Harmonic_Series.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Prime_Harmonic_Series-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Prime_Harmonic_Series-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Prime_Harmonic_Series-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Prime_Number_Theorem.html b/web/entries/Prime_Number_Theorem.html
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<h1 >
<span class='first'>T</span>he <span class='first'>P</span>rime <span class='first'>N</span>umber <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">September 19, 2018</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a short proof of the Prime Number
Theorem in several equivalent forms, most notably
&pi;(<em>x</em>) ~ <em>x</em>/ln
<em>x</em> where &pi;(<em>x</em>) is the
number of primes no larger than <em>x</em>. It also
defines other basic number-theoretic functions related to primes like
Chebyshev's functions &thetasym; and &psi; and the
&ldquo;<em>n</em>-th prime number&rdquo; function
p<sub><em>n</em></sub>. We also show various
bounds and relationship between these functions are shown. Lastly, we
derive Mertens' First and Second Theorem, i.&thinsp;e.
&sum;<sub><em>p</em>&le;<em>x</em></sub>
ln <em>p</em>/<em>p</em> = ln
<em>x</em> + <em>O</em>(1) and
&sum;<sub><em>p</em>&le;<em>x</em></sub>
1/<em>p</em> = ln ln <em>x</em> + M +
<em>O</em>(1/ln <em>x</em>). We also give
explicit bounds for the remainder terms.</p> <p>The proof
of the Prime Number Theorem builds on a library of Dirichlet series
and analytic combinatorics. We essentially follow the presentation by
Newman. The core part of the proof is a Tauberian theorem for
Dirichlet series, which is proven using complex analysis and then used
to strengthen Mertens' First Theorem to
&sum;<sub><em>p</em>&le;<em>x</em></sub>
ln <em>p</em>/<em>p</em> = ln
<em>x</em> + c + <em>o</em>(1).</p>
<p>A variant of this proof has been formalised before by
Harrison in HOL Light, and formalisations of Selberg's elementary
proof exist both by Avigad <em>et al.</em> in Isabelle and
by Carneiro in Metamath. The advantage of the analytic proof is that,
while it requires more powerful mathematical tools, it is considerably
shorter and clearer. This article attempts to provide a short and
clear formalisation of all components of that proof using the full
range of mathematical machinery available in Isabelle, staying as
close as possible to Newman's simple paper proof.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Prime_Number_Theorem</h3>
<ul>
<li><a href="../theories/prime_number_theorem/#Prime_Number_Theorem_Library">Prime_Number_Theorem_Library</a></li>
<li><a href="../theories/prime_number_theorem/#Newman_Ingham_Tauberian">Newman_Ingham_Tauberian</a></li>
<li><a href="../theories/prime_number_theorem/#Prime_Counting_Functions">Prime_Counting_Functions</a></li>
<li><a href="../theories/prime_number_theorem/#Prime_Number_Theorem">Prime_Number_Theorem</a></li>
<li><a href="../theories/prime_number_theorem/#Mertens_Theorems">Mertens_Theorems</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stirling_Formula.html">Stirling&rsquo;s formula</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Irrational_Series_Erdos_Straus.html">Irrationality Criteria for Series by Erdős and Straus</a></li><li><a href="../entries/Zeta_3_Irrational.html">The Irrationality of ζ(3)</a></li><li><a href="../entries/Transcendence_Series_Hancl_Rucki.html">The Transcendence of Certain Infinite Series</a></li><li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li>
<li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li>
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<p style="display:none;" id="bibtex-filename">Prime_Number_Theorem-AFP</p><pre id="copy-text">@article{Prime_Number_Theorem-AFP,
author = {Manuel Eberl and Lawrence C. Paulson},
title = {The Prime Number Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Prime_Number_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Prime_Number_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Prime_Number_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Prime_Number_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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<a href="https://www.isa-afp.org/release/afp-Prime_Number_Theorem-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Prime_Number_Theorem-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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diff --git a/web/entries/Priority_Queue_Braun.html b/web/entries/Priority_Queue_Braun.html
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and deletion take logarithmic time and preserve the balanced nature
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<h1 >
<span class='first'>P</span>riority <span class='first'>Q</span>ueues <span class='first'>B</span>ased on <span class='first'>B</span>raun <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">September 4, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry verifies priority queues based on Braun trees. Insertion
and deletion take logarithmic time and preserve the balanced nature
of Braun trees. Two implementations of deletion are provided.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>December 16, 2019</dt>
<dd>Added theory Priority_Queue_Braun2 with second version of del_min</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T., & Sewell, T. (2020). Proof pearl: Braun trees. Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs. <a href="https://doi.org/10.1145/3372885.3373834">https://doi.org/10.1145/3372885.3373834</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/cpp20.html">Open access</a>
</li></ul>
<h3>Session Priority_Queue_Braun</h3>
<ul>
<li><a href="../theories/priority_queue_braun/#Priority_Queue_Braun">Priority_Queue_Braun</a></li>
<li><a href="../theories/priority_queue_braun/#Priority_Queue_Braun2">Priority_Queue_Braun2</a></li>
<li><a href="../theories/priority_queue_braun/#Sorting_Braun">Sorting_Braun</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Priority_Queue_Braun-AFP</p><pre id="copy-text">@article{Priority_Queue_Braun-AFP,
author = {Tobias Nipkow},
title = {Priority Queues Based on Braun Trees},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Priority_Queue_Braun.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Priority_Queue_Braun-2014-09-04.tar.gz">Sep 4, 2014</a>: Isabelle2014
</li></ul>
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diff --git a/web/entries/Priority_Search_Trees.html b/web/entries/Priority_Search_Trees.html
--- a/web/entries/Priority_Search_Trees.html
+++ b/web/entries/Priority_Search_Trees.html
@@ -1,179 +1,181 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Priority Search Trees - Archive of Formal Proofs</title><meta name="description" content="We present a new, purely functional, simple and efficient data structure combining a search tree and a priority queue, which we call a priority search..."><meta property="og:title" content="Priority Search Trees" />
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<h1 >
<span class='first'>P</span>riority <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 25, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a new, purely functional, simple and efficient data
structure combining a search tree and a priority queue, which we call
a <em>priority search tree</em>. The salient feature of priority search
trees is that they offer a decrease-key operation, something that is
missing from other simple, purely functional priority queue
implementations. Priority search trees can be implemented on top of
any search tree. This entry does the implementation for red-black
trees. This entry formalizes the first part of our ITP-2019 proof
pearl <em>Purely Functional, Simple and Efficient Priority
Search Trees and Applications to Prim and Dijkstra</em>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Priority_Search_Trees</h3>
<ul>
<li><a href="../theories/priority_search_trees/#Prio_Map_Specs">Prio_Map_Specs</a></li>
<li><a href="../theories/priority_search_trees/#PST_General">PST_General</a></li>
<li><a href="../theories/priority_search_trees/#PST_RBT">PST_RBT</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Prim_Dijkstra_Simple.html">Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Priority_Search_Trees-AFP</p><pre id="copy-text">@article{Priority_Search_Trees-AFP,
author = {Peter Lammich and Tobias Nipkow},
title = {Priority Search Trees},
journal = {Archive of Formal Proofs},
month = {June},
year = {2019},
note = {\url{https://isa-afp.org/entries/Priority_Search_Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Priority_Search_Trees-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-Priority_Search_Trees-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>P</span>robabilistic <span class='first'>N</span>oninterference</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a>
</p>
<p class="date">March 11, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a probabilistic noninterference for a multi-threaded language with uniform scheduling, where probabilistic behaviour comes from both the scheduler and the individual threads. We define notions probabilistic noninterference in two variants: resumption-based and trace-based. For the resumption-based notions, we prove compositionality w.r.t. the language constructs and establish sound type-system-like syntactic criteria. This is a formalization of the mathematical development presented at CPP 2013 and CALCO 2013. It is the probabilistic variant of the Possibilistic Noninterference AFP entry.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Probabilistic_Noninterference</h3>
<ul>
<li><a href="../theories/probabilistic_noninterference/#Interface">Interface</a></li>
<li><a href="../theories/probabilistic_noninterference/#Language_Semantics">Language_Semantics</a></li>
<li><a href="../theories/probabilistic_noninterference/#Resumption_Based">Resumption_Based</a></li>
<li><a href="../theories/probabilistic_noninterference/#Trace_Based">Trace_Based</a></li>
<li><a href="../theories/probabilistic_noninterference/#Compositionality">Compositionality</a></li>
<li><a href="../theories/probabilistic_noninterference/#Syntactic_Criteria">Syntactic_Criteria</a></li>
<li><a href="../theories/probabilistic_noninterference/#Concrete">Concrete</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li><li><a href="../entries/Markov_Models.html">Markov Models</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Probabilistic_Noninterference-AFP</p><pre id="copy-text">@article{Probabilistic_Noninterference-AFP,
author = {Andrei Popescu and Johannes Hölzl},
title = {Probabilistic Noninterference},
journal = {Archive of Formal Proofs},
month = {March},
year = {2014},
note = {\url{https://isa-afp.org/entries/Probabilistic_Noninterference.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Probabilistic_Noninterference-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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diff --git a/web/entries/Probabilistic_Prime_Tests.html b/web/entries/Probabilistic_Prime_Tests.html
--- a/web/entries/Probabilistic_Prime_Tests.html
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@@ -1,191 +1,193 @@
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<h1 >
<span class='first'>P</span>robabilistic <span class='first'>P</span>rimality <span class='first'>T</span>esting</h1>
<div>
<p><a href="../authors/stuewe">Daniel Stüwe</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">February 11, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The most efficient known primality tests are
<em>probabilistic</em> in the sense that they use
randomness and may, with some probability, mistakenly classify a
composite number as prime &ndash; but never a prime number as
composite. Examples of this are the Miller&ndash;Rabin test, the
Solovay&ndash;Strassen test, and (in most cases) Fermat's
test.</p> <p>This entry defines these three tests and
proves their correctness. It also develops some of the
number-theoretic foundations, such as Carmichael numbers and the
Jacobi symbol with an efficient executable algorithm to compute
it.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Probabilistic_Prime_Tests</h3>
<ul>
<li><a href="../theories/probabilistic_prime_tests/#Legendre_Symbol">Legendre_Symbol</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Algebraic_Auxiliaries">Algebraic_Auxiliaries</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Jacobi_Symbol">Jacobi_Symbol</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Residues_Nat">Residues_Nat</a></li>
<li><a href="../theories/probabilistic_prime_tests/#QuadRes">QuadRes</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Euler_Witness">Euler_Witness</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Carmichael_Numbers">Carmichael_Numbers</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Fermat_Witness">Fermat_Witness</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Generalized_Primality_Test">Generalized_Primality_Test</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Fermat_Test">Fermat_Test</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Miller_Rabin_Test">Miller_Rabin_Test</a></li>
<li><a href="../theories/probabilistic_prime_tests/#Solovay_Strassen_Test">Solovay_Strassen_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Mersenne_Primes.html">Mersenne primes and the Lucas–Lehmer test</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Probabilistic_Prime_Tests-AFP</p><pre id="copy-text">@article{Probabilistic_Prime_Tests-AFP,
author = {Daniel Stüwe and Manuel Eberl},
title = {Probabilistic Primality Testing},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/Probabilistic_Prime_Tests.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Probabilistic_Prime_Tests-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>A</span> <span class='first'>Z</span>oo of <span class='first'>P</span>robabilistic <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a>, <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">May 27, 2015</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Numerous models of probabilistic systems are studied in the literature.
Coalgebra has been used to classify them into system types and compare their
expressiveness. We formalize the resulting hierarchy of probabilistic system
types by modeling the semantics of the different systems as codatatypes.
This approach yields simple and concise proofs, as bisimilarity coincides
with equality for codatatypes.
<p>
This work is described in detail in the ITP 2015 publication by the authors.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Probabilistic_System_Zoo</h3>
<ul>
<li><a href="../theories/probabilistic_system_zoo/#Bool_Bounded_Set">Bool_Bounded_Set</a></li>
<li><a href="../theories/probabilistic_system_zoo/#Finitely_Bounded_Set_Counterexample">Finitely_Bounded_Set_Counterexample</a></li>
<li><a href="../theories/probabilistic_system_zoo/#Nonempty_Bounded_Set">Nonempty_Bounded_Set</a></li>
<li><a href="../theories/probabilistic_system_zoo/#Probabilistic_Hierarchy">Probabilistic_Hierarchy</a></li>
<li><a href="../theories/probabilistic_system_zoo/#Vardi">Vardi</a></li>
<li><a href="../theories/probabilistic_system_zoo/#Vardi_Counterexample">Vardi_Counterexample</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Probabilistic_System_Zoo-AFP</p><pre id="copy-text">@article{Probabilistic_System_Zoo-AFP,
author = {Johannes Hölzl and Andreas Lochbihler and Dmitriy Traytel},
title = {A Zoo of Probabilistic Systems},
journal = {Archive of Formal Proofs},
month = {May},
year = {2015},
note = {\url{https://isa-afp.org/entries/Probabilistic_System_Zoo.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Probabilistic_Timed_Automata.html b/web/entries/Probabilistic_Timed_Automata.html
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+++ b/web/entries/Probabilistic_Timed_Automata.html
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<h1 >
<span class='first'>P</span>robabilistic <span class='first'>T</span>imed <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a> and <a href="../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a>
</p>
<p class="date">May 24, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of probabilistic timed automata (PTA) for
which we try to follow the formula MDP + TA = PTA as far as possible:
our work starts from our existing formalizations of Markov decision
processes (MDP) and timed automata (TA) and combines them modularly.
We prove the fundamental result for probabilistic timed automata: the
region construction that is known from timed automata carries over to
the probabilistic setting. In particular, this allows us to prove that
minimum and maximum reachability probabilities can be computed via a
reduction to MDP model checking, including the case where one wants to
disregard unrealizable behavior. Further information can be found in
our ITP paper [2].</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Probabilistic_Timed_Automata</h3>
<ul>
<li><a href="../theories/probabilistic_timed_automata/#MDP_Aux">MDP_Aux</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Finiteness">Finiteness</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Basic">Basic</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Sequence">Sequence</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Sequence_LTL">Sequence_LTL</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Instantiate_Existentials">Instantiate_Existentials</a></li>
<li><a href="../theories/probabilistic_timed_automata/#More_List">More_List</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Stream_More">Stream_More</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Graphs">Graphs</a></li>
<li><a href="../theories/probabilistic_timed_automata/#Lib">Lib</a></li>
<li><a href="../theories/probabilistic_timed_automata/#PTA">PTA</a></li>
<li><a href="../theories/probabilistic_timed_automata/#PTA_Reachability">PTA_Reachability</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Markov_Models.html">Markov Models</a></li><li><a href="../entries/Timed_Automata.html">Timed Automata</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/MDP-Rewards.html">Markov Decision Processes with Rewards</a></li>
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<p style="display:none;" id="bibtex-filename">Probabilistic_Timed_Automata-AFP</p><pre id="copy-text">@article{Probabilistic_Timed_Automata-AFP,
author = {Simon Wimmer and Johannes Hölzl},
title = {Probabilistic Timed Automata},
journal = {Archive of Formal Proofs},
month = {May},
year = {2018},
note = {\url{https://isa-afp.org/entries/Probabilistic_Timed_Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Probabilistic_While.html b/web/entries/Probabilistic_While.html
--- a/web/entries/Probabilistic_While.html
+++ b/web/entries/Probabilistic_While.html
@@ -1,191 +1,193 @@
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<h1 >
<span class='first'>P</span>robabilistic <span class='first'>W</span>hile <span class='first'>L</span>oop</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">May 5, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This AFP entry defines a probabilistic while operator based on
sub-probability mass functions and formalises zero-one laws and variant
rules for probabilistic loop termination. As applications, we
implement probabilistic algorithms for the Bernoulli, geometric and
arbitrary uniform distributions that only use fair coin flips, and
prove them correct and terminating with probability 1.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>February 2, 2018</dt>
<dd>Added a proof that probabilistic conditioning can be implemented by repeated sampling.
(revision 305867c4e911)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Probabilistic_While</h3>
<ul>
<li><a href="../theories/probabilistic_while/#While_SPMF">While_SPMF</a></li>
<li><a href="../theories/probabilistic_while/#Bernoulli">Bernoulli</a></li>
<li><a href="../theories/probabilistic_while/#Geometric">Geometric</a></li>
<li><a href="../theories/probabilistic_while/#Fast_Dice_Roll">Fast_Dice_Roll</a></li>
<li><a href="../theories/probabilistic_while/#Resampling">Resampling</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/MFMC_Countable.html">A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/CryptHOL.html">CryptHOL</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Probabilistic_While-AFP</p><pre id="copy-text">@article{Probabilistic_While-AFP,
author = {Andreas Lochbihler},
title = {Probabilistic while loop},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Probabilistic_While.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Probabilistic_While-2017-05-11.tar.gz">May 11, 2017</a>: Isabelle2016-1
</li></ul>
</div>
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\ No newline at end of file
diff --git a/web/entries/Program-Conflict-Analysis.html b/web/entries/Program-Conflict-Analysis.html
--- a/web/entries/Program-Conflict-Analysis.html
+++ b/web/entries/Program-Conflict-Analysis.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors - Archive of Formal Proofs</title><meta name="description" content="In this work we formally verify the soundness and precision of a static program analysis that detects conflicts (e. g. data races) in programs with..."><meta property="og:title" content="Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors" />
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>C</span>onflict <span class='first'>A</span>nalysis of <span class='first'>P</span>rograms <span class='first'>W</span>ith <span class='first'>P</span>rocedures, <span class='first'>T</span>hread <span class='first'>C</span>reation, and <span class='first'>M</span>onitors</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/olm">Markus Müller-Olm</a> <a href="http://cs.uni-muenster.de/u/mmo/">🌐</a>
</p>
<p class="date">December 14, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work we formally verify the soundness and precision of a static program analysis that detects conflicts (e. g. data races) in programs with procedures, thread creation and monitors with the Isabelle theorem prover. As common in static program analysis, our program model abstracts guarded branching by nondeterministic branching, but completely interprets the call-/return behavior of procedures, synchronization by monitors, and thread creation. The analysis is based on the observation that all conflicts already occur in a class of particularly restricted schedules. These restricted schedules are suited to constraint-system-based program analysis. The formalization is based upon a flowgraph-based program model with an operational semantics as reference point.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Program-Conflict-Analysis</h3>
<ul>
<li><a href="../theories/program-conflict-analysis/#Misc">Misc</a></li>
<li><a href="../theories/program-conflict-analysis/#Interleave">Interleave</a></li>
<li><a href="../theories/program-conflict-analysis/#ConsInterleave">ConsInterleave</a></li>
<li><a href="../theories/program-conflict-analysis/#AcquisitionHistory">AcquisitionHistory</a></li>
<li><a href="../theories/program-conflict-analysis/#LTS">LTS</a></li>
<li><a href="../theories/program-conflict-analysis/#ThreadTracking">ThreadTracking</a></li>
<li><a href="../theories/program-conflict-analysis/#Flowgraph">Flowgraph</a></li>
<li><a href="../theories/program-conflict-analysis/#Semantics">Semantics</a></li>
<li><a href="../theories/program-conflict-analysis/#Normalization">Normalization</a></li>
<li><a href="../theories/program-conflict-analysis/#ConstraintSystems">ConstraintSystems</a></li>
<li><a href="../theories/program-conflict-analysis/#MainResult">MainResult</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Program-Conflict-Analysis-AFP</p><pre id="copy-text">@article{Program-Conflict-Analysis-AFP,
author = {Peter Lammich and Markus Müller-Olm},
title = {Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors},
journal = {Archive of Formal Proofs},
month = {December},
year = {2007},
note = {\url{https://isa-afp.org/entries/Program-Conflict-Analysis.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Program-Conflict-Analysis-2007-12-20.tar.gz">Dec 20, 2007</a>: Isabelle2007
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Progress_Tracking.html b/web/entries/Progress_Tracking.html
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>T</span>imely <span class='first'>D</span>ataflow's <span class='first'>P</span>rogress <span class='first'>T</span>racking <span class='first'>P</span>rotocol</h1>
<div>
<p><a href="../authors/brun">Matthias Brun</a>, <a href="../authors/decova">Sára Decova</a>, <a href="../authors/lattuada">Andrea Lattuada</a> <a href="https://andrea.lattuada.me">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">April 13, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Large-scale stream processing systems often follow the dataflow
paradigm, which enforces a program structure that exposes a high
degree of parallelism. The Timely Dataflow distributed system supports
expressive cyclic dataflows for which it offers low-latency data- and
pipeline-parallel stream processing. To achieve high expressiveness
and performance, Timely Dataflow uses an intricate distributed
protocol for tracking the computation’s progress. We formalize this
progress tracking protocol and verify its safety. Our formalization is
described in detail in our forthcoming <a
href="https://traytel.bitbucket.io/papers/itp21-progress_tracking/safe.pdf">ITP'21
paper</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Progress_Tracking</h3>
<ul>
<li><a href="../theories/progress_tracking/#Auxiliary">Auxiliary</a></li>
<li><a href="../theories/progress_tracking/#Exchange_Abadi">Exchange_Abadi</a></li>
<li><a href="../theories/progress_tracking/#Exchange">Exchange</a></li>
<li><a href="../theories/progress_tracking/#Antichain">Antichain</a></li>
<li><a href="../theories/progress_tracking/#Graph">Graph</a></li>
<li><a href="../theories/progress_tracking/#Propagate">Propagate</a></li>
<li><a href="../theories/progress_tracking/#Combined">Combined</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Progress_Tracking-AFP</p><pre id="copy-text">@article{Progress_Tracking-AFP,
author = {Matthias Brun and Sára Decova and Andrea Lattuada and Dmitriy Traytel},
title = {Formalization of Timely Dataflow&#39;s Progress Tracking Protocol},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/Progress_Tracking.html},
Formal proof development},
ISSN = {2150-914x},
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<h1 >
<span class='first'>P</span>rojective <span class='first'>G</span>eometry</h1>
<div>
<p><a href="../authors/bordg">Anthony Bordg</a> <a href="https://sites.google.com/site/anthonybordg/">🌐</a>
</p>
<p class="date">June 14, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the basics of projective geometry. In particular, we give
a proof of the so-called Hessenberg's theorem in projective plane
geometry. We also provide a proof of the so-called Desargues's
theorem based on an axiomatization of (higher) projective space
geometry using the notion of rank of a matroid. This last approach
allows to handle incidence relations in an homogeneous way dealing
only with points and without the need of talking explicitly about
lines, planes or any higher entity.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Projective_Geometry</h3>
<ul>
<li><a href="../theories/projective_geometry/#Projective_Plane_Axioms">Projective_Plane_Axioms</a></li>
<li><a href="../theories/projective_geometry/#Pappus_Property">Pappus_Property</a></li>
<li><a href="../theories/projective_geometry/#Pascal_Property">Pascal_Property</a></li>
<li><a href="../theories/projective_geometry/#Desargues_Property">Desargues_Property</a></li>
<li><a href="../theories/projective_geometry/#Pappus_Desargues">Pappus_Desargues</a></li>
<li><a href="../theories/projective_geometry/#Higher_Projective_Space_Rank_Axioms">Higher_Projective_Space_Rank_Axioms</a></li>
<li><a href="../theories/projective_geometry/#Matroid_Rank_Properties">Matroid_Rank_Properties</a></li>
<li><a href="../theories/projective_geometry/#Desargues_2D">Desargues_2D</a></li>
<li><a href="../theories/projective_geometry/#Desargues_3D">Desargues_3D</a></li>
<li><a href="../theories/projective_geometry/#Projective_Space_Axioms">Projective_Space_Axioms</a></li>
<li><a href="../theories/projective_geometry/#Higher_Projective_Space_Axioms">Higher_Projective_Space_Axioms</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Projective_Geometry-AFP</p><pre id="copy-text">@article{Projective_Geometry-AFP,
author = {Anthony Bordg},
title = {Projective Geometry},
journal = {Archive of Formal Proofs},
month = {June},
year = {2018},
note = {\url{https://isa-afp.org/entries/Projective_Geometry.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Geometry-2018-06-15.tar.gz">Jun 15, 2018</a>: Isabelle2017
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diff --git a/web/entries/Projective_Measurements.html b/web/entries/Projective_Measurements.html
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<h1 >
<span class='first'>Q</span>uantum <span class='first'>P</span>rojective <span class='first'>M</span>easurements and the <span class='first'>C</span><span class='first'>H</span><span class='first'>S</span><span class='first'>H</span> <span class='first'>I</span>nequality</h1>
<div>
<p><a href="../authors/echenim">Mnacho Echenim</a> <a href="https://lig-membres.imag.fr/mechenim/">🌐</a>
</p>
<p class="date">March 3, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work contains a formalization of quantum projective measurements,
also known as von Neumann measurements, which are based on elements of
spectral theory. We also formalized the CHSH inequality, an inequality
involving expectations in a probability space that is violated by
quantum measurements, thus proving that quantum mechanics cannot be modeled with an underlying local hidden-variable theory.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/quantum-computing">Computer science/Algorithms/Quantum computing</a></li><li><a href="../topics/mathematics/physics/quantum-information">Mathematics/Physics/Quantum information</a></li></ul>
<h3>Session Projective_Measurements</h3>
<ul>
<li><a href="../theories/projective_measurements/#Linear_Algebra_Complements">Linear_Algebra_Complements</a></li>
<li><a href="../theories/projective_measurements/#Projective_Measurements">Projective_Measurements</a></li>
<li><a href="../theories/projective_measurements/#CHSH_Inequality">CHSH_Inequality</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Isabelle_Marries_Dirac.html">Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</a></li><li><a href="../entries/QHLProver.html">Quantum Hoare Logic</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Commuting_Hermitian.html">Simultaneous diagonalization of pairwise commuting Hermitian matrices</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Projective_Measurements-AFP</p><pre id="copy-text">@article{Projective_Measurements-AFP,
author = {Mnacho Echenim},
title = {Quantum projective measurements and the CHSH inequality},
journal = {Archive of Formal Proofs},
month = {March},
year = {2021},
note = {\url{https://isa-afp.org/entries/Projective_Measurements.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Projective_Measurements-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Projective_Measurements-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Projective_Measurements-2021-03-09.tar.gz">Mar 9, 2021</a>: Isabelle2021
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diff --git a/web/entries/Promela.html b/web/entries/Promela.html
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@@ -1,212 +1,214 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Promela Formalization - Archive of Formal Proofs</title><meta name="description" content="We present an executable formalization of the language Promela, the
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<h1 >
<span class='first'>P</span>romela <span class='first'>F</span>ormalization</h1>
<div>
<p><a href="../authors/neumann">René Neumann</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJyZW5lIiwibmV1bWFubiJdfQ==">📧</a>
</p>
<p class="date">May 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an executable formalization of the language Promela, the
description language for models of the model checker SPIN. This
formalization is part of the work for a completely verified model
checker (CAVA), but also serves as a useful (and executable!)
description of the semantics of the language itself, something that is
currently missing.
The formalization uses three steps: It takes an abstract syntax tree
generated from an SML parser, removes syntactic sugar and enriches it
with type information. This further gets translated into a transition
system, on which the semantic engine (read: successor function) operates.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li></ul>
<h3>Session Promela</h3>
<ul>
<li><a href="../theories/promela/#PromelaStatistics">PromelaStatistics</a></li>
<li><a href="../theories/promela/#PromelaAST">PromelaAST</a></li>
<li><a href="../theories/promela/#PromelaDatastructures">PromelaDatastructures</a></li>
<li><a href="../theories/promela/#PromelaInvariants">PromelaInvariants</a></li>
<li><a href="../theories/promela/#Promela">Promela</a></li>
<li><a href="../theories/promela/#PromelaLTL">PromelaLTL</a></li>
<li><a href="../theories/promela/#PromelaLTLConv">PromelaLTLConv</a></li>
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<h3>Depends on</h3>
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<ul class="horizontal-list"><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Promela-AFP</p><pre id="copy-text">@article{Promela-AFP,
author = {René Neumann},
title = {Promela Formalization},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/Promela.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Promela-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Promela-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Promela-2014-05-29.tar.gz">May 29, 2014</a>: Isabelle2013-2
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<h1 >
<span class='first'>P</span>roof <span class='first'>S</span>trategy <span class='first'>L</span>anguage</h1>
<div>
<p><a href="../authors/nagashima">Yutaka Nagashima</a>
</p>
<p class="date">December 20, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle includes various automatic tools for finding proofs under
certain conditions. However, for each conjecture, knowing which
automation to use, and how to tweak its parameters, is currently
labour intensive. We have developed a language, PSL, designed to
capture high level proof strategies. PSL offloads the construction of
human-readable fast-to-replay proof scripts to automatic search,
making use of search-time information about each conjecture. Our
preliminary evaluations show that PSL reduces the labour cost of
interactive theorem proving. This submission contains the
implementation of PSL and an example theory file, Example.thy, showing
how to write poof strategies in PSL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Proof_Strategy_Language</h3>
<ul>
<li><a href="../theories/proof_strategy_language/#Try_Hard">Try_Hard</a></li>
<li><a href="../theories/proof_strategy_language/#PSL">PSL</a></li>
<li><a href="../theories/proof_strategy_language/#Example">Example</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Proof_Strategy_Language-AFP</p><pre id="copy-text">@article{Proof_Strategy_Language-AFP,
author = {Yutaka Nagashima},
title = {Proof Strategy Language},
journal = {Archive of Formal Proofs},
month = {December},
year = {2016},
note = {\url{https://isa-afp.org/entries/Proof_Strategy_Language.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Proof_Strategy_Language-2016-12-21.tar.gz">Dec 21, 2016</a>: Isabelle2016-1
</li></ul>
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diff --git a/web/entries/PropResPI.html b/web/entries/PropResPI.html
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@@ -1,202 +1,204 @@
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<h1 >
<span class='first'>P</span>ropositional <span class='first'>R</span>esolution and <span class='first'>P</span>rime <span class='first'>I</span>mplicates <span class='first'>G</span>eneration</h1>
<div>
<p><a href="../authors/peltier">Nicolas Peltier</a> <a href="http://membres-lig.imag.fr/peltier/">🌐</a>
</p>
<p class="date">March 11, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide formal proofs in Isabelle-HOL (using mostly structured Isar
proofs) of the soundness and completeness of the Resolution rule in
propositional logic. The completeness proofs take into account the
usual redundancy elimination rules (tautology elimination and
subsumption), and several refinements of the Resolution rule are
considered: ordered resolution (with selection functions), positive
and negative resolution, semantic resolution and unit resolution (the
latter refinement is complete only for clause sets that are Horn-
renamable). We also define a concrete procedure for computing
saturated sets and establish its soundness and completeness. The
clause sets are not assumed to be finite, so that the results can be
applied to formulas obtained by grounding sets of first-order clauses
(however, a total ordering among atoms is assumed to be given).
Next, we show that the unrestricted Resolution rule is deductive-
complete, in the sense that it is able to generate all (prime)
implicates of any set of propositional clauses (i.e., all entailment-
minimal, non-valid, clausal consequences of the considered set). The
generation of prime implicates is an important problem, with many
applications in artificial intelligence and verification (for
abductive reasoning, knowledge compilation, diagnosis, debugging
etc.). We also show that implicates can be computed in an incremental
way, by fixing an ordering among all the atoms in the considered sets
and resolving upon these atoms one by one in the considered order
(with no backtracking). This feature is critical for the efficient
computation of prime implicates. Building on these results, we provide
a procedure for computing such implicates and establish its soundness
and completeness.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session PropResPI</h3>
<ul>
<li><a href="../theories/proprespi/#Propositional_Resolution">Propositional_Resolution</a></li>
<li><a href="../theories/proprespi/#Prime_Implicates">Prime_Implicates</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">PropResPI-AFP</p><pre id="copy-text">@article{PropResPI-AFP,
author = {Nicolas Peltier},
title = {Propositional Resolution and Prime Implicates Generation},
journal = {Archive of Formal Proofs},
month = {March},
year = {2016},
note = {\url{https://isa-afp.org/entries/PropResPI.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-PropResPI-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-PropResPI-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-PropResPI-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-PropResPI-2016-03-11.tar.gz">Mar 11, 2016</a>: Isabelle2016
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diff --git a/web/entries/Propositional_Proof_Systems.html b/web/entries/Propositional_Proof_Systems.html
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<h1 >
<span class='first'>P</span>ropositional <span class='first'>P</span>roof <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 21, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a range of proof systems for classical propositional
logic (sequent calculus, natural deduction, Hilbert systems,
resolution) and prove the most important meta-theoretic results about
semantics and proofs: compactness, soundness, completeness,
translations between proof systems, cut-elimination, interpolation and
model existence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Propositional_Proof_Systems</h3>
<ul>
<li><a href="../theories/propositional_proof_systems/#Formulas">Formulas</a></li>
<li><a href="../theories/propositional_proof_systems/#Sema">Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#Substitution">Substitution</a></li>
<li><a href="../theories/propositional_proof_systems/#Substitution_Sema">Substitution_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#CNF">CNF</a></li>
<li><a href="../theories/propositional_proof_systems/#CNF_Formulas">CNF_Formulas</a></li>
<li><a href="../theories/propositional_proof_systems/#CNF_Sema">CNF_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#CNF_Formulas_Sema">CNF_Formulas_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#CNF_To_Formula">CNF_To_Formula</a></li>
<li><a href="../theories/propositional_proof_systems/#Tseytin">Tseytin</a></li>
<li><a href="../theories/propositional_proof_systems/#Tseytin_Sema">Tseytin_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#MiniFormulas">MiniFormulas</a></li>
<li><a href="../theories/propositional_proof_systems/#MiniFormulas_Sema">MiniFormulas_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#Consistency">Consistency</a></li>
<li><a href="../theories/propositional_proof_systems/#Compactness">Compactness</a></li>
<li><a href="../theories/propositional_proof_systems/#Compactness_Consistency">Compactness_Consistency</a></li>
<li><a href="../theories/propositional_proof_systems/#Sema_Craig">Sema_Craig</a></li>
<li><a href="../theories/propositional_proof_systems/#SC">SC</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Cut">SC_Cut</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Depth">SC_Depth</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Gentzen">SC_Gentzen</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Sema">SC_Sema</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Depth_Limit">SC_Depth_Limit</a></li>
<li><a href="../theories/propositional_proof_systems/#SC_Compl_Consistency">SC_Compl_Consistency</a></li>
<li><a href="../theories/propositional_proof_systems/#ND">ND</a></li>
<li><a href="../theories/propositional_proof_systems/#ND_Sound">ND_Sound</a></li>
<li><a href="../theories/propositional_proof_systems/#ND_Compl_Truthtable">ND_Compl_Truthtable</a></li>
<li><a href="../theories/propositional_proof_systems/#ND_Compl_Truthtable_Compact">ND_Compl_Truthtable_Compact</a></li>
<li><a href="../theories/propositional_proof_systems/#HC">HC</a></li>
<li><a href="../theories/propositional_proof_systems/#HC_Compl_Consistency">HC_Compl_Consistency</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution">Resolution</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution_Sound">Resolution_Sound</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution_Compl">Resolution_Compl</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution_Compl_Consistency">Resolution_Compl_Consistency</a></li>
<li><a href="../theories/propositional_proof_systems/#HCSC">HCSC</a></li>
<li><a href="../theories/propositional_proof_systems/#SCND">SCND</a></li>
<li><a href="../theories/propositional_proof_systems/#NDHC">NDHC</a></li>
<li><a href="../theories/propositional_proof_systems/#HCSCND">HCSCND</a></li>
<li><a href="../theories/propositional_proof_systems/#LSC">LSC</a></li>
<li><a href="../theories/propositional_proof_systems/#LSC_Resolution">LSC_Resolution</a></li>
<li><a href="../theories/propositional_proof_systems/#ND_FiniteAssms">ND_FiniteAssms</a></li>
<li><a href="../theories/propositional_proof_systems/#ND_Compl_SC">ND_Compl_SC</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution_Compl_SC_Small">Resolution_Compl_SC_Small</a></li>
<li><a href="../theories/propositional_proof_systems/#Resolution_Compl_SC_Full">Resolution_Compl_SC_Full</a></li>
<li><a href="../theories/propositional_proof_systems/#MiniSC">MiniSC</a></li>
<li><a href="../theories/propositional_proof_systems/#MiniSC_HC">MiniSC_HC</a></li>
<li><a href="../theories/propositional_proof_systems/#MiniSC_Craig">MiniSC_Craig</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/AI_Planning_Languages_Semantics.html">AI Planning Languages Semantics</a></li><li><a href="../entries/Verified_SAT_Based_AI_Planning.html">Verified SAT-Based AI Planning</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Propositional_Proof_Systems-AFP</p><pre id="copy-text">@article{Propositional_Proof_Systems-AFP,
author = {Julius Michaelis and Tobias Nipkow},
title = {Propositional Proof Systems},
journal = {Archive of Formal Proofs},
month = {June},
year = {2017},
note = {\url{https://isa-afp.org/entries/Propositional_Proof_Systems.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Propositional_Proof_Systems-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Propositional_Proof_Systems-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Prpu_Maxflow.html b/web/entries/Prpu_Maxflow.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Formalizing Push-Relabel Algorithms - Archive of Formal Proofs</title><meta name="description" content="We present a formalization of push-relabel algorithms for computing
the maximum flow in a network. We start with Goldberg&#39;s et
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<h1 >
<span class='first'>F</span>ormalizing <span class='first'>P</span>ush-<span class='first'>R</span>elabel <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/sefidgar">S. Reza Sefidgar</a>
</p>
<p class="date">June 1, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of push-relabel algorithms for computing
the maximum flow in a network. We start with Goldberg's et
al.~generic push-relabel algorithm, for which we show correctness and
the time complexity bound of O(V^2E). We then derive the
relabel-to-front and FIFO implementation. Using stepwise refinement
techniques, we derive an efficient verified implementation. Our
formal proof of the abstract algorithms closely follows a standard
textbook proof. It is accessible even without being an expert in
Isabelle/HOL, the interactive theorem prover used for the
formalization.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Prpu_Maxflow</h3>
<ul>
<li><a href="../theories/prpu_maxflow/#Generic_Push_Relabel">Generic_Push_Relabel</a></li>
<li><a href="../theories/prpu_maxflow/#Prpu_Common_Inst">Prpu_Common_Inst</a></li>
<li><a href="../theories/prpu_maxflow/#Fifo_Push_Relabel">Fifo_Push_Relabel</a></li>
<li><a href="../theories/prpu_maxflow/#Graph_Topological_Ordering">Graph_Topological_Ordering</a></li>
<li><a href="../theories/prpu_maxflow/#Relabel_To_Front">Relabel_To_Front</a></li>
<li><a href="../theories/prpu_maxflow/#Prpu_Common_Impl">Prpu_Common_Impl</a></li>
<li><a href="../theories/prpu_maxflow/#Fifo_Push_Relabel_Impl">Fifo_Push_Relabel_Impl</a></li>
<li><a href="../theories/prpu_maxflow/#Relabel_To_Front_Impl">Relabel_To_Front_Impl</a></li>
<li><a href="../theories/prpu_maxflow/#Generated_Code_Test">Generated_Code_Test</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li>
<li><a href="../entries/Solidity.html">Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</a></li>
<li><a href="../entries/BTree.html">A Verified Imperative Implementation of B-Trees</a></li>
<li><a href="../entries/Pop_Refinement.html">Pop-Refinement</a></li>
<li><a href="../entries/Psi_Calculi.html">Psi-calculi in Isabelle</a></li>
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<p style="display:none;" id="bibtex-filename">Prpu_Maxflow-AFP</p><pre id="copy-text">@article{Prpu_Maxflow-AFP,
author = {Peter Lammich and S. Reza Sefidgar},
title = {Formalizing Push-Relabel Algorithms},
journal = {Archive of Formal Proofs},
month = {June},
year = {2017},
note = {\url{https://isa-afp.org/entries/Prpu_Maxflow.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Prpu_Maxflow-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/PseudoHoops.html b/web/entries/PseudoHoops.html
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<h1 >
<span class='first'>P</span>seudo <span class='first'>H</span>oops</h1>
<div>
<p><a href="../authors/georgescu">George Georgescu</a>, <a href="../authors/leustean">Laurentiu Leustean</a> and <a href="../authors/preoteasa">Viorel Preoteasa</a> <a href="http://users.abo.fi/vpreotea/">🌐</a>
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<p class="date">September 22, 2011</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Pseudo-hoops are algebraic structures introduced by B. Bosbach under the name of complementary semigroups. In this formalization we prove some properties of pseudo-hoops and we define the basic concepts of filter and normal filter. The lattice of normal filters is isomorphic with the lattice of congruences of a pseudo-hoop. We also study some important classes of pseudo-hoops. Bounded Wajsberg pseudo-hoops are equivalent to pseudo-Wajsberg algebras and bounded basic pseudo-hoops are equivalent to pseudo-BL algebras. Some examples of pseudo-hoops are given in the last section of the formalization.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session PseudoHoops</h3>
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<li><a href="../theories/pseudohoops/#Operations">Operations</a></li>
<li><a href="../theories/pseudohoops/#LeftComplementedMonoid">LeftComplementedMonoid</a></li>
<li><a href="../theories/pseudohoops/#RightComplementedMonoid">RightComplementedMonoid</a></li>
<li><a href="../theories/pseudohoops/#PseudoHoops">PseudoHoops</a></li>
<li><a href="../theories/pseudohoops/#PseudoHoopFilters">PseudoHoopFilters</a></li>
<li><a href="../theories/pseudohoops/#PseudoWaisbergAlgebra">PseudoWaisbergAlgebra</a></li>
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<h3>Depends on</h3>
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<p style="display:none;" id="bibtex-filename">PseudoHoops-AFP</p><pre id="copy-text">@article{PseudoHoops-AFP,
author = {George Georgescu and Laurentiu Leustean and Viorel Preoteasa},
title = {Pseudo Hoops},
journal = {Archive of Formal Proofs},
month = {September},
year = {2011},
note = {\url{https://isa-afp.org/entries/PseudoHoops.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-PseudoHoops-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-PseudoHoops-2011-09-27.tar.gz">Sep 27, 2011</a>: Isabelle2011
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diff --git a/web/entries/Psi_Calculi.html b/web/entries/Psi_Calculi.html
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<h1 >
<span class='first'>P</span>si-<span class='first'>C</span>alculi in <span class='first'>I</span>sabelle</h1>
<div>
<p><a href="../authors/bengtson">Jesper Bengtson</a> <a href="http://www.itu.dk/people/jebe">🌐</a>
</p>
<p class="date">May 29, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Psi-calculi are extensions of the pi-calculus, accommodating arbitrary nominal datatypes to represent not only data but also communication channels, assertions and conditions, giving it an expressive power beyond the applied pi-calculus and the concurrent constraint pi-calculus.
<p>
We have formalised psi-calculi in the interactive theorem prover Isabelle using its nominal datatype package. One distinctive feature is that the framework needs to treat binding sequences, as opposed to single binders, in an efficient way. While different methods for formalising single binder calculi have been proposed over the last decades, representations for such binding sequences are not very well explored.
<p>
The main effort in the formalisation is to keep the machine checked proofs as close to their pen-and-paper counterparts as possible. This includes treating all binding sequences as atomic elements, and creating custom induction and inversion rules that to remove the bulk of manual alpha-conversions.
<p>
This entry is described in detail in <a href="http://www.itu.dk/people/jebe/files/thesis.pdf">Bengtson's thesis</a>.</div>
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<ul><li><a href="../topics/computer-science/concurrency/process-calculi">Computer science/Concurrency/Process calculi</a></li></ul>
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<li><a href="../theories/psi_calculi/#Close_Subst">Close_Subst</a></li>
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<p style="display:none;" id="bibtex-filename">Psi_Calculi-AFP</p><pre id="copy-text">@article{Psi_Calculi-AFP,
author = {Jesper Bengtson},
title = {Psi-calculi in Isabelle},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Psi_Calculi.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Psi_Calculi-2012-06-14.tar.gz">Jun 14, 2012</a>: Isabelle2012
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<h1 >
<span class='first'>P</span>tolemy's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">August 7, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides an analytic proof to Ptolemy's Theorem using
polar form transformation and trigonometric identities.
In this formalization, we use ideas from John Harrison's HOL Light
formalization and the proof sketch on the Wikipedia entry of Ptolemy's Theorem.
This theorem is the 95th theorem of the Top 100 Theorems list.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Ptolemys_Theorem</h3>
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<p style="display:none;" id="bibtex-filename">Ptolemys_Theorem-AFP</p><pre id="copy-text">@article{Ptolemys_Theorem-AFP,
author = {Lukas Bulwahn},
title = {Ptolemy&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/Ptolemys_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Public_Announcement_Logic.html b/web/entries/Public_Announcement_Logic.html
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<h1 >
<span class='first'>P</span>ublic <span class='first'>A</span>nnouncement <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/from">Asta Halkjær From</a> <a href="https://people.compute.dtu.dk/ahfrom/">🌐</a>
</p>
<p class="date">June 17, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of public announcement logic with
countably many agents. It includes proofs of soundness and
completeness for a variant of the axiom system PA + DIST! + NEC!. The
completeness proof builds on the Epistemic Logic theory.
Paper: <a href="https://doi.org/10.1007/978-3-030-90138-7_2">doi.org/10.1007/978-3-030-90138-7_2</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session Public_Announcement_Logic</h3>
<ul>
<li><a href="../theories/public_announcement_logic/#PAL">PAL</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Epistemic_Logic.html">Epistemic Logic: Completeness of Modal Logics</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Stalnaker_Logic.html">Stalnaker&rsquo;s Epistemic Logic</a></li>
<li><a href="../entries/PAL.html">Automating Public Announcement Logic and the Wise Men Puzzle in Isabelle/HOL</a></li>
<li><a href="../entries/Verified-Prover.html">A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic</a></li>
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<p style="display:none;" id="bibtex-filename">Public_Announcement_Logic-AFP</p><pre id="copy-text">@article{Public_Announcement_Logic-AFP,
author = {Asta Halkjær From},
title = {Public Announcement Logic},
journal = {Archive of Formal Proofs},
month = {June},
year = {2021},
note = {\url{https://isa-afp.org/entries/Public_Announcement_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Public_Announcement_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/QHLProver.html b/web/entries/QHLProver.html
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<h1 >
<span class='first'>Q</span>uantum <span class='first'>H</span>oare <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/liu">Junyi Liu</a>, <a href="../authors/zhan">Bohua Zhan</a> <a href="http://lcs.ios.ac.cn/~bzhan/">🌐</a>, <a href="../authors/wang">Shuling Wang</a>, <a href="../authors/ying">Shenggang Ying</a>, <a href="../authors/liut">Tao Liu</a>, <a href="../authors/liy">Yangjia Li</a>, <a href="../authors/yingm">Mingsheng Ying</a> and <a href="../authors/zhann">Naijun Zhan</a>
</p>
<p class="date">March 24, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize quantum Hoare logic as given in [1]. In particular, we
specify the syntax and denotational semantics of a simple model of
quantum programs. Then, we write down the rules of quantum Hoare logic
for partial correctness, and show the soundness and completeness of
the resulting proof system. As an application, we verify the
correctness of Grover’s algorithm.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
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<li><a href="../theories/qhlprover/#Complex_Matrix">Complex_Matrix</a></li>
<li><a href="../theories/qhlprover/#Matrix_Limit">Matrix_Limit</a></li>
<li><a href="../theories/qhlprover/#Quantum_Program">Quantum_Program</a></li>
<li><a href="../theories/qhlprover/#Partial_State">Partial_State</a></li>
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<ul class="horizontal-list"><li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Projective_Measurements.html">Quantum projective measurements and the CHSH inequality</a></li></ul>
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<li><a href="../entries/TESL_Language.html">A Formal Development of a Polychronous Polytimed Coordination Language</a></li>
<li><a href="../entries/HyperCTL.html">A shallow embedding of HyperCTL*</a></li>
<li><a href="../entries/Launchbury.html">The Correctness of Launchbury&rsquo;s Natural Semantics for Lazy Evaluation</a></li>
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<p style="display:none;" id="bibtex-filename">QHLProver-AFP</p><pre id="copy-text">@article{QHLProver-AFP,
author = {Junyi Liu and Bohua Zhan and Shuling Wang and Shenggang Ying and Tao Liu and Yangjia Li and Mingsheng Ying and Naijun Zhan},
title = {Quantum Hoare Logic},
journal = {Archive of Formal Proofs},
month = {March},
year = {2019},
note = {\url{https://isa-afp.org/entries/QHLProver.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-QHLProver-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-QHLProver-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-QHLProver-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-QHLProver-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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diff --git a/web/entries/QR_Decomposition.html b/web/entries/QR_Decomposition.html
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<h1 >
<span class='first'>Q</span><span class='first'>R</span> <span class='first'>D</span>ecomposition</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>
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<p class="date">February 12, 2015</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">QR decomposition is an algorithm to decompose a real matrix A into the product of two other matrices Q and R, where Q is orthogonal and R is invertible and upper triangular. The algorithm is useful for the least squares problem; i.e., the computation of the best approximation of an unsolvable system of linear equations. As a side-product, the Gram-Schmidt process has also been formalized. A refinement using immutable arrays is presented as well. The development relies, among others, on the AFP entry "Implementing field extensions of the form Q[sqrt(b)]" by René Thiemann, which allows execution of the algorithm using symbolic computations. Verified code can be generated and executed using floats as well.</div>
<h3>License</h3>
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<dl><dt>June 18, 2015</dt>
<dd>The second part of the Fundamental Theorem of Linear Algebra has been generalized to more general inner product spaces.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session QR_Decomposition</h3>
<ul>
<li><a href="../theories/qr_decomposition/#Miscellaneous_QR">Miscellaneous_QR</a></li>
<li><a href="../theories/qr_decomposition/#Projections">Projections</a></li>
<li><a href="../theories/qr_decomposition/#Gram_Schmidt">Gram_Schmidt</a></li>
<li><a href="../theories/qr_decomposition/#QR_Decomposition">QR_Decomposition</a></li>
<li><a href="../theories/qr_decomposition/#Least_Squares_Approximation">Least_Squares_Approximation</a></li>
<li><a href="../theories/qr_decomposition/#Examples_QR_Abstract_Float">Examples_QR_Abstract_Float</a></li>
<li><a href="../theories/qr_decomposition/#Examples_QR_Abstract_Symbolic">Examples_QR_Abstract_Symbolic</a></li>
<li><a href="../theories/qr_decomposition/#IArray_Addenda_QR">IArray_Addenda_QR</a></li>
<li><a href="../theories/qr_decomposition/#Matrix_To_IArray_QR">Matrix_To_IArray_QR</a></li>
<li><a href="../theories/qr_decomposition/#Gram_Schmidt_IArrays">Gram_Schmidt_IArrays</a></li>
<li><a href="../theories/qr_decomposition/#QR_Decomposition_IArrays">QR_Decomposition_IArrays</a></li>
<li><a href="../theories/qr_decomposition/#Examples_QR_IArrays_Float">Examples_QR_IArrays_Float</a></li>
<li><a href="../theories/qr_decomposition/#Examples_QR_IArrays_Symbolic">Examples_QR_IArrays_Symbolic</a></li>
<li><a href="../theories/qr_decomposition/#Generalizations2">Generalizations2</a></li>
<li><a href="../theories/qr_decomposition/#QR_Efficient">QR_Efficient</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li><li><a href="../entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></li><li><a href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></li><li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Echelon_Form.html">Echelon Form</a></li>
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<p style="display:none;" id="bibtex-filename">QR_Decomposition-AFP</p><pre id="copy-text">@article{QR_Decomposition-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {QR Decomposition},
journal = {Archive of Formal Proofs},
month = {February},
year = {2015},
note = {\url{https://isa-afp.org/entries/QR_Decomposition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Quantales.html b/web/entries/Quantales.html
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@@ -1,183 +1,185 @@
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<h1 >
<span class='first'>Q</span>uantales</h1>
<div>
<p><a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">December 11, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These mathematical components formalise basic properties of quantales,
together with some important models, constructions, and concepts,
including quantic nuclei and conuclei.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Quantales</h3>
<ul>
<li><a href="../theories/quantales/#Dioid_Models_New">Dioid_Models_New</a></li>
<li><a href="../theories/quantales/#Quantales">Quantales</a></li>
<li><a href="../theories/quantales/#Quantale_Star">Quantale_Star</a></li>
<li><a href="../theories/quantales/#Quantale_Modules">Quantale_Modules</a></li>
<li><a href="../theories/quantales/#Quantale_Models">Quantale_Models</a></li>
<li><a href="../theories/quantales/#Quantic_Nuclei_Conuclei">Quantic_Nuclei_Conuclei</a></li>
<li><a href="../theories/quantales/#Quantale_Left_Sided">Quantale_Left_Sided</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li><li><a href="../entries/Order_Lattice_Props.html">Properties of Orderings and Lattices</a></li></ul>
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<ul class="horizontal-list"><li><a href="../entries/Transformer_Semantics.html">Transformer Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Quantales-AFP</p><pre id="copy-text">@article{Quantales-AFP,
author = {Georg Struth},
title = {Quantales},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Quantales.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>Q</span>uasi-<span class='first'>B</span>orel <span class='first'>S</span>paces</h1>
<div>
<p><a href="../authors/hirata">Michikazu Hirata</a>, <a href="../authors/minamide">Yasuhiko Minamide</a> <a href="https://sv.c.titech.ac.jp/minamide/index.en.html">🌐</a> and <a href="../authors/sato">Tetsuya Sato</a> <a href="https://sites.google.com/view/tetsuyasato/">🌐</a>
</p>
<p class="date">February 3, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The notion of quasi-Borel spaces was introduced by <a
href="https://dl.acm.org/doi/10.5555/3329995.3330072">
Heunen et al</a>. The theory provides a suitable
denotational model for higher-order probabilistic programming
languages with continuous distributions. This entry is a formalization
of the theory of quasi-Borel spaces, including construction of
quasi-Borel spaces (product, coproduct, function spaces), the
adjunction between the category of measurable spaces and the category
of quasi-Borel spaces, and the probability monad on quasi-Borel
spaces. This entry also contains the formalization of the Bayesian
regression presented in the work of Heunen et al. This work is a part
of the work by same authors, <i>Program Logic for Higher-Order
Probabilistic Programs in Isabelle/HOL</i>, which will be
published in the proceedings of the 16th International Symposium on
Functional and Logic Programming (FLOPS 2022).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Quasi_Borel_Spaces</h3>
<ul>
<li><a href="../theories/quasi_borel_spaces/#StandardBorel">StandardBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#QuasiBorel">QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Measure_QuasiBorel_Adjunction">Measure_QuasiBorel_Adjunction</a></li>
<li><a href="../theories/quasi_borel_spaces/#Binary_Product_QuasiBorel">Binary_Product_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Product_QuasiBorel">Product_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Binary_CoProduct_QuasiBorel">Binary_CoProduct_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#CoProduct_QuasiBorel">CoProduct_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Exponent_QuasiBorel">Exponent_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Probability_Space_QuasiBorel">Probability_Space_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Monad_QuasiBorel">Monad_QuasiBorel</a></li>
<li><a href="../theories/quasi_borel_spaces/#Pair_QuasiBorel_Measure">Pair_QuasiBorel_Measure</a></li>
<li><a href="../theories/quasi_borel_spaces/#Measure_as_QuasiBorel_Measure">Measure_as_QuasiBorel_Measure</a></li>
<li><a href="../theories/quasi_borel_spaces/#Bayesian_Linear_Regression">Bayesian_Linear_Regression</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Quasi_Borel_Spaces-AFP</p><pre id="copy-text">@article{Quasi_Borel_Spaces-AFP,
author = {Michikazu Hirata and Yasuhiko Minamide and Tetsuya Sato},
title = {Quasi-Borel Spaces},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/Quasi_Borel_Spaces.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Quasi_Borel_Spaces-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Quasi_Borel_Spaces-2022-02-04.tar.gz">Feb 4, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Quaternions.html b/web/entries/Quaternions.html
--- a/web/entries/Quaternions.html
+++ b/web/entries/Quaternions.html
@@ -1,177 +1,179 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Quaternions - Archive of Formal Proofs</title><meta name="description" content="This theory is inspired by the HOL Light development of quaternions,
but follows its own route. Quaternions are developed coinductively, as
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<h1 >
<span class='first'>Q</span>uaternions</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">September 5, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory is inspired by the HOL Light development of quaternions,
but follows its own route. Quaternions are developed coinductively, as
in the existing formalisation of the complex numbers. Quaternions are
quickly shown to belong to the type classes of real normed division
algebras and real inner product spaces. And therefore they inherit a
great body of facts involving algebraic laws, limits, continuity,
etc., which must be proved explicitly in the HOL Light version. The
development concludes with the geometric interpretation of the product
of imaginary quaternions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Quaternions</h3>
<ul>
<li><a href="../theories/quaternions/#Quaternions">Quaternions</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Quaternions-AFP</p><pre id="copy-text">@article{Quaternions-AFP,
author = {Lawrence C. Paulson},
title = {Quaternions},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Quaternions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Quaternions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Quaternions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Quaternions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Quaternions-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Quaternions-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Quaternions-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Quaternions-2018-09-07.tar.gz">Sep 7, 2018</a>: Isabelle2018
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Query_Optimization.html b/web/entries/Query_Optimization.html
--- a/web/entries/Query_Optimization.html
+++ b/web/entries/Query_Optimization.html
@@ -1,180 +1,185 @@
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consisting of the definitions of selectivities, query graphs, join
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<h1 >
<span class='first'>V</span>erification of <span class='first'>Q</span>uery <span class='first'>O</span>ptimization <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/stevens">Lukas Stevens</a> <a href="https://www21.in.tum.de/team/stevensl">🌐</a> and <a href="../authors/stoeckl">Bernhard Stöckl</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJzdG9lY2tsIl19">📧</a>
</p>
<p class="date">October 4, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalization includes a general framework for query optimization
consisting of the definitions of selectivities, query graphs, join
trees, and cost functions. Furthermore, it implements the join
ordering algorithm IKKBZ using these definitions. It verifies the
correctness of these definitions and proves that IKKBZ produces an
optimal solution within a restricted solution space.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-management-systems">Computer science/Data management systems</a></li></ul>
<h3>Session Query_Optimization</h3>
<ul>
<li><a href="../theories/query_optimization/#Misc">Misc</a></li>
<li><a href="../theories/query_optimization/#Graph_Theory_Batteries">Graph_Theory_Batteries</a></li>
<li><a href="../theories/query_optimization/#Graph_Definitions">Graph_Definitions</a></li>
<li><a href="../theories/query_optimization/#Shortest_Path_Tree">Shortest_Path_Tree</a></li>
<li><a href="../theories/query_optimization/#Selectivities">Selectivities</a></li>
<li><a href="../theories/query_optimization/#JoinTree">JoinTree</a></li>
<li><a href="../theories/query_optimization/#CostFunctions">CostFunctions</a></li>
<li><a href="../theories/query_optimization/#Graph_Additions">Graph_Additions</a></li>
<li><a href="../theories/query_optimization/#QueryGraph">QueryGraph</a></li>
<li><a href="../theories/query_optimization/#Directed_Tree_Additions">Directed_Tree_Additions</a></li>
<li><a href="../theories/query_optimization/#Dtree">Dtree</a></li>
<li><a href="../theories/query_optimization/#List_Dtree">List_Dtree</a></li>
<li><a href="../theories/query_optimization/#IKKBZ">IKKBZ</a></li>
<li><a href="../theories/query_optimization/#IKKBZ_Optimality">IKKBZ_Optimality</a></li>
<li><a href="../theories/query_optimization/#IKKBZ_Examples">IKKBZ_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Graph_Theory.html">Graph Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Query_Optimization-AFP</p><pre id="copy-text">@article{Query_Optimization-AFP,
author = {Lukas Stevens and Bernhard Stöckl},
title = {Verification of Query Optimization Algorithms},
journal = {Archive of Formal Proofs},
month = {October},
year = {2022},
note = {\url{https://isa-afp.org/entries/Query_Optimization.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Query_Optimization-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Query_Optimization-2022-10-05.tar.gz">Oct 5, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Quick_Sort_Cost.html b/web/entries/Quick_Sort_Cost.html
--- a/web/entries/Quick_Sort_Cost.html
+++ b/web/entries/Quick_Sort_Cost.html
@@ -1,201 +1,203 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The number of comparisons in QuickSort - Archive of Formal Proofs</title><meta name="description" content="We give a formal proof of the well-known results about the number of comparisons performed by two variants of QuickSort: first, the expected number of..."><meta property="og:title" content="The number of comparisons in QuickSort" />
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<h1 >
<span class='first'>T</span>he <span class='first'>N</span>umber of <span class='first'>C</span>omparisons in <span class='first'>Q</span>uick<span class='first'>S</span>ort</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">March 15, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>We give a formal proof of the well-known results about the
number of comparisons performed by two variants of QuickSort: first,
the expected number of comparisons of randomised QuickSort
(i.&thinsp;e.&nbsp;QuickSort with random pivot choice) is
<em>2&thinsp;(n+1)&thinsp;H<sub>n</sub> -
4&thinsp;n</em>, which is asymptotically equivalent to
<em>2&thinsp;n ln n</em>; second, the number of
comparisons performed by the classic non-randomised QuickSort has the
same distribution in the average case as the randomised one.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Quick_Sort_Cost</h3>
<ul>
<li><a href="../theories/quick_sort_cost/#Randomised_Quick_Sort">Randomised_Quick_Sort</a></li>
<li><a href="../theories/quick_sort_cost/#Quick_Sort_Average_Case">Quick_Sort_Average_Case</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Comparison_Sort_Lower_Bound.html">Lower bound on comparison-based sorting algorithms</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Random_BSTs.html">Expected Shape of Random Binary Search Trees</a></li></ul>
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<li><a href="../entries/Cartan_FP.html">The Cartan Fixed Point Theorems</a></li>
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<p style="display:none;" id="bibtex-filename">Quick_Sort_Cost-AFP</p><pre id="copy-text">@article{Quick_Sort_Cost-AFP,
author = {Manuel Eberl},
title = {The number of comparisons in QuickSort},
journal = {Archive of Formal Proofs},
month = {March},
year = {2017},
note = {\url{https://isa-afp.org/entries/Quick_Sort_Cost.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/RIPEMD-160-SPARK.html b/web/entries/RIPEMD-160-SPARK.html
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<h1 >
<span class='first'>R</span><span class='first'>I</span><span class='first'>P</span><span class='first'>E</span><span class='first'>M</span><span class='first'>D</span>-160</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJpbW1sZXIiXX0=">📧</a>
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<p class="date">January 10, 2011</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work presents a verification of an implementation in SPARK/ADA of the cryptographic hash-function RIPEMD-160. A functional specification of RIPEMD-160 is given in Isabelle/HOL. Proofs for the verification conditions generated by the static-analysis toolset of SPARK certify the functional correctness of the implementation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>November 9, 2015</dt>
<dd>Entry is now obsolete, moved to Isabelle distribution.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session RIPEMD-160-SPARK</h3>
<ul>
<li><a href="../theories/ripemd-160-spark/#RIPEMD_160_SPARK">RIPEMD_160_SPARK</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">RIPEMD-160-SPARK-AFP</p><pre id="copy-text">@article{RIPEMD-160-SPARK-AFP,
author = {Fabian Immler},
title = {RIPEMD-160},
journal = {Archive of Formal Proofs},
month = {January},
year = {2011},
note = {\url{https://isa-afp.org/entries/RIPEMD-160-SPARK.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/ROBDD.html b/web/entries/ROBDD.html
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<h1 >
<span class='first'>A</span>lgorithms for <span class='first'>R</span>educed <span class='first'>O</span>rdered <span class='first'>B</span>inary <span class='first'>D</span>ecision <span class='first'>D</span>iagrams</h1>
<div>
<p><a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a>, <a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a>, <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">April 27, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a verified and executable implementation of ROBDDs in
Isabelle/HOL. Our implementation relates pointer-based computation in
the Heap monad to operations on an abstract definition of boolean
functions. Internally, we implemented the if-then-else combinator in a
recursive fashion, following the Shannon decomposition of the argument
functions. The implementation mixes and adapts known techniques and is
built with efficiency in mind.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session ROBDD</h3>
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<li><a href="../theories/robdd/#Level_Collapse">Level_Collapse</a></li>
<li><a href="../theories/robdd/#BDD_Examples">BDD_Examples</a></li>
<li><a href="../theories/robdd/#BDD_Code">BDD_Code</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Simplicial_complexes_and_boolean_functions.html">Simplicial Complexes and Boolean functions</a></li></ul>
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author = {Julius Michaelis and Max W. Haslbeck and Peter Lammich and Lars Hupel},
title = {Algorithms for Reduced Ordered Binary Decision Diagrams},
journal = {Archive of Formal Proofs},
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year = {2016},
note = {\url{https://isa-afp.org/entries/ROBDD.html},
Formal proof development},
ISSN = {2150-914x},
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diff --git a/web/entries/RSAPSS.html b/web/entries/RSAPSS.html
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<h1 >
<span class='first'>S</span><span class='first'>H</span><span class='first'>A</span>1, <span class='first'>R</span><span class='first'>S</span><span class='first'>A</span>, <span class='first'>P</span><span class='first'>S</span><span class='first'>S</span> and <span class='first'>M</span>ore</h1>
<div>
<p><a href="../authors/lindenberg">Christina Lindenberg</a> and <a href="../authors/wirt">Kai Wirt</a>
</p>
<p class="date">May 2, 2005</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Formal verification is getting more and more important in computer science. However the state of the art formal verification methods in cryptography are very rudimentary. These theories are one step to provide a tool box allowing the use of formal methods in every aspect of cryptography. Moreover we present a proof of concept for the feasibility of verification techniques to a standard signature algorithm.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li></ul>
<h3>Session RSAPSS</h3>
<ul>
<li><a href="../theories/rsapss/#Word">Word</a></li>
<li><a href="../theories/rsapss/#WordOperations">WordOperations</a></li>
<li><a href="../theories/rsapss/#SHA1Padding">SHA1Padding</a></li>
<li><a href="../theories/rsapss/#SHA1">SHA1</a></li>
<li><a href="../theories/rsapss/#Wordarith">Wordarith</a></li>
<li><a href="../theories/rsapss/#EMSAPSS">EMSAPSS</a></li>
<li><a href="../theories/rsapss/#Mod">Mod</a></li>
<li><a href="../theories/rsapss/#Crypt">Crypt</a></li>
<li><a href="../theories/rsapss/#Pdifference">Pdifference</a></li>
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<li><a href="../theories/rsapss/#Cryptinverts">Cryptinverts</a></li>
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<p style="display:none;" id="bibtex-filename">RSAPSS-AFP</p><pre id="copy-text">@article{RSAPSS-AFP,
author = {Christina Lindenberg and Kai Wirt},
title = {SHA1, RSA, PSS and more},
journal = {Archive of Formal Proofs},
month = {May},
year = {2005},
note = {\url{https://isa-afp.org/entries/RSAPSS.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Ramsey-Infinite.html b/web/entries/Ramsey-Infinite.html
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<h1 >
<span class='first'>R</span>amsey's <span class='first'>T</span>heorem, <span class='first'>I</span>nfinitary <span class='first'>V</span>ersion</h1>
<div>
<p><a href="../authors/ridge">Tom Ridge</a>
</p>
<p class="date">September 20, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalization of Ramsey's theorem (infinitary version) is taken from Boolos and Jeffrey, <i>Computability and Logic</i>, 3rd edition, Chapter 26. It differs slightly from the text by assuming a slightly stronger hypothesis. In particular, the induction hypothesis is stronger, holding for any infinite subset of the naturals. This avoids the rather peculiar mapping argument between kj and aikj on p.263, which is unnecessary and slightly mars this really beautiful result.</div>
<h3>License</h3>
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<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Ramsey-Infinite</h3>
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<li><a href="../theories/ramsey-infinite/#Ramsey">Ramsey</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Ramsey-Infinite-AFP</p><pre id="copy-text">@article{Ramsey-Infinite-AFP,
author = {Tom Ridge},
title = {Ramsey&#39;s theorem, infinitary version},
journal = {Archive of Formal Proofs},
month = {September},
year = {2004},
note = {\url{https://isa-afp.org/entries/Ramsey-Infinite.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Expected Shape of Random Binary Search Trees - Archive of Formal Proofs</title><meta name="description" content="This entry contains proofs for the textbook results about the distributions of the height and internal path length of random binary search trees (BSTs),..."><meta property="og:title" content="Expected Shape of Random Binary Search Trees" />
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<h1 >
<span class='first'>E</span>xpected <span class='first'>S</span>hape of <span class='first'>R</span>andom <span class='first'>B</span>inary <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">April 4, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry contains proofs for the textbook results about the
distributions of the height and internal path length of random binary
search trees (BSTs), i.&thinsp;e. BSTs that are formed by taking
an empty BST and inserting elements from a fixed set in random
order.</p> <p>In particular, we prove a logarithmic upper
bound on the expected height and the <em>Θ(n log n)</em>
closed-form solution for the expected internal path length in terms of
the harmonic numbers. We also show how the internal path length
relates to the average-case cost of a lookup in a BST.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Random_BSTs</h3>
<ul>
<li><a href="../theories/random_bsts/#Random_BSTs">Random_BSTs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li><li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Randomised_BSTs.html">Randomised Binary Search Trees</a></li><li><a href="../entries/Treaps.html">Treaps</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<p style="display:none;" id="bibtex-filename">Random_BSTs-AFP</p><pre id="copy-text">@article{Random_BSTs-AFP,
author = {Manuel Eberl},
title = {Expected Shape of Random Binary Search Trees},
journal = {Archive of Formal Proofs},
month = {April},
year = {2017},
note = {\url{https://isa-afp.org/entries/Random_BSTs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Random_Graph_Subgraph_Threshold.html b/web/entries/Random_Graph_Subgraph_Threshold.html
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<h1 >
<span class='first'>P</span>roperties of <span class='first'>R</span>andom <span class='first'>G</span>raphs -- <span class='first'>S</span>ubgraph <span class='first'>C</span>ontainment</h1>
<div>
<p><a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
</p>
<p class="date">February 13, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Random graphs are graphs with a fixed number of vertices, where each edge is present with a fixed probability. We are interested in the probability that a random graph contains a certain pattern, for example a cycle or a clique. A very high edge probability gives rise to perhaps too many edges (which degrades performance for many algorithms), whereas a low edge probability might result in a disconnected graph. We prove a theorem about a threshold probability such that a higher edge probability will asymptotically almost surely produce a random graph with the desired subgraph.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Random_Graph_Subgraph_Threshold</h3>
<ul>
<li><a href="../theories/random_graph_subgraph_threshold/#Ugraph_Misc">Ugraph_Misc</a></li>
<li><a href="../theories/random_graph_subgraph_threshold/#Prob_Lemmas">Prob_Lemmas</a></li>
<li><a href="../theories/random_graph_subgraph_threshold/#Ugraph_Lemmas">Ugraph_Lemmas</a></li>
<li><a href="../theories/random_graph_subgraph_threshold/#Ugraph_Properties">Ugraph_Properties</a></li>
<li><a href="../theories/random_graph_subgraph_threshold/#Subgraph_Threshold">Subgraph_Threshold</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Roth_Arithmetic_Progressions.html">Roth&rsquo;s Theorem on Arithmetic Progressions</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Random_Graph_Subgraph_Threshold-AFP</p><pre id="copy-text">@article{Random_Graph_Subgraph_Threshold-AFP,
author = {Lars Hupel},
title = {Properties of Random Graphs -- Subgraph Containment},
journal = {Archive of Formal Proofs},
month = {February},
year = {2014},
note = {\url{https://isa-afp.org/entries/Random_Graph_Subgraph_Threshold.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Random_Graph_Subgraph_Threshold-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Random_Graph_Subgraph_Threshold-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Random_Graph_Subgraph_Threshold-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Random_Graph_Subgraph_Threshold-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Random_Graph_Subgraph_Threshold-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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@@ -1,186 +1,188 @@
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<h1 >
<span class='first'>R</span>andomised <span class='first'>B</span>inary <span class='first'>S</span>earch <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">October 19, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This work is a formalisation of the Randomised Binary Search
Trees introduced by Martínez and Roura, including definitions and
correctness proofs.</p> <p>Like randomised treaps, they
are a probabilistic data structure that behaves exactly as if elements
were inserted into a non-balancing BST in random order. However,
unlike treaps, they only use discrete probability distributions, but
their use of randomness is more complicated.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Randomised_BSTs</h3>
<ul>
<li><a href="../theories/randomised_bsts/#Randomised_BSTs">Randomised_BSTs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Monad_Normalisation.html">Monad normalisation</a></li><li><a href="../entries/Random_BSTs.html">Expected Shape of Random Binary Search Trees</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MFMC_Countable.html">A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Randomised_BSTs-AFP</p><pre id="copy-text">@article{Randomised_BSTs-AFP,
author = {Manuel Eberl},
title = {Randomised Binary Search Trees},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/Randomised_BSTs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_BSTs-2018-10-19.tar.gz">Oct 19, 2018</a>: Isabelle2018
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diff --git a/web/entries/Randomised_Social_Choice.html b/web/entries/Randomised_Social_Choice.html
--- a/web/entries/Randomised_Social_Choice.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Randomised Social Choice Theory - Archive of Formal Proofs</title><meta name="description" content="This work contains a formalisation of basic Randomised Social Choice,
including Stochastic Dominance and Social Decision Schemes (SDSs)
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<h1 >
<span class='first'>R</span>andomised <span class='first'>S</span>ocial <span class='first'>C</span>hoice <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
</p>
<p class="date">May 5, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work contains a formalisation of basic Randomised Social Choice,
including Stochastic Dominance and Social Decision Schemes (SDSs)
along with some of their most important properties (Anonymity,
Neutrality, ex-post- and SD-Efficiency, SD-Strategy-Proofness) and two
particular SDSs – Random Dictatorship and Random Serial Dictatorship
(with proofs of the properties that they satisfy). Many important
properties of these concepts are also proven – such as the two
equivalent characterisations of Stochastic Dominance and the fact that
SD-efficiency of a lottery only depends on the support. The entry
also provides convenient commands to define Preference Profiles, prove
their well-formedness, and automatically derive restrictions that
sufficiently nice SDSs need to satisfy on the defined profiles.
Currently, the formalisation focuses on weak preferences and
Stochastic Dominance, but it should be easy to extend it to other
domains – such as strict preferences – or other lottery extensions –
such as Bilinear Dominance or Pairwise Comparison.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Randomised_Social_Choice</h3>
<ul>
<li><a href="../theories/randomised_social_choice/#Order_Predicates">Order_Predicates</a></li>
<li><a href="../theories/randomised_social_choice/#Preference_Profiles">Preference_Profiles</a></li>
<li><a href="../theories/randomised_social_choice/#Elections">Elections</a></li>
<li><a href="../theories/randomised_social_choice/#Lotteries">Lotteries</a></li>
<li><a href="../theories/randomised_social_choice/#Utility_Functions">Utility_Functions</a></li>
<li><a href="../theories/randomised_social_choice/#Stochastic_Dominance">Stochastic_Dominance</a></li>
<li><a href="../theories/randomised_social_choice/#SD_Efficiency">SD_Efficiency</a></li>
<li><a href="../theories/randomised_social_choice/#Social_Decision_Schemes">Social_Decision_Schemes</a></li>
<li><a href="../theories/randomised_social_choice/#SDS_Lowering">SDS_Lowering</a></li>
<li><a href="../theories/randomised_social_choice/#Random_Dictatorship">Random_Dictatorship</a></li>
<li><a href="../theories/randomised_social_choice/#Random_Serial_Dictatorship">Random_Serial_Dictatorship</a></li>
<li><a href="../theories/randomised_social_choice/#Randomised_Social_Choice">Randomised_Social_Choice</a></li>
<li><a href="../theories/randomised_social_choice/#Preference_Profile_Cmd">Preference_Profile_Cmd</a></li>
<li><a href="../theories/randomised_social_choice/#QSOpt_Exact">QSOpt_Exact</a></li>
<li><a href="../theories/randomised_social_choice/#SDS_Automation">SDS_Automation</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/List-Index.html">List Index</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Fishburn_Impossibility.html">The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency</a></li><li><a href="../entries/SDS_Impossibility.html">The Incompatibility of SD-Efficiency and SD-Strategy-Proofness</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Randomised_Social_Choice-AFP</p><pre id="copy-text">@article{Randomised_Social_Choice-AFP,
author = {Manuel Eberl},
title = {Randomised Social Choice Theory},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Randomised_Social_Choice.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Randomised_Social_Choice-2016-05-05.tar.gz">May 5, 2016</a>: Isabelle2016
</li></ul>
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diff --git a/web/entries/Rank_Nullity_Theorem.html b/web/entries/Rank_Nullity_Theorem.html
--- a/web/entries/Rank_Nullity_Theorem.html
+++ b/web/entries/Rank_Nullity_Theorem.html
@@ -1,194 +1,196 @@
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<h1 >
<span class='first'>R</span>ank-<span class='first'>N</span>ullity <span class='first'>T</span>heorem in <span class='first'>L</span>inear <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a> and <a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>
</p>
<p class="date">January 16, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this contribution, we present some formalizations based on the HOL-Multivariate-Analysis session of Isabelle. Firstly, a generalization of several theorems of such library are presented. Secondly, some definitions and proofs involving Linear Algebra and the four fundamental subspaces of a matrix are shown. Finally, we present a proof of the result known in Linear Algebra as the ``Rank-Nullity Theorem'', which states that, given any linear map f from a finite dimensional vector space V to a vector space W, then the dimension of V is equal to the dimension of the kernel of f (which is a subspace of V) and the dimension of the range of f (which is a subspace of W). The proof presented here is based on the one given by Sheldon Axler in his book <i>Linear Algebra Done Right</i>. As a corollary of the previous theorem, and taking advantage of the relationship between linear maps and matrices, we prove that, for every matrix A (which has associated a linear map between finite dimensional vector spaces), the sum of its null space and its column space (which is equal to the range of the linear map) is equal to the number of columns of A.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 14, 2014</dt>
<dd>Added some generalizations that allow us to formalize the Rank-Nullity Theorem over finite dimensional vector spaces, instead of over the more particular euclidean spaces. Updated abstract.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Rank_Nullity_Theorem</h3>
<ul>
<li><a href="../theories/rank_nullity_theorem/#Dual_Order">Dual_Order</a></li>
<li><a href="../theories/rank_nullity_theorem/#Mod_Type">Mod_Type</a></li>
<li><a href="../theories/rank_nullity_theorem/#Miscellaneous">Miscellaneous</a></li>
<li><a href="../theories/rank_nullity_theorem/#Fundamental_Subspaces">Fundamental_Subspaces</a></li>
<li><a href="../theories/rank_nullity_theorem/#Dim_Formula">Dim_Formula</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li><li><a href="../entries/Echelon_Form.html">Echelon Form</a></li><li><a href="../entries/QR_Decomposition.html">QR Decomposition</a></li><li><a href="../entries/Gauss_Jordan.html">Gauss-Jordan Algorithm and Its Applications</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Rank_Nullity_Theorem-AFP</p><pre id="copy-text">@article{Rank_Nullity_Theorem-AFP,
author = {Jose Divasón and Jesús Aransay},
title = {Rank-Nullity Theorem in Linear Algebra},
journal = {Archive of Formal Proofs},
month = {January},
year = {2013},
note = {\url{https://isa-afp.org/entries/Rank_Nullity_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Rank_Nullity_Theorem-2013-01-16.tar.gz">Jan 16, 2013</a>: Isabelle2012
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<h1 >
<span class='first'>I</span>mplementing <span class='first'>F</span>ield <span class='first'>E</span>xtensions of the <span class='first'>F</span>orm <span class='first'>Q</span>[sqrt(b)]</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">February 6, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We apply data refinement to implement the real numbers, where we support all
numbers in the field extension Q[sqrt(b)], i.e., all numbers of the form p +
q * sqrt(b) for rational numbers p and q and some fixed natural number b. To
this end, we also developed algorithms to precisely compute roots of a
rational number, and to perform a factorization of natural numbers which
eliminates duplicate prime factors.
<p>
Our results have been used to certify termination proofs which involve
polynomial interpretations over the reals.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>July 11, 2014</dt>
<dd>Moved NthRoot_Impl to Sqrt-Babylonian.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Real_Impl</h3>
<ul>
<li><a href="../theories/real_impl/#Real_Impl_Auxiliary">Real_Impl_Auxiliary</a></li>
<li><a href="../theories/real_impl/#Prime_Product">Prime_Product</a></li>
<li><a href="../theories/real_impl/#Real_Impl">Real_Impl</a></li>
<li><a href="../theories/real_impl/#Real_Unique_Impl">Real_Unique_Impl</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li><li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Complex_Bounded_Operators.html">Complex Bounded Operators</a></li><li><a href="../entries/QR_Decomposition.html">QR Decomposition</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Real_Power.html">Real Exponents as the Limits of Sequences of Rational Exponents</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Real_Impl-AFP</p><pre id="copy-text">@article{Real_Impl-AFP,
author = {René Thiemann},
title = {Implementing field extensions of the form Q[sqrt(b)]},
journal = {Archive of Formal Proofs},
month = {February},
year = {2014},
note = {\url{https://isa-afp.org/entries/Real_Impl.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Real_Impl-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-Real_Impl-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Real_Impl-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Real_Impl-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Real_Impl-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Real_Impl-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Real_Impl-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Real_Impl-2014-02-11.tar.gz">Feb 11, 2014</a>: Isabelle2013-2
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<h1 >
<span class='first'>R</span>eal <span class='first'>E</span>xponents as the <span class='first'>L</span>imits of <span class='first'>S</span>equences of <span class='first'>R</span>ational <span class='first'>E</span>xponents</h1>
<div>
<p><a href="../authors/fleuriot">Jacques D. Fleuriot</a> <a href="https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html">🌐</a>
</p>
<p class="date">November 8, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this formalisation, we construct real exponents as the limits of
sequences of rational exponents. In particular, if $a \ge 1$ and $x
\in \mathbb{R}$, we choose an increasing rational sequence $r_n$ such
that $\lim_{n\to\infty} {r_n} = x$. Then the sequence $a^{r_n}$ is
increasing and if $r$ is any rational number such that $r > x$,
$a^{r_n}$ is bounded above by $a^r$. By the convergence criterion for
monotone sequences, $a^{r_n}$ converges. We define $a^ x =
\lim_{n\to\infty} a^{r_n}$ and show that it has the expected
properties (for $a \ge 0$). This particular construction of real
exponents is needed instead of the usual one using the natural
logarithm and exponential functions (which already exists in Isabelle)
to support our mechanical derivation of Euler's exponential
series as an ``infinite polynomial". Aside from helping us avoid
circular reasoning, this is, as far as we are aware, the first time
real exponents are mechanised in this way within a proof assistant.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Real_Power</h3>
<ul>
<li><a href="../theories/real_power/#RatPower">RatPower</a></li>
<li><a href="../theories/real_power/#RealPower">RealPower</a></li>
<li><a href="../theories/real_power/#Log">Log</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Real_Power-AFP</p><pre id="copy-text">@article{Real_Power-AFP,
author = {Jacques D. Fleuriot},
title = {Real Exponents as the Limits of Sequences of Rational Exponents},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Real_Power.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>eal-<span class='first'>T</span>ime <span class='first'>D</span>ouble-<span class='first'>E</span>nded <span class='first'>Q</span>ueue</h1>
<div>
<p><a href="../authors/toth">Balazs Toth</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsiYmFsYXpzIiwidG90aCJdfQ==">📧</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">June 23, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A double-ended queue (<em>deque</em>) is a queue where one
can enqueue and dequeue at both ends. We define and verify the <a
href="https://doi.org/10.1145/165180.165225">deque
implementation by Chuang and Goldberg</a>. It is purely
functional and all operations run in constant time.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Chuang, T.-R., & Goldberg, B. (1993). Real-time deques, multihead Turing machines, and purely functional programming. Proceedings of the Conference on Functional Programming Languages and Computer Architecture - FPCA ’93. <a href="https://doi.org/10.1145/165180.165225">https://doi.org/10.1145/165180.165225</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Double-ended_queue">Wikipedia</a>
</li></ul>
<h3>Session Real_Time_Deque</h3>
<ul>
<li><a href="../theories/real_time_deque/#Deque">Deque</a></li>
<li><a href="../theories/real_time_deque/#Type_Classes">Type_Classes</a></li>
<li><a href="../theories/real_time_deque/#Stack">Stack</a></li>
<li><a href="../theories/real_time_deque/#Current">Current</a></li>
<li><a href="../theories/real_time_deque/#Idle">Idle</a></li>
<li><a href="../theories/real_time_deque/#Common">Common</a></li>
<li><a href="../theories/real_time_deque/#Big">Big</a></li>
<li><a href="../theories/real_time_deque/#Small">Small</a></li>
<li><a href="../theories/real_time_deque/#States">States</a></li>
<li><a href="../theories/real_time_deque/#RealTimeDeque">RealTimeDeque</a></li>
<li><a href="../theories/real_time_deque/#RTD_Util">RTD_Util</a></li>
<li><a href="../theories/real_time_deque/#Stack_Proof">Stack_Proof</a></li>
<li><a href="../theories/real_time_deque/#Idle_Proof">Idle_Proof</a></li>
<li><a href="../theories/real_time_deque/#Current_Proof">Current_Proof</a></li>
<li><a href="../theories/real_time_deque/#Common_Proof">Common_Proof</a></li>
<li><a href="../theories/real_time_deque/#Big_Proof">Big_Proof</a></li>
<li><a href="../theories/real_time_deque/#Small_Proof">Small_Proof</a></li>
<li><a href="../theories/real_time_deque/#States_Proof">States_Proof</a></li>
<li><a href="../theories/real_time_deque/#RealTimeDeque_Dequeue">RealTimeDeque_Dequeue</a></li>
<li><a href="../theories/real_time_deque/#RealTimeDeque_Enqueue">RealTimeDeque_Enqueue</a></li>
<li><a href="../theories/real_time_deque/#RealTimeDeque_Proof">RealTimeDeque_Proof</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Real_Time_Deque-AFP</p><pre id="copy-text">@article{Real_Time_Deque-AFP,
author = {Balazs Toth and Tobias Nipkow},
title = {Real-Time Double-Ended Queue},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/Real_Time_Deque.html},
Formal proof development},
ISSN = {2150-914x},
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+ </li><li>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Real_Time_Deque-2022-06-30.tar.gz">Jun 30, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Recursion-Addition.html b/web/entries/Recursion-Addition.html
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<h1 >
<span class='first'>R</span>ecursion <span class='first'>T</span>heorem in <span class='first'>Z</span><span class='first'>F</span></h1>
<div>
<p><a href="../authors/dunaev">Georgy Dunaev</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZ2VvcmdlZHVuYWV2Il19">📧</a>
</p>
<p class="date">May 11, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains a proof of the recursion theorem. This is a
mechanization of the proof of the recursion theorem from the text <i>Introduction to
Set Theory</i>, by Karel Hrbacek and Thomas Jech. This
implementation may be used as the basis for a model of Peano arithmetic in
ZF. While recursion and the natural numbers are already available in Isabelle/ZF, this clean development
is much easier to follow.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Recursion-Addition</h3>
<ul>
<li><a href="../theories/recursion-addition/#recursion">recursion</a></li></ul><div class="flex-wrap">
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author = {Georgy Dunaev},
title = {Recursion Theorem in ZF},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Recursion-Addition.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-Recursion-Addition-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Recursion-Addition-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
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diff --git a/web/entries/Recursion-Theory-I.html b/web/entries/Recursion-Theory-I.html
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<h1 >
<span class='first'>R</span>ecursion <span class='first'>T</span>heory <span class='first'>I</span></h1>
<div>
<p><a href="../authors/nedzelsky">Michael Nedzelsky</a>
</p>
<p class="date">April 5, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document presents the formalization of introductory material from recursion theory --- definitions and basic properties of primitive recursive functions, Cantor pairing function and computably enumerable sets (including a proof of existence of a one-complete computably enumerable set and a proof of the Rice's theorem).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li></ul>
<h3>Session Recursion-Theory-I</h3>
<ul>
<li><a href="../theories/recursion-theory-i/#CPair">CPair</a></li>
<li><a href="../theories/recursion-theory-i/#PRecFun">PRecFun</a></li>
<li><a href="../theories/recursion-theory-i/#PRecList">PRecList</a></li>
<li><a href="../theories/recursion-theory-i/#PRecFun2">PRecFun2</a></li>
<li><a href="../theories/recursion-theory-i/#PRecFinSet">PRecFinSet</a></li>
<li><a href="../theories/recursion-theory-i/#PRecUnGr">PRecUnGr</a></li>
<li><a href="../theories/recursion-theory-i/#RecEnSet">RecEnSet</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Minsky_Machines.html">Minsky Machines</a></li></ul>
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author = {Michael Nedzelsky},
title = {Recursion Theory I},
journal = {Archive of Formal Proofs},
month = {April},
year = {2008},
note = {\url{https://isa-afp.org/entries/Recursion-Theory-I.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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+ <a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
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<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
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<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
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<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Recursion-Theory-I-2008-04-11.tar.gz">Apr 11, 2008</a>: Isabelle2007
</li></ul>
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>mperative <span class='first'>R</span>efinement <span class='first'>F</span>ramework</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">August 8, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the Imperative Refinement Framework (IRF), a tool that
supports a stepwise refinement based approach to imperative programs.
This entry is based on the material we presented in [ITP-2015,
CPP-2016]. It uses the Monadic Refinement Framework as a frontend for
the specification of the abstract programs, and Imperative/HOL as a
backend to generate executable imperative programs. The IRF comes
with tool support to synthesize imperative programs from more
abstract, functional ones, using efficient imperative implementations
for the abstract data structures. This entry also includes the
Imperative Isabelle Collection Framework (IICF), which provides a
library of re-usable imperative collection data structures. Moreover,
this entry contains a quickstart guide and a reference manual, which
provide an introduction to using the IRF for Isabelle/HOL experts. It
also provids a collection of (partly commented) practical examples,
some highlights being Dijkstra's Algorithm, Nested-DFS, and a generic
worklist algorithm with subsumption. Finally, this entry contains
benchmark scripts that compare the runtime of some examples against
reference implementations of the algorithms in Java and C++.
[ITP-2015] Peter Lammich: Refinement to Imperative/HOL. ITP 2015:
253--269 [CPP-2016] Peter Lammich: Refinement based verification of
imperative data structures. CPP 2016: 27--36</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Sepref_Prereq</h3>
<ul></ul>
<h3>Session Refine_Imperative_HOL</h3>
<ul>
<li><a href="../theories/refine_imperative_hol/#Concl_Pres_Clarification">Concl_Pres_Clarification</a></li>
<li><a href="../theories/refine_imperative_hol/#Named_Theorems_Rev">Named_Theorems_Rev</a></li>
<li><a href="../theories/refine_imperative_hol/#Pf_Add">Pf_Add</a></li>
<li><a href="../theories/refine_imperative_hol/#Pf_Mono_Prover">Pf_Mono_Prover</a></li>
<li><a href="../theories/refine_imperative_hol/#PO_Normalizer">PO_Normalizer</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Misc">Sepref_Misc</a></li>
<li><a href="../theories/refine_imperative_hol/#Structured_Apply">Structured_Apply</a></li>
<li><a href="../theories/refine_imperative_hol/#Term_Synth">Term_Synth</a></li>
<li><a href="../theories/refine_imperative_hol/#User_Smashing">User_Smashing</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_Tool">Sepref_Chapter_Tool</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Id_Op">Sepref_Id_Op</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Basic">Sepref_Basic</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Monadify">Sepref_Monadify</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Constraints">Sepref_Constraints</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Frame">Sepref_Frame</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Rules">Sepref_Rules</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Combinator_Setup">Sepref_Combinator_Setup</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Translate">Sepref_Translate</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Definition">Sepref_Definition</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Intf_Util">Sepref_Intf_Util</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Tool">Sepref_Tool</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_Setup">Sepref_Chapter_Setup</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_HOL_Bindings">Sepref_HOL_Bindings</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Foreach">Sepref_Foreach</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Improper">Sepref_Improper</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref">Sepref</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_IICF">Sepref_Chapter_IICF</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Set">IICF_Set</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_List_SetO">IICF_List_SetO</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Multiset">IICF_Multiset</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Prio_Bag">IICF_Prio_Bag</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_List_Mset">IICF_List_Mset</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_List_MsetO">IICF_List_MsetO</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_List">IICF_List</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Abs_Heap">IICF_Abs_Heap</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_HOL_List">IICF_HOL_List</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Array_List">IICF_Array_List</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Impl_Heap">IICF_Impl_Heap</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Map">IICF_Map</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Prio_Map">IICF_Prio_Map</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Abs_Heapmap">IICF_Abs_Heapmap</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Array">IICF_Array</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_MS_Array_List">IICF_MS_Array_List</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Indexed_Array_List">IICF_Indexed_Array_List</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Impl_Heapmap">IICF_Impl_Heapmap</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Matrix">IICF_Matrix</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Array_Matrix">IICF_Array_Matrix</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF_Sepl_Binding">IICF_Sepl_Binding</a></li>
<li><a href="../theories/refine_imperative_hol/#IICF">IICF</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_Userguides">Sepref_Chapter_Userguides</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Guide_Quickstart">Sepref_Guide_Quickstart</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Guide_Reference">Sepref_Guide_Reference</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Guide_General_Util">Sepref_Guide_General_Util</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_ICF_Bindings">Sepref_ICF_Bindings</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_WGraph">Sepref_WGraph</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_Examples">Sepref_Chapter_Examples</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Graph">Sepref_Graph</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_DFS">Sepref_DFS</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Dijkstra">Sepref_Dijkstra</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_NDFS">Sepref_NDFS</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Minitests">Sepref_Minitests</a></li>
<li><a href="../theories/refine_imperative_hol/#Worklist_Subsumption">Worklist_Subsumption</a></li>
<li><a href="../theories/refine_imperative_hol/#Worklist_Subsumption_Impl">Worklist_Subsumption_Impl</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Snip_Datatype">Sepref_Snip_Datatype</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Snip_Combinator">Sepref_Snip_Combinator</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_All_Examples">Sepref_All_Examples</a></li>
<li><a href="../theories/refine_imperative_hol/#Sepref_Chapter_Benchmarks">Sepref_Chapter_Benchmarks</a></li>
<li><a href="../theories/refine_imperative_hol/#Heapmap_Bench">Heapmap_Bench</a></li>
<li><a href="../theories/refine_imperative_hol/#Dijkstra_Benchmark">Dijkstra_Benchmark</a></li>
<li><a href="../theories/refine_imperative_hol/#NDFS_Benchmark">NDFS_Benchmark</a></li></ul>
<h3>Session Sepref_Basic</h3>
<ul></ul>
<h3>Session Sepref_IICF</h3>
<ul></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li><li><a href="../entries/DFS_Framework.html">A Framework for Verifying Depth-First Search Algorithms</a></li><li><a href="../entries/Dijkstra_Shortest_Path.html">Dijkstra&rsquo;s Shortest Path Algorithm</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/BTree.html">A Verified Imperative Implementation of B-Trees</a></li><li><a href="../entries/Kruskal.html">Kruskal&rsquo;s Algorithm for Minimum Spanning Forest</a></li><li><a href="../entries/Flow_Networks.html">Flow Networks and the Min-Cut-Max-Flow Theorem</a></li><li><a href="../entries/Floyd_Warshall.html">The Floyd-Warshall Algorithm for Shortest Paths</a></li><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Refine_Imperative_HOL-AFP</p><pre id="copy-text">@article{Refine_Imperative_HOL-AFP,
author = {Peter Lammich},
title = {The Imperative Refinement Framework},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/Refine_Imperative_HOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>efinement for <span class='first'>M</span>onadic <span class='first'>P</span>rograms</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
</p>
<p class="date">January 30, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a framework for program and data refinement in Isabelle/HOL.
The framework is based on a nondeterminism-monad with assertions, i.e.,
the monad carries a set of results or an assertion failure.
Recursion is expressed by fixed points. For convenience, we also provide
while and foreach combinators.
<p>
The framework provides tools to automatize canonical tasks, such as
verification condition generation, finding appropriate data refinement relations,
and refine an executable program to a form that is accepted by the
Isabelle/HOL code generator.
<p>
This submission comes with a collection of examples and a user-guide,
illustrating the usage of the framework.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Refine_Monadic</h3>
<ul>
<li><a href="../theories/refine_monadic/#Refine_Chapter">Refine_Chapter</a></li>
<li><a href="../theories/refine_monadic/#Refine_Mono_Prover">Refine_Mono_Prover</a></li>
<li><a href="../theories/refine_monadic/#Refine_Misc">Refine_Misc</a></li>
<li><a href="../theories/refine_monadic/#RefineG_Transfer">RefineG_Transfer</a></li>
<li><a href="../theories/refine_monadic/#RefineG_Domain">RefineG_Domain</a></li>
<li><a href="../theories/refine_monadic/#RefineG_Recursion">RefineG_Recursion</a></li>
<li><a href="../theories/refine_monadic/#RefineG_Assert">RefineG_Assert</a></li>
<li><a href="../theories/refine_monadic/#Refine_Basic">Refine_Basic</a></li>
<li><a href="../theories/refine_monadic/#Refine_Leof">Refine_Leof</a></li>
<li><a href="../theories/refine_monadic/#Refine_Heuristics">Refine_Heuristics</a></li>
<li><a href="../theories/refine_monadic/#Refine_More_Comb">Refine_More_Comb</a></li>
<li><a href="../theories/refine_monadic/#RefineG_While">RefineG_While</a></li>
<li><a href="../theories/refine_monadic/#Refine_While">Refine_While</a></li>
<li><a href="../theories/refine_monadic/#Refine_Det">Refine_Det</a></li>
<li><a href="../theories/refine_monadic/#Refine_Pfun">Refine_Pfun</a></li>
<li><a href="../theories/refine_monadic/#Refine_Transfer">Refine_Transfer</a></li>
<li><a href="../theories/refine_monadic/#Refine_Foreach">Refine_Foreach</a></li>
<li><a href="../theories/refine_monadic/#Refine_Automation">Refine_Automation</a></li>
<li><a href="../theories/refine_monadic/#Autoref_Monadic">Autoref_Monadic</a></li>
<li><a href="../theories/refine_monadic/#Refine_Monadic">Refine_Monadic</a></li>
<li><a href="../theories/refine_monadic/#Example_Chapter">Example_Chapter</a></li>
<li><a href="../theories/refine_monadic/#Breadth_First_Search">Breadth_First_Search</a></li>
<li><a href="../theories/refine_monadic/#WordRefine">WordRefine</a></li>
<li><a href="../theories/refine_monadic/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Kruskal.html">Kruskal&rsquo;s Algorithm for Minimum Spanning Forest</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li>
<li><a href="../entries/Complete_Non_Orders.html">Complete Non-Orders and Fixed Points</a></li>
<li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li>
<li><a href="../entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Refine_Monadic-AFP</p><pre id="copy-text">@article{Refine_Monadic-AFP,
author = {Peter Lammich},
title = {Refinement for Monadic Programs},
journal = {Archive of Formal Proofs},
month = {January},
year = {2012},
note = {\url{https://isa-afp.org/entries/Refine_Monadic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
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<a href="https://www.isa-afp.org/release/afp-Refine_Monadic-2012-02-10.tar.gz">Feb 10, 2012</a>: Isabelle2011-1
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<h1 >
<span class='first'>F</span>ormalization of <span class='first'>R</span>efinement <span class='first'>C</span>alculus for <span class='first'>R</span>eactive <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/preoteasa">Viorel Preoteasa</a> <a class="obfuscated" data="eyJob3N0IjpbImFhbHRvIiwiZmkiXSwidXNlciI6WyJ2aW9yZWwiLCJwcmVvdGVhc2EiXX0=">📧</a>
</p>
<p class="date">October 8, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formalization of refinement calculus for reactive systems.
Refinement calculus is based on monotonic predicate transformers
(monotonic functions from sets of post-states to sets of pre-states),
and it is a powerful formalism for reasoning about imperative programs.
We model reactive systems as monotonic property transformers
that transform sets of output infinite sequences into sets of input
infinite sequences. Within this semantics we can model
refinement of reactive systems, (unbounded) angelic and
demonic nondeterminism, sequential composition, and
other semantic properties. We can model systems that may
fail for some inputs, and we can model compatibility of systems.
We can specify systems that have liveness properties using
linear temporal logic, and we can refine system specifications
into systems based on symbolic transitions systems, suitable
for implementations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session RefinementReactive</h3>
<ul>
<li><a href="../theories/refinementreactive/#Temporal">Temporal</a></li>
<li><a href="../theories/refinementreactive/#Refinement">Refinement</a></li>
<li><a href="../theories/refinementreactive/#Reactive">Reactive</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">RefinementReactive-AFP</p><pre id="copy-text">@article{RefinementReactive-AFP,
author = {Viorel Preoteasa},
title = {Formalization of Refinement Calculus for Reactive Systems},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/RefinementReactive.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-RefinementReactive-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-RefinementReactive-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Regex_Equivalence.html b/web/entries/Regex_Equivalence.html
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<h1 >
<span class='first'>U</span>nified <span class='first'>D</span>ecision <span class='first'>P</span>rocedures for <span class='first'>R</span>egular <span class='first'>E</span>xpression <span class='first'>E</span>quivalence</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">January 30, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a unified framework for verified decision procedures for regular
expression equivalence. Five recently published formalizations of such
decision procedures (three based on derivatives, two on marked regular
expressions) can be obtained as instances of the framework. We discover that
the two approaches based on marked regular expressions, which were previously
thought to be the same, are different, and one seems to produce uniformly
smaller automata. The common framework makes it possible to compare the
performance of the different decision procedures in a meaningful way.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T., & Traytel, D. (2014). Unified Decision Procedures for Regular Expression Equivalence. Lecture Notes in Computer Science, 450–466. <a href="https://doi.org/10.1007/978-3-319-08970-6_29">https://doi.org/10.1007/978-3-319-08970-6_29</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/itp14.html">Open access</a>
</li></ul>
<h3>Session Regex_Equivalence</h3>
<ul>
<li><a href="../theories/regex_equivalence/#Automaton">Automaton</a></li>
<li><a href="../theories/regex_equivalence/#Derivatives_Finite">Derivatives_Finite</a></li>
<li><a href="../theories/regex_equivalence/#Deriv_PDeriv">Deriv_PDeriv</a></li>
<li><a href="../theories/regex_equivalence/#Deriv_Autos">Deriv_Autos</a></li>
<li><a href="../theories/regex_equivalence/#Position_Autos">Position_Autos</a></li>
<li><a href="../theories/regex_equivalence/#After2">After2</a></li>
<li><a href="../theories/regex_equivalence/#Before2">Before2</a></li>
<li><a href="../theories/regex_equivalence/#Regex_Equivalence">Regex_Equivalence</a></li>
<li><a href="../theories/regex_equivalence/#Examples">Examples</a></li>
<li><a href="../theories/regex_equivalence/#Benchmark">Benchmark</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Efficient-Mergesort.html">Efficient Mergesort</a></li><li><a href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></li><li><a href="../entries/SpecCheck.html">SpecCheck - Specification-Based Testing for Isabelle/ML</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/MSO_Regex_Equivalence.html">Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</a></li>
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<p style="display:none;" id="bibtex-filename">Regex_Equivalence-AFP</p><pre id="copy-text">@article{Regex_Equivalence-AFP,
author = {Tobias Nipkow and Dmitriy Traytel},
title = {Unified Decision Procedures for Regular Expression Equivalence},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/Regex_Equivalence.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2014-11-30.tar.gz">Nov 30, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regex_Equivalence-2014-01-30.tar.gz">Jan 30, 2014</a>: Isabelle2013-2
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Registers.html b/web/entries/Registers.html
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<h1 >
<span class='first'>Q</span>uantum and <span class='first'>C</span>lassical <span class='first'>R</span>egisters</h1>
<div>
<p><a href="../authors/unruh">Dominique Unruh</a> <a href="https://www.ut.ee/~unruh/">🌐</a>
</p>
<p class="date">October 28, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A formalization of the theory of quantum and classical registers as
developed by (Unruh, Quantum and Classical Registers). In a nutshell,
a register refers to a part of a larger memory or system that can be
accessed independently. Registers can be constructed from other
registers and several (compatible) registers can be composed. This
formalization develops both the generic theory of registers as well as
specific instantiations for classical and quantum registers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/quantum-computing">Computer science/Algorithms/Quantum computing</a></li><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Registers</h3>
<ul>
<li><a href="../theories/registers/#Axioms">Axioms</a></li>
<li><a href="../theories/registers/#Laws">Laws</a></li>
<li><a href="../theories/registers/#Axioms_Complement">Axioms_Complement</a></li>
<li><a href="../theories/registers/#Laws_Complement">Laws_Complement</a></li>
<li><a href="../theories/registers/#Axioms_Classical">Axioms_Classical</a></li>
<li><a href="../theories/registers/#Laws_Classical">Laws_Classical</a></li>
<li><a href="../theories/registers/#Misc">Misc</a></li>
<li><a href="../theories/registers/#Classical_Extra">Classical_Extra</a></li>
<li><a href="../theories/registers/#Finite_Tensor_Product">Finite_Tensor_Product</a></li>
<li><a href="../theories/registers/#Axioms_Quantum">Axioms_Quantum</a></li>
<li><a href="../theories/registers/#Laws_Quantum">Laws_Quantum</a></li>
<li><a href="../theories/registers/#Quantum">Quantum</a></li>
<li><a href="../theories/registers/#Quantum_Extra">Quantum_Extra</a></li>
<li><a href="../theories/registers/#QHoare">QHoare</a></li>
<li><a href="../theories/registers/#Finite_Tensor_Product_Matrices">Finite_Tensor_Product_Matrices</a></li>
<li><a href="../theories/registers/#Teleport">Teleport</a></li>
<li><a href="../theories/registers/#Axioms_Complement_Quantum">Axioms_Complement_Quantum</a></li>
<li><a href="../theories/registers/#Laws_Complement_Quantum">Laws_Complement_Quantum</a></li>
<li><a href="../theories/registers/#Quantum_Extra2">Quantum_Extra2</a></li>
<li><a href="../theories/registers/#Pure_States">Pure_States</a></li>
<li><a href="../theories/registers/#Check_Autogenerated_Files">Check_Autogenerated_Files</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Complex_Bounded_Operators.html">Complex Bounded Operators</a></li></ul>
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</div>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Registers/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">Registers-AFP</p><pre id="copy-text">@article{Registers-AFP,
author = {Dominique Unruh},
title = {Quantum and Classical Registers},
journal = {Archive of Formal Proofs},
month = {October},
year = {2021},
note = {\url{https://isa-afp.org/entries/Registers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Registers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Registers-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Registers-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Registers-2021-11-07.tar.gz">Nov 7, 2021</a>: Isabelle2021
</li></ul>
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diff --git a/web/entries/Regression_Test_Selection.html b/web/entries/Regression_Test_Selection.html
--- a/web/entries/Regression_Test_Selection.html
+++ b/web/entries/Regression_Test_Selection.html
@@ -1,188 +1,190 @@
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<h1 >
<span class='first'>R</span>egression <span class='first'>T</span>est <span class='first'>S</span>election</h1>
<div>
<p><a href="../authors/mansky">Susannah Mansky</a> <a class="obfuscated" data="eyJob3N0IjpbImlsbGlub2lzIiwiZWR1Il0sInVzZXIiOlsic2pvaG5zbjIiXX0=">📧</a>
</p>
<p class="date">April 30, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development provides a general definition for safe Regression
Test Selection (RTS) algorithms. RTS algorithms select which tests to
rerun on revised code, reducing the time required to check for newly
introduced errors. An RTS algorithm is considered safe if and only if
all deselected tests would have unchanged results. This definition is
instantiated with two class-collection-based RTS algorithms run over
the JVM as modeled by JinjaDCI. This is achieved with a general
definition for Collection Semantics, small-step semantics instrumented
to collect information during execution. As the RTS definition
mandates safety, these instantiations include proofs of safety. This
work is described in Mansky and Gunter's LSFA 2020 paper and
Mansky's doctoral thesis (UIUC, 2020).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Regression_Test_Selection</h3>
<ul>
<li><a href="../theories/regression_test_selection/#RTS_safe">RTS_safe</a></li>
<li><a href="../theories/regression_test_selection/#Semantics">Semantics</a></li>
<li><a href="../theories/regression_test_selection/#CollectionSemantics">CollectionSemantics</a></li>
<li><a href="../theories/regression_test_selection/#CollectionBasedRTS">CollectionBasedRTS</a></li>
<li><a href="../theories/regression_test_selection/#JVMSemantics">JVMSemantics</a></li>
<li><a href="../theories/regression_test_selection/#ClassesChanged">ClassesChanged</a></li>
<li><a href="../theories/regression_test_selection/#Subcls">Subcls</a></li>
<li><a href="../theories/regression_test_selection/#ClassesAbove">ClassesAbove</a></li>
<li><a href="../theories/regression_test_selection/#JVMCollectionSemantics">JVMCollectionSemantics</a></li>
<li><a href="../theories/regression_test_selection/#JVMExecStepInductive">JVMExecStepInductive</a></li>
<li><a href="../theories/regression_test_selection/#JVMCollectionBasedRTS">JVMCollectionBasedRTS</a></li>
<li><a href="../theories/regression_test_selection/#RTS">RTS</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/JinjaDCI.html">JinjaDCI: a Java semantics with dynamic class initialization</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Regression_Test_Selection-AFP</p><pre id="copy-text">@article{Regression_Test_Selection-AFP,
author = {Susannah Mansky},
title = {Regression Test Selection},
journal = {Archive of Formal Proofs},
month = {April},
year = {2021},
note = {\url{https://isa-afp.org/entries/Regression_Test_Selection.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Regression_Test_Selection-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Regression_Test_Selection-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Regression_Test_Selection-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regression_Test_Selection-2021-05-03.tar.gz">May 3, 2021</a>: Isabelle2021
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diff --git a/web/entries/Regular-Sets.html b/web/entries/Regular-Sets.html
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+++ b/web/entries/Regular-Sets.html
@@ -1,216 +1,218 @@
<!DOCTYPE html>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Regular Sets and Expressions - Archive of Formal Proofs</title><meta name="description" content="This is a library of constructions on regular expressions and languages. It provides the operations of concatenation, Kleene star and derivative on..."><meta property="og:title" content="Regular Sets and Expressions" />
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<h1 >
<span class='first'>R</span>egular <span class='first'>S</span>ets and <span class='first'>E</span>xpressions</h1>
<div>
<p><a href="../authors/krauss">Alexander Krauss</a> <a href="http://www.in.tum.de/~krauss">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
with contributions from <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a> and <a href="../authors/urban">Christian Urban</a> <a href="https://nms.kcl.ac.uk/christian.urban/">🌐</a>
</p>
<p class="date">May 12, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a library of constructions on regular expressions and languages. It provides the operations of concatenation, Kleene star and derivative on languages. Regular expressions and their meaning are defined. An executable equivalence checker for regular expressions is verified; it does not need automata but works directly on regular expressions. <i>By mapping regular expressions to binary relations, an automatic and complete proof method for (in)equalities of binary relations over union, concatenation and (reflexive) transitive closure is obtained.</i> <P> Extended regular expressions with complement and intersection are also defined and an equivalence checker is provided.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>May 10, 2012</dt>
<dd>Tobias Nipkow added equivalence checking with partial derivatives</dd><dt>August 26, 2011</dt>
<dd>Christian Urban added a theory about derivatives and partial derivatives of regular expressions<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul><h3>Related publications</h3>
<ul><li>
Krauss, A., & Nipkow, T. (2011). Proof Pearl: Regular Expression Equivalence and Relation Algebra. Journal of Automated Reasoning, 49(1), 95–106. <a href="https://doi.org/10.1007/s10817-011-9223-4">https://doi.org/10.1007/s10817-011-9223-4</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/jar12.html">Open access</a>
</li></ul>
<h3>Session Regular-Sets</h3>
<ul>
<li><a href="../theories/regular-sets/#Regular_Set">Regular_Set</a></li>
<li><a href="../theories/regular-sets/#Regular_Exp">Regular_Exp</a></li>
<li><a href="../theories/regular-sets/#NDerivative">NDerivative</a></li>
<li><a href="../theories/regular-sets/#Equivalence_Checking">Equivalence_Checking</a></li>
<li><a href="../theories/regular-sets/#Relation_Interpretation">Relation_Interpretation</a></li>
<li><a href="../theories/regular-sets/#Regexp_Method">Regexp_Method</a></li>
<li><a href="../theories/regular-sets/#Regexp_Constructions">Regexp_Constructions</a></li>
<li><a href="../theories/regular-sets/#Derivatives">Derivatives</a></li>
<li><a href="../theories/regular-sets/#pEquivalence_Checking">pEquivalence_Checking</a></li>
<li><a href="../theories/regular-sets/#Regular_Exp2">Regular_Exp2</a></li>
<li><a href="../theories/regular-sets/#Equivalence_Checking2">Equivalence_Checking2</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li><li><a href="../entries/Lambda_Free_KBOs.html">Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Posix-Lexing.html">POSIX Lexing with Derivatives of Regular Expressions</a></li><li><a href="../entries/List_Update.html">Analysis of List Update Algorithms</a></li><li><a href="../entries/Finite_Automata_HF.html">Finite Automata in Hereditarily Finite Set Theory</a></li><li><a href="../entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></li><li><a href="../entries/Coinductive_Languages.html">A Codatatype of Formal Languages</a></li><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/Transitive-Closure-II.html">Executable Transitive Closures</a></li><li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Functional-Automata.html">Functional Automata</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Regular-Sets-AFP</p><pre id="copy-text">@article{Regular-Sets-AFP,
author = {Alexander Krauss and Tobias Nipkow},
title = {Regular Sets and Expressions},
journal = {Archive of Formal Proofs},
month = {May},
year = {2010},
note = {\url{https://isa-afp.org/entries/Regular-Sets.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Regular-Sets-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Regular-Sets-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Regular-Sets-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2013-03-02.tar.gz">Mar 2, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular-Sets-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li></ul>
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<h1 >
<span class='first'>R</span>egular <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/fosters">Simon Foster</a> <a href="https://www-users.cs.york.ac.uk/~simonf/">🌐</a> and <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">May 21, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Regular algebras axiomatise the equational theory of regular expressions as induced by
regular language identity. We use Isabelle/HOL for a detailed systematic study of regular
algebras given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between
these classes, formalise a soundness proof for the smallest class (Salomaa's) and obtain
completeness of the largest one (Boffa's) relative to a deep result by Krob. In addition
we provide a large collection of regular identities in the general setting of Boffa's axiom.
Our regular algebra hierarchy is orthogonal to the Kleene algebra hierarchy in the Archive
of Formal Proofs; we have not aimed at an integration for pragmatic reasons.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Regular_Algebras</h3>
<ul>
<li><a href="../theories/regular_algebras/#Dioid_Power_Sum">Dioid_Power_Sum</a></li>
<li><a href="../theories/regular_algebras/#Regular_Algebras">Regular_Algebras</a></li>
<li><a href="../theories/regular_algebras/#Regular_Algebra_Models">Regular_Algebra_Models</a></li>
<li><a href="../theories/regular_algebras/#Pratts_Counterexamples">Pratts_Counterexamples</a></li>
<li><a href="../theories/regular_algebras/#Regular_Algebra_Variants">Regular_Algebra_Variants</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Regular_Algebras-AFP</p><pre id="copy-text">@article{Regular_Algebras-AFP,
author = {Simon Foster and Georg Struth},
title = {Regular Algebras},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/Regular_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Regular_Algebras-2014-05-22.tar.gz">May 22, 2014</a>: Isabelle2013-2
</li></ul>
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<h1 >
<span class='first'>R</span>egular <span class='first'>T</span>ree <span class='first'>R</span>elations</h1>
<div>
<p><a href="../authors/lochmann">Alexander Lochmann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWxleGFuZGVyIiwibG9jaG1hbm4iXX0=">📧</a>, <a href="../authors/felgenhauer">Bertram Felgenhauer</a>, <a href="../authors/sternagel">Christian Sternagel</a> <a href="http://cl-informatik.uibk.ac.at/users/griff/">🌐</a>, <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a> and <a href="../authors/sternagelt">Thomas Sternagel</a>
</p>
<p class="date">December 15, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Tree automata have good closure properties and therefore a commonly
used to prove/disprove properties. This formalization contains among
other things the proofs of many closure properties of tree automata
(anchored) ground tree transducers and regular relations. Additionally
it includes the well known pumping lemma and a lifting of the Myhill
Nerode theorem for regular languages to tree languages. We want to
mention the existence of a <a
href="https://www.isa-afp.org/entries/Tree-Automata.html">tree
automata APF-entry</a> developed by Peter Lammich. His work is
based on epsilon free top-down tree automata, while this entry builds
on bottom-up tree auotamta with epsilon transitions. Moreover our
formalization relies on the <a
href="https://www.isa-afp.org/entries/Collections.html">Collections
Framework</a>, also by Peter Lammich, to obtain efficient code.
All proven constructions of the closure properties are exportable
using the Isabelle/HOL code generation facilities.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Regular_Tree_Relations</h3>
<ul>
<li><a href="../theories/regular_tree_relations/#Term_Context">Term_Context</a></li>
<li><a href="../theories/regular_tree_relations/#Basic_Utils">Basic_Utils</a></li>
<li><a href="../theories/regular_tree_relations/#Ground_Terms">Ground_Terms</a></li>
<li><a href="../theories/regular_tree_relations/#FSet_Utils">FSet_Utils</a></li>
<li><a href="../theories/regular_tree_relations/#Ground_Ctxt">Ground_Ctxt</a></li>
<li><a href="../theories/regular_tree_relations/#Ground_Closure">Ground_Closure</a></li>
<li><a href="../theories/regular_tree_relations/#Horn_Inference">Horn_Inference</a></li>
<li><a href="../theories/regular_tree_relations/#Horn_List">Horn_List</a></li>
<li><a href="../theories/regular_tree_relations/#Horn_Fset">Horn_Fset</a></li>
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<li><a href="../theories/regular_tree_relations/#Tree_Automata_Det">Tree_Automata_Det</a></li>
<li><a href="../theories/regular_tree_relations/#Tree_Automata_Complement">Tree_Automata_Complement</a></li>
<li><a href="../theories/regular_tree_relations/#Tree_Automata_Pumping">Tree_Automata_Pumping</a></li>
<li><a href="../theories/regular_tree_relations/#Myhill_Nerode">Myhill_Nerode</a></li>
<li><a href="../theories/regular_tree_relations/#GTT">GTT</a></li>
<li><a href="../theories/regular_tree_relations/#GTT_Compose">GTT_Compose</a></li>
<li><a href="../theories/regular_tree_relations/#GTT_Transitive_Closure">GTT_Transitive_Closure</a></li>
<li><a href="../theories/regular_tree_relations/#Pair_Automaton">Pair_Automaton</a></li>
<li><a href="../theories/regular_tree_relations/#AGTT">AGTT</a></li>
<li><a href="../theories/regular_tree_relations/#RRn_Automata">RRn_Automata</a></li>
<li><a href="../theories/regular_tree_relations/#RR2_Infinite">RR2_Infinite</a></li>
<li><a href="../theories/regular_tree_relations/#Tree_Automata_Abstract_Impl">Tree_Automata_Abstract_Impl</a></li>
<li><a href="../theories/regular_tree_relations/#Tree_Automata_Class_Instances_Impl">Tree_Automata_Class_Instances_Impl</a></li>
<li><a href="../theories/regular_tree_relations/#Tree_Automata_Impl">Tree_Automata_Impl</a></li>
<li><a href="../theories/regular_tree_relations/#RR2_Infinite_Q_infinity">RR2_Infinite_Q_infinity</a></li>
<li><a href="../theories/regular_tree_relations/#Regular_Relation_Abstract_Impl">Regular_Relation_Abstract_Impl</a></li>
<li><a href="../theories/regular_tree_relations/#Regular_Relation_Impl">Regular_Relation_Impl</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Rewrite_Properties_Reduction.html">Reducing Rewrite Properties to Properties on Ground Terms</a></li><li><a href="../entries/FO_Theory_Rewriting.html">First-Order Theory of Rewriting</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li>
<li><a href="../entries/Tree-Automata.html">Tree Automata</a></li>
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<p style="display:none;" id="bibtex-filename">Regular_Tree_Relations-AFP</p><pre id="copy-text">@article{Regular_Tree_Relations-AFP,
author = {Alexander Lochmann and Bertram Felgenhauer and Christian Sternagel and René Thiemann and Thomas Sternagel},
title = {Regular Tree Relations},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/Regular_Tree_Relations.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Regular_Tree_Relations-2021-12-29.tar.gz">Dec 29, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>R</span>elation <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/fosters">Simon Foster</a> <a class="obfuscated" data="eyJob3N0IjpbInlvcmsiLCJhYyIsInVrIl0sInVzZXIiOlsic2ltb24iLCJmb3N0ZXIiXX0=">📧</a>, <a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a> and <a href="../authors/weber">Tjark Weber</a> <a href="http://user.it.uu.se/~tjawe125/">🌐</a>
</p>
<p class="date">January 25, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Tarski's algebra of binary relations is formalised along the lines of
the standard textbooks of Maddux and Schmidt and Ströhlein. This
includes relation-algebraic concepts such as subidentities, vectors and
a domain operation as well as various notions associated to functions.
Relation algebras are also expanded by a reflexive transitive closure
operation, and they are linked with Kleene algebras and models of binary
relations and Boolean matrices.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Relation_Algebra</h3>
<ul>
<li><a href="../theories/relation_algebra/#More_Boolean_Algebra">More_Boolean_Algebra</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra">Relation_Algebra</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_Vectors">Relation_Algebra_Vectors</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_Tests">Relation_Algebra_Tests</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_Functions">Relation_Algebra_Functions</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_Direct_Products">Relation_Algebra_Direct_Products</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_RTC">Relation_Algebra_RTC</a></li>
<li><a href="../theories/relation_algebra/#Relation_Algebra_Models">Relation_Algebra_Models</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Relational_Paths.html">Relational Characterisations of Paths</a></li><li><a href="../entries/Residuated_Lattices.html">Residuated Lattices</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li>
<li><a href="../entries/Multirelations.html">Binary Multirelations</a></li>
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<p style="display:none;" id="bibtex-filename">Relation_Algebra-AFP</p><pre id="copy-text">@article{Relation_Algebra-AFP,
author = {Alasdair Armstrong and Simon Foster and Georg Struth and Tjark Weber},
title = {Relation Algebra},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/Relation_Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Relational-Incorrectness-Logic.html b/web/entries/Relational-Incorrectness-Logic.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>An Under-Approximate Relational Logic - Archive of Formal Proofs</title><meta name="description" content="Recently, authors have proposed under-approximate logics for reasoning
about programs. So far, all such logics have been confined to
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<h1 >
<span class='first'>A</span>n <span class='first'>U</span>nder-<span class='first'>A</span>pproximate <span class='first'>R</span>elational <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/murray">Toby Murray</a> <a href="https://people.eng.unimelb.edu.au/tobym/">🌐</a>
</p>
<p class="date">March 12, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Recently, authors have proposed under-approximate logics for reasoning
about programs. So far, all such logics have been confined to
reasoning about individual program behaviours. Yet there exist many
over-approximate relational logics for reasoning about pairs of
programs and relating their behaviours. We present the first
under-approximate relational logic, for the simple imperative language
IMP. We prove our logic is both sound and complete. Additionally, we
show how reasoning in this logic can be decomposed into non-relational
reasoning in an under-approximate Hoare logic, mirroring Beringer’s
result for over-approximate relational logics. We illustrate the
application of our logic on some small examples in which we provably
demonstrate the presence of insecurity.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Relational-Incorrectness-Logic</h3>
<ul>
<li><a href="../theories/relational-incorrectness-logic/#RelationalIncorrectness">RelationalIncorrectness</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Relational-Incorrectness-Logic-AFP</p><pre id="copy-text">@article{Relational-Incorrectness-Logic-AFP,
author = {Toby Murray},
title = {An Under-Approximate Relational Logic},
journal = {Archive of Formal Proofs},
month = {March},
year = {2020},
note = {\url{https://isa-afp.org/entries/Relational-Incorrectness-Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>elational <span class='first'>D</span>isjoint-<span class='first'>S</span>et <span class='first'>F</span>orests</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">August 26, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We give a simple relation-algebraic semantics of read and write
operations on associative arrays. The array operations seamlessly
integrate with assignments in the Hoare-logic library. Using relation
algebras and Kleene algebras we verify the correctness of an
array-based implementation of disjoint-set forests with a naive union
operation and a find operation with path compression.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 19, 2021</dt>
<dd>added path halving, path splitting, relational Peano structures, union by rank
(revision 98c7aa03457d)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Relational_Disjoint_Set_Forests</h3>
<ul>
<li><a href="../theories/relational_disjoint_set_forests/#Disjoint_Set_Forests">Disjoint_Set_Forests</a></li>
<li><a href="../theories/relational_disjoint_set_forests/#More_Disjoint_Set_Forests">More_Disjoint_Set_Forests</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stone_Kleene_Relation_Algebras.html">Stone-Kleene Relation Algebras</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Relational_Minimum_Spanning_Trees.html">Relational Minimum Spanning Tree Algorithms</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Relational_Disjoint_Set_Forests-AFP</p><pre id="copy-text">@article{Relational_Disjoint_Set_Forests-AFP,
author = {Walter Guttmann},
title = {Relational Disjoint-Set Forests},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/Relational_Disjoint_Set_Forests.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Relational_Disjoint_Set_Forests-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Relational_Disjoint_Set_Forests-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Relational_Forests.html b/web/entries/Relational_Forests.html
--- a/web/entries/Relational_Forests.html
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@@ -1,173 +1,175 @@
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<h1 >
<span class='first'>R</span>elational <span class='first'>F</span>orests</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">August 3, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We study second-order formalisations of graph properties expressed as
first-order formulas in relation algebras extended with a Kleene star.
The formulas quantify over relations while still avoiding
quantification over elements of the base set. We formalise the
property of undirected graphs being acyclic this way. This involves a
study of various kinds of orientation of graphs. We also verify basic
algorithms to constructively prove several second-order properties.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Relational_Forests</h3>
<ul>
<li><a href="../theories/relational_forests/#Forests">Forests</a></li>
<li><a href="../theories/relational_forests/#Algorithms">Algorithms</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stone_Kleene_Relation_Algebras.html">Stone-Kleene Relation Algebras</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Relational_Forests-AFP</p><pre id="copy-text">@article{Relational_Forests-AFP,
author = {Walter Guttmann},
title = {Relational Forests},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/Relational_Forests.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>T</span>he <span class='first'>R</span>elational <span class='first'>M</span>ethod <span class='first'>W</span>ith <span class='first'>M</span>essage <span class='first'>A</span>nonymity for the <span class='first'>V</span>erification of <span class='first'>C</span>ryptographic <span class='first'>P</span>rotocols</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">December 5, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This paper introduces a new method for the formal verification of
cryptographic protocols, the relational method, derived from
Paulson's inductive method by means of some enhancements aimed at
streamlining formal definitions and proofs, specially for protocols
using public key cryptography. Moreover, this paper proposes a method
to formalize a further security property, message anonymity, in
addition to message confidentiality and authenticity. The relational
method, including message anonymity, is then applied to the
verification of a sample authentication protocol, comprising Password
Authenticated Connection Establishment (PACE) with Chip Authentication
Mapping followed by the explicit verification of an additional
password over the PACE secure channel.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Relational_Method</h3>
<ul>
<li><a href="../theories/relational_method/#Definitions">Definitions</a></li>
<li><a href="../theories/relational_method/#Authentication">Authentication</a></li>
<li><a href="../theories/relational_method/#Anonymity">Anonymity</a></li>
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<p style="display:none;" id="bibtex-filename">Relational_Method-AFP</p><pre id="copy-text">@article{Relational_Method-AFP,
author = {Pasquale Noce},
title = {The Relational Method with Message Anonymity for the Verification of Cryptographic Protocols},
journal = {Archive of Formal Proofs},
month = {December},
year = {2020},
note = {\url{https://isa-afp.org/entries/Relational_Method.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>elational <span class='first'>M</span>inimum <span class='first'>S</span>panning <span class='first'>T</span>ree <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a> and <a href="../authors/brien">Nicolas Robinson-O&rsquo;Brien</a>
</p>
<p class="date">December 8, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We verify the correctness of Prim's, Kruskal's and
Borůvka's minimum spanning tree algorithms based on algebras for
aggregation and minimisation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Relational_Minimum_Spanning_Trees</h3>
<ul>
<li><a href="../theories/relational_minimum_spanning_trees/#Kruskal">Kruskal</a></li>
<li><a href="../theories/relational_minimum_spanning_trees/#Prim">Prim</a></li>
<li><a href="../theories/relational_minimum_spanning_trees/#Boruvka">Boruvka</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Aggregation_Algebras.html">Aggregation Algebras</a></li><li><a href="../entries/Relational_Disjoint_Set_Forests.html">Relational Disjoint-Set Forests</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Relational_Minimum_Spanning_Trees-AFP</p><pre id="copy-text">@article{Relational_Minimum_Spanning_Trees-AFP,
author = {Walter Guttmann and Nicolas Robinson-O'Brien},
title = {Relational Minimum Spanning Tree Algorithms},
journal = {Archive of Formal Proofs},
month = {December},
year = {2020},
note = {\url{https://isa-afp.org/entries/Relational_Minimum_Spanning_Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Relational_Paths.html b/web/entries/Relational_Paths.html
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<h1 >
<span class='first'>R</span>elational <span class='first'>C</span>haracterisations of <span class='first'>P</span>aths</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a> and <a href="../authors/hoefner">Peter Höfner</a> <a href="http://www.hoefner-online.de/">🌐</a>
</p>
<p class="date">July 13, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Binary relations are one of the standard ways to encode, characterise
and reason about graphs. Relation algebras provide equational axioms
for a large fragment of the calculus of binary relations. Although
relations are standard tools in many areas of mathematics and
computing, researchers usually fall back to point-wise reasoning when
it comes to arguments about paths in a graph. We present a purely
algebraic way to specify different kinds of paths in Kleene relation
algebras, which are relation algebras equipped with an operation for
reflexive transitive closure. We study the relationship between paths
with a designated root vertex and paths without such a vertex. Since
we stay in first-order logic this development helps with mechanising
proofs. To demonstrate the applicability of the algebraic framework we
verify the correctness of three basic graph algorithms.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Relational_Paths</h3>
<ul>
<li><a href="../theories/relational_paths/#More_Relation_Algebra">More_Relation_Algebra</a></li>
<li><a href="../theories/relational_paths/#Paths">Paths</a></li>
<li><a href="../theories/relational_paths/#Rooted_Paths">Rooted_Paths</a></li>
<li><a href="../theories/relational_paths/#Path_Algorithms">Path_Algorithms</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Relation_Algebra.html">Relation Algebra</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/FOL_Axiomatic.html">Soundness and Completeness of an Axiomatic System for First-Order Logic</a></li>
<li><a href="../entries/FOL_Seq_Calc1.html">A Sequent Calculus for First-Order Logic</a></li>
<li><a href="../entries/Abstract_Soundness.html">Abstract Soundness</a></li>
<li><a href="../entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></li>
<li><a href="../entries/Completeness.html">Completeness theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Relational_Paths-AFP</p><pre id="copy-text">@article{Relational_Paths-AFP,
author = {Walter Guttmann and Peter Höfner},
title = {Relational Characterisations of Paths},
journal = {Archive of Formal Proofs},
month = {July},
year = {2020},
note = {\url{https://isa-afp.org/entries/Relational_Paths.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>epresentations of <span class='first'>F</span>inite <span class='first'>G</span>roups</h1>
<div>
<p><a href="../authors/sylvestre">Jeremy Sylvestre</a> <a href="http://ualberta.ca/~jsylvest/">🌐</a>
</p>
<p class="date">August 12, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a formal framework for the theory of representations of finite groups, as modules over the group ring. Along the way, we develop the general theory of groups (relying on the group_add class for the basics), modules, and vector spaces, to the extent required for theory of group representations. We then provide formal proofs of several important introductory theorems in the subject, including Maschke's theorem, Schur's lemma, and Frobenius reciprocity. We also prove that every irreducible representation is isomorphic to a submodule of the group ring, leading to the fact that for a finite group there are only finitely many isomorphism classes of irreducible representations. In all of this, no restriction is made on the characteristic of the ring or field of scalars until the definition of a group representation, and then the only restriction made is that the characteristic must not divide the order of the group.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Rep_Fin_Groups</h3>
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<p style="display:none;" id="bibtex-filename">Rep_Fin_Groups-AFP</p><pre id="copy-text">@article{Rep_Fin_Groups-AFP,
author = {Jeremy Sylvestre},
title = {Representations of Finite Groups},
journal = {Archive of Formal Proofs},
month = {August},
year = {2015},
note = {\url{https://isa-afp.org/entries/Rep_Fin_Groups.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>esiduated <span class='first'>T</span>ransition <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/stark">Eugene W. Stark</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwic3Rvbnlicm9vayIsImVkdSJdLCJ1c2VyIjpbInN0YXJrIl19">📧</a>
</p>
<p class="date">February 28, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> A <em>residuated transition system</em> (RTS) is
a transition system that is equipped with a certain partial binary
operation, called <em>residuation</em>, on transitions.
Using the residuation operation, one can express nuances, such as a
distinction between nondeterministic and concurrent choice, as well as
partial commutativity relationships between transitions, which are not
captured by ordinary transition systems. A version of residuated
transition systems was introduced in previous work by the author, in
which they were called “concurrent transition systems” in view of the
original motivation for their definition from the study of
concurrency. In the first part of the present article, we give a
formal development that generalizes and subsumes the original
presentation. We give an axiomatic definition of residuated transition
systems that assumes only a single partial binary operation as given
structure. From the axioms, we derive notions of “arrow“ (transition),
“source”, “target”, “identity”, as well as “composition” and “join” of
transitions; thereby recovering structure that in the previous work
was assumed as given. We formalize and generalize the result, that
residuation extends from transitions to transition paths, and we
systematically develop the properties of this extension. A significant
generalization made in the present work is the identification of a
general notion of congruence on RTS’s, along with an associated
quotient construction. </p> <p> In the second part of this
article, we use the RTS framework to formalize several results in the
theory of reduction in Church’s λ-calculus. Using a de Bruijn
index-based syntax in which terms represent parallel reduction steps,
we define residuation on terms and show that it satisfies the axioms
for an RTS. An application of the results on paths from the first part
of the article allows us to prove the classical Church-Rosser Theorem
with little additional effort. We then use residuation to define the
notion of “development” and we prove the Finite Developments Theorem,
that every development is finite, formalizing and adapting to de
Bruijn indices a proof by de Vrijer. We also use residuation to define
the notion of a “standard reduction path”, and we prove the
Standardization Theorem: that every reduction path is congruent to a
standard one. As a corollary of the Standardization Theorem, we obtain
the Leftmost Reduction Theorem: that leftmost reduction is a
normalizing strategy. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li><li><a href="../topics/computer-science/programming-languages/lambda-calculi">Computer science/Programming languages/Lambda calculi</a></li></ul>
<h3>Session ResiduatedTransitionSystem</h3>
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<p style="display:none;" id="bibtex-filename">ResiduatedTransitionSystem-AFP</p><pre id="copy-text">@article{ResiduatedTransitionSystem-AFP,
author = {Eugene W. Stark},
title = {Residuated Transition Systems},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/ResiduatedTransitionSystem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Residuated_Lattices.html b/web/entries/Residuated_Lattices.html
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<h1 >
<span class='first'>R</span>esiduated <span class='first'>L</span>attices</h1>
<div>
<p><a href="../authors/gomes">Victor B. F. Gomes</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJ2Ym9yZ2VzZmVycmVpcmFnb21lczEiXX0=">📧</a> and <a href="../authors/struth">Georg Struth</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJnIiwic3RydXRoIl19">📧</a>
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<p class="date">April 15, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The theory of residuated lattices, first proposed by Ward and Dilworth, is
formalised in Isabelle/HOL. This includes concepts of residuated functions;
their adjoints and conjugates. It also contains necessary and sufficient
conditions for the existence of these operations in an arbitrary lattice.
The mathematical components for residuated lattices are linked to the AFP
entry for relation algebra. In particular, we prove Jonsson and Tsinakis
conditions for a residuated boolean algebra to form a relation algebra.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Residuated_Lattices</h3>
<ul>
<li><a href="../theories/residuated_lattices/#Residuated_Lattices">Residuated_Lattices</a></li>
<li><a href="../theories/residuated_lattices/#Residuated_Boolean_Algebras">Residuated_Boolean_Algebras</a></li>
<li><a href="../theories/residuated_lattices/#Involutive_Residuated">Involutive_Residuated</a></li>
<li><a href="../theories/residuated_lattices/#Action_Algebra">Action_Algebra</a></li>
<li><a href="../theories/residuated_lattices/#Action_Algebra_Models">Action_Algebra_Models</a></li>
<li><a href="../theories/residuated_lattices/#Residuated_Relation_Algebra">Residuated_Relation_Algebra</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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<li><a href="../entries/Irrationals_From_THEBOOK.html">Irrational numbers from THE BOOK</a></li>
<li><a href="../entries/BD_Security_Compositional.html">Compositional BD Security</a></li>
<li><a href="../entries/Core_SC_DOM.html">The Safely Composable DOM</a></li>
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<p style="display:none;" id="bibtex-filename">Residuated_Lattices-AFP</p><pre id="copy-text">@article{Residuated_Lattices-AFP,
author = {Victor B. F. Gomes and Georg Struth},
title = {Residuated Lattices},
journal = {Archive of Formal Proofs},
month = {April},
year = {2015},
note = {\url{https://isa-afp.org/entries/Residuated_Lattices.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2019-06-28.tar.gz">Jun 28, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Residuated_Lattices-2015-04-16.tar.gz">Apr 16, 2015</a>: Isabelle2014
</li></ul>
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<h1 >
<span class='first'>T</span>he <span class='first'>R</span>esolution <span class='first'>C</span>alculus for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/schlichtkrull">Anders Schlichtkrull</a> <a href="https://people.compute.dtu.dk/andschl/">🌐</a>
</p>
<p class="date">June 30, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory is a formalization of the resolution calculus for
first-order logic. It is proven sound and complete. The soundness
proof uses the substitution lemma, which shows a correspondence
between substitutions and updates to an environment. The completeness
proof uses semantic trees, i.e. trees whose paths are partial Herbrand
interpretations. It employs Herbrand's theorem in a formulation which
states that an unsatisfiable set of clauses has a finite closed
semantic tree. It also uses the lifting lemma which lifts resolution
derivation steps from the ground world up to the first-order world.
The theory is presented in a paper in the Journal of Automated Reasoning
[Sch18] which extends a paper presented at the International Conference
on Interactive Theorem Proving [Sch16]. An earlier version was
presented in an MSc thesis [Sch15]. The formalization mostly follows
textbooks by Ben-Ari [BA12], Chang and Lee [CL73], and Leitsch [Lei97].
The theory is part of the IsaFoL project [IsaFoL]. <p>
<a name="Sch18"></a>[Sch18] Anders Schlichtkrull. "Formalization of the
Resolution Calculus for First-Order Logic". Journal of Automated
Reasoning, 2018.<br> <a name="Sch16"></a>[Sch16] Anders
Schlichtkrull. "Formalization of the Resolution Calculus for First-Order
Logic". In: ITP 2016. Vol. 9807. LNCS. Springer, 2016.<br>
<a name="Sch15"></a>[Sch15] Anders Schlichtkrull. <a href="https://people.compute.dtu.dk/andschl/Thesis.pdf">
"Formalization of Resolution Calculus in Isabelle"</a>.
<a href="https://people.compute.dtu.dk/andschl/Thesis.pdf">https://people.compute.dtu.dk/andschl/Thesis.pdf</a>.
MSc thesis. Technical University of Denmark, 2015.<br>
<a name="BA12"></a>[BA12] Mordechai Ben-Ari. <i>Mathematical Logic for
Computer Science</i>. 3rd. Springer, 2012.<br> <a
name="CL73"></a>[CL73] Chin-Liang Chang and Richard Char-Tung Lee.
<i>Symbolic Logic and Mechanical Theorem Proving</i>. 1st. Academic
Press, Inc., 1973.<br> <a name="Lei97"></a>[Lei97] Alexander
Leitsch. <i>The Resolution Calculus</i>. Texts in theoretical computer
science. Springer, 1997.<br> <a name="IsaFoL"></a>[IsaFoL]
IsaFoL authors. <a href="https://bitbucket.org/jasmin_blanchette/isafol">
IsaFoL: Isabelle Formalization of Logic</a>.
<a href="https://bitbucket.org/jasmin_blanchette/isafol">https://bitbucket.org/jasmin_blanchette/isafol</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 20, 2018</dt>
<dd>added a concrete instance of the unification and completeness theorems using the First-Order Terms AFP-entry from IsaFoR as described in the papers</dd><dt>January 24, 2018</dt>
<dd>added several new versions of the soundness and completeness theorems as described in the paper</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Resolution_FOL</h3>
<ul>
<li><a href="../theories/resolution_fol/#TermsAndLiterals">TermsAndLiterals</a></li>
<li><a href="../theories/resolution_fol/#Tree">Tree</a></li>
<li><a href="../theories/resolution_fol/#Resolution">Resolution</a></li>
<li><a href="../theories/resolution_fol/#Completeness">Completeness</a></li>
<li><a href="../theories/resolution_fol/#Examples">Examples</a></li>
<li><a href="../theories/resolution_fol/#Unification_Theorem">Unification_Theorem</a></li>
<li><a href="../theories/resolution_fol/#Completeness_Instance">Completeness_Instance</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Order_Terms.html">First-Order Terms</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Resolution_FOL-AFP</p><pre id="copy-text">@article{Resolution_FOL-AFP,
author = {Anders Schlichtkrull},
title = {The Resolution Calculus for First-Order Logic},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Resolution_FOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Resolution_FOL-2016-06-30.tar.gz">Jun 30, 2016</a>: Isabelle2016
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diff --git a/web/entries/Rewrite_Properties_Reduction.html b/web/entries/Rewrite_Properties_Reduction.html
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<h1 >
<span class='first'>R</span>educing <span class='first'>R</span>ewrite <span class='first'>P</span>roperties to <span class='first'>P</span>roperties on <span class='first'>G</span>round <span class='first'>T</span>erms</h1>
<div>
<p><a href="../authors/lochmann">Alexander Lochmann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWxleGFuZGVyIiwibG9jaG1hbm4iXX0=">📧</a>
</p>
<p class="date">June 2, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This AFP entry relates important rewriting properties between the set
of terms and the set of ground terms induced by a given signature. The
properties considered are confluence, strong/local confluence, the
normal form property, unique normal forms with respect to reduction
and conversion, commutation, conversion equivalence, and normalization
equivalence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Rewrite_Properties_Reduction</h3>
<ul>
<li><a href="../theories/rewrite_properties_reduction/#Terms_Positions">Terms_Positions</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Rewriting">Rewriting</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Replace_Constant">Replace_Constant</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Rewriting_Properties">Rewriting_Properties</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Rewriting_LLRG_LV_Mondaic">Rewriting_LLRG_LV_Mondaic</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Rewriting_GTRS">Rewriting_GTRS</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Ground_Reduction_on_LLRG">Ground_Reduction_on_LLRG</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Ground_Reduction_on_GTRS">Ground_Reduction_on_GTRS</a></li>
<li><a href="../theories/rewrite_properties_reduction/#Ground_Reduction_on_LV">Ground_Reduction_on_LV</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Regular_Tree_Relations.html">Regular Tree Relations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Rewrite_Properties_Reduction-AFP</p><pre id="copy-text">@article{Rewrite_Properties_Reduction-AFP,
author = {Alexander Lochmann},
title = {Reducing Rewrite Properties to Properties on Ground Terms},
journal = {Archive of Formal Proofs},
month = {June},
year = {2022},
note = {\url{https://isa-afp.org/entries/Rewrite_Properties_Reduction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Rewrite_Properties_Reduction-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Rewrite_Properties_Reduction-2022-06-06.tar.gz">Jun 6, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>T</span>he <span class='first'>Z</span> <span class='first'>P</span>roperty</h1>
<div>
<p><a href="../authors/felgenhauer">Bertram Felgenhauer</a>, <a href="../authors/nagele">Julian Nagele</a>, <a href="../authors/oostrom">Vincent van Oostrom</a> and <a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">June 30, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the Z property introduced by Dehornoy and van Oostrom.
First we show that for any abstract rewrite system, Z implies
confluence. Then we give two examples of proofs using Z: confluence of
lambda-calculus with respect to beta-reduction and confluence of
combinatory logic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Rewriting_Z</h3>
<ul>
<li><a href="../theories/rewriting_z/#Z">Z</a></li>
<li><a href="../theories/rewriting_z/#Lambda_Z">Lambda_Z</a></li>
<li><a href="../theories/rewriting_z/#CL_Z">CL_Z</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Nominal2.html">Nominal 2</a></li></ul>
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<li><a href="../entries/Decreasing-Diagrams-II.html">Decreasing Diagrams II</a></li>
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author = {Bertram Felgenhauer and Julian Nagele and Vincent van Oostrom and Christian Sternagel},
title = {The Z Property},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Rewriting_Z.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>R</span>ibbon <span class='first'>P</span>roofs</h1>
<div>
<p><a href="../authors/wickerson">John Wickerson</a>
</p>
<p class="date">January 19, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document concerns the theory of ribbon proofs: a diagrammatic proof system, based on separation logic, for verifying program correctness. We include the syntax, proof rules, and soundness results for two alternative formalisations of ribbon proofs. <p> Compared to traditional proof outlines, ribbon proofs emphasise the structure of a proof, so are intelligible and pedagogical. Because they contain less redundancy than proof outlines, and allow each proof step to be checked locally, they may be more scalable. Where proof outlines are cumbersome to modify, ribbon proofs can be visually manoeuvred to yield proofs of variant programs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Ribbon_Proofs</h3>
<ul>
<li><a href="../theories/ribbon_proofs/#More_Finite_Map">More_Finite_Map</a></li>
<li><a href="../theories/ribbon_proofs/#JHelper">JHelper</a></li>
<li><a href="../theories/ribbon_proofs/#Proofchain">Proofchain</a></li>
<li><a href="../theories/ribbon_proofs/#Ribbons_Basic">Ribbons_Basic</a></li>
<li><a href="../theories/ribbon_proofs/#Ribbons_Interfaces">Ribbons_Interfaces</a></li>
<li><a href="../theories/ribbon_proofs/#Ribbons_Stratified">Ribbons_Stratified</a></li>
<li><a href="../theories/ribbon_proofs/#Ribbons_Graphical">Ribbons_Graphical</a></li>
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<p style="display:none;" id="bibtex-filename">Ribbon_Proofs-AFP</p><pre id="copy-text">@article{Ribbon_Proofs-AFP,
author = {John Wickerson},
title = {Ribbon Proofs},
journal = {Archive of Formal Proofs},
month = {January},
year = {2013},
note = {\url{https://isa-afp.org/entries/Ribbon_Proofs.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Risk_Free_Lending.html b/web/entries/Risk_Free_Lending.html
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+++ b/web/entries/Risk_Free_Lending.html
@@ -1,172 +1,177 @@
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<h1 >
<span class='first'>R</span>isk-<span class='first'>F</span>ree <span class='first'>L</span>ending</h1>
<div>
<p><a href="../authors/doty">Matthew Doty</a> <a class="obfuscated" data="eyJob3N0IjpbInctZCIsIm9yZyJdLCJ1c2VyIjpbIm1hdHQiXX0=">📧</a>
</p>
<p class="date">September 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We construct an abstract ledger supporting the <em>risk-free
lending</em> protocol. The risk-free lending protocol is a
system for issuing and exchanging novel financial products we call
<em>risk-free loan</em>. The system allows one party to
lend money at 0&#37; APY to another party in exchange for a good
or service. On every update of the ledger, accounts have interest
distributed to them. Holders of lent assets keep interest accrued by
those assets. After distributing interest, the system returns a fixed
fraction of each loan. These fixed fractions determine <em>loan
periods</em>. Loans for longer periods have a smaller fixed
fraction returned. Loans may be re-lent or used as collateral for
other loans. We give a sufficient criterion to enforce all accounts
will forever be solvent. We give a protocol for maintaining this
invariant when transferring or lending funds. We also show this
invariant holds after update. Even though the system does not track
counter-party obligations, we show that all credited and debited loans
cancel and the monetary supply grows at a specified interest rate.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Risk_Free_Lending</h3>
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<li><a href="../theories/risk_free_lending/#Risk_Free_Lending">Risk_Free_Lending</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Risk_Free_Lending-AFP</p><pre id="copy-text">@article{Risk_Free_Lending-AFP,
author = {Matthew Doty},
title = {Risk-Free Lending},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Risk_Free_Lending.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/Robbins-Conjecture.html b/web/entries/Robbins-Conjecture.html
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>omplete <span class='first'>P</span>roof of the <span class='first'>R</span>obbins <span class='first'>C</span>onjecture</h1>
<div>
<p><a href="../authors/doty">Matthew Doty</a>
</p>
<p class="date">May 22, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document gives a formalization of the proof of the Robbins conjecture, following A. Mann, <i>A Complete Proof of the Robbins Conjecture</i>, 2003.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Robbins-Conjecture</h3>
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<li><a href="../theories/robbins-conjecture/#Robbins_Conjecture">Robbins_Conjecture</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Robbins-Conjecture-AFP</p><pre id="copy-text">@article{Robbins-Conjecture-AFP,
author = {Matthew Doty},
title = {A Complete Proof of the Robbins Conjecture},
journal = {Archive of Formal Proofs},
month = {May},
year = {2010},
note = {\url{https://isa-afp.org/entries/Robbins-Conjecture.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robbins-Conjecture-2010-05-27.tar.gz">May 27, 2010</a>: Isabelle2009-1
</li></ul>
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diff --git a/web/entries/Robinson_Arithmetic.html b/web/entries/Robinson_Arithmetic.html
--- a/web/entries/Robinson_Arithmetic.html
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<h1 >
<span class='first'>R</span>obinson <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We instantiate our syntax-independent logic infrastructure developed
in <a
href="https://www.isa-afp.org/entries/Syntax_Independent_Logic.html">a
separate AFP entry</a> to the FOL theory of Robinson arithmetic
(also known as Q). The latter was formalised using Nominal Isabelle by
adapting <a
href="https://www.isa-afp.org/entries/Incompleteness.html">Larry
Paulson’s formalization of the Hereditarily Finite Set
theory</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Robinson_Arithmetic</h3>
<ul>
<li><a href="../theories/robinson_arithmetic/#Robinson_Arithmetic">Robinson_Arithmetic</a></li>
<li><a href="../theories/robinson_arithmetic/#Instance">Instance</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Nominal2.html">Nominal 2</a></li><li><a href="../entries/Syntax_Independent_Logic.html">Syntax-Independent Logic Infrastructure</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Robinson_Arithmetic-AFP</p><pre id="copy-text">@article{Robinson_Arithmetic-AFP,
author = {Andrei Popescu and Dmitriy Traytel},
title = {Robinson Arithmetic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Robinson_Arithmetic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Robinson_Arithmetic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Robinson_Arithmetic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Robinson_Arithmetic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robinson_Arithmetic-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Robinson_Arithmetic-2020-09-18.tar.gz">Sep 18, 2020</a>: Isabelle2020
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diff --git a/web/entries/Root_Balanced_Tree.html b/web/entries/Root_Balanced_Tree.html
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+++ b/web/entries/Root_Balanced_Tree.html
@@ -1,209 +1,211 @@
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<h1 >
<span class='first'>R</span>oot-<span class='first'>B</span>alanced <span class='first'>T</span>ree</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">August 20, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Andersson introduced <em>general balanced trees</em>,
search trees based on the design principle of partial rebuilding:
perform update operations naively until the tree becomes too
unbalanced, at which point a whole subtree is rebalanced. This article
defines and analyzes a functional version of general balanced trees,
which we call <em>root-balanced trees</em>. Using a lightweight model
of execution time, amortized logarithmic complexity is verified in
the theorem prover Isabelle.
</p>
<p>
This is the Isabelle formalization of the material decribed in the APLAS 2017 article
<a href="http://www21.in.tum.de/~nipkow/pubs/aplas17.html">Verified Root-Balanced Trees</a>
by the same author, which also presents experimental results that show
competitiveness of root-balanced with AVL and red-black trees.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Nipkow, T. (2017). Verified Root-Balanced Trees. Lecture Notes in Computer Science, 255–272. <a href="https://doi.org/10.1007/978-3-319-71237-6_13">https://doi.org/10.1007/978-3-319-71237-6_13</a>
</li><li>
<a href="https://www.in.tum.de/~nipkow/pubs/aplas17.html">Open access</a>
</li></ul>
<h3>Session Root_Balanced_Tree</h3>
<ul>
<li><a href="../theories/root_balanced_tree/#Time_Monad">Time_Monad</a></li>
<li><a href="../theories/root_balanced_tree/#Root_Balanced_Tree">Root_Balanced_Tree</a></li>
<li><a href="../theories/root_balanced_tree/#Root_Balanced_Tree_Tab">Root_Balanced_Tree_Tab</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Amortized_Complexity.html">Amortized Complexity Verified</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Closest_Pair_Points.html">Closest Pair of Points Algorithms</a></li><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Root_Balanced_Tree-AFP</p><pre id="copy-text">@article{Root_Balanced_Tree-AFP,
author = {Tobias Nipkow},
title = {Root-Balanced Tree},
journal = {Archive of Formal Proofs},
month = {August},
year = {2017},
note = {\url{https://isa-afp.org/entries/Root_Balanced_Tree.html},
Formal proof development},
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<h1 >
<span class='first'>R</span>oth's <span class='first'>T</span>heorem on <span class='first'>A</span>rithmetic <span class='first'>P</span>rogressions</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a>, <a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">December 28, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise a proof of Roth's Theorem on Arithmetic
Progressions, a major result in additive combinatorics on the
existence of 3-term arithmetic progressions in subsets of natural
numbers. To this end, we follow a proof using graph regularity. We
employ our recent formalisation of Szemerédi's Regularity Lemma,
a major result in extremal graph theory, which we use here to prove
the Triangle Counting Lemma and the Triangle Removal Lemma. Our
sources are Yufei Zhao's MIT lecture notes
"<a href="https://yufeizhao.com/gtac/gtac.pdf">Graph Theory and Additive Combinatorics</a>"
(latest version <a href="https://yufeizhao.com/gtacbook/">here</a>)
and W.T. Gowers's Cambridge lecture notes
"<a href="https://www.dpmms.cam.ac.uk/~par31/notes/tic.pdf">Topics in Combinatorics</a>".
We also refer to the University of
Georgia notes by Stephanie Bell and Will Grodzicki,
"<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.432.327">Using Szemerédi's Regularity Lemma to Prove Roth's Theorem</a>".</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Roth_Arithmetic_Progressions</h3>
<ul>
<li><a href="../theories/roth_arithmetic_progressions/#Roth_Arithmetic_Progressions">Roth_Arithmetic_Progressions</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Ergodic_Theory.html">Ergodic Theory</a></li><li><a href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></li><li><a href="../entries/Random_Graph_Subgraph_Threshold.html">Properties of Random Graphs &ndash; Subgraph Containment</a></li><li><a href="../entries/Szemeredi_Regularity.html">Szemerédi&rsquo;s Regularity Lemma</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Roth_Arithmetic_Progressions-AFP</p><pre id="copy-text">@article{Roth_Arithmetic_Progressions-AFP,
author = {Chelsea Edmonds and Angeliki Koutsoukou-Argyraki and Lawrence C. Paulson},
title = {Roth&#39;s Theorem on Arithmetic Progressions},
journal = {Archive of Formal Proofs},
month = {December},
year = {2021},
note = {\url{https://isa-afp.org/entries/Roth_Arithmetic_Progressions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
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+ </li><li>
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diff --git a/web/entries/Routing.html b/web/entries/Routing.html
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+++ b/web/entries/Routing.html
@@ -1,191 +1,193 @@
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<h1 >
<span class='first'>R</span>outing</h1>
<div>
<p><a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>
</p>
<p class="date">August 31, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains definitions for routing with routing
tables/longest prefix matching. A routing table entry is modelled as
a record of a prefix match, a metric, an output port, and an optional
next hop. A routing table is a list of entries, sorted by prefix
length and metric. Additionally, a parser and serializer for the
output of the ip-route command, a function to create a relation from
output port to corresponding destination IP space, and a model of a
Linux-style router are included.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session Routing</h3>
<ul>
<li><a href="../theories/routing/#Linorder_Helper">Linorder_Helper</a></li>
<li><a href="../theories/routing/#Routing_Table">Routing_Table</a></li>
<li><a href="../theories/routing/#Linux_Router">Linux_Router</a></li>
<li><a href="../theories/routing/#IpRoute_Parser">IpRoute_Parser</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Simple_Firewall.html">Simple Firewall</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Iptables_Semantics.html">Iptables Semantics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Routing-AFP</p><pre id="copy-text">@article{Routing-AFP,
author = {Julius Michaelis and Cornelius Diekmann},
title = {Routing},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/Routing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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</li><li>
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</li><li>
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<a href="https://www.isa-afp.org/release/afp-Routing-2016-08-31.tar.gz">Aug 31, 2016</a>: Isabelle2016
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diff --git a/web/entries/Roy_Floyd_Warshall.html b/web/entries/Roy_Floyd_Warshall.html
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<h1 >
<span class='first'>T</span>ransitive <span class='first'>C</span>losure <span class='first'>A</span>ccording to <span class='first'>R</span>oy-<span class='first'>F</span>loyd-<span class='first'>W</span>arshall</h1>
<div>
<p><a href="../authors/wenzel">Makarius Wenzel</a>
</p>
<p class="date">May 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formulation of the Roy-Floyd-Warshall algorithm for the
transitive closure bypasses matrices and arrays, but uses a more direct
mathematical model with adjacency functions for immediate predecessors and
successors. This can be implemented efficiently in functional programming
languages and is particularly adequate for sparse relations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Roy_Floyd_Warshall</h3>
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<p style="display:none;" id="bibtex-filename">Roy_Floyd_Warshall-AFP</p><pre id="copy-text">@article{Roy_Floyd_Warshall-AFP,
author = {Makarius Wenzel},
title = {Transitive closure according to Roy-Floyd-Warshall},
journal = {Archive of Formal Proofs},
month = {May},
year = {2014},
note = {\url{https://isa-afp.org/entries/Roy_Floyd_Warshall.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/SATSolverVerification.html b/web/entries/SATSolverVerification.html
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<h1 >
<span class='first'>F</span>ormal <span class='first'>V</span>erification of <span class='first'>M</span>odern <span class='first'>S</span><span class='first'>A</span><span class='first'>T</span> <span class='first'>S</span>olvers</h1>
<div>
<p><a href="../authors/maricf">Filip Marić</a> <a href="http://www.matf.bg.ac.rs/~filip">🌐</a>
</p>
<p class="date">July 23, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains formal correctness proofs of modern SAT solvers. Following (Krstic et al, 2007) and (Nieuwenhuis et al., 2006), solvers are described using state-transition systems. Several different SAT solver descriptions are given and their partial correctness and termination is proved. These include: <ul> <li> a solver based on classical DPLL procedure (using only a backtrack-search with unit propagation),</li> <li> a very general solver with backjumping and learning (similar to the description given in (Nieuwenhuis et al., 2006)), and</li> <li> a solver with a specific conflict analysis algorithm (similar to the description given in (Krstic et al., 2007)).</li> </ul> Within the SAT solver correctness proofs, a large number of lemmas about propositional logic and CNF formulae are proved. This theory is self-contained and could be used for further exploring of properties of CNF based SAT algorithms.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session SATSolverVerification</h3>
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<li><a href="../theories/satsolververification/#MoreList">MoreList</a></li>
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<li><a href="../theories/satsolververification/#KrsticGoel">KrsticGoel</a></li>
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<li><a href="../theories/satsolververification/#AssertLiteral">AssertLiteral</a></li>
<li><a href="../theories/satsolververification/#UnitPropagate">UnitPropagate</a></li>
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<li><a href="../theories/satsolververification/#ConflictAnalysis">ConflictAnalysis</a></li>
<li><a href="../theories/satsolververification/#Decide">Decide</a></li>
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<p style="display:none;" id="bibtex-filename">SATSolverVerification-AFP</p><pre id="copy-text">@article{SATSolverVerification-AFP,
author = {Filip Marić},
title = {Formal Verification of Modern SAT Solvers},
journal = {Archive of Formal Proofs},
month = {July},
year = {2008},
note = {\url{https://isa-afp.org/entries/SATSolverVerification.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/SCC_Bloemen_Sequential.html b/web/entries/SCC_Bloemen_Sequential.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Correctness of a Set-based Algorithm for Computing Strongly Connected Components of a Graph - Archive of Formal Proofs</title><meta name="description" content="We prove the correctness of a sequential algorithm for computing
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<h1 >
<span class='first'>C</span>orrectness of a <span class='first'>S</span>et-<span class='first'>B</span>ased <span class='first'>A</span>lgorithm for <span class='first'>C</span>omputing <span class='first'>S</span>trongly <span class='first'>C</span>onnected <span class='first'>C</span>omponents of a <span class='first'>G</span>raph</h1>
<div>
<p><a href="../authors/merz">Stephan Merz</a> <a class="obfuscated" data="eyJob3N0IjpbImxvcmlhIiwiZnIiXSwidXNlciI6WyJTdGVwaGFuIiwiTWVyeiJdfQ==">📧</a> and <a href="../authors/trelat">Vincent Trélat</a> <a class="obfuscated" data="eyJob3N0IjpbImRlcGluZm9uYW5jeSIsIm5ldCJdLCJ1c2VyIjpbInZpbmNlbnQiLCJ0cmVsYXQiXX0=">📧</a>
</p>
<p class="date">August 17, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We prove the correctness of a sequential algorithm for computing
maximal strongly connected components (SCCs) of a graph due to Vincent
Bloemen.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session SCC_Bloemen_Sequential</h3>
<ul>
<li><a href="../theories/scc_bloemen_sequential/#SCC_Bloemen_Sequential">SCC_Bloemen_Sequential</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SCC_Bloemen_Sequential-AFP</p><pre id="copy-text">@article{SCC_Bloemen_Sequential-AFP,
author = {Stephan Merz and Vincent Trélat},
title = {Correctness of a Set-based Algorithm for Computing Strongly Connected Components of a Graph},
journal = {Archive of Formal Proofs},
month = {August},
year = {2022},
note = {\url{https://isa-afp.org/entries/SCC_Bloemen_Sequential.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-SCC_Bloemen_Sequential-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SCC_Bloemen_Sequential-2022-09-09.tar.gz">Sep 9, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/SC_DOM_Components.html b/web/entries/SC_DOM_Components.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>S</span>afely <span class='first'>C</span>omposable <span class='first'>W</span>eb <span class='first'>C</span>omponents</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">September 28, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">While the (safely composable) DOM with shadow trees provide the
technical basis for defining web components, it does neither defines
the concept of web components nor specifies the safety properties that
web components should guarantee. Consequently, the standard also does
not discuss how or even if the methods for modifying the DOM respect
component boundaries. In AFP entry, we present a formally verified
model of safely composable web components and define safety properties
which ensure that different web components can only interact with each
other using well-defined interfaces. Moreover, our verification of the
application programming interface (API) of the DOM revealed numerous
invariants that implementations of the DOM API need to preserve to
ensure the integrity of components. In comparison to the strict
standard compliance formalization of Web Components in the AFP entry
"DOM_Components", the notion of components in this entry
(based on "SC_DOM" and "Shadow_SC_DOM") provides
much stronger safety guarantees.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session SC_DOM_Components</h3>
<ul>
<li><a href="../theories/sc_dom_components/#Core_DOM_DOM_Components">Core_DOM_DOM_Components</a></li>
<li><a href="../theories/sc_dom_components/#Core_DOM_SC_DOM_Components">Core_DOM_SC_DOM_Components</a></li>
<li><a href="../theories/sc_dom_components/#Shadow_DOM_DOM_Components">Shadow_DOM_DOM_Components</a></li>
<li><a href="../theories/sc_dom_components/#Shadow_DOM_SC_DOM_Components">Shadow_DOM_SC_DOM_Components</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Shadow_SC_DOM.html">A Formal Model of the Safely Composable Document Object Model with Shadow Roots</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/DOM_Components.html">A Formalization of Web Components</a></li>
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<p style="display:none;" id="bibtex-filename">SC_DOM_Components-AFP</p><pre id="copy-text">@article{SC_DOM_Components-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {A Formalization of Safely Composable Web Components},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/SC_DOM_Components.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-SC_DOM_Components-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-SC_DOM_Components-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SC_DOM_Components-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SC_DOM_Components-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-SC_DOM_Components-2020-11-27.tar.gz">Nov 27, 2020</a>: Isabelle2020
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diff --git a/web/entries/SDS_Impossibility.html b/web/entries/SDS_Impossibility.html
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>ncompatibility of <span class='first'>S</span><span class='first'>D</span>-<span class='first'>E</span>fficiency and <span class='first'>S</span><span class='first'>D</span>-<span class='first'>S</span>trategy-<span class='first'>P</span>roofness</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
</p>
<p class="date">May 4, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalisation contains the proof that there is no anonymous and
neutral Social Decision Scheme for at least four voters and
alternatives that fulfils both SD-Efficiency and SD-Strategy-
Proofness. The proof is a fully structured and quasi-human-redable
one. It was derived from the (unstructured) SMT proof of the case for
exactly four voters and alternatives by Brandl et al. Their proof
relies on an unverified translation of the original problem to SMT,
and the proof that lifts the argument for exactly four voters and
alternatives to the general case is also not machine-checked. In this
Isabelle proof, on the other hand, all of these steps are fully
proven and machine-checked. This is particularly important seeing as a
previously published informal proof of a weaker statement contained a
mistake in precisely this lifting step.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session SDS_Impossibility</h3>
<ul>
<li><a href="../theories/sds_impossibility/#SDS_Impossibility">SDS_Impossibility</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Randomised_Social_Choice.html">Randomised Social Choice Theory</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Fishburn_Impossibility.html">The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency</a></li>
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<p style="display:none;" id="bibtex-filename">SDS_Impossibility-AFP</p><pre id="copy-text">@article{SDS_Impossibility-AFP,
author = {Manuel Eberl},
title = {The Incompatibility of SD-Efficiency and SD-Strategy-Proofness},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/SDS_Impossibility.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SDS_Impossibility-2016-05-05.tar.gz">May 5, 2016</a>: Isabelle2016
</li></ul>
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<h1 >
<span class='first'>S</span>ecure <span class='first'>I</span>nformation <span class='first'>F</span>low and <span class='first'>P</span>rogram <span class='first'>L</span>ogics</h1>
<div>
<p><a href="../authors/beringer">Lennart Beringer</a> and <a href="../authors/hofmann">Martin Hofmann</a> <a href="http://www.tcs.informatik.uni-muenchen.de/~mhofmann">🌐</a>
</p>
<p class="date">November 10, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present interpretations of type systems for secure information flow in Hoare logic, complementing previous encodings in relational program logics. We first treat the imperative language IMP, extended by a simple procedure call mechanism. For this language we consider base-line non-interference in the style of Volpano et al. and the flow-sensitive type system by Hunt and Sands. In both cases, we show how typing derivations may be used to automatically generate proofs in the program logic that certify the absence of illicit flows. We then add instructions for object creation and manipulation, and derive appropriate proof rules for base-line non-interference. As a consequence of our work, standard verification technology may be used for verifying that a concrete program satisfies the non-interference property.<br><br>The present proof development represents an update of the formalisation underlying our paper [CSF 2007] and is intended to resolve any ambiguities that may be present in the paper.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session SIFPL</h3>
<ul>
<li><a href="../theories/sifpl/#IMP">IMP</a></li>
<li><a href="../theories/sifpl/#VDM">VDM</a></li>
<li><a href="../theories/sifpl/#VS">VS</a></li>
<li><a href="../theories/sifpl/#ContextVS">ContextVS</a></li>
<li><a href="../theories/sifpl/#Lattice">Lattice</a></li>
<li><a href="../theories/sifpl/#HuntSands">HuntSands</a></li>
<li><a href="../theories/sifpl/#OBJ">OBJ</a></li>
<li><a href="../theories/sifpl/#VDM_OBJ">VDM_OBJ</a></li>
<li><a href="../theories/sifpl/#PBIJ">PBIJ</a></li>
<li><a href="../theories/sifpl/#VS_OBJ">VS_OBJ</a></li>
<li><a href="../theories/sifpl/#ContextOBJ">ContextOBJ</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SIFPL-AFP</p><pre id="copy-text">@article{SIFPL-AFP,
author = {Lennart Beringer and Martin Hofmann},
title = {Secure information flow and program logics},
journal = {Archive of Formal Proofs},
month = {November},
year = {2008},
note = {\url{https://isa-afp.org/entries/SIFPL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
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<a href="https://www.isa-afp.org/release/afp-SIFPL-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFPL-2008-11-13.tar.gz">Nov 13, 2008</a>: Isabelle2008
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\ No newline at end of file
diff --git a/web/entries/SIFUM_Type_Systems.html b/web/entries/SIFUM_Type_Systems.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>A</span>ssumptions and <span class='first'>G</span>uarantees for <span class='first'>C</span>ompositional <span class='first'>N</span>oninterference</h1>
<div>
<p><a href="../authors/grewe">Sylvia Grewe</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJncmV3ZSJdfQ==">📧</a>, <a href="../authors/mantel">Heiko Mantel</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJtYW50ZWwiXX0=">📧</a> and <a href="../authors/schoepe">Daniel Schoepe</a> <a class="obfuscated" data="eyJob3N0IjpbInNjaG9lcGUiLCJvcmciXSwidXNlciI6WyJkYW5pZWwiXX0=">📧</a>
</p>
<p class="date">April 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Research in information-flow security aims at developing methods to
identify undesired information leaks within programs from private
(high) sources to public (low) sinks. For a concurrent system, it is
desirable to have compositional analysis methods that allow for
analyzing each thread independently and that nevertheless guarantee
that the parallel composition of successfully analyzed threads
satisfies a global security guarantee. However, such a compositional
analysis should not be overly pessimistic about what an environment
might do with shared resources. Otherwise, the analysis will reject
many intuitively secure programs.
<p>
The paper "Assumptions and Guarantees for Compositional
Noninterference" by Mantel et. al. presents one solution for this problem:
an approach for compositionally reasoning about non-interference in
concurrent programs via rely-guarantee-style reasoning. We present an
Isabelle/HOL formalization of the concepts and proofs of this approach.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session SIFUM_Type_Systems</h3>
<ul>
<li><a href="../theories/sifum_type_systems/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/sifum_type_systems/#Security">Security</a></li>
<li><a href="../theories/sifum_type_systems/#Compositionality">Compositionality</a></li>
<li><a href="../theories/sifum_type_systems/#Language">Language</a></li>
<li><a href="../theories/sifum_type_systems/#TypeSystem">TypeSystem</a></li>
<li><a href="../theories/sifum_type_systems/#LocallySoundModeUse">LocallySoundModeUse</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SIFUM_Type_Systems-AFP</p><pre id="copy-text">@article{SIFUM_Type_Systems-AFP,
author = {Sylvia Grewe and Heiko Mantel and Daniel Schoepe},
title = {A Formalization of Assumptions and Guarantees for Compositional Noninterference},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/SIFUM_Type_Systems.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2014-04-25.tar.gz">Apr 25, 2014</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-SIFUM_Type_Systems-2014-04-24.tar.gz">Apr 24, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/SPARCv8.html b/web/entries/SPARCv8.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor - Archive of Formal Proofs</title><meta name="description" content="We formalise the SPARCv8 instruction set architecture (ISA) which is
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel for the <span class='first'>S</span><span class='first'>P</span><span class='first'>A</span><span class='first'>R</span><span class='first'>C</span>v8 <span class='first'>I</span><span class='first'>S</span><span class='first'>A</span> and a <span class='first'>P</span>roof of <span class='first'>N</span>on-<span class='first'>I</span>nterference for the <span class='first'>L</span><span class='first'>E</span><span class='first'>O</span><span class='first'>N</span>3 <span class='first'>P</span>rocessor</h1>
<div>
<p><a href="../authors/hou">Zhe Hou</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsiemhlIiwiaG91Il19">📧</a>, <a href="../authors/sanan">David Sanan</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsic2FuYW4iXX0=">📧</a>, <a href="../authors/tiu">Alwen Tiu</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsiQVRpdSJdfQ==">📧</a> and <a href="../authors/liuy">Yang Liu</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsieWFuZ2xpdSJdfQ==">📧</a>
</p>
<p class="date">October 19, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalise the SPARCv8 instruction set architecture (ISA) which is
used in processors such as LEON3. Our formalisation can be specialised
to any SPARCv8 CPU, here we use LEON3 as a running example. Our model
covers the operational semantics for all the instructions in the
integer unit of the SPARCv8 architecture and it supports Isabelle code
export, which effectively turns the Isabelle model into a SPARCv8 CPU
simulator. We prove the language-based non-interference property for
the LEON3 processor. Our model is based on deterministic monad, which
is a modified version of the non-deterministic monad from NICTA/l4v.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/hardware">Computer science/Hardware</a></li></ul>
<h3>Session SPARCv8</h3>
<ul>
<li><a href="../theories/sparcv8/#WordDecl">WordDecl</a></li>
<li><a href="../theories/sparcv8/#Sparc_Types">Sparc_Types</a></li>
<li><a href="../theories/sparcv8/#Lib">Lib</a></li>
<li><a href="../theories/sparcv8/#DetMonad">DetMonad</a></li>
<li><a href="../theories/sparcv8/#DetMonadLemmas">DetMonadLemmas</a></li>
<li><a href="../theories/sparcv8/#RegistersOps">RegistersOps</a></li>
<li><a href="../theories/sparcv8/#MMU">MMU</a></li>
<li><a href="../theories/sparcv8/#Sparc_State">Sparc_State</a></li>
<li><a href="../theories/sparcv8/#Sparc_Instruction">Sparc_Instruction</a></li>
<li><a href="../theories/sparcv8/#Sparc_Execution">Sparc_Execution</a></li>
<li><a href="../theories/sparcv8/#Sparc_Properties">Sparc_Properties</a></li>
<li><a href="../theories/sparcv8/#Sparc_Init_State">Sparc_Init_State</a></li>
<li><a href="../theories/sparcv8/#Sparc_Code_Gen">Sparc_Code_Gen</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/SPARCv8/outline.pdf">Proof
outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/SPARCv8/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">SPARCv8-AFP</p><pre id="copy-text">@article{SPARCv8-AFP,
author = {Zhe Hou and David Sanan and Alwen Tiu and Yang Liu},
title = {A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/SPARCv8.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-SPARCv8-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-SPARCv8-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SPARCv8-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SPARCv8-2016-10-19.tar.gz">Oct 19, 2016</a>: Isabelle2016
</li></ul>
</div>
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\ No newline at end of file
diff --git a/web/entries/Safe_Distance.html b/web/entries/Safe_Distance.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles - Archive of Formal Proofs</title><meta name="description" content="The Vienna Convention on Road Traffic defines the safe distance
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormally <span class='first'>V</span>erified <span class='first'>C</span>hecker of the <span class='first'>S</span>afe <span class='first'>D</span>istance <span class='first'>T</span>raffic <span class='first'>R</span>ules for <span class='first'>A</span>utonomous <span class='first'>V</span>ehicles</h1>
<div>
<p><a href="../authors/rizaldi">Albert Rizaldi</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsiYWxiZXJ0Iiwicml6YWxkaSJdfQ==">📧</a> and <a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>
</p>
<p class="date">June 1, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Vienna Convention on Road Traffic defines the safe distance
traffic rules informally. This could make autonomous vehicle liable
for safe-distance-related accidents because there is no clear
definition of how large a safe distance is. We provide a formally
proven prescriptive definition of a safe distance, and checkers which
can decide whether an autonomous vehicle is obeying the safe distance
rule. Not only does our work apply to the domain of law, but it also
serves as a specification for autonomous vehicle manufacturers and for
online verification of path planners.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/mathematics/physics">Mathematics/Physics</a></li></ul>
<h3>Session Safe_Distance</h3>
<ul>
<li><a href="../theories/safe_distance/#Safe_Distance">Safe_Distance</a></li>
<li><a href="../theories/safe_distance/#Safe_Distance_Reaction">Safe_Distance_Reaction</a></li>
<li><a href="../theories/safe_distance/#Evaluation">Evaluation</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li></ul>
</div>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/Safe_Distance/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">Safe_Distance-AFP</p><pre id="copy-text">@article{Safe_Distance-AFP,
author = {Albert Rizaldi and Fabian Immler},
title = {A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles},
journal = {Archive of Formal Proofs},
month = {June},
year = {2020},
note = {\url{https://isa-afp.org/entries/Safe_Distance.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Safe_Distance-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Safe_Distance-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Safe_Distance-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_Distance-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_Distance-2020-06-03.tar.gz">Jun 3, 2020</a>: Isabelle2020
</li></ul>
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diff --git a/web/entries/Safe_OCL.html b/web/entries/Safe_OCL.html
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<h1 >
<span class='first'>S</span>afe <span class='first'>O</span><span class='first'>C</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/nikiforov">Denis Nikiforov</a>
</p>
<p class="date">March 9, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>The theory is a formalization of the
<a href="https://www.omg.org/spec/OCL/">OCL</a> type system, its abstract
syntax and expression typing rules. The theory does not define a concrete
syntax and a semantics. In contrast to
<a href="https://www.isa-afp.org/entries/Featherweight_OCL.html">Featherweight OCL</a>,
it is based on a deep embedding approach. The type system is defined from scratch,
it is not based on the Isabelle HOL type system.</p>
<p>The Safe OCL distincts nullable and non-nullable types. Also the theory gives a
formal definition of <a href="http://ceur-ws.org/Vol-1512/paper07.pdf">safe
navigation operations</a>. The Safe OCL typing rules are much stricter than rules
given in the OCL specification. It allows one to catch more errors on a type
checking phase.</p>
<p>The type theory presented is four-layered: classes, basic types, generic types,
errorable types. We introduce the following new types: non-nullable types (T[1]),
nullable types (T[?]), OclSuper. OclSuper is a supertype of all other types (basic
types, collections, tuples). This type allows us to define a total supremum function,
so types form an upper semilattice. It allows us to define rich expression typing
rules in an elegant manner.</p>
<p>The Preliminaries Chapter of the theory defines a number of helper lemmas for
transitive closures and tuples. It defines also a generic object model independent
from OCL. It allows one to use the theory as a reference for formalization of analogous languages.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session Safe_OCL</h3>
<ul>
<li><a href="../theories/safe_ocl/#Errorable">Errorable</a></li>
<li><a href="../theories/safe_ocl/#Transitive_Closure_Ext">Transitive_Closure_Ext</a></li>
<li><a href="../theories/safe_ocl/#Finite_Map_Ext">Finite_Map_Ext</a></li>
<li><a href="../theories/safe_ocl/#Tuple">Tuple</a></li>
<li><a href="../theories/safe_ocl/#Object_Model">Object_Model</a></li>
<li><a href="../theories/safe_ocl/#OCL_Basic_Types">OCL_Basic_Types</a></li>
<li><a href="../theories/safe_ocl/#OCL_Types">OCL_Types</a></li>
<li><a href="../theories/safe_ocl/#OCL_Syntax">OCL_Syntax</a></li>
<li><a href="../theories/safe_ocl/#OCL_Object_Model">OCL_Object_Model</a></li>
<li><a href="../theories/safe_ocl/#OCL_Typing">OCL_Typing</a></li>
<li><a href="../theories/safe_ocl/#OCL_Normalization">OCL_Normalization</a></li>
<li><a href="../theories/safe_ocl/#OCL_Examples">OCL_Examples</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Safe_OCL-AFP</p><pre id="copy-text">@article{Safe_OCL-AFP,
author = {Denis Nikiforov},
title = {Safe OCL},
journal = {Archive of Formal Proofs},
month = {March},
year = {2019},
note = {\url{https://isa-afp.org/entries/Safe_OCL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Safe_OCL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Safe_OCL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Safe_OCL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_OCL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_OCL-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_OCL-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Safe_OCL-2019-03-14.tar.gz">Mar 14, 2019</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Safe_Range_RC.html b/web/entries/Safe_Range_RC.html
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<h1 >
<span class='first'>M</span>aking <span class='first'>A</span>rbitrary <span class='first'>R</span>elational <span class='first'>C</span>alculus <span class='first'>Q</span>ueries <span class='first'>S</span>afe-<span class='first'>R</span>ange</h1>
<div>
<p><a href="../authors/raszyk">Martin Raszyk</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbIm1hcnRpbiIsInJhc3p5ayJdfQ==">📧</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 28, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The relational calculus (RC), i.e., first-order logic with equality
but without function symbols, is a concise, declarative database query
language. In contrast to relational algebra or SQL, which are the
traditional query languages of choice in the database community, RC
queries can evaluate to an infinite relation. Moreover, even in cases
where the evaluation result of an RC query would be finite it is not
clear how to efficiently compute it. Safe-range RC is an interesting
syntactic subclass of RC, because all safe-range queries evaluate to a
finite result and it is <a
href="http://webdam.inria.fr/Alice/pdfs/Chapter-5.pdf">well-known</a>
how to evaluate such queries by translating them to relational
algebra. We formalize and prove correct <a
href="https://doi.org/10.4230/LIPIcs.ICDT.2022.11">our
recent translation</a> of an arbitrary RC query into a pair of
safe-range queries. Assuming an infinite domain, the two queries have
the following meaning: The first is closed and characterizes the
original query's relative safety, i.e., whether given a fixed
database (interpretation of atomic predicates with finite relations),
the original query evaluates to a finite relation. The second
safe-range query is equivalent to the original query, if the latter is
relatively safe. The formalization uses the Refinement Framework to
go from the non-deterministic algorithm described in the paper to a
deterministic, executable query translation. Our executable query
translation is a first step towards a verified tool that efficiently
evaluates arbitrary RC queries. This very problem is also solved by
the AFP entry <a
href="https://isa-afp.org/entries/Eval_FO.html">Eval_FO</a>
with a theoretically incomparable but practically worse time
complexity. (The latter is demonstrated by <a
href="https://doi.org/10.4230/LIPIcs.ICDT.2022.11">our
empirical evaluation</a>.)</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-management-systems">Computer science/Data management systems</a></li><li><a href="../topics/logic/general-logic/classical-first-order-logic">Logic/General logic/Classical first-order logic</a></li></ul>
<h3>Session Safe_Range_RC</h3>
<ul>
<li><a href="../theories/safe_range_rc/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/safe_range_rc/#Relational_Calculus">Relational_Calculus</a></li>
<li><a href="../theories/safe_range_rc/#Restrict_Bounds">Restrict_Bounds</a></li>
<li><a href="../theories/safe_range_rc/#Restrict_Bounds_Impl">Restrict_Bounds_Impl</a></li>
<li><a href="../theories/safe_range_rc/#Restrict_Frees">Restrict_Frees</a></li>
<li><a href="../theories/safe_range_rc/#Restrict_Frees_Impl">Restrict_Frees_Impl</a></li>
<li><a href="../theories/safe_range_rc/#Examples">Examples</a></li>
<li><a href="../theories/safe_range_rc/#Results">Results</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/List-Index.html">List Index</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Safe_Range_RC-AFP</p><pre id="copy-text">@article{Safe_Range_RC-AFP,
author = {Martin Raszyk and Dmitriy Traytel},
title = {Making Arbitrary Relational Calculus Queries Safe-Range},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Safe_Range_RC.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Safe_Range_RC-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Safe_Range_RC-2022-09-29.tar.gz">Sep 29, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Saturation_Framework.html b/web/entries/Saturation_Framework.html
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@@ -1,191 +1,193 @@
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>omprehensive <span class='first'>F</span>ramework for <span class='first'>S</span>aturation <span class='first'>T</span>heorem <span class='first'>P</span>roving</h1>
<div>
<p><a href="../authors/tourret">Sophie Tourret</a> <a href="https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret/">🌐</a>
</p>
<p class="date">April 9, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization is the companion of the technical
report “A comprehensive framework for saturation theorem proving”,
itself companion of the eponym IJCAR 2020 paper, written by Uwe
Waldmann, Sophie Tourret, Simon Robillard and Jasmin Blanchette. It
verifies a framework for formal refutational completeness proofs of
abstract provers that implement saturation calculi, such as ordered
resolution or superposition, and allows to model entire prover
architectures in such a way that the static refutational completeness
of a calculus immediately implies the dynamic refutational
completeness of a prover implementing the calculus using a variant of
the given clause loop. The technical report “A comprehensive
framework for saturation theorem proving” is available <a
href="http://matryoshka.gforge.inria.fr/pubs/satur_report.pdf">on
the Matryoshka website</a>. The names of the Isabelle lemmas and
theorems corresponding to the results in the report are indicated in
the margin of the report.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Saturation_Framework</h3>
<ul>
<li><a href="../theories/saturation_framework/#Calculus">Calculus</a></li>
<li><a href="../theories/saturation_framework/#Intersection_Calculus">Intersection_Calculus</a></li>
<li><a href="../theories/saturation_framework/#Calculus_Variations">Calculus_Variations</a></li>
<li><a href="../theories/saturation_framework/#Lifting_to_Non_Ground_Calculi">Lifting_to_Non_Ground_Calculi</a></li>
<li><a href="../theories/saturation_framework/#Labeled_Lifting_to_Non_Ground_Calculi">Labeled_Lifting_to_Non_Ground_Calculi</a></li>
<li><a href="../theories/saturation_framework/#Given_Clause_Architectures">Given_Clause_Architectures</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Lambda_Free_RPOs.html">Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</a></li><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Saturation_Framework-AFP</p><pre id="copy-text">@article{Saturation_Framework-AFP,
author = {Sophie Tourret},
title = {A Comprehensive Framework for Saturation Theorem Proving},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Saturation_Framework.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Saturation_Framework-2020-04-10.tar.gz">Apr 10, 2020</a>: Isabelle2019
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diff --git a/web/entries/Saturation_Framework_Extensions.html b/web/entries/Saturation_Framework_Extensions.html
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@@ -1,195 +1,197 @@
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<h1 >
<span class='first'>E</span>xtensions to the <span class='first'>C</span>omprehensive <span class='first'>F</span>ramework for <span class='first'>S</span>aturation <span class='first'>T</span>heorem <span class='first'>P</span>roving</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a href="https://www.cs.vu.nl/~jbe248/">🌐</a> and <a href="../authors/tourret">Sophie Tourret</a> <a href="https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret/">🌐</a>
</p>
<p class="date">August 25, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This Isabelle/HOL formalization extends the AFP entry
<em>Saturation_Framework</em> with the following
contributions: <ul> <li>an application of the framework
to prove Bachmair and Ganzinger's resolution prover RP
refutationally complete, which was formalized in a more ad hoc fashion
by Schlichtkrull et al. in the AFP entry
<em>Ordered_Resultion_Prover</em>;</li>
<li>generalizations of various basic concepts formalized by
Schlichtkrull et al., which were needed to verify RP and could be
useful to formalize other calculi, such as superposition;</li>
<li>alternative proofs of fairness (and hence saturation and
ultimately refutational completeness) for the given clause procedures
GC and LGC, based on invariance.</li> </ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Saturation_Framework_Extensions</h3>
<ul>
<li><a href="../theories/saturation_framework_extensions/#Soundness">Soundness</a></li>
<li><a href="../theories/saturation_framework_extensions/#Standard_Redundancy_Criterion">Standard_Redundancy_Criterion</a></li>
<li><a href="../theories/saturation_framework_extensions/#Clausal_Calculus">Clausal_Calculus</a></li>
<li><a href="../theories/saturation_framework_extensions/#FO_Ordered_Resolution_Prover_Revisited">FO_Ordered_Resolution_Prover_Revisited</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Order_Terms.html">First-Order Terms</a></li><li><a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a></li><li><a href="../entries/Saturation_Framework.html">A Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></li></ul>
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<li><a href="../entries/Clique_and_Monotone_Circuits.html">Clique is not solvable by monotone circuits of polynomial size</a></li>
<li><a href="../entries/Concurrent_Revisions.html">Formalization of Concurrent Revisions</a></li>
<li><a href="../entries/Nested_Multisets_Ordinals.html">Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</a></li>
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<p style="display:none;" id="bibtex-filename">Saturation_Framework_Extensions-AFP</p><pre id="copy-text">@article{Saturation_Framework_Extensions-AFP,
author = {Jasmin Christian Blanchette and Sophie Tourret},
title = {Extensions to the Comprehensive Framework for Saturation Theorem Proving},
journal = {Archive of Formal Proofs},
month = {August},
year = {2020},
note = {\url{https://isa-afp.org/entries/Saturation_Framework_Extensions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>chutz' <span class='first'>I</span>ndependent <span class='first'>A</span>xioms for <span class='first'>M</span>inkowski <span class='first'>S</span>pacetime</h1>
<div>
<p><a href="../authors/schmoetten">Richard Schmoetten</a> <a class="obfuscated" data="eyJob3N0IjpbInNtcyIsImVkIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInMxMzExMzI1Il19">📧</a>, <a href="../authors/palmer">Jake Palmer</a> <a class="obfuscated" data="eyJob3N0IjpbImVkIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbImpha2UiLCJwYWxtZXIiXX0=">📧</a> and <a href="../authors/fleuriot">Jacques D. Fleuriot</a> <a href="https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html">🌐</a>
</p>
<p class="date">July 27, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalisation of Schutz' system of axioms for Minkowski
spacetime published under the name "Independent axioms for
Minkowski space-time" in 1997, as well as most of the results in
the third chapter ("Temporal Order on a Path") of the above
monograph. Many results are proven here that cannot be found in
Schutz, either preceding the theorem they are needed for, or within
their own thematic section.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/physics">Mathematics/Physics</a></li><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Schutz_Spacetime</h3>
<ul>
<li><a href="../theories/schutz_spacetime/#Util">Util</a></li>
<li><a href="../theories/schutz_spacetime/#TernaryOrdering">TernaryOrdering</a></li>
<li><a href="../theories/schutz_spacetime/#Minkowski">Minkowski</a></li>
<li><a href="../theories/schutz_spacetime/#TemporalOrderOnPath">TemporalOrderOnPath</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Schutz_Spacetime-AFP</p><pre id="copy-text">@article{Schutz_Spacetime-AFP,
author = {Richard Schmoetten and Jake Palmer and Jacques D. Fleuriot},
title = {Schutz&#39; Independent Axioms for Minkowski Spacetime},
journal = {Archive of Formal Proofs},
month = {July},
year = {2021},
note = {\url{https://isa-afp.org/entries/Schutz_Spacetime.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Schutz_Spacetime-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Secondary_Sylow.html b/web/entries/Secondary_Sylow.html
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<h1 >
<span class='first'>S</span>econdary <span class='first'>S</span>ylow <span class='first'>T</span>heorems</h1>
<div>
<p><a href="../authors/raumer">Jakob von Raumer</a> <a class="obfuscated" data="eyJob3N0IjpbIm5vdHRpbmdoYW0iLCJhYyIsInVrIl0sInVzZXIiOlsicHN4anY0Il19">📧</a>
</p>
<p class="date">January 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories extend the existing proof of the first Sylow theorem
(written by Florian Kammueller and L. C. Paulson) by what are often
called the second, third and fourth Sylow theorems. These theorems
state propositions about the number of Sylow p-subgroups of a group
and the fact that they are conjugate to each other. The proofs make
use of an implementation of group actions and their properties.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Secondary_Sylow</h3>
<ul>
<li><a href="../theories/secondary_sylow/#GroupAction">GroupAction</a></li>
<li><a href="../theories/secondary_sylow/#SubgroupConjugation">SubgroupConjugation</a></li>
<li><a href="../theories/secondary_sylow/#SndSylow">SndSylow</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Hoelder.html">The Jordan-Hölder Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Secondary_Sylow-AFP</p><pre id="copy-text">@article{Secondary_Sylow-AFP,
author = {Jakob von Raumer},
title = {Secondary Sylow Theorems},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/Secondary_Sylow.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Security_Protocol_Refinement.html b/web/entries/Security_Protocol_Refinement.html
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<h1 >
<span class='first'>D</span>eveloping <span class='first'>S</span>ecurity <span class='first'>P</span>rotocols by <span class='first'>R</span>efinement</h1>
<div>
<p><a href="../authors/sprenger">Christoph Sprenger</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInNwcmVuZ2VyIl19">📧</a> and <a href="../authors/somaini">Ivano Somaini</a>
</p>
<p class="date">May 24, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We propose a development method for security protocols based on
stepwise refinement. Our refinement strategy transforms abstract
security goals into protocols that are secure when operating over an
insecure channel controlled by a Dolev-Yao-style intruder. As
intermediate levels of abstraction, we employ messageless guard
protocols and channel protocols communicating over channels with
security properties. These abstractions provide insights on why
protocols are secure and foster the development of families of
protocols sharing common structure and properties. We have implemented
our method in Isabelle/HOL and used it to develop different entity
authentication and key establishment protocols, including realistic
features such as key confirmation, replay caches, and encrypted
tickets. Our development highlights that guard protocols and channel
protocols provide fundamental abstractions for bridging the gap
between security properties and standard protocol descriptions based
on cryptographic messages. It also shows that our refinement approach
scales to protocols of nontrivial size and complexity.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Security_Protocol_Refinement</h3>
<ul>
<li><a href="../theories/security_protocol_refinement/#Infra">Infra</a></li>
<li><a href="../theories/security_protocol_refinement/#Refinement">Refinement</a></li>
<li><a href="../theories/security_protocol_refinement/#Agents">Agents</a></li>
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<li><a href="../theories/security_protocol_refinement/#Atoms">Atoms</a></li>
<li><a href="../theories/security_protocol_refinement/#Runs">Runs</a></li>
<li><a href="../theories/security_protocol_refinement/#Channels">Channels</a></li>
<li><a href="../theories/security_protocol_refinement/#Message">Message</a></li>
<li><a href="../theories/security_protocol_refinement/#s0g_secrecy">s0g_secrecy</a></li>
<li><a href="../theories/security_protocol_refinement/#a0n_agree">a0n_agree</a></li>
<li><a href="../theories/security_protocol_refinement/#a0i_agree">a0i_agree</a></li>
<li><a href="../theories/security_protocol_refinement/#m1_auth">m1_auth</a></li>
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<li><a href="../theories/security_protocol_refinement/#m2_confid_chan">m2_confid_chan</a></li>
<li><a href="../theories/security_protocol_refinement/#m3_sig">m3_sig</a></li>
<li><a href="../theories/security_protocol_refinement/#m3_enc">m3_enc</a></li>
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<li><a href="../theories/security_protocol_refinement/#m1_keydist_iirn">m1_keydist_iirn</a></li>
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<p style="display:none;" id="bibtex-filename">Security_Protocol_Refinement-AFP</p><pre id="copy-text">@article{Security_Protocol_Refinement-AFP,
author = {Christoph Sprenger and Ivano Somaini},
title = {Developing Security Protocols by Refinement},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Security_Protocol_Refinement.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Security_Protocol_Refinement-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<h1 >
<span class='first'>V</span>erification of <span class='first'>S</span>election and <span class='first'>H</span>eap <span class='first'>S</span>ort <span class='first'>U</span>sing <span class='first'>L</span>ocales</h1>
<div>
<p><a href="../authors/petrovic">Danijela Petrovic</a> <a href="http://www.matf.bg.ac.rs/~danijela">🌐</a>
</p>
<p class="date">February 11, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Stepwise program refinement techniques can be used to simplify
program verification. Programs are better understood since their
main properties are clearly stated, and verification of rather
complex algorithms is reduced to proving simple statements
connecting successive program specifications. Additionally, it is
easy to analyze similar algorithms and to compare their properties
within a single formalization. Usually, formal analysis is not done
in educational setting due to complexity of verification and a lack
of tools and procedures to make comparison easy. Verification of an
algorithm should not only give correctness proof, but also better
understanding of an algorithm. If the verification is based on small
step program refinement, it can become simple enough to be
demonstrated within the university-level computer science
curriculum. In this paper we demonstrate this and give a formal
analysis of two well known algorithms (Selection Sort and Heap Sort)
using proof assistant Isabelle/HOL and program refinement
techniques.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Selection_Heap_Sort</h3>
<ul>
<li><a href="../theories/selection_heap_sort/#Sort">Sort</a></li>
<li><a href="../theories/selection_heap_sort/#RemoveMax">RemoveMax</a></li>
<li><a href="../theories/selection_heap_sort/#SelectionSort_Functional">SelectionSort_Functional</a></li>
<li><a href="../theories/selection_heap_sort/#Heap">Heap</a></li>
<li><a href="../theories/selection_heap_sort/#HeapFunctional">HeapFunctional</a></li>
<li><a href="../theories/selection_heap_sort/#HeapImperative">HeapImperative</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Selection_Heap_Sort-AFP</p><pre id="copy-text">@article{Selection_Heap_Sort-AFP,
author = {Danijela Petrovic},
title = {Verification of Selection and Heap Sort Using Locales},
journal = {Archive of Formal Proofs},
month = {February},
year = {2014},
note = {\url{https://isa-afp.org/entries/Selection_Heap_Sort.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Selection_Heap_Sort-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Some classical results in Social Choice Theory - Archive of Formal Proofs</title><meta name="description" content="Drawing on Sen&#39;s landmark work &#34;Collective Choice and Social Welfare&#34; (1970), this development proves Arrow&#39;s General Possibility Theorem, Sen&#39;s Liberal..."><meta property="og:title" content="Some classical results in Social Choice Theory" />
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<h1 >
<span class='first'>S</span>ome <span class='first'>C</span>lassical <span class='first'>R</span>esults in <span class='first'>S</span>ocial <span class='first'>C</span>hoice <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">November 9, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Drawing on Sen's landmark work "Collective Choice and Social Welfare" (1970), this development proves Arrow's General Possibility Theorem, Sen's Liberal Paradox and May's Theorem in a general setting. The goal was to make precise the classical statements and proofs of these results, and to provide a foundation for more recent results such as the Gibbard-Satterthwaite and Duggan-Schwartz theorems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session SenSocialChoice</h3>
<ul>
<li><a href="../theories/sensocialchoice/#FSext">FSext</a></li>
<li><a href="../theories/sensocialchoice/#RPRs">RPRs</a></li>
<li><a href="../theories/sensocialchoice/#SCFs">SCFs</a></li>
<li><a href="../theories/sensocialchoice/#Arrow">Arrow</a></li>
<li><a href="../theories/sensocialchoice/#Sen">Sen</a></li>
<li><a href="../theories/sensocialchoice/#May">May</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SenSocialChoice-AFP</p><pre id="copy-text">@article{SenSocialChoice-AFP,
author = {Peter Gammie},
title = {Some classical results in Social Choice Theory},
journal = {Archive of Formal Proofs},
month = {November},
year = {2008},
note = {\url{https://isa-afp.org/entries/SenSocialChoice.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-SenSocialChoice-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2012-03-15.tar.gz">Mar 15, 2012</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-SenSocialChoice-2008-11-17.tar.gz">Nov 17, 2008</a>: Isabelle2008
</li></ul>
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<h1 >
<span class='first'>S</span>eparata: <span class='first'>I</span>sabelle <span class='first'>T</span>actics for <span class='first'>S</span>eparation <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/hou">Zhe Hou</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsiemhlIiwiaG91Il19">📧</a>, <a href="../authors/sanan">David Sanan</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsic2FuYW4iXX0=">📧</a>, <a href="../authors/tiu">Alwen Tiu</a> <a class="obfuscated" data="eyJob3N0IjpbIm50dSIsImVkdSIsInNnIl0sInVzZXIiOlsiQVRpdSJdfQ==">📧</a>, <a href="../authors/gore">Rajeev Gore</a> <a class="obfuscated" data="eyJob3N0IjpbImFudSIsImVkdSIsImF1Il0sInVzZXIiOlsicmFqZWV2IiwiZ29yZSJdfQ==">📧</a> and <a href="../authors/clouston">Ranald Clouston</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiYXUiLCJkayJdLCJ1c2VyIjpbInJhbmFsZCIsImNsb3VzdG9uIl19">📧</a>
</p>
<p class="date">November 16, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We bring the labelled sequent calculus $LS_{PASL}$ for propositional
abstract separation logic to Isabelle. The tactics given here are
directly applied on an extension of the Separation Algebra in the AFP.
In addition to the cancellative separation algebra, we further
consider some useful properties in the heap model of separation logic,
such as indivisible unit, disjointness, and cross-split. The tactics
are essentially a proof search procedure for the calculus $LS_{PASL}$.
We wrap the tactics in an Isabelle method called separata, and give a
few examples of separation logic formulae which are provable by
separata.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Separata</h3>
<ul>
<li><a href="../theories/separata/#Separata">Separata</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Separation_Algebra.html">Separation Algebra</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Separation_Logic_Unbounded.html">Unbounded Separation Logic</a></li>
<li><a href="../entries/FOL_Seq_Calc2.html">A Sequent Calculus Prover for First-Order Logic with Functions</a></li>
<li><a href="../entries/Auto2_Imperative_HOL.html">Verifying Imperative Programs using Auto2</a></li>
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<p style="display:none;" id="bibtex-filename">Separata-AFP</p><pre id="copy-text">@article{Separata-AFP,
author = {Zhe Hou and David Sanan and Alwen Tiu and Rajeev Gore and Ranald Clouston},
title = {Separata: Isabelle tactics for Separation Algebra},
journal = {Archive of Formal Proofs},
month = {November},
year = {2016},
note = {\url{https://isa-afp.org/entries/Separata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Separata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Separata-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Separata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Separata-2016-11-17.tar.gz">Nov 17, 2016</a>: Isabelle2016
</li></ul>
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<h1 >
<span class='first'>S</span>eparation <span class='first'>A</span>lgebra</h1>
<div>
<p><a href="../authors/klein">Gerwin Klein</a> <a class="obfuscated" data="eyJob3N0IjpbInVuc3ciLCJlZHUiLCJhdSJdLCJ1c2VyIjpbImtsZWluZyJdfQ==">📧</a>, <a href="../authors/kolanski">Rafal Kolanski</a> <a class="obfuscated" data="eyJob3N0IjpbIm5pY3RhIiwiY29tIiwiYXUiXSwidXNlciI6WyJyYWZhbCIsImtvbGFuc2tpIl19">📧</a> and <a href="../authors/boyton">Andrew Boyton</a> <a class="obfuscated" data="eyJob3N0IjpbIm5pY3RhIiwiY29tIiwiYXUiXSwidXNlciI6WyJhbmRyZXciLCJib3l0b24iXX0=">📧</a>
</p>
<p class="date">May 11, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a generic type class implementation of separation algebra for Isabelle/HOL as well as lemmas and generic tactics which can be used directly for any instantiation of the type class. <P> The ex directory contains example instantiations that include structures such as a heap or virtual memory. <P> The abstract separation algebra is based upon "Abstract Separation Logic" by Calcagno et al. These theories are also the basis of the ITP 2012 rough diamond "Mechanised Separation Algebra" by the authors. <P> The aim of this work is to support and significantly reduce the effort for future separation logic developments in Isabelle/HOL by factoring out the part of separation logic that can be treated abstractly once and for all. This includes developing typical default rule sets for reasoning as well as automated tactic support for separation logic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Separation_Algebra</h3>
<ul>
<li><a href="../theories/separation_algebra/#Separation_Algebra">Separation_Algebra</a></li>
<li><a href="../theories/separation_algebra/#Sep_Heap_Instance">Sep_Heap_Instance</a></li>
<li><a href="../theories/separation_algebra/#Sep_Tactics">Sep_Tactics</a></li>
<li><a href="../theories/separation_algebra/#Simple_Separation_Example">Simple_Separation_Example</a></li>
<li><a href="../theories/separation_algebra/#Sep_Tactics_Test">Sep_Tactics_Test</a></li>
<li><a href="../theories/separation_algebra/#Map_Extra">Map_Extra</a></li>
<li><a href="../theories/separation_algebra/#VM_Example">VM_Example</a></li>
<li><a href="../theories/separation_algebra/#Separation_Algebra_Alt">Separation_Algebra_Alt</a></li>
<li><a href="../theories/separation_algebra/#Sep_Eq">Sep_Eq</a></li>
<li><a href="../theories/separation_algebra/#Types_D">Types_D</a></li>
<li><a href="../theories/separation_algebra/#Abstract_Separation_D">Abstract_Separation_D</a></li>
<li><a href="../theories/separation_algebra/#Separation_D">Separation_D</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hoare_Time.html">Hoare Logics for Time Bounds</a></li><li><a href="../entries/Separata.html">Separata: Isabelle tactics for Separation Algebra</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Separation_Algebra-AFP</p><pre id="copy-text">@article{Separation_Algebra-AFP,
author = {Gerwin Klein and Rafal Kolanski and Andrew Boyton},
title = {Separation Algebra},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Separation_Algebra.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Separation_Logic_Imperative_HOL.html b/web/entries/Separation_Logic_Imperative_HOL.html
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>eparation <span class='first'>L</span>ogic <span class='first'>F</span>ramework for <span class='first'>I</span>mperative <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/meis">Rene Meis</a> <a class="obfuscated" data="eyJob3N0IjpbInVuaS1kdWUiLCJkZSJdLCJ1c2VyIjpbInJlbmUiLCJtZWlzIl19">📧</a>
</p>
<p class="date">November 14, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a framework for separation-logic based correctness proofs of
Imperative HOL programs. Our framework comes with a set of proof methods to
automate canonical tasks such as verification condition generation and
frame inference. Moreover, we provide a set of examples that show the
applicability of our framework. The examples include algorithms on lists,
hash-tables, and union-find trees. We also provide abstract interfaces for
lists, maps, and sets, that allow to develop generic imperative algorithms
and use data-refinement techniques.
<br>
As we target Imperative HOL, our programs can be translated to
efficiently executable code in various target languages, including
ML, OCaml, Haskell, and Scala.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Separation_Logic_Imperative_HOL</h3>
<ul>
<li><a href="../theories/separation_logic_imperative_hol/#Imperative_HOL_Add">Imperative_HOL_Add</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Syntax_Match">Syntax_Match</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Run">Run</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Assertions">Assertions</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Hoare_Triple">Hoare_Triple</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Automation">Automation</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Sep_Main">Sep_Main</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Imp_List_Spec">Imp_List_Spec</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#List_Seg">List_Seg</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Open_List">Open_List</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Circ_List">Circ_List</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Imp_Map_Spec">Imp_Map_Spec</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Hash_Table">Hash_Table</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Hash_Map">Hash_Map</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Hash_Map_Impl">Hash_Map_Impl</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Imp_Set_Spec">Imp_Set_Spec</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Hash_Set_Impl">Hash_Set_Impl</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#To_List_GA">To_List_GA</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Union_Find">Union_Find</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Idioms">Idioms</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Default_Insts">Default_Insts</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Array_Blit">Array_Blit</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Array_Map_Impl">Array_Map_Impl</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Array_Set_Impl">Array_Set_Impl</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#From_List_GA">From_List_GA</a></li>
<li><a href="../theories/separation_logic_imperative_hol/#Sep_Examples">Sep_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Refine_Imperative_HOL.html">The Imperative Refinement Framework</a></li><li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li>
<li><a href="../entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></li>
<li><a href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></li>
<li><a href="../entries/Tree-Automata.html">Tree Automata</a></li>
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<p style="display:none;" id="bibtex-filename">Separation_Logic_Imperative_HOL-AFP</p><pre id="copy-text">@article{Separation_Logic_Imperative_HOL-AFP,
author = {Peter Lammich and Rene Meis},
title = {A Separation Logic Framework for Imperative HOL},
journal = {Archive of Formal Proofs},
month = {November},
year = {2012},
note = {\url{https://isa-afp.org/entries/Separation_Logic_Imperative_HOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>U</span>nbounded <span class='first'>S</span>eparation <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/dardinier">Thibault Dardinier</a> <a href="https://dardinier.me/">🌐</a>
</p>
<p class="date">September 5, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Many separation logics support fractional permissions to distinguish
between read and write access to a heap location, for instance, to
allow concurrent reads while enforcing exclusive writes. Fractional
permissions extend to composite assertions such as (co)inductive
predicates and magic wands by allowing those to be multiplied by a
fraction. Typical separation logic proofs require that this
multiplication has three key properties: it needs to distribute over
assertions, it should permit fractions to be factored out from
assertions, and two fractions of the same assertion should be
combinable into one larger fraction. Existing formal semantics
incorporating fractional assertions into a separation logic define
multiplication semantically (via models), resulting in a semantics in
which distributivity and combinability do not hold for key resource
assertions such as magic wands, and fractions cannot be factored out
from a separating conjunction. By contrast, existing automatic
separation logic verifiers define multiplication syntactically,
resulting in a different semantics for which it is unknown whether
distributivity and combinability hold for all assertions. In this
entry (which accompanies an <a
href="https://dardinier.me/papers/multiplication.pdf">OOPSLA'22
paper</a>), we present and formalize an unbounded version of
separation logic, a novel semantics for separation logic assertions
that allows states to hold more than a full permission to a heap
location during the evaluation of an assertion. By reimposing upper
bounds on the permissions held per location at statement boundaries,
we retain key properties of separation logic, in particular, we prove
that the frame rule still holds. We also prove that our assertion
semantics unifies semantic and syntactic multiplication and thereby
reconciles the discrepancy between separation logic theory and tools
and enjoys distributivity, factorisability, and combinability.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Separation_Logic_Unbounded</h3>
<ul>
<li><a href="../theories/separation_logic_unbounded/#UnboundedLogic">UnboundedLogic</a></li>
<li><a href="../theories/separation_logic_unbounded/#Distributivity">Distributivity</a></li>
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<li><a href="../theories/separation_logic_unbounded/#WandProperties">WandProperties</a></li>
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author = {Thibault Dardinier},
title = {Unbounded Separation Logic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Separation_Logic_Unbounded.html},
Formal proof development},
ISSN = {2150-914x},
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+ <a href="https://www.isa-afp.org/release/afp-Separation_Logic_Unbounded-2022-09-14.tar.gz">Sep 14, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/SequentInvertibility.html b/web/entries/SequentInvertibility.html
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<h1 >
<span class='first'>I</span>nvertibility in <span class='first'>S</span>equent <span class='first'>C</span>alculi</h1>
<div>
<p><a href="../authors/chapman">Peter Chapman</a>
</p>
<p class="date">August 28, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The invertibility of the rules of a sequent calculus is important for guiding proof search and can be used in some formalised proofs of Cut admissibility. We present sufficient conditions for when a rule is invertible with respect to a calculus. We illustrate the conditions with examples. It must be noted we give purely syntactic criteria; no guarantees are given as to the suitability of the rules.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session SequentInvertibility</h3>
<ul>
<li><a href="../theories/sequentinvertibility/#MultiSequents">MultiSequents</a></li>
<li><a href="../theories/sequentinvertibility/#SingleSuccedent">SingleSuccedent</a></li>
<li><a href="../theories/sequentinvertibility/#NominalSequents">NominalSequents</a></li>
<li><a href="../theories/sequentinvertibility/#ModalSequents">ModalSequents</a></li>
<li><a href="../theories/sequentinvertibility/#SRCTransforms">SRCTransforms</a></li>
<li><a href="../theories/sequentinvertibility/#SequentInvertibility">SequentInvertibility</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SequentInvertibility-AFP</p><pre id="copy-text">@article{SequentInvertibility-AFP,
author = {Peter Chapman},
title = {Invertibility in Sequent Calculi},
journal = {Archive of Formal Proofs},
month = {August},
year = {2009},
note = {\url{https://isa-afp.org/entries/SequentInvertibility.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-SequentInvertibility-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<a href="https://www.isa-afp.org/release/afp-SequentInvertibility-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-SequentInvertibility-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-SequentInvertibility-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SequentInvertibility-2009-09-01.tar.gz">Sep 1, 2009</a>: Isabelle2009
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diff --git a/web/entries/Shadow_DOM.html b/web/entries/Shadow_DOM.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel of the <span class='first'>D</span>ocument <span class='first'>O</span>bject <span class='first'>M</span>odel <span class='first'>W</span>ith <span class='first'>S</span>hadow <span class='first'>R</span>oots</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">September 28, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we extend our formalization of the core DOM with
Shadow Roots. Shadow roots are a recent proposal of the web community
to support a component-based development approach for client-side web
applications. Shadow roots are a significant extension to the DOM
standard and, as web standards are condemned to be backward
compatible, such extensions often result in complex specification that
may contain unwanted subtleties that can be detected by a
formalization. Our Isabelle/HOL formalization is, in the sense of
object-orientation, an extension of our formalization of the core DOM
and enjoys the same basic properties, i.e., it is extensible, i.e.,
can be extended without the need of re-proving already proven
properties and executable, i.e., we can generate executable code from
our specification. We exploit the executability to show that our
formalization complies to the official standard of the W3C,
respectively, the WHATWG.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Shadow_DOM</h3>
<ul>
<li><a href="../theories/shadow_dom/#ShadowRootClass">ShadowRootClass</a></li>
<li><a href="../theories/shadow_dom/#ShadowRootMonad">ShadowRootMonad</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM">Shadow_DOM</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_BaseTest">Shadow_DOM_BaseTest</a></li>
<li><a href="../theories/shadow_dom/#slots">slots</a></li>
<li><a href="../theories/shadow_dom/#slots_fallback">slots_fallback</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_Document_adoptNode">Shadow_DOM_Document_adoptNode</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_Document_getElementById">Shadow_DOM_Document_getElementById</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_Node_insertBefore">Shadow_DOM_Node_insertBefore</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_Node_removeChild">Shadow_DOM_Node_removeChild</a></li>
<li><a href="../theories/shadow_dom/#Shadow_DOM_Tests">Shadow_DOM_Tests</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Core_DOM.html">A Formal Model of the Document Object Model</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/DOM_Components.html">A Formalization of Web Components</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Shadow_SC_DOM.html">A Formal Model of the Safely Composable Document Object Model with Shadow Roots</a></li>
</ul>
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<p style="display:none;" id="bibtex-filename">Shadow_DOM-AFP</p><pre id="copy-text">@article{Shadow_DOM-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {A Formal Model of the Document Object Model with Shadow Roots},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Shadow_DOM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Shadow_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Shadow_DOM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Shadow_DOM-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Shadow_DOM-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Shadow_SC_DOM.html b/web/entries/Shadow_SC_DOM.html
--- a/web/entries/Shadow_SC_DOM.html
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@@ -1,208 +1,210 @@
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>M</span>odel of the <span class='first'>S</span>afely <span class='first'>C</span>omposable <span class='first'>D</span>ocument <span class='first'>O</span>bject <span class='first'>M</span>odel <span class='first'>W</span>ith <span class='first'>S</span>hadow <span class='first'>R</span>oots</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a> and <a href="../authors/herzberg">Michael Herzberg</a> <a href="http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg">🌐</a>
</p>
<p class="date">September 28, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this AFP entry, we extend our formalization of the safely
composable DOM with Shadow Roots. This is a proposal for Shadow Roots
with stricter safety guarantess than the standard compliant
formalization (see "Shadow DOM"). Shadow Roots are a recent
proposal of the web community to support a component-based development
approach for client-side web applications. Shadow roots are a
significant extension to the DOM standard and, as web standards are
condemned to be backward compatible, such extensions often result in
complex specification that may contain unwanted subtleties that can be
detected by a formalization. Our Isabelle/HOL formalization is, in
the sense of object-orientation, an extension of our formalization of
the core DOM and enjoys the same basic properties, i.e., it is
extensible, i.e., can be extended without the need of re-proving
already proven properties and executable, i.e., we can generate
executable code from our specification. We exploit the executability
to show that our formalization complies to the official standard of
the W3C, respectively, the WHATWG.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Shadow_SC_DOM</h3>
<ul>
<li><a href="../theories/shadow_sc_dom/#ShadowRootClass">ShadowRootClass</a></li>
<li><a href="../theories/shadow_sc_dom/#ShadowRootMonad">ShadowRootMonad</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM">Shadow_DOM</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM_BaseTest">Shadow_DOM_BaseTest</a></li>
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<li><a href="../theories/shadow_sc_dom/#slots_fallback">slots_fallback</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM_Document_adoptNode">Shadow_DOM_Document_adoptNode</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM_Document_getElementById">Shadow_DOM_Document_getElementById</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM_Node_insertBefore">Shadow_DOM_Node_insertBefore</a></li>
<li><a href="../theories/shadow_sc_dom/#Shadow_DOM_Node_removeChild">Shadow_DOM_Node_removeChild</a></li>
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<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Core_SC_DOM.html">The Safely Composable DOM</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/SC_DOM_Components.html">A Formalization of Safely Composable Web Components</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Shadow_DOM.html">A Formal Model of the Document Object Model with Shadow Roots</a></li>
<li><a href="../entries/Core_DOM.html">A Formal Model of the Document Object Model</a></li>
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<p style="display:none;" id="bibtex-filename">Shadow_SC_DOM-AFP</p><pre id="copy-text">@article{Shadow_SC_DOM-AFP,
author = {Achim D. Brucker and Michael Herzberg},
title = {A Formal Model of the Safely Composable Document Object Model with Shadow Roots},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Shadow_SC_DOM.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Shadow_SC_DOM-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>S</span>hivers' <span class='first'>C</span>ontrol <span class='first'>F</span>low <span class='first'>A</span>nalysis</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a class="obfuscated" data="eyJob3N0IjpbImpvYWNoaW0tYnJlaXRuZXIiLCJkZSJdLCJ1c2VyIjpbIm1haWwiXX0=">📧</a>
</p>
<p class="date">November 16, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In his dissertation, Olin Shivers introduces a concept of control flow graphs
for functional languages, provides an algorithm to statically derive a safe
approximation of the control flow graph and proves this algorithm correct. In
this research project, Shivers' algorithms and proofs are formalized
in the HOLCF extension of HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Shivers-CFA</h3>
<ul>
<li><a href="../theories/shivers-cfa/#HOLCFUtils">HOLCFUtils</a></li>
<li><a href="../theories/shivers-cfa/#CPSScheme">CPSScheme</a></li>
<li><a href="../theories/shivers-cfa/#Eval">Eval</a></li>
<li><a href="../theories/shivers-cfa/#Utils">Utils</a></li>
<li><a href="../theories/shivers-cfa/#SetMap">SetMap</a></li>
<li><a href="../theories/shivers-cfa/#AbsCF">AbsCF</a></li>
<li><a href="../theories/shivers-cfa/#ExCF">ExCF</a></li>
<li><a href="../theories/shivers-cfa/#AbsCFCorrect">AbsCFCorrect</a></li>
<li><a href="../theories/shivers-cfa/#ExCFSV">ExCFSV</a></li>
<li><a href="../theories/shivers-cfa/#Computability">Computability</a></li>
<li><a href="../theories/shivers-cfa/#FixTransform">FixTransform</a></li>
<li><a href="../theories/shivers-cfa/#CPSUtils">CPSUtils</a></li>
<li><a href="../theories/shivers-cfa/#MapSets">MapSets</a></li>
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<p style="display:none;" id="bibtex-filename">Shivers-CFA-AFP</p><pre id="copy-text">@article{Shivers-CFA-AFP,
author = {Joachim Breitner},
title = {Shivers&#39; Control Flow Analysis},
journal = {Archive of Formal Proofs},
month = {November},
year = {2010},
note = {\url{https://isa-afp.org/entries/Shivers-CFA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Shivers-CFA-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
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<h1 >
<span class='first'>A</span>n <span class='first'>A</span>xiomatic <span class='first'>C</span>haracterization of the <span class='first'>S</span>ingle-<span class='first'>S</span>ource <span class='first'>S</span>hortest <span class='first'>P</span>ath <span class='first'>P</span>roblem</h1>
<div>
<p><a href="../authors/rizkallah">Christine Rizkallah</a> <a href="https://www.mpi-inf.mpg.de/~crizkall/">🌐</a>
</p>
<p class="date">May 22, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory is split into two sections. In the first section, we give a formal proof that a well-known axiomatic characterization of the single-source shortest path problem is correct. Namely, we prove that in a directed graph with a non-negative cost function on the edges the single-source shortest path function is the only function that satisfies a set of four axioms. In the second section, we give a formal proof of the correctness of an axiomatic characterization of the single-source shortest path problem for directed graphs with general cost functions. The axioms here are more involved because we have to account for potential negative cycles in the graph. The axioms are summarized in three Isabelle locales.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session ShortestPath</h3>
<ul>
<li><a href="../theories/shortestpath/#ShortestPath">ShortestPath</a></li>
<li><a href="../theories/shortestpath/#ShortestPathNeg">ShortestPathNeg</a></li></ul><div class="flex-wrap">
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<ul class="horizontal-list"><li><a href="../entries/Graph_Theory.html">Graph Theory</a></li></ul>
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<p style="display:none;" id="bibtex-filename">ShortestPath-AFP</p><pre id="copy-text">@article{ShortestPath-AFP,
author = {Christine Rizkallah},
title = {An Axiomatic Characterization of the Single-Source Shortest Path Problem},
journal = {Archive of Formal Proofs},
month = {May},
year = {2013},
note = {\url{https://isa-afp.org/entries/ShortestPath.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-ShortestPath-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-ShortestPath-2013-05-30.tar.gz">May 30, 2013</a>: Isabelle2013
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<h1 >
<span class='first'>H</span>askell's <span class='first'>S</span>how <span class='first'>C</span>lass in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">July 29, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implemented a type class for "to-string" functions, similar to
Haskell's Show class. Moreover, we provide instantiations for Isabelle/HOL's
standard types like bool, prod, sum, nats, ints, and rats. It is further
possible, to automatically derive show functions for arbitrary user defined
datatypes similar to Haskell's "deriving Show".</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>April 10, 2015</dt>
<dd>Moved development for old-style datatypes into subdirectory
"Old_Datatype".<br></dd><dt>March 11, 2015</dt>
<dd>Adapted development to new-style (BNF-based) datatypes.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Show</h3>
<ul>
<li><a href="../theories/show/#Show">Show</a></li>
<li><a href="../theories/show/#Show_Instances">Show_Instances</a></li>
<li><a href="../theories/show/#Show_Poly">Show_Poly</a></li>
<li><a href="../theories/show/#Show_Real">Show_Real</a></li>
<li><a href="../theories/show/#Show_Complex">Show_Complex</a></li>
<li><a href="../theories/show/#Show_Real_Impl">Show_Real_Impl</a></li></ul>
<h3>Session Old_Datatype_Show</h3>
<ul>
<li><a href="../theories/old_datatype_show/#Old_Show">Old_Show</a></li>
<li><a href="../theories/old_datatype_show/#Old_Show_Generator">Old_Show_Generator</a></li>
<li><a href="../theories/old_datatype_show/#Old_Show_Instances">Old_Show_Instances</a></li>
<li><a href="../theories/old_datatype_show/#Old_Show_Examples">Old_Show_Examples</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/MiniSail.html">MiniSail - A kernel language for the ISA specification language SAIL</a></li><li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li><li><a href="../entries/AI_Planning_Languages_Semantics.html">AI Planning Languages Semantics</a></li><li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li><li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li><li><a href="../entries/CakeML.html">CakeML</a></li><li><a href="../entries/Dict_Construction.html">Dictionary Construction</a></li><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Formula_Derivatives.html">Derivatives of Logical Formulas</a></li><li><a href="../entries/Certification_Monads.html">Certification Monads</a></li><li><a href="../entries/XML.html">XML</a></li><li><a href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></li><li><a href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Show-AFP</p><pre id="copy-text">@article{Show-AFP,
author = {Christian Sternagel and René Thiemann},
title = {Haskell&#39;s Show Class in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/Show.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Show-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Show-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Show-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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diff --git a/web/entries/Sigma_Commit_Crypto.html b/web/entries/Sigma_Commit_Crypto.html
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<h1 >
<span class='first'>S</span>igma <span class='first'>P</span>rotocols and <span class='first'>C</span>ommitment <span class='first'>S</span>chemes</h1>
<div>
<p><a href="../authors/butler">David Butler</a> <a href="https://www.turing.ac.uk/people/doctoral-students/david-butler">🌐</a> and <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">October 7, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We use CryptHOL to formalise commitment schemes and Sigma-protocols.
Both are widely used fundamental two party cryptographic primitives.
Security for commitment schemes is considered using game-based
definitions whereas the security of Sigma-protocols is considered
using both the game-based and simulation-based security paradigms. In
this work, we first define security for both primitives and then prove
secure multiple case studies: the Schnorr, Chaum-Pedersen and
Okamoto Sigma-protocols as well as a construction that allows for
compound (AND and OR statements) Sigma-protocols and the Pedersen and
Rivest commitment schemes. We also prove that commitment schemes can
be constructed from Sigma-protocols. We formalise this proof at an
abstract level, only assuming the existence of a Sigma-protocol;
consequently, the instantiations of this result for the concrete
Sigma-protocols we consider come for free.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security/cryptography">Computer science/Security/Cryptography</a></li></ul>
<h3>Session Sigma_Commit_Crypto</h3>
<ul>
<li><a href="../theories/sigma_commit_crypto/#Commitment_Schemes">Commitment_Schemes</a></li>
<li><a href="../theories/sigma_commit_crypto/#Cyclic_Group_Ext">Cyclic_Group_Ext</a></li>
<li><a href="../theories/sigma_commit_crypto/#Discrete_Log">Discrete_Log</a></li>
<li><a href="../theories/sigma_commit_crypto/#Number_Theory_Aux">Number_Theory_Aux</a></li>
<li><a href="../theories/sigma_commit_crypto/#Uniform_Sampling">Uniform_Sampling</a></li>
<li><a href="../theories/sigma_commit_crypto/#Pedersen">Pedersen</a></li>
<li><a href="../theories/sigma_commit_crypto/#Rivest">Rivest</a></li>
<li><a href="../theories/sigma_commit_crypto/#Sigma_Protocols">Sigma_Protocols</a></li>
<li><a href="../theories/sigma_commit_crypto/#Schnorr_Sigma_Commit">Schnorr_Sigma_Commit</a></li>
<li><a href="../theories/sigma_commit_crypto/#Chaum_Pedersen_Sigma_Commit">Chaum_Pedersen_Sigma_Commit</a></li>
<li><a href="../theories/sigma_commit_crypto/#Okamoto_Sigma_Commit">Okamoto_Sigma_Commit</a></li>
<li><a href="../theories/sigma_commit_crypto/#Xor">Xor</a></li>
<li><a href="../theories/sigma_commit_crypto/#Sigma_AND">Sigma_AND</a></li>
<li><a href="../theories/sigma_commit_crypto/#Sigma_OR">Sigma_OR</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/CryptHOL.html">CryptHOL</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Constructive_Cryptography_CM.html">Constructive Cryptography in HOL: the Communication Modeling Aspect</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<p style="display:none;" id="bibtex-filename">Sigma_Commit_Crypto-AFP</p><pre id="copy-text">@article{Sigma_Commit_Crypto-AFP,
author = {David Butler and Andreas Lochbihler},
title = {Sigma Protocols and Commitment Schemes},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/Sigma_Commit_Crypto.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Sigma_Commit_Crypto-2019-10-08.tar.gz">Oct 8, 2019</a>: Isabelle2019
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diff --git a/web/entries/Signature_Groebner.html b/web/entries/Signature_Groebner.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Signature-Based Gröbner Basis Algorithms - Archive of Formal Proofs</title><meta name="description" content="This article formalizes signature-based algorithms for computing Gr&amp;ouml;bner bases. Such algorithms are, in general, superior to other algorithms in terms..."><meta property="og:title" content="Signature-Based Gröbner Basis Algorithms" />
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<h1 >
<span class='first'>S</span>ignature-<span class='first'>B</span>ased <span class='first'>G</span>röbner <span class='first'>B</span>asis <span class='first'>A</span>lgorithms</h1>
<div>
<p><a href="../authors/maletzky">Alexander Maletzky</a> <a href="https://risc.jku.at/m/alexander-maletzky/">🌐</a>
</p>
<p class="date">September 20, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article formalizes signature-based algorithms for computing
Gr&ouml;bner bases. Such algorithms are, in general, superior to
other algorithms in terms of efficiency, and have not been formalized
in any proof assistant so far. The present development is both
generic, in the sense that most known variants of signature-based
algorithms are covered by it, and effectively executable on concrete
input thanks to Isabelle's code generator. Sample computations of
benchmark problems show that the verified implementation of
signature-based algorithms indeed outperforms the existing
implementation of Buchberger's algorithm in Isabelle/HOL.</p>
<p>Besides total correctness of the algorithms, the article also proves
that under certain conditions they a-priori detect and avoid all
useless zero-reductions, and always return 'minimal' (in
some sense) Gr&ouml;bner bases if an input parameter is chosen in
the right way.</p><p>The formalization follows the recent survey article by
Eder and Faug&egrave;re.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Signature_Groebner</h3>
<ul>
<li><a href="../theories/signature_groebner/#Prelims">Prelims</a></li>
<li><a href="../theories/signature_groebner/#More_MPoly">More_MPoly</a></li>
<li><a href="../theories/signature_groebner/#Signature_Groebner">Signature_Groebner</a></li>
<li><a href="../theories/signature_groebner/#Signature_Examples">Signature_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Groebner_Bases.html">Gröbner Bases Theory</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/BirdKMP.html">Putting the `K' into Bird&rsquo;s derivation of Knuth-Morris-Pratt string matching</a></li>
<li><a href="../entries/Weight_Balanced_Trees.html">Weight-Balanced Trees</a></li>
<li><a href="../entries/Buchi_Complementation.html">Büchi Complementation</a></li>
<li><a href="../entries/EdmondsKarp_Maxflow.html">Formalizing the Edmonds-Karp Algorithm</a></li>
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<p style="display:none;" id="bibtex-filename">Signature_Groebner-AFP</p><pre id="copy-text">@article{Signature_Groebner-AFP,
author = {Alexander Maletzky},
title = {Signature-Based Gröbner Basis Algorithms},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Signature_Groebner.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Signature_Groebner-2018-09-20.tar.gz">Sep 20, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Simpl.html b/web/entries/Simpl.html
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<h1 >
<span class='first'>A</span> <span class='first'>S</span>equential <span class='first'>I</span>mperative <span class='first'>P</span>rogramming <span class='first'>L</span>anguage <span class='first'>S</span>yntax, <span class='first'>S</span>emantics, <span class='first'>H</span>oare <span class='first'>L</span>ogics and <span class='first'>V</span>erification <span class='first'>E</span>nvironment</h1>
<div>
<p><a href="../authors/schirmer">Norbert Schirmer</a>
</p>
<p class="date">February 29, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the theory of Simpl, a sequential imperative programming language. We introduce its syntax, its semantics (big and small-step operational semantics) and Hoare logics for both partial as well as total correctness. We prove soundness and completeness of the Hoare logic. We integrate and automate the Hoare logic in Isabelle/HOL to obtain a practically usable verification environment for imperative programs. Simpl is independent of a concrete programming language but expressive enough to cover all common language features: mutually recursive procedures, abrupt termination and exceptions, runtime faults, local and global variables, pointers and heap, expressions with side effects, pointers to procedures, partial application and closures, dynamic method invocation and also unbounded nondeterminism.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session Simpl</h3>
<ul>
<li><a href="../theories/simpl/#Language">Language</a></li>
<li><a href="../theories/simpl/#Semantic">Semantic</a></li>
<li><a href="../theories/simpl/#HoarePartialDef">HoarePartialDef</a></li>
<li><a href="../theories/simpl/#HoarePartialProps">HoarePartialProps</a></li>
<li><a href="../theories/simpl/#HoarePartial">HoarePartial</a></li>
<li><a href="../theories/simpl/#Termination">Termination</a></li>
<li><a href="../theories/simpl/#SmallStep">SmallStep</a></li>
<li><a href="../theories/simpl/#HoareTotalDef">HoareTotalDef</a></li>
<li><a href="../theories/simpl/#HoareTotalProps">HoareTotalProps</a></li>
<li><a href="../theories/simpl/#HoareTotal">HoareTotal</a></li>
<li><a href="../theories/simpl/#Hoare">Hoare</a></li>
<li><a href="../theories/simpl/#StateSpace">StateSpace</a></li>
<li><a href="../theories/simpl/#AlternativeSmallStep">AlternativeSmallStep</a></li>
<li><a href="../theories/simpl/#Simpl_Heap">Simpl_Heap</a></li>
<li><a href="../theories/simpl/#HeapList">HeapList</a></li>
<li><a href="../theories/simpl/#Generalise">Generalise</a></li>
<li><a href="../theories/simpl/#Vcg">Vcg</a></li>
<li><a href="../theories/simpl/#SyntaxTest">SyntaxTest</a></li>
<li><a href="../theories/simpl/#VcgEx">VcgEx</a></li>
<li><a href="../theories/simpl/#VcgExSP">VcgExSP</a></li>
<li><a href="../theories/simpl/#VcgExTotal">VcgExTotal</a></li>
<li><a href="../theories/simpl/#Quicksort">Quicksort</a></li>
<li><a href="../theories/simpl/#XVcg">XVcg</a></li>
<li><a href="../theories/simpl/#XVcgEx">XVcgEx</a></li>
<li><a href="../theories/simpl/#ProcParEx">ProcParEx</a></li>
<li><a href="../theories/simpl/#ProcParExSP">ProcParExSP</a></li>
<li><a href="../theories/simpl/#Closure">Closure</a></li>
<li><a href="../theories/simpl/#ClosureEx">ClosureEx</a></li>
<li><a href="../theories/simpl/#Compose">Compose</a></li>
<li><a href="../theories/simpl/#ComposeEx">ComposeEx</a></li>
<li><a href="../theories/simpl/#UserGuide">UserGuide</a></li>
<li><a href="../theories/simpl/#Simpl">Simpl</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Planarity_Certificates.html">Planarity Certificates</a></li><li><a href="../entries/BDD.html">BDD Normalisation</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Simpl-AFP</p><pre id="copy-text">@article{Simpl-AFP,
author = {Norbert Schirmer},
title = {A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment},
journal = {Archive of Formal Proofs},
month = {February},
year = {2008},
note = {\url{https://isa-afp.org/entries/Simpl.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Simpl-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Simpl-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Simpl-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2009-09-12.tar.gz">Sep 12, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2008-06-10.tar.gz">Jun 10, 2008</a>: Isabelle2008
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simpl-2008-03-07.tar.gz">Mar 7, 2008</a>: Isabelle2007
</li></ul>
</div>
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<h1 >
<span class='first'>S</span>imple <span class='first'>F</span>irewall</h1>
<div>
<p><a href="../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>, <a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a>
</p>
<p class="date">August 24, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a simple model of a firewall. The firewall can accept or
drop a packet and can match on interfaces, IP addresses, protocol, and
ports. It was designed to feature nice mathematical properties: The
type of match expressions was carefully crafted such that the
conjunction of two match expressions is only one match expression.
This model is too simplistic to mirror all aspects of the real world.
In the upcoming entry "Iptables Semantics", we will translate the
Linux firewall iptables to this model. For a fixed service (e.g. ssh,
http), we provide an algorithm to compute an overview of the
firewall's filtering behavior. The algorithm computes minimal service
matrices, i.e. graphs which partition the complete IPv4 and IPv6
address space and visualize the allowed accesses between partitions.
For a detailed description, see
<a href="http://dl.ifip.org/db/conf/networking/networking2016/1570232858.pdf">Verified iptables Firewall
Analysis</a>, IFIP Networking 2016.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session Simple_Firewall</h3>
<ul>
<li><a href="../theories/simple_firewall/#Lib_Enum_toString">Lib_Enum_toString</a></li>
<li><a href="../theories/simple_firewall/#L4_Protocol">L4_Protocol</a></li>
<li><a href="../theories/simple_firewall/#Simple_Packet">Simple_Packet</a></li>
<li><a href="../theories/simple_firewall/#Firewall_Common_Decision_State">Firewall_Common_Decision_State</a></li>
<li><a href="../theories/simple_firewall/#Iface">Iface</a></li>
<li><a href="../theories/simple_firewall/#SimpleFw_Syntax">SimpleFw_Syntax</a></li>
<li><a href="../theories/simple_firewall/#SimpleFw_Semantics">SimpleFw_Semantics</a></li>
<li><a href="../theories/simple_firewall/#List_Product_More">List_Product_More</a></li>
<li><a href="../theories/simple_firewall/#Option_Helpers">Option_Helpers</a></li>
<li><a href="../theories/simple_firewall/#Generic_SimpleFw">Generic_SimpleFw</a></li>
<li><a href="../theories/simple_firewall/#Shadowed">Shadowed</a></li>
<li><a href="../theories/simple_firewall/#IP_Partition_Preliminaries">IP_Partition_Preliminaries</a></li>
<li><a href="../theories/simple_firewall/#GroupF">GroupF</a></li>
<li><a href="../theories/simple_firewall/#IP_Addr_WordInterval_toString">IP_Addr_WordInterval_toString</a></li>
<li><a href="../theories/simple_firewall/#Primitives_toString">Primitives_toString</a></li>
<li><a href="../theories/simple_firewall/#Service_Matrix">Service_Matrix</a></li>
<li><a href="../theories/simple_firewall/#SimpleFw_toString">SimpleFw_toString</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/IP_Addresses.html">IP Addresses</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Routing.html">Routing</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Monad_Memo_DP.html">Monadification, Memoization and Dynamic Programming</a></li>
<li><a href="../entries/UpDown_Scheme.html">Verification of the UpDown Scheme</a></li>
<li><a href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></li>
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<p style="display:none;" id="bibtex-filename">Simple_Firewall-AFP</p><pre id="copy-text">@article{Simple_Firewall-AFP,
author = {Cornelius Diekmann and Julius Michaelis and Max W. Haslbeck},
title = {Simple Firewall},
journal = {Archive of Formal Proofs},
month = {August},
year = {2016},
note = {\url{https://isa-afp.org/entries/Simple_Firewall.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simple_Firewall-2016-08-24.tar.gz">Aug 24, 2016</a>: Isabelle2016
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<h1 >
<span class='first'>A</span>n <span class='first'>I</span>ncremental <span class='first'>S</span>implex <span class='first'>A</span>lgorithm <span class='first'>W</span>ith <span class='first'>U</span>nsatisfiable <span class='first'>C</span>ore <span class='first'>G</span>eneration</h1>
<div>
<p><a href="../authors/maricf">Filip Marić</a> <a class="obfuscated" data="eyJob3N0IjpbIm1hdGYiLCJiZyIsImFjIiwicnMiXSwidXNlciI6WyJmaWxpcCJdfQ==">📧</a>, <a href="../authors/spasic">Mirko Spasić</a> <a class="obfuscated" data="eyJob3N0IjpbIm1hdGYiLCJiZyIsImFjIiwicnMiXSwidXNlciI6WyJtaXJrbyJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">August 24, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an Isabelle/HOL formalization and total correctness proof
for the incremental version of the Simplex algorithm which is used in
most state-of-the-art SMT solvers. It supports extraction of
satisfying assignments, extraction of minimal unsatisfiable cores, incremental
assertion of constraints and backtracking. The formalization relies on
stepwise program refinement, starting from a simple specification,
going through a number of refinement steps, and ending up in a fully
executable functional implementation. Symmetries present in the
algorithm are handled with special care.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/optimization">Computer science/Algorithms/Optimization</a></li></ul>
<h3>Session Simplex</h3>
<ul>
<li><a href="../theories/simplex/#Simplex_Auxiliary">Simplex_Auxiliary</a></li>
<li><a href="../theories/simplex/#Rel_Chain">Rel_Chain</a></li>
<li><a href="../theories/simplex/#Simplex_Algebra">Simplex_Algebra</a></li>
<li><a href="../theories/simplex/#Abstract_Linear_Poly">Abstract_Linear_Poly</a></li>
<li><a href="../theories/simplex/#Linear_Poly_Maps">Linear_Poly_Maps</a></li>
<li><a href="../theories/simplex/#QDelta">QDelta</a></li>
<li><a href="../theories/simplex/#Simplex">Simplex</a></li>
<li><a href="../theories/simplex/#Simplex_Incremental">Simplex_Incremental</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Farkas.html">Farkas' Lemma and Motzkin&rsquo;s Transposition Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Simplex-AFP</p><pre id="copy-text">@article{Simplex-AFP,
author = {Filip Marić and Mirko Spasić and René Thiemann},
title = {An Incremental Simplex Algorithm with Unsatisfiable Core Generation},
journal = {Archive of Formal Proofs},
month = {August},
year = {2018},
note = {\url{https://isa-afp.org/entries/Simplex.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Simplex-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Simplex-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Simplex-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Simplex-2020-01-14.tar.gz">Jan 14, 2020</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simplex-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Simplex-2018-08-27.tar.gz">Aug 27, 2018</a>: Isabelle2018
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<h1 >
<span class='first'>S</span>implicial <span class='first'>C</span>omplexes and <span class='first'>B</span>oolean <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/aransay">Jesús Aransay</a> <a href="https://www.unirioja.es/cu/jearansa">🌐</a>, <a href="../authors/campo">Alejandro del Campo</a> <a class="obfuscated" data="eyJob3N0IjpbImFsdW0iLCJ1bmlyaW9qYSIsImVzIl0sInVzZXIiOlsiYWxlamFuZHJvIiwiZGVsLWNhbXBvIl19">📧</a> and <a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a>
</p>
<p class="date">November 29, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In this work we formalise the isomorphism between simplicial complexes
of dimension $n$ and monotone Boolean functions in $n$ variables,
mainly following the definitions and results as introduced by N. A.
Scoville. We also take advantage of the AFP
representation of <a href="https://www.isa-afp.org/entries/ROBDD.html">ROBDD</a>
(Reduced Ordered Binary Decision Diagrams) to compute the ROBDD representation of a
given simplicial complex (by means of the isomorphism to Boolean
functions). Some examples of simplicial complexes and associated
Boolean functions are also presented.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/topology">Mathematics/Topology</a></li></ul>
<h3>Session Simplicial_complexes_and_boolean_functions</h3>
<ul>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#Boolean_functions">Boolean_functions</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#Simplicial_complex">Simplicial_complex</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#Bij_betw_simplicial_complex_bool_func">Bij_betw_simplicial_complex_bool_func</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#MkIfex">MkIfex</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#Evasive">Evasive</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#ListLexorder">ListLexorder</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#BDD">BDD</a></li>
<li><a href="../theories/simplicial_complexes_and_boolean_functions/#Binary_operations">Binary_operations</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/ROBDD.html">Algorithms for Reduced Ordered Binary Decision Diagrams</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Simplicial_complexes_and_boolean_functions-AFP</p><pre id="copy-text">@article{Simplicial_complexes_and_boolean_functions-AFP,
author = {Jesús Aransay and Alejandro del Campo and Julius Michaelis},
title = {Simplicial Complexes and Boolean functions},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Simplicial_complexes_and_boolean_functions.html},
Formal proof development},
ISSN = {2150-914x},
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- <a href="https://www.isa-afp.org/release/afp-Simplicial_complexes_and_boolean_functions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Simplicial_complexes_and_boolean_functions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/SimplifiedOntologicalArgument.html b/web/entries/SimplifiedOntologicalArgument.html
--- a/web/entries/SimplifiedOntologicalArgument.html
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@@ -1,182 +1,184 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content="Simplified variants of Gödel&#39;s ontological argument are explored. Among those is a particularly interesting simplified argument which is (i) valid already..."><meta property="og:title" content="Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL" />
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<h1 >
<span class='first'>E</span>xploring <span class='first'>S</span>implified <span class='first'>V</span>ariants of <span class='first'>G</span>ödel’s <span class='first'>O</span>ntological <span class='first'>A</span>rgument in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a>
</p>
<p class="date">November 8, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Simplified variants of Gödel's ontological argument are
explored. Among those is a particularly interesting simplified
argument which is (i) valid already in basic
modal logics K or KT, (ii) which does not suffer from modal collapse,
and (iii) which avoids the rather complex predicates of essence (Ess.)
and necessary existence (NE) as used by Gödel.
</p><p>
Whether the presented variants increase or decrease the
attractiveness and persuasiveness of the ontological argument is a
question I would like to pass on to philosophy and theology.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li><li><a href="../topics/logic/general-logic/modal-logic">Logic/General logic/Modal logic</a></li></ul>
<h3>Session SimplifiedOntologicalArgument</h3>
<ul>
<li><a href="../theories/simplifiedontologicalargument/#HOML">HOML</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimplifiedOntologicalArgument">SimplifiedOntologicalArgument</a></li>
<li><a href="../theories/simplifiedontologicalargument/#MFilter">MFilter</a></li>
<li><a href="../theories/simplifiedontologicalargument/#BaseDefs">BaseDefs</a></li>
<li><a href="../theories/simplifiedontologicalargument/#ScottVariant">ScottVariant</a></li>
<li><a href="../theories/simplifiedontologicalargument/#UFilterVariant">UFilterVariant</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimpleVariant">SimpleVariant</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimpleVariantPG">SimpleVariantPG</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimpleVariantSE">SimpleVariantSE</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimpleVariantSEinT">SimpleVariantSEinT</a></li>
<li><a href="../theories/simplifiedontologicalargument/#SimpleVariantHF">SimpleVariantHF</a></li>
<li><a href="../theories/simplifiedontologicalargument/#KanckosLethenNo2Possibilist">KanckosLethenNo2Possibilist</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SimplifiedOntologicalArgument-AFP</p><pre id="copy-text">@article{SimplifiedOntologicalArgument-AFP,
author = {Christoph Benzmüller},
title = {Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/SimplifiedOntologicalArgument.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-SimplifiedOntologicalArgument-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-SimplifiedOntologicalArgument-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SimplifiedOntologicalArgument-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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diff --git a/web/entries/Skew_Heap.html b/web/entries/Skew_Heap.html
--- a/web/entries/Skew_Heap.html
+++ b/web/entries/Skew_Heap.html
@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>S</span>kew <span class='first'>H</span>eap</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">August 13, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Skew heaps are an amazingly simple and lightweight implementation of
priority queues. They were invented by Sleator and Tarjan [SIAM 1986]
and have logarithmic amortized complexity. This entry provides executable
and verified functional skew heaps.
<p>
The amortized complexity of skew heaps is analyzed in the AFP entry
<a href="http://isa-afp.org/entries/Amortized_Complexity.html">Amortized Complexity</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Skew Heaps in <a href="https://functional-algorithms-verified.org">Functional Algorithms, Verified!</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Skew_heap">Wikipedia</a>
</li></ul>
<h3>Session Skew_Heap</h3>
<ul>
<li><a href="../theories/skew_heap/#Skew_Heap">Skew_Heap</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Amortized_Complexity.html">Amortized Complexity Verified</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Skew_Heap-AFP</p><pre id="copy-text">@article{Skew_Heap-AFP,
author = {Tobias Nipkow},
title = {Skew Heap},
journal = {Archive of Formal Proofs},
month = {August},
year = {2014},
note = {\url{https://isa-afp.org/entries/Skew_Heap.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>kip <span class='first'>L</span>ists</h1>
<div>
<p><a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">January 9, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> Skip lists are sorted linked lists enhanced with shortcuts
and are an alternative to binary search trees. A skip lists consists
of multiple levels of sorted linked lists where a list on level n is a
subsequence of the list on level n − 1. In the ideal case, elements
are skipped in such a way that a lookup in a skip lists takes O(log n)
time. In a randomised skip list the skipped elements are choosen
randomly. </p> <p> This entry contains formalized proofs
of the textbook results about the expected height and the expected
length of a search path in a randomised skip list. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Skip_Lists</h3>
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<li><a href="../theories/skip_lists/#Pi_pmf">Pi_pmf</a></li>
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<p style="display:none;" id="bibtex-filename">Skip_Lists-AFP</p><pre id="copy-text">@article{Skip_Lists-AFP,
author = {Max W. Haslbeck and Manuel Eberl},
title = {Skip Lists},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Skip_Lists.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Slicing.html b/web/entries/Slicing.html
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<h1 >
<span class='first'>T</span>owards <span class='first'>C</span>ertified <span class='first'>S</span>licing</h1>
<div>
<p><a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">September 16, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Slicing is a widely-used technique with applications in e.g. compiler technology and software security. Thus verification of algorithms in these areas is often based on the correctness of slicing, which should ideally be proven independent of concrete programming languages and with the help of well-known verifying techniques such as proof assistants. As a first step in this direction, this contribution presents a framework for dynamic and static intraprocedural slicing based on control flow and program dependence graphs. Abstracting from concrete syntax we base the framework on a graph representation of the program fulfilling certain structural and well-formedness properties.<br><br>The formalization consists of the basic framework (in subdirectory Basic/), the correctness proof for dynamic slicing (in subdirectory Dynamic/), the correctness proof for static intraprocedural slicing (in subdirectory StaticIntra/) and instantiations of the framework with a simple While language (in subdirectory While/) and the sophisticated object-oriented bytecode language of Jinja (in subdirectory JinjaVM/). For more information on the framework, see the TPHOLS 2008 paper by Wasserrab and Lochbihler and the PLAS 2009 paper by Wasserrab et al.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/static-analysis">Computer science/Programming languages/Static analysis</a></li></ul>
<h3>Session Slicing</h3>
<ul>
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<li><a href="../theories/slicing/#DynStandardControlDependence">DynStandardControlDependence</a></li>
<li><a href="../theories/slicing/#DynWeakControlDependence">DynWeakControlDependence</a></li>
<li><a href="../theories/slicing/#DynPDG">DynPDG</a></li>
<li><a href="../theories/slicing/#DependentLiveVariables">DependentLiveVariables</a></li>
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<li><a href="../theories/slicing/#Distance">Distance</a></li>
<li><a href="../theories/slicing/#DataDependence">DataDependence</a></li>
<li><a href="../theories/slicing/#Slice">Slice</a></li>
<li><a href="../theories/slicing/#StandardControlDependence">StandardControlDependence</a></li>
<li><a href="../theories/slicing/#WeakControlDependence">WeakControlDependence</a></li>
<li><a href="../theories/slicing/#PDG">PDG</a></li>
<li><a href="../theories/slicing/#WeakOrderDependence">WeakOrderDependence</a></li>
<li><a href="../theories/slicing/#CDepInstantiations">CDepInstantiations</a></li>
<li><a href="../theories/slicing/#ControlDependenceRelations">ControlDependenceRelations</a></li>
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<li><a href="../theories/slicing/#JVMPostdomination">JVMPostdomination</a></li>
<li><a href="../theories/slicing/#JVMCFG_wf">JVMCFG_wf</a></li>
<li><a href="../theories/slicing/#JVMControlDependences">JVMControlDependences</a></li>
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<li><a href="../theories/slicing/#Slicing">Slicing</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jinja.html">Jinja is not Java</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Formal_SSA.html">Verified Construction of Static Single Assignment Form</a></li><li><a href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Slicing-AFP</p><pre id="copy-text">@article{Slicing-AFP,
author = {Daniel Wasserrab},
title = {Towards Certified Slicing},
journal = {Archive of Formal Proofs},
month = {September},
year = {2008},
note = {\url{https://isa-afp.org/entries/Slicing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>ormalization of an <span class='first'>A</span>lgorithm for <span class='first'>G</span>reedily <span class='first'>C</span>omputing <span class='first'>A</span>ssociative <span class='first'>A</span>ggregations on <span class='first'>S</span>liding <span class='first'>W</span>indows</h1>
<div>
<p><a href="../authors/heimes">Lukas Heimes</a>, <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a> and <a href="../authors/schneider">Joshua Schneider</a>
</p>
<p class="date">April 10, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Basin et al.'s <a
href="https://doi.org/10.1016/j.ipl.2014.09.009">sliding
window algorithm (SWA)</a> is an algorithm for combining the
elements of subsequences of a sequence with an associative operator.
It is greedy and minimizes the number of operator applications. We
formalize the algorithm and verify its functional correctness. We
extend the algorithm with additional operations and provide an
alternative interface to the slide operation that does not require the
entire input sequence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Sliding_Window_Algorithm</h3>
<ul>
<li><a href="../theories/sliding_window_algorithm/#SWA">SWA</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Sliding_Window_Algorithm-AFP</p><pre id="copy-text">@article{Sliding_Window_Algorithm-AFP,
author = {Lukas Heimes and Dmitriy Traytel and Joshua Schneider},
title = {Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Sliding_Window_Algorithm.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Smith_Normal_Form.html b/web/entries/Smith_Normal_Form.html
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>A</span>lgorithm for <span class='first'>C</span>omputing the <span class='first'>S</span>mith <span class='first'>N</span>ormal <span class='first'>F</span>orm of a <span class='first'>M</span>atrix</h1>
<div>
<p><a href="../authors/divason">Jose Divasón</a> <a href="https://www.unirioja.es/cu/jodivaso/">🌐</a>
</p>
<p class="date">May 23, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work presents a formal proof in Isabelle/HOL of an algorithm to
transform a matrix into its Smith normal form, a canonical matrix
form, in a general setting: the algorithm is parameterized by
operations to prove its existence over elementary divisor rings, while
execution is guaranteed over Euclidean domains. We also provide a
formal proof on some results about the generality of this algorithm as
well as the uniqueness of the Smith normal form. Since Isabelle/HOL
does not feature dependent types, the development is carried out
switching conveniently between two different existing libraries: the
Hermite normal form (based on HOL Analysis) and the Jordan normal form
AFP entries. This permits to reuse results from both developments and
it is done by means of the lifting and transfer package together with
the use of local type definitions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Smith_Normal_Form</h3>
<ul>
<li><a href="../theories/smith_normal_form/#Smith_Normal_Form">Smith_Normal_Form</a></li>
<li><a href="../theories/smith_normal_form/#Diagonal_To_Smith">Diagonal_To_Smith</a></li>
<li><a href="../theories/smith_normal_form/#Mod_Type_Connect">Mod_Type_Connect</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Missing_Lemmas">SNF_Missing_Lemmas</a></li>
<li><a href="../theories/smith_normal_form/#Cauchy_Binet">Cauchy_Binet</a></li>
<li><a href="../theories/smith_normal_form/#Smith_Normal_Form_JNF">Smith_Normal_Form_JNF</a></li>
<li><a href="../theories/smith_normal_form/#Rings2_Extended">Rings2_Extended</a></li>
<li><a href="../theories/smith_normal_form/#Finite_Field_Mod_Type_Connection">Finite_Field_Mod_Type_Connection</a></li>
<li><a href="../theories/smith_normal_form/#Admits_SNF_From_Diagonal_Iff_Bezout_Ring">Admits_SNF_From_Diagonal_Iff_Bezout_Ring</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Uniqueness">SNF_Uniqueness</a></li>
<li><a href="../theories/smith_normal_form/#Cauchy_Binet_HOL_Analysis">Cauchy_Binet_HOL_Analysis</a></li>
<li><a href="../theories/smith_normal_form/#Diagonalize">Diagonalize</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Algorithm_Two_Steps">SNF_Algorithm_Two_Steps</a></li>
<li><a href="../theories/smith_normal_form/#Diagonal_To_Smith_JNF">Diagonal_To_Smith_JNF</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Algorithm_Two_Steps_JNF">SNF_Algorithm_Two_Steps_JNF</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Algorithm">SNF_Algorithm</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Algorithm_HOL_Analysis">SNF_Algorithm_HOL_Analysis</a></li>
<li><a href="../theories/smith_normal_form/#Elementary_Divisor_Rings">Elementary_Divisor_Rings</a></li>
<li><a href="../theories/smith_normal_form/#SNF_Algorithm_Euclidean_Domain">SNF_Algorithm_Euclidean_Domain</a></li>
<li><a href="../theories/smith_normal_form/#Smith_Certified">Smith_Certified</a></li>
<li><a href="../theories/smith_normal_form/#Alternative_Proofs">Alternative_Proofs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li><li><a href="../entries/Hermite.html">Hermite Normal Form</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Types_To_Sets_Extension.html">Extension of Types-To-Sets</a></li>
<li><a href="../entries/Modular_arithmetic_LLL_and_HNF_algorithms.html">Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</a></li>
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<p style="display:none;" id="bibtex-filename">Smith_Normal_Form-AFP</p><pre id="copy-text">@article{Smith_Normal_Form-AFP,
author = {Jose Divasón},
title = {A verified algorithm for computing the Smith normal form of a matrix},
journal = {Archive of Formal Proofs},
month = {May},
year = {2020},
note = {\url{https://isa-afp.org/entries/Smith_Normal_Form.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>mooth <span class='first'>M</span>anifolds</h1>
<div>
<p><a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a> and <a href="../authors/zhan">Bohua Zhan</a> <a href="http://lcs.ios.ac.cn/~bzhan/">🌐</a>
</p>
<p class="date">October 22, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the definition and basic properties of smooth manifolds
in Isabelle/HOL. Concepts covered include partition of unity, tangent
and cotangent spaces, and the fundamental theorem of path integrals.
We also examine some concrete manifolds such as spheres and projective
spaces. The formalization makes extensive use of the analysis and
linear algebra libraries in Isabelle/HOL, in particular its
“types-to-sets” mechanism.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/topology">Mathematics/Topology</a></li></ul>
<h3>Session Smooth_Manifolds</h3>
<ul>
<li><a href="../theories/smooth_manifolds/#Analysis_More">Analysis_More</a></li>
<li><a href="../theories/smooth_manifolds/#Smooth">Smooth</a></li>
<li><a href="../theories/smooth_manifolds/#Bump_Function">Bump_Function</a></li>
<li><a href="../theories/smooth_manifolds/#Chart">Chart</a></li>
<li><a href="../theories/smooth_manifolds/#Topological_Manifold">Topological_Manifold</a></li>
<li><a href="../theories/smooth_manifolds/#Differentiable_Manifold">Differentiable_Manifold</a></li>
<li><a href="../theories/smooth_manifolds/#Partition_Of_Unity">Partition_Of_Unity</a></li>
<li><a href="../theories/smooth_manifolds/#Tangent_Space">Tangent_Space</a></li>
<li><a href="../theories/smooth_manifolds/#Cotangent_Space">Cotangent_Space</a></li>
<li><a href="../theories/smooth_manifolds/#Product_Manifold">Product_Manifold</a></li>
<li><a href="../theories/smooth_manifolds/#Sphere">Sphere</a></li>
<li><a href="../theories/smooth_manifolds/#Projective_Space">Projective_Space</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Smooth_Manifolds-AFP</p><pre id="copy-text">@article{Smooth_Manifolds-AFP,
author = {Fabian Immler and Bohua Zhan},
title = {Smooth Manifolds},
journal = {Archive of Formal Proofs},
month = {October},
year = {2018},
note = {\url{https://isa-afp.org/entries/Smooth_Manifolds.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Solidity.html b/web/entries/Solidity.html
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@@ -1,185 +1,190 @@
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<h1 >
<span class='first'>I</span>sabelle/<span class='first'>S</span>olidity: <span class='first'>A</span> <span class='first'>D</span>eep <span class='first'>E</span>mbedding of <span class='first'>S</span>olidity in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/marmsoler">Diego Marmsoler</a> <a href="http://marmsoler.com">🌐</a> and <a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a>
</p>
<p class="date">July 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Smart contracts are automatically executed programs, usually
representing legal agreements such as financial transactions. Thus,
bugs in smart contracts can lead to large financial losses. For
example, an incorrectly initialized contract was the root cause of the
Parity Wallet bug that saw $280M worth of Ether destroyed. Ether is
the cryptocurrency of the Ethereum blockchain that uses Solidity for
expressing smart contracts. We address this problem by formalizing an
executable denotational semantics for Solidity in the interactive
theorem prover Isabelle/HOL. This formal semantics builds the
foundation of an interactive program verification environment for
Solidity programs and allows for inspecting them by (symbolic)
execution. We combine the latter with grammar based fuzzing to ensure
that our formal semantics complies to the Solidity implementation on
the Ethereum Blockchain. Finally, we demonstrate the formal
verification of Solidity programs by two examples: constant folding
and a simple verified token.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages">Computer science/Programming languages</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Solidity</h3>
<ul>
<li><a href="../theories/solidity/#Solidity_Symbex">Solidity_Symbex</a></li>
<li><a href="../theories/solidity/#ReadShow">ReadShow</a></li>
<li><a href="../theories/solidity/#StateMonad">StateMonad</a></li>
<li><a href="../theories/solidity/#Valuetypes">Valuetypes</a></li>
<li><a href="../theories/solidity/#Storage">Storage</a></li>
<li><a href="../theories/solidity/#Accounts">Accounts</a></li>
<li><a href="../theories/solidity/#Environment">Environment</a></li>
<li><a href="../theories/solidity/#Statements">Statements</a></li>
<li><a href="../theories/solidity/#Solidity_Main">Solidity_Main</a></li>
<li><a href="../theories/solidity/#Solidity_Evaluator">Solidity_Evaluator</a></li>
<li><a href="../theories/solidity/#Constant_Folding">Constant_Folding</a></li>
<li><a href="../theories/solidity/#Reentrancy">Reentrancy</a></li>
<li><a href="../theories/solidity/#Compile_Evaluator">Compile_Evaluator</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Solidity-AFP</p><pre id="copy-text">@article{Solidity-AFP,
author = {Diego Marmsoler and Achim D. Brucker},
title = {Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/Solidity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Solidity-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Solidity-2022-08-12.tar.gz">Aug 12, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Sophomores_Dream.html b/web/entries/Sophomores_Dream.html
--- a/web/entries/Sophomores_Dream.html
+++ b/web/entries/Sophomores_Dream.html
@@ -1,161 +1,166 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>ophomore's <span class='first'>D</span>ream</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">April 10, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a brief formalisation of the two
equations known as the <em>Sophomore's Dream</em>,
first discovered by Johann Bernoulli in 1697:</p> \[\int_0^1
x^{-x}\,\text{d}x = \sum_{n=1}^\infty n^{-n} \quad\text{and}\quad
\int_0^1 x^x\,\text{d}x = -\sum_{n=1}^\infty (-n)^{-n}\]</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Sophomores_Dream</h3>
<ul>
<li><a href="../theories/sophomores_dream/#Sophomores_Dream">Sophomores_Dream</a></li></ul><div class="flex-wrap">
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author = {Manuel Eberl},
title = {The Sophomore&#39;s Dream},
journal = {Archive of Formal Proofs},
month = {April},
year = {2022},
note = {\url{https://isa-afp.org/entries/Sophomores_Dream.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Sophomores_Dream-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Sophomores_Dream-2022-05-09.tar.gz">May 9, 2022</a>: Isabelle2021-1
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<h1 >
<span class='first'>S</span>ound and <span class='first'>C</span>omplete <span class='first'>S</span>ort <span class='first'>E</span>ncodings for <span class='first'>F</span>irst-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/blanchette">Jasmin Christian Blanchette</a> <a href="http://www21.in.tum.de/~blanchet">🌐</a> and <a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a>
</p>
<p class="date">June 27, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a formalization of the soundness and completeness properties
for various efficient encodings of sorts in unsorted first-order logic
used by Isabelle's Sledgehammer tool.
<p>
Essentially, the encodings proceed as follows:
a many-sorted problem is decorated with (as few as possible) tags or
guards that make the problem monotonic; then sorts can be soundly
erased.
<p>
The development employs a formalization of many-sorted first-order logic
in clausal form (clauses, structures and the basic properties
of the satisfaction relation), which could be of interest as the starting
point for other formalizations of first-order logic metatheory.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Sort_Encodings</h3>
<ul>
<li><a href="../theories/sort_encodings/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/sort_encodings/#TermsAndClauses">TermsAndClauses</a></li>
<li><a href="../theories/sort_encodings/#Sig">Sig</a></li>
<li><a href="../theories/sort_encodings/#M">M</a></li>
<li><a href="../theories/sort_encodings/#CM">CM</a></li>
<li><a href="../theories/sort_encodings/#Mono">Mono</a></li>
<li><a href="../theories/sort_encodings/#Mcalc">Mcalc</a></li>
<li><a href="../theories/sort_encodings/#T_G_Prelim">T_G_Prelim</a></li>
<li><a href="../theories/sort_encodings/#Mcalc2">Mcalc2</a></li>
<li><a href="../theories/sort_encodings/#Mcalc2C">Mcalc2C</a></li>
<li><a href="../theories/sort_encodings/#G">G</a></li>
<li><a href="../theories/sort_encodings/#T">T</a></li>
<li><a href="../theories/sort_encodings/#U">U</a></li>
<li><a href="../theories/sort_encodings/#CU">CU</a></li>
<li><a href="../theories/sort_encodings/#E">E</a></li>
<li><a href="../theories/sort_encodings/#Encodings">Encodings</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Sort_Encodings-AFP</p><pre id="copy-text">@article{Sort_Encodings-AFP,
author = {Jasmin Christian Blanchette and Andrei Popescu},
title = {Sound and Complete Sort Encodings for First-Order Logic},
journal = {Archive of Formal Proofs},
month = {June},
year = {2013},
note = {\url{https://isa-afp.org/entries/Sort_Encodings.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2013-07-04.tar.gz">Jul 4, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sort_Encodings-2013-07-01.tar.gz">Jul 1, 2013</a>: Isabelle2013
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Source_Coding_Theorem.html b/web/entries/Source_Coding_Theorem.html
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<h1 >
<span class='first'>S</span>ource <span class='first'>C</span>oding <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/hibon">Quentin Hibon</a> <a class="obfuscated" data="eyJob3N0IjpbImNsIiwiY2FtIiwiYWMiLCJ1ayJdLCJ1c2VyIjpbInFoMjI1Il19">📧</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJscDE1Il19">📧</a>
</p>
<p class="date">October 19, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document contains a proof of the necessary condition on the code
rate of a source code, namely that this code rate is bounded by the
entropy of the source. This represents one half of Shannon's source
coding theorem, which is itself an equivalence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li></ul>
<h3>Session Source_Coding_Theorem</h3>
<ul>
<li><a href="../theories/source_coding_theorem/#Source_Coding_Theorem">Source_Coding_Theorem</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Source_Coding_Theorem-AFP</p><pre id="copy-text">@article{Source_Coding_Theorem-AFP,
author = {Quentin Hibon and Lawrence C. Paulson},
title = {Source Coding Theorem},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Source_Coding_Theorem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Source_Coding_Theorem-2016-10-19.tar.gz">Oct 19, 2016</a>: Isabelle2016
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diff --git a/web/entries/SpecCheck.html b/web/entries/SpecCheck.html
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@@ -1,180 +1,182 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>SpecCheck - Specification-Based Testing for Isabelle/ML - Archive of Formal Proofs</title><meta name="description" content="SpecCheck is a QuickCheck-like testing framework for Isabelle/ML. You can use it to write specifications for ML functions. SpecCheck then checks whether..."><meta property="og:title" content="SpecCheck - Specification-Based Testing for Isabelle/ML" />
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<h1 >
<span class='first'>S</span>pec<span class='first'>C</span>heck - <span class='first'>S</span>pecification-<span class='first'>B</span>ased <span class='first'>T</span>esting for <span class='first'>I</span>sabelle/<span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/kappelmann">Kevin Kappelmann</a> <a href="https://www21.in.tum.de/team/kappelmk/">🌐</a>, <a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a> and <a href="../authors/willenbrink">Sebastian Willenbrink</a> <a class="obfuscated" data="eyJob3N0IjpbInR1bSIsImRlIl0sInVzZXIiOlsic2ViYXN0aWFuIiwid2lsbGVuYnJpbmsiXX0=">📧</a>
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<p class="date">July 1, 2021</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">SpecCheck is a <a
href="https://en.wikipedia.org/wiki/QuickCheck">QuickCheck</a>-like
testing framework for Isabelle/ML. You can use it to write
specifications for ML functions. SpecCheck then checks whether your
specification holds by testing your function against a given number of
generated inputs. It helps you to identify bugs by printing
counterexamples on failure and provides you timing information.
SpecCheck is customisable and allows you to specify your own input
generators, test output formats, as well as pretty printers and
shrinking functions for counterexamples among other things.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session SpecCheck</h3>
<ul>
<li><a href="../theories/speccheck/#SpecCheck_Base">SpecCheck_Base</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Generators">SpecCheck_Generators</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Show">SpecCheck_Show</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Output_Style">SpecCheck_Output_Style</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Shrink">SpecCheck_Shrink</a></li>
<li><a href="../theories/speccheck/#SpecCheck">SpecCheck</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Dynamic">SpecCheck_Dynamic</a></li>
<li><a href="../theories/speccheck/#SpecCheck_Examples">SpecCheck_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Conditional_Transfer_Rule.html">Conditional Transfer Rule</a></li><li><a href="../entries/Types_To_Sets_Extension.html">Extension of Types-To-Sets</a></li><li><a href="../entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></li></ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/SpecCheck/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">SpecCheck-AFP</p><pre id="copy-text">@article{SpecCheck-AFP,
author = {Kevin Kappelmann and Lukas Bulwahn and Sebastian Willenbrink},
title = {SpecCheck - Specification-Based Testing for Isabelle/ML},
journal = {Archive of Formal Proofs},
month = {July},
year = {2021},
note = {\url{https://isa-afp.org/entries/SpecCheck.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
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+ <a href="https://www.isa-afp.org/release/afp-SpecCheck-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-SpecCheck-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-SpecCheck-2021-07-08.tar.gz">Jul 8, 2021</a>: Isabelle2021
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diff --git a/web/entries/Special_Function_Bounds.html b/web/entries/Special_Function_Bounds.html
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<h1 >
<span class='first'>R</span>eal-<span class='first'>V</span>alued <span class='first'>S</span>pecial <span class='first'>F</span>unctions: <span class='first'>U</span>pper and <span class='first'>L</span>ower <span class='first'>B</span>ounds</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">August 29, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This development proves upper and lower bounds for several familiar real-valued functions. For sin, cos, exp and sqrt, it defines and verifies infinite families of upper and lower bounds, mostly based on Taylor series expansions. For arctan, ln and exp, it verifies a finite collection of upper and lower bounds, originally obtained from the functions' continued fraction expansions using the computer algebra system Maple. A common theme in these proofs is to take the difference between a function and its approximation, which should be zero at one point, and then consider the sign of the derivative. The immediate purpose of this development is to verify axioms used by MetiTarski, an automatic theorem prover for real-valued special functions. Crucial to MetiTarski's operation is the provision of upper and lower bounds for each function of interest.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Special_Function_Bounds</h3>
<ul>
<li><a href="../theories/special_function_bounds/#Bounds_Lemmas">Bounds_Lemmas</a></li>
<li><a href="../theories/special_function_bounds/#Atan_CF_Bounds">Atan_CF_Bounds</a></li>
<li><a href="../theories/special_function_bounds/#Exp_Bounds">Exp_Bounds</a></li>
<li><a href="../theories/special_function_bounds/#Log_CF_Bounds">Log_CF_Bounds</a></li>
<li><a href="../theories/special_function_bounds/#Sin_Cos_Bounds">Sin_Cos_Bounds</a></li>
<li><a href="../theories/special_function_bounds/#Sqrt_Bounds">Sqrt_Bounds</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Special_Function_Bounds-AFP</p><pre id="copy-text">@article{Special_Function_Bounds-AFP,
author = {Lawrence C. Paulson},
title = {Real-Valued Special Functions: Upper and Lower Bounds},
journal = {Archive of Formal Proofs},
month = {August},
year = {2014},
note = {\url{https://isa-afp.org/entries/Special_Function_Bounds.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2014-09-05.tar.gz">Sep 5, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Special_Function_Bounds-2014-08-29.tar.gz">Aug 29, 2014</a>: Isabelle2014
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Splay_Tree.html b/web/entries/Splay_Tree.html
--- a/web/entries/Splay_Tree.html
+++ b/web/entries/Splay_Tree.html
@@ -1,194 +1,196 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Splay Tree - Archive of Formal Proofs</title><meta name="description" content="Splay trees are self-adjusting binary search trees which were invented by Sleator and Tarjan [JACM 1985]. This entry provides executable and verified..."><meta property="og:title" content="Splay Tree" />
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<h1 >
<span class='first'>S</span>play <span class='first'>T</span>ree</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">August 12, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Splay trees are self-adjusting binary search trees which were invented by Sleator and Tarjan [JACM 1985].
This entry provides executable and verified functional splay trees
as well as the related splay heaps (due to Okasaki).
<p>
The amortized complexity of splay trees and heaps is analyzed in the AFP entry
<a href="http://isa-afp.org/entries/Amortized_Complexity.html">Amortized Complexity</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 12, 2016</dt>
<dd>Moved splay heaps here from Amortized_Complexity</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Splay Trees in <a href="https://functional-algorithms-verified.org">Functional Algorithms, Verified!</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Splay_tree">Wikipedia</a>
</li></ul>
<h3>Session Splay_Tree</h3>
<ul>
<li><a href="../theories/splay_tree/#Splay_Tree">Splay_Tree</a></li>
<li><a href="../theories/splay_tree/#Splay_Map">Splay_Map</a></li>
<li><a href="../theories/splay_tree/#Splay_Heap">Splay_Heap</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Splay_Tree-AFP</p><pre id="copy-text">@article{Splay_Tree-AFP,
author = {Tobias Nipkow},
title = {Splay Tree},
journal = {Archive of Formal Proofs},
month = {August},
year = {2014},
note = {\url{https://isa-afp.org/entries/Splay_Tree.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Splay_Tree-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Splay_Tree-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Splay_Tree-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Splay_Tree-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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diff --git a/web/entries/Sqrt_Babylonian.html b/web/entries/Sqrt_Babylonian.html
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@@ -1,202 +1,204 @@
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<h1 >
<span class='first'>C</span>omputing <span class='first'>N</span>-<span class='first'>T</span>h <span class='first'>R</span>oots <span class='first'>U</span>sing the <span class='first'>B</span>abylonian <span class='first'>M</span>ethod</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">January 3, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We implement the Babylonian method to compute n-th roots of numbers.
We provide precise algorithms for naturals, integers and rationals, and
offer an approximation algorithm for square roots over linear ordered fields. Moreover, there
are precise algorithms to compute the floor and the ceiling of n-th roots.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>History</h3>
<dl><dt>July 11, 2014</dt>
<dd>Moved NthRoot_Impl from Real-Impl to this entry.</dd><dt>October 16, 2013</dt>
<dd>Added algorithms to compute floor and ceiling of sqrt of integers.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Sqrt_Babylonian</h3>
<ul>
<li><a href="../theories/sqrt_babylonian/#Sqrt_Babylonian_Auxiliary">Sqrt_Babylonian_Auxiliary</a></li>
<li><a href="../theories/sqrt_babylonian/#Log_Impl">Log_Impl</a></li>
<li><a href="../theories/sqrt_babylonian/#NthRoot_Impl">NthRoot_Impl</a></li>
<li><a href="../theories/sqrt_babylonian/#Sqrt_Babylonian">Sqrt_Babylonian</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Cauchy.html">Cauchy&rsquo;s Mean Theorem and the Cauchy-Schwarz Inequality</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li><li><a href="../entries/QR_Decomposition.html">QR Decomposition</a></li><li><a href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Sqrt_Babylonian-AFP</p><pre id="copy-text">@article{Sqrt_Babylonian-AFP,
author = {René Thiemann},
title = {Computing N-th Roots using the Babylonian Method},
journal = {Archive of Formal Proofs},
month = {January},
year = {2013},
note = {\url{https://isa-afp.org/entries/Sqrt_Babylonian.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stable_Matching.html b/web/entries/Stable_Matching.html
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<h1 >
<span class='first'>S</span>table <span class='first'>M</span>atching</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">October 24, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We mechanize proofs of several results from the matching with
contracts literature, which generalize those of the classical
two-sided matching scenarios that go by the name of stable marriage.
Our focus is on game theoretic issues. Along the way we develop
executable algorithms for computing optimal stable matches.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Stable_Matching</h3>
<ul>
<li><a href="../theories/stable_matching/#Sotomayor">Sotomayor</a></li>
<li><a href="../theories/stable_matching/#Basis">Basis</a></li>
<li><a href="../theories/stable_matching/#Choice_Functions">Choice_Functions</a></li>
<li><a href="../theories/stable_matching/#Contracts">Contracts</a></li>
<li><a href="../theories/stable_matching/#COP">COP</a></li>
<li><a href="../theories/stable_matching/#Bossiness">Bossiness</a></li>
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<p style="display:none;" id="bibtex-filename">Stable_Matching-AFP</p><pre id="copy-text">@article{Stable_Matching-AFP,
author = {Peter Gammie},
title = {Stable Matching},
journal = {Archive of Formal Proofs},
month = {October},
year = {2016},
note = {\url{https://isa-afp.org/entries/Stable_Matching.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stalnaker_Logic.html b/web/entries/Stalnaker_Logic.html
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<h1 >
<span class='first'>S</span>talnaker's <span class='first'>E</span>pistemic <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/guzman">Laura P. Gamboa Guzman</a> <a href="https://sites.google.com/view/lpgamboa/home">🌐</a>
</p>
<p class="date">September 23, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work is a formalization of Stalnaker's epistemic logic with
countably many agents and its soundness and completeness theorems, as
well as the equivalence between the axiomatization of S4 available in
the Epistemic Logic theory and the topological one. It builds on the
Epistemic Logic theory.</div>
<h3>License</h3>
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<ul><li><a href="../topics/logic/general-logic/logics-of-knowledge-and-belief">Logic/General logic/Logics of knowledge and belief</a></li></ul>
<h3>Session Stalnaker_Logic</h3>
<ul>
<li><a href="../theories/stalnaker_logic/#Stalnaker_Logic">Stalnaker_Logic</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Epistemic_Logic.html">Epistemic Logic: Completeness of Modal Logics</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stalnaker_Logic-AFP</p><pre id="copy-text">@article{Stalnaker_Logic-AFP,
author = {Laura P. Gamboa Guzman},
title = {Stalnaker&#39;s Epistemic Logic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Stalnaker_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Stalnaker_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Stalnaker_Logic-2022-09-26.tar.gz">Sep 26, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Statecharts.html b/web/entries/Statecharts.html
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<h1 >
<span class='first'>F</span>ormalizing <span class='first'>S</span>tatecharts <span class='first'>U</span>sing <span class='first'>H</span>ierarchical <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/helke">Steffen Helke</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtYmVybGluIiwiZGUiXSwidXNlciI6WyJoZWxrZSJdfQ==">📧</a> and <a href="../authors/kammueller">Florian Kammüller</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtYmVybGluIiwiZGUiXSwidXNlciI6WyJmbG9rYW0iXX0=">📧</a>
</p>
<p class="date">August 8, 2010</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize in Isabelle/HOL the abtract syntax and a synchronous
step semantics for the specification language Statecharts. The formalization
is based on Hierarchical Automata which allow a structural decomposition of
Statecharts into Sequential Automata. To support the composition of
Statecharts, we introduce calculating operators to construct a Hierarchical
Automaton in a stepwise manner. Furthermore, we present a complete semantics
of Statecharts including a theory of data spaces, which enables the modelling
of racing effects. We also adapt CTL for
Statecharts to build a bridge for future combinations with model
checking. However the main motivation of this work is to provide a sound and
complete basis for reasoning on Statecharts. As a central meta theorem we
prove that the well-formedness of a Statechart is preserved by the semantics.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Statecharts</h3>
<ul>
<li><a href="../theories/statecharts/#Contrib">Contrib</a></li>
<li><a href="../theories/statecharts/#DataSpace">DataSpace</a></li>
<li><a href="../theories/statecharts/#Data">Data</a></li>
<li><a href="../theories/statecharts/#Update">Update</a></li>
<li><a href="../theories/statecharts/#Expr">Expr</a></li>
<li><a href="../theories/statecharts/#SA">SA</a></li>
<li><a href="../theories/statecharts/#HA">HA</a></li>
<li><a href="../theories/statecharts/#HASem">HASem</a></li>
<li><a href="../theories/statecharts/#Kripke">Kripke</a></li>
<li><a href="../theories/statecharts/#HAKripke">HAKripke</a></li>
<li><a href="../theories/statecharts/#HAOps">HAOps</a></li>
<li><a href="../theories/statecharts/#CarAudioSystem">CarAudioSystem</a></li></ul><div class="flex-wrap">
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<h4>PDFs</h4>
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<p style="display:none;" id="bibtex-filename">Statecharts-AFP</p><pre id="copy-text">@article{Statecharts-AFP,
author = {Steffen Helke and Florian Kammüller},
title = {Formalizing Statecharts using Hierarchical Automata},
journal = {Archive of Formal Proofs},
month = {August},
year = {2010},
note = {\url{https://isa-afp.org/entries/Statecharts.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Statecharts-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Statecharts-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Statecharts-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Statecharts-2010-08-18.tar.gz">Aug 18, 2010</a>: Isabelle2009-2
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Stateful_Protocol_Composition_and_Typing.html b/web/entries/Stateful_Protocol_Composition_and_Typing.html
--- a/web/entries/Stateful_Protocol_Composition_and_Typing.html
+++ b/web/entries/Stateful_Protocol_Composition_and_Typing.html
@@ -1,200 +1,202 @@
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<h1 >
<span class='first'>S</span>tateful <span class='first'>P</span>rotocol <span class='first'>C</span>omposition and <span class='first'>T</span>yping</h1>
<div>
<p><a href="../authors/hess">Andreas V. Hess</a> <a class="obfuscated" data="eyJob3N0IjpbImR0dSIsImRrIl0sInVzZXIiOlsiYXZoZSJdfQ==">📧</a>, <a href="../authors/moedersheim">Sebastian Mödersheim</a> <a href="https://people.compute.dtu.dk/samo/">🌐</a> and <a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a>
</p>
<p class="date">April 8, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide in this AFP entry several relative soundness results for
security protocols. In particular, we prove typing and
compositionality results for stateful protocols (i.e., protocols with
mutable state that may span several sessions), and that focuses on
reachability properties. Such results are useful to simplify protocol
verification by reducing it to a simpler problem: Typing results give
conditions under which it is safe to verify a protocol in a typed
model where only "well-typed" attacks can occur whereas
compositionality results allow us to verify a composed protocol by
only verifying the component protocols in isolation. The conditions on
the protocols under which the results hold are furthermore syntactic
in nature allowing for full automation. The foundation presented here
is used in another entry to provide fully automated and formalized
security proofs of stateful protocols.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session Stateful_Protocol_Composition_and_Typing</h3>
<ul>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Miscellaneous">Miscellaneous</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Messages">Messages</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#More_Unification">More_Unification</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Intruder_Deduction">Intruder_Deduction</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Strands_and_Constraints">Strands_and_Constraints</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Lazy_Intruder">Lazy_Intruder</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Typed_Model">Typed_Model</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Typing_Result">Typing_Result</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Stateful_Strands">Stateful_Strands</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Stateful_Typing">Stateful_Typing</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Labeled_Strands">Labeled_Strands</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Parallel_Compositionality">Parallel_Compositionality</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Labeled_Stateful_Strands">Labeled_Stateful_Strands</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Stateful_Compositionality">Stateful_Compositionality</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Example_Keyserver">Example_Keyserver</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Example_TLS">Example_TLS</a></li>
<li><a href="../theories/stateful_protocol_composition_and_typing/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/First_Order_Terms.html">First-Order Terms</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Automated_Stateful_Protocol_Verification.html">Automated Stateful Protocol Verification</a></li></ul>
</div>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Stateful_Protocol_Composition_and_Typing/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">Stateful_Protocol_Composition_and_Typing-AFP</p><pre id="copy-text">@article{Stateful_Protocol_Composition_and_Typing-AFP,
author = {Andreas V. Hess and Sebastian Mödersheim and Achim D. Brucker},
title = {Stateful Protocol Composition and Typing},
journal = {Archive of Formal Proofs},
month = {April},
year = {2020},
note = {\url{https://isa-afp.org/entries/Stateful_Protocol_Composition_and_Typing.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Stateful_Protocol_Composition_and_Typing-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Stateful_Protocol_Composition_and_Typing-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Stateful_Protocol_Composition_and_Typing-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stateful_Protocol_Composition_and_Typing-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stateful_Protocol_Composition_and_Typing-2020-05-20.tar.gz">May 20, 2020</a>: Isabelle2020
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/Stellar_Quorums.html b/web/entries/Stellar_Quorums.html
--- a/web/entries/Stellar_Quorums.html
+++ b/web/entries/Stellar_Quorums.html
@@ -1,169 +1,171 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Stellar Quorum Systems - Archive of Formal Proofs</title><meta name="description" content="We formalize the static properties of personal Byzantine quorum
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<h1 >
<span class='first'>S</span>tellar <span class='first'>Q</span>uorum <span class='first'>S</span>ystems</h1>
<div>
<p><a href="../authors/losa">Giuliano Losa</a> <a class="obfuscated" data="eyJob3N0IjpbImdhbG9pcyIsImNvbSJdLCJ1c2VyIjpbImdpdWxpYW5vIl19">📧</a>
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<p class="date">August 1, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the static properties of personal Byzantine quorum
systems (PBQSs) and Stellar quorum systems, as described in the paper
``Stellar Consensus by Reduction'' (to appear at DISC 2019).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul>
<h3>Session Stellar_Quorums</h3>
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<li><a href="../theories/stellar_quorums/#Stellar_Quorums">Stellar_Quorums</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Stellar_Quorums-AFP</p><pre id="copy-text">@article{Stellar_Quorums-AFP,
author = {Giuliano Losa},
title = {Stellar Quorum Systems},
journal = {Archive of Formal Proofs},
month = {August},
year = {2019},
note = {\url{https://isa-afp.org/entries/Stellar_Quorums.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Stellar_Quorums-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Stern_Brocot.html b/web/entries/Stern_Brocot.html
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>tern-<span class='first'>B</span>rocot <span class='first'>T</span>ree</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a> and <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
</p>
<p class="date">December 22, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Stern-Brocot tree contains all rational numbers exactly once and in their lowest terms. We formalise the Stern-Brocot tree as a coinductive tree using recursive and iterative specifications, which we have proven equivalent, and show that it indeed contains all the numbers as stated. Following Hinze, we prove that the Stern-Brocot tree can be linearised looplessly into Stern's diatonic sequence (also known as Dijkstra's fusc function) and that it is a permutation of the Bird tree.
</p><p>
The reasoning stays at an abstract level by appealing to the uniqueness of solutions of guarded recursive equations and lifting algebraic laws point-wise to trees and streams using applicative functors.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Stern_Brocot</h3>
<ul>
<li><a href="../theories/stern_brocot/#Cotree">Cotree</a></li>
<li><a href="../theories/stern_brocot/#Cotree_Algebra">Cotree_Algebra</a></li>
<li><a href="../theories/stern_brocot/#Stern_Brocot_Tree">Stern_Brocot_Tree</a></li>
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<p style="display:none;" id="bibtex-filename">Stern_Brocot-AFP</p><pre id="copy-text">@article{Stern_Brocot-AFP,
author = {Peter Gammie and Andreas Lochbihler},
title = {The Stern-Brocot Tree},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Stern_Brocot.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stewart_Apollonius.html b/web/entries/Stewart_Apollonius.html
--- a/web/entries/Stewart_Apollonius.html
+++ b/web/entries/Stewart_Apollonius.html
@@ -1,194 +1,196 @@
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<h1 >
<span class='first'>S</span>tewart's <span class='first'>T</span>heorem and <span class='first'>A</span>pollonius' <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">July 31, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry formalizes the two geometric theorems, Stewart's and
Apollonius' theorem. Stewart's Theorem relates the length of
a triangle's cevian to the lengths of the triangle's two
sides. Apollonius' Theorem is a specialisation of Stewart's
theorem, restricting the cevian to be the median. The proof applies
the law of cosines, some basic geometric facts about triangles and
then simply transforms the terms algebraically to yield the
conjectured relation. The formalization in Isabelle can closely follow
the informal proofs described in the Wikipedia articles of those two
theorems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Stewart_Apollonius</h3>
<ul>
<li><a href="../theories/stewart_apollonius/#Stewart_Apollonius">Stewart_Apollonius</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Triangle.html">Basic Geometric Properties of Triangles</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stewart_Apollonius-AFP</p><pre id="copy-text">@article{Stewart_Apollonius-AFP,
author = {Lukas Bulwahn},
title = {Stewart&#39;s Theorem and Apollonius&#39; Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/Stewart_Apollonius.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>S</span>tirling's <span class='first'>F</span>ormula</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">September 1, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This work contains a proof of Stirling's formula both for the factorial $n! \sim \sqrt{2\pi n} (n/e)^n$ on natural numbers and the real
Gamma function $\Gamma(x)\sim \sqrt{2\pi/x} (x/e)^x$. The proof is based on work by <a
href="http://www.maths.lancs.ac.uk/~jameson/stirlgamma.pdf">Graham Jameson</a>.</p>
<p>This is then extended to the full asymptotic expansion
$$\log\Gamma(z) = \big(z - \tfrac{1}{2}\big)\log z - z + \tfrac{1}{2}\log(2\pi) + \sum_{k=1}^{n-1} \frac{B_{k+1}}{k(k+1)} z^{-k}\\
{} - \frac{1}{n} \int_0^\infty B_n([t])(t + z)^{-n}\,\text{d}t$$
uniformly for all complex $z\neq 0$ in the cone $\text{arg}(z)\leq \alpha$ for any $\alpha\in(0,\pi)$, with which the above asymptotic
relation for &Gamma; is also extended to complex arguments.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Stirling_Formula</h3>
<ul>
<li><a href="../theories/stirling_formula/#Stirling_Formula">Stirling_Formula</a></li>
<li><a href="../theories/stirling_formula/#Gamma_Asymptotics">Gamma_Asymptotics</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bernoulli.html">Bernoulli Numbers</a></li><li><a href="../entries/Landau_Symbols.html">Landau Symbols</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Clique_and_Monotone_Circuits.html">Clique is not solvable by monotone circuits of polynomial size</a></li><li><a href="../entries/Irrationals_From_THEBOOK.html">Irrational numbers from THE BOOK</a></li><li><a href="../entries/Lambert_W.html">The Lambert W Function on the Reals</a></li><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li><li><a href="../entries/Comparison_Sort_Lower_Bound.html">Lower bound on comparison-based sorting algorithms</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stirling_Formula-AFP</p><pre id="copy-text">@article{Stirling_Formula-AFP,
author = {Manuel Eberl},
title = {Stirling&#39;s formula},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Stirling_Formula.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stochastic_Matrices.html b/web/entries/Stochastic_Matrices.html
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<h1 >
<span class='first'>S</span>tochastic <span class='first'>M</span>atrices and the <span class='first'>P</span>erron-<span class='first'>F</span>robenius <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a>
</p>
<p class="date">November 22, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Stochastic matrices are a convenient way to model discrete-time and
finite state Markov chains. The Perron&ndash;Frobenius theorem
tells us something about the existence and uniqueness of non-negative
eigenvectors of a stochastic matrix. In this entry, we formalize
stochastic matrices, link the formalization to the existing AFP-entry
on Markov chains, and apply the Perron&ndash;Frobenius theorem to
prove that stationary distributions always exist, and they are unique
if the stochastic matrix is irreducible.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Stochastic_Matrices</h3>
<ul>
<li><a href="../theories/stochastic_matrices/#Stochastic_Matrix">Stochastic_Matrix</a></li>
<li><a href="../theories/stochastic_matrices/#Stochastic_Vector_PMF">Stochastic_Vector_PMF</a></li>
<li><a href="../theories/stochastic_matrices/#Stochastic_Matrix_Markov_Models">Stochastic_Matrix_Markov_Models</a></li>
<li><a href="../theories/stochastic_matrices/#Eigenspace">Eigenspace</a></li>
<li><a href="../theories/stochastic_matrices/#Stochastic_Matrix_Perron_Frobenius">Stochastic_Matrix_Perron_Frobenius</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Markov_Models.html">Markov Models</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stochastic_Matrices-AFP</p><pre id="copy-text">@article{Stochastic_Matrices-AFP,
author = {René Thiemann},
title = {Stochastic Matrices and the Perron-Frobenius Theorem},
journal = {Archive of Formal Proofs},
month = {November},
year = {2017},
note = {\url{https://isa-afp.org/entries/Stochastic_Matrices.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stone_Algebras.html b/web/entries/Stone_Algebras.html
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<h1 >
<span class='first'>S</span>tone <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">September 6, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A range of algebras between lattices and Boolean algebras generalise
the notion of a complement. We develop a hierarchy of these
pseudo-complemented algebras that includes Stone algebras.
Independently of this theory we study filters based on partial orders.
Both theories are combined to prove Chen and Grätzer's construction
theorem for Stone algebras. The latter involves extensive reasoning
about algebraic structures in addition to reasoning in algebraic
structures.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session Stone_Algebras</h3>
<ul>
<li><a href="../theories/stone_algebras/#Lattice_Basics">Lattice_Basics</a></li>
<li><a href="../theories/stone_algebras/#P_Algebras">P_Algebras</a></li>
<li><a href="../theories/stone_algebras/#Filters">Filters</a></li>
<li><a href="../theories/stone_algebras/#Stone_Construction">Stone_Construction</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Subset_Boolean_Algebras.html">A Hierarchy of Algebras for Boolean Subsets</a></li><li><a href="../entries/Stone_Relation_Algebras.html">Stone Relation Algebras</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stone_Algebras-AFP</p><pre id="copy-text">@article{Stone_Algebras-AFP,
author = {Walter Guttmann},
title = {Stone Algebras},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/Stone_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Stone_Kleene_Relation_Algebras.html b/web/entries/Stone_Kleene_Relation_Algebras.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Stone-Kleene Relation Algebras - Archive of Formal Proofs</title><meta name="description" content="We develop Stone-Kleene relation algebras, which expand Stone relation
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<h1 >
<span class='first'>S</span>tone-<span class='first'>K</span>leene <span class='first'>R</span>elation <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">July 6, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop Stone-Kleene relation algebras, which expand Stone relation
algebras with a Kleene star operation to describe reachability in
weighted graphs. Many properties of the Kleene star arise as a special
case of a more general theory of iteration based on Conway semirings
extended by simulation axioms. This includes several theorems
representing complex program transformations. We formally prove the
correctness of Conway's automata-based construction of the Kleene
star of a matrix. We prove numerous results useful for reasoning about
weighted graphs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Stone_Kleene_Relation_Algebras</h3>
<ul>
<li><a href="../theories/stone_kleene_relation_algebras/#Iterings">Iterings</a></li>
<li><a href="../theories/stone_kleene_relation_algebras/#Kleene_Algebras">Kleene_Algebras</a></li>
<li><a href="../theories/stone_kleene_relation_algebras/#Kleene_Relation_Algebras">Kleene_Relation_Algebras</a></li>
<li><a href="../theories/stone_kleene_relation_algebras/#Kleene_Relation_Subalgebras">Kleene_Relation_Subalgebras</a></li>
<li><a href="../theories/stone_kleene_relation_algebras/#Matrix_Kleene_Algebras">Matrix_Kleene_Algebras</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stone_Relation_Algebras.html">Stone Relation Algebras</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Correctness_Algebras.html">Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</a></li><li><a href="../entries/Relational_Forests.html">Relational Forests</a></li><li><a href="../entries/Relational_Disjoint_Set_Forests.html">Relational Disjoint-Set Forests</a></li><li><a href="../entries/Aggregation_Algebras.html">Aggregation Algebras</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Kleene_Algebra.html">Kleene Algebra</a></li>
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<p style="display:none;" id="bibtex-filename">Stone_Kleene_Relation_Algebras-AFP</p><pre id="copy-text">@article{Stone_Kleene_Relation_Algebras-AFP,
author = {Walter Guttmann},
title = {Stone-Kleene Relation Algebras},
journal = {Archive of Formal Proofs},
month = {July},
year = {2017},
note = {\url{https://isa-afp.org/entries/Stone_Kleene_Relation_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Stone_Kleene_Relation_Algebras-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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diff --git a/web/entries/Stone_Relation_Algebras.html b/web/entries/Stone_Relation_Algebras.html
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@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>S</span>tone <span class='first'>R</span>elation <span class='first'>A</span>lgebras</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a>
</p>
<p class="date">February 7, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We develop Stone relation algebras, which generalise relation algebras
by replacing the underlying Boolean algebra structure with a Stone
algebra. We show that finite matrices over extended real numbers form
an instance. As a consequence, relation-algebraic concepts and methods
can be used for reasoning about weighted graphs. We also develop a
fixpoint calculus and apply it to compare different definitions of
reflexive-transitive closures in semirings.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>July 5, 2017</dt>
<dd>generalised extended reals to linear orders
(revision b8e703159177)</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Stone_Relation_Algebras</h3>
<ul>
<li><a href="../theories/stone_relation_algebras/#Fixpoints">Fixpoints</a></li>
<li><a href="../theories/stone_relation_algebras/#Semirings">Semirings</a></li>
<li><a href="../theories/stone_relation_algebras/#Relation_Algebras">Relation_Algebras</a></li>
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<p style="display:none;" id="bibtex-filename">Stone_Relation_Algebras-AFP</p><pre id="copy-text">@article{Stone_Relation_Algebras-AFP,
author = {Walter Guttmann},
title = {Stone Relation Algebras},
journal = {Archive of Formal Proofs},
month = {February},
year = {2017},
note = {\url{https://isa-afp.org/entries/Stone_Relation_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Stone_Relation_Algebras-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Stone_Relation_Algebras-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Stone_Relation_Algebras-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stone_Relation_Algebras-2017-02-09.tar.gz">Feb 9, 2017</a>: Isabelle2016-1
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<h1 >
<span class='first'>A</span> <span class='first'>R</span>eduction <span class='first'>T</span>heorem for <span class='first'>S</span>tore <span class='first'>B</span>uffers</h1>
<div>
<p><a href="../authors/cohen">Ernie Cohen</a> <a class="obfuscated" data="eyJob3N0IjpbImFtYXpvbiIsImNvbSJdLCJ1c2VyIjpbImVjb2hlbiJdfQ==">📧</a> and <a href="../authors/schirmer">Norbert Schirmer</a> <a class="obfuscated" data="eyJob3N0IjpbIndlYiIsImRlIl0sInVzZXIiOlsibm9yYmVydCIsInNjaGlybWVyIl19">📧</a>
</p>
<p class="date">January 7, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">When verifying a concurrent program, it is usual to assume that memory
is sequentially consistent. However, most modern multiprocessors
depend on store buffering for efficiency, and provide native
sequential consistency only at a substantial performance penalty. To
regain sequential consistency, a programmer has to follow an
appropriate programming discipline. However, na&iuml;ve disciplines,
such as protecting all shared accesses with locks, are not flexible
enough for building high-performance multiprocessor software. We
present a new discipline for concurrent programming under TSO (total
store order, with store buffer forwarding). It does not depend on
concurrency primitives, such as locks. Instead, threads use ghost
operations to acquire and release ownership of memory addresses. A
thread can write to an address only if no other thread owns it, and
can read from an address only if it owns it or it is shared and the
thread has flushed its store buffer since it last wrote to an address
it did not own. This discipline covers both coarse-grained concurrency
(where data is protected by locks) as well as fine-grained concurrency
(where atomic operations race to memory). We formalize this
discipline in Isabelle/HOL, and prove that if every execution of a
program in a system without store buffers follows the discipline, then
every execution of the program with store buffers is sequentially
consistent. Thus, we can show sequential consistency under TSO by
ordinary assertional reasoning about the program, without having to
consider store buffers at all.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li></ul>
<h3>Session Store_Buffer_Reduction</h3>
<ul>
<li><a href="../theories/store_buffer_reduction/#ReduceStoreBuffer">ReduceStoreBuffer</a></li>
<li><a href="../theories/store_buffer_reduction/#ReduceStoreBufferSimulation">ReduceStoreBufferSimulation</a></li>
<li><a href="../theories/store_buffer_reduction/#PIMP">PIMP</a></li>
<li><a href="../theories/store_buffer_reduction/#SyntaxTweaks">SyntaxTweaks</a></li>
<li><a href="../theories/store_buffer_reduction/#Abbrevs">Abbrevs</a></li>
<li><a href="../theories/store_buffer_reduction/#Variants">Variants</a></li>
<li><a href="../theories/store_buffer_reduction/#Text">Text</a></li>
<li><a href="../theories/store_buffer_reduction/#Preliminaries">Preliminaries</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Store_Buffer_Reduction-AFP</p><pre id="copy-text">@article{Store_Buffer_Reduction-AFP,
author = {Ernie Cohen and Norbert Schirmer},
title = {A Reduction Theorem for Store Buffers},
journal = {Archive of Formal Proofs},
month = {January},
year = {2019},
note = {\url{https://isa-afp.org/entries/Store_Buffer_Reduction.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Store_Buffer_Reduction-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Store_Buffer_Reduction-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Store_Buffer_Reduction-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Store_Buffer_Reduction-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Store_Buffer_Reduction-2019-01-11.tar.gz">Jan 11, 2019</a>: Isabelle2018
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diff --git a/web/entries/Stream-Fusion.html b/web/entries/Stream-Fusion.html
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<h1 >
<span class='first'>S</span>tream <span class='first'>F</span>usion</h1>
<div>
<p><a href="../authors/huffman">Brian Huffman</a> <a href="http://cs.pdx.edu/~brianh/">🌐</a>
</p>
<p class="date">April 29, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Stream Fusion is a system for removing intermediate list structures from Haskell programs; it consists of a Haskell library along with several compiler rewrite rules. (The library is available <a href="http://hackage.haskell.org/package/stream-fusion">online</a>.)<br><br>These theories contain a formalization of much of the Stream Fusion library in HOLCF. Lazy list and stream types are defined, along with coercions between the two types, as well as an equivalence relation for streams that generate the same list. List and stream versions of map, filter, foldr, enumFromTo, append, zipWith, and concatMap are defined, and the stream versions are shown to respect stream equivalence.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Stream-Fusion</h3>
<ul>
<li><a href="../theories/stream-fusion/#LazyList">LazyList</a></li>
<li><a href="../theories/stream-fusion/#Stream">Stream</a></li>
<li><a href="../theories/stream-fusion/#StreamFusion">StreamFusion</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Stream-Fusion-AFP</p><pre id="copy-text">@article{Stream-Fusion-AFP,
author = {Brian Huffman},
title = {Stream Fusion},
journal = {Archive of Formal Proofs},
month = {April},
year = {2009},
note = {\url{https://isa-afp.org/entries/Stream-Fusion.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2009-05-13.tar.gz">May 13, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stream-Fusion-2009-05-11.tar.gz">May 11, 2009</a>: Isabelle2009
</li></ul>
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--- a/web/entries/Stream_Fusion_Code.html
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@@ -1,194 +1,196 @@
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<h1 >
<span class='first'>S</span>tream <span class='first'>F</span>usion in <span class='first'>H</span><span class='first'>O</span><span class='first'>L</span> <span class='first'>W</span>ith <span class='first'>C</span>ode <span class='first'>G</span>eneration</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/maximova">Alexandra Maximova</a> <a class="obfuscated" data="eyJob3N0IjpbInN0dWRlbnQiLCJldGh6IiwiY2giXSwidXNlciI6WyJhbWF4aW1vdiJdfQ==">📧</a>
</p>
<p class="date">October 10, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Stream Fusion is a system for removing intermediate list data structures from functional programs, in particular Haskell. This entry adapts stream fusion to Isabelle/HOL and its code generator. We define stream types for finite and possibly infinite lists and stream versions for most of the fusible list functions in the theories List and Coinductive_List, and prove them correct with respect to the conversion functions between lists and streams. The Stream Fusion transformation itself is implemented as a simproc in the preprocessor of the code generator. [Brian Huffman's <a href="http://isa-afp.org/entries/Stream-Fusion.html">AFP entry</a> formalises stream fusion in HOLCF for the domain of lazy lists to prove the GHC compiler rewrite rules correct. In contrast, this work enables Isabelle's code generator to perform stream fusion itself. To that end, it covers both finite and coinductive lists from the HOL library and the Coinductive entry. The fusible list functions require specification and proof principles different from Huffman's.]</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Stream_Fusion_Code</h3>
<ul>
<li><a href="../theories/stream_fusion_code/#Stream_Fusion">Stream_Fusion</a></li>
<li><a href="../theories/stream_fusion_code/#Stream_Fusion_List">Stream_Fusion_List</a></li>
<li><a href="../theories/stream_fusion_code/#Stream_Fusion_LList">Stream_Fusion_LList</a></li>
<li><a href="../theories/stream_fusion_code/#Stream_Fusion_Examples">Stream_Fusion_Examples</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Coinductive.html">Coinductive</a></li></ul>
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<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Stream-Fusion.html">Stream Fusion</a></li>
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<p style="display:none;" id="bibtex-filename">Stream_Fusion_Code-AFP</p><pre id="copy-text">@article{Stream_Fusion_Code-AFP,
author = {Andreas Lochbihler and Alexandra Maximova},
title = {Stream Fusion in HOL with Code Generation},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/Stream_Fusion_Code.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Stream_Fusion_Code-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Strong_Security.html b/web/entries/Strong_Security.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Formalization of Strong Security - Archive of Formal Proofs</title><meta name="description" content="Research in information-flow security aims at developing methods to identify undesired information leaks within programs from private sources to public..."><meta property="og:title" content="A Formalization of Strong Security" />
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>S</span>trong <span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/grewe">Sylvia Grewe</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJncmV3ZSJdfQ==">📧</a>, <a href="../authors/lux">Alexander Lux</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJsdXgiXX0=">📧</a>, <a href="../authors/mantel">Heiko Mantel</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJtYW50ZWwiXX0=">📧</a> and <a href="../authors/sauer">Jens Sauer</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJzYXVlciJdfQ==">📧</a>
</p>
<p class="date">April 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Research in information-flow security aims at developing methods to
identify undesired information leaks within programs from private
sources to public sinks. Noninterference captures this
intuition. Strong security from Sabelfeld and Sands
formalizes noninterference for concurrent systems.
<p>
We present an Isabelle/HOL formalization of strong security for
arbitrary security lattices (Sabelfeld and Sands use
a two-element security lattice in the original publication).
The formalization includes
compositionality proofs for strong security and a soundness proof
for a security type system that checks strong security for programs
in a simple while language with dynamic thread creation.
<p>
Our formalization of the security type system is abstract in the
language for expressions and in the semantic side conditions for
expressions. It can easily be instantiated with different syntactic
approximations for these side conditions. The soundness proof of
such an instantiation boils down to showing that these syntactic
approximations imply the semantic side conditions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session Strong_Security</h3>
<ul>
<li><a href="../theories/strong_security/#Types">Types</a></li>
<li><a href="../theories/strong_security/#Expr">Expr</a></li>
<li><a href="../theories/strong_security/#Domain_example">Domain_example</a></li>
<li><a href="../theories/strong_security/#MWLf">MWLf</a></li>
<li><a href="../theories/strong_security/#Strong_Security">Strong_Security</a></li>
<li><a href="../theories/strong_security/#Up_To_Technique">Up_To_Technique</a></li>
<li><a href="../theories/strong_security/#Parallel_Composition">Parallel_Composition</a></li>
<li><a href="../theories/strong_security/#Strongly_Secure_Skip_Assign">Strongly_Secure_Skip_Assign</a></li>
<li><a href="../theories/strong_security/#Language_Composition">Language_Composition</a></li>
<li><a href="../theories/strong_security/#Type_System">Type_System</a></li>
<li><a href="../theories/strong_security/#Type_System_example">Type_System_example</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/WHATandWHERE_Security.html">A Formalization of Declassification with WHAT-and-WHERE-Security</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Strong_Security-AFP</p><pre id="copy-text">@article{Strong_Security-AFP,
author = {Sylvia Grewe and Alexander Lux and Heiko Mantel and Jens Sauer},
title = {A Formalization of Strong Security},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/Strong_Security.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Strong_Security-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Strong_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Strong_Security-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Strong_Security-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Strong_Security-2014-04-24.tar.gz">Apr 24, 2014</a>: Isabelle2013-2
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diff --git a/web/entries/Sturm_Sequences.html b/web/entries/Sturm_Sequences.html
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<h1 >
<span class='first'>S</span>turm's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">January 11, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Sturm's Theorem states that polynomial sequences with certain
properties, so-called Sturm sequences, can be used to count the number
of real roots of a real polynomial. This work contains a proof of
Sturm's Theorem and code for constructing Sturm sequences efficiently.
It also provides the “sturm” proof method, which can decide certain
statements about the roots of real polynomials, such as “the polynomial
P has exactly n roots in the interval I” or “P(x) > Q(x) for all x
&#8712; &#8477;”.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Sturm_Sequences</h3>
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<li><a href="../theories/sturm_sequences/#Sturm_Library_Document">Sturm_Library_Document</a></li>
<li><a href="../theories/sturm_sequences/#Misc_Polynomial">Misc_Polynomial</a></li>
<li><a href="../theories/sturm_sequences/#Sturm_Library">Sturm_Library</a></li>
<li><a href="../theories/sturm_sequences/#Sturm_Theorem">Sturm_Theorem</a></li>
<li><a href="../theories/sturm_sequences/#Sturm_Method">Sturm_Method</a></li>
<li><a href="../theories/sturm_sequences/#Sturm">Sturm</a></li>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Safe_Distance.html">A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles</a></li><li><a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a></li><li><a href="../entries/Algebraic_Numbers.html">Algebraic Numbers in Isabelle/HOL</a></li><li><a href="../entries/Special_Function_Bounds.html">Real-Valued Special Functions: Upper and Lower Bounds</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Sturm_Sequences-AFP</p><pre id="copy-text">@article{Sturm_Sequences-AFP,
author = {Manuel Eberl},
title = {Sturm&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {January},
year = {2014},
note = {\url{https://isa-afp.org/entries/Sturm_Sequences.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
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- <a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Sequences-2014-01-12.tar.gz">Jan 12, 2014</a>: Isabelle2013-2
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\ No newline at end of file
diff --git a/web/entries/Sturm_Tarski.html b/web/entries/Sturm_Tarski.html
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>turm-<span class='first'>T</span>arski <span class='first'>T</span>heorem</h1>
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<p><a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">September 19, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We have formalized the Sturm-Tarski theorem (also referred as the Tarski theorem), which generalizes Sturm's theorem. Sturm's theorem is usually used as a way to count distinct real roots, while the Sturm-Tarksi theorem forms the basis for Tarski's classic quantifier elimination for real closed field.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Sturm_Tarski</h3>
<ul>
<li><a href="../theories/sturm_tarski/#PolyMisc">PolyMisc</a></li>
<li><a href="../theories/sturm_tarski/#Sturm_Tarski">Sturm_Tarski</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/BenOr_Kozen_Reif.html">The BKR Decision Procedure for Univariate Real Arithmetic</a></li><li><a href="../entries/Budan_Fourier.html">The Budan-Fourier Theorem and Counting Real Roots with Multiplicity</a></li><li><a href="../entries/Count_Complex_Roots.html">Count the Number of Complex Roots</a></li><li><a href="../entries/Winding_Number_Eval.html">Evaluate Winding Numbers through Cauchy Indices</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Sturm_Tarski-AFP</p><pre id="copy-text">@article{Sturm_Tarski-AFP,
author = {Wenda Li},
title = {The Sturm-Tarski Theorem},
journal = {Archive of Formal Proofs},
month = {September},
year = {2014},
note = {\url{https://isa-afp.org/entries/Sturm_Tarski.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2014-12-05.tar.gz">Dec 5, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Sturm_Tarski-2014-09-20.tar.gz">Sep 20, 2014</a>: Isabelle2014
</li></ul>
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diff --git a/web/entries/Stuttering_Equivalence.html b/web/entries/Stuttering_Equivalence.html
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+++ b/web/entries/Stuttering_Equivalence.html
@@ -1,199 +1,201 @@
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<h1 >
<span class='first'>S</span>tuttering <span class='first'>E</span>quivalence</h1>
<div>
<p><a href="../authors/merz">Stephan Merz</a> <a href="http://www.loria.fr/~merz">🌐</a>
</p>
<p class="date">May 7, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Two omega-sequences are stuttering equivalent if they differ only by finite repetitions of elements. Stuttering equivalence is a fundamental concept in the theory of concurrent and distributed systems. Notably, Lamport argues that refinement notions for such systems should be insensitive to finite stuttering. Peled and Wilke showed that all PLTL (propositional linear-time temporal logic) properties that are insensitive to stuttering equivalence can be expressed without the next-time operator. Stuttering equivalence is also important for certain verification techniques such as partial-order reduction for model checking.</p> <p>We formalize stuttering equivalence in Isabelle/HOL. Our development relies on the notion of stuttering sampling functions that may skip blocks of identical sequence elements. We also encode PLTL and prove the theorem due to Peled and Wilke.</p></div>
<h3>License</h3>
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<dl><dt>January 31, 2013</dt>
<dd>Added encoding of PLTL and proved Peled and Wilke's theorem. Adjusted abstract accordingly.</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Stuttering_Equivalence</h3>
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<li><a href="../theories/stuttering_equivalence/#Samplers">Samplers</a></li>
<li><a href="../theories/stuttering_equivalence/#StutterEquivalence">StutterEquivalence</a></li>
<li><a href="../theories/stuttering_equivalence/#PLTL">PLTL</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/LTL.html">Linear Temporal Logic</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Partial_Order_Reduction.html">Partial Order Reduction</a></li><li><a href="../entries/Consensus_Refined.html">Consensus Refined</a></li><li><a href="../entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></li><li><a href="../entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></li><li><a href="../entries/Heard_Of.html">Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Stuttering_Equivalence-AFP</p><pre id="copy-text">@article{Stuttering_Equivalence-AFP,
author = {Stephan Merz},
title = {Stuttering Equivalence},
journal = {Archive of Formal Proofs},
month = {May},
year = {2012},
note = {\url{https://isa-afp.org/entries/Stuttering_Equivalence.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2013-02-02.tar.gz">Feb 2, 2013</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Stuttering_Equivalence-2012-05-08.tar.gz">May 8, 2012</a>: Isabelle2011-1
</li></ul>
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<h1 >
<span class='first'>S</span>ubresultants</h1>
<div>
<p><a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsic2ViYXN0aWFhbiIsImpvb3N0ZW4iXX0=">📧</a>, <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">April 6, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the theory of subresultants and the subresultant
polynomial remainder sequence as described by Brown and Traub. As a
result, we obtain efficient certified algorithms for computing the
resultant and the greatest common divisor of polynomials.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Subresultants</h3>
<ul>
<li><a href="../theories/subresultants/#Resultant_Prelim">Resultant_Prelim</a></li>
<li><a href="../theories/subresultants/#Dichotomous_Lazard">Dichotomous_Lazard</a></li>
<li><a href="../theories/subresultants/#Binary_Exponentiation">Binary_Exponentiation</a></li>
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<li><a href="../theories/subresultants/#Coeff_Int">Coeff_Int</a></li>
<li><a href="../theories/subresultants/#Subresultant">Subresultant</a></li>
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Subresultants-AFP</p><pre id="copy-text">@article{Subresultants-AFP,
author = {Sebastiaan J. C. Joosten and René Thiemann and Akihisa Yamada},
title = {Subresultants},
journal = {Archive of Formal Proofs},
month = {April},
year = {2017},
note = {\url{https://isa-afp.org/entries/Subresultants.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Subset_Boolean_Algebras.html b/web/entries/Subset_Boolean_Algebras.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Hierarchy of Algebras for Boolean Subsets - Archive of Formal Proofs</title><meta name="description" content="We present a collection of axiom systems for the construction of
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<h1 >
<span class='first'>A</span> <span class='first'>H</span>ierarchy of <span class='first'>A</span>lgebras for <span class='first'>B</span>oolean <span class='first'>S</span>ubsets</h1>
<div>
<p><a href="../authors/guttmann">Walter Guttmann</a> <a href="https://www.cosc.canterbury.ac.nz/walter.guttmann/">🌐</a> and <a href="../authors/moeller">Bernhard Möller</a> <a href="https://www.informatik.uni-augsburg.de/en/chairs/dbis/pmi/staff/moeller/">🌐</a>
</p>
<p class="date">January 31, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a collection of axiom systems for the construction of
Boolean subalgebras of larger overall algebras. The subalgebras are
defined as the range of a complement-like operation on a semilattice.
This technique has been used, for example, with the antidomain
operation, dynamic negation and Stone algebras. We present a common
ground for these constructions based on a new equational
axiomatisation of Boolean algebras.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Subset_Boolean_Algebras</h3>
<ul>
<li><a href="../theories/subset_boolean_algebras/#Subset_Boolean_Algebras">Subset_Boolean_Algebras</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Stone_Algebras.html">Stone Algebras</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Correctness_Algebras.html">Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Subset_Boolean_Algebras-AFP</p><pre id="copy-text">@article{Subset_Boolean_Algebras-AFP,
author = {Walter Guttmann and Bernhard Möller},
title = {A Hierarchy of Algebras for Boolean Subsets},
journal = {Archive of Formal Proofs},
month = {January},
year = {2020},
note = {\url{https://isa-afp.org/entries/Subset_Boolean_Algebras.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/SumSquares.html b/web/entries/SumSquares.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Sums of Two and Four Squares - Archive of Formal Proofs</title><meta name="description" content="This document presents the mechanised proofs of the following results:any prime number of the form 4m&#43;1 can be written as the sum of two squares;any..."><meta property="og:title" content="Sums of Two and Four Squares" />
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<h1 >
<span class='first'>S</span>ums of <span class='first'>T</span>wo and <span class='first'>F</span>our <span class='first'>S</span>quares</h1>
<div>
<p><a href="../authors/oosterhuis">Roelof Oosterhuis</a>
</p>
<p class="date">August 12, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This document presents the mechanised proofs of the following results:<ul><li>any prime number of the form 4m+1 can be written as the sum of two squares;</li><li>any natural number can be written as the sum of four squares</li></ul></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session SumSquares</h3>
<ul>
<li><a href="../theories/sumsquares/#TwoSquares">TwoSquares</a></li>
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author = {Roelof Oosterhuis},
title = {Sums of Two and Four Squares},
journal = {Archive of Formal Proofs},
month = {August},
year = {2007},
note = {\url{https://isa-afp.org/entries/SumSquares.html},
Formal proof development},
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diff --git a/web/entries/Sunflowers.html b/web/entries/Sunflowers.html
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<h1 >
<span class='first'>T</span>he <span class='first'>S</span>unflower <span class='first'>L</span>emma of <span class='first'>E</span>rdős and <span class='first'>R</span>ado</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">February 25, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formally define sunflowers and provide a formalization of the
sunflower lemma of Erd&odblac;s and Rado: whenever a set of
size-<i>k</i>-sets has a larger cardinality than
<i>(r - 1)<sup>k</sup> &middot; k!</i>,
then it contains a sunflower of cardinality <i>r</i>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Sunflowers</h3>
<ul>
<li><a href="../theories/sunflowers/#Sunflower">Sunflower</a></li>
<li><a href="../theories/sunflowers/#Erdos_Rado_Sunflower">Erdos_Rado_Sunflower</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Clique_and_Monotone_Circuits.html">Clique is not solvable by monotone circuits of polynomial size</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Sunflowers-AFP</p><pre id="copy-text">@article{Sunflowers-AFP,
author = {René Thiemann},
title = {The Sunflower Lemma of Erdős and Rado},
journal = {Archive of Formal Proofs},
month = {February},
year = {2021},
note = {\url{https://isa-afp.org/entries/Sunflowers.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/SuperCalc.html b/web/entries/SuperCalc.html
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<h1 >
<span class='first'>A</span> <span class='first'>V</span>ariant of the <span class='first'>S</span>uperposition <span class='first'>C</span>alculus</h1>
<div>
<p><a href="../authors/peltier">Nicolas Peltier</a> <a href="http://membres-lig.imag.fr/peltier/">🌐</a>
</p>
<p class="date">September 6, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a formalization of a variant of the superposition
calculus, together with formal proofs of soundness and refutational
completeness (w.r.t. the usual redundancy criteria based on clause
ordering). This version of the calculus uses all the standard
restrictions of the superposition rules, together with the following
refinement, inspired by the basic superposition calculus: each clause
is associated with a set of terms which are assumed to be in normal
form -- thus any application of the replacement rule on these terms is
blocked. The set is initially empty and terms may be added or removed
at each inference step. The set of terms that are assumed to be in
normal form includes any term introduced by previous unifiers as well
as any term occurring in the parent clauses at a position that is
smaller (according to some given ordering on positions) than a
previously replaced term. The standard superposition calculus
corresponds to the case where the set of irreducible terms is always
empty.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session SuperCalc</h3>
<ul>
<li><a href="../theories/supercalc/#multisets_continued">multisets_continued</a></li>
<li><a href="../theories/supercalc/#well_founded_continued">well_founded_continued</a></li>
<li><a href="../theories/supercalc/#terms">terms</a></li>
<li><a href="../theories/supercalc/#equational_clausal_logic">equational_clausal_logic</a></li>
<li><a href="../theories/supercalc/#superposition">superposition</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">SuperCalc-AFP</p><pre id="copy-text">@article{SuperCalc-AFP,
author = {Nicolas Peltier},
title = {A Variant of the Superposition Calculus},
journal = {Archive of Formal Proofs},
month = {September},
year = {2016},
note = {\url{https://isa-afp.org/entries/SuperCalc.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Surprise_Paradox.html b/web/entries/Surprise_Paradox.html
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<h1 >
<span class='first'>S</span>urprise <span class='first'>P</span>aradox</h1>
<div>
<p><a href="../authors/breitner">Joachim Breitner</a> <a href="http://pp.ipd.kit.edu/~breitner">🌐</a>
</p>
<p class="date">July 17, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In 1964, Fitch showed that the paradox of the surprise hanging can be
resolved by showing that the judge’s verdict is inconsistent. His
formalization builds on Gödel’s coding of provability. In this
theory, we reproduce his proof in Isabelle, building on Paulson’s
formalisation of Gödel’s incompleteness theorems.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Surprise_Paradox</h3>
<ul>
<li><a href="../theories/surprise_paradox/#Surprise_Paradox">Surprise_Paradox</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Incompleteness.html">Gödel&rsquo;s Incompleteness Theorems</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/E_Transcendental.html">The Transcendence of e</a></li>
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<p style="display:none;" id="bibtex-filename">Surprise_Paradox-AFP</p><pre id="copy-text">@article{Surprise_Paradox-AFP,
author = {Joachim Breitner},
title = {Surprise Paradox},
journal = {Archive of Formal Proofs},
month = {July},
year = {2016},
note = {\url{https://isa-afp.org/entries/Surprise_Paradox.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Surprise_Paradox-2016-07-17.tar.gz">Jul 17, 2016</a>: Isabelle2016
</li></ul>
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diff --git a/web/entries/Symmetric_Polynomials.html b/web/entries/Symmetric_Polynomials.html
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<h1 >
<span class='first'>S</span>ymmetric <span class='first'>P</span>olynomials</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">September 25, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>A symmetric polynomial is a polynomial in variables
<em>X</em><sub>1</sub>,&hellip;,<em>X</em><sub>n</sub>
that does not discriminate between its variables, i.&thinsp;e. it
is invariant under any permutation of them. These polynomials are
important in the study of the relationship between the coefficients of
a univariate polynomial and its roots in its algebraic
closure.</p> <p>This article provides a definition of
symmetric polynomials and the elementary symmetric polynomials
e<sub>1</sub>,&hellip;,e<sub>n</sub> and
proofs of their basic properties, including three notable
ones:</p> <ul> <li> Vieta's formula, which
gives an explicit expression for the <em>k</em>-th
coefficient of a univariate monic polynomial in terms of its roots
<em>x</em><sub>1</sub>,&hellip;,<em>x</em><sub>n</sub>,
namely
<em>c</em><sub><em>k</em></sub> = (-1)<sup><em>n</em>-<em>k</em></sup>&thinsp;e<sub><em>n</em>-<em>k</em></sub>(<em>x</em><sub>1</sub>,&hellip;,<em>x</em><sub>n</sub>).</li>
<li>Second, the Fundamental Theorem of Symmetric Polynomials,
which states that any symmetric polynomial is itself a uniquely
determined polynomial combination of the elementary symmetric
polynomials.</li> <li>Third, as a corollary of the
previous two, that given a polynomial over some ring
<em>R</em>, any symmetric polynomial combination of its
roots is also in <em>R</em> even when the roots are not.
</ul> <p> Both the symmetry property itself and the
witness for the Fundamental Theorem are executable. </p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Symmetric_Polynomials</h3>
<ul>
<li><a href="../theories/symmetric_polynomials/#Vieta">Vieta</a></li>
<li><a href="../theories/symmetric_polynomials/#Symmetric_Polynomials">Symmetric_Polynomials</a></li>
<li><a href="../theories/symmetric_polynomials/#Symmetric_Polynomials_Code">Symmetric_Polynomials_Code</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Power_Sum_Polynomials.html">Power Sum Polynomials</a></li><li><a href="../entries/Pi_Transcendental.html">The Transcendence of π</a></li></ul>
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<h3>Auto-related entries</h3>
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<p style="display:none;" id="bibtex-filename">Symmetric_Polynomials-AFP</p><pre id="copy-text">@article{Symmetric_Polynomials-AFP,
author = {Manuel Eberl},
title = {Symmetric Polynomials},
journal = {Archive of Formal Proofs},
month = {September},
year = {2018},
note = {\url{https://isa-afp.org/entries/Symmetric_Polynomials.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Symmetric_Polynomials-2018-09-26.tar.gz">Sep 26, 2018</a>: Isabelle2018
</li></ul>
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diff --git a/web/entries/Syntax_Independent_Logic.html b/web/entries/Syntax_Independent_Logic.html
--- a/web/entries/Syntax_Independent_Logic.html
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@@ -1,195 +1,197 @@
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<h1 >
<span class='first'>S</span>yntax-<span class='first'>I</span>ndependent <span class='first'>L</span>ogic <span class='first'>I</span>nfrastructure</h1>
<div>
<p><a href="../authors/popescu">Andrei Popescu</a> <a href="https://www.andreipopescu.uk">🌐</a> and <a href="../authors/traytel">Dmitriy Traytel</a> <a href="https://traytel.bitbucket.io/">🌐</a>
</p>
<p class="date">September 16, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize a notion of logic whose terms and formulas are kept
abstract. In particular, logical connectives, substitution, free
variables, and provability are not defined, but characterized by their
general properties as locale assumptions. Based on this abstract
characterization, we develop further reusable reasoning
infrastructure. For example, we define parallel substitution (along
with proving its characterizing theorems) from single-point
substitution. Similarly, we develop a natural deduction style proof
system starting from the abstract Hilbert-style one. These one-time
efforts benefit different concrete logics satisfying our locales'
assumptions. We instantiate the syntax-independent logic
infrastructure to Robinson arithmetic (also known as Q) in the AFP
entry <a
href="https://www.isa-afp.org/entries/Robinson_Arithmetic.html">Robinson_Arithmetic</a>
and to hereditarily finite set theory in the AFP entries <a
href="https://www.isa-afp.org/entries/Goedel_HFSet_Semantic.html">Goedel_HFSet_Semantic</a>
and <a
href="https://www.isa-afp.org/entries/Goedel_HFSet_Semanticless.html">Goedel_HFSet_Semanticless</a>,
which are part of our formalization of G&ouml;del's
Incompleteness Theorems described in our CADE-27 paper <a
href="https://dx.doi.org/10.1007/978-3-030-29436-6_26">A
Formally Verified Abstract Account of Gödel's Incompleteness
Theorems</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/proof-theory">Logic/Proof theory</a></li></ul>
<h3>Session Syntax_Independent_Logic</h3>
<ul>
<li><a href="../theories/syntax_independent_logic/#Prelim">Prelim</a></li>
<li><a href="../theories/syntax_independent_logic/#Syntax">Syntax</a></li>
<li><a href="../theories/syntax_independent_logic/#Deduction">Deduction</a></li>
<li><a href="../theories/syntax_independent_logic/#Natural_Deduction">Natural_Deduction</a></li>
<li><a href="../theories/syntax_independent_logic/#Pseudo_Term">Pseudo_Term</a></li>
<li><a href="../theories/syntax_independent_logic/#Standard_Model">Standard_Model</a></li>
<li><a href="../theories/syntax_independent_logic/#Syntax_Arith">Syntax_Arith</a></li>
<li><a href="../theories/syntax_independent_logic/#Deduction_Q">Deduction_Q</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Goedel_Incompleteness.html">An Abstract Formalization of Gödel&rsquo;s Incompleteness Theorems</a></li><li><a href="../entries/Robinson_Arithmetic.html">Robinson Arithmetic</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Syntax_Independent_Logic-AFP</p><pre id="copy-text">@article{Syntax_Independent_Logic-AFP,
author = {Andrei Popescu and Dmitriy Traytel},
title = {Syntax-Independent Logic Infrastructure},
journal = {Archive of Formal Proofs},
month = {September},
year = {2020},
note = {\url{https://isa-afp.org/entries/Syntax_Independent_Logic.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Syntax_Independent_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Syntax_Independent_Logic-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Syntax_Independent_Logic-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<h1 >
<span class='first'>S</span>zemerédi's <span class='first'>R</span>egularity <span class='first'>L</span>emma</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a>, <a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cst.cam.ac.uk/people/ak2110">🌐</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">November 5, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><a
href="https://en.wikipedia.org/wiki/Szemerédi_regularity_lemma">Szemerédi's
regularity lemma</a> is a key result in the study of large
graphs. It asserts the existence of an upper bound on the number of parts
the vertices of a graph need to be partitioned into such that the
edges between the parts are random in a certain sense. This bound
depends only on the desired precision and not on the graph itself, in
the spirit of Ramsey's theorem. The formalisation follows online
course notes by <a href="https://www.dpmms.cam.ac.uk/~par31/notes/tic.pdf">Tim
Gowers</a> and <a href="https://yufeizhao.com/gtacbook/">Yufei
Zhao</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Szemeredi_Regularity</h3>
<ul>
<li><a href="../theories/szemeredi_regularity/#Szemeredi">Szemeredi</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Roth_Arithmetic_Progressions.html">Roth&rsquo;s Theorem on Arithmetic Progressions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Roth_Arithmetic_Progressions.html">Roth&rsquo;s Theorem on Arithmetic Progressions</a></li>
<li><a href="../entries/Pratt_Certificate.html">Pratt&rsquo;s Primality Certificates</a></li>
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<p style="display:none;" id="bibtex-filename">Szemeredi_Regularity-AFP</p><pre id="copy-text">@article{Szemeredi_Regularity-AFP,
author = {Chelsea Edmonds and Angeliki Koutsoukou-Argyraki and Lawrence C. Paulson},
title = {Szemerédi&#39;s Regularity Lemma},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Szemeredi_Regularity.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>O</span>rder <span class='first'>E</span>xtension and <span class='first'>S</span>zpilrajn's <span class='first'>E</span>xtension <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/zeller">Peter Zeller</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidW5pLWtsIiwiZGUiXSwidXNlciI6WyJwX3plbGxlciJdfQ==">📧</a> and <a href="../authors/stevens">Lukas Stevens</a> <a href="https://www21.in.tum.de/team/stevensl">🌐</a>
</p>
<p class="date">July 27, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry is concerned with the principle of order extension, i.e. the extension of an order relation to a total order relation.
To this end, we prove a more general version of Szpilrajn's extension theorem employing terminology from the book "Consistency, Choice, and Rationality" by Bossert and Suzumura.
We also formalize theorem 2.7 of their book.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>March 22, 2021</dt>
<dd>(by Lukas Stevens) generalise Szpilrajn's extension theorem and add material from the book "Consistency, Choice, and Rationality"</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/order">Mathematics/Order</a></li></ul>
<h3>Session Szpilrajn</h3>
<ul>
<li><a href="../theories/szpilrajn/#Szpilrajn">Szpilrajn</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
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<p style="display:none;" id="bibtex-filename">Szpilrajn-AFP</p><pre id="copy-text">@article{Szpilrajn-AFP,
author = {Peter Zeller and Lukas Stevens},
title = {Order Extension and Szpilrajn&#39;s Extension Theorem},
journal = {Archive of Formal Proofs},
month = {July},
year = {2019},
note = {\url{https://isa-afp.org/entries/Szpilrajn.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/TESL_Language.html b/web/entries/TESL_Language.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormal <span class='first'>D</span>evelopment of a <span class='first'>P</span>olychronous <span class='first'>P</span>olytimed <span class='first'>C</span>oordination <span class='first'>L</span>anguage</h1>
<div>
<p><a href="../authors/van">Hai Nguyen Van</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiaGFpIiwibmd1eWVudmFuIiwicGhpZSJdfQ==">📧</a>, <a href="../authors/boulanger">Frédéric Boulanger</a> <a class="obfuscated" data="eyJob3N0IjpbImNlbnRyYWxlc3VwZWxlYyIsImZyIl0sInVzZXIiOlsiZnJlZGVyaWMiLCJib3VsYW5nZXIiXX0=">📧</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">July 30, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The design of complex systems involves different formalisms for
modeling their different parts or aspects. The global model of a
system may therefore consist of a coordination of concurrent
sub-models that use different paradigms. We develop here a theory for
a language used to specify the timed coordination of such
heterogeneous subsystems by addressing the following issues:
<ul><li>the
behavior of the sub-systems is observed only at a series of discrete
instants,</li><li>events may occur in different sub-systems at unrelated
times, leading to polychronous systems, which do not necessarily have
a common base clock,</li><li>coordination between subsystems involves
causality, so the occurrence of an event may enforce the occurrence of
other events, possibly after a certain duration has elapsed or an
event has occurred a given number of times,</li><li>the domain of time
(discrete, rational, continuous...) may be different in the
subsystems, leading to polytimed systems,</li><li>the time frames of
different sub-systems may be related (for instance, time in a GPS
satellite and in a GPS receiver on Earth are related although they are
not the same).</li></ul>
Firstly, a denotational semantics of the language is
defined. Then, in order to be able to incrementally check the behavior
of systems, an operational semantics is given, with proofs of
progress, soundness and completeness with regard to the denotational
semantics. These proofs are made according to a setup that can scale
up when new operators are added to the language. In order for
specifications to be composed in a clean way, the language should be
invariant by stuttering (i.e., adding observation instants at which
nothing happens). The proof of this invariance is also given.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/system-description-languages">Computer science/System description languages</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li><li><a href="../topics/computer-science/concurrency">Computer science/Concurrency</a></li></ul>
<h3>Session TESL_Language</h3>
<ul>
<li><a href="../theories/tesl_language/#Introduction">Introduction</a></li>
<li><a href="../theories/tesl_language/#TESL">TESL</a></li>
<li><a href="../theories/tesl_language/#Run">Run</a></li>
<li><a href="../theories/tesl_language/#Denotational">Denotational</a></li>
<li><a href="../theories/tesl_language/#SymbolicPrimitive">SymbolicPrimitive</a></li>
<li><a href="../theories/tesl_language/#Operational">Operational</a></li>
<li><a href="../theories/tesl_language/#Corecursive_Prop">Corecursive_Prop</a></li>
<li><a href="../theories/tesl_language/#Hygge_Theory">Hygge_Theory</a></li>
<li><a href="../theories/tesl_language/#StutteringDefs">StutteringDefs</a></li>
<li><a href="../theories/tesl_language/#StutteringLemmas">StutteringLemmas</a></li>
<li><a href="../theories/tesl_language/#Stuttering">Stuttering</a></li>
<li><a href="../theories/tesl_language/#Config_Morphisms">Config_Morphisms</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">TESL_Language-AFP</p><pre id="copy-text">@article{TESL_Language-AFP,
author = {Hai Nguyen Van and Frédéric Boulanger and Burkhart Wolff},
title = {A Formal Development of a Polychronous Polytimed Coordination Language},
journal = {Archive of Formal Proofs},
month = {July},
year = {2019},
note = {\url{https://isa-afp.org/entries/TESL_Language.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-TESL_Language-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-TESL_Language-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-TESL_Language-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/TLA.html b/web/entries/TLA.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Definitional Encoding of TLA* in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content="We mechanise the logic TLA* [Merz 1999], an extension of Lamport&#39;s Temporal Logic of Actions (TLA) [Lamport 1994] for specifying and reasoning about..."><meta property="og:title" content="A Definitional Encoding of TLA* in Isabelle/HOL" />
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<h1 >
<span class='first'>A</span> <span class='first'>D</span>efinitional <span class='first'>E</span>ncoding of <span class='first'>T</span><span class='first'>L</span><span class='first'>A</span>* in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/grov">Gudmund Grov</a> <a href="http://homepages.inf.ed.ac.uk/ggrov">🌐</a> and <a href="../authors/merz">Stephan Merz</a> <a href="http://www.loria.fr/~merz">🌐</a>
</p>
<p class="date">November 19, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We mechanise the logic TLA*
<a href="http://www.springerlink.com/content/ax3qk557qkdyt7n6/">[Merz 1999]</a>,
an extension of Lamport's Temporal Logic of Actions (TLA)
<a href="http://dl.acm.org/citation.cfm?doid=177492.177726">[Lamport 1994]</a>
for specifying and reasoning
about concurrent and reactive systems. Aiming at a framework for mechanising] the verification of TLA (or TLA*) specifications, this contribution reuses
some elements from a previous axiomatic encoding of TLA in Isabelle/HOL
by the second author [Merz 1998], which has been part of the Isabelle
distribution. In contrast to that previous work, we give here a shallow,
definitional embedding, with the following highlights:
<ul>
<li>a theory of infinite sequences, including a formalisation of the concepts of stuttering invariance central to TLA and TLA*;
<li>a definition of the semantics of TLA*, which extends TLA by a mutually-recursive definition of formulas and pre-formulas, generalising TLA action formulas;
<li>a substantial set of derived proof rules, including the TLA* axioms and Lamport's proof rules for system verification;
<li>a set of examples illustrating the usage of Isabelle/TLA* for reasoning about systems.
</ul>
Note that this work is unrelated to the ongoing development of a proof system
for the specification language TLA+, which includes an encoding of TLA+ as a
new Isabelle object logic <a href="http://www.springerlink.com/content/354026160p14j175/">[Chaudhuri et al 2010]</a>.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session TLA</h3>
<ul>
<li><a href="../theories/tla/#Sequence">Sequence</a></li>
<li><a href="../theories/tla/#Intensional">Intensional</a></li>
<li><a href="../theories/tla/#Semantics">Semantics</a></li>
<li><a href="../theories/tla/#PreFormulas">PreFormulas</a></li>
<li><a href="../theories/tla/#Rules">Rules</a></li>
<li><a href="../theories/tla/#Liveness">Liveness</a></li>
<li><a href="../theories/tla/#State">State</a></li>
<li><a href="../theories/tla/#Even">Even</a></li>
<li><a href="../theories/tla/#Inc">Inc</a></li>
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<p style="display:none;" id="bibtex-filename">TLA-AFP</p><pre id="copy-text">@article{TLA-AFP,
author = {Gudmund Grov and Stephan Merz},
title = {A Definitional Encoding of TLA* in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {November},
year = {2011},
note = {\url{https://isa-afp.org/entries/TLA.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-TLA-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-TLA-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-TLA-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-TLA-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
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</li><li>
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</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-TLA-2011-11-27.tar.gz">Nov 27, 2011</a>: Isabelle2011-1
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diff --git a/web/entries/Tail_Recursive_Functions.html b/web/entries/Tail_Recursive_Functions.html
--- a/web/entries/Tail_Recursive_Functions.html
+++ b/web/entries/Tail_Recursive_Functions.html
@@ -1,193 +1,195 @@
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<h1 >
<span class='first'>A</span> <span class='first'>G</span>eneral <span class='first'>M</span>ethod for the <span class='first'>P</span>roof of <span class='first'>T</span>heorems on <span class='first'>T</span>ail-<span class='first'>R</span>ecursive <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/noce">Pasquale Noce</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsicGFzcXVhbGUiLCJub2NlIiwibGF2b3JvIl19">📧</a>
</p>
<p class="date">December 1, 2013</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
Tail-recursive function definitions are sometimes more straightforward than
alternatives, but proving theorems on them may be roundabout because of the
peculiar form of the resulting recursion induction rules.
</p><p>
This paper describes a proof method that provides a general solution to
this problem by means of suitable invariants over inductive sets, and
illustrates the application of such method by examining two case studies.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Tail_Recursive_Functions</h3>
<ul>
<li><a href="../theories/tail_recursive_functions/#Method">Method</a></li>
<li><a href="../theories/tail_recursive_functions/#CaseStudy1">CaseStudy1</a></li>
<li><a href="../theories/tail_recursive_functions/#CaseStudy2">CaseStudy2</a></li></ul><div class="flex-wrap">
</div>
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<p style="display:none;" id="bibtex-filename">Tail_Recursive_Functions-AFP</p><pre id="copy-text">@article{Tail_Recursive_Functions-AFP,
author = {Pasquale Noce},
title = {A General Method for the Proof of Theorems on Tail-recursive Functions},
journal = {Archive of Formal Proofs},
month = {December},
year = {2013},
note = {\url{https://isa-afp.org/entries/Tail_Recursive_Functions.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Tail_Recursive_Functions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Tail_Recursive_Functions-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Tail_Recursive_Functions-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Tail_Recursive_Functions-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>ndependence of <span class='first'>T</span>arski's <span class='first'>E</span>uclidean <span class='first'>A</span>xiom</h1>
<div>
<p><a href="../authors/makarios">T. J. M. Makarios</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsidGptMTk4MyJdfQ==">📧</a>
</p>
<p class="date">October 30, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Tarski's axioms of plane geometry are formalized and, using the standard
real Cartesian model, shown to be consistent. A substantial theory of
the projective plane is developed. Building on this theory, the
Klein-Beltrami model of the hyperbolic plane is defined and shown to
satisfy all of Tarski's axioms except his Euclidean axiom; thus Tarski's
Euclidean axiom is shown to be independent of his other axioms of plane
geometry.
<p>
An earlier version of this work was the subject of the author's
<a href="http://researcharchive.vuw.ac.nz/handle/10063/2315">MSc thesis</a>,
which contains natural-language explanations of some of the
more interesting proofs.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Tarskis_Geometry</h3>
<ul>
<li><a href="../theories/tarskis_geometry/#Metric">Metric</a></li>
<li><a href="../theories/tarskis_geometry/#Miscellany">Miscellany</a></li>
<li><a href="../theories/tarskis_geometry/#Tarski">Tarski</a></li>
<li><a href="../theories/tarskis_geometry/#Euclid_Tarski">Euclid_Tarski</a></li>
<li><a href="../theories/tarskis_geometry/#Linear_Algebra2">Linear_Algebra2</a></li>
<li><a href="../theories/tarskis_geometry/#Action">Action</a></li>
<li><a href="../theories/tarskis_geometry/#Projective">Projective</a></li>
<li><a href="../theories/tarskis_geometry/#Hyperbolic_Tarski">Hyperbolic_Tarski</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Tarskis_Geometry-AFP</p><pre id="copy-text">@article{Tarskis_Geometry-AFP,
author = {T. J. M. Makarios},
title = {The independence of Tarski&#39;s Euclidean axiom},
journal = {Archive of Formal Proofs},
month = {October},
year = {2012},
note = {\url{https://isa-afp.org/entries/Tarskis_Geometry.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2012-11-09.tar.gz">Nov 9, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-Tarskis_Geometry-2012-11-08.tar.gz">Nov 8, 2012</a>: Isabelle2012
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diff --git a/web/entries/Taylor_Models.html b/web/entries/Taylor_Models.html
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+++ b/web/entries/Taylor_Models.html
@@ -1,197 +1,199 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Taylor Models - Archive of Formal Proofs</title><meta name="description" content="We present a formally verified implementation of multivariate Taylor
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<h1 >
<span class='first'>T</span>aylor <span class='first'>M</span>odels</h1>
<div>
<p><a href="../authors/traut">Christoph Traut</a> and <a href="../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a>
</p>
<p class="date">January 8, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formally verified implementation of multivariate Taylor
models. Taylor models are a form of rigorous polynomial approximation,
consisting of an approximation polynomial based on Taylor expansions,
combined with a rigorous bound on the approximation error. Taylor
models were introduced as a tool to mitigate the dependency problem of
interval arithmetic. Our implementation automatically computes Taylor
models for the class of elementary functions, expressed by composition
of arithmetic operations and basic functions like exp, sin, or square
root.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Taylor_Models</h3>
<ul>
<li><a href="../theories/taylor_models/#Polynomial_Expression">Polynomial_Expression</a></li>
<li><a href="../theories/taylor_models/#Float_Topology">Float_Topology</a></li>
<li><a href="../theories/taylor_models/#Horner_Eval">Horner_Eval</a></li>
<li><a href="../theories/taylor_models/#Polynomial_Expression_Additional">Polynomial_Expression_Additional</a></li>
<li><a href="../theories/taylor_models/#Taylor_Models_Misc">Taylor_Models_Misc</a></li>
<li><a href="../theories/taylor_models/#Taylor_Models">Taylor_Models</a></li>
<li><a href="../theories/taylor_models/#Experiments">Experiments</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></li></ul>
</div>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Padic_Ints.html">Hensel&rsquo;s Lemma for the p-adic Integers</a></li>
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<p style="display:none;" id="bibtex-filename">Taylor_Models-AFP</p><pre id="copy-text">@article{Taylor_Models-AFP,
author = {Christoph Traut and Fabian Immler},
title = {Taylor Models},
journal = {Archive of Formal Proofs},
month = {January},
year = {2018},
note = {\url{https://isa-afp.org/entries/Taylor_Models.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Taylor_Models-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/Three_Circles.html b/web/entries/Three_Circles.html
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+++ b/web/entries/Three_Circles.html
@@ -1,184 +1,186 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>heorem of <span class='first'>T</span>hree <span class='first'>C</span>ircles</h1>
<div>
<p><a href="../authors/thomson">Fox Thomson</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZm94dGhvbXNvbjAiXX0=">📧</a> and <a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">August 21, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Descartes test based on Bernstein coefficients and Descartes’ rule
of signs effectively (over-)approximates the number of real roots of a
univariate polynomial over an interval. In this entry we formalise the
theorem of three circles, which gives sufficient conditions for when
the Descartes test returns 0 or 1. This is the first step for
efficient root isolation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Three_Circles</h3>
<ul>
<li><a href="../theories/three_circles/#RRI_Misc">RRI_Misc</a></li>
<li><a href="../theories/three_circles/#Bernstein_01">Bernstein_01</a></li>
<li><a href="../theories/three_circles/#Bernstein">Bernstein</a></li>
<li><a href="../theories/three_circles/#Normal_Poly">Normal_Poly</a></li>
<li><a href="../theories/three_circles/#Three_Circles">Three_Circles</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Budan_Fourier.html">The Budan-Fourier Theorem and Counting Real Roots with Multiplicity</a></li><li><a href="../entries/Polynomial_Interpolation.html">Polynomial Interpolation</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/Symmetric_Polynomials.html">Symmetric Polynomials</a></li>
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<p style="display:none;" id="bibtex-filename">Three_Circles-AFP</p><pre id="copy-text">@article{Three_Circles-AFP,
author = {Fox Thomson and Wenda Li},
title = {The Theorem of Three Circles},
journal = {Archive of Formal Proofs},
month = {August},
year = {2021},
note = {\url{https://isa-afp.org/entries/Three_Circles.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Three_Circles-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Three_Circles-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Three_Circles-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Three_Circles-2021-09-01.tar.gz">Sep 1, 2021</a>: Isabelle2021
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diff --git a/web/entries/Timed_Automata.html b/web/entries/Timed_Automata.html
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<h1 >
<span class='first'>T</span>imed <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>
</p>
<p class="date">March 8, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Timed automata are a widely used formalism for modeling real-time
systems, which is employed in a class of successful model checkers
such as UPPAAL [LPY97], HyTech [HHWt97] or Kronos [Yov97]. This work
formalizes the theory for the subclass of diagonal-free timed
automata, which is sufficient to model many interesting problems. We
first define the basic concepts and semantics of diagonal-free timed
automata. Based on this, we prove two types of decidability results
for the language emptiness problem. The first is the classic result
of Alur and Dill [AD90, AD94], which uses a finite partitioning of
the state space into so-called `regions`. Our second result focuses
on an approach based on `Difference Bound Matrices (DBMs)`, which is
practically used by model checkers. We prove the correctness of the
basic forward analysis operations on DBMs. One of these operations is
the Floyd-Warshall algorithm for the all-pairs shortest paths problem.
To obtain a finite search space, a widening operation has to be used
for this kind of analysis. We use Patricia Bouyer's [Bou04] approach
to prove that this widening operation is correct in the sense that
DBM-based forward analysis in combination with the widening operation
also decides language emptiness. The interesting property of this
proof is that the first decidability result is reused to obtain the
second one.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Timed_Automata</h3>
<ul>
<li><a href="../theories/timed_automata/#Floyd_Warshall">Floyd_Warshall</a></li>
<li><a href="../theories/timed_automata/#Timed_Automata">Timed_Automata</a></li>
<li><a href="../theories/timed_automata/#DBM">DBM</a></li>
<li><a href="../theories/timed_automata/#Paths_Cycles">Paths_Cycles</a></li>
<li><a href="../theories/timed_automata/#DBM_Basics">DBM_Basics</a></li>
<li><a href="../theories/timed_automata/#DBM_Operations">DBM_Operations</a></li>
<li><a href="../theories/timed_automata/#DBM_Zone_Semantics">DBM_Zone_Semantics</a></li>
<li><a href="../theories/timed_automata/#Misc">Misc</a></li>
<li><a href="../theories/timed_automata/#DBM_Normalization">DBM_Normalization</a></li>
<li><a href="../theories/timed_automata/#Regions_Beta">Regions_Beta</a></li>
<li><a href="../theories/timed_automata/#Regions">Regions</a></li>
<li><a href="../theories/timed_automata/#Closure">Closure</a></li>
<li><a href="../theories/timed_automata/#Approx_Beta">Approx_Beta</a></li>
<li><a href="../theories/timed_automata/#Normalized_Zone_Semantics">Normalized_Zone_Semantics</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Probabilistic_Timed_Automata.html">Probabilistic Timed Automata</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Timed_Automata-AFP</p><pre id="copy-text">@article{Timed_Automata-AFP,
author = {Simon Wimmer},
title = {Timed Automata},
journal = {Archive of Formal Proofs},
month = {March},
year = {2016},
note = {\url{https://isa-afp.org/entries/Timed_Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Timed_Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Timed_Automata-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Timed_Automata-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Timed_Automata-2016-03-11.tar.gz">Mar 11, 2016</a>: Isabelle2016
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diff --git a/web/entries/Topological_Semantics.html b/web/entries/Topological_Semantics.html
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@@ -1,191 +1,193 @@
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<h1 >
<span class='first'>T</span>opological <span class='first'>S</span>emantics for <span class='first'>P</span>araconsistent and <span class='first'>P</span>aracomplete <span class='first'>L</span>ogics</h1>
<div>
<p><a href="../authors/fuenmayor">David Fuenmayor</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZGF2ZnVlbm1heW9yIl19">📧</a>
</p>
<p class="date">December 17, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We introduce a generalized topological semantics for paraconsistent
and paracomplete logics by drawing upon early works on topological
Boolean algebras (cf. works by Kuratowski, Zarycki, McKinsey &
Tarski, etc.). In particular, this work exemplarily illustrates the
shallow semantical embeddings approach (<a
href="http://dx.doi.org/10.1007/s11787-012-0052-y">SSE</a>)
employing the proof assistant Isabelle/HOL. By means of the SSE
technique we can effectively harness theorem provers, model finders
and 'hammers' for reasoning with quantified non-classical
logics.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic">Logic/General logic</a></li></ul>
<h3>Session Topological_Semantics</h3>
<ul>
<li><a href="../theories/topological_semantics/#sse_boolean_algebra">sse_boolean_algebra</a></li>
<li><a href="../theories/topological_semantics/#sse_boolean_algebra_quantification">sse_boolean_algebra_quantification</a></li>
<li><a href="../theories/topological_semantics/#sse_operation_positive">sse_operation_positive</a></li>
<li><a href="../theories/topological_semantics/#sse_operation_positive_quantification">sse_operation_positive_quantification</a></li>
<li><a href="../theories/topological_semantics/#sse_operation_negative">sse_operation_negative</a></li>
<li><a href="../theories/topological_semantics/#sse_operation_negative_quantification">sse_operation_negative_quantification</a></li>
<li><a href="../theories/topological_semantics/#topo_operators_basic">topo_operators_basic</a></li>
<li><a href="../theories/topological_semantics/#topo_operators_derivative">topo_operators_derivative</a></li>
<li><a href="../theories/topological_semantics/#topo_alexandrov">topo_alexandrov</a></li>
<li><a href="../theories/topological_semantics/#topo_frontier_algebra">topo_frontier_algebra</a></li>
<li><a href="../theories/topological_semantics/#topo_negation_conditions">topo_negation_conditions</a></li>
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<li><a href="../theories/topological_semantics/#topo_closure_algebra">topo_closure_algebra</a></li>
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<p style="display:none;" id="bibtex-filename">Topological_Semantics-AFP</p><pre id="copy-text">@article{Topological_Semantics-AFP,
author = {David Fuenmayor},
title = {Topological semantics for paraconsistent and paracomplete logics},
journal = {Archive of Formal Proofs},
month = {December},
year = {2020},
note = {\url{https://isa-afp.org/entries/Topological_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Topology.html b/web/entries/Topology.html
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<h1 >
<span class='first'>T</span>opology</h1>
<div>
<p><a href="../authors/friedrich">Stefan Friedrich</a>
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<p class="date">April 26, 2004</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains two theories. The first, <tt>Topology</tt>, develops the basic notions of general topology. The second, which can be viewed as a demonstration of the first, is called <tt>LList_Topology</tt>. It develops the topology of lazy lists.</div>
<h3>License</h3>
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<h3>Session Topology</h3>
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<li><a href="../theories/topology/#Topology">Topology</a></li>
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<h3>Depends on</h3>
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<p style="display:none;" id="bibtex-filename">Topology-AFP</p><pre id="copy-text">@article{Topology-AFP,
author = {Stefan Friedrich},
title = {Topology},
journal = {Archive of Formal Proofs},
month = {April},
year = {2004},
note = {\url{https://isa-afp.org/entries/Topology.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/TortoiseHare.html b/web/entries/TortoiseHare.html
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+++ b/web/entries/TortoiseHare.html
@@ -1,175 +1,177 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>ortoise and <span class='first'>H</span>are <span class='first'>A</span>lgorithm</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">November 18, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the Tortoise and Hare cycle-finding algorithm ascribed to Floyd by Knuth, and an improved version due to Brent.</div>
<h3>License</h3>
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<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session TortoiseHare</h3>
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author = {Peter Gammie},
title = {The Tortoise and Hare Algorithm},
journal = {Archive of Formal Proofs},
month = {November},
year = {2015},
note = {\url{https://isa-afp.org/entries/TortoiseHare.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Transcendence_Series_Hancl_Rucki.html b/web/entries/Transcendence_Series_Hancl_Rucki.html
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+++ b/web/entries/Transcendence_Series_Hancl_Rucki.html
@@ -1,192 +1,194 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>ranscendence of <span class='first'>C</span>ertain <span class='first'>I</span>nfinite <span class='first'>S</span>eries</h1>
<div>
<p><a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a href="https://www.cl.cam.ac.uk/~ak2110/">🌐</a> and <a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">March 27, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize the proofs of two transcendence criteria by J. Hančl
and P. Rucki that assert the transcendence of the sums of certain
infinite series built up by sequences that fulfil certain properties.
Both proofs make use of Roth's celebrated theorem on diophantine
approximations to algebraic numbers from 1955 which we implement as
an assumption without having formalised its proof.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Transcendence_Series_Hancl_Rucki</h3>
<ul>
<li><a href="../theories/transcendence_series_hancl_rucki/#Transcendence_Series">Transcendence_Series</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
<li><a href="../entries/Hermite_Lindemann.html">The Hermite–Lindemann–Weierstraß Transcendence Theorem</a></li>
<li><a href="../entries/Nullstellensatz.html">Hilbert&rsquo;s Nullstellensatz</a></li>
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<p style="display:none;" id="bibtex-filename">Transcendence_Series_Hancl_Rucki-AFP</p><pre id="copy-text">@article{Transcendence_Series_Hancl_Rucki-AFP,
author = {Angeliki Koutsoukou-Argyraki and Wenda Li},
title = {The Transcendence of Certain Infinite Series},
journal = {Archive of Formal Proofs},
month = {March},
year = {2019},
note = {\url{https://isa-afp.org/entries/Transcendence_Series_Hancl_Rucki.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>T</span>ransformer <span class='first'>S</span>emantics</h1>
<div>
<p><a href="../authors/struth">Georg Struth</a> <a href="http://staffwww.dcs.shef.ac.uk/people/G.Struth/">🌐</a>
</p>
<p class="date">December 11, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These mathematical components formalise predicate transformer
semantics for programs, yet currently only for partial correctness and
in the absence of faults. A first part for isotone (or monotone),
Sup-preserving and Inf-preserving transformers follows Back and von
Wright's approach, with additional emphasis on the quantalic
structure of algebras of transformers. The second part develops
Sup-preserving and Inf-preserving predicate transformers from the
powerset monad, via its Kleisli category and Eilenberg-Moore algebras,
with emphasis on adjunctions and dualities, as well as isomorphisms
between relations, state transformers and predicate transformers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session Transformer_Semantics</h3>
<ul>
<li><a href="../theories/transformer_semantics/#Isotone_Transformers">Isotone_Transformers</a></li>
<li><a href="../theories/transformer_semantics/#Sup_Inf_Preserving_Transformers">Sup_Inf_Preserving_Transformers</a></li>
<li><a href="../theories/transformer_semantics/#Powerset_Monad">Powerset_Monad</a></li>
<li><a href="../theories/transformer_semantics/#Kleisli_Transformers">Kleisli_Transformers</a></li>
<li><a href="../theories/transformer_semantics/#Kleisli_Quantaloid">Kleisli_Quantaloid</a></li>
<li><a href="../theories/transformer_semantics/#Kleisli_Quantale">Kleisli_Quantale</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Order_Lattice_Props.html">Properties of Orderings and Lattices</a></li><li><a href="../entries/Quantales.html">Quantales</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Hybrid_Systems_VCs.html">Verification Components for Hybrid Systems</a></li></ul>
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<h3>Auto-related entries</h3>
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<li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li>
<li><a href="../entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></li>
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<p style="display:none;" id="bibtex-filename">Transformer_Semantics-AFP</p><pre id="copy-text">@article{Transformer_Semantics-AFP,
author = {Georg Struth},
title = {Transformer Semantics},
journal = {Archive of Formal Proofs},
month = {December},
year = {2018},
note = {\url{https://isa-afp.org/entries/Transformer_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>T</span>ransition <span class='first'>S</span>ystems and <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/brunner">Julian Brunner</a> <a href="http://www21.in.tum.de/~brunnerj/">🌐</a>
</p>
<p class="date">October 19, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides a very abstract theory of transition systems that
can be instantiated to express various types of automata. A transition
system is typically instantiated by providing a set of initial states,
a predicate for enabled transitions, and a transition execution
function. From this, it defines the concepts of finite and infinite
paths as well as the set of reachable states, among other things. Many
useful theorems, from basic path manipulation rules to coinduction and
run construction rules, are proven in this abstract transition system
context. The library comes with instantiations for DFAs, NFAs, and
Büchi automata.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Transition_Systems_and_Automata</h3>
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<li><a href="../theories/transition_systems_and_automata/#Basic">Basic</a></li>
<li><a href="../theories/transition_systems_and_automata/#Sequence">Sequence</a></li>
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<li><a href="../theories/transition_systems_and_automata/#Transition_System_Extra">Transition_System_Extra</a></li>
<li><a href="../theories/transition_systems_and_automata/#Transition_System_Construction">Transition_System_Construction</a></li>
<li><a href="../theories/transition_systems_and_automata/#Deterministic">Deterministic</a></li>
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<li><a href="../theories/transition_systems_and_automata/#DBA">DBA</a></li>
<li><a href="../theories/transition_systems_and_automata/#DGBA">DGBA</a></li>
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<li><a href="../theories/transition_systems_and_automata/#DCA">DCA</a></li>
<li><a href="../theories/transition_systems_and_automata/#DGCA">DGCA</a></li>
<li><a href="../theories/transition_systems_and_automata/#DCA_Combine">DCA_Combine</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA">DRA</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Combine">DRA_Combine</a></li>
<li><a href="../theories/transition_systems_and_automata/#Refine">Refine</a></li>
<li><a href="../theories/transition_systems_and_automata/#Acceptance_Refine">Acceptance_Refine</a></li>
<li><a href="../theories/transition_systems_and_automata/#Transition_System_Refine">Transition_System_Refine</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Refine">DRA_Refine</a></li>
<li><a href="../theories/transition_systems_and_automata/#Implement">Implement</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Implement">DRA_Implement</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Nodes">DRA_Nodes</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Explicit">DRA_Explicit</a></li>
<li><a href="../theories/transition_systems_and_automata/#DRA_Translate">DRA_Translate</a></li>
<li><a href="../theories/transition_systems_and_automata/#NBA">NBA</a></li>
<li><a href="../theories/transition_systems_and_automata/#NGBA">NGBA</a></li>
<li><a href="../theories/transition_systems_and_automata/#NBA_Combine">NBA_Combine</a></li>
<li><a href="../theories/transition_systems_and_automata/#NBA_Graphs">NBA_Graphs</a></li>
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<p style="display:none;" id="bibtex-filename">Transition_Systems_and_Automata-AFP</p><pre id="copy-text">@article{Transition_Systems_and_Automata-AFP,
author = {Julian Brunner},
title = {Transition Systems and Automata},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Transition_Systems_and_Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>xecutable <span class='first'>T</span>ransitive <span class='first'>C</span>losures</h1>
<div>
<p><a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">February 29, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
We provide a generic work-list algorithm to compute the
(reflexive-)transitive closure of relations where only successors of newly
detected states are generated.
In contrast to our previous work, the relations do not have to be finite,
but each element must only have finitely many (indirect) successors.
Moreover, a subsumption relation can be used instead of pure equality.
An executable variant of the algorithm is available where the generic operations
are instantiated with list operations.
</p><p>
This formalization was performed as part of the IsaFoR/CeTA project,
and it has been used to certify size-change
termination proofs where large transitive closures have to be computed.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Transitive-Closure-II</h3>
<ul>
<li><a href="../theories/transitive-closure-ii/#RTrancl">RTrancl</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Transitive-Closure-II-AFP</p><pre id="copy-text">@article{Transitive-Closure-II-AFP,
author = {René Thiemann},
title = {Executable Transitive Closures},
journal = {Archive of Formal Proofs},
month = {February},
year = {2012},
note = {\url{https://isa-afp.org/entries/Transitive-Closure-II.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>E</span>xecutable <span class='first'>T</span>ransitive <span class='first'>C</span>losures of <span class='first'>F</span>inite <span class='first'>R</span>elations</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">March 14, 2011</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We provide a generic work-list algorithm to compute the transitive closure of finite relations where only successors of newly detected states are generated. This algorithm is then instantiated for lists over arbitrary carriers and red black trees (which are faster but require a linear order on the carrier), respectively. Our formalization was performed as part of the IsaFoR/CeTA project where reflexive transitive closures of large tree automata have to be computed.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li></ul>
<h3>Session Transitive-Closure</h3>
<ul>
<li><a href="../theories/transitive-closure/#Transitive_Closure_Impl">Transitive_Closure_Impl</a></li>
<li><a href="../theories/transitive-closure/#Transitive_Closure_List_Impl">Transitive_Closure_List_Impl</a></li>
<li><a href="../theories/transitive-closure/#RBT_Map_Set_Extension">RBT_Map_Set_Extension</a></li>
<li><a href="../theories/transitive-closure/#Transitive_Closure_RBT_Impl">Transitive_Closure_RBT_Impl</a></li>
<li><a href="../theories/transitive-closure/#Finite_Transitive_Closure_Simprocs">Finite_Transitive_Closure_Simprocs</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></li></ul>
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<ul class="horizontal-list"><li><a href="../entries/Planarity_Certificates.html">Planarity Certificates</a></li><li><a href="../entries/Network_Security_Policy_Verification.html">Network Security Policy Verification</a></li><li><a href="../entries/KBPs.html">Knowledge-based programs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Transitive-Closure-AFP</p><pre id="copy-text">@article{Transitive-Closure-AFP,
author = {Christian Sternagel and René Thiemann},
title = {Executable Transitive Closures of Finite Relations},
journal = {Archive of Formal Proofs},
month = {March},
year = {2011},
note = {\url{https://isa-afp.org/entries/Transitive-Closure.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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<h1 >
<span class='first'>T</span>ransitive <span class='first'>M</span>odels of <span class='first'>F</span>ragments of <span class='first'>Z</span><span class='first'>F</span><span class='first'>C</span></h1>
<div>
<p><a href="../authors/gunther">Emmanuel Gunther</a> <a class="obfuscated" data="eyJob3N0IjpbImZhbWFmIiwidW5jIiwiZWR1IiwiYXIiXSwidXNlciI6WyJndW50aGVyIl19">📧</a>, <a href="../authors/pagano">Miguel Pagano</a> <a href="https://cs.famaf.unc.edu.ar/~mpagano/">🌐</a>, <a href="../authors/terraf">Pedro Sánchez Terraf</a> <a href="https://cs.famaf.unc.edu.ar/~pedro/home_en.html">🌐</a> and <a href="../authors/steinberg">Matías Steinberg</a> <a class="obfuscated" data="eyJob3N0IjpbIm1pIiwidW5jIiwiZWR1IiwiYXIiXSwidXNlciI6WyJtYXRpYXMiLCJzdGVpbmJlcmciXX0=">📧</a>
</p>
<p class="date">March 3, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We extend the ZF-Constructibility library by relativizing theories of
the Isabelle/ZF and Delta System Lemma sessions to a transitive class.
We also relativize Paulson's work on Aleph and our former
treatment of the Axiom of Dependent Choices. This work is a
prerrequisite to our formalization of the independence of the
Continuum Hypothesis.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Transitive_Models</h3>
<ul>
<li><a href="../theories/transitive_models/#Utils">Utils</a></li>
<li><a href="../theories/transitive_models/#Nat_Miscellanea">Nat_Miscellanea</a></li>
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<li><a href="../theories/transitive_models/#Renaming">Renaming</a></li>
<li><a href="../theories/transitive_models/#Renaming_Auto">Renaming_Auto</a></li>
<li><a href="../theories/transitive_models/#M_Basic_No_Repl">M_Basic_No_Repl</a></li>
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<li><a href="../theories/transitive_models/#Lambda_Replacement">Lambda_Replacement</a></li>
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<li><a href="../theories/transitive_models/#Univ_Relative">Univ_Relative</a></li>
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<li><a href="../theories/transitive_models/#CardinalArith_Relative">CardinalArith_Relative</a></li>
<li><a href="../theories/transitive_models/#Aleph_Relative">Aleph_Relative</a></li>
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<li><a href="../theories/transitive_models/#FiniteFun_Relative">FiniteFun_Relative</a></li>
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<li><a href="../theories/transitive_models/#Cardinal_Library_Relative">Cardinal_Library_Relative</a></li>
<li><a href="../theories/transitive_models/#Delta_System_Relative">Delta_System_Relative</a></li>
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<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Delta_System_Lemma.html">Cofinality and the Delta System Lemma</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Independence_CH.html">The Independence of the Continuum Hypothesis in Isabelle/ZF</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Independence_CH.html">The Independence of the Continuum Hypothesis in Isabelle/ZF</a></li>
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<p style="display:none;" id="bibtex-filename">Transitive_Models-AFP</p><pre id="copy-text">@article{Transitive_Models-AFP,
author = {Emmanuel Gunther and Miguel Pagano and Pedro Sánchez Terraf and Matías Steinberg},
title = {Transitive Models of Fragments of ZFC},
journal = {Archive of Formal Proofs},
month = {March},
year = {2022},
note = {\url{https://isa-afp.org/entries/Transitive_Models.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Transitive_Models-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Transitive_Models-2022-03-04.tar.gz">Mar 4, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Treaps.html b/web/entries/Treaps.html
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<h1 >
<span class='first'>T</span>reaps</h1>
<div>
<p><a href="../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a>, <a href="../authors/eberl">Manuel Eberl</a> <a href="https://www.in.tum.de/~eberlm">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">February 6, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p> A Treap is a binary tree whose nodes contain pairs
consisting of some payload and an associated priority. It must have
the search-tree property w.r.t. the payloads and the heap property
w.r.t. the priorities. Treaps are an interesting data structure that
is related to binary search trees (BSTs) in the following way: if one
forgets all the priorities of a treap, the resulting BST is exactly
the same as if one had inserted the elements into an empty BST in
order of ascending priority. This means that a treap behaves like a
BST where we can pretend the elements were inserted in a different
order from the one in which they were actually inserted. </p>
<p> In particular, by choosing these priorities at random upon
insertion of an element, we can pretend that we inserted the elements
in <em>random order</em>, so that the shape of the
resulting tree is that of a random BST no matter in what order we
insert the elements. This is the main result of this
formalisation.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
Eberl, M., Haslbeck, M. W., & Nipkow, T. (2020). Verified Analysis of Random Binary Tree Structures. Journal of Automated Reasoning, 64(5), 879–910. <a href="https://doi.org/10.1007/s10817-020-09545-0">https://doi.org/10.1007/s10817-020-09545-0</a>
</li><li>
<a href="https://en.wikipedia.org/wiki/Treap">Wikipedia</a>
</li></ul>
<h3>Session Treaps</h3>
<ul>
<li><a href="../theories/treaps/#Probability_Misc">Probability_Misc</a></li>
<li><a href="../theories/treaps/#Treap">Treap</a></li>
<li><a href="../theories/treaps/#Random_List_Permutation">Random_List_Permutation</a></li>
<li><a href="../theories/treaps/#Treap_Sort_and_BSTs">Treap_Sort_and_BSTs</a></li>
<li><a href="../theories/treaps/#Random_Treap">Random_Treap</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Comparison_Sort_Lower_Bound.html">Lower bound on comparison-based sorting algorithms</a></li><li><a href="../entries/Random_BSTs.html">Expected Shape of Random Binary Search Trees</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Treaps-AFP</p><pre id="copy-text">@article{Treaps-AFP,
author = {Max W. Haslbeck and Manuel Eberl and Tobias Nipkow},
title = {Treaps},
journal = {Archive of Formal Proofs},
month = {February},
year = {2018},
note = {\url{https://isa-afp.org/entries/Treaps.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Tree-Automata.html b/web/entries/Tree-Automata.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Tree Automata - Archive of Formal Proofs</title><meta name="description" content="This work presents a machine-checked tree automata library for Standard-ML, OCaml and Haskell. The algorithms are efficient by using appropriate data..."><meta property="og:title" content="Tree Automata" />
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<h1 >
<span class='first'>T</span>ree <span class='first'>A</span>utomata</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a>
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<p class="date">November 25, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This work presents a machine-checked tree automata library for Standard-ML, OCaml and Haskell. The algorithms are efficient by using appropriate data structures like RB-trees. The available algorithms for non-deterministic automata include membership query, reduction, intersection, union, and emptiness check with computation of a witness for non-emptiness. The executable algorithms are derived from less-concrete, non-executable algorithms using data-refinement techniques. The concrete data structures are from the Isabelle Collections Framework. Moreover, this work contains a formalization of the class of tree-regular languages and its closure properties under set operations.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Tree-Automata</h3>
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<p style="display:none;" id="bibtex-filename">Tree-Automata-AFP</p><pre id="copy-text">@article{Tree-Automata-AFP,
author = {Peter Lammich},
title = {Tree Automata},
journal = {Archive of Formal Proofs},
month = {November},
year = {2009},
note = {\url{https://isa-afp.org/entries/Tree-Automata.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Tree-Automata-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-Tree-Automata-2009-11-29.tar.gz">Nov 29, 2009</a>: Isabelle2009
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<h1 >
<span class='first'>T</span>ree <span class='first'>D</span>ecomposition</h1>
<div>
<p><a href="../authors/dittmann">Christoph Dittmann</a> <a href="http://logic.las.tu-berlin.de/Members/Dittmann/">🌐</a>
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<p class="date">May 31, 2016</p>
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</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We formalize tree decompositions and tree width in Isabelle/HOL,
proving that trees have treewidth 1. We also show that every edge of
a tree decomposition is a separation of the underlying graph. As an
application of this theorem we prove that complete graphs of size n
have treewidth n-1.</div>
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<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Tree_Decomposition</h3>
<ul>
<li><a href="../theories/tree_decomposition/#Graph">Graph</a></li>
<li><a href="../theories/tree_decomposition/#Tree">Tree</a></li>
<li><a href="../theories/tree_decomposition/#TreeDecomposition">TreeDecomposition</a></li>
<li><a href="../theories/tree_decomposition/#TreewidthTree">TreewidthTree</a></li>
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<p style="display:none;" id="bibtex-filename">Tree_Decomposition-AFP</p><pre id="copy-text">@article{Tree_Decomposition-AFP,
author = {Christoph Dittmann},
title = {Tree Decomposition},
journal = {Archive of Formal Proofs},
month = {May},
year = {2016},
note = {\url{https://isa-afp.org/entries/Tree_Decomposition.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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</li><li>
<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2016-06-01.tar.gz">Jun 1, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Tree_Decomposition-2016-05-31.tar.gz">May 31, 2016</a>: Isabelle2016
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<h1 >
<span class='first'>B</span>asic <span class='first'>G</span>eometric <span class='first'>P</span>roperties of <span class='first'>T</span>riangles</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>
This entry contains a definition of angles between vectors and between three
points. Building on this, we prove basic geometric properties of triangles, such
as the Isosceles Triangle Theorem, the Law of Sines and the Law of Cosines, that
the sum of the angles of a triangle is π, and the congruence theorems for
triangles.
</p><p>
The definitions and proofs were developed following those by John Harrison in
HOL Light. However, due to Isabelle's type class system, all definitions and
theorems in the Isabelle formalisation hold for all real inner product spaces.
</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/geometry">Mathematics/Geometry</a></li></ul>
<h3>Session Triangle</h3>
<ul>
<li><a href="../theories/triangle/#Angles">Angles</a></li>
<li><a href="../theories/triangle/#Triangle">Triangle</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Stewart_Apollonius.html">Stewart&rsquo;s Theorem and Apollonius' Theorem</a></li><li><a href="../entries/Chord_Segments.html">Intersecting Chords Theorem</a></li><li><a href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Triangle-AFP</p><pre id="copy-text">@article{Triangle-AFP,
author = {Manuel Eberl},
title = {Basic Geometric Properties of Triangles},
journal = {Archive of Formal Proofs},
month = {December},
year = {2015},
note = {\url{https://isa-afp.org/entries/Triangle.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Triangle-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Triangle-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Triangle-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Triangle-2016-01-05.tar.gz">Jan 5, 2016</a>: Isabelle2015
</li></ul>
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diff --git a/web/entries/Trie.html b/web/entries/Trie.html
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<h1 >
<span class='first'>T</span>rie</h1>
<div>
<p><a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
</p>
<p class="date">March 30, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalizes the ``trie'' data structure invented by
Fredkin [CACM 1960]. It also provides a specialization where the entries
in the trie are lists.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Extra 0</h3>
<p>
Origin: This article was extracted from existing articles by the authors.</p><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Trie</h3>
<ul>
<li><a href="../theories/trie/#Trie">Trie</a></li>
<li><a href="../theories/trie/#Tries">Tries</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Containers.html">Light-weight Containers</a></li><li><a href="../entries/KBPs.html">Knowledge-based programs</a></li><li><a href="../entries/Collections.html">Collections Framework</a></li><li><a href="../entries/JinjaThreads.html">Jinja with Threads</a></li><li><a href="../entries/Flyspeck-Tame.html">Flyspeck I: Tame Graphs</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Trie-AFP</p><pre id="copy-text">@article{Trie-AFP,
author = {Andreas Lochbihler and Tobias Nipkow},
title = {Trie},
journal = {Archive of Formal Proofs},
month = {March},
year = {2015},
note = {\url{https://isa-afp.org/entries/Trie.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Trie-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Trie-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Trie-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Trie-2015-03-30.tar.gz">Mar 30, 2015</a>: Isabelle2014
</li></ul>
</div>
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diff --git a/web/entries/Twelvefold_Way.html b/web/entries/Twelvefold_Way.html
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+++ b/web/entries/Twelvefold_Way.html
@@ -1,201 +1,203 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>T</span>welvefold <span class='first'>W</span>ay</h1>
<div>
<p><a href="../authors/bulwahn">Lukas Bulwahn</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJidWx3YWhuIl19">📧</a>
</p>
<p class="date">December 29, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides all cardinality theorems of the Twelvefold Way.
The Twelvefold Way systematically classifies twelve related
combinatorial problems concerning two finite sets, which include
counting permutations, combinations, multisets, set partitions and
number partitions. This development builds upon the existing formal
developments with cardinality theorems for those structures. It
provides twelve bijections from the various structures to different
equivalence classes on finite functions, and hence, proves cardinality
formulae for these equivalence classes on finite functions.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Twelvefold_Way</h3>
<ul>
<li><a href="../theories/twelvefold_way/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Core">Twelvefold_Way_Core</a></li>
<li><a href="../theories/twelvefold_way/#Equiv_Relations_on_Functions">Equiv_Relations_on_Functions</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry1">Twelvefold_Way_Entry1</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry2">Twelvefold_Way_Entry2</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry4">Twelvefold_Way_Entry4</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry5">Twelvefold_Way_Entry5</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry6">Twelvefold_Way_Entry6</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry7">Twelvefold_Way_Entry7</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry8">Twelvefold_Way_Entry8</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry9">Twelvefold_Way_Entry9</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry3">Twelvefold_Way_Entry3</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry10">Twelvefold_Way_Entry10</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry11">Twelvefold_Way_Entry11</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way_Entry12">Twelvefold_Way_Entry12</a></li>
<li><a href="../theories/twelvefold_way/#Card_Bijections">Card_Bijections</a></li>
<li><a href="../theories/twelvefold_way/#Card_Bijections_Direct">Card_Bijections_Direct</a></li>
<li><a href="../theories/twelvefold_way/#Twelvefold_Way">Twelvefold_Way</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bell_Numbers_Spivey.html">Spivey&rsquo;s Generalized Recurrence for Bell Numbers</a></li><li><a href="../entries/Card_Multisets.html">Cardinality of Multisets</a></li><li><a href="../entries/Card_Number_Partitions.html">Cardinality of Number Partitions</a></li><li><a href="../entries/Card_Partitions.html">Cardinality of Set Partitions</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">Twelvefold_Way-AFP</p><pre id="copy-text">@article{Twelvefold_Way-AFP,
author = {Lukas Bulwahn},
title = {The Twelvefold Way},
journal = {Archive of Formal Proofs},
month = {December},
year = {2016},
note = {\url{https://isa-afp.org/entries/Twelvefold_Way.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Tycon.html b/web/entries/Tycon.html
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<h1 >
<span class='first'>T</span>ype <span class='first'>C</span>onstructor <span class='first'>C</span>lasses and <span class='first'>M</span>onad <span class='first'>T</span>ransformers</h1>
<div>
<p><a href="../authors/huffman">Brian Huffman</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJodWZmbWFuIl19">📧</a>
</p>
<p class="date">June 26, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">These theories contain a formalization of first class type constructors
and axiomatic constructor classes for HOLCF. This work is described
in detail in the ICFP 2012 paper <i>Formal Verification of Monad
Transformers</i> by the author. The formalization is a revised and
updated version of earlier joint work with Matthews and White.
<P>
Based on the hierarchy of type classes in Haskell, we define classes
for functors, monads, monad-plus, etc. Each one includes all the
standard laws as axioms. We also provide a new user command,
tycondef, for defining new type constructors in HOLCF. Using tycondef,
we instantiate the type class hierarchy with various monads and monad
transformers.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session Tycon</h3>
<ul>
<li><a href="../theories/tycon/#TypeApp">TypeApp</a></li>
<li><a href="../theories/tycon/#Coerce">Coerce</a></li>
<li><a href="../theories/tycon/#Functor">Functor</a></li>
<li><a href="../theories/tycon/#Monad">Monad</a></li>
<li><a href="../theories/tycon/#Monad_Zero">Monad_Zero</a></li>
<li><a href="../theories/tycon/#Monad_Plus">Monad_Plus</a></li>
<li><a href="../theories/tycon/#Monad_Zero_Plus">Monad_Zero_Plus</a></li>
<li><a href="../theories/tycon/#Lazy_List_Monad">Lazy_List_Monad</a></li>
<li><a href="../theories/tycon/#Maybe_Monad">Maybe_Monad</a></li>
<li><a href="../theories/tycon/#Error_Monad">Error_Monad</a></li>
<li><a href="../theories/tycon/#Writer_Monad">Writer_Monad</a></li>
<li><a href="../theories/tycon/#Binary_Tree_Monad">Binary_Tree_Monad</a></li>
<li><a href="../theories/tycon/#Lift_Monad">Lift_Monad</a></li>
<li><a href="../theories/tycon/#Resumption_Transformer">Resumption_Transformer</a></li>
<li><a href="../theories/tycon/#State_Transformer">State_Transformer</a></li>
<li><a href="../theories/tycon/#Error_Transformer">Error_Transformer</a></li>
<li><a href="../theories/tycon/#Writer_Transformer">Writer_Transformer</a></li>
<li><a href="../theories/tycon/#Monad_Transformer">Monad_Transformer</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Tycon-AFP</p><pre id="copy-text">@article{Tycon-AFP,
author = {Brian Huffman},
title = {Type Constructor Classes and Monad Transformers},
journal = {Archive of Formal Proofs},
month = {June},
year = {2012},
note = {\url{https://isa-afp.org/entries/Tycon.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Types_Tableaus_and_Goedels_God.html b/web/entries/Types_Tableaus_and_Goedels_God.html
--- a/web/entries/Types_Tableaus_and_Goedels_God.html
+++ b/web/entries/Types_Tableaus_and_Goedels_God.html
@@ -1,189 +1,191 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Types, Tableaus and Gödel’s God in Isabelle/HOL - Archive of Formal Proofs</title><meta name="description" content="A computer-formalisation of the essential parts of Fitting&#39;s
textbook &#34;Types, Tableaus and Gödel&#39;s God&#34; in
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<h1 >
<span class='first'>T</span>ypes, <span class='first'>T</span>ableaus and <span class='first'>G</span>ödel’s <span class='first'>G</span>od in <span class='first'>I</span>sabelle/<span class='first'>H</span><span class='first'>O</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/fuenmayor">David Fuenmayor</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiZGF2ZnVlbm1heW9yIl19">📧</a> and <a href="../authors/benzmueller">Christoph Benzmüller</a> <a href="http://christoph-benzmueller.de">🌐</a>
</p>
<p class="date">May 1, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A computer-formalisation of the essential parts of Fitting's
textbook "Types, Tableaus and Gödel's God" in
Isabelle/HOL is presented. In particular, Fitting's (and
Anderson's) variant of the ontological argument is verified and
confirmed. This variant avoids the modal collapse, which has been
criticised as an undesirable side-effect of Kurt Gödel's (and
Dana Scott's) versions of the ontological argument.
Fitting's work is employing an intensional higher-order modal
logic, which we shallowly embed here in classical higher-order logic.
We then utilize the embedded logic for the formalisation of
Fitting's argument. (See also the earlier AFP entry ``Gödel's God in Isabelle/HOL''.)</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/philosophical-aspects">Logic/Philosophical aspects</a></li></ul>
<h3>Session Types_Tableaus_and_Goedels_God</h3>
<ul>
<li><a href="../theories/types_tableaus_and_goedels_god/#Relations">Relations</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#IHOML">IHOML</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#IHOML_Examples">IHOML_Examples</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#GoedelProof_P1">GoedelProof_P1</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#GoedelProof_P2">GoedelProof_P2</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#FittingProof">FittingProof</a></li>
<li><a href="../theories/types_tableaus_and_goedels_god/#AndersonProof">AndersonProof</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Types_Tableaus_and_Goedels_God-AFP</p><pre id="copy-text">@article{Types_Tableaus_and_Goedels_God-AFP,
author = {David Fuenmayor and Christoph Benzmüller},
title = {Types, Tableaus and Gödel’s God in Isabelle/HOL},
journal = {Archive of Formal Proofs},
month = {May},
year = {2017},
note = {\url{https://isa-afp.org/entries/Types_Tableaus_and_Goedels_God.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Types_Tableaus_and_Goedels_God-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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\ No newline at end of file
diff --git a/web/entries/Types_To_Sets_Extension.html b/web/entries/Types_To_Sets_Extension.html
--- a/web/entries/Types_To_Sets_Extension.html
+++ b/web/entries/Types_To_Sets_Extension.html
@@ -1,246 +1,248 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Extension of Types-To-Sets - Archive of Formal Proofs</title><meta name="description" content="In their article titled From Types to Sets by Local Type Definitions in Higher-Order Logic and published in the proceedings of the conference Interactive..."><meta property="og:title" content="Extension of Types-To-Sets" />
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<h1 >
<span class='first'>E</span>xtension of <span class='first'>T</span>ypes-to-<span class='first'>S</span>ets</h1>
<div>
<p><a href="../authors/milehins">Mihails Milehins</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWloYWlsc21pbGVoaW5zIl19">📧</a>
</p>
<p class="date">September 6, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In their article titled <i>From Types to Sets by Local Type
Definitions in Higher-Order Logic</i> and published in the
proceedings of the conference <i>Interactive Theorem
Proving</i> in 2016, Ondřej Kunčar and Andrei Popescu propose an
extension of the logic Isabelle/HOL and an associated algorithm for
the relativization of the <i>type-based theorems</i> to
more flexible <i>set-based theorems</i>, collectively
referred to as <i>Types-To-Sets</i>. One of the aims of
their work was to open an opportunity for the development of a
software tool for applied relativization in the implementation of the
logic Isabelle/HOL of the proof assistant Isabelle. In this article,
we provide a prototype of a software framework for the interactive
automated relativization of theorems in Isabelle/HOL, developed as an
extension of the proof language Isabelle/Isar. The software framework
incorporates the implementation of the proposed extension of the
logic, and builds upon some of the ideas for further work expressed in
the original article on Types-To-Sets by Ondřej Kunčar and Andrei
Popescu and the subsequent article <i>Smooth Manifolds and Types
to Sets for Linear Algebra in Isabelle/HOL</i> that was written
by Fabian Immler and Bohua Zhan and published in the proceedings of
the <i>International Conference on Certified Programs and
Proofs</i> in 2019.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>November 15, 2021</dt>
<dd>integration with SpecCheck (revision 61e152c118d4)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/tools">Tools</a></li></ul>
<h3>Session Types_To_Sets_Extension</h3>
<ul>
<li><a href="../theories/types_to_sets_extension/#ETTS_Tools">ETTS_Tools</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS">ETTS</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Auxiliary">ETTS_Auxiliary</a></li>
<li><a href="../theories/types_to_sets_extension/#Manual_Prerequisites">Manual_Prerequisites</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Tests">ETTS_Tests</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Introduction">ETTS_Introduction</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Theory">ETTS_Theory</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Syntax">ETTS_Syntax</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_Examples">ETTS_Examples</a></li>
<li><a href="../theories/types_to_sets_extension/#ETTS_CR">ETTS_CR</a></li>
<li><a href="../theories/types_to_sets_extension/#Introduction">Introduction</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Introduction">SML_Introduction</a></li>
<li><a href="../theories/types_to_sets_extension/#Set_Ext">Set_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#Lifting_Set_Ext">Lifting_Set_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#Product_Type_Ext">Product_Type_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#Transfer_Ext">Transfer_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Relations">SML_Relations</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Simple_Orders">SML_Simple_Orders</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Semigroups">SML_Semigroups</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Monoids">SML_Monoids</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Groups">SML_Groups</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Semirings">SML_Semirings</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Rings">SML_Rings</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Semilattices">SML_Semilattices</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Lattices">SML_Lattices</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Complete_Lattices">SML_Complete_Lattices</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Linorders">SML_Linorders</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Topological_Space">SML_Topological_Space</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Topological_Space_Countability">SML_Topological_Space_Countability</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Ordered_Topological_Spaces">SML_Ordered_Topological_Spaces</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Product_Topology">SML_Product_Topology</a></li>
<li><a href="../theories/types_to_sets_extension/#SML_Conclusions">SML_Conclusions</a></li>
<li><a href="../theories/types_to_sets_extension/#VS_Prerequisites">VS_Prerequisites</a></li>
<li><a href="../theories/types_to_sets_extension/#VS_Groups">VS_Groups</a></li>
<li><a href="../theories/types_to_sets_extension/#VS_Modules">VS_Modules</a></li>
<li><a href="../theories/types_to_sets_extension/#VS_Vector_Spaces">VS_Vector_Spaces</a></li>
<li><a href="../theories/types_to_sets_extension/#VS_Conclusions">VS_Conclusions</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Introduction">FNDS_Introduction</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Set_Ext">FNDS_Set_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Definite_Description">FNDS_Definite_Description</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Auxiliary">FNDS_Auxiliary</a></li>
<li><a href="../theories/types_to_sets_extension/#Type_Simple_Orders">Type_Simple_Orders</a></li>
<li><a href="../theories/types_to_sets_extension/#Set_Simple_Orders">Set_Simple_Orders</a></li>
<li><a href="../theories/types_to_sets_extension/#Type_Semigroups">Type_Semigroups</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Lifting_Set_Ext">FNDS_Lifting_Set_Ext</a></li>
<li><a href="../theories/types_to_sets_extension/#Set_Semigroups">Set_Semigroups</a></li>
<li><a href="../theories/types_to_sets_extension/#FNDS_Conclusions">FNDS_Conclusions</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Conditional_Transfer_Rule.html">Conditional Transfer Rule</a></li><li><a href="../entries/SpecCheck.html">SpecCheck - Specification-Based Testing for Isabelle/ML</a></li></ul>
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<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Smith_Normal_Form.html">A verified algorithm for computing the Smith normal form of a matrix</a></li>
<li><a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a></li>
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<p style="display:none;" id="bibtex-filename">Types_To_Sets_Extension-AFP</p><pre id="copy-text">@article{Types_To_Sets_Extension-AFP,
author = {Mihails Milehins},
title = {Extension of Types-To-Sets},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Types_To_Sets_Extension.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Types_To_Sets_Extension-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Types_To_Sets_Extension-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Types_To_Sets_Extension-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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diff --git a/web/entries/UPF.html b/web/entries/UPF.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Unified Policy Framework (UPF) - Archive of Formal Proofs</title><meta name="description" content="We present the Unified Policy Framework (UPF), a generic framework
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<h1 >
<span class='first'>T</span>he <span class='first'>U</span>nified <span class='first'>P</span>olicy <span class='first'>F</span>ramework (<span class='first'>U</span><span class='first'>P</span><span class='first'>F</span>)</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a class="obfuscated" data="eyJob3N0IjpbIjB4NWYiLCJvcmciXSwidXNlciI6WyJhZGJydWNrZXIiXX0=">📧</a>, <a href="../authors/bruegger">Lukas Brügger</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibHVrYXMiLCJhIiwiYnJ1ZWdnZXIiXX0=">📧</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">November 28, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present the Unified Policy Framework (UPF), a generic framework
for modelling security (access-control) policies. UPF emphasizes
the view that a policy is a policy decision function that grants or
denies access to resources, permissions, etc. In other words,
instead of modelling the relations of permitted or prohibited
requests directly, we model the concrete function that implements
the policy decision point in a system. In more detail, UPF is
based on the following four principles: 1) Functional representation
of policies, 2) No conflicts are possible, 3) Three-valued decision
type (allow, deny, undefined), 4) Output type not containing the
decision only.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session UPF</h3>
<ul>
<li><a href="../theories/upf/#Monads">Monads</a></li>
<li><a href="../theories/upf/#UPFCore">UPFCore</a></li>
<li><a href="../theories/upf/#ElementaryPolicies">ElementaryPolicies</a></li>
<li><a href="../theories/upf/#SeqComposition">SeqComposition</a></li>
<li><a href="../theories/upf/#ParallelComposition">ParallelComposition</a></li>
<li><a href="../theories/upf/#Normalisation">Normalisation</a></li>
<li><a href="../theories/upf/#NormalisationTestSpecification">NormalisationTestSpecification</a></li>
<li><a href="../theories/upf/#Analysis">Analysis</a></li>
<li><a href="../theories/upf/#UPF">UPF</a></li>
<li><a href="../theories/upf/#Service">Service</a></li>
<li><a href="../theories/upf/#ServiceExample">ServiceExample</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/UPF_Firewall.html">Formal Network Models and Their Application to Firewall Policies</a></li></ul>
</div>
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<p style="display:none;" id="bibtex-filename">UPF-AFP</p><pre id="copy-text">@article{UPF-AFP,
author = {Achim D. Brucker and Lukas Brügger and Burkhart Wolff},
title = {The Unified Policy Framework (UPF)},
journal = {Archive of Formal Proofs},
month = {November},
year = {2014},
note = {\url{https://isa-afp.org/entries/UPF.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-UPF-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-UPF-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-UPF-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-UPF-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-UPF-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-UPF-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-UPF-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
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<a href="https://www.isa-afp.org/release/afp-UPF-2015-01-28.tar.gz">Jan 28, 2015</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF-2014-11-30.tar.gz">Nov 30, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>F</span>ormal <span class='first'>N</span>etwork <span class='first'>M</span>odels and <span class='first'>T</span>heir <span class='first'>A</span>pplication to <span class='first'>F</span>irewall <span class='first'>P</span>olicies</h1>
<div>
<p><a href="../authors/brucker">Achim D. Brucker</a> <a href="https://www.brucker.ch/">🌐</a>, <a href="../authors/bruegger">Lukas Brügger</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a href="https://www.lri.fr/~wolff/">🌐</a>
</p>
<p class="date">January 8, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present a formal model of network protocols and their application
to modeling firewall policies. The formalization is based on the
Unified Policy Framework (UPF). The formalization was originally
developed with for generating test cases for testing the security
configuration actual firewall and router (middle-boxes) using
HOL-TestGen. Our work focuses on modeling application level protocols
on top of tcp/ip.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/networks">Computer science/Networks</a></li></ul>
<h3>Session UPF_Firewall</h3>
<ul>
<li><a href="../theories/upf_firewall/#NetworkCore">NetworkCore</a></li>
<li><a href="../theories/upf_firewall/#DatatypeAddress">DatatypeAddress</a></li>
<li><a href="../theories/upf_firewall/#DatatypePort">DatatypePort</a></li>
<li><a href="../theories/upf_firewall/#IntegerAddress">IntegerAddress</a></li>
<li><a href="../theories/upf_firewall/#IntegerPort">IntegerPort</a></li>
<li><a href="../theories/upf_firewall/#IntegerPort_TCPUDP">IntegerPort_TCPUDP</a></li>
<li><a href="../theories/upf_firewall/#IPv4">IPv4</a></li>
<li><a href="../theories/upf_firewall/#IPv4_TCPUDP">IPv4_TCPUDP</a></li>
<li><a href="../theories/upf_firewall/#NetworkModels">NetworkModels</a></li>
<li><a href="../theories/upf_firewall/#PolicyCore">PolicyCore</a></li>
<li><a href="../theories/upf_firewall/#PolicyCombinators">PolicyCombinators</a></li>
<li><a href="../theories/upf_firewall/#PortCombinators">PortCombinators</a></li>
<li><a href="../theories/upf_firewall/#ProtocolPortCombinators">ProtocolPortCombinators</a></li>
<li><a href="../theories/upf_firewall/#Ports">Ports</a></li>
<li><a href="../theories/upf_firewall/#PacketFilter">PacketFilter</a></li>
<li><a href="../theories/upf_firewall/#NAT">NAT</a></li>
<li><a href="../theories/upf_firewall/#FWNormalisationCore">FWNormalisationCore</a></li>
<li><a href="../theories/upf_firewall/#NormalisationGenericProofs">NormalisationGenericProofs</a></li>
<li><a href="../theories/upf_firewall/#NormalisationIntegerPortProof">NormalisationIntegerPortProof</a></li>
<li><a href="../theories/upf_firewall/#NormalisationIPPProofs">NormalisationIPPProofs</a></li>
<li><a href="../theories/upf_firewall/#ElementaryRules">ElementaryRules</a></li>
<li><a href="../theories/upf_firewall/#FWNormalisation">FWNormalisation</a></li>
<li><a href="../theories/upf_firewall/#LTL_alike">LTL_alike</a></li>
<li><a href="../theories/upf_firewall/#StatefulCore">StatefulCore</a></li>
<li><a href="../theories/upf_firewall/#FTP">FTP</a></li>
<li><a href="../theories/upf_firewall/#FTP_WithPolicy">FTP_WithPolicy</a></li>
<li><a href="../theories/upf_firewall/#VOIP">VOIP</a></li>
<li><a href="../theories/upf_firewall/#FTPVOIP">FTPVOIP</a></li>
<li><a href="../theories/upf_firewall/#StatefulFW">StatefulFW</a></li>
<li><a href="../theories/upf_firewall/#UPF-Firewall">UPF-Firewall</a></li>
<li><a href="../theories/upf_firewall/#DMZDatatype">DMZDatatype</a></li>
<li><a href="../theories/upf_firewall/#DMZInteger">DMZInteger</a></li>
<li><a href="../theories/upf_firewall/#DMZ">DMZ</a></li>
<li><a href="../theories/upf_firewall/#Voice_over_IP">Voice_over_IP</a></li>
<li><a href="../theories/upf_firewall/#Transformation01">Transformation01</a></li>
<li><a href="../theories/upf_firewall/#Transformation02">Transformation02</a></li>
<li><a href="../theories/upf_firewall/#Transformation">Transformation</a></li>
<li><a href="../theories/upf_firewall/#NAT-FW">NAT-FW</a></li>
<li><a href="../theories/upf_firewall/#PersonalFirewallInt">PersonalFirewallInt</a></li>
<li><a href="../theories/upf_firewall/#PersonalFirewallIpv4">PersonalFirewallIpv4</a></li>
<li><a href="../theories/upf_firewall/#PersonalFirewallDatatype">PersonalFirewallDatatype</a></li>
<li><a href="../theories/upf_firewall/#PersonalFirewall">PersonalFirewall</a></li>
<li><a href="../theories/upf_firewall/#Examples">Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/UPF.html">The Unified Policy Framework (UPF)</a></li></ul>
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<h4>PDFs</h4>
<a href="https://www.isa-afp.org/browser_info/current/AFP/UPF_Firewall/outline.pdf">Proof
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<a href="https://www.isa-afp.org/browser_info/current/AFP/UPF_Firewall/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">UPF_Firewall-AFP</p><pre id="copy-text">@article{UPF_Firewall-AFP,
author = {Achim D. Brucker and Lukas Brügger and Burkhart Wolff},
title = {Formal Network Models and Their Application to Firewall Policies},
journal = {Archive of Formal Proofs},
month = {January},
year = {2017},
note = {\url{https://isa-afp.org/entries/UPF_Firewall.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a class="close" href="#">&times;</a>
<a href="https://www.isa-afp.org/release//afp-UPF_Firewall-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-UPF_Firewall-2017-01-11.tar.gz">Jan 11, 2017</a>: Isabelle2016-1
</li></ul>
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<h1 >
<span class='first'>I</span>sabelle/<span class='first'>U</span><span class='first'>T</span><span class='first'>P</span>: <span class='first'>M</span>echanised <span class='first'>T</span>heory <span class='first'>E</span>ngineering for <span class='first'>U</span>nifying <span class='first'>T</span>heories of <span class='first'>P</span>rogramming</h1>
<div>
<p><a href="../authors/fosters">Simon Foster</a> <a href="https://www-users.cs.york.ac.uk/~simonf/">🌐</a>, <a href="../authors/zeyda">Frank Zeyda</a>, <a href="../authors/nemouchi">Yakoub Nemouchi</a> <a class="obfuscated" data="eyJob3N0IjpbInlvcmsiLCJhYyIsInVrIl0sInVzZXIiOlsieWFrb3ViIiwibmVtb3VjaGkiXX0=">📧</a>, <a href="../authors/ribeiro">Pedro Ribeiro</a> and <a href="../authors/wolff">Burkhart Wolff</a> <a class="obfuscated" data="eyJob3N0IjpbImxyaSIsImZyIl0sInVzZXIiOlsiYnVya2hhcnQiLCJ3b2xmZiJdfQ==">📧</a>
</p>
<p class="date">February 1, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Isabelle/UTP is a mechanised theory engineering toolkit based on Hoare
and He’s Unifying Theories of Programming (UTP). UTP enables the
creation of denotational, algebraic, and operational semantics for
different programming languages using an alphabetised relational
calculus. We provide a semantic embedding of the alphabetised
relational calculus in Isabelle/HOL, including new type definitions,
relational constructors, automated proof tactics, and accompanying
algebraic laws. Isabelle/UTP can be used to both capture laws of
programming for different languages, and put these fundamental
theorems to work in the creation of associated verification tools,
using calculi like Hoare logics. This document describes the
relational core of the UTP in Isabelle/HOL.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li></ul>
<h3>Session UTP-Toolkit</h3>
<ul>
<li><a href="../theories/utp-toolkit/#List_Extra">List_Extra</a></li>
<li><a href="../theories/utp-toolkit/#Sequence">Sequence</a></li>
<li><a href="../theories/utp-toolkit/#FSet_Extra">FSet_Extra</a></li>
<li><a href="../theories/utp-toolkit/#Countable_Set_Extra">Countable_Set_Extra</a></li>
<li><a href="../theories/utp-toolkit/#Map_Extra">Map_Extra</a></li>
<li><a href="../theories/utp-toolkit/#List_Lexord_Alt">List_Lexord_Alt</a></li>
<li><a href="../theories/utp-toolkit/#Partial_Fun">Partial_Fun</a></li>
<li><a href="../theories/utp-toolkit/#Finite_Fun">Finite_Fun</a></li>
<li><a href="../theories/utp-toolkit/#Infinity">Infinity</a></li>
<li><a href="../theories/utp-toolkit/#Positive">Positive</a></li>
<li><a href="../theories/utp-toolkit/#Total_Recall">Total_Recall</a></li>
<li><a href="../theories/utp-toolkit/#utp_toolkit">utp_toolkit</a></li></ul>
<h3>Session UTP</h3>
<ul>
<li><a href="../theories/utp/#utp_parser_utils">utp_parser_utils</a></li>
<li><a href="../theories/utp/#utp_var">utp_var</a></li>
<li><a href="../theories/utp/#utp_expr">utp_expr</a></li>
<li><a href="../theories/utp/#utp_expr_insts">utp_expr_insts</a></li>
<li><a href="../theories/utp/#utp_expr_funcs">utp_expr_funcs</a></li>
<li><a href="../theories/utp/#utp_unrest">utp_unrest</a></li>
<li><a href="../theories/utp/#utp_usedby">utp_usedby</a></li>
<li><a href="../theories/utp/#utp_subst">utp_subst</a></li>
<li><a href="../theories/utp/#utp_tactics">utp_tactics</a></li>
<li><a href="../theories/utp/#utp_meta_subst">utp_meta_subst</a></li>
<li><a href="../theories/utp/#utp_pred">utp_pred</a></li>
<li><a href="../theories/utp/#utp_alphabet">utp_alphabet</a></li>
<li><a href="../theories/utp/#utp_lift">utp_lift</a></li>
<li><a href="../theories/utp/#utp_pred_laws">utp_pred_laws</a></li>
<li><a href="../theories/utp/#utp_healthy">utp_healthy</a></li>
<li><a href="../theories/utp/#utp_rel">utp_rel</a></li>
<li><a href="../theories/utp/#utp_recursion">utp_recursion</a></li>
<li><a href="../theories/utp/#utp_sequent">utp_sequent</a></li>
<li><a href="../theories/utp/#utp_rel_laws">utp_rel_laws</a></li>
<li><a href="../theories/utp/#utp_theory">utp_theory</a></li>
<li><a href="../theories/utp/#utp_hoare">utp_hoare</a></li>
<li><a href="../theories/utp/#utp_wp">utp_wp</a></li>
<li><a href="../theories/utp/#utp_dynlog">utp_dynlog</a></li>
<li><a href="../theories/utp/#utp_state_parser">utp_state_parser</a></li>
<li><a href="../theories/utp/#utp_rel_opsem">utp_rel_opsem</a></li>
<li><a href="../theories/utp/#utp_sym_eval">utp_sym_eval</a></li>
<li><a href="../theories/utp/#utp_sp">utp_sp</a></li>
<li><a href="../theories/utp/#utp_concurrency">utp_concurrency</a></li>
<li><a href="../theories/utp/#utp">utp</a></li>
<li><a href="../theories/utp/#utp_expr_ovld">utp_expr_ovld</a></li>
<li><a href="../theories/utp/#utp_full">utp_full</a></li>
<li><a href="../theories/utp/#utp_easy_parser">utp_easy_parser</a></li>
<li><a href="../theories/utp/#sum_list">sum_list</a></li>
<li><a href="../theories/utp/#utp_simple_time">utp_simple_time</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Optics.html">Optics</a></li></ul>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/UTP/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">UTP-AFP</p><pre id="copy-text">@article{UTP-AFP,
author = {Simon Foster and Frank Zeyda and Yakoub Nemouchi and Pedro Ribeiro and Burkhart Wolff},
title = {Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/UTP.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>U</span>ndirected <span class='first'>G</span>raph <span class='first'>T</span>heory</h1>
<div>
<p><a href="../authors/edmonds">Chelsea Edmonds</a> <a href="https://www.cst.cam.ac.uk/people/cle47">🌐</a>
</p>
<p class="date">September 29, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry presents a general library for undirected graph theory -
enabling reasoning on simple graphs and undirected graphs with loops.
It primarily is inspired by Noschinski's basic ugraph definition
in the <a href="../entries/Girth_Chromatic.html">Girth Chromatic Entry</a>,
however generalises it in a number of
ways and significantly expands on the range of basic graph theory
definitions formalised. Notably, this library removes the constraint
of vertices being a type synonym with the natural numbers which causes
issues in more complex mathematical reasoning using graphs, such as
the Balog Szemeredi Gowers theorem which this library is used for.
Secondly this library also presents a locale-centric approach,
enabling more concise, flexible, and reusable modelling of different
types of graphs. Using this approach enables easy links to be made
with more expansive formalisations of other combinatorial structures,
such as incidence systems, as well as various types of formal
representations of graphs. Further inspiration is also taken from
Noschinski's Directed Graph library for some proofs and
definitions on walks, paths and cycles, however these are much
simplified using the set based representation of graphs, and also
extended on in this formalisation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/graph-theory">Mathematics/Graph theory</a></li></ul>
<h3>Session Undirected_Graph_Theory</h3>
<ul>
<li><a href="../theories/undirected_graph_theory/#Undirected_Graph_Basics">Undirected_Graph_Basics</a></li>
<li><a href="../theories/undirected_graph_theory/#Undirected_Graph_Walks">Undirected_Graph_Walks</a></li>
<li><a href="../theories/undirected_graph_theory/#Connectivity">Connectivity</a></li>
<li><a href="../theories/undirected_graph_theory/#Girth_Independence">Girth_Independence</a></li>
<li><a href="../theories/undirected_graph_theory/#Graph_Triangles">Graph_Triangles</a></li>
<li><a href="../theories/undirected_graph_theory/#Bipartite_Graphs">Bipartite_Graphs</a></li>
<li><a href="../theories/undirected_graph_theory/#Graph_Theory_Relations">Graph_Theory_Relations</a></li>
<li><a href="../theories/undirected_graph_theory/#Undirected_Graphs_Root">Undirected_Graphs_Root</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Design_Theory.html">Combinatorial Design Theory</a></li><li><a href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Undirected_Graph_Theory-AFP</p><pre id="copy-text">@article{Undirected_Graph_Theory-AFP,
author = {Chelsea Edmonds},
title = {Undirected Graph Theory},
journal = {Archive of Formal Proofs},
month = {September},
year = {2022},
note = {\url{https://isa-afp.org/entries/Undirected_Graph_Theory.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Undirected_Graph_Theory-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Undirected_Graph_Theory-2022-10-01.tar.gz">Oct 1, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Universal_Hash_Families.html b/web/entries/Universal_Hash_Families.html
--- a/web/entries/Universal_Hash_Families.html
+++ b/web/entries/Universal_Hash_Families.html
@@ -1,187 +1,192 @@
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<h1 >
<span class='first'>U</span>niversal <span class='first'>H</span>ash <span class='first'>F</span>amilies</h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a>
</p>
<p class="date">February 20, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A <i>k</i>-universal hash family is a probability
space of functions, which have uniform distribution and form
<i>k</i>-wise independent random variables. They can often be used
in place of classic (or cryptographic) hash functions and allow the
rigorous analysis of the performance of randomized algorithms and
data structures that rely on hash functions. In 1981
<a href="https://doi.org/10.1016/0022-0000(81)90033-7">Wegman and Carter</a>
introduced a generic construction for such families with arbitrary
<i>k</i> using polynomials over a finite field. This entry
contains a formalization of them and establishes the property of
<i>k</i>-universality. To be useful the formalization also provides
an explicit construction of finite fields using the factor ring of
integers modulo a prime. Additionally, some generic results about
independent families are shown that might be of independent interest.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session Universal_Hash_Families</h3>
<ul>
<li><a href="../theories/universal_hash_families/#Definitions">Definitions</a></li>
<li><a href="../theories/universal_hash_families/#Preliminary_Results">Preliminary_Results</a></li>
<li><a href="../theories/universal_hash_families/#Carter_Wegman_Hash_Family">Carter_Wegman_Hash_Family</a></li>
<li><a href="../theories/universal_hash_families/#Field">Field</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Finite_Fields.html">Finite Fields</a></li><li><a href="../entries/Interpolation_Polynomials_HOL_Algebra.html">Interpolation Polynomials (in HOL-Algebra)</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Lehmer.html">Lehmer&rsquo;s Theorem</a></li>
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<p style="display:none;" id="bibtex-filename">Universal_Hash_Families-AFP</p><pre id="copy-text">@article{Universal_Hash_Families-AFP,
author = {Emin Karayel},
title = {Universal Hash Families},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/Universal_Hash_Families.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
+ <ul><li>
+ <a href="https://www.isa-afp.org/release/afp-Universal_Hash_Families-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Universal_Hash_Families-2022-02-21.tar.gz">Feb 21, 2022</a>: Isabelle2021-1
+ </li></ul>
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diff --git a/web/entries/Universal_Turing_Machine.html b/web/entries/Universal_Turing_Machine.html
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@@ -1,228 +1,230 @@
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<h1 >
<span class='first'>U</span>niversal <span class='first'>T</span>uring <span class='first'>M</span>achine</h1>
<div>
<p><a href="../authors/xu">Jian Xu</a>, <a href="../authors/zhangx">Xingyuan Zhang</a>, <a href="../authors/urban">Christian Urban</a> <a href="https://nms.kcl.ac.uk/christian.urban/">🌐</a>, <a href="../authors/joosten">Sebastiaan J. C. Joosten</a> <a href="https://sjcjoosten.nl/">🌐</a> and <a href="../authors/regensburger">Franz Regensburger</a> <a href="https://www.thi.de/suche/mitarbeiter/prof-dr-rer-nat-franz-regensburger">🌐</a>
</p>
<p class="date">February 8, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry formalises results from computability theory,
for example recursive functions,
undecidability of the halting problem, the existence of a
universal Turing machine and so on. This formalisation is the AFP entry
corresponding to the paper Mechanising Turing Machines and Computability Theory
in Isabelle/HOL from ITP 2013. The main book used for this formalisation is
by Boolos, Burgess, and Jeffrey on <i>Computability and Logic</i>.</p>
<p>Joosten contributed by making the files ready for the
AFP in 2019. His need for a formalisation of Turing Machines arose from
realising that the current formalisation of saturation graphs
(also in the AFP) was missing a key undecidability result
present in his paper on <i>Finding models through graph saturation</i>.</p>
<p>Regensburger contributed in 2022 by adding definitions for
concepts like Turing Decidability, Turing Computability and Turing Reducibility
for problem reduction. He also enhanced the result about the
undecidability of the General Halting Problem given in the original AFP entry
by first proving the undecidability of the Special Halting Problem and then
proving its reducibility to the general problem. The original version of this
AFP entry did only prove a weak form of the undecidability theorem.
The main motivation behind this contribution is to make the AFP entry
accessible for bachelor and master students.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>September 7, 2022</dt>
<dd>Franz Regensburger added substantial material and made some modifications.<br>
</dd><dt>January 16, 2019</dt>
<dd>Sebastiaan Joosten made the code ready for the AFP.<br>
</dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/logic/computability">Logic/Computability</a></li><li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li></ul>
<h3>Session Universal_Turing_Machine</h3>
<ul>
<li><a href="../theories/universal_turing_machine/#Turing">Turing</a></li>
<li><a href="../theories/universal_turing_machine/#Turing_aux">Turing_aux</a></li>
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<li><a href="../theories/universal_turing_machine/#TuringDecidable">TuringDecidable</a></li>
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<li><a href="../theories/universal_turing_machine/#SimpleGoedelEncoding">SimpleGoedelEncoding</a></li>
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<li><a href="../theories/universal_turing_machine/#DitherTM">DitherTM</a></li>
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<li><a href="../theories/universal_turing_machine/#TuringUnComputable_H2">TuringUnComputable_H2</a></li>
<li><a href="../theories/universal_turing_machine/#TuringUnComputable_H2_original">TuringUnComputable_H2_original</a></li>
<li><a href="../theories/universal_turing_machine/#Abacus_Mopup">Abacus_Mopup</a></li>
<li><a href="../theories/universal_turing_machine/#Abacus">Abacus</a></li>
<li><a href="../theories/universal_turing_machine/#Abacus_alt_Compile">Abacus_alt_Compile</a></li>
<li><a href="../theories/universal_turing_machine/#Abacus_Hoare">Abacus_Hoare</a></li>
<li><a href="../theories/universal_turing_machine/#Rec_Def">Rec_Def</a></li>
<li><a href="../theories/universal_turing_machine/#Rec_Ex">Rec_Ex</a></li>
<li><a href="../theories/universal_turing_machine/#Recursive">Recursive</a></li>
<li><a href="../theories/universal_turing_machine/#Recs_alt_Def">Recs_alt_Def</a></li>
<li><a href="../theories/universal_turing_machine/#Recs_alt_Ex">Recs_alt_Ex</a></li>
<li><a href="../theories/universal_turing_machine/#UF">UF</a></li>
<li><a href="../theories/universal_turing_machine/#UTM">UTM</a></li>
<li><a href="../theories/universal_turing_machine/#GeneratedCode">GeneratedCode</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Universal_Turing_Machine-AFP</p><pre id="copy-text">@article{Universal_Turing_Machine-AFP,
author = {Jian Xu and Xingyuan Zhang and Christian Urban and Sebastiaan J. C. Joosten and Franz Regensburger},
title = {Universal Turing Machine},
journal = {Archive of Formal Proofs},
month = {February},
year = {2019},
note = {\url{https://isa-afp.org/entries/Universal_Turing_Machine.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/UpDown_Scheme.html b/web/entries/UpDown_Scheme.html
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<h1 >
<span class='first'>V</span>erification of the <span class='first'>U</span>p<span class='first'>D</span>own <span class='first'>S</span>cheme</h1>
<div>
<p><a href="../authors/hoelzl">Johannes Hölzl</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJob2VsemwiXX0=">📧</a>
</p>
<p class="date">January 28, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The UpDown scheme is a recursive scheme used to compute the stiffness matrix
on a special form of sparse grids. Usually, when discretizing a Euclidean
space of dimension d we need O(n^d) points, for n points along each dimension.
Sparse grids are a hierarchical representation where the number of points is
reduced to O(n * log(n)^d). One disadvantage of such sparse grids is that the
algorithm now operate recursively in the dimensions and levels of the sparse grid.
<p>
The UpDown scheme allows us to compute the stiffness matrix on such a sparse
grid. The stiffness matrix represents the influence of each representation
function on the L^2 scalar product. For a detailed description see
Dirk Pflüger's PhD thesis. This formalization was developed as an
interdisciplinary project (IDP) at the Technische Universität München.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session UpDown_Scheme</h3>
<ul>
<li><a href="../theories/updown_scheme/#Grid_Point">Grid_Point</a></li>
<li><a href="../theories/updown_scheme/#Grid">Grid</a></li>
<li><a href="../theories/updown_scheme/#Triangular_Function">Triangular_Function</a></li>
<li><a href="../theories/updown_scheme/#UpDown_Scheme">UpDown_Scheme</a></li>
<li><a href="../theories/updown_scheme/#Up">Up</a></li>
<li><a href="../theories/updown_scheme/#Down">Down</a></li>
<li><a href="../theories/updown_scheme/#Up_Down">Up_Down</a></li>
<li><a href="../theories/updown_scheme/#Imperative">Imperative</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></li></ul>
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<li><a href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></li>
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<p style="display:none;" id="bibtex-filename">UpDown_Scheme-AFP</p><pre id="copy-text">@article{UpDown_Scheme-AFP,
author = {Johannes Hölzl},
title = {Verification of the UpDown Scheme},
journal = {Archive of Formal Proofs},
month = {January},
year = {2015},
note = {\url{https://isa-afp.org/entries/UpDown_Scheme.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
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diff --git a/web/entries/VYDRA_MDL.html b/web/entries/VYDRA_MDL.html
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<h1 >
<span class='first'>M</span>ulti-<span class='first'>H</span>ead <span class='first'>M</span>onitoring of <span class='first'>M</span>etric <span class='first'>D</span>ynamic <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/raszyk">Martin Raszyk</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbIm1hcnRpbiIsInJhc3p5ayJdfQ==">📧</a>
</p>
<p class="date">February 13, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>Runtime monitoring (or runtime verification) is an approach to
checking compliance of a system's execution with a specification
(e.g., a temporal formula). The system's execution is logged into a
<i>trace</i>&mdash;a sequence of time-points, each consisting of a
time-stamp and observed events. A <i>monitor</i> is an algorithm that
produces <i>verdicts</i> on the satisfaction of a temporal formula on
a trace.</p>
<p>We formalize the time-stamps as an abstract algebraic structure
satisfying certain assumptions. Instances of this structure include
natural numbers, real numbers, and lexicographic combinations of
them. We also include the formalization of a conversion from the
abstract time domain introduced by Koymans (1990) to our
time-stamps.</p>
<p>We formalize a monitoring algorithm for metric dynamic logic, an
extension of metric temporal logic with regular expressions. The
monitor computes whether a given formula is satisfied at every
position in an input trace of time-stamped events. Our monitor
follows the multi-head paradigm: it reads the input simultaneously at
multiple positions and moves its reading heads asynchronously. This
mode of operation results in unprecedented time and space complexity
guarantees for metric dynamic logic: The monitor's amortized time
complexity to process a time-point and the monitor's space complexity
neither depends on the event-rate, i.e., the number of events within
a fixed time-unit, nor on the numeric constants occurring in the
quantitative temporal constraints in the given formula.</p>
<p>The multi-head monitoring algorithm for metric dynamic logic is
reported in our paper ``Multi-Head Monitoring of Metric Dynamic
Logic'' published at ATVA 2020. We have also formalized unpublished
specialized algorithms for the temporal operators of metric temporal
logic.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>February 23, 2022</dt>
<dd>added conversion from the abstract time
domain by Koymans (1990) to our time domain; refactored assumptions
on time domain (revision c9f94b0ae10e)<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session VYDRA_MDL</h3>
<ul>
<li><a href="../theories/vydra_mdl/#Timestamp">Timestamp</a></li>
<li><a href="../theories/vydra_mdl/#Interval">Interval</a></li>
<li><a href="../theories/vydra_mdl/#Trace">Trace</a></li>
<li><a href="../theories/vydra_mdl/#MDL">MDL</a></li>
<li><a href="../theories/vydra_mdl/#Metric_Point_Structure">Metric_Point_Structure</a></li>
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<li><a href="../theories/vydra_mdl/#Monitor">Monitor</a></li>
<li><a href="../theories/vydra_mdl/#Preliminaries">Preliminaries</a></li>
<li><a href="../theories/vydra_mdl/#Monitor_Code">Monitor_Code</a></li>
<li><a href="../theories/vydra_mdl/#Timestamp_Lex">Timestamp_Lex</a></li>
<li><a href="../theories/vydra_mdl/#Timestamp_Prod">Timestamp_Prod</a></li></ul><div class="flex-wrap">
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<h3>Auto-related entries</h3>
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<li><a href="../entries/MFODL_Monitor_Optimized.html">Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</a></li>
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<p style="display:none;" id="bibtex-filename">VYDRA_MDL-AFP</p><pre id="copy-text">@article{VYDRA_MDL-AFP,
author = {Martin Raszyk},
title = {Multi-Head Monitoring of Metric Dynamic Logic},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/VYDRA_MDL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<h1 >
<span class='first'>F</span>undamental <span class='first'>P</span>roperties of <span class='first'>V</span>aluation <span class='first'>T</span>heory and <span class='first'>H</span>ensel's <span class='first'>L</span>emma</h1>
<div>
<p><a href="../authors/kobayashi">Hidetsune Kobayashi</a>
</p>
<p class="date">August 8, 2007</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Convergence with respect to a valuation is discussed as convergence of a Cauchy sequence. Cauchy sequences of polynomials are defined. They are used to formalize Hensel's lemma.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session Valuation</h3>
<ul>
<li><a href="../theories/valuation/#Valuation1">Valuation1</a></li>
<li><a href="../theories/valuation/#Valuation2">Valuation2</a></li>
<li><a href="../theories/valuation/#Valuation3">Valuation3</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Group-Ring-Module.html">Groups, Rings and Modules</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Valuation-AFP</p><pre id="copy-text">@article{Valuation-AFP,
author = {Hidetsune Kobayashi},
title = {Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma},
journal = {Archive of Formal Proofs},
month = {August},
year = {2007},
note = {\url{https://isa-afp.org/entries/Valuation.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Valuation-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Valuation-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Valuation-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
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<a href="https://www.isa-afp.org/release/afp-Valuation-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Valuation-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
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<a href="https://www.isa-afp.org/release/afp-Valuation-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-Valuation-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
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<a href="https://www.isa-afp.org/release/afp-Valuation-2009-04-30.tar.gz">Apr 30, 2009</a>: Isabelle2009
</li><li>
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diff --git a/web/entries/Van_Emde_Boas_Trees.html b/web/entries/Van_Emde_Boas_Trees.html
--- a/web/entries/Van_Emde_Boas_Trees.html
+++ b/web/entries/Van_Emde_Boas_Trees.html
@@ -1,232 +1,234 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>van Emde Boas Trees - Archive of Formal Proofs</title><meta name="description" content="The van Emde Boas tree or van Emde Boas priority queue is a data structure supporting membership test, insertion, predecessor and successor search, minimum..."><meta property="og:title" content="van Emde Boas Trees" />
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<h1 >
<span class='first'>V</span>an <span class='first'>E</span>mde <span class='first'>B</span>oas <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/ammer">Thomas Ammer</a> and <a href="../authors/lammich">Peter Lammich</a>
</p>
<p class="date">November 23, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The <em>van Emde Boas tree</em> or <em>van Emde Boas
priority queue</em> is a data structure supporting membership
test, insertion, predecessor and successor search, minimum and maximum
determination and deletion in <em>O(log log U)</em> time, where <em>U =
0,...,2<sup>n-1</sup></em> is the overall range to be
considered. <p/> The presented formalization follows Chapter 20
of the popular <em>Introduction to Algorithms (3rd
ed.)</em> by Cormen, Leiserson, Rivest and Stein (CLRS),
extending the list of formally verified CLRS algorithms. Our current
formalization is based on the first author's bachelor's
thesis. <p/> First, we prove correct a
<em>functional</em> implementation, w.r.t. an abstract
data type for sets. Apart from functional correctness, we show a
resource bound, and runtime bounds w.r.t. manually defined timing
functions for the operations. <p/> Next, we refine the
operations to Imperative HOL with time, and show correctness and
complexity. This yields a practically more efficient implementation,
and eliminates the manually defined timing functions from the trusted
base of the proof.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Van_Emde_Boas_Trees</h3>
<ul>
<li><a href="../theories/van_emde_boas_trees/#Heap_Time_Monad">Heap_Time_Monad</a></li>
<li><a href="../theories/van_emde_boas_trees/#Array_Time">Array_Time</a></li>
<li><a href="../theories/van_emde_boas_trees/#Heap">Heap</a></li>
<li><a href="../theories/van_emde_boas_trees/#Ref_Time">Ref_Time</a></li>
<li><a href="../theories/van_emde_boas_trees/#Imperative_HOL_Time">Imperative_HOL_Time</a></li>
<li><a href="../theories/van_emde_boas_trees/#Syntax_Match">Syntax_Match</a></li>
<li><a href="../theories/van_emde_boas_trees/#Assertions">Assertions</a></li>
<li><a href="../theories/van_emde_boas_trees/#Hoare_Triple">Hoare_Triple</a></li>
<li><a href="../theories/van_emde_boas_trees/#Refine_Imp_Hol">Refine_Imp_Hol</a></li>
<li><a href="../theories/van_emde_boas_trees/#Automation">Automation</a></li>
<li><a href="../theories/van_emde_boas_trees/#Sep_Main">Sep_Main</a></li>
<li><a href="../theories/van_emde_boas_trees/#Imperative_HOL_Add">Imperative_HOL_Add</a></li>
<li><a href="../theories/van_emde_boas_trees/#Time_Reasoning">Time_Reasoning</a></li>
<li><a href="../theories/van_emde_boas_trees/#Simple_TBOUND_Cond">Simple_TBOUND_Cond</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Example_Setup">VEBT_Example_Setup</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Definitions">VEBT_Definitions</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Member">VEBT_Member</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Insert">VEBT_Insert</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_InsertCorrectness">VEBT_InsertCorrectness</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_MinMax">VEBT_MinMax</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Succ">VEBT_Succ</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Pred">VEBT_Pred</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Delete">VEBT_Delete</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_DeleteCorrectness">VEBT_DeleteCorrectness</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Uniqueness">VEBT_Uniqueness</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Height">VEBT_Height</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Bounds">VEBT_Bounds</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_DeleteBounds">VEBT_DeleteBounds</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Space">VEBT_Space</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Intf_Functional">VEBT_Intf_Functional</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_List_Assn">VEBT_List_Assn</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_BuildupMemImp">VEBT_BuildupMemImp</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_SuccPredImperative">VEBT_SuccPredImperative</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_DelImperative">VEBT_DelImperative</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Intf_Imperative">VEBT_Intf_Imperative</a></li>
<li><a href="../theories/van_emde_boas_trees/#VEBT_Example">VEBT_Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></li><li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li></ul>
</div>
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author = {Thomas Ammer and Peter Lammich},
title = {van Emde Boas Trees},
journal = {Archive of Formal Proofs},
month = {November},
year = {2021},
note = {\url{https://isa-afp.org/entries/Van_Emde_Boas_Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Van_der_Waerden.html b/web/entries/Van_der_Waerden.html
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<h1 >
<span class='first'>V</span>an <span class='first'>D</span>er <span class='first'>W</span>aerden's <span class='first'>T</span>heorem</h1>
<div>
<p><a href="../authors/kreuzer">Katharina Kreuzer</a> <a href="https://www21.in.tum.de/team/kreuzer/">🌐</a> and <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">June 22, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This article formalises the proof of Van der Waerden's Theorem
from Ramsey theory. Van der Waerden's Theorem states that for
integers $k$ and $l$ there exists a number $N$ which guarantees that
if an integer interval of length at least $N$ is coloured with $k$
colours, there will always be an arithmetic progression of length $l$
of the same colour in said interval. The proof goes along the lines of
\cite{Swan}. The smallest number $N_{k,l}$ fulfilling Van der
Waerden's Theorem is then called the Van der Waerden Number.
Finding the Van der Waerden Number is still an open problem for most
values of $k$ and $l$.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Van_der_Waerden</h3>
<ul>
<li><a href="../theories/van_der_waerden/#Digits">Digits</a></li>
<li><a href="../theories/van_der_waerden/#Van_der_Waerden">Van_der_Waerden</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Van_der_Waerden-AFP</p><pre id="copy-text">@article{Van_der_Waerden-AFP,
author = {Katharina Kreuzer and Manuel Eberl},
title = {Van der Waerden&#39;s Theorem},
journal = {Archive of Formal Proofs},
month = {June},
year = {2021},
note = {\url{https://isa-afp.org/entries/Van_der_Waerden.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Van_der_Waerden-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/VectorSpace.html b/web/entries/VectorSpace.html
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@@ -1,189 +1,191 @@
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<h1 >
<span class='first'>V</span>ector <span class='first'>S</span>paces</h1>
<div>
<p><a href="../authors/lee">Holden Lee</a> <a class="obfuscated" data="eyJob3N0IjpbInByaW5jZXRvbiIsImVkdSJdLCJ1c2VyIjpbImhvbGRlbmwiXX0=">📧</a>
</p>
<p class="date">August 29, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This formalisation of basic linear algebra is based completely on locales, building off HOL-Algebra. It includes basic definitions: linear combinations, span, linear independence; linear transformations; interpretation of function spaces as vector spaces; the direct sum of vector spaces, sum of subspaces; the replacement theorem; existence of bases in finite-dimensional; vector spaces, definition of dimension; the rank-nullity theorem. Some concepts are actually defined and proved for modules as they also apply there. Infinite-dimensional vector spaces are supported, but dimension is only supported for finite-dimensional vector spaces. The proofs are standard; the proofs of the replacement theorem and rank-nullity theorem roughly follow the presentation in Linear Algebra by Friedberg, Insel, and Spence. The rank-nullity theorem generalises the existing development in the Archive of Formal Proof (originally using type classes, now using a mix of type classes and locales).</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li></ul>
<h3>Session VectorSpace</h3>
<ul>
<li><a href="../theories/vectorspace/#RingModuleFacts">RingModuleFacts</a></li>
<li><a href="../theories/vectorspace/#FunctionLemmas">FunctionLemmas</a></li>
<li><a href="../theories/vectorspace/#MonoidSums">MonoidSums</a></li>
<li><a href="../theories/vectorspace/#LinearCombinations">LinearCombinations</a></li>
<li><a href="../theories/vectorspace/#SumSpaces">SumSpaces</a></li>
<li><a href="../theories/vectorspace/#VectorSpace">VectorSpace</a></li></ul><div class="flex-wrap">
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Isabelle_Marries_Dirac.html">Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</a></li><li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li><li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li></ul>
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<p style="display:none;" id="bibtex-filename">VectorSpace-AFP</p><pre id="copy-text">@article{VectorSpace-AFP,
author = {Holden Lee},
title = {Vector Spaces},
journal = {Archive of Formal Proofs},
month = {August},
year = {2014},
note = {\url{https://isa-afp.org/entries/VectorSpace.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-VectorSpace-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-VectorSpace-2014-09-07.tar.gz">Sep 7, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-VectorSpace-2014-08-31.tar.gz">Aug 31, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-VectorSpace-2014-08-29.tar.gz">Aug 29, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>A</span> <span class='first'>G</span>eneric <span class='first'>F</span>ramework for <span class='first'>V</span>erified <span class='first'>C</span>ompilers</h1>
<div>
<p><a href="../authors/desharnais">Martin Desharnais</a> <a href="https://martin.desharnais.me">🌐</a>
</p>
<p class="date">February 10, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a generic framework for formalizing compiler transformations.
It leverages Isabelle/HOL’s locales to abstract over concrete
languages and transformations. It states common definitions for
language semantics, program behaviours, forward and backward
simulations, and compilers. We provide generic operations, such as
simulation and compiler composition, and prove general (partial)
correctness theorems, resulting in reusable proof components.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/compiling">Computer science/Programming languages/Compiling</a></li></ul>
<h3>Session VeriComp</h3>
<ul>
<li><a href="../theories/vericomp/#Behaviour">Behaviour</a></li>
<li><a href="../theories/vericomp/#Well_founded">Well_founded</a></li>
<li><a href="../theories/vericomp/#Inf">Inf</a></li>
<li><a href="../theories/vericomp/#Transfer_Extras">Transfer_Extras</a></li>
<li><a href="../theories/vericomp/#Semantics">Semantics</a></li>
<li><a href="../theories/vericomp/#Language">Language</a></li>
<li><a href="../theories/vericomp/#Simulation">Simulation</a></li>
<li><a href="../theories/vericomp/#Compiler">Compiler</a></li>
<li><a href="../theories/vericomp/#Fixpoint">Fixpoint</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Interpreter_Optimizations.html">Inline Caching and Unboxing Optimization for Interpreters</a></li></ul>
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<p style="display:none;" id="bibtex-filename">VeriComp-AFP</p><pre id="copy-text">@article{VeriComp-AFP,
author = {Martin Desharnais},
title = {A Generic Framework for Verified Compilers},
journal = {Archive of Formal Proofs},
month = {February},
year = {2020},
note = {\url{https://isa-afp.org/entries/VeriComp.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Verified-Prover.html b/web/entries/Verified-Prover.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic - Archive of Formal Proofs</title><meta name="description" content="Soundness and completeness for a system of first order logic are formally proved, building on James Margetson&#39;s formalization of work by Wainer and Wallen...."><meta property="og:title" content="A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic" />
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<h1 >
<span class='first'>A</span> <span class='first'>M</span>echanically <span class='first'>V</span>erified, <span class='first'>E</span>fficient, <span class='first'>S</span>ound and <span class='first'>C</span>omplete <span class='first'>T</span>heorem <span class='first'>P</span>rover for <span class='first'>F</span>irst <span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/ridge">Tom Ridge</a>
</p>
<p class="date">September 28, 2004</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Soundness and completeness for a system of first order logic are formally proved, building on James Margetson's formalization of work by Wainer and Wallen. The completeness proofs naturally suggest an algorithm to derive proofs. This algorithm, which can be implemented tail recursively, is formalized in Isabelle/HOL. The algorithm can be executed via the rewriting tactics of Isabelle. Alternatively, the definitions can be exported to OCaml, yielding a directly executable program.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/general-logic/mechanization-of-proofs">Logic/General logic/Mechanization of proofs</a></li></ul>
<h3>Session Verified-Prover</h3>
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<p style="display:none;" id="bibtex-filename">Verified-Prover-AFP</p><pre id="copy-text">@article{Verified-Prover-AFP,
author = {Tom Ridge},
title = {A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic},
journal = {Archive of Formal Proofs},
month = {September},
year = {2004},
note = {\url{https://isa-afp.org/entries/Verified-Prover.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/Verified_SAT_Based_AI_Planning.html b/web/entries/Verified_SAT_Based_AI_Planning.html
--- a/web/entries/Verified_SAT_Based_AI_Planning.html
+++ b/web/entries/Verified_SAT_Based_AI_Planning.html
@@ -1,192 +1,194 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Verified SAT-Based AI Planning - Archive of Formal Proofs</title><meta name="description" content="We present an executable formally verified SAT encoding of classical
AI planning that is based on the encodings by Kautz and Selman and the
one by Rintanen..."><meta property="og:title" content="Verified SAT-Based AI Planning" />
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<h1 >
<span class='first'>V</span>erified <span class='first'>S</span><span class='first'>A</span><span class='first'>T</span>-<span class='first'>B</span>ased <span class='first'>A</span><span class='first'>I</span> <span class='first'>P</span>lanning</h1>
<div>
<p><a href="../authors/abdulaziz">Mohammad Abdulaziz</a> <a href="http://home.in.tum.de/~mansour/">🌐</a> and <a href="../authors/kurz">Friedrich Kurz</a>
</p>
<p class="date">October 29, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We present an executable formally verified SAT encoding of classical
AI planning that is based on the encodings by Kautz and Selman and the
one by Rintanen et al. The encoding was experimentally tested and
shown to be usable for reasonably sized standard AI planning
benchmarks. We also use it as a reference to test a state-of-the-art
SAT-based planner, showing that it sometimes falsely claims that
problems have no solutions of certain lengths. The formalisation in
this submission was described in an independent publication.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/artificial-intelligence">Computer science/Artificial intelligence</a></li></ul>
<h3>Session Verified_SAT_Based_AI_Planning</h3>
<ul>
<li><a href="../theories/verified_sat_based_ai_planning/#List_Supplement">List_Supplement</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#Map_Supplement">Map_Supplement</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#CNF_Supplement">CNF_Supplement</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#CNF_Semantics_Supplement">CNF_Semantics_Supplement</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#State_Variable_Representation">State_Variable_Representation</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#STRIPS_Representation">STRIPS_Representation</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#STRIPS_Semantics">STRIPS_Semantics</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAS_Plus_Representation">SAS_Plus_Representation</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAS_Plus_Semantics">SAS_Plus_Semantics</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAS_Plus_STRIPS">SAS_Plus_STRIPS</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAT_Plan_Base">SAT_Plan_Base</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAT_Plan_Extensions">SAT_Plan_Extensions</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#SAT_Solve_SAS_Plus">SAT_Solve_SAS_Plus</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#AST_SAS_Plus_Equivalence">AST_SAS_Plus_Equivalence</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#Set2_Join_RBT">Set2_Join_RBT</a></li>
<li><a href="../theories/verified_sat_based_ai_planning/#Solve_SASP">Solve_SASP</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/AI_Planning_Languages_Semantics.html">AI Planning Languages Semantics</a></li><li><a href="../entries/List-Index.html">List Index</a></li><li><a href="../entries/Propositional_Proof_Systems.html">Propositional Proof Systems</a></li></ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/Verified_SAT_Based_AI_Planning/document.pdf">Proof
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author = {Mohammad Abdulaziz and Friedrich Kurz},
title = {Verified SAT-Based AI Planning},
journal = {Archive of Formal Proofs},
month = {October},
year = {2020},
note = {\url{https://isa-afp.org/entries/Verified_SAT_Based_AI_Planning.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Verified_SAT_Based_AI_Planning-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Verified_SAT_Based_AI_Planning-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Verified_SAT_Based_AI_Planning-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Verified_SAT_Based_AI_Planning-2020-11-13.tar.gz">Nov 13, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Verified_SAT_Based_AI_Planning-2020-11-03.tar.gz">Nov 3, 2020</a>: Isabelle2020
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diff --git a/web/entries/VerifyThis2018.html b/web/entries/VerifyThis2018.html
--- a/web/entries/VerifyThis2018.html
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@@ -1,197 +1,199 @@
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<h1 >
<span class='first'>V</span>erify<span class='first'>T</span>his 2018 - <span class='first'>P</span>olished <span class='first'>I</span>sabelle <span class='first'>S</span>olutions</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>
</p>
<p class="date">April 27, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><a
href="http://www.pm.inf.ethz.ch/research/verifythis.html">VerifyThis
2018</a> was a program verification competition associated with
ETAPS 2018. It was the 7th event in the VerifyThis competition series.
In this entry, we present polished and completed versions of our
solutions that we created during the competition.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session VerifyThis2018</h3>
<ul>
<li><a href="../theories/verifythis2018/#Dynamic_Array">Dynamic_Array</a></li>
<li><a href="../theories/verifythis2018/#DRAT_Misc">DRAT_Misc</a></li>
<li><a href="../theories/verifythis2018/#Array_Map_Default">Array_Map_Default</a></li>
<li><a href="../theories/verifythis2018/#Synth_Definition">Synth_Definition</a></li>
<li><a href="../theories/verifythis2018/#Exc_Nres_Monad">Exc_Nres_Monad</a></li>
<li><a href="../theories/verifythis2018/#VTcomp">VTcomp</a></li>
<li><a href="../theories/verifythis2018/#DF_System">DF_System</a></li>
<li><a href="../theories/verifythis2018/#Snippets">Snippets</a></li>
<li><a href="../theories/verifythis2018/#Challenge1">Challenge1</a></li>
<li><a href="../theories/verifythis2018/#Challenge1_short">Challenge1_short</a></li>
<li><a href="../theories/verifythis2018/#Challenge2">Challenge2</a></li>
<li><a href="../theories/verifythis2018/#Challenge3">Challenge3</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/VerifyThis2019.html">VerifyThis 2019 &ndash; Polished Isabelle Solutions</a></li>
</ul>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/VerifyThis2018/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">VerifyThis2018-AFP</p><pre id="copy-text">@article{VerifyThis2018-AFP,
author = {Peter Lammich and Simon Wimmer},
title = {VerifyThis 2018 - Polished Isabelle Solutions},
journal = {Archive of Formal Proofs},
month = {April},
year = {2018},
note = {\url{https://isa-afp.org/entries/VerifyThis2018.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2018-2018-04-30.tar.gz">Apr 30, 2018</a>: Isabelle2017
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/VerifyThis2019.html b/web/entries/VerifyThis2019.html
--- a/web/entries/VerifyThis2019.html
+++ b/web/entries/VerifyThis2019.html
@@ -1,190 +1,192 @@
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was a program verification competition associated with ETAPS 2019. It
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<h1 >
<span class='first'>V</span>erify<span class='first'>T</span>his 2019 -- <span class='first'>P</span>olished <span class='first'>I</span>sabelle <span class='first'>S</span>olutions</h1>
<div>
<p><a href="../authors/lammich">Peter Lammich</a> and <a href="../authors/wimmer">Simon Wimmer</a> <a href="http://home.in.tum.de/~wimmers/">🌐</a>
</p>
<p class="date">October 16, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">VerifyThis 2019 (http://www.pm.inf.ethz.ch/research/verifythis.html)
was a program verification competition associated with ETAPS 2019. It
was the 8th event in the VerifyThis competition series. In this entry,
we present polished and completed versions of our solutions that we
created during the competition.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li></ul>
<h3>Session VerifyThis2019</h3>
<ul>
<li><a href="../theories/verifythis2019/#Exc_Nres_Monad">Exc_Nres_Monad</a></li>
<li><a href="../theories/verifythis2019/#VTcomp">VTcomp</a></li>
<li><a href="../theories/verifythis2019/#Challenge1A">Challenge1A</a></li>
<li><a href="../theories/verifythis2019/#Challenge1B">Challenge1B</a></li>
<li><a href="../theories/verifythis2019/#Challenge2A">Challenge2A</a></li>
<li><a href="../theories/verifythis2019/#Challenge2B">Challenge2B</a></li>
<li><a href="../theories/verifythis2019/#Parallel_Multiset_Fold">Parallel_Multiset_Fold</a></li>
<li><a href="../theories/verifythis2019/#Challenge3">Challenge3</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
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</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/VerifyThis2018.html">VerifyThis 2018 - Polished Isabelle Solutions</a></li>
</ul>
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<a href="https://www.isa-afp.org/browser_info/current/AFP/VerifyThis2019/document.pdf">Proof
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<p style="display:none;" id="bibtex-filename">VerifyThis2019-AFP</p><pre id="copy-text">@article{VerifyThis2019-AFP,
author = {Peter Lammich and Simon Wimmer},
title = {VerifyThis 2019 -- Polished Isabelle Solutions},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/VerifyThis2019.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release//afp-VerifyThis2019-current.tar.gz" download>Download latest</a>
<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-VerifyThis2019-2019-10-25.tar.gz">Oct 25, 2019</a>: Isabelle2019
</li></ul>
</div>
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diff --git a/web/entries/Vickrey_Clarke_Groves.html b/web/entries/Vickrey_Clarke_Groves.html
--- a/web/entries/Vickrey_Clarke_Groves.html
+++ b/web/entries/Vickrey_Clarke_Groves.html
@@ -1,203 +1,205 @@
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Groves) is a generalization of the single-good, second price Vickrey
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<h1 >
<span class='first'>V</span><span class='first'>C</span><span class='first'>G</span> - <span class='first'>C</span>ombinatorial <span class='first'>V</span>ickrey-<span class='first'>C</span>larke-<span class='first'>G</span>roves <span class='first'>A</span>uctions</h1>
<div>
<p><a href="../authors/caminati">Marco B. Caminati</a>, <a href="../authors/kerber">Manfred Kerber</a> <a href="http://www.cs.bham.ac.uk/~mmk">🌐</a>, <a href="../authors/lange">Christoph Lange</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsibWF0aCIsInNlbWFudGljIiwid2ViIl19">📧</a> and <a href="../authors/rowat">Colin Rowat</a> <a class="obfuscated" data="eyJob3N0IjpbImJoYW0iLCJhYyIsInVrIl0sInVzZXIiOlsiYyIsInJvd2F0Il19">📧</a>
</p>
<p class="date">April 30, 2015</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">A VCG auction (named after their inventors Vickrey, Clarke, and
Groves) is a generalization of the single-good, second price Vickrey
auction to the case of a combinatorial auction (multiple goods, from
which any participant can bid on each possible combination). We
formalize in this entry VCG auctions, including tie-breaking and prove
that the functions for the allocation and the price determination are
well-defined. Furthermore we show that the allocation function
allocates goods only to participants, only goods in the auction are
allocated, and no good is allocated twice. We also show that the price
function is non-negative. These properties also hold for the
automatically extracted Scala code.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/games-and-economics">Mathematics/Games and economics</a></li></ul>
<h3>Session Vickrey_Clarke_Groves</h3>
<ul>
<li><a href="../theories/vickrey_clarke_groves/#SetUtils">SetUtils</a></li>
<li><a href="../theories/vickrey_clarke_groves/#Partitions">Partitions</a></li>
<li><a href="../theories/vickrey_clarke_groves/#Argmax">Argmax</a></li>
<li><a href="../theories/vickrey_clarke_groves/#RelationOperators">RelationOperators</a></li>
<li><a href="../theories/vickrey_clarke_groves/#RelationProperties">RelationProperties</a></li>
<li><a href="../theories/vickrey_clarke_groves/#MiscTools">MiscTools</a></li>
<li><a href="../theories/vickrey_clarke_groves/#StrictCombinatorialAuction">StrictCombinatorialAuction</a></li>
<li><a href="../theories/vickrey_clarke_groves/#Universes">Universes</a></li>
<li><a href="../theories/vickrey_clarke_groves/#UniformTieBreaking">UniformTieBreaking</a></li>
<li><a href="../theories/vickrey_clarke_groves/#CombinatorialAuction">CombinatorialAuction</a></li>
<li><a href="../theories/vickrey_clarke_groves/#CombinatorialAuctionCodeExtraction">CombinatorialAuctionCodeExtraction</a></li>
<li><a href="../theories/vickrey_clarke_groves/#FirstPrice">FirstPrice</a></li>
<li><a href="../theories/vickrey_clarke_groves/#CombinatorialAuctionExamples">CombinatorialAuctionExamples</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Vickrey_Clarke_Groves-AFP</p><pre id="copy-text">@article{Vickrey_Clarke_Groves-AFP,
author = {Marco B. Caminati and Manfred Kerber and Christoph Lange and Colin Rowat},
title = {VCG - Combinatorial Vickrey-Clarke-Groves Auctions},
journal = {Archive of Formal Proofs},
month = {April},
year = {2015},
note = {\url{https://isa-afp.org/entries/Vickrey_Clarke_Groves.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2015-05-09.tar.gz">May 9, 2015</a>: Isabelle2014
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<a href="https://www.isa-afp.org/release/afp-Vickrey_Clarke_Groves-2015-04-30.tar.gz">Apr 30, 2015</a>: Isabelle2014
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diff --git a/web/entries/Virtual_Substitution.html b/web/entries/Virtual_Substitution.html
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<h1 >
<span class='first'>V</span>erified <span class='first'>Q</span>uadratic <span class='first'>V</span>irtual <span class='first'>S</span>ubstitution for <span class='first'>R</span>eal <span class='first'>A</span>rithmetic</h1>
<div>
<p><a href="../authors/scharager">Matias Scharager</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsibXNjaGFyYWciXX0=">📧</a>, <a href="../authors/cordwell">Katherine Cordwell</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsia2NvcmR3ZWwiXX0=">📧</a>, <a href="../authors/mitsch">Stefan Mitsch</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsic21pdHNjaCJdfQ==">📧</a> and <a href="../authors/platzer">André Platzer</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsiYXBsYXR6ZXIiXX0=">📧</a>
</p>
<p class="date">October 2, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This paper presents a formally verified quantifier elimination (QE)
algorithm for first-order real arithmetic by linear and quadratic
virtual substitution (VS) in Isabelle/HOL. The Tarski-Seidenberg
theorem established that the first-order logic of real arithmetic is
decidable by QE. However, in practice, QE algorithms are highly
complicated and often combine multiple methods for performance. VS is
a practically successful method for QE that targets formulas with
low-degree polynomials. To our knowledge, this is the first work to
formalize VS for quadratic real arithmetic including inequalities. The
proofs necessitate various contributions to the existing multivariate
polynomial libraries in Isabelle/HOL. Our framework is modularized and
easily expandable (to facilitate integrating future optimizations),
and could serve as a basis for developing practical general-purpose QE
algorithms. Further, as our formalization is designed with
practicality in mind, we export our development to SML and test the
resulting code on 378 benchmarks from the literature, comparing to
Redlog, Z3, Wolfram Engine, and SMT-RAT. This identified
inconsistencies in some tools, underscoring the significance of a
verified approach for the intricacies of real arithmetic.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/mathematical">Computer science/Algorithms/Mathematical</a></li></ul>
<h3>Session Virtual_Substitution</h3>
<ul>
<li><a href="../theories/virtual_substitution/#QE">QE</a></li>
<li><a href="../theories/virtual_substitution/#MPolyExtension">MPolyExtension</a></li>
<li><a href="../theories/virtual_substitution/#ExecutiblePolyProps">ExecutiblePolyProps</a></li>
<li><a href="../theories/virtual_substitution/#PolyAtoms">PolyAtoms</a></li>
<li><a href="../theories/virtual_substitution/#Debruijn">Debruijn</a></li>
<li><a href="../theories/virtual_substitution/#Reindex">Reindex</a></li>
<li><a href="../theories/virtual_substitution/#Optimizations">Optimizations</a></li>
<li><a href="../theories/virtual_substitution/#OptimizationProofs">OptimizationProofs</a></li>
<li><a href="../theories/virtual_substitution/#VSAlgos">VSAlgos</a></li>
<li><a href="../theories/virtual_substitution/#Heuristic">Heuristic</a></li>
<li><a href="../theories/virtual_substitution/#PrettyPrinting">PrettyPrinting</a></li>
<li><a href="../theories/virtual_substitution/#Exports">Exports</a></li>
<li><a href="../theories/virtual_substitution/#LinearCase">LinearCase</a></li>
<li><a href="../theories/virtual_substitution/#QuadraticCase">QuadraticCase</a></li>
<li><a href="../theories/virtual_substitution/#EliminateVariable">EliminateVariable</a></li>
<li><a href="../theories/virtual_substitution/#LuckyFind">LuckyFind</a></li>
<li><a href="../theories/virtual_substitution/#EqualityVS">EqualityVS</a></li>
<li><a href="../theories/virtual_substitution/#UniAtoms">UniAtoms</a></li>
<li><a href="../theories/virtual_substitution/#NegInfinity">NegInfinity</a></li>
<li><a href="../theories/virtual_substitution/#NegInfinityUni">NegInfinityUni</a></li>
<li><a href="../theories/virtual_substitution/#Infinitesimals">Infinitesimals</a></li>
<li><a href="../theories/virtual_substitution/#InfinitesimalsUni">InfinitesimalsUni</a></li>
<li><a href="../theories/virtual_substitution/#DNFUni">DNFUni</a></li>
<li><a href="../theories/virtual_substitution/#GeneralVSProofs">GeneralVSProofs</a></li>
<li><a href="../theories/virtual_substitution/#DNF">DNF</a></li>
<li><a href="../theories/virtual_substitution/#VSQuad">VSQuad</a></li>
<li><a href="../theories/virtual_substitution/#HeuristicProofs">HeuristicProofs</a></li>
<li><a href="../theories/virtual_substitution/#ExportProofs">ExportProofs</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Virtual_Substitution-AFP</p><pre id="copy-text">@article{Virtual_Substitution-AFP,
author = {Matias Scharager and Katherine Cordwell and Stefan Mitsch and André Platzer},
title = {Verified Quadratic Virtual Substitution for Real Arithmetic},
journal = {Archive of Formal Proofs},
month = {October},
year = {2021},
note = {\url{https://isa-afp.org/entries/Virtual_Substitution.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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diff --git a/web/entries/VolpanoSmith.html b/web/entries/VolpanoSmith.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>A Correctness Proof for the Volpano/Smith Security Typing System - Archive of Formal Proofs</title><meta name="description" content="The Volpano/Smith/Irvine security type systems requires that variables are annotated as high (secret) or low (public), and provides typing rules which..."><meta property="og:title" content="A Correctness Proof for the Volpano/Smith Security Typing System" />
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<h1 >
<span class='first'>A</span> <span class='first'>C</span>orrectness <span class='first'>P</span>roof for the <span class='first'>V</span>olpano/<span class='first'>S</span>mith <span class='first'>S</span>ecurity <span class='first'>T</span>yping <span class='first'>S</span>ystem</h1>
<div>
<p><a href="../authors/snelting">Gregor Snelting</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/gregor_snelting.php">🌐</a> and <a href="../authors/wasserrab">Daniel Wasserrab</a> <a href="http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php">🌐</a>
</p>
<p class="date">September 2, 2008</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">The Volpano/Smith/Irvine security type systems requires that variables are annotated as high (secret) or low (public), and provides typing rules which guarantee that secret values cannot leak to public output ports. This property of a program is called confidentiality. For a simple while-language without threads, our proof shows that typeability in the Volpano/Smith system guarantees noninterference. Noninterference means that if two initial states for program execution are low-equivalent, then the final states are low-equivalent as well. This indeed implies that secret values cannot leak to public ports. The proof defines an abstract syntax and operational semantics for programs, formalizes noninterference, and then proceeds by rule induction on the operational semantics. The mathematically most intricate part is the treatment of implicit flows. Note that the Volpano/Smith system is not flow-sensitive and thus quite unprecise, resulting in false alarms. However, due to the correctness property, all potential breaks of confidentiality are discovered.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li><li><a href="../topics/computer-science/security">Computer science/Security</a></li></ul>
<h3>Session VolpanoSmith</h3>
<ul>
<li><a href="../theories/volpanosmith/#Semantics">Semantics</a></li>
<li><a href="../theories/volpanosmith/#secTypes">secTypes</a></li>
<li><a href="../theories/volpanosmith/#Execute">Execute</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">VolpanoSmith-AFP</p><pre id="copy-text">@article{VolpanoSmith-AFP,
author = {Gregor Snelting and Daniel Wasserrab},
title = {A Correctness Proof for the Volpano/Smith Security Typing System},
journal = {Archive of Formal Proofs},
month = {September},
year = {2008},
note = {\url{https://isa-afp.org/entries/VolpanoSmith.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
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<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
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<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
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<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
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<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
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<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
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</li><li>
<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2009-04-29.tar.gz">Apr 29, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-VolpanoSmith-2008-09-05.tar.gz">Sep 5, 2008</a>: Isabelle2008
</li></ul>
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diff --git a/web/entries/WHATandWHERE_Security.html b/web/entries/WHATandWHERE_Security.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>D</span>eclassification <span class='first'>W</span>ith <span class='first'>W</span><span class='first'>H</span><span class='first'>A</span><span class='first'>T</span>-and-<span class='first'>W</span><span class='first'>H</span><span class='first'>E</span><span class='first'>R</span><span class='first'>E</span>-<span class='first'>S</span>ecurity</h1>
<div>
<p><a href="../authors/grewe">Sylvia Grewe</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJncmV3ZSJdfQ==">📧</a>, <a href="../authors/lux">Alexander Lux</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJsdXgiXX0=">📧</a>, <a href="../authors/mantel">Heiko Mantel</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJtYW50ZWwiXX0=">📧</a> and <a href="../authors/sauer">Jens Sauer</a> <a class="obfuscated" data="eyJob3N0IjpbIm1haXMiLCJpbmZvcm1hdGlrIiwidHUtZGFybXN0YWR0IiwiZGUiXSwidXNlciI6WyJzYXVlciJdfQ==">📧</a>
</p>
<p class="date">April 23, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Research in information-flow security aims at developing methods to
identify undesired information leaks within programs from private
sources to public sinks. Noninterference captures this intuition by
requiring that no information whatsoever flows from private sources
to public sinks. However, in practice this definition is often too
strict: Depending on the intuitive desired security policy, the
controlled declassification of certain private information (WHAT) at
certain points in the program (WHERE) might not result in an
undesired information leak.
<p>
We present an Isabelle/HOL formalization of such a security property
for controlled declassification, namely WHAT&WHERE-security from
"Scheduler-Independent Declassification" by Lux, Mantel, and Perner.
The formalization includes
compositionality proofs for and a soundness proof for a security
type system that checks for programs in a simple while language with
dynamic thread creation.
<p>
Our formalization of the security type system is abstract in the
language for expressions and in the semantic side conditions for
expressions. It can easily be instantiated with different syntactic
approximations for these side conditions. The soundness proof of
such an instantiation boils down to showing that these syntactic
approximations imply the semantic side conditions.
<p>
This Isabelle/HOL formalization uses theories from the entry
Strong Security.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/security">Computer science/Security</a></li><li><a href="../topics/computer-science/programming-languages/type-systems">Computer science/Programming languages/Type systems</a></li></ul>
<h3>Session WHATandWHERE_Security</h3>
<ul>
<li><a href="../theories/whatandwhere_security/#WHATWHERE_Security">WHATWHERE_Security</a></li>
<li><a href="../theories/whatandwhere_security/#Up_To_Technique">Up_To_Technique</a></li>
<li><a href="../theories/whatandwhere_security/#MWLs">MWLs</a></li>
<li><a href="../theories/whatandwhere_security/#Parallel_Composition">Parallel_Composition</a></li>
<li><a href="../theories/whatandwhere_security/#WHATWHERE_Secure_Skip_Assign">WHATWHERE_Secure_Skip_Assign</a></li>
<li><a href="../theories/whatandwhere_security/#Language_Composition">Language_Composition</a></li>
<li><a href="../theories/whatandwhere_security/#Type_System">Type_System</a></li>
<li><a href="../theories/whatandwhere_security/#Type_System_example">Type_System_example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Strong_Security.html">A Formalization of Strong Security</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/SIFUM_Type_Systems.html">A Formalization of Assumptions and Guarantees for Compositional Noninterference</a></li>
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<p style="display:none;" id="bibtex-filename">WHATandWHERE_Security-AFP</p><pre id="copy-text">@article{WHATandWHERE_Security-AFP,
author = {Sylvia Grewe and Alexander Lux and Heiko Mantel and Jens Sauer},
title = {A Formalization of Declassification with WHAT-and-WHERE-Security},
journal = {Archive of Formal Proofs},
month = {April},
year = {2014},
note = {\url{https://isa-afp.org/entries/WHATandWHERE_Security.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
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<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-WHATandWHERE_Security-2014-04-24.tar.gz">Apr 24, 2014</a>: Isabelle2013-2
</li></ul>
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diff --git a/web/entries/WOOT_Strong_Eventual_Consistency.html b/web/entries/WOOT_Strong_Eventual_Consistency.html
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@@ -1,203 +1,205 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Strong Eventual Consistency of the Collaborative Editing Framework WOOT - Archive of Formal Proofs</title><meta name="description" content="Commutative Replicated Data Types (CRDTs) are a promising new class of
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<h1 >
<span class='first'>S</span>trong <span class='first'>E</span>ventual <span class='first'>C</span>onsistency of the <span class='first'>C</span>ollaborative <span class='first'>E</span>diting <span class='first'>F</span>ramework <span class='first'>W</span><span class='first'>O</span><span class='first'>O</span><span class='first'>T</span></h1>
<div>
<p><a href="../authors/karayel">Emin Karayel</a> <a href="https://orcid.org/0000-0003-3290-5034">🌐</a> and <a href="../authors/gonzalez">Edgar Gonzàlez</a> <a class="obfuscated" data="eyJob3N0IjpbImdvb2dsZSIsImNvbSJdLCJ1c2VyIjpbImVkZ2FyZ2lwIl19">📧</a>
</p>
<p class="date">March 25, 2020</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Commutative Replicated Data Types (CRDTs) are a promising new class of
data structures for large-scale shared mutable content in applications
that only require eventual consistency. The WithOut Operational
Transforms (WOOT) framework is a CRDT for collaborative text editing
introduced by Oster et al. (CSCW 2006) for which the eventual
consistency property was verified only for a bounded model to date. We
contribute a formal proof for WOOTs strong eventual consistency.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/algorithms/distributed">Computer science/Algorithms/Distributed</a></li></ul><h3>Related publications</h3>
<ul><li>
Karayel, E., & Gonzàlez, E. (2022). Strong eventual consistency of the collaborative editing framework WOOT. Distributed Computing, 35(2), 145–164. <a href="https://doi.org/10.1007/s00446-021-00414-6">https://doi.org/10.1007/s00446-021-00414-6</a>
</li></ul>
<h3>Session WOOT_Strong_Eventual_Consistency</h3>
<ul>
<li><a href="../theories/woot_strong_eventual_consistency/#ErrorMonad">ErrorMonad</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#Data">Data</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#BasicAlgorithms">BasicAlgorithms</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#CreateAlgorithms">CreateAlgorithms</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#IntegrateAlgorithm">IntegrateAlgorithm</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#DistributedExecution">DistributedExecution</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#SortKeys">SortKeys</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#Psi">Psi</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#Sorting">Sorting</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#Consistency">Consistency</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#CreateConsistent">CreateConsistent</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#IntegrateInsertCommute">IntegrateInsertCommute</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#StrongConvergence">StrongConvergence</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#SEC">SEC</a></li>
<li><a href="../theories/woot_strong_eventual_consistency/#Example">Example</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Certification_Monads.html">Certification Monads</a></li><li><a href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/OpSets.html">OpSets: Sequential Specifications for Replicated Datatypes</a></li>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/WOOT_Strong_Eventual_Consistency/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">WOOT_Strong_Eventual_Consistency-AFP</p><pre id="copy-text">@article{WOOT_Strong_Eventual_Consistency-AFP,
author = {Emin Karayel and Edgar Gonzàlez},
title = {Strong Eventual Consistency of the Collaborative Editing Framework WOOT},
journal = {Archive of Formal Proofs},
month = {March},
year = {2020},
note = {\url{https://isa-afp.org/entries/WOOT_Strong_Eventual_Consistency.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-WOOT_Strong_Eventual_Consistency-2020-03-26.tar.gz">Mar 26, 2020</a>: Isabelle2019
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/WebAssembly.html b/web/entries/WebAssembly.html
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<h1 >
<span class='first'>W</span>eb<span class='first'>A</span>ssembly</h1>
<div>
<p><a href="../authors/watt">Conrad Watt</a> <a href="http://www.cl.cam.ac.uk/~caw77/">🌐</a>
</p>
<p class="date">April 29, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This is a mechanised specification of the WebAssembly language, drawn
mainly from the previously published paper formalisation of Haas et
al. Also included is a full proof of soundness of the type system,
together with a verified type checker and interpreter. We include only
a partial procedure for the extraction of the type checker and
interpreter here. For more details, please see our paper in CPP 2018.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/programming-languages/language-definitions">Computer science/Programming languages/Language definitions</a></li></ul>
<h3>Session WebAssembly</h3>
<ul>
<li><a href="../theories/webassembly/#Wasm_Ast">Wasm_Ast</a></li>
<li><a href="../theories/webassembly/#Wasm_Type_Abs">Wasm_Type_Abs</a></li>
<li><a href="../theories/webassembly/#Wasm_Base_Defs">Wasm_Base_Defs</a></li>
<li><a href="../theories/webassembly/#Wasm">Wasm</a></li>
<li><a href="../theories/webassembly/#Wasm_Axioms">Wasm_Axioms</a></li>
<li><a href="../theories/webassembly/#Wasm_Properties_Aux">Wasm_Properties_Aux</a></li>
<li><a href="../theories/webassembly/#Wasm_Properties">Wasm_Properties</a></li>
<li><a href="../theories/webassembly/#Wasm_Soundness">Wasm_Soundness</a></li>
<li><a href="../theories/webassembly/#Wasm_Checker_Types">Wasm_Checker_Types</a></li>
<li><a href="../theories/webassembly/#Wasm_Checker">Wasm_Checker</a></li>
<li><a href="../theories/webassembly/#Wasm_Checker_Properties">Wasm_Checker_Properties</a></li>
<li><a href="../theories/webassembly/#Wasm_Interpreter">Wasm_Interpreter</a></li>
<li><a href="../theories/webassembly/#Wasm_Interpreter_Properties">Wasm_Interpreter_Properties</a></li>
<li><a href="../theories/webassembly/#Wasm_Checker_Printing">Wasm_Checker_Printing</a></li>
<li><a href="../theories/webassembly/#Wasm_Interpreter_Printing">Wasm_Interpreter_Printing</a></li>
<li><a href="../theories/webassembly/#Wasm_Type_Abs_Printing">Wasm_Type_Abs_Printing</a></li>
<li><a href="../theories/webassembly/#Wasm_Printing">Wasm_Printing</a></li>
<li><a href="../theories/webassembly/#Wasm_Interpreter_Printing_Pure">Wasm_Interpreter_Printing_Pure</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Native_Word.html">Native Word</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Physical_Quantities.html">A Sound Type System for Physical Quantities, Units, and Measurements</a></li>
<li><a href="../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></li>
<li><a href="../entries/Dependent_SIFUM_Type_Systems.html">A Dependent Security Type System for Concurrent Imperative Programs</a></li>
</ul>
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</div>
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<h4>PDFs</h4>
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outline</a>
<a href="https://www.isa-afp.org/browser_info/current/AFP/WebAssembly/document.pdf">Proof
document</a>
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<p style="display:none;" id="bibtex-filename">WebAssembly-AFP</p><pre id="copy-text">@article{WebAssembly-AFP,
author = {Conrad Watt},
title = {WebAssembly},
journal = {Archive of Formal Proofs},
month = {April},
year = {2018},
note = {\url{https://isa-afp.org/entries/WebAssembly.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-WebAssembly-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-WebAssembly-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-WebAssembly-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2018-04-30.tar.gz">Apr 30, 2018</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-WebAssembly-2018-04-29.tar.gz">Apr 29, 2018</a>: Isabelle2017
</li></ul>
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diff --git a/web/entries/Weight_Balanced_Trees.html b/web/entries/Weight_Balanced_Trees.html
--- a/web/entries/Weight_Balanced_Trees.html
+++ b/web/entries/Weight_Balanced_Trees.html
@@ -1,183 +1,185 @@
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<h1 >
<span class='first'>W</span>eight-<span class='first'>B</span>alanced <span class='first'>T</span>rees</h1>
<div>
<p><a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a> and <a href="../authors/dirix">Stefan Dirix</a>
</p>
<p class="date">March 13, 2018</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This theory provides a verified implementation of weight-balanced
trees following the work of <a
href="https://doi.org/10.1017/S0956796811000104">Hirai
and Yamamoto</a> who proved that all parameters in a certain
range are valid, i.e. guarantee that insertion and deletion preserve
weight-balance. Instead of a general theorem we provide parameterized
proofs of preservation of the invariant that work for many (all?)
valid parameters.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul><h3>Related publications</h3>
<ul><li>
HIRAI, Y., & YAMAMOTO, K. (2011). Balancing weight-balanced trees. Journal of Functional Programming, 21(3), 287–307. https://doi.org/10.1017/s0956796811000104
</li><li>
<a href="https://en.wikipedia.org/wiki/Weight-balanced_tree">Wikipedia</a>
</li></ul>
<h3>Session Weight_Balanced_Trees</h3>
<ul>
<li><a href="../theories/weight_balanced_trees/#Weight_Balanced_Trees_log">Weight_Balanced_Trees_log</a></li>
<li><a href="../theories/weight_balanced_trees/#Weight_Balanced_Trees">Weight_Balanced_Trees</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Weight_Balanced_Trees-AFP</p><pre id="copy-text">@article{Weight_Balanced_Trees-AFP,
author = {Tobias Nipkow and Stefan Dirix},
title = {Weight-Balanced Trees},
journal = {Archive of Formal Proofs},
month = {March},
year = {2018},
note = {\url{https://isa-afp.org/entries/Weight_Balanced_Trees.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Weight_Balanced_Trees-2018-03-13.tar.gz">Mar 13, 2018</a>: Isabelle2017
</li></ul>
</div>
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<h1 >
<span class='first'>P</span>ólya’s <span class='first'>P</span>roof of the <span class='first'>W</span>eighted <span class='first'>A</span>rithmetic–<span class='first'>G</span>eometric <span class='first'>M</span>ean <span class='first'>I</span>nequality</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">July 11, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of the Weighted
Arithmetic–Geometric Mean Inequality: given non-negative reals $a_1,
\ldots, a_n$ and non-negative weights $w_1, \ldots, w_n$ such that
$w_1 + \ldots + w_n = 1$, we have \[\prod\limits_{i=1}^n a_i^{w_i}
\leq \sum\limits_{i=1}^n w_i a_i\ .\] If the weights are additionally
all non-zero, equality holds if and only if $a_1 = \ldots =
a_n$.</p> <p>As a corollary with $w_1 = \ldots = w_n =
1/n$, the regular arithmetic–geometric mean inequality follows, namely
that \[\sqrt[n]{a_1\,\cdots\, a_n} \leq \tfrac{1}{n}(a_1 + \ldots +
a_n)\ .\]</p> <p>I follow Pólya's elegant proof,
which uses the inequality $1 + x \leq e^x$ as a starting point. Pólya
claims that this proof came to him in a dream, and that it was “the
best mathematics he had ever dreamt.”</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Weighted_Arithmetic_Geometric_Mean</h3>
<ul>
<li><a href="../theories/weighted_arithmetic_geometric_mean/#Weighted_Arithmetic_Geometric_Mean">Weighted_Arithmetic_Geometric_Mean</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Weighted_Arithmetic_Geometric_Mean-AFP</p><pre id="copy-text">@article{Weighted_Arithmetic_Geometric_Mean-AFP,
author = {Manuel Eberl},
title = {Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/Weighted_Arithmetic_Geometric_Mean.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Weighted_Arithmetic_Geometric_Mean-2022-07-11.tar.gz">Jul 11, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Weighted_Path_Order.html b/web/entries/Weighted_Path_Order.html
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<h1 >
<span class='first'>A</span> <span class='first'>F</span>ormalization of <span class='first'>W</span>eighted <span class='first'>P</span>ath <span class='first'>O</span>rders and <span class='first'>R</span>ecursive <span class='first'>P</span>ath <span class='first'>O</span>rders</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>, <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbImFpc3QiLCJnbyIsImpwIl0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
</p>
<p class="date">September 16, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">We define the weighted path order (WPO) and formalize several
properties such as strong normalization, the subterm property, and
closure properties under substitutions and contexts. Our definition of
WPO extends the original definition by also permitting multiset
comparisons of arguments instead of just lexicographic extensions.
Therefore, our WPO not only subsumes lexicographic path orders (LPO),
but also recursive path orders (RPO). We formally prove these
subsumptions and therefore all of the mentioned properties of WPO are
automatically transferable to LPO and RPO as well. Such a
transformation is not required for Knuth&ndash;Bendix orders
(KBO), since they have already been formalized. Nevertheless, we still
provide a proof that WPO subsumes KBO and thereby underline the
generality of WPO.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li></ul>
<h3>Session Weighted_Path_Order</h3>
<ul>
<li><a href="../theories/weighted_path_order/#Status">Status</a></li>
<li><a href="../theories/weighted_path_order/#Precedence">Precedence</a></li>
<li><a href="../theories/weighted_path_order/#Relations">Relations</a></li>
<li><a href="../theories/weighted_path_order/#List_Order">List_Order</a></li>
<li><a href="../theories/weighted_path_order/#Multiset_Extension_Pair">Multiset_Extension_Pair</a></li>
<li><a href="../theories/weighted_path_order/#Multiset_Extension_Pair_Impl">Multiset_Extension_Pair_Impl</a></li>
<li><a href="../theories/weighted_path_order/#Multiset_Extension2">Multiset_Extension2</a></li>
<li><a href="../theories/weighted_path_order/#Multiset_Extension2_Impl">Multiset_Extension2_Impl</a></li>
<li><a href="../theories/weighted_path_order/#WPO">WPO</a></li>
<li><a href="../theories/weighted_path_order/#RPO">RPO</a></li>
<li><a href="../theories/weighted_path_order/#LPO">LPO</a></li>
<li><a href="../theories/weighted_path_order/#KBO_Transformation">KBO_Transformation</a></li>
<li><a href="../theories/weighted_path_order/#KBO_as_WPO">KBO_as_WPO</a></li>
<li><a href="../theories/weighted_path_order/#Executable_Orders">Executable_Orders</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Multiset_Ordering_NPC.html">The Generalized Multiset Ordering is NP-Complete</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Weighted_Path_Order-AFP</p><pre id="copy-text">@article{Weighted_Path_Order-AFP,
author = {Christian Sternagel and René Thiemann and Akihisa Yamada},
title = {A Formalization of Weighted Path Orders and Recursive Path Orders},
journal = {Archive of Formal Proofs},
month = {September},
year = {2021},
note = {\url{https://isa-afp.org/entries/Weighted_Path_Order.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Weighted_Path_Order-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Weighted_Path_Order-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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diff --git a/web/entries/Well_Quasi_Orders.html b/web/entries/Well_Quasi_Orders.html
--- a/web/entries/Well_Quasi_Orders.html
+++ b/web/entries/Well_Quasi_Orders.html
@@ -1,230 +1,232 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Well-Quasi-Orders - Archive of Formal Proofs</title><meta name="description" content="Based on Isabelle/HOL&#39;s type class for preorders, we introduce a type class for well-quasi-orders (wqo) which is characterized by the absence of &#34;bad&#34;..."><meta property="og:title" content="Well-Quasi-Orders" />
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<h1 >
<span class='first'>W</span>ell-<span class='first'>Q</span>uasi-<span class='first'>O</span>rders</h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a>
</p>
<p class="date">April 13, 2012</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Based on Isabelle/HOL's type class for preorders,
we introduce a type class for well-quasi-orders (wqo)
which is characterized by the absence of "bad" sequences
(our proofs are along the lines of the proof of Nash-Williams,
from which we also borrow terminology). Our main results are
instantiations for the product type, the list type, and a type of finite trees,
which (almost) directly follow from our proofs of (1) Dickson's Lemma, (2)
Higman's Lemma, and (3) Kruskal's Tree Theorem. More concretely:
<ul>
<li>If the sets A and B are wqo then their Cartesian product is wqo.</li>
<li>If the set A is wqo then the set of finite lists over A is wqo.</li>
<li>If the set A is wqo then the set of finite trees over A is wqo.</li>
</ul>
The research was funded by the Austrian Science Fund (FWF): J3202.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>History</h3>
<dl><dt>June 8, 2017</dt>
<dd>Proved (classical) equivalence to inductive definition of
almost-full relations according to the ITP 2012 paper "Stop When You Are
Almost-Full" by Vytiniotis, Coquand, and Wahlstedt.</dd><dt>January 3, 2016</dt>
<dd>An alternative proof of Higman's lemma by open induction.<br></dd><dt>July 9, 2014</dt>
<dd>Simplified proofs of Higman's lemma and Kruskal's tree theorem,
based on homogeneous sequences.<br>
</dd><dt>May 16, 2013</dt>
<dd>Simplified construction of minimal bad sequences.<br></dd><dt>December 19, 2012</dt>
<dd>New variant of Kruskal's tree theorem for terms (as opposed to
variadic terms, i.e., trees), plus finite version of the tree theorem as
corollary.<br>
</dd><dt>June 11, 2012</dt>
<dd>Added Kruskal's Tree Theorem.<br></dd></dl><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li></ul>
<h3>Session Well_Quasi_Orders</h3>
<ul>
<li><a href="../theories/well_quasi_orders/#Infinite_Sequences">Infinite_Sequences</a></li>
<li><a href="../theories/well_quasi_orders/#Minimal_Elements">Minimal_Elements</a></li>
<li><a href="../theories/well_quasi_orders/#Least_Enum">Least_Enum</a></li>
<li><a href="../theories/well_quasi_orders/#Almost_Full">Almost_Full</a></li>
<li><a href="../theories/well_quasi_orders/#Minimal_Bad_Sequences">Minimal_Bad_Sequences</a></li>
<li><a href="../theories/well_quasi_orders/#Higman_OI">Higman_OI</a></li>
<li><a href="../theories/well_quasi_orders/#Almost_Full_Relations">Almost_Full_Relations</a></li>
<li><a href="../theories/well_quasi_orders/#Well_Quasi_Orders">Well_Quasi_Orders</a></li>
<li><a href="../theories/well_quasi_orders/#Kruskal">Kruskal</a></li>
<li><a href="../theories/well_quasi_orders/#Kruskal_Examples">Kruskal_Examples</a></li>
<li><a href="../theories/well_quasi_orders/#Wqo_Instances">Wqo_Instances</a></li>
<li><a href="../theories/well_quasi_orders/#Multiset_Extension">Multiset_Extension</a></li>
<li><a href="../theories/well_quasi_orders/#Wqo_Multiset">Wqo_Multiset</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></li><li><a href="../entries/Open_Induction.html">Open Induction</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Saturation_Framework_Extensions.html">Extensions to the Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Saturation_Framework.html">A Comprehensive Framework for Saturation Theorem Proving</a></li><li><a href="../entries/Decreasing-Diagrams-II.html">Decreasing Diagrams II</a></li><li><a href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></li><li><a href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Well_Quasi_Orders-AFP</p><pre id="copy-text">@article{Well_Quasi_Orders-AFP,
author = {Christian Sternagel},
title = {Well-Quasi-Orders},
journal = {Archive of Formal Proofs},
month = {April},
year = {2012},
note = {\url{https://isa-afp.org/entries/Well_Quasi_Orders.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<a href="https://www.isa-afp.org/release/afp-Well_Quasi_Orders-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
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<a href="https://www.isa-afp.org/release/afp-Well_Quasi_Orders-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
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diff --git a/web/entries/Wetzels_Problem.html b/web/entries/Wetzels_Problem.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>Wetzel&#39;s Problem and the Continuum Hypothesis - Archive of Formal Proofs</title><meta name="description" content="Let $F$ be a set of analytic functions on the complex plane such that, for each $z\in\mathbb{C}$, the set $\{f(z) \mid f\in F\}$ is countable; must then..."><meta property="og:title" content="Wetzel&#39;s Problem and the Continuum Hypothesis" />
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<h1 >
<span class='first'>W</span>etzel's <span class='first'>P</span>roblem and the <span class='first'>C</span>ontinuum <span class='first'>H</span>ypothesis</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a>
</p>
<p class="date">February 18, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Let $F$ be a set of analytic functions on the complex plane such that,
for each $z\in\mathbb{C}$, the set $\{f(z) \mid f\in F\}$ is
countable; must then $F$ itself be countable? The answer is yes if the
Continuum Hypothesis is false, i.e., if the cardinality of
$\mathbb{R}$ exceeds $\aleph_1$. But if CH is true then such an $F$,
of cardinality $\aleph_1$, can be constructed by transfinite
recursion. The formal proof illustrates reasoning about complex
analysis (analytic and homomorphic functions) and set theory
(transfinite cardinalities) in a single setting. The mathematical text
comes from <em>Proofs from THE BOOK</em> by Aigner and
Ziegler.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session Wetzels_Problem</h3>
<ul>
<li><a href="../theories/wetzels_problem/#Wetzels_Problem">Wetzels_Problem</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/ZFC_in_HOL.html">Zermelo Fraenkel Set Theory in Higher-Order Logic</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
<ul class="horizontal-list">
<li><a href="../entries/Lucas_Theorem.html">Lucas&rsquo;s Theorem</a></li>
<li><a href="../entries/Winding_Number_Eval.html">Evaluate Winding Numbers through Cauchy Indices</a></li>
<li><a href="../entries/Quick_Sort_Cost.html">The number of comparisons in QuickSort</a></li>
<li><a href="../entries/Cartan_FP.html">The Cartan Fixed Point Theorems</a></li>
<li><a href="../entries/ShortestPath.html">An Axiomatic Characterization of the Single-Source Shortest Path Problem</a></li>
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<p style="display:none;" id="bibtex-filename">Wetzels_Problem-AFP</p><pre id="copy-text">@article{Wetzels_Problem-AFP,
author = {Lawrence C. Paulson},
title = {Wetzel&#39;s Problem and the Continuum Hypothesis},
journal = {Archive of Formal Proofs},
month = {February},
year = {2022},
note = {\url{https://isa-afp.org/entries/Wetzels_Problem.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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-
+ <p>Older releases:</p>
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+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Wetzels_Problem-2022-02-21.tar.gz">Feb 21, 2022</a>: Isabelle2021-1
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diff --git a/web/entries/Winding_Number_Eval.html b/web/entries/Winding_Number_Eval.html
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<h1 >
<span class='first'>E</span>valuate <span class='first'>W</span>inding <span class='first'>N</span>umbers <span class='first'>T</span>hrough <span class='first'>C</span>auchy <span class='first'>I</span>ndices</h1>
<div>
<p><a href="../authors/li">Wenda Li</a> <a href="https://www.cl.cam.ac.uk/~wl302/">🌐</a>
</p>
<p class="date">October 17, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">In complex analysis, the winding number measures the number of times a
path (counterclockwise) winds around a point, while the Cauchy index
can approximate how the path winds. This entry provides a
formalisation of the Cauchy index, which is then shown to be related
to the winding number. In addition, this entry also offers a tactic
that enables users to evaluate the winding number by calculating
Cauchy indices.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Winding_Number_Eval</h3>
<ul>
<li><a href="../theories/winding_number_eval/#Missing_Topology">Missing_Topology</a></li>
<li><a href="../theories/winding_number_eval/#Missing_Algebraic">Missing_Algebraic</a></li>
<li><a href="../theories/winding_number_eval/#Missing_Transcendental">Missing_Transcendental</a></li>
<li><a href="../theories/winding_number_eval/#Missing_Analysis">Missing_Analysis</a></li>
<li><a href="../theories/winding_number_eval/#Cauchy_Index_Theorem">Cauchy_Index_Theorem</a></li>
<li><a href="../theories/winding_number_eval/#Winding_Number_Eval">Winding_Number_Eval</a></li>
<li><a href="../theories/winding_number_eval/#Winding_Number_Eval_Examples">Winding_Number_Eval_Examples</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Budan_Fourier.html">The Budan-Fourier Theorem and Counting Real Roots with Multiplicity</a></li><li><a href="../entries/Sturm_Tarski.html">The Sturm-Tarski Theorem</a></li></ul>
</div><div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Count_Complex_Roots.html">Count the Number of Complex Roots</a></li><li><a href="../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></li></ul>
</div>
<div>
<h3>Auto-related entries</h3>
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<li><a href="../entries/Wetzels_Problem.html">Wetzel&rsquo;s Problem and the Continuum Hypothesis</a></li>
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<p style="display:none;" id="bibtex-filename">Winding_Number_Eval-AFP</p><pre id="copy-text">@article{Winding_Number_Eval-AFP,
author = {Wenda Li},
title = {Evaluate Winding Numbers through Cauchy Indices},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Winding_Number_Eval.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Winding_Number_Eval-2017-10-18.tar.gz">Oct 18, 2017</a>: Isabelle2017
</li></ul>
</div>
</div>
</div>
</div>
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</html>
\ No newline at end of file
diff --git a/web/entries/Word_Lib.html b/web/entries/Word_Lib.html
--- a/web/entries/Word_Lib.html
+++ b/web/entries/Word_Lib.html
@@ -1,231 +1,233 @@
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<h1 >
<span class='first'>F</span>inite <span class='first'>M</span>achine <span class='first'>W</span>ord <span class='first'>L</span>ibrary</h1>
<div>
<p><a href="../authors/beeren">Joel Beeren</a>, <a href="../authors/fernandez">Matthew Fernandez</a>, <a href="../authors/gao">Xin Gao</a>, <a href="../authors/klein">Gerwin Klein</a> <a href="http://www.cse.unsw.edu.au/~kleing/">🌐</a>, <a href="../authors/kolanski">Rafal Kolanski</a>, <a href="../authors/lim">Japheth Lim</a>, <a href="../authors/lewis">Corey Lewis</a>, <a href="../authors/matichuk">Daniel Matichuk</a> and <a href="../authors/sewell">Thomas Sewell</a>
</p>
<p class="date">June 9, 2016</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry contains an extension to the Isabelle library for
fixed-width machine words. In particular, the entry adds quickcheck setup
for words, printing as hexadecimals, additional operations, reasoning
about alignment, signed words, enumerations of words, normalisation of
word numerals, and an extensive library of properties about generic
fixed-width words, as well as an instantiation of many of these to the
commonly used 32 and 64-bit bases.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session Word_Lib</h3>
<ul>
<li><a href="../theories/word_lib/#More_Arithmetic">More_Arithmetic</a></li>
<li><a href="../theories/word_lib/#Even_More_List">Even_More_List</a></li>
<li><a href="../theories/word_lib/#More_Sublist">More_Sublist</a></li>
<li><a href="../theories/word_lib/#More_Misc">More_Misc</a></li>
<li><a href="../theories/word_lib/#More_Divides">More_Divides</a></li>
<li><a href="../theories/word_lib/#More_Word">More_Word</a></li>
<li><a href="../theories/word_lib/#Strict_part_mono">Strict_part_mono</a></li>
<li><a href="../theories/word_lib/#Many_More">Many_More</a></li>
<li><a href="../theories/word_lib/#Bit_Shifts_Infix_Syntax">Bit_Shifts_Infix_Syntax</a></li>
<li><a href="../theories/word_lib/#Aligned">Aligned</a></li>
<li><a href="../theories/word_lib/#Next_and_Prev">Next_and_Prev</a></li>
<li><a href="../theories/word_lib/#Signed_Division_Word">Signed_Division_Word</a></li>
<li><a href="../theories/word_lib/#Bit_Comprehension">Bit_Comprehension</a></li>
<li><a href="../theories/word_lib/#Most_significant_bit">Most_significant_bit</a></li>
<li><a href="../theories/word_lib/#Least_significant_bit">Least_significant_bit</a></li>
<li><a href="../theories/word_lib/#Generic_set_bit">Generic_set_bit</a></li>
<li><a href="../theories/word_lib/#Bits_Int">Bits_Int</a></li>
<li><a href="../theories/word_lib/#Typedef_Morphisms">Typedef_Morphisms</a></li>
<li><a href="../theories/word_lib/#Singleton_Bit_Shifts">Singleton_Bit_Shifts</a></li>
<li><a href="../theories/word_lib/#Legacy_Aliases">Legacy_Aliases</a></li>
<li><a href="../theories/word_lib/#Reversed_Bit_Lists">Reversed_Bit_Lists</a></li>
<li><a href="../theories/word_lib/#Bitwise">Bitwise</a></li>
<li><a href="../theories/word_lib/#Examples">Examples</a></li>
<li><a href="../theories/word_lib/#Bit_Comprehension_Int">Bit_Comprehension_Int</a></li>
<li><a href="../theories/word_lib/#Signed_Words">Signed_Words</a></li>
<li><a href="../theories/word_lib/#Bitwise_Signed">Bitwise_Signed</a></li>
<li><a href="../theories/word_lib/#Enumeration">Enumeration</a></li>
<li><a href="../theories/word_lib/#Enumeration_Word">Enumeration_Word</a></li>
<li><a href="../theories/word_lib/#Hex_Words">Hex_Words</a></li>
<li><a href="../theories/word_lib/#Norm_Words">Norm_Words</a></li>
<li><a href="../theories/word_lib/#Rsplit">Rsplit</a></li>
<li><a href="../theories/word_lib/#Syntax_Bundles">Syntax_Bundles</a></li>
<li><a href="../theories/word_lib/#Type_Syntax">Type_Syntax</a></li>
<li><a href="../theories/word_lib/#Word_EqI">Word_EqI</a></li>
<li><a href="../theories/word_lib/#Word_Lemmas">Word_Lemmas</a></li>
<li><a href="../theories/word_lib/#Word_8">Word_8</a></li>
<li><a href="../theories/word_lib/#Word_16">Word_16</a></li>
<li><a href="../theories/word_lib/#Word_Syntax">Word_Syntax</a></li>
<li><a href="../theories/word_lib/#Word_Names">Word_Names</a></li>
<li><a href="../theories/word_lib/#More_Word_Operations">More_Word_Operations</a></li>
<li><a href="../theories/word_lib/#Word_32">Word_32</a></li>
<li><a href="../theories/word_lib/#Word_Lib_Sumo">Word_Lib_Sumo</a></li>
<li><a href="../theories/word_lib/#Machine_Word_32_Basics">Machine_Word_32_Basics</a></li>
<li><a href="../theories/word_lib/#Machine_Word_32">Machine_Word_32</a></li>
<li><a href="../theories/word_lib/#Word_64">Word_64</a></li>
<li><a href="../theories/word_lib/#Machine_Word_64_Basics">Machine_Word_64_Basics</a></li>
<li><a href="../theories/word_lib/#Machine_Word_64">Machine_Word_64</a></li>
<li><a href="../theories/word_lib/#Guide">Guide</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/X86_Semantics.html">X86 instruction semantics and basic block symbolic execution</a></li><li><a href="../entries/Interval_Arithmetic_Word32.html">Interval Arithmetic on 32-bit Words</a></li><li><a href="../entries/CakeML.html">CakeML</a></li><li><a href="../entries/Complx.html">COMPLX: A Verification Framework for Concurrent Imperative Programs</a></li><li><a href="../entries/SPARCv8.html">A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor</a></li><li><a href="../entries/IP_Addresses.html">IP Addresses</a></li><li><a href="../entries/Native_Word.html">Native Word</a></li><li><a href="../entries/IEEE_Floating_Point.html">A Formal Model of IEEE Floating Point Arithmetic</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Word_Lib-AFP</p><pre id="copy-text">@article{Word_Lib-AFP,
author = {Joel Beeren and Matthew Fernandez and Xin Gao and Gerwin Klein and Rafal Kolanski and Japheth Lim and Corey Lewis and Daniel Matichuk and Thomas Sewell},
title = {Finite Machine Word Library},
journal = {Archive of Formal Proofs},
month = {June},
year = {2016},
note = {\url{https://isa-afp.org/entries/Word_Lib.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-Word_Lib-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Word_Lib-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Word_Lib-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Word_Lib-2016-06-09.tar.gz">Jun 9, 2016</a>: Isabelle2016
</li></ul>
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\ No newline at end of file
diff --git a/web/entries/WorkerWrapper.html b/web/entries/WorkerWrapper.html
--- a/web/entries/WorkerWrapper.html
+++ b/web/entries/WorkerWrapper.html
@@ -1,210 +1,212 @@
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Worker/Wrapper Transformation - Archive of Formal Proofs</title><meta name="description" content="Gill and Hutton formalise the worker/wrapper transformation, building on the work of Launchbury and Peyton-Jones who developed it as a way of changing the..."><meta property="og:title" content="The Worker/Wrapper Transformation" />
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<h1 >
<span class='first'>T</span>he <span class='first'>W</span>orker/<span class='first'>W</span>rapper <span class='first'>T</span>ransformation</h1>
<div>
<p><a href="../authors/gammie">Peter Gammie</a> <a href="http://peteg.org">🌐</a>
</p>
<p class="date">October 30, 2009</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Gill and Hutton formalise the worker/wrapper transformation, building on the work of Launchbury and Peyton-Jones who developed it as a way of changing the type at which a recursive function operates. This development establishes the soundness of the technique and several examples of its use.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li></ul>
<h3>Session WorkerWrapper</h3>
<ul>
<li><a href="../theories/workerwrapper/#Nats">Nats</a></li>
<li><a href="../theories/workerwrapper/#LList">LList</a></li>
<li><a href="../theories/workerwrapper/#Maybe">Maybe</a></li>
<li><a href="../theories/workerwrapper/#FixedPointTheorems">FixedPointTheorems</a></li>
<li><a href="../theories/workerwrapper/#WorkerWrapper">WorkerWrapper</a></li>
<li><a href="../theories/workerwrapper/#CounterExample">CounterExample</a></li>
<li><a href="../theories/workerwrapper/#WorkerWrapperNew">WorkerWrapperNew</a></li>
<li><a href="../theories/workerwrapper/#Accumulator">Accumulator</a></li>
<li><a href="../theories/workerwrapper/#UnboxedNats">UnboxedNats</a></li>
<li><a href="../theories/workerwrapper/#Streams">Streams</a></li>
<li><a href="../theories/workerwrapper/#Continuations">Continuations</a></li>
<li><a href="../theories/workerwrapper/#Backtracking">Backtracking</a></li>
<li><a href="../theories/workerwrapper/#Nub">Nub</a></li>
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<p style="display:none;" id="bibtex-filename">WorkerWrapper-AFP</p><pre id="copy-text">@article{WorkerWrapper-AFP,
author = {Peter Gammie},
title = {The Worker/Wrapper Transformation},
journal = {Archive of Formal Proofs},
month = {October},
year = {2009},
note = {\url{https://isa-afp.org/entries/WorkerWrapper.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2014-08-28.tar.gz">Aug 28, 2014</a>: Isabelle2014
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2013-12-11.tar.gz">Dec 11, 2013</a>: Isabelle2013-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2013-11-17.tar.gz">Nov 17, 2013</a>: Isabelle2013-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2013-02-16.tar.gz">Feb 16, 2013</a>: Isabelle2013
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2012-05-24.tar.gz">May 24, 2012</a>: Isabelle2012
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2011-10-11.tar.gz">Oct 11, 2011</a>: Isabelle2011-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2011-02-11.tar.gz">Feb 11, 2011</a>: Isabelle2011
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2010-07-01.tar.gz">Jul 1, 2010</a>: Isabelle2009-2
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2009-12-12.tar.gz">Dec 12, 2009</a>: Isabelle2009-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2009-10-31.tar.gz">Oct 31, 2009</a>: Isabelle2009
</li><li>
<a href="https://www.isa-afp.org/release/afp-WorkerWrapper-2009-10-30.tar.gz">Oct 30, 2009</a>: Isabelle2009
</li></ul>
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\ No newline at end of file
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<h1 >
<span class='first'>X</span>86 <span class='first'>I</span>nstruction <span class='first'>S</span>emantics and <span class='first'>B</span>asic <span class='first'>B</span>lock <span class='first'>S</span>ymbolic <span class='first'>E</span>xecution</h1>
<div>
<p><a href="../authors/verbeek">Freek Verbeek</a> <a class="obfuscated" data="eyJob3N0IjpbInZ0IiwiZWR1Il0sInVzZXIiOlsiZnJlZWsiXX0=">📧</a>, <a href="../authors/bharadwaj">Abhijith Bharadwaj</a>, <a href="../authors/bockenek">Joshua Bockenek</a>, <a href="../authors/roessle">Ian Roessle</a>, <a href="../authors/weerwag">Timmy Weerwag</a> and <a href="../authors/ravindran">Binoy Ravindran</a>
</p>
<p class="date">October 13, 2021</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This AFP entry provides semantics for roughly 120 different X86-64
assembly instructions. These instructions include various moves,
arithmetic/logical operations, jumps, call/return, SIMD extensions and
others. External functions are supported by allowing a user to provide
custom semantics for these calls. Floating-point operations are mapped
to uninterpreted functions. The model provides semantics for register
aliasing and a byte-level little-endian memory model. The semantics
are purposefully incomplete, but overapproximative. For example, the
precise effect of flags may be undefined for certain instructions, or
instructions may simply have no semantics at all. In those cases, the
semantics are mapped to universally quantified uninterpreted terms
from a locale. Second, this entry provides a method to symbolic
execution of basic blocks. The method, called
''se_step'' (for: symbolic execution step) fetches
an instruction and updates the current symbolic state while keeping
track of assumptions made over the memory model. A key component is a
set of theorems that prove how reads from memory resolve after writes
have occurred. Thirdly, this entry provides a parser that allows the
user to copy-paste the output of the standard disassembly tool objdump
into Isabelle/HOL. A couple small and explanatory examples are
included, including functions from the word count program. Several
examples can be supplied upon request (they are not included due to
the running time of verification): functions from the floating-point
modulo function from FDLIBM, the GLIBC strlen function and the
CoreUtils SHA256 implementation.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/hardware">Computer science/Hardware</a></li><li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li></ul>
<h3>Session X86_Semantics</h3>
<ul>
<li><a href="../theories/x86_semantics/#BitByte">BitByte</a></li>
<li><a href="../theories/x86_semantics/#Memory">Memory</a></li>
<li><a href="../theories/x86_semantics/#State">State</a></li>
<li><a href="../theories/x86_semantics/#X86_InstructionSemantics">X86_InstructionSemantics</a></li>
<li><a href="../theories/x86_semantics/#StateCleanUp">StateCleanUp</a></li>
<li><a href="../theories/x86_semantics/#SymbolicExecution">SymbolicExecution</a></li>
<li><a href="../theories/x86_semantics/#Examples">Examples</a></li>
<li><a href="../theories/x86_semantics/#X86_Parse">X86_Parse</a></li>
<li><a href="../theories/x86_semantics/#Example_WC">Example_WC</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Word_Lib.html">Finite Machine Word Library</a></li></ul>
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<h4>PDFs</h4>
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<p style="display:none;" id="bibtex-filename">X86_Semantics-AFP</p><pre id="copy-text">@article{X86_Semantics-AFP,
author = {Freek Verbeek and Abhijith Bharadwaj and Joshua Bockenek and Ian Roessle and Timmy Weerwag and Binoy Ravindran},
title = {X86 instruction semantics and basic block symbolic execution},
journal = {Archive of Formal Proofs},
month = {October},
year = {2021},
note = {\url{https://isa-afp.org/entries/X86_Semantics.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-X86_Semantics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-X86_Semantics-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-X86_Semantics-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-X86_Semantics-2021-10-31.tar.gz">Oct 31, 2021</a>: Isabelle2021
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diff --git a/web/entries/XML.html b/web/entries/XML.html
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<h1 >
<span class='first'>X</span><span class='first'>M</span><span class='first'>L</span></h1>
<div>
<p><a href="../authors/sternagel">Christian Sternagel</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiYyIsInN0ZXJuYWdlbCJdfQ==">📧</a> and <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a>
</p>
<p class="date">October 3, 2014</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">This entry provides an XML library for Isabelle/HOL. This includes parsing
and pretty printing of XML trees as well as combinators for transforming XML
trees into arbitrary user-defined data. The main contribution of this entry is
an interface (fit for code generation) that allows for communication between
verified programs formalized in Isabelle/HOL and the outside world via XML.
This library was developed as part of the IsaFoR/CeTA project
to which we refer for examples of its usage.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li><li><a href="../topics/computer-science/data-structures">Computer science/Data structures</a></li></ul>
<h3>Session XML</h3>
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<li><a href="../theories/xml/#Xml">Xml</a></li>
<li><a href="../theories/xml/#Xmlt">Xmlt</a></li></ul><div class="flex-wrap">
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<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Certification_Monads.html">Certification Monads</a></li><li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li></ul>
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<li><a href="../entries/Containers.html">Light-weight Containers</a></li>
<li><a href="../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></li>
<li><a href="../entries/Deriving.html">Deriving class instances for datatypes</a></li>
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<p style="display:none;" id="bibtex-filename">XML-AFP</p><pre id="copy-text">@article{XML-AFP,
author = {Christian Sternagel and René Thiemann},
title = {XML},
journal = {Archive of Formal Proofs},
month = {October},
year = {2014},
note = {\url{https://isa-afp.org/entries/XML.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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<p>Older releases:</p>
<ul><li>
- <a href="https://www.isa-afp.org/release/afp-XML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-XML-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-XML-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2020-04-20.tar.gz">Apr 20, 2020</a>: Isabelle2020
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2019-06-11.tar.gz">Jun 11, 2019</a>: Isabelle2019
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2018-08-16.tar.gz">Aug 16, 2018</a>: Isabelle2018
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2017-10-10.tar.gz">Oct 10, 2017</a>: Isabelle2017
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2016-12-17.tar.gz">Dec 17, 2016</a>: Isabelle2016-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2016-02-22.tar.gz">Feb 22, 2016</a>: Isabelle2016
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2015-05-27.tar.gz">May 27, 2015</a>: Isabelle2015
</li><li>
<a href="https://www.isa-afp.org/release/afp-XML-2014-10-08.tar.gz">Oct 8, 2014</a>: Isabelle2014
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<h1 >
<span class='first'>Y</span>oung's <span class='first'>I</span>nequality for <span class='first'>I</span>ncreasing <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">January 31, 2022</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process">Young's inequality states that $$ ab \leq \int_0^a f(x)dx +
\int_0^b f^{-1}(y) dy $$ where $a\geq 0$, $b\geq 0$ and $f$ is
strictly increasing and continuous. Its proof is formalised following
<a href="https://www.jstor.org/stable/2318018">the
development</a> by Cunningham and Grossman. Their idea is to
make the intuitive, geometric folklore proof rigorous by reasoning
about step functions. The lack of the Riemann integral makes the
development longer than one would like, but their argument is
reproduced faithfully.</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Youngs_Inequality</h3>
<ul>
<li><a href="../theories/youngs_inequality/#Youngs">Youngs</a></li></ul><div class="flex-wrap">
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<p style="display:none;" id="bibtex-filename">Youngs_Inequality-AFP</p><pre id="copy-text">@article{Youngs_Inequality-AFP,
author = {Lawrence C. Paulson},
title = {Young&#39;s Inequality for Increasing Functions},
journal = {Archive of Formal Proofs},
month = {January},
year = {2022},
note = {\url{https://isa-afp.org/entries/Youngs_Inequality.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <ul><li>
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+ </li><li>
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<h1 >
<span class='first'>Z</span>ermelo <span class='first'>F</span>raenkel <span class='first'>S</span>et <span class='first'>T</span>heory in <span class='first'>H</span>igher-<span class='first'>O</span>rder <span class='first'>L</span>ogic</h1>
<div>
<p><a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
</p>
<p class="date">October 24, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry is a new formalisation of ZFC set theory in Isabelle/HOL. It is
logically equivalent to Obua's HOLZF; the point is to have the closest
possible integration with the rest of Isabelle/HOL, minimising the amount of
new notations and exploiting type classes.</p>
<p>There is a type <em>V</em> of sets and a function <em>elts :: V =&gt; V
set</em> mapping a set to its elements. Classes simply have type <em>V
set</em>, and a predicate identifies the small classes: those that correspond
to actual sets. Type classes connected with orders and lattices are used to
minimise the amount of new notation for concepts such as the subset relation,
union and intersection. Basic concepts — Cartesian products, disjoint sums,
natural numbers, functions, etc. — are formalised.</p>
<p>More advanced set-theoretic concepts, such as transfinite induction,
ordinals, cardinals and the transitive closure of a set, are also provided.
The definition of addition and multiplication for general sets (not just
ordinals) follows Kirby.</p>
<p>The theory provides two type classes with the aim of facilitating
developments that combine <em>V</em> with other Isabelle/HOL types:
<em>embeddable</em>, the class of types that can be injected into <em>V</em>
(including <em>V</em> itself as well as <em>V*V</em>, etc.), and
<em>small</em>, the class of types that correspond to some ZF set.</p>
extra-history =
Change history:
[2020-01-28]: Generalisation of the "small" predicate and order types to arbitrary sets;
ordinal exponentiation;
introduction of the coercion ord_of_nat :: "nat => V";
numerous new lemmas. (revision 6081d5be8d08)</div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/logic/set-theory">Logic/Set theory</a></li></ul>
<h3>Session ZFC_in_HOL</h3>
<ul>
<li><a href="../theories/zfc_in_hol/#ZFC_Library">ZFC_Library</a></li>
<li><a href="../theories/zfc_in_hol/#ZFC_in_HOL">ZFC_in_HOL</a></li>
<li><a href="../theories/zfc_in_hol/#ZFC_Cardinals">ZFC_Cardinals</a></li>
<li><a href="../theories/zfc_in_hol/#Kirby">Kirby</a></li>
<li><a href="../theories/zfc_in_hol/#Ordinal_Exp">Ordinal_Exp</a></li>
<li><a href="../theories/zfc_in_hol/#Cantor_NF">Cantor_NF</a></li>
<li><a href="../theories/zfc_in_hol/#ZFC_Typeclasses">ZFC_Typeclasses</a></li></ul><div class="flex-wrap">
<div>
<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Wetzels_Problem.html">Wetzel&rsquo;s Problem and the Continuum Hypothesis</a></li><li><a href="../entries/CZH_Foundations.html">Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</a></li><li><a href="../entries/Ordinal_Partitions.html">Ordinal Partitions</a></li><li><a href="../entries/Category3.html">Category Theory with Adjunctions and Limits</a></li></ul>
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<p style="display:none;" id="bibtex-filename">ZFC_in_HOL-AFP</p><pre id="copy-text">@article{ZFC_in_HOL-AFP,
author = {Lawrence C. Paulson},
title = {Zermelo Fraenkel Set Theory in Higher-Order Logic},
journal = {Archive of Formal Proofs},
month = {October},
year = {2019},
note = {\url{https://isa-afp.org/entries/ZFC_in_HOL.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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+ <a href="https://www.isa-afp.org/release/afp-ZFC_in_HOL-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-ZFC_in_HOL-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-ZFC_in_HOL-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Zeta_3_Irrational.html b/web/entries/Zeta_3_Irrational.html
--- a/web/entries/Zeta_3_Irrational.html
+++ b/web/entries/Zeta_3_Irrational.html
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<meta name="viewport" content="width=device-width, initial-scale=1"><title>The Irrationality of ζ(3) - Archive of Formal Proofs</title><meta name="description" content="This article provides a formalisation of Beukers&#39;s straightforward analytic proof that ζ(3) is irrational. This was first proven by Apéry (which is why..."><meta property="og:title" content="The Irrationality of ζ(3)" />
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<h1 >
<span class='first'>T</span>he <span class='first'>I</span>rrationality of Ζ(3)</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">December 27, 2019</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This article provides a formalisation of Beukers's
straightforward analytic proof that ζ(3) is irrational. This was first
proven by Apéry (which is why this result is also often called
‘Apéry's Theorem’) using a more algebraic approach. This
formalisation follows <a
href="http://people.math.sc.edu/filaseta/gradcourses/Math785/Math785Notes4.pdf">Filaseta's
presentation</a> of Beukers's proof.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li></ul>
<h3>Session Zeta_3_Irrational</h3>
<ul>
<li><a href="../theories/zeta_3_irrational/#Zeta_3_Irrational">Zeta_3_Irrational</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/E_Transcendental.html">The Transcendence of e</a></li><li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li></ul>
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<li><a href="../entries/Hello_World.html">Hello World</a></li>
<li><a href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></li>
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<p style="display:none;" id="bibtex-filename">Zeta_3_Irrational-AFP</p><pre id="copy-text">@article{Zeta_3_Irrational-AFP,
author = {Manuel Eberl},
title = {The Irrationality of ζ(3)},
journal = {Archive of Formal Proofs},
month = {December},
year = {2019},
note = {\url{https://isa-afp.org/entries/Zeta_3_Irrational.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Zeta_3_Irrational-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Zeta_3_Irrational-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
+ <a href="https://www.isa-afp.org/release/afp-Zeta_3_Irrational-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021-1
</li><li>
<a href="https://www.isa-afp.org/release/afp-Zeta_3_Irrational-2021-02-23.tar.gz">Feb 23, 2021</a>: Isabelle2021
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diff --git a/web/entries/Zeta_Function.html b/web/entries/Zeta_Function.html
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@@ -1,198 +1,200 @@
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<h1 >
<span class='first'>T</span>he <span class='first'>H</span>urwitz and <span class='first'>R</span>iemann Ζ <span class='first'>F</span>unctions</h1>
<div>
<p><a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
</p>
<p class="date">October 12, 2017</p>
</div>
</header><div><main><h3>Abstract</h3>
<div class="abstract mathjax_process"><p>This entry builds upon the results about formal and analytic Dirichlet
series to define the Hurwitz &zeta; function &zeta;(<em>a</em>,<em>s</em>) and,
based on that, the Riemann &zeta; function &zeta;(<em>s</em>).
This is done by first defining them for &real;(<em>z</em>) > 1
and then successively extending the domain to the left using the
Euler&ndash;MacLaurin formula.</p>
<p>Apart from the most basic facts such as analyticity, the following
results are provided:</p>
<ul>
<li>the Stieltjes constants and the Laurent expansion of
&zeta;(<em>s</em>) at <em>s</em> = 1</li>
<li>the non-vanishing of &zeta;(<em>s</em>)
for &real;(<em>z</em>) &ge; 1</li>
<li>the relationship between &zeta;(<em>a</em>,<em>s</em>) and &Gamma;</li>
<li>the special values at negative integers and positive even integers</li>
<li>Hurwitz's formula and the reflection formula for &zeta;(<em>s</em>)</li>
<li>the <a href="https://arxiv.org/abs/math/0405478">
Hadjicostas&ndash;Chapman formula</a></li>
</ul>
<p>The entry also contains Euler's analytic proof of the infinitude of primes,
based on the fact that &zeta;(<i>s</i>) has a pole at <i>s</i> = 1.</p></div>
<h3>License</h3>
<div><a href="https://isa-afp.org/LICENSE">BSD License</a></div><h3>Topics</h3>
<ul><li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li><li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li></ul>
<h3>Session Zeta_Function</h3>
<ul>
<li><a href="../theories/zeta_function/#Zeta_Library">Zeta_Library</a></li>
<li><a href="../theories/zeta_function/#Zeta_Function">Zeta_Function</a></li>
<li><a href="../theories/zeta_function/#Zeta_Laurent_Expansion">Zeta_Laurent_Expansion</a></li>
<li><a href="../theories/zeta_function/#Hadjicostas_Chapman">Hadjicostas_Chapman</a></li></ul><div class="flex-wrap">
<div>
<h3>Depends on</h3>
<ul class="horizontal-list"><li><a href="../entries/Bernoulli.html">Bernoulli Numbers</a></li><li><a href="../entries/Dirichlet_Series.html">Dirichlet Series</a></li><li><a href="../entries/Euler_MacLaurin.html">The Euler–MacLaurin Formula</a></li><li><a href="../entries/Winding_Number_Eval.html">Evaluate Winding Numbers through Cauchy Indices</a></li></ul>
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<h3>Used by</h3>
<ul class="horizontal-list"><li><a href="../entries/Prime_Distribution_Elementary.html">Elementary Facts About the Distribution of Primes</a></li><li><a href="../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></li><li><a href="../entries/Dirichlet_L.html">Dirichlet L-Functions and Dirichlet&rsquo;s Theorem</a></li></ul>
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<p style="display:none;" id="bibtex-filename">Zeta_Function-AFP</p><pre id="copy-text">@article{Zeta_Function-AFP,
author = {Manuel Eberl},
title = {The Hurwitz and Riemann ζ Functions},
journal = {Archive of Formal Proofs},
month = {October},
year = {2017},
note = {\url{https://isa-afp.org/entries/Zeta_Function.html},
Formal proof development},
ISSN = {2150-914x},
}</pre>
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- <a href="https://www.isa-afp.org/release/afp-Zeta_Function-2021-12-14.tar.gz">Dec 14, 2021</a>: Isabelle2021
+ <a href="https://www.isa-afp.org/release/afp-Zeta_Function-2022-10-27.tar.gz">Oct 27, 2022</a>: Isabelle2022
+ </li><li>
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<h1 >
<span class='first'>P</span><span class='first'>G</span><span class='first'>C</span><span class='first'>L</span> for <span class='first'>I</span>sabelle</h1>
<div>
<p><a href="../authors/cock">David Cock</a> <a class="obfuscated" data="eyJob3N0IjpbIm5pY3RhIiwiY29tIiwiYXUiXSwidXNlciI6WyJkYXZpZCIsImNvY2siXX0=">📧</a>
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<p class="date">July 13, 2014</p>
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<div class="abstract mathjax_process"><p>pGCL is both a programming language and a specification language that
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manner. Program verification is by refinement or annotation (or both), using
either Hoare triples, or weakest-precondition entailment, in the style of
GCL.</p>
<p> This package provides both a shallow embedding of the language
primitives, and an annotation and refinement framework. The generated
document includes a brief tutorial.</p></div>
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author = {David Cock},
title = {pGCL for Isabelle},
journal = {Archive of Formal Proofs},
month = {July},
year = {2014},
note = {\url{https://isa-afp.org/entries/pGCL.html},
Formal proof development},
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