diff --git a/metadata/authors.toml b/metadata/authors.toml --- a/metadata/authors.toml +++ b/metadata/authors.toml @@ -1,3551 +1,3488 @@ [lange] name = "Christoph Lange" [lange.emails] lange_email = "math.semantic.web@gmail.com" [lange.homepages] [petrovic] name = "Danijela Petrovic" [petrovic.emails] [petrovic.homepages] petrovic_homepage = "http://www.matf.bg.ac.rs/~danijela" [schimpf] name = "Alexander Schimpf" [schimpf.emails] schimpf_email = "schimpfa@informatik.uni-freiburg.de" [schimpf.homepages] [murao] name = "H. Murao" [murao.emails] [murao.homepages] [bourke] name = "Timothy Bourke" [bourke.emails] bourke_email = "tim@tbrk.org" [bourke.homepages] bourke_homepage = "http://www.tbrk.org" [schaeffeler] name = "Maximilian Schäffeler" [schaeffeler.emails] schaeffeler_email = "schaeffm@in.tum.de" [schaeffeler.homepages] [liut] name = "Tao Liu" [liut.emails] [liut.homepages] [sickert] name = "Salomon Sickert" [sickert.emails] sickert_email = "s.sickert@tum.de" -sickert_email1 = "sickert@in.tum.de" [sickert.homepages] sickert_homepage = "https://www7.in.tum.de/~sickert" [lutz] name = "Bianca Lutz" [lutz.emails] lutz_email = "sowilo@cs.tu-berlin.de" [lutz.homepages] [rizkallah] name = "Christine Rizkallah" [rizkallah.emails] [rizkallah.homepages] rizkallah_homepage = "https://www.mpi-inf.mpg.de/~crizkall/" [pollak] name = "Florian Pollak" [pollak.emails] pollak_email = "florian.pollak@gmail.com" [pollak.homepages] [sulejmani] name = "Ujkan Sulejmani" [sulejmani.emails] [sulejmani.homepages] [biendarra] name = "Julian Biendarra" [biendarra.emails] [biendarra.homepages] [saile] name = "Christian Saile" [saile.emails] [saile.homepages] saile_homepage = "http://dss.in.tum.de/staff/christian-saile.html" [friedrich] name = "Stefan Friedrich" [friedrich.emails] [friedrich.homepages] [maximova] name = "Alexandra Maximova" [maximova.emails] maximova_email = "amaximov@student.ethz.ch" [maximova.homepages] [stricker] name = "Christian Stricker" [stricker.emails] [stricker.homepages] stricker_homepage = "http://dss.in.tum.de/staff/christian-stricker.html" [dyckhoff] name = "Roy Dyckhoff" [dyckhoff.emails] [dyckhoff.homepages] dyckhoff_homepage = "https://rd.host.cs.st-andrews.ac.uk" [weidner] name = "Arno Wilhelm-Weidner" [weidner.emails] weidner_email = "arno.wilhelm-weidner@tu-berlin.de" [weidner.homepages] [thomson] name = "Fox Thomson" [thomson.emails] thomson_email = "foxthomson0@gmail.com" [thomson.homepages] [he] name = "Yijun He" [he.emails] he_email = "yh403@cam.ac.uk" [he.homepages] [kammueller] name = "Florian Kammüller" [kammueller.emails] kammueller_email = "flokam@cs.tu-berlin.de" kammueller_email1 = "florian.kammuller@gmail.com" [kammueller.homepages] kammueller_homepage = "http://www.cs.mdx.ac.uk/people/florian-kammueller/" [oostrom] name = "Vincent van Oostrom" [oostrom.emails] [oostrom.homepages] [klein] name = "Gerwin Klein" [klein.emails] -klein_email = "kleing@cse.unsw.edu.au" -klein_email1 = "kleing@unsw.edu.au" +klein_email = "kleing@unsw.edu.au" [klein.homepages] klein_homepage = "http://www.cse.unsw.edu.au/~kleing/" [simic] name = "Danijela Simić" [simic.emails] simic_email = "danijela@matf.bg.ac.rs" [simic.homepages] simic_homepage = "http://poincare.matf.bg.ac.rs/~danijela" [gao] name = "Xin Gao" [gao.emails] [gao.homepages] [guttmann] name = "Walter Guttmann" [guttmann.emails] guttmann_email = "walter.guttmann@canterbury.ac.nz" -guttmann_email1 = "walter.guttman@canterbury.ac.nz" [guttmann.homepages] -guttmann_homepage = "http://www.cosc.canterbury.ac.nz/walter.guttmann/" -guttmann_homepage1 = "https://www.cosc.canterbury.ac.nz/walter.guttmann/" +guttmann_homepage = "https://www.cosc.canterbury.ac.nz/walter.guttmann/" [mantel] name = "Heiko Mantel" [mantel.emails] mantel_email = "mantel@mais.informatik.tu-darmstadt.de" [mantel.homepages] [schlichtkrull] name = "Anders Schlichtkrull" [schlichtkrull.emails] schlichtkrull_email = "andschl@dtu.dk" [schlichtkrull.homepages] schlichtkrull_homepage = "https://people.compute.dtu.dk/andschl/" [jaskolka] name = "Jason Jaskolka" [jaskolka.emails] jaskolka_email = "jason.jaskolka@carleton.ca" [jaskolka.homepages] jaskolka_homepage = "https://carleton.ca/jaskolka/" [rau] name = "Martin Rau" [rau.emails] rau_email = "martin.rau@tum.de" rau_email1 = "mrtnrau@googlemail.com" [rau.homepages] [bottesch] name = "Ralph Bottesch" [bottesch.emails] bottesch_email = "ralph.bottesch@uibk.ac.at" [bottesch.homepages] bottesch_homepage = "http://cl-informatik.uibk.ac.at/users/bottesch/" [bella] name = "Giampaolo Bella" [bella.emails] bella_email = "giamp@dmi.unict.it" [bella.homepages] bella_homepage = "http://www.dmi.unict.it/~giamp/" [dirix] name = "Stefan Dirix" [dirix.emails] [dirix.homepages] [nielsen] name = "Finn Nielsen" [nielsen.emails] nielsen_email = "finn.nielsen@uni-muenster.de" [nielsen.homepages] [mansky] name = "Susannah Mansky" [mansky.emails] mansky_email = "sjohnsn2@illinois.edu" mansky_email1 = "susannahej@gmail.com" [mansky.homepages] [dunaev] name = "Georgy Dunaev" [dunaev.emails] dunaev_email = "georgedunaev@gmail.com" [dunaev.homepages] [li] name = "Wenda Li" [li.emails] li_email = "wl302@cam.ac.uk" li_email1 = "liwenda1990@hotmail.com" [li.homepages] li_homepage = "https://www.cl.cam.ac.uk/~wl302/" -li_homepage1 = "http://www.cl.cam.ac.uk/~wl302/" [stevens] name = "Lukas Stevens" [stevens.emails] [stevens.homepages] stevens_homepage = "https://www21.in.tum.de/team/stevensl" [tourret] name = "Sophie Tourret" [tourret.emails] tourret_email = "stourret@mpi-inf.mpg.de" [tourret.homepages] tourret_homepage = "https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret/" -tourret_homepage1 = "https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret" [yu] name = "Lei Yu" [yu.emails] yu_email = "ly271@cam.ac.uk" [yu.homepages] [grewe] name = "Sylvia Grewe" [grewe.emails] -grewe_email = "grewe@st.informatik.tu-darmstadt.de" -grewe_email1 = "grewe@cs.tu-darmstadt.de" +grewe_email = "grewe@cs.tu-darmstadt.de" [grewe.homepages] [coghetto] name = "Roland Coghetto" [coghetto.emails] coghetto_email = "roland_coghetto@hotmail.com" [coghetto.homepages] [schirmer] name = "Norbert Schirmer" [schirmer.emails] schirmer_email = "norbert.schirmer@web.de" -schirmer_email1 = "schirmer@in.tum.de" [schirmer.homepages] [immler] name = "Fabian Immler" [immler.emails] immler_email = "immler@in.tum.de" immler_email1 = "fimmler@cs.cmu.edu" -immler_email2 = "fimmler@andrew.cmu.edu" [immler.homepages] -immler_homepage = "http://www21.in.tum.de/~immler" -immler_homepage1 = "https://home.in.tum.de/~immler/" -immler_homepage2 = "http://home.in.tum.de/~immler/" +immler_homepage = "https://home.in.tum.de/~immler/" [tiu] name = "Alwen Tiu" [tiu.emails] tiu_email = "ATiu@ntu.edu.sg" [tiu.homepages] tiu_homepage = "http://users.cecs.anu.edu.au/~tiu/" [henrio] name = "Ludovic Henrio" [henrio.emails] henrio_email = "Ludovic.Henrio@sophia.inria.fr" [henrio.homepages] [urban] name = "Christian Urban" [urban.emails] urban_email = "christian.urban@kcl.ac.uk" [urban.homepages] -urban_homepage = "http://www.inf.kcl.ac.uk/staff/urbanc/" -urban_homepage1 = "https://nms.kcl.ac.uk/christian.urban/" +urban_homepage = "https://nms.kcl.ac.uk/christian.urban/" [michaelis] name = "Julius Michaelis" [michaelis.emails] michaelis_email = "isabelleopenflow@liftm.de" michaelis_email1 = "maintainafpppt@liftm.de" michaelis_email2 = "bdd@liftm.de" michaelis_email3 = "afp@liftm.de" [michaelis.homepages] -michaelis_homepage = "http://liftm.de" -michaelis_homepage1 = "http://liftm.de/" +michaelis_homepage = "http://liftm.de/" [scott] name = "Dana Scott" [scott.emails] [scott.homepages] scott_homepage = "http://www.cs.cmu.edu/~scott/" [wenzel] name = "Makarius Wenzel" [wenzel.emails] wenzel_email = "Makarius.wenzel@lri.fr" [wenzel.homepages] [dardinier] name = "Thibault Dardinier" [dardinier.emails] dardinier_email = "thibault.dardinier@inf.ethz.ch" -dardinier_email1 = "tdardini@student.ethz.ch" [dardinier.homepages] dardinier_homepage = "https://dardinier.me/" [lallemand] name = "Joseph Lallemand" [lallemand.emails] lallemand_email = "joseph.lallemand@loria.fr" [lallemand.homepages] [schmoetten] name = "Richard Schmoetten" [schmoetten.emails] schmoetten_email = "s1311325@sms.ed.ac.uk" [schmoetten.homepages] [cohen] name = "Ernie Cohen" [cohen.emails] cohen_email = "ecohen@amazon.com" [cohen.homepages] [chapman] name = "Peter Chapman" [chapman.emails] chapman_email = "pc@cs.st-andrews.ac.uk" [chapman.homepages] [rickmann] name = "Christina Rickmann" [rickmann.emails] rickmann_email = "c.rickmann@tu-berlin.de" [rickmann.homepages] [raya] name = "Rodrigo Raya" [raya.emails] [raya.homepages] raya_homepage = "https://people.epfl.ch/rodrigo.raya" [kadzioka] name = "Jakub Kądziołka" [kadzioka.emails] kadzioka_email = "kuba@kadziolka.net" [kadzioka.homepages] [foster] name = "Michael Foster" [foster.emails] foster_email = "m.foster@sheffield.ac.uk" [foster.homepages] [zhann] name = "Naijun Zhan" [zhann.emails] [zhann.homepages] [fuenmayor] name = "David Fuenmayor" [fuenmayor.emails] fuenmayor_email = "davfuenmayor@gmail.com" [fuenmayor.homepages] [iwama] name = "Fumiya Iwama" [iwama.emails] iwama_email = "d1623001@s.konan-u.ac.jp" [iwama.homepages] [feliachi] name = "Abderrahmane Feliachi" [feliachi.emails] feliachi_email = "abderrahmane.feliachi@lri.fr" [feliachi.homepages] [sudbrock] name = "Henning Sudbrock" [sudbrock.emails] sudbrock_email = "sudbrock@mais.informatik.tu-darmstadt.de" [sudbrock.homepages] [bauer] name = "Gertrud Bauer" [bauer.emails] [bauer.homepages] [lux] name = "Alexander Lux" [lux.emails] lux_email = "lux@mais.informatik.tu-darmstadt.de" [lux.homepages] [seidler] name = "Henning Seidler" [seidler.emails] seidler_email = "henning.seidler@mailbox.tu-berlin.de" [seidler.homepages] [desharnais] name = "Martin Desharnais" [desharnais.emails] desharnais_email = "martin.desharnais@unibw.de" [desharnais.homepages] desharnais_homepage = "https://martin.desharnais.me" [wasserrab] name = "Daniel Wasserrab" [wasserrab.emails] [wasserrab.homepages] wasserrab_homepage = "http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php" [fell] name = "Julian Fell" [fell.emails] fell_email = "julian.fell@uq.net.au" [fell.homepages] [zhan] name = "Bohua Zhan" [zhan.emails] zhan_email = "bzhan@ios.ac.cn" [zhan.homepages] zhan_homepage = "http://lcs.ios.ac.cn/~bzhan/" [stephan] name = "Werner Stephan" [stephan.emails] stephan_email = "stephan@dfki.de" [stephan.homepages] [david] name = "Marco David" [david.emails] david_email = "marco.david@hotmail.de" [david.homepages] [olm] name = "Markus Müller-Olm" [olm.emails] [olm.homepages] olm_homepage = "http://cs.uni-muenster.de/u/mmo/" [havle] name = "Oto Havle" [havle.emails] havle_email = "oha@sysgo.com" [havle.homepages] [margetson] name = "James Margetson" [margetson.emails] [margetson.homepages] [scharager] name = "Matias Scharager" [scharager.emails] scharager_email = "mscharag@cs.cmu.edu" [scharager.homepages] [haftmann] name = "Florian Haftmann" [haftmann.emails] haftmann_email = "florian.haftmann@informatik.tu-muenchen.de" [haftmann.homepages] haftmann_homepage = "http://isabelle.in.tum.de/~haftmann" [schoepe] name = "Daniel Schoepe" [schoepe.emails] schoepe_email = "daniel@schoepe.org" [schoepe.homepages] [nagele] name = "Julian Nagele" [nagele.emails] nagele_email = "julian.nagele@uibk.ac.at" [nagele.homepages] [hoefner] name = "Peter Höfner" [hoefner.emails] hoefner_email = "peter@hoefner-online.de" [hoefner.homepages] hoefner_homepage = "http://www.hoefner-online.de/" [derrick] name = "John Derrick" [derrick.emails] derrick_email = "j.derrick@sheffield.ac.uk" [derrick.homepages] [beeren] name = "Joel Beeren" [beeren.emails] [beeren.homepages] [echenim] name = "Mnacho Echenim" [echenim.emails] echenim_email = "mnacho.echenim@univ-grenoble-alpes.fr" [echenim.homepages] -echenim_homepage = "http://lig-membres.imag.fr/mechenim/" -echenim_homepage1 = "https://lig-membres.imag.fr/mechenim/" +echenim_homepage = "https://lig-membres.imag.fr/mechenim/" [vytiniotis] name = "Dimitrios Vytiniotis" [vytiniotis.emails] [vytiniotis.homepages] vytiniotis_homepage = "http://research.microsoft.com/en-us/people/dimitris/" [beringer] name = "Lennart Beringer" [beringer.emails] beringer_email = "lennart.beringer@ifi.lmu.de" [beringer.homepages] [wickerson] name = "John Wickerson" [wickerson.emails] [wickerson.homepages] wickerson_homepage = "http://www.doc.ic.ac.uk/~jpw48" [eberl] name = "Manuel Eberl" [eberl.emails] eberl_email = "manuel@pruvisto.org" eberl_email1 = "manuel.eberl@tum.de" [eberl.homepages] -eberl_homepage = "https://pruvisto.org" -eberl_homepage1 = "https://pruvisto.org/" +eberl_homepage = "https://pruvisto.org/" eberl_homepage2 = "https://www.in.tum.de/~eberlm" [noce] name = "Pasquale Noce" [noce.emails] noce_email = "pasquale.noce.lavoro@gmail.com" [noce.homepages] [gunther] name = "Emmanuel Gunther" [gunther.emails] gunther_email = "gunther@famaf.unc.edu.ar" [gunther.homepages] [nemouchi] name = "Yakoub Nemouchi" [nemouchi.emails] nemouchi_email = "nemouchi@lri.fr" nemouchi_email1 = "yakoub.nemouchi@york.ac.uk" [nemouchi.homepages] [stueber] name = "Anke Stüber" [stueber.emails] stueber_email = "anke.stueber@campus.tu-berlin.de" [stueber.homepages] [sternagel] name = "Christian Sternagel" [sternagel.emails] sternagel_email = "c.sternagel@gmail.com" sternagel_email1 = "christian.sternagel@uibk.ac.at" [sternagel.homepages] sternagel_homepage = "http://cl-informatik.uibk.ac.at/users/griff/" [sachtleben] name = "Robert Sachtleben" [sachtleben.emails] sachtleben_email = "rob_sac@uni-bremen.de" [sachtleben.homepages] [kastermans] name = "Bart Kastermans" [kastermans.emails] [kastermans.homepages] kastermans_homepage = "http://kasterma.net" [pal] name = "Abhik Pal" [pal.emails] [pal.homepages] [thiemann] name = "René Thiemann" [thiemann.emails] thiemann_email = "rene.thiemann@uibk.ac.at" [thiemann.homepages] -thiemann_homepage = "http://cl-informatik.uibk.ac.at/~thiemann" -thiemann_homepage1 = "http://cl-informatik.uibk.ac.at/~thiemann/" -thiemann_homepage2 = "http://cl-informatik.uibk.ac.at/users/thiemann/" +thiemann_homepage = "http://cl-informatik.uibk.ac.at/users/thiemann/" [campo] name = "Alejandro del Campo" [campo.emails] campo_email = "alejandro.del-campo@alum.unirioja.es" [campo.homepages] [raska] name = "Martin Raška" [raska.emails] [raska.homepages] [stannett] name = "Mike Stannett" [stannett.emails] stannett_email = "m.stannett@sheffield.ac.uk" [stannett.homepages] [back] name = "Ralph-Johan Back" [back.emails] [back.homepages] back_homepage = "http://users.abo.fi/Ralph-Johan.Back/" [bruegger] name = "Lukas Brügger" [bruegger.emails] bruegger_email = "lukas.a.bruegger@gmail.com" [bruegger.homepages] [kuncak] name = "Viktor Kuncak" [kuncak.emails] [kuncak.homepages] kuncak_homepage = "http://lara.epfl.ch/~kuncak/" [gaudel] name = "Marie-Claude Gaudel" [gaudel.emails] gaudel_email = "mcg@lri.fr" [gaudel.homepages] [sison] name = "Robert Sison" [sison.emails] [sison.homepages] [benzmueller] name = "Christoph Benzmüller" [benzmueller.emails] benzmueller_email = "c.benzmueller@gmail.com" benzmueller_email1 = "c.benzmueller@fu-berlin.de" [benzmueller.homepages] benzmueller_homepage = "http://christoph-benzmueller.de" benzmueller_homepage1 = "http://page.mi.fu-berlin.de/cbenzmueller/" -benzmueller_homepage2 = "http://www.christoph-benzmueller.de" [from] name = "Asta Halkjær From" [from.emails] from_email = "ahfrom@dtu.dk" [from.homepages] from_homepage = "https://people.compute.dtu.dk/ahfrom/" [tuongj] name = "Joseph Tuong" [tuongj.emails] [tuongj.homepages] [zeller] name = "Peter Zeller" [zeller.emails] zeller_email = "p_zeller@cs.uni-kl.de" [zeller.homepages] [schmidinger] name = "Lukas Schmidinger" [schmidinger.emails] [schmidinger.homepages] [ravindran] name = "Binoy Ravindran" [ravindran.emails] [ravindran.homepages] [rizaldi] name = "Albert Rizaldi" [rizaldi.emails] rizaldi_email = "albert.rizaldi@ntu.edu.sg" [rizaldi.homepages] [sabouret] name = "Nicolas Sabouret" [sabouret.emails] [sabouret.homepages] [butler] name = "David Butler" [butler.emails] butler_email = "dbutler@turing.ac.uk" [butler.homepages] butler_homepage = "https://www.turing.ac.uk/people/doctoral-students/david-butler" [sprenger] name = "Christoph Sprenger" [sprenger.emails] sprenger_email = "sprenger@inf.ethz.ch" [sprenger.homepages] [bordg] name = "Anthony Bordg" [bordg.emails] bordg_email = "apdb3@cam.ac.uk" [bordg.homepages] bordg_homepage = "https://sites.google.com/site/anthonybordg/" [bhatt] name = "Bhargav Bhatt" [bhatt.emails] bhatt_email = "bhargav.bhatt@inf.ethz.ch" [bhatt.homepages] [gonzalez] name = "Edgar Gonzàlez" [gonzalez.emails] gonzalez_email = "edgargip@google.com" [gonzalez.homepages] [adelsberger] name = "Stephan Adelsberger" [adelsberger.emails] adelsberger_email = "stvienna@gmail.com" [adelsberger.homepages] adelsberger_homepage = "http://nm.wu.ac.at/nm/sadelsbe" [schleicher] name = "Dierk Schleicher" [schleicher.emails] [schleicher.homepages] [ying] name = "Shenggang Ying" [ying.emails] [ying.homepages] [brien] name = "Nicolas Robinson-O'Brien" [brien.emails] [brien.homepages] [kobayashi] name = "Hidetsune Kobayashi" [kobayashi.emails] [kobayashi.homepages] [krauss] name = "Alexander Krauss" [krauss.emails] krauss_email = "krauss@in.tum.de" [krauss.homepages] krauss_homepage = "http://www.in.tum.de/~krauss" [somaini] name = "Ivano Somaini" [somaini.emails] [somaini.homepages] [seidl] name = "Benedikt Seidl" [seidl.emails] seidl_email = "benedikt.seidl@tum.de" [seidl.homepages] [edmonds] name = "Chelsea Edmonds" [edmonds.emails] edmonds_email = "cle47@cam.ac.uk" [edmonds.homepages] edmonds_homepage = "https://www.cst.cam.ac.uk/people/cle47" [debrat] name = "Henri Debrat" [debrat.emails] debrat_email = "henri.debrat@loria.fr" [debrat.homepages] [holub] name = "Štěpán Holub" [holub.emails] holub_email = "holub@karlin.mff.cuni.cz" [holub.homepages] holub_homepage = "https://www2.karlin.mff.cuni.cz/~holub/" [beresford] name = "Alastair R. Beresford" [beresford.emails] beresford_email = "arb33@cam.ac.uk" -beresford_email1 = "arb33@cl.cam.ac.uk" [beresford.homepages] [terraf] name = "Pedro Sánchez Terraf" [terraf.emails] -terraf_email = "sterraf@famaf.unc.edu.ar" -terraf_email1 = "psterraf@unc.edu.ar" +terraf_email = "psterraf@unc.edu.ar" [terraf.homepages] terraf_homepage = "https://cs.famaf.unc.edu.ar/~pedro/home_en.html" -terraf_homepage1 = "https://cs.famaf.unc.edu.ar/~pedro/home_en" -terraf_homepage2 = "https://cs.famaf.unc.edu.ar/~pedro" [raumer] name = "Jakob von Raumer" [raumer.emails] raumer_email = "psxjv4@nottingham.ac.uk" [raumer.homepages] [pagano] name = "Miguel Pagano" [pagano.emails] -pagano_email = "pagano@famaf.unc.edu.ar" -pagano_email1 = "miguel.pagano@unc.edu.ar" +pagano_email = "miguel.pagano@unc.edu.ar" [pagano.homepages] pagano_homepage = "https://cs.famaf.unc.edu.ar/~mpagano/" [coglio] name = "Alessandro Coglio" [coglio.emails] coglio_email = "coglio@kestrel.edu" [coglio.homepages] coglio_homepage = "http://www.kestrel.edu/~coglio" [caballero] name = "José Manuel Rodríguez Caballero" [caballero.emails] caballero_email = "jose.manuel.rodriguez.caballero@ut.ee" [caballero.homepages] caballero_homepage = "https://josephcmac.github.io/" [grechuk] name = "Bogdan Grechuk" [grechuk.emails] grechuk_email = "grechukbogdan@yandex.ru" [grechuk.homepages] [sewell] name = "Thomas Sewell" [sewell.emails] [sewell.homepages] [leustean] name = "Laurentiu Leustean" [leustean.emails] [leustean.homepages] [rosskopf] name = "Simon Roßkopf" [rosskopf.emails] rosskopf_email = "rosskops@in.tum.de" [rosskopf.homepages] rosskopf_homepage = "http://www21.in.tum.de/~rosskops" [aspinall] name = "David Aspinall" [aspinall.emails] [aspinall.homepages] aspinall_homepage = "http://homepages.inf.ed.ac.uk/da/" [ausaf] name = "Fahad Ausaf" [ausaf.emails] [ausaf.homepages] ausaf_homepage = "http://kcl.academia.edu/FahadAusaf" [diekmann] name = "Cornelius Diekmann" [diekmann.emails] diekmann_email = "diekmann@net.in.tum.de" [diekmann.homepages] diekmann_homepage = "http://net.in.tum.de/~diekmann" [fouillard] name = "Valentin Fouillard" [fouillard.emails] fouillard_email = "valentin.fouillard@limsi.fr" [fouillard.homepages] [willenbrink] name = "Sebastian Willenbrink" [willenbrink.emails] willenbrink_email = "sebastian.willenbrink@tum.de" [willenbrink.homepages] [xu] name = "Jian Xu" [xu.emails] [xu.homepages] [wang] name = "Shuling Wang" [wang.emails] [wang.homepages] [ridge] name = "Tom Ridge" [ridge.emails] [ridge.homepages] [kleppmann] name = "Martin Kleppmann" [kleppmann.emails] kleppmann_email = "martin.kleppmann@cl.cam.ac.uk" -kleppmann_email1 = "mk428@cl.cam.ac.uk" [kleppmann.homepages] [kreuzer] name = "Katharina Kreuzer" [kreuzer.emails] kreuzer_email = "kreuzerk@in.tum.de" [kreuzer.homepages] kreuzer_homepage = "https://www21.in.tum.de/team/kreuzer/" [traut] name = "Christoph Traut" [traut.emails] [traut.homepages] [blanchette] name = "Jasmin Christian Blanchette" [blanchette.emails] blanchette_email = "jasmin.blanchette@gmail.com" blanchette_email1 = "j.c.blanchette@vu.nl" [blanchette.homepages] blanchette_homepage = "http://www21.in.tum.de/~blanchet" blanchette_homepage1 = "https://www.cs.vu.nl/~jbe248/" [van] name = "Hai Nguyen Van" [van.emails] van_email = "hai.nguyenvan.phie@gmail.com" [van.homepages] [brunner] name = "Julian Brunner" [brunner.emails] brunner_email = "brunnerj@in.tum.de" [brunner.homepages] brunner_homepage = "http://www21.in.tum.de/~brunnerj/" [reiche] name = "Sebastian Reiche" [reiche.emails] [reiche.homepages] reiche_homepage = "https://www.linkedin.com/in/sebastian-reiche-0b2093178" [eriksson] name = "Lars-Henrik Eriksson" [eriksson.emails] eriksson_email = "lhe@it.uu.se" [eriksson.homepages] [nipkow] name = "Tobias Nipkow" [nipkow.emails] nipkow_email = "nipkow@in.tum.de" [nipkow.homepages] -nipkow_homepage = "http://www21.in.tum.de/~nipkow" -nipkow_homepage1 = "http://www.in.tum.de/~nipkow/" -nipkow_homepage2 = "http://www.in.tum.de/~nipkow" -nipkow_homepage3 = "https://www.in.tum.de/~nipkow" -nipkow_homepage4 = "http://www21.in.tum.de/~nipkow/" +nipkow_homepage = "https://www21.in.tum.de/~nipkow/" [divason] name = "Jose Divasón" [divason.emails] -divason_email = "jose.divasonm@unirioja.es" -divason_email1 = "jose.divason@unirioja.es" +divason_email = "jose.divason@unirioja.es" [divason.homepages] -divason_homepage = "http://www.unirioja.es/cu/jodivaso" -divason_homepage1 = "http://www.unirioja.es/cu/jodivaso/" -divason_homepage2 = "https://www.unirioja.es/cu/jodivaso/" +divason_homepage = "https://www.unirioja.es/cu/jodivaso/" [barsotti] name = "Damián Barsotti" [barsotti.emails] [barsotti.homepages] barsotti_homepage = "http://www.cs.famaf.unc.edu.ar/~damian/" [nagashima] name = "Yutaka Nagashima" [nagashima.emails] nagashima_email = "Yutaka.Nagashima@data61.csiro.au" [nagashima.homepages] [avigad] name = "Jeremy Avigad" [avigad.emails] avigad_email = "avigad@cmu.edu" [avigad.homepages] avigad_homepage = "http://www.andrew.cmu.edu/user/avigad/" [abdulaziz] name = "Mohammad Abdulaziz" [abdulaziz.emails] -abdulaziz_email = "mansour@in.tum.de" +abdulaziz_email = "mohammad.abdulaziz@in.tum.de" abdulaziz_email1 = "mohammad.abdulaziz8@gmail.com" -abdulaziz_email2 = "mohammad.abdulaziz@in.tum.de" [abdulaziz.homepages] abdulaziz_homepage = "http://home.in.tum.de/~mansour/" [kuncar] name = "Ondřej Kunčar" [kuncar.emails] [kuncar.homepages] kuncar_homepage = "http://www21.in.tum.de/~kuncar/" [borgstroem] name = "Johannes Borgström" [borgstroem.emails] borgstroem_email = "johannes.borgstrom@it.uu.se" [borgstroem.homepages] [kurz] name = "Friedrich Kurz" [kurz.emails] kurz_email = "friedrich.kurz@tum.de" [kurz.homepages] [noschinski] name = "Lars Noschinski" [noschinski.emails] noschinski_email = "noschinl@gmail.com" [noschinski.homepages] noschinski_homepage = "http://www21.in.tum.de/~noschinl/" [liy] name = "Yangjia Li" [liy.emails] [liy.homepages] [wimmer] name = "Simon Wimmer" [wimmer.emails] wimmer_email = "simon.wimmer@tum.de" -wimmer_email1 = "wimmers@in.tum.de" [wimmer.homepages] -wimmer_homepage = "http://in.tum.de/~wimmers" -wimmer_homepage1 = "http://home.in.tum.de/~wimmers/" +wimmer_homepage = "http://home.in.tum.de/~wimmers/" [gammie] name = "Peter Gammie" [gammie.emails] gammie_email = "peteg42@gmail.com" [gammie.homepages] gammie_homepage = "http://peteg.org" [snelting] name = "Gregor Snelting" [snelting.emails] [snelting.homepages] snelting_homepage = "http://pp.info.uni-karlsruhe.de/personhp/gregor_snelting.php" [stark] name = "Eugene W. Stark" [stark.emails] stark_email = "stark@cs.stonybrook.edu" [stark.homepages] [engelhardt] name = "Kai Engelhardt" [engelhardt.emails] [engelhardt.homepages] [fleury] name = "Mathias Fleury" [fleury.emails] fleury_email = "fleury@mpi-inf.mpg.de" fleury_email1 = "mathias.fleury@jku.at" [fleury.homepages] fleury_homepage = "http://fmv.jku.at/fleury" [griebel] name = "Simon Griebel" [griebel.emails] griebel_email = "s.griebel@tum.de" [griebel.homepages] [zhang] name = "Yu Zhang" [zhang.emails] [zhang.homepages] [spichkova] name = "Maria Spichkova" [spichkova.emails] spichkova_email = "maria.spichkova@rmit.edu.au" [spichkova.homepages] [andronick] name = "June Andronick" [andronick.emails] [andronick.homepages] [lammich] name = "Peter Lammich" [lammich.emails] lammich_email = "lammich@in.tum.de" lammich_email1 = "peter.lammich@uni-muenster.de" [lammich.homepages] lammich_homepage = "http://www21.in.tum.de/~lammich" [maricf] name = "Filip Marić" [maricf.emails] maricf_email = "filip@matf.bg.ac.rs" [maricf.homepages] maricf_homepage = "http://www.matf.bg.ac.rs/~filip" -maricf_homepage1 = "http://poincare.matf.bg.ac.rs/~filip/" [popescu] name = "Andrei Popescu" [popescu.emails] popescu_email = "a.popescu@sheffield.ac.uk" popescu_email1 = "uuomul@yahoo.com" popescu_email2 = "a.popescu@mdx.ac.uk" [popescu.homepages] popescu_homepage = "https://www.andreipopescu.uk" [chen] name = "L. Chen" [chen.emails] [chen.homepages] [helke] name = "Steffen Helke" [helke.emails] helke_email = "helke@cs.tu-berlin.de" [helke.homepages] [pohjola] name = "Johannes Åman Pohjola" [pohjola.emails] [pohjola.homepages] [yingm] name = "Mingsheng Ying" [yingm.emails] [yingm.homepages] [fosterj] name = "J. Nathan Foster" [fosterj.emails] [fosterj.homepages] fosterj_homepage = "http://www.cs.cornell.edu/~jnfoster/" [verbeek] name = "Freek Verbeek" [verbeek.emails] verbeek_email = "Freek.Verbeek@ou.nl" verbeek_email1 = "freek@vt.edu" [verbeek.homepages] [struth] name = "Georg Struth" [struth.emails] struth_email = "g.struth@sheffield.ac.uk" -struth_email1 = "g.struth@dcs.shef.ac.uk" [struth.homepages] -struth_homepage = "http://www.dcs.shef.ac.uk/~georg" -struth_homepage1 = "http://staffwww.dcs.shef.ac.uk/people/G.Struth/" +struth_homepage = "http://staffwww.dcs.shef.ac.uk/people/G.Struth/" [mitsch] name = "Stefan Mitsch" [mitsch.emails] mitsch_email = "smitsch@cs.cmu.edu" [mitsch.homepages] [nordhoff] name = "Benedikt Nordhoff" [nordhoff.emails] nordhoff_email = "b.n@wwu.de" nordhoff_email1 = "b_nord01@uni-muenster.de" [nordhoff.homepages] [kirchner] name = "Daniel Kirchner" [kirchner.emails] kirchner_email = "daniel@ekpyron.org" [kirchner.homepages] [merz] name = "Stephan Merz" [merz.emails] merz_email = "Stephan.Merz@loria.fr" [merz.homepages] merz_homepage = "http://www.loria.fr/~merz" [fernandez] name = "Matthew Fernandez" [fernandez.emails] [fernandez.homepages] [kolanski] name = "Rafal Kolanski" [kolanski.emails] kolanski_email = "rafal.kolanski@nicta.com.au" [kolanski.homepages] [strnisa] name = "Rok Strniša" [strnisa.emails] strnisa_email = "rok@strnisa.com" [strnisa.homepages] strnisa_homepage = "http://rok.strnisa.com/lj/" [liuy] name = "Yang Liu" [liuy.emails] liuy_email = "yangliu@ntu.edu.sg" [liuy.homepages] [jacobsen] name = "Frederik Krogsdal Jacobsen" [jacobsen.emails] jacobsen_email = "fkjac@dtu.dk" [jacobsen.homepages] jacobsen_homepage = "http://people.compute.dtu.dk/fkjac/" [crighton] name = "Aaron Crighton" [crighton.emails] crighton_email = "crightoa@mcmaster.ca" [crighton.homepages] [matiyasevich] name = "Yuri Matiyasevich" [matiyasevich.emails] [matiyasevich.homepages] [kaliszyk] name = "Cezary Kaliszyk" [kaliszyk.emails] kaliszyk_email = "cezary.kaliszyk@uibk.ac.at" [kaliszyk.homepages] kaliszyk_homepage = "http://cl-informatik.uibk.ac.at/users/cek/" -kaliszyk_homepage1 = "http://cl-informatik.uibk.ac.at/cek/" [voisin] name = "Frederic Voisin" [voisin.emails] [voisin.homepages] [kaufmann] name = "Daniela Kaufmann" [kaufmann.emails] [kaufmann.homepages] kaufmann_homepage = "http://fmv.jku.at/kaufmann" [milehins] name = "Mihails Milehins" [milehins.emails] milehins_email = "user9716869@gmail.com" milehins_email1 = "mihailsmilehins@gmail.com" [milehins.homepages] [cordwell] name = "Katherine Cordwell" [cordwell.emails] cordwell_email = "kcordwel@cs.cmu.edu" [cordwell.homepages] cordwell_homepage = "https://www.cs.cmu.edu/~kcordwel/" [smaus] name = "Jan-Georg Smaus" [smaus.emails] [smaus.homepages] smaus_homepage = "http://www.irit.fr/~Jan-Georg.Smaus" [sefidgar] name = "S. Reza Sefidgar" [sefidgar.emails] sefidgar_email = "reza.sefidgar@inf.ethz.ch" [sefidgar.homepages] [steinberg] name = "Matías Steinberg" [steinberg.emails] steinberg_email = "matias.steinberg@mi.unc.edu.ar" [steinberg.homepages] [furusawa] name = "Hitoshi Furusawa" [furusawa.emails] [furusawa.homepages] furusawa_homepage = "http://www.sci.kagoshima-u.ac.jp/~furusawa/" [unruh] name = "Dominique Unruh" [unruh.emails] unruh_email = "unruh@ut.ee" [unruh.homepages] -unruh_homepage = "http://kodu.ut.ee/~unruh/" -unruh_homepage1 = "https://www.ut.ee/~unruh/" +unruh_homepage = "https://www.ut.ee/~unruh/" [yamada] name = "Akihisa Yamada" [yamada.emails] yamada_email = "akihisa.yamada@uibk.ac.at" yamada_email1 = "ayamada@trs.cm.is.nagoya-u.ac.jp" yamada_email2 = "akihisa.yamada@aist.go.jp" yamada_email3 = "akihisayamada@nii.ac.jp" [yamada.homepages] yamada_homepage = "http://group-mmm.org/~ayamada/" [smola] name = "Filip Smola" [smola.emails] smola_email = "f.smola@sms.ed.ac.uk" [smola.homepages] [pusch] name = "Cornelia Pusch" [pusch.emails] [pusch.homepages] [ogawa] name = "Mizuhito Ogawa" [ogawa.emails] [ogawa.homepages] [bulwahn] name = "Lukas Bulwahn" [bulwahn.emails] bulwahn_email = "lukas.bulwahn@gmail.com" [bulwahn.homepages] [obua] name = "Steven Obua" [obua.emails] obua_email = "steven@recursivemind.com" [obua.homepages] [bayer] name = "Jonas Bayer" [bayer.emails] bayer_email = "jonas.bayer999@gmail.com" [bayer.homepages] [brun] name = "Matthias Brun" [brun.emails] brun_email = "matthias.brun@inf.ethz.ch" [brun.homepages] [aransay] name = "Jesús Aransay" [aransay.emails] aransay_email = "jesus-maria.aransay@unirioja.es" [aransay.homepages] -aransay_homepage = "http://www.unirioja.es/cu/jearansa" -aransay_homepage1 = "https://www.unirioja.es/cu/jearansa" +aransay_homepage = "https://www.unirioja.es/cu/jearansa" [gioiosa] name = "Gianpaolo Gioiosa" [gioiosa.emails] [gioiosa.homepages] [karayel] name = "Emin Karayel" [karayel.emails] karayel_email = "me@eminkarayel.de" karayel_email1 = "eminkarayel@google.com" [karayel.homepages] karayel_homepage = "https://orcid.org/0000-0003-3290-5034" [koller] name = "Lukas Koller" [koller.emails] koller_email = "lukas.koller@tum.de" [koller.homepages] [starosta] name = "Štěpán Starosta" [starosta.emails] starosta_email = "stepan.starosta@fit.cvut.cz" [starosta.homepages] starosta_homepage = "https://users.fit.cvut.cz/~staroste/" [zhangx] name = "Xingyuan Zhang" [zhangx.emails] [zhangx.homepages] [katovsky] name = "Alexander Katovsky" [katovsky.emails] katovsky_email = "apk32@cam.ac.uk" katovsky_email1 = "alexander.katovsky@cantab.net" [katovsky.homepages] [roessle] name = "Ian Roessle" [roessle.emails] [roessle.homepages] [schoepf] name = "Jonas Schöpf" [schoepf.emails] schoepf_email = "jonas.schoepf@uibk.ac.at" [schoepf.homepages] [gheri] name = "Lorenzo Gheri" [gheri.emails] gheri_email = "lor.gheri@gmail.com" [gheri.homepages] [oosterhuis] name = "Roelof Oosterhuis" [oosterhuis.emails] oosterhuis_email = "roelofoosterhuis@gmail.com" [oosterhuis.homepages] [robillard] name = "Simon Robillard" [robillard.emails] [robillard.homepages] robillard_homepage = "https://simon-robillard.net/" [rauch] name = "Nicole Rauch" [rauch.emails] rauch_email = "rauch@informatik.uni-kl.de" [rauch.homepages] [wolff] name = "Burkhart Wolff" [wolff.emails] -wolff_email = "wolff@lri.fr" -wolff_email1 = "burkhart.wolff@lri.fr" +wolff_email = "burkhart.wolff@lri.fr" [wolff.homepages] wolff_homepage = "https://www.lri.fr/~wolff/" [lattuada] name = "Andrea Lattuada" [lattuada.emails] [lattuada.homepages] lattuada_homepage = "https://andrea.lattuada.me" [pierzchalski] name = "Edward Pierzchalski" [pierzchalski.emails] [pierzchalski.homepages] [chaieb] name = "Amine Chaieb" [chaieb.emails] [chaieb.homepages] [raszyk] name = "Martin Raszyk" [raszyk.emails] raszyk_email = "martin.raszyk@inf.ethz.ch" raszyk_email1 = "m.raszyk@gmail.com" [raszyk.homepages] [zee] name = "Karen Zee" [zee.emails] zee_email = "kkz@mit.edu" [zee.homepages] zee_homepage = "http://www.mit.edu/~kkz/" [jensen] name = "Alexander Birch Jensen" [jensen.emails] jensen_email = "aleje@dtu.dk" [jensen.homepages] jensen_homepage = "https://people.compute.dtu.dk/aleje/" [murray] name = "Toby Murray" [murray.emails] murray_email = "toby.murray@unimelb.edu.au" [murray.homepages] -murray_homepage = "http://people.eng.unimelb.edu.au/tobym/" -murray_homepage1 = "https://people.eng.unimelb.edu.au/tobym/" +murray_homepage = "https://people.eng.unimelb.edu.au/tobym/" [hupel] name = "Lars Hupel" [hupel.emails] hupel_email = "hupel@in.tum.de" hupel_email1 = "lars@hupel.info" [hupel.homepages] hupel_homepage = "https://www21.in.tum.de/~hupel/" hupel_homepage1 = "https://lars.hupel.info/" [rowat] name = "Colin Rowat" [rowat.emails] rowat_email = "c.rowat@bham.ac.uk" [rowat.homepages] [schneider] name = "Joshua Schneider" [schneider.emails] schneider_email = "joshua.schneider@inf.ethz.ch" [schneider.homepages] [cousin] name = "Marie Cousin" [cousin.emails] cousin_email = "marie.cousin@grenoble-inp.org" [cousin.homepages] [parsert] name = "Julian Parsert" [parsert.emails] parsert_email = "julian.parsert@gmail.com" parsert_email1 = "julian.parsert@uibk.ac.at" [parsert.homepages] parsert_homepage = "http://www.parsert.com/" [aehlig] name = "Klaus Aehlig" [aehlig.emails] [aehlig.homepages] aehlig_homepage = "http://www.linta.de/~aehlig/" [argyraki] name = "Angeliki Koutsoukou-Argyraki" [argyraki.emails] argyraki_email = "ak2110@cam.ac.uk" [argyraki.homepages] argyraki_homepage = "https://www.cl.cam.ac.uk/~ak2110/" -argyraki_homepage1 = "http://www.cl.cam.ac.uk/~ak2110/" argyraki_homepage2 = "https://www.cst.cam.ac.uk/people/ak2110" [ye] name = "Lina Ye" [ye.emails] ye_email = "lina.ye@lri.fr" [ye.homepages] [moeller] name = "Bernhard Möller" [moeller.emails] [moeller.homepages] moeller_homepage = "https://www.informatik.uni-augsburg.de/en/chairs/dbis/pmi/staff/moeller/" [zankl] name = "Harald Zankl" [zankl.emails] zankl_email = "Harald.Zankl@uibk.ac.at" [zankl.homepages] zankl_homepage = "http://cl-informatik.uibk.ac.at/users/hzankl" [langenstein] name = "Bruno Langenstein" [langenstein.emails] langenstein_email = "langenstein@dfki.de" [langenstein.homepages] [breitner] name = "Joachim Breitner" [breitner.emails] breitner_email = "mail@joachim-breitner.de" breitner_email1 = "joachim@cis.upenn.edu" [breitner.homepages] breitner_homepage = "http://pp.ipd.kit.edu/~breitner" [thommes] name = "Joseph Thommes" [thommes.emails] thommes_email = "joseph-thommes@gmx.de" [thommes.homepages] [loibl] name = "Matthias Loibl" [loibl.emails] [loibl.homepages] [cock] name = "David Cock" [cock.emails] cock_email = "david.cock@nicta.com.au" [cock.homepages] [stuewe] name = "Daniel Stüwe" [stuewe.emails] [stuewe.homepages] [decova] name = "Sára Decova" [decova.emails] [decova.homepages] [nikiforov] name = "Denis Nikiforov" [nikiforov.emails] nikiforov_email = "denis.nikif@gmail.com" [nikiforov.homepages] [traytel] name = "Dmitriy Traytel" [traytel.emails] traytel_email = "traytel@in.tum.de" traytel_email1 = "traytel@inf.ethz.ch" traytel_email2 = "traytel@di.ku.dk" [traytel.homepages] -traytel_homepage = "https://traytel.bitbucket.io" -traytel_homepage1 = "https://traytel.bitbucket.io/" +traytel_homepage = "https://traytel.bitbucket.io/" [tverdyshev] name = "Sergey Tverdyshev" [tverdyshev.emails] tverdyshev_email = "stv@sysgo.com" [tverdyshev.homepages] [wassell] name = "Mark Wassell" [wassell.emails] wassell_email = "mpwassell@gmail.com" [wassell.homepages] [ijbema] name = "Mark Ijbema" [ijbema.emails] ijbema_email = "ijbema@fmf.nl" [ijbema.homepages] [wirt] name = "Kai Wirt" [wirt.emails] [wirt.homepages] [matache] name = "Cristina Matache" [matache.emails] matache_email = "cris.matache@gmail.com" [matache.homepages] [ito] name = "Yosuke Ito" [ito.emails] ito_email = "glacier345@gmail.com" [ito.homepages] [maric] name = "Ognjen Marić" [maric.emails] maric_email = "ogi.afp@mynosefroze.com" [maric.homepages] [heimes] name = "Lukas Heimes" [heimes.emails] heimes_email = "heimesl@student.ethz.ch" [heimes.homepages] [parrow] name = "Joachim Parrow" [parrow.emails] parrow_email = "joachim.parrow@it.uu.se" [parrow.homepages] [naraschewski] name = "Wolfgang Naraschewski" [naraschewski.emails] [naraschewski.homepages] [amani] name = "Sidney Amani" [amani.emails] amani_email = "sidney.amani@data61.csiro.au" [amani.homepages] [palmer] name = "Jake Palmer" [palmer.emails] palmer_email = "jake.palmer@ed.ac.uk" [palmer.homepages] [bockenek] name = "Joshua Bockenek" [bockenek.emails] [bockenek.homepages] [lachnitt] name = "Hanna Lachnitt" [lachnitt.emails] lachnitt_email = "lachnitt@stanford.edu" [lachnitt.homepages] [rabe] name = "Markus N. Rabe" [rabe.emails] [rabe.homepages] rabe_homepage = "http://www.react.uni-saarland.de/people/rabe.html" [munive] name = "Jonathan Julian Huerta y Munive" [munive.emails] munive_email = "jjhuertaymunive1@sheffield.ac.uk" munive_email1 = "jonjulian23@gmail.com" [munive.homepages] [gouezel] name = "Sebastien Gouezel" [gouezel.emails] gouezel_email = "sebastien.gouezel@univ-rennes1.fr" [gouezel.homepages] gouezel_homepage = "http://www.math.sciences.univ-nantes.fr/~gouezel/" [brucker] name = "Achim D. Brucker" [brucker.emails] brucker_email = "a.brucker@exeter.ac.uk" brucker_email1 = "brucker@spamfence.net" brucker_email2 = "adbrucker@0x5f.org" [brucker.homepages] brucker_homepage = "https://www.brucker.ch/" -brucker_homepage1 = "https://www.brucker.ch" [sato] name = "Tetsuya Sato" [sato.emails] sato_email = "tsato@c.titech.ac.jp" [sato.homepages] sato_homepage = "https://sites.google.com/view/tetsuyasato/" [huffman] name = "Brian Huffman" [huffman.emails] huffman_email = "huffman@in.tum.de" huffman_email1 = "brianh@cs.pdx.edu" [huffman.homepages] -huffman_homepage = "http://web.cecs.pdx.edu/~brianh/" -huffman_homepage1 = "http://cs.pdx.edu/~brianh" +huffman_homepage = "http://cs.pdx.edu/~brianh/" [fleuriot] name = "Jacques D. Fleuriot" [fleuriot.emails] fleuriot_email = "Jacques.Fleuriot@ed.ac.uk" fleuriot_email1 = "jdf@ed.ac.uk" [fleuriot.homepages] fleuriot_homepage = "https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html" [hess] name = "Andreas V. Hess" [hess.emails] hess_email = "avhe@dtu.dk" hess_email1 = "andreasvhess@gmail.com" [hess.homepages] [marmsoler] name = "Diego Marmsoler" [marmsoler.emails] marmsoler_email = "diego.marmsoler@tum.de" [marmsoler.homepages] marmsoler_homepage = "http://marmsoler.com" [hibon] name = "Quentin Hibon" [hibon.emails] hibon_email = "qh225@cl.cam.ac.uk" [hibon.homepages] [tasch] name = "Markus Tasch" [tasch.emails] tasch_email = "tasch@mais.informatik.tu-darmstadt.de" [tasch.homepages] [doty] name = "Matthew Wampler-Doty" [doty.emails] [doty.homepages] [berghofer] name = "Stefan Berghofer" [berghofer.emails] berghofer_email = "berghofe@in.tum.de" [berghofer.homepages] berghofer_homepage = "http://www.in.tum.de/~berghofe" [hirata] name = "Michikazu Hirata" [hirata.emails] hirata_email = "hirata.m.ac@m.titech.ac.jp" [hirata.homepages] [sylvestre] name = "Jeremy Sylvestre" [sylvestre.emails] sylvestre_email = "jeremy.sylvestre@ualberta.ca" sylvestre_email1 = "jsylvest@ualberta.ca" [sylvestre.homepages] sylvestre_homepage = "http://ualberta.ca/~jsylvest/" [lindenberg] name = "Christina Lindenberg" [lindenberg.emails] [lindenberg.homepages] [joosten] name = "Sebastiaan J. C. Joosten" [joosten.emails] joosten_email = "sebastiaan.joosten@uibk.ac.at" joosten_email1 = "sjcjoosten@gmail.com" joosten_email2 = "s.j.c.joosten@utwente.nl" [joosten.homepages] -joosten_homepage = "https://sjcjoosten.nl" -joosten_homepage1 = "https://sjcjoosten.nl/" +joosten_homepage = "https://sjcjoosten.nl/" [blumson] name = "Ben Blumson" [blumson.emails] blumson_email = "benblumson@gmail.com" [blumson.homepages] -blumson_homepage = "https://philpapers.org/profile/805" -blumson_homepage1 = "https://philpeople.org/profiles/ben-blumson" +blumson_homepage = "https://philpeople.org/profiles/ben-blumson" [hosking] name = "Tony Hosking" [hosking.emails] [hosking.homepages] hosking_homepage = "https://www.cs.purdue.edu/homes/hosking/" [preoteasa] name = "Viorel Preoteasa" [preoteasa.emails] preoteasa_email = "viorel.preoteasa@aalto.fi" [preoteasa.homepages] preoteasa_homepage = "http://users.abo.fi/vpreotea/" [gutkovas] name = "Ramunas Gutkovas" [gutkovas.emails] gutkovas_email = "ramunas.gutkovas@it.uu.se" [gutkovas.homepages] [minamide] name = "Yasuhiko Minamide" [minamide.emails] minamide_email = "minamide@is.titech.ac.jp" [minamide.homepages] minamide_homepage = "https://sv.c.titech.ac.jp/minamide/index.en.html" [waldmann] name = "Uwe Waldmann" [waldmann.emails] waldmann_email = "waldmann@mpi-inf.mpg.de" -waldmann_email1 = "uwe@mpi-inf.mpg.de" [waldmann.homepages] [lewis] name = "Corey Lewis" [lewis.emails] lewis_email = "corey.lewis@data61.csiro.au" [lewis.homepages] [peters] name = "Kirstin Peters" [peters.emails] peters_email = "kirstin.peters@tu-berlin.de" [peters.homepages] [ortner] name = "Veronika Ortner" [ortner.emails] [ortner.homepages] [fiedler] name = "Ben Fiedler" [fiedler.emails] fiedler_email = "ben.fiedler@inf.ethz.ch" [fiedler.homepages] [becker] name = "Heiko Becker" [becker.emails] becker_email = "hbecker@mpi-sws.org" [becker.homepages] [bracevac] name = "Oliver Bračevac" [bracevac.emails] bracevac_email = "bracevac@st.informatik.tu-darmstadt.de" [bracevac.homepages] [bohrer] name = "Rose Bohrer" [bohrer.emails] bohrer_email = "rose.bohrer.cs@gmail.com" [bohrer.homepages] [londono] name = "Alejandro Gómez-Londoño" [londono.emails] londono_email = "alejandro.gomez@chalmers.se" [londono.homepages] [armstrong] name = "Alasdair Armstrong" [armstrong.emails] [armstrong.homepages] [glabbeek] name = "Rob van Glabbeek" [glabbeek.emails] [glabbeek.homepages] glabbeek_homepage = "http://theory.stanford.edu/~rvg/" [jiangd] name = "Dongchen Jiang" [jiangd.emails] jiangd_email = "dongchenjiang@googlemail.com" [jiangd.homepages] [meis] name = "Rene Meis" [meis.emails] meis_email = "rene.meis@uni-muenster.de" meis_email1 = "rene.meis@uni-due.de" [meis.homepages] [hofmann] name = "Martin Hofmann" [hofmann.emails] [hofmann.homepages] hofmann_homepage = "http://www.tcs.informatik.uni-muenchen.de/~mhofmann" [kerber] name = "Manfred Kerber" [kerber.emails] kerber_email = "mnfrd.krbr@gmail.com" [kerber.homepages] kerber_homepage = "http://www.cs.bham.ac.uk/~mmk" [linker] name = "Sven Linker" [linker.emails] linker_email = "s.linker@liverpool.ac.uk" [linker.homepages] [balbach] name = "Frank J. Balbach" [balbach.emails] balbach_email = "frank-balbach@gmx.de" [balbach.homepages] [weber] name = "Tjark Weber" [weber.emails] weber_email = "tjark.weber@it.uu.se" [weber.homepages] weber_homepage = "http://user.it.uu.se/~tjawe125/" [hellauer] name = "Fabian Hellauer" [hellauer.emails] hellauer_email = "hellauer@in.tum.de" [hellauer.homepages] [reiter] name = "Markus Reiter" [reiter.emails] [reiter.homepages] [herzberg] name = "Michael Herzberg" [herzberg.emails] herzberg_email = "mail@michael-herzberg.de" [herzberg.homepages] herzberg_homepage = "http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg" [overbeek] name = "Roy Overbeek" [overbeek.emails] overbeek_email = "Roy.Overbeek@cwi.nl" [overbeek.homepages] [koerner] name = "Stefan Körner" [koerner.emails] koerner_email = "s_koer03@uni-muenster.de" [koerner.homepages] [tan] name = "Yong Kiam Tan" [tan.emails] tan_email = "yongkiat@cs.cmu.edu" [tan.homepages] tan_homepage = "https://www.cs.cmu.edu/~yongkiat/" [esparza] name = "Javier Esparza" [esparza.emails] [esparza.homepages] esparza_homepage = "https://www7.in.tum.de/~esparza/" [platzer] name = "André Platzer" [platzer.emails] platzer_email = "aplatzer@cs.cmu.edu" [platzer.homepages] platzer_homepage = "https://www.cs.cmu.edu/~aplatzer/" -platzer_homepage1 = "http://www.cs.cmu.edu/~aplatzer/" [matichuk] name = "Daniel Matichuk" [matichuk.emails] [matichuk.homepages] [rawson] name = "Michael Rawson" [rawson.emails] rawson_email = "michaelrawson76@gmail.com" rawson_email1 = "mr644@cam.ac.uk" [rawson.homepages] [bisping] name = "Benjamin Bisping" [bisping.emails] bisping_email = "benjamin.bisping@campus.tu-berlin.de" [bisping.homepages] [sanan] name = "David Sanan" [sanan.emails] sanan_email = "sanan@ntu.edu.sg" [sanan.homepages] [jungnickel] name = "Tim Jungnickel" [jungnickel.emails] jungnickel_email = "tim.jungnickel@tu-berlin.de" [jungnickel.homepages] [ammer] name = "Thomas Ammer" [ammer.emails] [ammer.homepages] [mulligan] name = "Dominic P. Mulligan" [mulligan.emails] mulligan_email = "dominic.p.mulligan@googlemail.com" mulligan_email1 = "Dominic.Mulligan@arm.com" [mulligan.homepages] [georgescu] name = "George Georgescu" [georgescu.emails] [georgescu.homepages] [aissat] name = "Romain Aissat" [aissat.emails] [aissat.homepages] [gore] name = "Rajeev Gore" [gore.emails] gore_email = "rajeev.gore@anu.edu.au" [gore.homepages] [gomes] name = "Victor B. F. Gomes" [gomes.emails] gomes_email = "victor.gomes@cl.cam.ac.uk" -gomes_email1 = "vb358@cam.ac.uk" gomes_email2 = "victorborgesfg@gmail.com" -gomes_email3 = "vb358@cl.cam.ac.uk" gomes_email4 = "vborgesferreiragomes1@sheffield.ac.uk" [gomes.homepages] gomes_homepage = "http://www.dcs.shef.ac.uk/~victor" [trachtenherz] name = "David Trachtenherz" [trachtenherz.emails] [trachtenherz.homepages] [lohner] name = "Denis Lohner" [lohner.emails] lohner_email = "denis.lohner@kit.edu" [lohner.homepages] lohner_homepage = "http://pp.ipd.kit.edu/person.php?id=88" [richter] name = "Stefan Richter" [richter.emails] richter_email = "richter@informatik.rwth-aachen.de" [richter.homepages] richter_homepage = "http://www-lti.informatik.rwth-aachen.de/~richter/" [nemeti] name = "István Németi" [nemeti.emails] [nemeti.homepages] nemeti_homepage = "http://www.renyi.hu/~nemeti/" [bentkamp] name = "Alexander Bentkamp" [bentkamp.emails] bentkamp_email = "bentkamp@gmail.com" bentkamp_email1 = "a.bentkamp@vu.nl" [bentkamp.homepages] bentkamp_homepage = "https://www.cs.vu.nl/~abp290/" [zeyda] name = "Frank Zeyda" [zeyda.emails] zeyda_email = "frank.zeyda@york.ac.uk" [zeyda.homepages] [tuerk] name = "Thomas Tuerk" [tuerk.emails] [tuerk.homepages] [ribeiro] name = "Pedro Ribeiro" [ribeiro.emails] [ribeiro.homepages] [raedle] name = "Jonas Rädle" [raedle.emails] raedle_email = "jonas.raedle@gmail.com" raedle_email1 = "jonas.raedle@tum.de" [raedle.homepages] [peltier] name = "Nicolas Peltier" [peltier.emails] peltier_email = "Nicolas.Peltier@imag.fr" [peltier.homepages] peltier_homepage = "http://membres-lig.imag.fr/peltier/" [kappelmann] name = "Kevin Kappelmann" [kappelmann.emails] kappelmann_email = "kevin.kappelmann@tum.de" [kappelmann.homepages] kappelmann_homepage = "https://www21.in.tum.de/team/kappelmk/" [hoelzl] name = "Johannes Hölzl" [hoelzl.emails] hoelzl_email = "hoelzl@in.tum.de" [hoelzl.homepages] -hoelzl_homepage = "http://in.tum.de/~hoelzl" -hoelzl_homepage1 = "http://home.in.tum.de/~hoelzl" +hoelzl_homepage = "http://home.in.tum.de/~hoelzl" [ballarin] name = "Clemens Ballarin" [ballarin.emails] ballarin_email = "ballarin@in.tum.de" [ballarin.homepages] ballarin_homepage = "http://www21.in.tum.de/~ballarin/" [wu] name = "Chunhan Wu" [wu.emails] [wu.homepages] [paulson] name = "Lawrence C. Paulson" [paulson.emails] paulson_email = "lp15@cam.ac.uk" -paulson_email1 = "lcp@cl.cam.ac.uk" [paulson.homepages] -paulson_homepage = "http://www.cl.cam.ac.uk/~lp15/" -paulson_homepage1 = "https://www.cl.cam.ac.uk/~lp15/" +paulson_homepage = "https://www.cl.cam.ac.uk/~lp15/" [paleo] name = "Bruno Woltzenlogel Paleo" [paleo.emails] [paleo.homepages] paleo_homepage = "http://www.logic.at/staff/bruno/" [wagner] name = "Max Wagner" [wagner.emails] wagner_email = "max@trollbu.de" [wagner.homepages] [lochbihler] name = "Andreas Lochbihler" [lochbihler.emails] lochbihler_email = "andreas.lochbihler@digitalasset.com" lochbihler_email1 = "mail@andreas-lochbihler.de" [lochbihler.homepages] -lochbihler_homepage = "http://www.andreas-lochbihler.de" -lochbihler_homepage1 = "http://www.andreas-lochbihler.de/" +lochbihler_homepage = "http://www.andreas-lochbihler.de/" [porter] name = "Benjamin Porter" [porter.emails] [porter.homepages] [boehme] name = "Sascha Böhme" [boehme.emails] boehme_email = "boehmes@in.tum.de" [boehme.homepages] boehme_homepage = "http://www21.in.tum.de/~boehmes/" [hou] name = "Zhe Hou" [hou.emails] hou_email = "zhe.hou@ntu.edu.sg" [hou.homepages] [mitchell] name = "Neil Mitchell" [mitchell.emails] [mitchell.homepages] [gay] name = "Richard Gay" [gay.emails] gay_email = "gay@mais.informatik.tu-darmstadt.de" [gay.homepages] [oldenburg] name = "Lennart Oldenburg" [oldenburg.emails] [oldenburg.homepages] [lochmann] name = "Alexander Lochmann" [lochmann.emails] lochmann_email = "alexander.lochmann@uibk.ac.at" [lochmann.homepages] [lim] name = "Japheth Lim" [lim.emails] [lim.homepages] [keinholz] name = "Jonas Keinholz" [keinholz.emails] [keinholz.homepages] [taylor] name = "Ramsay G. Taylor" [taylor.emails] taylor_email = "r.g.taylor@sheffield.ac.uk" [taylor.homepages] [bauereiss] name = "Thomas Bauereiss" [bauereiss.emails] bauereiss_email = "thomas@bauereiss.name" [bauereiss.homepages] [lee] name = "Holden Lee" [lee.emails] lee_email = "holdenl@princeton.edu" [lee.homepages] [weerwag] name = "Timmy Weerwag" [weerwag.emails] [weerwag.homepages] [sudhof] name = "Henry Sudhof" [sudhof.emails] sudhof_email = "hsudhof@cs.tu-berlin.de" [sudhof.homepages] [nedzelsky] name = "Michael Nedzelsky" [nedzelsky.emails] nedzelsky_email = "MichaelNedzelsky@yandex.ru" [nedzelsky.homepages] [romanos] name = "Ralph Romanos" [romanos.emails] romanos_email = "ralph.romanos@student.ecp.fr" [romanos.homepages] [doczkal] name = "Christian Doczkal" [doczkal.emails] doczkal_email = "doczkal@ps.uni-saarland.de" [doczkal.homepages] [buyse] name = "Maxime Buyse" [buyse.emails] buyse_email = "maxime.buyse@polytechnique.edu" [buyse.homepages] [guiol] name = "Hervé Guiol" [guiol.emails] guiol_email = "herve.guiol@univ-grenoble-alpes.fr" [guiol.homepages] [brodmann] name = "Paul-David Brodmann" [brodmann.emails] brodmann_email = "p.brodmann@tu-berlin.de" [brodmann.homepages] [moedersheim] name = "Sebastian Mödersheim" [moedersheim.emails] moedersheim_email = "samo@dtu.dk" [moedersheim.homepages] moedersheim_homepage = "https://people.compute.dtu.dk/samo/" [hu] name = "Shuwei Hu" [hu.emails] hu_email = "shuwei.hu@tum.de" [hu.homepages] [wand] name = "Daniel Wand" [wand.emails] wand_email = "dwand@mpi-inf.mpg.de" [wand.homepages] [velykis] name = "Andrius Velykis" [velykis.emails] [velykis.homepages] velykis_homepage = "http://andrius.velykis.lt" [felgenhauer] name = "Bertram Felgenhauer" [felgenhauer.emails] felgenhauer_email = "bertram.felgenhauer@uibk.ac.at" felgenhauer_email1 = "int-e@gmx.de" [felgenhauer.homepages] [sauer] name = "Jens Sauer" [sauer.emails] sauer_email = "sauer@mais.informatik.tu-darmstadt.de" [sauer.homepages] [dittmann] name = "Christoph Dittmann" [dittmann.emails] dittmann_email = "isabelle@christoph-d.de" [dittmann.homepages] dittmann_homepage = "http://logic.las.tu-berlin.de/Members/Dittmann/" [muendler] name = "Niels Mündler" [muendler.emails] muendler_email = "n.muendler@tum.de" [muendler.homepages] [somogyi] name = "Dániel Somogyi" [somogyi.emails] [somogyi.homepages] [makarios] name = "T. J. M. Makarios" [makarios.emails] makarios_email = "tjm1983@gmail.com" [makarios.homepages] [nishihara] name = "Toshiaki Nishihara" [nishihara.emails] [nishihara.homepages] [losa] name = "Giuliano Losa" [losa.emails] losa_email = "giuliano.losa@epfl.ch" losa_email1 = "giuliano@galois.com" losa_email2 = "giuliano@losa.fr" [losa.homepages] [grov] name = "Gudmund Grov" [grov.emails] grov_email = "ggrov@inf.ed.ac.uk" [grov.homepages] grov_homepage = "http://homepages.inf.ed.ac.uk/ggrov" [bharadwaj] name = "Abhijith Bharadwaj" [bharadwaj.emails] [bharadwaj.homepages] [clouston] name = "Ranald Clouston" [clouston.emails] clouston_email = "ranald.clouston@cs.au.dk" [clouston.homepages] [jaskelioff] name = "Mauro Jaskelioff" [jaskelioff.emails] [jaskelioff.homepages] jaskelioff_homepage = "http://www.fceia.unr.edu.ar/~mauro/" [caminati] name = "Marco B. Caminati" [caminati.emails] [caminati.homepages] [bengtson] name = "Jesper Bengtson" [bengtson.emails] [bengtson.homepages] bengtson_homepage = "http://www.itu.dk/people/jebe" [boutry] name = "Pierre Boutry" [boutry.emails] boutry_email = "boutry@unistra.fr" [boutry.homepages] [sternagelt] name = "Thomas Sternagel" [sternagelt.emails] [sternagelt.homepages] [guerraoui] name = "Rachid Guerraoui" [guerraoui.emails] guerraoui_email = "rachid.guerraoui@epfl.ch" [guerraoui.homepages] [dongol] name = "Brijesh Dongol" [dongol.emails] dongol_email = "brijesh.dongol@brunel.ac.uk" [dongol.homepages] [tuong] name = "Frédéric Tuong" [tuong.emails] tuong_email = "tuong@users.gforge.inria.fr" tuong_email1 = "ftuong@lri.fr" [tuong.homepages] tuong_homepage = "https://www.lri.fr/~ftuong/" [ullrich] name = "Sebastian Ullrich" [ullrich.emails] ullrich_email = "sebasti@nullri.ch" [ullrich.homepages] [essmann] name = "Robin Eßmann" [essmann.emails] essmann_email = "robin.essmann@tum.de" [essmann.homepages] [liu] name = "Junyi Liu" [liu.emails] [liu.homepages] [villadsen] name = "Jørgen Villadsen" [villadsen.emails] villadsen_email = "jovi@dtu.dk" [villadsen.homepages] villadsen_homepage = "https://people.compute.dtu.dk/jovi/" [fosters] name = "Simon Foster" [fosters.emails] fosters_email = "simon.foster@york.ac.uk" [fosters.homepages] fosters_homepage = "https://www-users.cs.york.ac.uk/~simonf/" -fosters_homepage1 = "http://www-users.cs.york.ac.uk/~simonf" [dubut] name = "Jérémy Dubut" [dubut.emails] dubut_email = "dubut@nii.ac.jp" [dubut.homepages] dubut_homepage = "http://group-mmm.org/~dubut/" [jiang] name = "Nan Jiang" [jiang.emails] jiang_email = "nanjiang@whu.edu.cn" [jiang.homepages] [hetzl] name = "Stefan Hetzl" [hetzl.emails] hetzl_email = "hetzl@logic.at" [hetzl.homepages] hetzl_homepage = "http://www.logic.at/people/hetzl/" [parkinson] name = "Matthew Parkinson" [parkinson.emails] [parkinson.homepages] parkinson_homepage = "http://research.microsoft.com/people/mattpark/" [maletzky] name = "Alexander Maletzky" [maletzky.emails] maletzky_email = "alexander.maletzky@risc.jku.at" maletzky_email1 = "alexander.maletzky@risc-software.at" [maletzky.homepages] maletzky_homepage = "https://risc.jku.at/m/alexander-maletzky/" [keefe] name = "Greg O'Keefe" [keefe.emails] [keefe.homepages] keefe_homepage = "http://users.rsise.anu.edu.au/~okeefe/" [brandt] name = "Felix Brandt" [brandt.emails] [brandt.homepages] brandt_homepage = "http://dss.in.tum.de/staff/brandt.html" [blasum] name = "Holger Blasum" [blasum.emails] blasum_email = "holger.blasum@sysgo.com" [blasum.homepages] [messner] name = "Florian Messner" [messner.emails] messner_email = "florian.g.messner@uibk.ac.at" [messner.homepages] [diaz] name = "Javier Díaz" [diaz.emails] diaz_email = "javier.diaz.manzi@gmail.com" [diaz.homepages] [prathamesh] name = "T.V.H. Prathamesh" [prathamesh.emails] prathamesh_email = "prathamesh@imsc.res.in" [prathamesh.homepages] [nestmann] name = "Uwe Nestmann" [nestmann.emails] [nestmann.homepages] nestmann_homepage = "https://www.mtv.tu-berlin.de/nestmann/" [siek] name = "Jeremy Siek" [siek.emails] siek_email = "jsiek@indiana.edu" [siek.homepages] siek_homepage = "http://homes.soic.indiana.edu/jsiek/" [stock] name = "Benedikt Stock" [stock.emails] stock_email = "benedikt1999@freenet.de" [stock.homepages] [boyton] name = "Andrew Boyton" [boyton.emails] boyton_email = "andrew.boyton@nicta.com.au" [boyton.homepages] [taha] name = "Safouan Taha" [taha.emails] taha_email = "safouan.taha@lri.fr" [taha.homepages] [ghourabi] name = "Fadoua Ghourabi" [ghourabi.emails] ghourabi_email = "fadouaghourabi@gmail.com" [ghourabi.homepages] [brinkop] name = "Hauke Brinkop" [brinkop.emails] brinkop_email = "hauke.brinkop@googlemail.com" [brinkop.homepages] [neumann] name = "René Neumann" [neumann.emails] -neumann_email = "neumannr@in.tum.de" -neumann_email1 = "rene.neumann@in.tum.de" +neumann_email = "rene.neumann@in.tum.de" [neumann.homepages] [schmaltz] name = "Julien Schmaltz" [schmaltz.emails] schmaltz_email = "Julien.Schmaltz@ou.nl" [schmaltz.homepages] [haslbeck] name = "Max W. Haslbeck" [haslbeck.emails] haslbeck_email = "maximilian.haslbeck@uibk.ac.at" haslbeck_email1 = "haslbecm@in.tum.de" haslbeck_email2 = "max.haslbeck@gmx.de" [haslbeck.homepages] haslbeck_homepage = "http://cl-informatik.uibk.ac.at/users/mhaslbeck/" -haslbeck_homepage1 = "http://cl-informatik.uibk.ac.at/users/mhaslbeck//" [reynaud] name = "Alban Reynaud" [reynaud.emails] [reynaud.homepages] [boulanger] name = "Frédéric Boulanger" [boulanger.emails] boulanger_email = "frederic.boulanger@centralesupelec.fr" [boulanger.homepages] [spasic] name = "Mirko Spasić" [spasic.emails] spasic_email = "mirko@matf.bg.ac.rs" [spasic.homepages] [heller] name = "Armin Heller" [heller.emails] [heller.homepages] [watt] name = "Conrad Watt" [watt.emails] watt_email = "caw77@cam.ac.uk" [watt.homepages] watt_homepage = "http://www.cl.cam.ac.uk/~caw77/" [hayes] name = "Ian J. Hayes" [hayes.emails] hayes_email = "ian.hayes@itee.uq.edu.au" -hayes_email1 = "Ian.Hayes@itee.uq.edu.au" [hayes.homepages] [haslbeckm] name = "Maximilian P. L. Haslbeck" [haslbeckm.emails] haslbeckm_email = "haslbema@in.tum.de" [haslbeckm.homepages] -haslbeckm_homepage = "http://www.in.tum.de/~haslbema" -haslbeckm_homepage1 = "http://in.tum.de/~haslbema/" +haslbeckm_homepage = "http://in.tum.de/~haslbema/" [bortin] name = "Maksym Bortin" [bortin.emails] -bortin_email = "Maksym.Bortin@nicta.com.au" -bortin_email1 = "maksym.bortin@nicta.com.au" +bortin_email = "maksym.bortin@nicta.com.au" [bortin.homepages] diff --git a/metadata/entries/Approximation_Algorithms.toml b/metadata/entries/Approximation_Algorithms.toml --- a/metadata/entries/Approximation_Algorithms.toml +++ b/metadata/entries/Approximation_Algorithms.toml @@ -1,36 +1,36 @@ title = "Verified Approximation Algorithms" date = 2020-01-16 topics = [ "Computer science/Algorithms/Approximation", ] abstract = """ 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. A detailed description of our work (excluding center selection) has been published in the proceedings of IJCAR 2020.""" license = "bsd" note = "" [authors] [authors.essmann] email = "essmann_email" [authors.nipkow] -homepage = "nipkow_homepage1" +homepage = "nipkow_homepage" [authors.robillard] homepage = "robillard_homepage" [authors.sulejmani] [contributors] [notify] nipkow = "nipkow_email" [history] [extra] diff --git a/metadata/entries/CAVA_LTL_Modelchecker.toml b/metadata/entries/CAVA_LTL_Modelchecker.toml --- a/metadata/entries/CAVA_LTL_Modelchecker.toml +++ b/metadata/entries/CAVA_LTL_Modelchecker.toml @@ -1,53 +1,53 @@ title = "A Fully Verified Executable LTL Model Checker" date = 2014-05-28 topics = [ "Computer science/Automata and formal languages", ] abstract = """ 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.

An early version of this model checker is described in the CAV 2013 paper with the same title.""" license = "bsd" note = "" [authors] [authors.esparza] homepage = "esparza_homepage" [authors.lammich] homepage = "lammich_homepage" [authors.neumann] -email = "neumann_email1" +email = "neumann_email" [authors.nipkow] homepage = "nipkow_homepage" [authors.schimpf] email = "schimpf_email" [authors.smaus] homepage = "smaus_homepage" [contributors] [notify] lammich = "lammich_email" [history] [extra] diff --git a/metadata/entries/CRDT.toml b/metadata/entries/CRDT.toml --- a/metadata/entries/CRDT.toml +++ b/metadata/entries/CRDT.toml @@ -1,47 +1,47 @@ title = "A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes" date = 2017-07-07 topics = [ "Computer science/Algorithms/Distributed", "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.gomes] -email = "gomes_email1" +email = "gomes_email" [authors.kleppmann] email = "kleppmann_email" [authors.mulligan] email = "mulligan_email" [authors.beresford] email = "beresford_email" [contributors] [notify] -gomes = "gomes_email1" +gomes = "gomes_email" mulligan = "mulligan_email" [history] [extra] diff --git a/metadata/entries/CYK.toml b/metadata/entries/CYK.toml --- a/metadata/entries/CYK.toml +++ b/metadata/entries/CYK.toml @@ -1,28 +1,28 @@ title = "A formalisation of the Cocke-Younger-Kasami algorithm" date = 2016-04-27 topics = [ "Computer science/Algorithms", "Computer science/Automata and formal languages", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bortin] email = "bortin_email" [contributors] [notify] -bortin = "bortin_email1" +bortin = "bortin_email" [history] [extra] diff --git a/metadata/entries/Category.toml b/metadata/entries/Category.toml --- a/metadata/entries/Category.toml +++ b/metadata/entries/Category.toml @@ -1,23 +1,23 @@ title = "Category Theory to Yoneda's Lemma" date = 2005-04-21 topics = [ "Mathematics/Category theory", ] abstract = "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." license = "lgpl" note = "" [authors] [authors.keefe] homepage = "keefe_homepage" [contributors] [notify] -paulson = "paulson_email1" +paulson = "paulson_email" [history] 2010-04-23 = "The definition of the constant equinumerous was slightly too weak in the original submission and has been fixed in revision 8c2b5b3c995f." [extra] diff --git a/metadata/entries/Closest_Pair_Points.toml b/metadata/entries/Closest_Pair_Points.toml --- a/metadata/entries/Closest_Pair_Points.toml +++ b/metadata/entries/Closest_Pair_Points.toml @@ -1,33 +1,33 @@ title = "Closest Pair of Points Algorithms" date = 2020-01-13 topics = [ "Computer science/Algorithms/Geometry", ] abstract = """ This entry provides two related verified divide-and-conquer algorithms solving the fundamental Closest Pair of Points problem in Computational Geometry. Functional correctness and the optimal running time of O(n log n) are proved. Executable code is generated which is empirically competitive with handwritten reference implementations.""" license = "bsd" note = "" [authors] [authors.rau] email = "rau_email" [authors.nipkow] -homepage = "nipkow_homepage2" +homepage = "nipkow_homepage" [contributors] [notify] rau = "rau_email" nipkow = "nipkow_email" [history] 2020-04-14 = "Incorporate Time_Monad of the AFP entry Root_Balanced_Tree." [extra] diff --git a/metadata/entries/Complex_Bounded_Operators.toml b/metadata/entries/Complex_Bounded_Operators.toml --- a/metadata/entries/Complex_Bounded_Operators.toml +++ b/metadata/entries/Complex_Bounded_Operators.toml @@ -1,37 +1,37 @@ title = "Complex Bounded Operators" date = 2021-09-18 topics = [ "Mathematics/Analysis", ] abstract = """ 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 (cblinfun) 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 Jordan_Normal_Form AFP entry.""" license = "bsd" note = "" [authors] [authors.caballero] homepage = "caballero_homepage" [authors.unruh] -homepage = "unruh_homepage1" +homepage = "unruh_homepage" [contributors] [notify] unruh = "unruh_email" [history] [extra] diff --git a/metadata/entries/Concurrent_Ref_Alg.toml b/metadata/entries/Concurrent_Ref_Alg.toml --- a/metadata/entries/Concurrent_Ref_Alg.toml +++ b/metadata/entries/Concurrent_Ref_Alg.toml @@ -1,46 +1,46 @@ title = "Concurrent Refinement Algebra and Rely Quotients" date = 2016-12-30 topics = [ "Computer science/Concurrency", ] abstract = """ 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 c and i is the process that, if executed in parallel with i implements c. It represents an abstract version of a rely condition generalised to a process.""" license = "bsd" note = "" [authors] [authors.fell] email = "fell_email" [authors.hayes] email = "hayes_email" [authors.velykis] homepage = "velykis_homepage" [contributors] [notify] -hayes = "hayes_email1" +hayes = "hayes_email" [history] [extra] diff --git a/metadata/entries/Constructive_Cryptography.toml b/metadata/entries/Constructive_Cryptography.toml --- a/metadata/entries/Constructive_Cryptography.toml +++ b/metadata/entries/Constructive_Cryptography.toml @@ -1,36 +1,36 @@ title = "Constructive Cryptography in HOL" date = 2018-12-17 topics = [ "Computer science/Security/Cryptography", "Mathematics/Probability theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.lochbihler] -homepage = "lochbihler_homepage1" +homepage = "lochbihler_homepage" [authors.sefidgar] [contributors] [notify] lochbihler = "lochbihler_email1" sefidgar = "sefidgar_email" [history] [extra] diff --git a/metadata/entries/Core_SC_DOM.toml b/metadata/entries/Core_SC_DOM.toml --- a/metadata/entries/Core_SC_DOM.toml +++ b/metadata/entries/Core_SC_DOM.toml @@ -1,40 +1,40 @@ title = "The Safely Composable DOM" date = 2020-09-28 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.herzberg] homepage = "herzberg_homepage" [contributors] [notify] brucker = "brucker_email2" herzberg = "herzberg_email" [history] [extra] diff --git a/metadata/entries/Correctness_Algebras.toml b/metadata/entries/Correctness_Algebras.toml --- a/metadata/entries/Correctness_Algebras.toml +++ b/metadata/entries/Correctness_Algebras.toml @@ -1,34 +1,34 @@ title = "Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations" date = 2021-10-12 topics = [ "Computer science/Programming languages/Logics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.guttmann] -homepage = "guttmann_homepage1" +homepage = "guttmann_homepage" [contributors] [notify] guttmann = "guttmann_email" [history] [extra] diff --git a/metadata/entries/DOM_Components.toml b/metadata/entries/DOM_Components.toml --- a/metadata/entries/DOM_Components.toml +++ b/metadata/entries/DOM_Components.toml @@ -1,38 +1,38 @@ title = "A Formalization of Web Components" date = 2020-09-28 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.herzberg] homepage = "herzberg_homepage" [contributors] [notify] brucker = "brucker_email2" herzberg = "herzberg_email" [history] [extra] diff --git a/metadata/entries/Design_Theory.toml b/metadata/entries/Design_Theory.toml --- a/metadata/entries/Design_Theory.toml +++ b/metadata/entries/Design_Theory.toml @@ -1,41 +1,41 @@ title = "Combinatorial Design Theory" date = 2021-08-13 topics = [ "Mathematics/Combinatorics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.edmonds] homepage = "edmonds_homepage" [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] edmonds = "edmonds_email" [history] [extra] diff --git a/metadata/entries/Differential_Game_Logic.toml b/metadata/entries/Differential_Game_Logic.toml --- a/metadata/entries/Differential_Game_Logic.toml +++ b/metadata/entries/Differential_Game_Logic.toml @@ -1,35 +1,35 @@ title = "Differential Game Logic" date = 2019-06-03 topics = [ "Computer science/Programming languages/Logics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.platzer] -homepage = "platzer_homepage1" +homepage = "platzer_homepage" [contributors] [notify] platzer = "platzer_email" [history] [extra] diff --git a/metadata/entries/Factored_Transition_System_Bounding.toml b/metadata/entries/Factored_Transition_System_Bounding.toml --- a/metadata/entries/Factored_Transition_System_Bounding.toml +++ b/metadata/entries/Factored_Transition_System_Bounding.toml @@ -1,43 +1,43 @@ title = "Upper Bounding Diameters of State Spaces of Factored Transition Systems" date = 2018-10-12 topics = [ "Computer science/Automata and formal languages", "Mathematics/Graph theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.kurz] [authors.abdulaziz] homepage = "abdulaziz_homepage" [contributors] [notify] kurz = "kurz_email" -abdulaziz = "abdulaziz_email2" +abdulaziz = "abdulaziz_email" [history] [extra] diff --git a/metadata/entries/Farkas.toml b/metadata/entries/Farkas.toml --- a/metadata/entries/Farkas.toml +++ b/metadata/entries/Farkas.toml @@ -1,36 +1,36 @@ title = "Farkas' Lemma and Motzkin's Transposition Theorem" date = 2019-01-17 topics = [ "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bottesch] homepage = "bottesch_homepage" [authors.haslbeck] homepage = "haslbeck_homepage" [authors.thiemann] -homepage = "thiemann_homepage1" +homepage = "thiemann_homepage" [contributors] [notify] thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/First_Order_Terms.toml b/metadata/entries/First_Order_Terms.toml --- a/metadata/entries/First_Order_Terms.toml +++ b/metadata/entries/First_Order_Terms.toml @@ -1,36 +1,36 @@ title = "First-Order Terms" date = 2018-02-06 topics = [ "Logic/Rewriting", "Computer science/Algorithms", ] abstract = """ 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 Isabelle Formalization of Rewriting IsaFoR, 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.""" license = "lgpl" note = "" [authors] [authors.sternagel] email = "sternagel_email" [authors.thiemann] -homepage = "thiemann_homepage2" +homepage = "thiemann_homepage" [contributors] [notify] sternagel = "sternagel_email" thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/Floyd_Warshall.toml b/metadata/entries/Floyd_Warshall.toml --- a/metadata/entries/Floyd_Warshall.toml +++ b/metadata/entries/Floyd_Warshall.toml @@ -1,38 +1,38 @@ title = "The Floyd-Warshall Algorithm for Shortest Paths" date = 2017-05-08 topics = [ "Computer science/Algorithms/Graph", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.wimmer] homepage = "wimmer_homepage" [authors.lammich] homepage = "lammich_homepage" [contributors] [notify] -wimmer = "wimmer_email1" +wimmer = "wimmer_email" [history] [extra] diff --git a/metadata/entries/Forcing.toml b/metadata/entries/Forcing.toml --- a/metadata/entries/Forcing.toml +++ b/metadata/entries/Forcing.toml @@ -1,34 +1,34 @@ title = "Formalization of Forcing in Isabelle/ZF" date = 2020-05-06 topics = [ "Logic/Set theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.gunther] email = "gunther_email" [authors.pagano] homepage = "pagano_homepage" [authors.terraf] -homepage = "terraf_homepage1" +homepage = "terraf_homepage" [contributors] [notify] gunther = "gunther_email" pagano = "pagano_email" terraf = "terraf_email" [history] [extra] diff --git a/metadata/entries/Fourier.toml b/metadata/entries/Fourier.toml --- a/metadata/entries/Fourier.toml +++ b/metadata/entries/Fourier.toml @@ -1,27 +1,27 @@ title = "Fourier Series" date = 2019-09-06 topics = [ "Mathematics/Analysis", ] abstract = """ 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""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Generic_Join.toml b/metadata/entries/Generic_Join.toml --- a/metadata/entries/Generic_Join.toml +++ b/metadata/entries/Generic_Join.toml @@ -1,31 +1,31 @@ title = "Formalization of Multiway-Join Algorithms" date = 2019-09-16 topics = [ "Computer science/Algorithms", ] abstract = """ 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, Ngo, Ré, and Rudra 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.""" license = "bsd" note = "" [authors] [authors.dardinier] [contributors] [notify] -dardinier = "dardinier_email1" +dardinier = "dardinier_email" traytel = "traytel_email1" [history] [extra] diff --git a/metadata/entries/Grothendieck_Schemes.toml b/metadata/entries/Grothendieck_Schemes.toml --- a/metadata/entries/Grothendieck_Schemes.toml +++ b/metadata/entries/Grothendieck_Schemes.toml @@ -1,35 +1,35 @@ title = "Grothendieck's Schemes in Algebraic Geometry" date = 2021-03-29 topics = [ "Mathematics/Algebra", "Mathematics/Geometry", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bordg] homepage = "bordg_homepage" [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [authors.li] homepage = "li_homepage" [contributors] [notify] bordg = "bordg_email" paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Hidden_Markov_Models.toml b/metadata/entries/Hidden_Markov_Models.toml --- a/metadata/entries/Hidden_Markov_Models.toml +++ b/metadata/entries/Hidden_Markov_Models.toml @@ -1,33 +1,33 @@ title = "Hidden Markov Models" date = 2018-05-25 topics = [ "Mathematics/Probability theory", "Computer science/Algorithms", ] abstract = """ 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].""" license = "bsd" note = "" [authors] [authors.wimmer] homepage = "wimmer_homepage" [contributors] [notify] -wimmer = "wimmer_email1" +wimmer = "wimmer_email" [history] [extra] diff --git a/metadata/entries/Hoare_Time.toml b/metadata/entries/Hoare_Time.toml --- a/metadata/entries/Hoare_Time.toml +++ b/metadata/entries/Hoare_Time.toml @@ -1,36 +1,36 @@ title = "Hoare Logics for Time Bounds" date = 2018-02-26 topics = [ "Computer science/Programming languages/Logics", ] abstract = """ 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 et al. and a separation logic 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.""" license = "bsd" note = "" [authors] [authors.haslbeckm] homepage = "haslbeckm_homepage" [authors.nipkow] -homepage = "nipkow_homepage3" +homepage = "nipkow_homepage" [contributors] [notify] haslbeckm = "haslbeckm_email" [history] [extra] diff --git a/metadata/entries/Independence_CH.toml b/metadata/entries/Independence_CH.toml --- a/metadata/entries/Independence_CH.toml +++ b/metadata/entries/Independence_CH.toml @@ -1,36 +1,36 @@ title = "The Independence of the Continuum Hypothesis in Isabelle/ZF" date = 2022-03-06 topics = [ "Logic/Set theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.gunther] email = "gunther_email" [authors.pagano] homepage = "pagano_homepage" [authors.terraf] -homepage = "terraf_homepage2" +homepage = "terraf_homepage" [authors.steinberg] email = "steinberg_email" [contributors] [notify] -terraf = "terraf_email1" -pagano = "pagano_email1" +terraf = "terraf_email" +pagano = "pagano_email" [history] [extra] diff --git a/metadata/entries/Irrationality_J_Hancl.toml b/metadata/entries/Irrationality_J_Hancl.toml --- a/metadata/entries/Irrationality_J_Hancl.toml +++ b/metadata/entries/Irrationality_J_Hancl.toml @@ -1,33 +1,33 @@ title = "Irrational Rapidly Convergent Series" date = 2018-05-23 topics = [ "Mathematics/Number theory", "Mathematics/Analysis", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.argyraki] -homepage = "argyraki_homepage1" +homepage = "argyraki_homepage" [authors.li] -homepage = "li_homepage1" +homepage = "li_homepage" [contributors] [notify] argyraki = "argyraki_email" li = "li_email" [history] [extra] diff --git a/metadata/entries/Irrationals_From_THEBOOK.toml b/metadata/entries/Irrationals_From_THEBOOK.toml --- a/metadata/entries/Irrationals_From_THEBOOK.toml +++ b/metadata/entries/Irrationals_From_THEBOOK.toml @@ -1,32 +1,32 @@ title = "Irrational numbers from THE BOOK" date = 2022-01-08 topics = [ "Mathematics/Number theory", ] abstract = """ An elementary proof is formalised: that exp r is irrational for every nonzero rational number r. The mathematical development comes from the well-known volume Proofs from THE BOOK, 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.""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/JiveDataStoreModel.toml b/metadata/entries/JiveDataStoreModel.toml --- a/metadata/entries/JiveDataStoreModel.toml +++ b/metadata/entries/JiveDataStoreModel.toml @@ -1,25 +1,25 @@ title = "Jive Data and Store Model" date = 2005-06-20 topics = [ "Computer science/Programming languages/Misc", ] abstract = "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." license = "lgpl" note = "" [authors] [authors.rauch] email = "rauch_email" [authors.schirmer] [contributors] [notify] klein = "klein_email" -schirmer = "schirmer_email1" +schirmer = "schirmer_email" [history] [extra] diff --git a/metadata/entries/KAD.toml b/metadata/entries/KAD.toml --- a/metadata/entries/KAD.toml +++ b/metadata/entries/KAD.toml @@ -1,49 +1,49 @@ title = "Kleene Algebras with Domain" date = 2016-04-12 topics = [ "Computer science/Programming languages/Logics", "Computer science/Automata and formal languages", "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.gomes] homepage = "gomes_homepage" [authors.guttmann] homepage = "guttmann_homepage" [authors.hoefner] homepage = "hoefner_homepage" [authors.struth] homepage = "struth_homepage" [authors.weber] homepage = "weber_homepage" [contributors] [notify] -guttmann = "guttmann_email1" +guttmann = "guttmann_email" struth = "struth_email" weber = "weber_email" [history] [extra] diff --git a/metadata/entries/KAT_and_DRA.toml b/metadata/entries/KAT_and_DRA.toml --- a/metadata/entries/KAT_and_DRA.toml +++ b/metadata/entries/KAT_and_DRA.toml @@ -1,38 +1,38 @@ title = "Kleene Algebra with Tests and Demonic Refinement Algebras" date = 2014-01-23 topics = [ "Computer science/Programming languages/Logics", "Computer science/Automata and formal languages", "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.armstrong] [authors.gomes] homepage = "gomes_homepage" [authors.struth] homepage = "struth_homepage" [contributors] [notify] -struth = "struth_email1" +struth = "struth_email" [history] [extra] diff --git a/metadata/entries/Kleene_Algebra.toml b/metadata/entries/Kleene_Algebra.toml --- a/metadata/entries/Kleene_Algebra.toml +++ b/metadata/entries/Kleene_Algebra.toml @@ -1,52 +1,52 @@ title = "Kleene Algebra" date = 2013-01-15 topics = [ "Computer science/Programming languages/Logics", "Computer science/Automata and formal languages", "Mathematics/Algebra", ] abstract = """ 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.

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).

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.""" license = "bsd" note = "" [authors] [authors.armstrong] [authors.struth] -homepage = "struth_homepage1" +homepage = "struth_homepage" [authors.weber] homepage = "weber_homepage" [contributors] [notify] struth = "struth_email" weber = "weber_email" [history] [extra] diff --git a/metadata/entries/Knuth_Bendix_Order.toml b/metadata/entries/Knuth_Bendix_Order.toml --- a/metadata/entries/Knuth_Bendix_Order.toml +++ b/metadata/entries/Knuth_Bendix_Order.toml @@ -1,31 +1,31 @@ title = "A Formalization of Knuth–Bendix Orders" date = 2020-05-13 topics = [ "Logic/Rewriting", ] abstract = """ We define a generalized version of Knuth–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.""" license = "bsd" note = "" [authors] [authors.sternagel] email = "sternagel_email" [authors.thiemann] -homepage = "thiemann_homepage1" +homepage = "thiemann_homepage" [contributors] [notify] sternagel = "sternagel_email" thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/Kruskal.toml b/metadata/entries/Kruskal.toml --- a/metadata/entries/Kruskal.toml +++ b/metadata/entries/Kruskal.toml @@ -1,36 +1,36 @@ title = "Kruskal's Algorithm for Minimum Spanning Forest" date = 2019-02-14 topics = [ "Computer science/Algorithms/Graph", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.haslbeckm] -homepage = "haslbeckm_homepage1" +homepage = "haslbeckm_homepage" [authors.lammich] homepage = "lammich_homepage" [authors.biendarra] [contributors] [notify] haslbeckm = "haslbeckm_email" lammich = "lammich_email" [history] [extra] diff --git a/metadata/entries/LLL_Basis_Reduction.toml b/metadata/entries/LLL_Basis_Reduction.toml --- a/metadata/entries/LLL_Basis_Reduction.toml +++ b/metadata/entries/LLL_Basis_Reduction.toml @@ -1,58 +1,58 @@ title = "A verified LLL algorithm" date = 2018-02-02 topics = [ "Computer science/Algorithms/Mathematical", "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bottesch] [authors.divason] -homepage = "divason_homepage1" +homepage = "divason_homepage" [authors.haslbeck] homepage = "haslbeck_homepage" [authors.joosten] -homepage = "joosten_homepage1" +homepage = "joosten_homepage" [authors.thiemann] -homepage = "thiemann_homepage2" +homepage = "thiemann_homepage" [authors.yamada] [contributors] [notify] bottesch = "bottesch_email" -divason = "divason_email1" +divason = "divason_email" haslbeck = "haslbeck_email" joosten = "joosten_email2" thiemann = "thiemann_email" yamada = "yamada_email1" [history] 2018-04-16 = """ Integrated formal complexity bounds (Haslbeck, Thiemann) """ 2018-05-25 = "Integrated much faster LLL implementation based on integer arithmetic (Bottesch, Haslbeck, Thiemann)" [extra] diff --git a/metadata/entries/LLL_Factorization.toml b/metadata/entries/LLL_Factorization.toml --- a/metadata/entries/LLL_Factorization.toml +++ b/metadata/entries/LLL_Factorization.toml @@ -1,47 +1,47 @@ title = "A verified factorization algorithm for integer polynomials with polynomial complexity" date = 2018-02-06 topics = [ "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.divason] -homepage = "divason_homepage1" +homepage = "divason_homepage" [authors.joosten] -homepage = "joosten_homepage1" +homepage = "joosten_homepage" [authors.thiemann] -homepage = "thiemann_homepage2" +homepage = "thiemann_homepage" [authors.yamada] email = "yamada_email1" [contributors] [notify] -divason = "divason_email1" +divason = "divason_email" joosten = "joosten_email2" thiemann = "thiemann_email" yamada = "yamada_email1" [history] [extra] diff --git a/metadata/entries/LTL.toml b/metadata/entries/LTL.toml --- a/metadata/entries/LTL.toml +++ b/metadata/entries/LTL.toml @@ -1,32 +1,32 @@ title = "Linear Temporal Logic" date = 2016-03-01 topics = [ "Logic/General logic/Temporal logic", "Computer science/Automata and formal languages", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.sickert] homepage = "sickert_homepage" [contributors] [contributors.seidl] email = "seidl_email" [notify] -sickert = "sickert_email1" +sickert = "sickert_email" [history] [extra] diff --git a/metadata/entries/LTL_to_DRA.toml b/metadata/entries/LTL_to_DRA.toml --- a/metadata/entries/LTL_to_DRA.toml +++ b/metadata/entries/LTL_to_DRA.toml @@ -1,26 +1,26 @@ title = "Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata" date = 2015-09-04 topics = [ "Computer science/Automata and formal languages", ] abstract = "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." license = "bsd" note = "" [authors] [authors.sickert] -email = "sickert_email1" +email = "sickert_email" [contributors] [notify] -sickert = "sickert_email1" +sickert = "sickert_email" [history] 2015-09-23 = """ Enable code export for the eager unfolding optimisation and reduce running time of the generated tool. Moreover, add support for the mlton SML compiler.
""" 2016-03-24 = "Make use of the LTL entry and include the simplifier." [extra] diff --git a/metadata/entries/Laplace_Transform.toml b/metadata/entries/Laplace_Transform.toml --- a/metadata/entries/Laplace_Transform.toml +++ b/metadata/entries/Laplace_Transform.toml @@ -1,29 +1,29 @@ title = "Laplace Transform" date = 2019-08-14 topics = [ "Mathematics/Analysis", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.immler] -homepage = "immler_homepage1" +homepage = "immler_homepage" [contributors] [notify] immler = "immler_email1" [history] [extra] diff --git a/metadata/entries/Lazy-Lists-II.toml b/metadata/entries/Lazy-Lists-II.toml --- a/metadata/entries/Lazy-Lists-II.toml +++ b/metadata/entries/Lazy-Lists-II.toml @@ -1,21 +1,21 @@ title = "Lazy Lists II" date = 2004-04-26 topics = [ "Computer science/Data structures", ] abstract = "This theory contains some useful extensions to the LList (lazy list) theory by Larry Paulson, 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." license = "bsd" note = "" [authors] [authors.friedrich] [contributors] [notify] -paulson = "paulson_email1" +paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Linear_Inequalities.toml b/metadata/entries/Linear_Inequalities.toml --- a/metadata/entries/Linear_Inequalities.toml +++ b/metadata/entries/Linear_Inequalities.toml @@ -1,35 +1,35 @@ title = "Linear Inequalities" date = 2019-06-21 topics = [ "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bottesch] homepage = "bottesch_homepage" [authors.reynaud] [authors.thiemann] -homepage = "thiemann_homepage1" +homepage = "thiemann_homepage" [contributors] [notify] thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/Linear_Programming.toml b/metadata/entries/Linear_Programming.toml --- a/metadata/entries/Linear_Programming.toml +++ b/metadata/entries/Linear_Programming.toml @@ -1,32 +1,32 @@ title = "Linear Programming" date = 2019-08-06 topics = [ "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.parsert] homepage = "parsert_homepage" [authors.kaliszyk] -homepage = "kaliszyk_homepage1" +homepage = "kaliszyk_homepage" [contributors] [notify] parsert = "parsert_email" kaliszyk = "kaliszyk_email" [history] [extra] diff --git a/metadata/entries/List_Update.toml b/metadata/entries/List_Update.toml --- a/metadata/entries/List_Update.toml +++ b/metadata/entries/List_Update.toml @@ -1,35 +1,35 @@ title = "Analysis of List Update Algorithms" date = 2016-02-17 topics = [ "Computer science/Algorithms/Online", ] abstract = """

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 Online Computation and Competitive Analysis by Borodin and El-Yaniv.

For an informal description see the FSTTCS 2016 publication Verified Analysis of List Update Algorithms by Haslbeck and Nipkow.

""" license = "bsd" note = "" [authors] [authors.haslbeckm] -homepage = "haslbeckm_homepage1" +homepage = "haslbeckm_homepage" [authors.nipkow] homepage = "nipkow_homepage" [contributors] [notify] nipkow = "nipkow_email" [history] [extra] diff --git a/metadata/entries/Lowe_Ontological_Argument.toml b/metadata/entries/Lowe_Ontological_Argument.toml --- a/metadata/entries/Lowe_Ontological_Argument.toml +++ b/metadata/entries/Lowe_Ontological_Argument.toml @@ -1,34 +1,34 @@ title = "Computer-assisted Reconstruction and Assessment of E. J. Lowe's Modal Ontological Argument" date = 2017-09-21 topics = [ "Logic/Philosophical aspects", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.fuenmayor] email = "fuenmayor_email" [authors.benzmueller] -homepage = "benzmueller_homepage2" +homepage = "benzmueller_homepage" [contributors] [notify] fuenmayor = "fuenmayor_email" benzmueller = "benzmueller_email" [history] [extra] diff --git a/metadata/entries/Mereology.toml b/metadata/entries/Mereology.toml --- a/metadata/entries/Mereology.toml +++ b/metadata/entries/Mereology.toml @@ -1,24 +1,24 @@ title = "Mereology" date = 2021-03-01 topics = [ "Logic/Philosophical aspects", ] abstract = """ We use Isabelle/HOL to verify elementary theorems and alternative axiomatizations of classical extensional mereology.""" license = "bsd" note = "" [authors] [authors.blumson] -homepage = "blumson_homepage1" +homepage = "blumson_homepage" [contributors] [notify] blumson = "blumson_email" [history] [extra] diff --git a/metadata/entries/Modular_arithmetic_LLL_and_HNF_algorithms.toml b/metadata/entries/Modular_arithmetic_LLL_and_HNF_algorithms.toml --- a/metadata/entries/Modular_arithmetic_LLL_and_HNF_algorithms.toml +++ b/metadata/entries/Modular_arithmetic_LLL_and_HNF_algorithms.toml @@ -1,39 +1,39 @@ title = "Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation" date = 2021-03-12 topics = [ "Computer science/Algorithms/Mathematical", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.bottesch] [authors.divason] -homepage = "divason_homepage2" +homepage = "divason_homepage" [authors.thiemann] email = "thiemann_email" [contributors] [notify] thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/Monad_Memo_DP.toml b/metadata/entries/Monad_Memo_DP.toml --- a/metadata/entries/Monad_Memo_DP.toml +++ b/metadata/entries/Monad_Memo_DP.toml @@ -1,40 +1,40 @@ title = "Monadification, Memoization and Dynamic Programming" date = 2018-05-22 topics = [ "Computer science/Programming languages/Transformations", "Computer science/Algorithms", "Computer science/Functional programming", ] abstract = """ 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].""" license = "bsd" note = "" [authors] [authors.wimmer] -homepage = "wimmer_homepage1" +homepage = "wimmer_homepage" [authors.hu] email = "hu_email" [authors.nipkow] -homepage = "nipkow_homepage4" +homepage = "nipkow_homepage" [contributors] [notify] -wimmer = "wimmer_email1" +wimmer = "wimmer_email" [history] [extra] diff --git a/metadata/entries/Nash_Williams.toml b/metadata/entries/Nash_Williams.toml --- a/metadata/entries/Nash_Williams.toml +++ b/metadata/entries/Nash_Williams.toml @@ -1,28 +1,28 @@ title = "The Nash-Williams Partition Theorem" date = 2020-05-16 topics = [ "Mathematics/Combinatorics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Octonions.toml b/metadata/entries/Octonions.toml --- a/metadata/entries/Octonions.toml +++ b/metadata/entries/Octonions.toml @@ -1,31 +1,31 @@ title = "Octonions" date = 2018-09-14 topics = [ "Mathematics/Algebra", "Mathematics/Geometry", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.argyraki] -homepage = "argyraki_homepage1" +homepage = "argyraki_homepage" [contributors] [notify] argyraki = "argyraki_email" [history] [extra] diff --git a/metadata/entries/OpSets.toml b/metadata/entries/OpSets.toml --- a/metadata/entries/OpSets.toml +++ b/metadata/entries/OpSets.toml @@ -1,47 +1,47 @@ title = "OpSets: Sequential Specifications for Replicated Datatypes" date = 2018-05-10 topics = [ "Computer science/Algorithms/Distributed", "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.kleppmann] -email = "kleppmann_email1" +email = "kleppmann_email" [authors.gomes] -email = "gomes_email3" +email = "gomes_email" [authors.mulligan] email = "mulligan_email1" [authors.beresford] -email = "beresford_email1" +email = "beresford_email" [contributors] [notify] -gomes = "gomes_email1" +gomes = "gomes_email" [history] [extra] diff --git a/metadata/entries/Optimal_BST.toml b/metadata/entries/Optimal_BST.toml --- a/metadata/entries/Optimal_BST.toml +++ b/metadata/entries/Optimal_BST.toml @@ -1,31 +1,31 @@ title = "Optimal Binary Search Trees" date = 2018-05-27 topics = [ "Computer science/Algorithms", "Computer science/Data structures", ] abstract = """ 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 Monadification, Memoization and Dynamic Programming, thus yielding dynamic programming algorithms.""" license = "bsd" note = "" [authors] [authors.nipkow] -homepage = "nipkow_homepage3" +homepage = "nipkow_homepage" [authors.somogyi] [contributors] [notify] nipkow = "nipkow_email" [history] [extra] diff --git a/metadata/entries/Order_Lattice_Props.toml b/metadata/entries/Order_Lattice_Props.toml --- a/metadata/entries/Order_Lattice_Props.toml +++ b/metadata/entries/Order_Lattice_Props.toml @@ -1,30 +1,30 @@ title = "Properties of Orderings and Lattices" date = 2018-12-11 topics = [ "Mathematics/Order", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.struth] -homepage = "struth_homepage1" +homepage = "struth_homepage" [contributors] [notify] struth = "struth_email" [history] [extra] diff --git a/metadata/entries/Ordered_Resolution_Prover.toml b/metadata/entries/Ordered_Resolution_Prover.toml --- a/metadata/entries/Ordered_Resolution_Prover.toml +++ b/metadata/entries/Ordered_Resolution_Prover.toml @@ -1,39 +1,39 @@ title = "Formalization of Bachmair and Ganzinger's Ordered Resolution Prover" date = 2018-01-18 topics = [ "Logic/General logic/Mechanization of proofs", ] abstract = """ This Isabelle/HOL formalization covers Sections 2 to 4 of Bachmair and Ganzinger's \"Resolution Theorem Proving\" chapter in the Handbook of Automated Reasoning. 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.""" license = "bsd" note = "" [authors] [authors.schlichtkrull] homepage = "schlichtkrull_homepage" [authors.blanchette] email = "blanchette_email1" [authors.traytel] homepage = "traytel_homepage" [authors.waldmann] -email = "waldmann_email1" +email = "waldmann_email" [contributors] [notify] schlichtkrull = "schlichtkrull_email" blanchette = "blanchette_email1" [history] [extra] diff --git a/metadata/entries/Ordinal.toml b/metadata/entries/Ordinal.toml --- a/metadata/entries/Ordinal.toml +++ b/metadata/entries/Ordinal.toml @@ -1,22 +1,22 @@ title = "Countable Ordinals" date = 2005-11-11 topics = [ "Logic/Set theory", ] abstract = "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." license = "bsd" note = "" [authors] [authors.huffman] homepage = "huffman_homepage" [contributors] [notify] -paulson = "paulson_email1" +paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Ordinal_Partitions.toml b/metadata/entries/Ordinal_Partitions.toml --- a/metadata/entries/Ordinal_Partitions.toml +++ b/metadata/entries/Ordinal_Partitions.toml @@ -1,39 +1,39 @@ title = "Ordinal Partitions" date = 2020-08-03 topics = [ "Mathematics/Combinatorics", "Logic/Set theory", ] abstract = """ 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: $\\omega^{1+\\alpha\\cdot n} \\to (\\omega^{1+\\alpha}, 2^n)^2$.""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Poincare_Bendixson.toml b/metadata/entries/Poincare_Bendixson.toml --- a/metadata/entries/Poincare_Bendixson.toml +++ b/metadata/entries/Poincare_Bendixson.toml @@ -1,37 +1,37 @@ title = "The Poincaré-Bendixson Theorem" date = 2019-12-18 topics = [ "Mathematics/Analysis", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.immler] -homepage = "immler_homepage2" +homepage = "immler_homepage" [authors.tan] homepage = "tan_homepage" [contributors] [notify] immler = "immler_email1" tan = "tan_email" [history] [extra] diff --git a/metadata/entries/Prime_Number_Theorem.toml b/metadata/entries/Prime_Number_Theorem.toml --- a/metadata/entries/Prime_Number_Theorem.toml +++ b/metadata/entries/Prime_Number_Theorem.toml @@ -1,60 +1,60 @@ title = "The Prime Number Theorem" date = 2018-09-19 topics = [ "Mathematics/Number theory", ] abstract = """

This article provides a short proof of the Prime Number Theorem in several equivalent forms, most notably π(x) ~ x/ln x where π(x) is the number of primes no larger than x. It also defines other basic number-theoretic functions related to primes like Chebyshev's functions ϑ and ψ and the “n-th prime number” function pn. We also show various bounds and relationship between these functions are shown. Lastly, we derive Mertens' First and Second Theorem, i. e. ∑px ln p/p = ln x + O(1) and ∑px 1/p = ln ln x + M + O(1/ln x). We also give explicit bounds for the remainder terms.

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 ∑px ln p/p = ln x + c + o(1).

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 et al. 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.

""" license = "bsd" note = "" [authors] [authors.eberl] homepage = "eberl_homepage" [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] eberl = "eberl_email" [history] [extra] diff --git a/metadata/entries/Probabilistic_Timed_Automata.toml b/metadata/entries/Probabilistic_Timed_Automata.toml --- a/metadata/entries/Probabilistic_Timed_Automata.toml +++ b/metadata/entries/Probabilistic_Timed_Automata.toml @@ -1,38 +1,38 @@ title = "Probabilistic Timed Automata" date = 2018-05-24 topics = [ "Mathematics/Probability theory", "Computer science/Automata and formal languages", ] abstract = """ 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].""" license = "bsd" note = "" [authors] [authors.wimmer] homepage = "wimmer_homepage" [authors.hoelzl] -homepage = "hoelzl_homepage1" +homepage = "hoelzl_homepage" [contributors] [notify] -wimmer = "wimmer_email1" +wimmer = "wimmer_email" hoelzl = "hoelzl_email" [history] [extra] diff --git a/metadata/entries/Progress_Tracking.toml b/metadata/entries/Progress_Tracking.toml --- a/metadata/entries/Progress_Tracking.toml +++ b/metadata/entries/Progress_Tracking.toml @@ -1,41 +1,41 @@ title = "Formalization of Timely Dataflow's Progress Tracking Protocol" date = 2021-04-13 topics = [ "Computer science/Algorithms/Distributed", ] abstract = """ 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 ITP'21 paper.""" license = "bsd" note = "" [authors] [authors.brun] [authors.decova] [authors.lattuada] homepage = "lattuada_homepage" [authors.traytel] -homepage = "traytel_homepage1" +homepage = "traytel_homepage" [contributors] [notify] brun = "brun_email" traytel = "traytel_email2" [history] [extra] diff --git a/metadata/entries/Projective_Measurements.toml b/metadata/entries/Projective_Measurements.toml --- a/metadata/entries/Projective_Measurements.toml +++ b/metadata/entries/Projective_Measurements.toml @@ -1,28 +1,28 @@ title = "Quantum projective measurements and the CHSH inequality" date = 2021-03-03 topics = [ "Computer science/Algorithms/Quantum computing", "Mathematics/Physics/Quantum information", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.echenim] -homepage = "echenim_homepage1" +homepage = "echenim_homepage" [contributors] [notify] echenim = "echenim_email" [history] [extra] diff --git a/metadata/entries/Promela.toml b/metadata/entries/Promela.toml --- a/metadata/entries/Promela.toml +++ b/metadata/entries/Promela.toml @@ -1,31 +1,31 @@ title = "Promela Formalization" date = 2014-05-28 topics = [ "Computer science/System description languages", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.neumann] -email = "neumann_email1" +email = "neumann_email" [contributors] [notify] [history] [extra] diff --git a/metadata/entries/Quantales.toml b/metadata/entries/Quantales.toml --- a/metadata/entries/Quantales.toml +++ b/metadata/entries/Quantales.toml @@ -1,25 +1,25 @@ title = "Quantales" date = 2018-12-11 topics = [ "Mathematics/Algebra", ] abstract = """ These mathematical components formalise basic properties of quantales, together with some important models, constructions, and concepts, including quantic nuclei and conuclei.""" license = "bsd" note = "" [authors] [authors.struth] -homepage = "struth_homepage1" +homepage = "struth_homepage" [contributors] [notify] struth = "struth_email" [history] [extra] diff --git a/metadata/entries/Quaternions.toml b/metadata/entries/Quaternions.toml --- a/metadata/entries/Quaternions.toml +++ b/metadata/entries/Quaternions.toml @@ -1,32 +1,32 @@ title = "Quaternions" date = 2018-09-05 topics = [ "Mathematics/Algebra", "Mathematics/Geometry", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/ROBDD.toml b/metadata/entries/ROBDD.toml --- a/metadata/entries/ROBDD.toml +++ b/metadata/entries/ROBDD.toml @@ -1,40 +1,40 @@ title = "Algorithms for Reduced Ordered Binary Decision Diagrams" date = 2016-04-27 topics = [ "Computer science/Algorithms", "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.michaelis] homepage = "michaelis_homepage" [authors.haslbeck] -homepage = "haslbeck_homepage1" +homepage = "haslbeck_homepage" [authors.lammich] homepage = "lammich_homepage" [authors.hupel] homepage = "hupel_homepage" [contributors] [notify] michaelis = "michaelis_email2" haslbeck = "haslbeck_email1" [history] [extra] diff --git a/metadata/entries/Registers.toml b/metadata/entries/Registers.toml --- a/metadata/entries/Registers.toml +++ b/metadata/entries/Registers.toml @@ -1,31 +1,31 @@ title = "Quantum and Classical Registers" date = 2021-10-28 topics = [ "Computer science/Algorithms/Quantum computing", "Computer science/Programming languages/Logics", "Computer science/Semantics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.unruh] -homepage = "unruh_homepage1" +homepage = "unruh_homepage" [contributors] [notify] unruh = "unruh_email" [history] [extra] diff --git a/metadata/entries/Regular_Algebras.toml b/metadata/entries/Regular_Algebras.toml --- a/metadata/entries/Regular_Algebras.toml +++ b/metadata/entries/Regular_Algebras.toml @@ -1,35 +1,35 @@ title = "Regular Algebras" date = 2014-05-21 topics = [ "Computer science/Automata and formal languages", "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.fosters] -homepage = "fosters_homepage1" +homepage = "fosters_homepage" [authors.struth] homepage = "struth_homepage" [contributors] [notify] fosters = "fosters_email" struth = "struth_email" [history] [extra] diff --git a/metadata/entries/Regular_Tree_Relations.toml b/metadata/entries/Regular_Tree_Relations.toml --- a/metadata/entries/Regular_Tree_Relations.toml +++ b/metadata/entries/Regular_Tree_Relations.toml @@ -1,48 +1,48 @@ title = "Regular Tree Relations" date = 2021-12-15 topics = [ "Computer science/Automata and formal languages", ] abstract = """ 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 tree automata APF-entry 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 Collections Framework, also by Peter Lammich, to obtain efficient code. All proven constructions of the closure properties are exportable using the Isabelle/HOL code generation facilities.""" license = "bsd" note = "" [authors] [authors.lochmann] email = "lochmann_email" [authors.felgenhauer] [authors.sternagel] homepage = "sternagel_homepage" [authors.thiemann] -homepage = "thiemann_homepage2" +homepage = "thiemann_homepage" [authors.sternagelt] [contributors] [notify] lochmann = "lochmann_email" [history] [extra] diff --git a/metadata/entries/Relation_Algebra.toml b/metadata/entries/Relation_Algebra.toml --- a/metadata/entries/Relation_Algebra.toml +++ b/metadata/entries/Relation_Algebra.toml @@ -1,38 +1,38 @@ title = "Relation Algebra" date = 2014-01-25 topics = [ "Mathematics/Algebra", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.armstrong] [authors.fosters] email = "fosters_email" [authors.struth] -homepage = "struth_homepage1" +homepage = "struth_homepage" [authors.weber] homepage = "weber_homepage" [contributors] [notify] struth = "struth_email" weber = "weber_email" [history] [extra] diff --git a/metadata/entries/Relational-Incorrectness-Logic.toml b/metadata/entries/Relational-Incorrectness-Logic.toml --- a/metadata/entries/Relational-Incorrectness-Logic.toml +++ b/metadata/entries/Relational-Incorrectness-Logic.toml @@ -1,35 +1,35 @@ title = "An Under-Approximate Relational Logic" date = 2020-03-12 topics = [ "Computer science/Programming languages/Logics", "Computer science/Security", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.murray] -homepage = "murray_homepage1" +homepage = "murray_homepage" [contributors] [notify] murray = "murray_email" [history] [extra] diff --git a/metadata/entries/Relational_Forests.toml b/metadata/entries/Relational_Forests.toml --- a/metadata/entries/Relational_Forests.toml +++ b/metadata/entries/Relational_Forests.toml @@ -1,29 +1,29 @@ title = "Relational Forests" date = 2021-08-03 topics = [ "Mathematics/Graph theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.guttmann] -homepage = "guttmann_homepage1" +homepage = "guttmann_homepage" [contributors] [notify] guttmann = "guttmann_email" [history] [extra] diff --git a/metadata/entries/Roth_Arithmetic_Progressions.toml b/metadata/entries/Roth_Arithmetic_Progressions.toml --- a/metadata/entries/Roth_Arithmetic_Progressions.toml +++ b/metadata/entries/Roth_Arithmetic_Progressions.toml @@ -1,44 +1,44 @@ title = "Roth's Theorem on Arithmetic Progressions" date = 2021-12-28 topics = [ "Mathematics/Graph theory", "Mathematics/Combinatorics", ] abstract = """ 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 \"Graph Theory and Additive Combinatorics\" (revised version here) and W.T. Gowers's Cambridge lecture notes \"Topics in Combinatorics\". We also refer to the University of Georgia notes by Stephanie Bell and Will Grodzicki, \"Using Szemerédi's Regularity Lemma to Prove Roth's Theorem\".""" license = "bsd" note = "" [authors] [authors.edmonds] homepage = "edmonds_homepage" [authors.argyraki] homepage = "argyraki_homepage" [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/SATSolverVerification.toml b/metadata/entries/SATSolverVerification.toml --- a/metadata/entries/SATSolverVerification.toml +++ b/metadata/entries/SATSolverVerification.toml @@ -1,21 +1,21 @@ title = "Formal Verification of Modern SAT Solvers" date = 2008-07-23 topics = [ "Computer science/Algorithms", ] abstract = "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: 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." license = "bsd" note = "" [authors] [authors.maricf] -homepage = "maricf_homepage1" +homepage = "maricf_homepage" [contributors] [notify] [history] [extra] diff --git a/metadata/entries/SC_DOM_Components.toml b/metadata/entries/SC_DOM_Components.toml --- a/metadata/entries/SC_DOM_Components.toml +++ b/metadata/entries/SC_DOM_Components.toml @@ -1,42 +1,42 @@ title = "A Formalization of Safely Composable Web Components" date = 2020-09-28 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.herzberg] homepage = "herzberg_homepage" [contributors] [notify] brucker = "brucker_email2" herzberg = "herzberg_email" [history] [extra] diff --git a/metadata/entries/SIFUM_Type_Systems.toml b/metadata/entries/SIFUM_Type_Systems.toml --- a/metadata/entries/SIFUM_Type_Systems.toml +++ b/metadata/entries/SIFUM_Type_Systems.toml @@ -1,44 +1,44 @@ title = "A Formalization of Assumptions and Guarantees for Compositional Noninterference" date = 2014-04-23 topics = [ "Computer science/Security", "Computer science/Programming languages/Type systems", ] abstract = """ 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.

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.""" license = "bsd" note = "" [authors] [authors.grewe] -email = "grewe_email1" +email = "grewe_email" [authors.mantel] email = "mantel_email" [authors.schoepe] email = "schoepe_email" [contributors] [notify] [history] [extra] diff --git a/metadata/entries/Safe_Distance.toml b/metadata/entries/Safe_Distance.toml --- a/metadata/entries/Safe_Distance.toml +++ b/metadata/entries/Safe_Distance.toml @@ -1,37 +1,37 @@ title = "A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles" date = 2020-06-01 topics = [ "Computer science/Algorithms/Mathematical", "Mathematics/Physics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.rizaldi] email = "rizaldi_email" [authors.immler] -homepage = "immler_homepage2" +homepage = "immler_homepage" [contributors] [notify] rizaldi = "rizaldi_email" -immler = "immler_email2" +immler = "immler_email1" rau = "rau_email" [history] [extra] diff --git a/metadata/entries/Saturation_Framework_Extensions.toml b/metadata/entries/Saturation_Framework_Extensions.toml --- a/metadata/entries/Saturation_Framework_Extensions.toml +++ b/metadata/entries/Saturation_Framework_Extensions.toml @@ -1,38 +1,38 @@ title = "Extensions to the Comprehensive Framework for Saturation Theorem Proving" date = 2020-08-25 topics = [ "Logic/General logic/Mechanization of proofs", ] abstract = """ This Isabelle/HOL formalization extends the AFP entry Saturation_Framework with the following contributions:

""" license = "bsd" note = "" [authors] [authors.blanchette] homepage = "blanchette_homepage1" [authors.tourret] -homepage = "tourret_homepage1" +homepage = "tourret_homepage" [contributors] [notify] blanchette = "blanchette_email" [history] [extra] diff --git a/metadata/entries/Shadow_DOM.toml b/metadata/entries/Shadow_DOM.toml --- a/metadata/entries/Shadow_DOM.toml +++ b/metadata/entries/Shadow_DOM.toml @@ -1,41 +1,41 @@ title = "A Formal Model of the Document Object Model with Shadow Roots" date = 2020-09-28 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.herzberg] homepage = "herzberg_homepage" [contributors] [notify] brucker = "brucker_email2" herzberg = "herzberg_email" [history] [extra] diff --git a/metadata/entries/Shadow_SC_DOM.toml b/metadata/entries/Shadow_SC_DOM.toml --- a/metadata/entries/Shadow_SC_DOM.toml +++ b/metadata/entries/Shadow_SC_DOM.toml @@ -1,43 +1,43 @@ title = "A Formal Model of the Safely Composable Document Object Model with Shadow Roots" date = 2020-09-28 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.herzberg] homepage = "herzberg_homepage" [contributors] [notify] brucker = "brucker_email2" herzberg = "herzberg_email" [history] [extra] diff --git a/metadata/entries/Simple_Firewall.toml b/metadata/entries/Simple_Firewall.toml --- a/metadata/entries/Simple_Firewall.toml +++ b/metadata/entries/Simple_Firewall.toml @@ -1,44 +1,44 @@ title = "Simple Firewall" date = 2016-08-24 topics = [ "Computer science/Networks", ] abstract = """ 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 Verified iptables Firewall Analysis, IFIP Networking 2016.""" license = "bsd" note = "" [authors] [authors.diekmann] homepage = "diekmann_homepage" [authors.michaelis] homepage = "michaelis_homepage" [authors.haslbeck] -homepage = "haslbeck_homepage1" +homepage = "haslbeck_homepage" [contributors] [notify] diekmann = "diekmann_email" haslbeck = "haslbeck_email2" [history] [extra] diff --git a/metadata/entries/Simplex.toml b/metadata/entries/Simplex.toml --- a/metadata/entries/Simplex.toml +++ b/metadata/entries/Simplex.toml @@ -1,37 +1,37 @@ title = "An Incremental Simplex Algorithm with Unsatisfiable Core Generation" date = 2018-08-24 topics = [ "Computer science/Algorithms/Optimization", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.maricf] email = "maricf_email" [authors.spasic] email = "spasic_email" [authors.thiemann] -homepage = "thiemann_homepage1" +homepage = "thiemann_homepage" [contributors] [notify] thiemann = "thiemann_email" [history] [extra] diff --git a/metadata/entries/Simplicial_complexes_and_boolean_functions.toml b/metadata/entries/Simplicial_complexes_and_boolean_functions.toml --- a/metadata/entries/Simplicial_complexes_and_boolean_functions.toml +++ b/metadata/entries/Simplicial_complexes_and_boolean_functions.toml @@ -1,37 +1,37 @@ title = "Simplicial Complexes and Boolean functions" date = 2021-11-29 topics = [ "Mathematics/Topology", ] abstract = """ 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 ROBDD (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.""" license = "bsd" note = "" [authors] [authors.aransay] -homepage = "aransay_homepage1" +homepage = "aransay_homepage" [authors.campo] email = "campo_email" [authors.michaelis] -homepage = "michaelis_homepage1" +homepage = "michaelis_homepage" [contributors] [notify] aransay = "aransay_email" [history] [extra] diff --git a/metadata/entries/Skip_Lists.toml b/metadata/entries/Skip_Lists.toml --- a/metadata/entries/Skip_Lists.toml +++ b/metadata/entries/Skip_Lists.toml @@ -1,34 +1,34 @@ title = "Skip Lists" date = 2020-01-09 topics = [ "Computer science/Data structures", ] abstract = """

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.

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.

""" license = "bsd" note = "" [authors] [authors.haslbeck] homepage = "haslbeck_homepage" [authors.eberl] -homepage = "eberl_homepage1" +homepage = "eberl_homepage" [contributors] [notify] haslbeck = "haslbeck_email2" [history] [extra] diff --git a/metadata/entries/Smith_Normal_Form.toml b/metadata/entries/Smith_Normal_Form.toml --- a/metadata/entries/Smith_Normal_Form.toml +++ b/metadata/entries/Smith_Normal_Form.toml @@ -1,36 +1,36 @@ title = "A verified algorithm for computing the Smith normal form of a matrix" date = 2020-05-23 topics = [ "Mathematics/Algebra", "Computer science/Algorithms/Mathematical", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.divason] -homepage = "divason_homepage2" +homepage = "divason_homepage" [contributors] [notify] -divason = "divason_email1" +divason = "divason_email" [history] [extra] diff --git a/metadata/entries/Smooth_Manifolds.toml b/metadata/entries/Smooth_Manifolds.toml --- a/metadata/entries/Smooth_Manifolds.toml +++ b/metadata/entries/Smooth_Manifolds.toml @@ -1,34 +1,34 @@ title = "Smooth Manifolds" date = 2018-10-22 topics = [ "Mathematics/Analysis", "Mathematics/Topology", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.immler] -homepage = "immler_homepage2" +homepage = "immler_homepage" [authors.zhan] homepage = "zhan_homepage" [contributors] [notify] immler = "immler_email" zhan = "zhan_email" [history] [extra] diff --git a/metadata/entries/Stream-Fusion.toml b/metadata/entries/Stream-Fusion.toml --- a/metadata/entries/Stream-Fusion.toml +++ b/metadata/entries/Stream-Fusion.toml @@ -1,22 +1,22 @@ title = "Stream Fusion" date = 2009-04-29 topics = [ "Computer science/Functional programming", ] abstract = "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 online.)

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." license = "bsd" note = "" [authors] [authors.huffman] -homepage = "huffman_homepage1" +homepage = "huffman_homepage" [contributors] [notify] huffman = "huffman_email1" [history] [extra] diff --git a/metadata/entries/Strong_Security.toml b/metadata/entries/Strong_Security.toml --- a/metadata/entries/Strong_Security.toml +++ b/metadata/entries/Strong_Security.toml @@ -1,51 +1,51 @@ title = "A Formalization of Strong Security" date = 2014-04-23 topics = [ "Computer science/Security", "Computer science/Programming languages/Type systems", ] abstract = """ 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.

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.

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.""" license = "bsd" note = "" [authors] [authors.grewe] -email = "grewe_email1" +email = "grewe_email" [authors.lux] email = "lux_email" [authors.mantel] email = "mantel_email" [authors.sauer] email = "sauer_email" [contributors] [notify] [history] [extra] diff --git a/metadata/entries/Szemeredi_Regularity.toml b/metadata/entries/Szemeredi_Regularity.toml --- a/metadata/entries/Szemeredi_Regularity.toml +++ b/metadata/entries/Szemeredi_Regularity.toml @@ -1,42 +1,42 @@ title = "Szemerédi's Regularity Lemma" date = 2021-11-05 topics = [ "Mathematics/Graph theory", "Mathematics/Combinatorics", ] abstract = """ Szemerédi's regularity lemma 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 Tim Gowers and Yufei Zhao.""" license = "bsd" note = "" [authors] [authors.edmonds] homepage = "edmonds_homepage" [authors.argyraki] homepage = "argyraki_homepage2" [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/TESL_Language.toml b/metadata/entries/TESL_Language.toml --- a/metadata/entries/TESL_Language.toml +++ b/metadata/entries/TESL_Language.toml @@ -1,59 +1,59 @@ title = "A Formal Development of a Polychronous Polytimed Coordination Language" date = 2019-07-30 topics = [ "Computer science/System description languages", "Computer science/Semantics", "Computer science/Concurrency", ] abstract = """ 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:

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.""" license = "bsd" note = "" [authors] [authors.van] email = "van_email" [authors.boulanger] email = "boulanger_email" [authors.wolff] -email = "wolff_email1" +email = "wolff_email" [contributors] [notify] boulanger = "boulanger_email" -wolff = "wolff_email1" +wolff = "wolff_email" [history] [extra] diff --git a/metadata/entries/Timed_Automata.toml b/metadata/entries/Timed_Automata.toml --- a/metadata/entries/Timed_Automata.toml +++ b/metadata/entries/Timed_Automata.toml @@ -1,43 +1,43 @@ title = "Timed Automata" date = 2016-03-08 topics = [ "Computer science/Automata and formal languages", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.wimmer] homepage = "wimmer_homepage" [contributors] [notify] -wimmer = "wimmer_email1" +wimmer = "wimmer_email" [history] [extra] diff --git a/metadata/entries/Topology.toml b/metadata/entries/Topology.toml --- a/metadata/entries/Topology.toml +++ b/metadata/entries/Topology.toml @@ -1,21 +1,21 @@ title = "Topology" date = 2004-04-26 topics = [ "Mathematics/Topology", ] abstract = "This entry contains two theories. The first, Topology, develops the basic notions of general topology. The second, which can be viewed as a demonstration of the first, is called LList_Topology. It develops the topology of lazy lists." license = "bsd" note = "" [authors] [authors.friedrich] [contributors] [notify] -paulson = "paulson_email1" +paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/Transformer_Semantics.toml b/metadata/entries/Transformer_Semantics.toml --- a/metadata/entries/Transformer_Semantics.toml +++ b/metadata/entries/Transformer_Semantics.toml @@ -1,33 +1,33 @@ title = "Transformer Semantics" date = 2018-12-11 topics = [ "Mathematics/Algebra", "Computer science/Semantics", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.struth] -homepage = "struth_homepage1" +homepage = "struth_homepage" [contributors] [notify] struth = "struth_email" [history] [extra] diff --git a/metadata/entries/Transitive_Models.toml b/metadata/entries/Transitive_Models.toml --- a/metadata/entries/Transitive_Models.toml +++ b/metadata/entries/Transitive_Models.toml @@ -1,38 +1,38 @@ title = "Transitive Models of Fragments of ZFC" date = 2022-03-03 topics = [ "Logic/Set theory", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.gunther] email = "gunther_email" [authors.pagano] homepage = "pagano_homepage" [authors.terraf] -homepage = "terraf_homepage2" +homepage = "terraf_homepage" [authors.steinberg] email = "steinberg_email" [contributors] [notify] terraf = "terraf_email" -pagano = "pagano_email1" +pagano = "pagano_email" [history] [extra] diff --git a/metadata/entries/Treaps.toml b/metadata/entries/Treaps.toml --- a/metadata/entries/Treaps.toml +++ b/metadata/entries/Treaps.toml @@ -1,44 +1,44 @@ title = "Treaps" date = 2018-02-06 topics = [ "Computer science/Data structures", ] abstract = """

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.

In particular, by choosing these priorities at random upon insertion of an element, we can pretend that we inserted the elements in random order, 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.

""" license = "bsd" note = "" [authors] [authors.haslbeck] homepage = "haslbeck_homepage" [authors.eberl] homepage = "eberl_homepage2" [authors.nipkow] -homepage = "nipkow_homepage3" +homepage = "nipkow_homepage" [contributors] [notify] eberl = "eberl_email" [history] [extra] diff --git a/metadata/entries/Types_Tableaus_and_Goedels_God.toml b/metadata/entries/Types_Tableaus_and_Goedels_God.toml --- a/metadata/entries/Types_Tableaus_and_Goedels_God.toml +++ b/metadata/entries/Types_Tableaus_and_Goedels_God.toml @@ -1,37 +1,37 @@ title = "Types, Tableaus and Gödel’s God in Isabelle/HOL" date = 2017-05-01 topics = [ "Logic/Philosophical aspects", ] abstract = """ 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''.)""" license = "bsd" note = "" [authors] [authors.fuenmayor] email = "fuenmayor_email" [authors.benzmueller] -homepage = "benzmueller_homepage2" +homepage = "benzmueller_homepage" [contributors] [notify] fuenmayor = "fuenmayor_email" benzmueller = "benzmueller_email" [history] [extra] diff --git a/metadata/entries/UPF_Firewall.toml b/metadata/entries/UPF_Firewall.toml --- a/metadata/entries/UPF_Firewall.toml +++ b/metadata/entries/UPF_Firewall.toml @@ -1,35 +1,35 @@ title = "Formal Network Models and Their Application to Firewall Policies" date = 2017-01-08 topics = [ "Computer science/Security", "Computer science/Networks", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.brucker] -homepage = "brucker_homepage1" +homepage = "brucker_homepage" [authors.bruegger] [authors.wolff] homepage = "wolff_homepage" [contributors] [notify] brucker = "brucker_email2" [history] [extra] diff --git a/metadata/entries/Universal_Turing_Machine.toml b/metadata/entries/Universal_Turing_Machine.toml --- a/metadata/entries/Universal_Turing_Machine.toml +++ b/metadata/entries/Universal_Turing_Machine.toml @@ -1,36 +1,36 @@ title = "Universal Turing Machine" date = 2019-02-08 topics = [ "Logic/Computability", "Computer science/Automata and formal languages", ] abstract = """ We formalise results from computability theory: recursive functions, undecidability of the halting problem, and the existence of a universal Turing machine. This formalisation is the AFP entry corresponding to the paper Mechanising Turing Machines and Computability Theory in Isabelle/HOL, ITP 2013.""" license = "bsd" note = "" [authors] [authors.xu] [authors.zhangx] [authors.urban] -homepage = "urban_homepage1" +homepage = "urban_homepage" [authors.joosten] -homepage = "joosten_homepage1" +homepage = "joosten_homepage" [contributors] [notify] joosten = "joosten_email1" urban = "urban_email" [history] [extra] diff --git a/metadata/entries/Van_der_Waerden.toml b/metadata/entries/Van_der_Waerden.toml --- a/metadata/entries/Van_der_Waerden.toml +++ b/metadata/entries/Van_der_Waerden.toml @@ -1,36 +1,36 @@ title = "Van der Waerden's Theorem" date = 2021-06-22 topics = [ "Mathematics/Combinatorics", ] abstract = """ 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 $l$.""" license = "bsd" note = "" [authors] [authors.kreuzer] homepage = "kreuzer_homepage" [authors.eberl] -homepage = "eberl_homepage1" +homepage = "eberl_homepage" [contributors] [notify] kreuzer = "kreuzer_email" eberl = "eberl_email" [history] [extra] diff --git a/metadata/entries/VerifyThis2019.toml b/metadata/entries/VerifyThis2019.toml --- a/metadata/entries/VerifyThis2019.toml +++ b/metadata/entries/VerifyThis2019.toml @@ -1,30 +1,30 @@ title = "VerifyThis 2019 -- Polished Isabelle Solutions" date = 2019-10-16 topics = [ "Computer science/Algorithms", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.lammich] [authors.wimmer] -homepage = "wimmer_homepage1" +homepage = "wimmer_homepage" [contributors] [notify] lammich = "lammich_email" -wimmer = "wimmer_email1" +wimmer = "wimmer_email" [history] [extra] diff --git a/metadata/entries/WHATandWHERE_Security.toml b/metadata/entries/WHATandWHERE_Security.toml --- a/metadata/entries/WHATandWHERE_Security.toml +++ b/metadata/entries/WHATandWHERE_Security.toml @@ -1,58 +1,58 @@ title = "A Formalization of Declassification with WHAT-and-WHERE-Security" date = 2014-04-23 topics = [ "Computer science/Security", "Computer science/Programming languages/Type systems", ] abstract = """ 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.

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.

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.

This Isabelle/HOL formalization uses theories from the entry Strong Security.""" license = "bsd" note = "" [authors] [authors.grewe] -email = "grewe_email1" +email = "grewe_email" [authors.lux] email = "lux_email" [authors.mantel] email = "mantel_email" [authors.sauer] email = "sauer_email" [contributors] [notify] [history] [extra] diff --git a/metadata/entries/Weight_Balanced_Trees.toml b/metadata/entries/Weight_Balanced_Trees.toml --- a/metadata/entries/Weight_Balanced_Trees.toml +++ b/metadata/entries/Weight_Balanced_Trees.toml @@ -1,32 +1,32 @@ title = "Weight-Balanced Trees" date = 2018-03-13 topics = [ "Computer science/Data structures", ] abstract = """ This theory provides a verified implementation of weight-balanced trees following the work of Hirai and Yamamoto 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.""" license = "bsd" note = "" [authors] [authors.nipkow] -homepage = "nipkow_homepage3" +homepage = "nipkow_homepage" [authors.dirix] [contributors] [notify] nipkow = "nipkow_email" [history] [extra] diff --git a/metadata/entries/Word_Lib.toml b/metadata/entries/Word_Lib.toml --- a/metadata/entries/Word_Lib.toml +++ b/metadata/entries/Word_Lib.toml @@ -1,45 +1,45 @@ title = "Finite Machine Word Library" date = 2016-06-09 topics = [ "Computer science/Data structures", ] abstract = """ 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.""" license = "bsd" note = "" [authors] [authors.beeren] [authors.fernandez] [authors.gao] [authors.klein] homepage = "klein_homepage" [authors.kolanski] [authors.lim] [authors.lewis] [authors.matichuk] [authors.sewell] [contributors] [notify] -klein = "klein_email1" +klein = "klein_email" [history] [extra] diff --git a/metadata/entries/Youngs_Inequality.toml b/metadata/entries/Youngs_Inequality.toml --- a/metadata/entries/Youngs_Inequality.toml +++ b/metadata/entries/Youngs_Inequality.toml @@ -1,31 +1,31 @@ title = "Young's Inequality for Increasing Functions" date = 2022-01-31 topics = [ "Mathematics/Analysis", ] abstract = """ 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 the development 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.""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/metadata/entries/ZFC_in_HOL.toml b/metadata/entries/ZFC_in_HOL.toml --- a/metadata/entries/ZFC_in_HOL.toml +++ b/metadata/entries/ZFC_in_HOL.toml @@ -1,48 +1,48 @@ title = "Zermelo Fraenkel Set Theory in Higher-Order Logic" date = 2019-10-24 topics = [ "Logic/Set theory", ] abstract = """

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.

There is a type V of sets and a function elts :: V => V set mapping a set to its elements. Classes simply have type V set, 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.

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.

The theory provides two type classes with the aim of facilitating developments that combine V with other Isabelle/HOL types: embeddable, the class of types that can be injected into V (including V itself as well as V*V, etc.), and small, the class of types that correspond to some ZF set.

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)""" license = "bsd" note = "" [authors] [authors.paulson] -homepage = "paulson_homepage1" +homepage = "paulson_homepage" [contributors] [notify] paulson = "paulson_email" [history] [extra] diff --git a/web/authors/abdulaziz/index.html b/web/authors/abdulaziz/index.html --- a/web/authors/abdulaziz/index.html +++ b/web/authors/abdulaziz/index.html @@ -1,140 +1,140 @@ abdulaziz - Archive of Formal Proofs

Mohammad Abdulaziz

Homepages 🌐

E-Mails 📧

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Entries

2021

Dec 16
+
Markov Decision Processes with Rewards

by Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧
Dec 16

2020

Verified SAT-Based AI Planning

by Mohammad Abdulaziz 🌐 and Friedrich Kurz
Oct 29
AI Planning Languages Semantics

by Mohammad Abdulaziz 🌐 and Peter Lammich 🌐
Oct 29

2018

Upper Bounding Diameters of State Spaces of Factored Transition Systems

by Friedrich Kurz and Mohammad Abdulaziz 🌐
Oct 12
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An Isabelle/HOL formalisation of Green's Theorem

by Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐
+
An Isabelle/HOL formalisation of Green's Theorem

by Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐 Jan 11
\ No newline at end of file diff --git a/web/authors/aehlig/index.html b/web/authors/aehlig/index.html --- a/web/authors/aehlig/index.html +++ b/web/authors/aehlig/index.html @@ -1,98 +1,98 @@ aehlig - Archive of Formal Proofs

Klaus Aehlig

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Entries

2008

Feb 18
\ No newline at end of file diff --git a/web/authors/aissat/index.html b/web/authors/aissat/index.html --- a/web/authors/aissat/index.html +++ b/web/authors/aissat/index.html @@ -1,95 +1,95 @@ aissat - Archive of Formal Proofs

Romain Aissat

Entries

2016

Aug 18
\ No newline at end of file diff --git a/web/authors/aransay/index.html b/web/authors/aransay/index.html --- a/web/authors/aransay/index.html +++ b/web/authors/aransay/index.html @@ -1,139 +1,139 @@ aransay - Archive of Formal Proofs

Jesús Aransay

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2015

Jul 07
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QR Decomposition

by Jose Divasón 🌐 and Jesús Aransay 🌐
Feb 12
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Echelon Form

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Echelon Form

by Jose Divasón 🌐 and Jesús Aransay 🌐 Feb 12

2014

-
Gauss-Jordan Algorithm and Its Applications

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Gauss-Jordan Algorithm and Its Applications

by Jose Divasón 🌐 and Jesús Aransay 🌐 Sep 03

2013

-
Rank-Nullity Theorem in Linear Algebra

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Rank-Nullity Theorem in Linear Algebra

by Jose Divasón 🌐 and Jesús Aransay 🌐 Jan 16
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Angeliki Koutsoukou-Argyraki

Homepages 🌐

- +

Entries

2022

2021

2020

2019

2018

Sep 14
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Irrational Rapidly Convergent Series

by Angeliki Koutsoukou-Argyraki 🌐 and Wenda Li 🌐
May 23 \ No newline at end of file diff --git a/web/authors/armstrong/index.html b/web/authors/armstrong/index.html --- a/web/authors/armstrong/index.html +++ b/web/authors/armstrong/index.html @@ -1,111 +1,111 @@ armstrong - Archive of Formal Proofs

Alasdair Armstrong

Entries

2014

Jan 23

2013

Jan 15
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Fahad Ausaf

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Entries

2016

May 24
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Gertrud Bauer

Entries

2006

May 22
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Alexander Bentkamp

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Entries

2018

2016

2015

2010

Aug 10
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Christoph Benzmüller

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- +

Entries

2021

2018

2017

Sep 21
+
Types, Tableaus and Gödel’s God in Isabelle/HOL

by David Fuenmayor 📧 and Christoph Benzmüller 🌐
May 01

2013

Gödel's God in Isabelle/HOL

by Christoph Benzmüller 🌐 and Bruno Woltzenlogel Paleo 🌐
Nov 12
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Alastair R. Beresford

E-Mails 📧

- +

Entries

2018

May 10

2017

+
A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes

by Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧
Jul 07 \ No newline at end of file diff --git a/web/authors/berghofer/index.html b/web/authors/berghofer/index.html --- a/web/authors/berghofer/index.html +++ b/web/authors/berghofer/index.html @@ -1,132 +1,132 @@ berghofer - Archive of Formal Proofs

Stefan Berghofer

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Entries

2017

2013

Feb 21

2009

Dec 03

2007

Aug 02
Aug 02
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Bhargav Bhatt

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Entries

2017

May 05
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Julian Biendarra

Entries

2019

2017

Jan 17
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Jasmin Christian Blanchette

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Entries

2020

Aug 25

2018

+
A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧 and Dmitriy Traytel 🌐
Nov 23
-
Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧
+
Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧 Jan 18

2017

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Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Dec 19
-
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Feb 10

2016

-
Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

by Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐
+
Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

by Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐 Nov 12
Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms

by Heiko Becker 📧, Jasmin Christian Blanchette 📧, Uwe Waldmann 📧 and Daniel Wand 📧
Nov 12
Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms

by Jasmin Christian Blanchette 📧, Uwe Waldmann 📧 and Daniel Wand 📧
Sep 23

2014

-
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Apr 16

2013

Sound and Complete Sort Encodings for First-Order Logic

by Jasmin Christian Blanchette 🌐 and Andrei Popescu 🌐
Jun 27

2008

The Textbook Proof of Huffman's Algorithm

by Jasmin Christian Blanchette 🌐
Oct 15
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Holger Blasum

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Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
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Ben Blumson

Homepages 🌐

- +

Entries

2021

2017

Sep 06
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Maksym Bortin

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- +

Entries

2016

Apr 27
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Ralph Bottesch

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Entries

2021

2019

Jun 21
+
Farkas' Lemma and Motzkin's Transposition Theorem

by Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐
Jan 17

2018

-
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada Feb 02
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Andrew Boyton

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Entries

2012

May 11
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Oliver Bračevac

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Entries

2018

May 07
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Felix Brandt

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Entries

2018

Mar 22
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Nicolas Robinson-O'Brien

Entries

2020

Dec 08
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Hauke Brinkop

E-Mails 📧

Entries

2016

Jul 14
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Achim D. Brucker

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- +

E-Mails 📧

Entries

2020

-
Sep 28
+
A Formalization of Web Components

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Sep 28
-
A Formal Model of the Safely Composable Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
+
A Formalization of Safely Composable Web Components

by Achim D. Brucker 🌐 and Michael Herzberg 🌐 Sep 28
-
A Formal Model of the Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
+
A Formal Model of the Safely Composable Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐 + + Sep 28 + +
+
+
+
A Formal Model of the Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Sep 28
Inference of Extended Finite State Machines

by Michael Foster 📧, Achim D. Brucker 📧, Ramsay G. Taylor 📧 and John Derrick 📧
Sep 07
A Formal Model of Extended Finite State Machines

by Michael Foster 📧, Achim D. Brucker 📧, Ramsay G. Taylor 📧 and John Derrick 📧
Sep 07
Stateful Protocol Composition and Typing

by Andreas V. Hess 📧, Sebastian Mödersheim 🌐 and Achim D. Brucker 🌐
Apr 08
Automated Stateful Protocol Verification

by Andreas V. Hess 📧, Sebastian Mödersheim 🌐, Achim D. Brucker 🌐 and Anders Schlichtkrull 🌐
Apr 08

2018

A Formal Model of the Document Object Model

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Dec 26

2017

-
Formal Network Models and Their Application to Firewall Policies

by Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐
+
Formal Network Models and Their Application to Firewall Policies

by Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐 Jan 08

2014

-
The Unified Policy Framework (UPF)

by Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧
+
The Unified Policy Framework (UPF)

by Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧 Nov 28
-
Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5

by Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧
+
Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5

by Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧 Jan 16
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Lukas Brügger

E-Mails 📧

Entries

2017

Jan 08

2014

+
The Unified Policy Framework (UPF)

by Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧
Nov 28 \ No newline at end of file diff --git a/web/authors/brun/index.html b/web/authors/brun/index.html --- a/web/authors/brun/index.html +++ b/web/authors/brun/index.html @@ -1,104 +1,104 @@ brun - Archive of Formal Proofs

Matthias Brun

Entries

2021

2019

May 14
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Lukas Bulwahn

E-Mails 📧

Entries

2021

2017

Jan 24

2016

Dec 29
Oct 11
Aug 07
Jun 26
May 24
May 04
Jan 14

2015

Dec 12
Nov 19
Jun 27
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David Butler

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E-Mails 📧

Entries

2019

Oct 07
May 09
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José Manuel Rodríguez Caballero

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E-Mails 📧

Entries

2021

2020

May 02
Feb 01
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Thibault Dardinier

Homepages 🌐

Entries

2022

2020

Apr 09

2019

Sep 16
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Cornelius Diekmann

Homepages 🌐

Entries

2020

2016

Oct 21
Sep 09
+
Routing

by Julius Michaelis 🌐 and Cornelius Diekmann 🌐
Aug 31
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Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐
+
Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐 Aug 24
-
IP Addresses

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐
+
IP Addresses

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐 Jun 28

2014

Network Security Policy Verification

by Cornelius Diekmann 🌐
Jul 04
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Stefan Dirix

Entries

2018

Mar 13
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Jose Divasón

Homepages 🌐

- +

Entries

2021

2020

2018

Feb 06
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
Feb 02

2016

-
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
+
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧 Oct 14
-
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧
+
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧 May 20

2015

-
Hermite Normal Form

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Hermite Normal Form

by Jose Divasón 🌐 and Jesús Aransay 🌐 Jul 07
-
QR Decomposition

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
QR Decomposition

by Jose Divasón 🌐 and Jesús Aransay 🌐 Feb 12
-
Echelon Form

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Echelon Form

by Jose Divasón 🌐 and Jesús Aransay 🌐 Feb 12

2014

-
Gauss-Jordan Algorithm and Its Applications

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Gauss-Jordan Algorithm and Its Applications

by Jose Divasón 🌐 and Jesús Aransay 🌐 Sep 03

2013

-
Rank-Nullity Theorem in Linear Algebra

by Jose Divasón 🌐 and Jesús Aransay 🌐
+
Rank-Nullity Theorem in Linear Algebra

by Jose Divasón 🌐 and Jesús Aransay 🌐 Jan 16
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Roy Dyckhoff

Homepages 🌐

Entries

2016

May 24
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Manuel Eberl

Homepages 🌐

- +

E-Mails 📧

Entries

2022

Apr 10
+
A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent

by Manuel Eberl 🌐
Mar 15

2021

-
Factorization of Polynomials with Algebraic Coefficients

by Manuel Eberl 🌐 and René Thiemann 📧
+
Factorization of Polynomials with Algebraic Coefficients

by Manuel Eberl 🌐 and René Thiemann 📧 Nov 08
-
Finitely Generated Abelian Groups

by Joseph Thommes and Manuel Eberl 🌐
+
Finitely Generated Abelian Groups

by Joseph Thommes and Manuel Eberl 🌐 Jul 07
Van der Waerden's Theorem

by Katharina Kreuzer 🌐 and Manuel Eberl 🌐
Jun 22
-
The Hermite–Lindemann–Weierstraß Transcendence Theorem

by Manuel Eberl 🌐
+
The Hermite–Lindemann–Weierstraß Transcendence Theorem

by Manuel Eberl 🌐 Mar 03
-
Formal Puiseux Series

by Manuel Eberl 🌐
+
Formal Puiseux Series

by Manuel Eberl 🌐 Feb 17
-
The Laws of Large Numbers

by Manuel Eberl 🌐
+
The Laws of Large Numbers

by Manuel Eberl 🌐 Feb 10

2020

-
The Lambert W Function on the Reals

by Manuel Eberl 🌐
- - Apr 24 - -
-
-
-
Power Sum Polynomials

by Manuel Eberl 🌐
+
The Lambert W Function on the Reals

by Manuel Eberl 🌐 Apr 24
-
Gaussian Integers

by Manuel Eberl 🌐
+
Power Sum Polynomials

by Manuel Eberl 🌐 Apr 24
-
Furstenberg's topology and his proof of the infinitude of primes

by Manuel Eberl 🌐
+
Gaussian Integers

by Manuel Eberl 🌐 + + Apr 24 + +
+
+
+
Furstenberg's topology and his proof of the infinitude of primes

by Manuel Eberl 🌐
Mar 22
-
Mersenne primes and the Lucas–Lehmer test

by Manuel Eberl 🌐
+
Mersenne primes and the Lucas–Lehmer test

by Manuel Eberl 🌐 Jan 17
Skip Lists

by Max W. Haslbeck 🌐 and Manuel Eberl 🌐
Jan 09

2019

-
The Irrationality of ζ(3)

by Manuel Eberl 🌐
+
The Irrationality of ζ(3)

by Manuel Eberl 🌐 Dec 27
-
Gauss Sums and the Pólya–Vinogradov Inequality

by Rodrigo Raya 🌐 and Manuel Eberl 🌐
+
Gauss Sums and the Pólya–Vinogradov Inequality

by Rodrigo Raya 🌐 and Manuel Eberl 🌐 Dec 10
-
Selected Problems from the International Mathematical Olympiad 2019

by Manuel Eberl 🌐
+
Selected Problems from the International Mathematical Olympiad 2019

by Manuel Eberl 🌐 Aug 05
-
Elementary Facts About the Distribution of Primes

by Manuel Eberl 🌐
+
Elementary Facts About the Distribution of Primes

by Manuel Eberl 🌐 Feb 21
-
Probabilistic Primality Testing

by Daniel Stüwe and Manuel Eberl 🌐
+
Probabilistic Primality Testing

by Daniel Stüwe and Manuel Eberl 🌐 Feb 11
-
The Inversions of a List

by Manuel Eberl 🌐
+
The Inversions of a List

by Manuel Eberl 🌐 Feb 01

2018

-
Randomised Binary Search Trees

by Manuel Eberl 🌐
+
Randomised Binary Search Trees

by Manuel Eberl 🌐 Oct 19
-
The Transcendence of π

by Manuel Eberl 🌐
+
The Transcendence of π

by Manuel Eberl 🌐 Sep 28
-
Symmetric Polynomials

by Manuel Eberl 🌐
+
Symmetric Polynomials

by Manuel Eberl 🌐 Sep 25
-
The Prime Number Theorem

by Manuel Eberl 🌐 and Lawrence C. Paulson 🌐
+
The Prime Number Theorem

by Manuel Eberl 🌐 and Lawrence C. Paulson 🌐 Sep 19
-
Pell's Equation

by Manuel Eberl 🌐
+
Pell's Equation

by Manuel Eberl 🌐 Jun 23
-
The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency

by Felix Brandt 🌐, Manuel Eberl 🌐, Christian Saile 🌐 and Christian Stricker 🌐
+
The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency

by Felix Brandt 🌐, Manuel Eberl 🌐, Christian Saile 🌐 and Christian Stricker 🌐 Mar 22
-
Treaps

by Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐
+
Treaps

by Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐 Feb 06
-
The Error Function

by Manuel Eberl 🌐
+
The Error Function

by Manuel Eberl 🌐 Feb 06

2017

-
The Median-of-Medians Selection Algorithm

by Manuel Eberl 🌐
- - Dec 21 - -
-
-
-
The Mason–Stothers Theorem

by Manuel Eberl 🌐
- - Dec 21 - -
-
-
-
Dirichlet L-Functions and Dirichlet's Theorem

by Manuel Eberl 🌐
+
The Median-of-Medians Selection Algorithm

by Manuel Eberl 🌐 Dec 21
-
The Hurwitz and Riemann ζ Functions

by Manuel Eberl 🌐
+
The Mason–Stothers Theorem

by Manuel Eberl 🌐 + + Dec 21 + +
+
+
+
Dirichlet L-Functions and Dirichlet's Theorem

by Manuel Eberl 🌐
+ + Dec 21 + +
+
+
+
The Hurwitz and Riemann ζ Functions

by Manuel Eberl 🌐
Oct 12
-
Linear Recurrences

by Manuel Eberl 🌐
+
Linear Recurrences

by Manuel Eberl 🌐 Oct 12
-
Dirichlet Series

by Manuel Eberl 🌐
+
Dirichlet Series

by Manuel Eberl 🌐 Oct 12
-
Minkowski's Theorem

by Manuel Eberl 🌐
+
Minkowski's Theorem

by Manuel Eberl 🌐 Jul 13
-
Buffon's Needle Problem

by Manuel Eberl 🌐
+
Buffon's Needle Problem

by Manuel Eberl 🌐 Jun 06
-
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐
+
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐 May 05
-
Expected Shape of Random Binary Search Trees

by Manuel Eberl 🌐
+
Expected Shape of Random Binary Search Trees

by Manuel Eberl 🌐 Apr 04
-
The number of comparisons in QuickSort

by Manuel Eberl 🌐
+
The number of comparisons in QuickSort

by Manuel Eberl 🌐 Mar 15
-
Lower bound on comparison-based sorting algorithms

by Manuel Eberl 🌐
+
Lower bound on comparison-based sorting algorithms

by Manuel Eberl 🌐 Mar 15
-
The Euler–MacLaurin Formula

by Manuel Eberl 🌐
+
The Euler–MacLaurin Formula

by Manuel Eberl 🌐 Mar 10
-
Bernoulli Numbers

by Lukas Bulwahn 📧 and Manuel Eberl 🌐
+
Bernoulli Numbers

by Lukas Bulwahn 📧 and Manuel Eberl 🌐 Jan 24
-
Bertrand's postulate

by Julian Biendarra and Manuel Eberl 🌐
+
Bertrand's postulate

by Julian Biendarra and Manuel Eberl 🌐 Jan 17
-
The Transcendence of e

by Manuel Eberl 🌐
+
The Transcendence of e

by Manuel Eberl 🌐 Jan 12

2016

-
Fisher–Yates shuffle

by Manuel Eberl 🌐
+
Fisher–Yates shuffle

by Manuel Eberl 🌐 Sep 30
-
Stirling's formula

by Manuel Eberl 🌐
+
Stirling's formula

by Manuel Eberl 🌐 Sep 01
-
Catalan Numbers

by Manuel Eberl 🌐
+
Catalan Numbers

by Manuel Eberl 🌐 Jun 21
Randomised Social Choice Theory

by Manuel Eberl 📧
May 05
The Incompatibility of SD-Efficiency and SD-Strategy-Proofness

by Manuel Eberl 📧
May 04

2015

-
The Divergence of the Prime Harmonic Series

by Manuel Eberl 🌐
- - Dec 28 - -
-
-
-
Liouville numbers

by Manuel Eberl 🌐
+
The Divergence of the Prime Harmonic Series

by Manuel Eberl 🌐 Dec 28
-
Descartes' Rule of Signs

by Manuel Eberl 🌐
+
Liouville numbers

by Manuel Eberl 🌐 Dec 28
-
Basic Geometric Properties of Triangles

by Manuel Eberl 🌐
+
Descartes' Rule of Signs

by Manuel Eberl 🌐 Dec 28
-
The Akra-Bazzi theorem and the Master theorem

by Manuel Eberl 🌐
+
Basic Geometric Properties of Triangles

by Manuel Eberl 🌐 + + Dec 28 + +
+
+
+
The Akra-Bazzi theorem and the Master theorem

by Manuel Eberl 🌐
Jul 14
-
Landau Symbols

by Manuel Eberl 🌐
+
Landau Symbols

by Manuel Eberl 🌐 Jul 14

2014

-
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐
+
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐 Oct 09
-
Sturm's Theorem

by Manuel Eberl 🌐
+
Sturm's Theorem

by Manuel Eberl 🌐 Jan 11
\ No newline at end of file diff --git a/web/authors/echenim/index.html b/web/authors/echenim/index.html --- a/web/authors/echenim/index.html +++ b/web/authors/echenim/index.html @@ -1,117 +1,117 @@ echenim - Archive of Formal Proofs

Mnacho Echenim

Homepages 🌐

- +

E-Mails 📧

Entries

2021

2018

Jul 16
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Javier Esparza

Homepages 🌐

Entries

2014

May 28
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Robin Eßmann

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Entries

2020

Jan 16
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Abderrahmane Feliachi

E-Mails 📧

Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18

2012

+
Isabelle/Circus

by Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Marie-Claude Gaudel 📧
May 27 \ No newline at end of file diff --git a/web/authors/fiedler/index.html b/web/authors/fiedler/index.html --- a/web/authors/fiedler/index.html +++ b/web/authors/fiedler/index.html @@ -1,98 +1,98 @@ fiedler - Archive of Formal Proofs

Ben Fiedler

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Entries

2020

Jul 21
\ No newline at end of file diff --git a/web/authors/fleury/index.html b/web/authors/fleury/index.html --- a/web/authors/fleury/index.html +++ b/web/authors/fleury/index.html @@ -1,110 +1,110 @@ fleury - Archive of Formal Proofs

Mathias Fleury

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E-Mails 📧

Entries

2020

2016

Nov 12
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Simon Foster

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- +

E-Mails 📧

Entries

2020

2019

Feb 01

2017

May 25

2014

+
Regular Algebras

by Simon Foster 🌐 and Georg Struth 🌐
May 21
Relation Algebra

by Alasdair Armstrong, Simon Foster 📧, Georg Struth 🌐 and Tjark Weber 🌐
Jan 25
\ No newline at end of file diff --git a/web/authors/fuenmayor/index.html b/web/authors/fuenmayor/index.html --- a/web/authors/fuenmayor/index.html +++ b/web/authors/fuenmayor/index.html @@ -1,123 +1,123 @@ fuenmayor - Archive of Formal Proofs

David Fuenmayor

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Entries

2020

2018

2017

Sep 21
+
Types, Tableaus and Gödel’s God in Isabelle/HOL

by David Fuenmayor 📧 and Christoph Benzmüller 🌐
May 01 \ No newline at end of file diff --git a/web/authors/furusawa/index.html b/web/authors/furusawa/index.html --- a/web/authors/furusawa/index.html +++ b/web/authors/furusawa/index.html @@ -1,98 +1,98 @@ furusawa - Archive of Formal Proofs

Hitoshi Furusawa

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Entries

2015

Jun 11
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Peter Gammie

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Entries

2020

2017

2016

2015

Dec 22
Nov 18
Apr 13
Apr 13

2012

Jul 01

2011

May 17

2009

Oct 30

2008

Nov 09
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Marie-Claude Gaudel

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Entries

2012

May 27
\ No newline at end of file diff --git a/web/authors/gay/index.html b/web/authors/gay/index.html --- a/web/authors/gay/index.html +++ b/web/authors/gay/index.html @@ -1,98 +1,98 @@ gay - Archive of Formal Proofs

Richard Gay

E-Mails 📧

Entries

2018

May 07
\ No newline at end of file diff --git a/web/authors/gomes/index.html b/web/authors/gomes/index.html --- a/web/authors/gomes/index.html +++ b/web/authors/gomes/index.html @@ -1,158 +1,158 @@ gomes - Archive of Formal Proofs

Victor B. F. Gomes

Homepages 🌐

E-Mails 📧

- +

Entries

2018

May 10

2017

Aug 16
+
A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes

by Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧
Jul 07
Partial Semigroups and Convolution Algebras

by Brijesh Dongol 📧, Victor B. F. Gomes 📧, Ian J. Hayes 📧 and Georg Struth 📧
Jun 13

2016

Program Construction and Verification Components Based on Kleene Algebra

by Victor B. F. Gomes 📧 and Georg Struth 📧
Jun 18
-
Kleene Algebras with Domain

by Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐
+
Kleene Algebras with Domain

by Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐 Apr 12

2015

Residuated Lattices

by Victor B. F. Gomes 📧 and Georg Struth 📧
Apr 15

2014

-
Kleene Algebra with Tests and Demonic Refinement Algebras

by Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐
+
Kleene Algebra with Tests and Demonic Refinement Algebras

by Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐 Jan 23
\ No newline at end of file diff --git a/web/authors/grewe/index.html b/web/authors/grewe/index.html --- a/web/authors/grewe/index.html +++ b/web/authors/grewe/index.html @@ -1,121 +1,121 @@ grewe - Archive of Formal Proofs

Sylvia Grewe

E-Mails 📧

- +

Entries

2018

May 07

2014

Apr 23
Apr 23
Apr 23
\ No newline at end of file diff --git a/web/authors/gunther/index.html b/web/authors/gunther/index.html --- a/web/authors/gunther/index.html +++ b/web/authors/gunther/index.html @@ -1,114 +1,114 @@ gunther - Archive of Formal Proofs

Emmanuel Gunther

E-Mails 📧

Entries

2022

Mar 06
+
Transitive Models of Fragments of ZFC

by Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧
Mar 03

2020

-
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐
+
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐 May 06
\ No newline at end of file diff --git a/web/authors/guttmann/index.html b/web/authors/guttmann/index.html --- a/web/authors/guttmann/index.html +++ b/web/authors/guttmann/index.html @@ -1,176 +1,176 @@ guttmann - Archive of Formal Proofs

Walter Guttmann

Homepages 🌐

- +

Entries

2021

2020

Dec 08
+
Relational Disjoint-Set Forests

by Walter Guttmann 🌐
Aug 26
-
Relational Characterisations of Paths

by Walter Guttmann 🌐 and Peter Höfner 🌐
+
Relational Characterisations of Paths

by Walter Guttmann 🌐 and Peter Höfner 🌐 Jul 13
-
A Hierarchy of Algebras for Boolean Subsets

by Walter Guttmann 🌐 and Bernhard Möller 🌐
+
A Hierarchy of Algebras for Boolean Subsets

by Walter Guttmann 🌐 and Bernhard Möller 🌐 Jan 31

2018

-
Aggregation Algebras

by Walter Guttmann 🌐
+
Aggregation Algebras

by Walter Guttmann 🌐 Sep 15

2017

-
Stone-Kleene Relation Algebras

by Walter Guttmann 🌐
+
Stone-Kleene Relation Algebras

by Walter Guttmann 🌐 Jul 06
-
Stone Relation Algebras

by Walter Guttmann 🌐
+
Stone Relation Algebras

by Walter Guttmann 🌐 Feb 07

2016

-
Stone Algebras

by Walter Guttmann 🌐
+
Stone Algebras

by Walter Guttmann 🌐 Sep 06
-
Kleene Algebras with Domain

by Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐
+
Kleene Algebras with Domain

by Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐 Apr 12
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Florian Haftmann

Homepages 🌐

Entries

2014

2010

Aug 10
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Max W. Haslbeck

Homepages 🌐

- +

Entries

2020

2019

Jan 17

2018

+
Treaps

by Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐
Feb 06
-
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada Feb 02

2016

-
Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐
+
Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐 Aug 24
-
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐
+
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐 Apr 27
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Maximilian P. L. Haslbeck

Homepages 🌐

- +

Entries

2019

2018

Feb 26

2016

+
Analysis of List Update Algorithms

by Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐
Feb 17 \ No newline at end of file diff --git a/web/authors/havle/index.html b/web/authors/havle/index.html --- a/web/authors/havle/index.html +++ b/web/authors/havle/index.html @@ -1,98 +1,98 @@ havle - Archive of Formal Proofs

Oto Havle

E-Mails 📧

Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/heimes/index.html b/web/authors/heimes/index.html --- a/web/authors/heimes/index.html +++ b/web/authors/heimes/index.html @@ -1,102 +1,102 @@ heimes - Archive of Formal Proofs

Lukas Heimes

Entries

2020

Apr 10
+
Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations

by Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐
Apr 09 \ No newline at end of file diff --git a/web/authors/herzberg/index.html b/web/authors/herzberg/index.html --- a/web/authors/herzberg/index.html +++ b/web/authors/herzberg/index.html @@ -1,135 +1,135 @@ herzberg - Archive of Formal Proofs

Michael Herzberg

Homepages 🌐

Entries

2020

-
Sep 28
+
A Formalization of Web Components

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Sep 28
-
A Formal Model of the Safely Composable Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
+
A Formalization of Safely Composable Web Components

by Achim D. Brucker 🌐 and Michael Herzberg 🌐 Sep 28
-
A Formal Model of the Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
+
A Formal Model of the Safely Composable Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐 + + Sep 28 + +
+
+
+
A Formal Model of the Document Object Model with Shadow Roots

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Sep 28

2018

A Formal Model of the Document Object Model

by Achim D. Brucker 🌐 and Michael Herzberg 🌐
Dec 26
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Peter Höfner

Homepages 🌐

Entries

2020

Jul 13

2016

+
Kleene Algebras with Domain

by Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐
Apr 12

2014

Loop freedom of the (untimed) AODV routing protocol

by Timothy Bourke 🌐 and Peter Höfner 🌐
Oct 23
\ No newline at end of file diff --git a/web/authors/hoelzl/index.html b/web/authors/hoelzl/index.html --- a/web/authors/hoelzl/index.html +++ b/web/authors/hoelzl/index.html @@ -1,156 +1,156 @@ hoelzl - Archive of Formal Proofs

Johannes Hölzl

Homepages 🌐

- +

E-Mails 📧

Entries

2018

May 24

2015

+
A Zoo of Probabilistic Systems

by Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐
May 27
Verification of the UpDown Scheme

by Johannes Hölzl 📧
Jan 28

2014

-
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐
+
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐 Oct 09
-
Probabilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 🌐
+
Probabilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 🌐 Mar 11

2012

Possibilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 📧
Sep 10
-
Ordinary Differential Equations

by Fabian Immler 🌐 and Johannes Hölzl 🌐
+
Ordinary Differential Equations

by Fabian Immler 🌐 and Johannes Hölzl 🌐 Apr 26
-
Markov Models

by Johannes Hölzl 🌐 and Tobias Nipkow 🌐
+
Markov Models

by Johannes Hölzl 🌐 and Tobias Nipkow 🌐 Jan 03
\ No newline at end of file diff --git a/web/authors/hu/index.html b/web/authors/hu/index.html --- a/web/authors/hu/index.html +++ b/web/authors/hu/index.html @@ -1,98 +1,98 @@ hu - Archive of Formal Proofs

Shuwei Hu

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Entries

2018

May 22
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Brian Huffman

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- +

E-Mails 📧

Entries

2017

2012

2010

Mar 29

2009

+
Stream Fusion

by Brian Huffman 🌐
Apr 29

2005

-
Countable Ordinals

by Brian Huffman 🌐
+
Countable Ordinals

by Brian Huffman 🌐 Nov 11
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Lars Hupel

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E-Mails 📧

Entries

2020

2019

2018

2017

2016

Jun 28
+
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐
Apr 27

2014

Properties of Random Graphs -- Subgraph Containment

by Lars Hupel 📧
Feb 13
\ No newline at end of file diff --git a/web/authors/immler/index.html b/web/authors/immler/index.html --- a/web/authors/immler/index.html +++ b/web/authors/immler/index.html @@ -1,178 +1,178 @@ immler - Archive of Formal Proofs

Fabian Immler

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- +

E-Mails 📧

Entries

2020

Jun 01

2019

+
The Poincaré-Bendixson Theorem

by Fabian Immler 🌐 and Yong Kiam Tan 🌐
Dec 18
Laplace Transform

by Fabian Immler 🌐
Aug 14

2018

-
Smooth Manifolds

by Fabian Immler 🌐 and Bohua Zhan 🌐
+
Smooth Manifolds

by Fabian Immler 🌐 and Bohua Zhan 🌐 Oct 22
-
Taylor Models

by Christoph Traut and Fabian Immler 🌐
+
Taylor Models

by Christoph Traut and Fabian Immler 🌐 Jan 08

2016

-
Gröbner Bases Theory

by Fabian Immler 🌐 and Alexander Maletzky 🌐
+
Gröbner Bases Theory

by Fabian Immler 🌐 and Alexander Maletzky 🌐 May 02

2014

-
Affine Arithmetic

by Fabian Immler 🌐
+
Affine Arithmetic

by Fabian Immler 🌐 Feb 07

2012

-
Ordinary Differential Equations

by Fabian Immler 🌐 and Johannes Hölzl 🌐
+
Ordinary Differential Equations

by Fabian Immler 🌐 and Johannes Hölzl 🌐 Apr 26

2011

RIPEMD-160

by Fabian Immler 📧
Jan 10

2010

-
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧
+
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧 Aug 10
\ No newline at end of file diff --git a/web/authors/jiangd/index.html b/web/authors/jiangd/index.html --- a/web/authors/jiangd/index.html +++ b/web/authors/jiangd/index.html @@ -1,98 +1,98 @@ jiangd - Archive of Formal Proofs

Dongchen Jiang

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Entries

2010

Dec 17
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Sebastiaan J. C. Joosten

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- +

E-Mails 📧

Entries

2021

Apr 23

2019

Feb 08

2018

Nov 23
+
A verified factorization algorithm for integer polynomials with polynomial complexity

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada 📧
Feb 06
-
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada Feb 02

2017

Subresultants

by Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
Apr 06

2016

-
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
+
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧 Oct 14

2015

Algebraic Numbers in Isabelle/HOL

by René Thiemann 📧, Akihisa Yamada 📧 and Sebastiaan J. C. Joosten 📧
Dec 22
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Cezary Kaliszyk

Homepages 🌐

- +

Entries

2019

Aug 06

2018

Jul 04

2017

Sep 01

2013

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Nominal 2

by Christian Urban 🌐, Stefan Berghofer 🌐 and Cezary Kaliszyk 🌐
Feb 21 \ No newline at end of file diff --git a/web/authors/klein/index.html b/web/authors/klein/index.html --- a/web/authors/klein/index.html +++ b/web/authors/klein/index.html @@ -1,119 +1,119 @@ klein - Archive of Formal Proofs

Gerwin Klein

Homepages 🌐

E-Mails 📧

- +

Entries

2016

2012

May 11

2005

+
Jinja is not Java

by Gerwin Klein 🌐 and Tobias Nipkow 🌐
Jun 01 \ No newline at end of file diff --git a/web/authors/kleppmann/index.html b/web/authors/kleppmann/index.html --- a/web/authors/kleppmann/index.html +++ b/web/authors/kleppmann/index.html @@ -1,107 +1,107 @@ kleppmann - Archive of Formal Proofs

Martin Kleppmann

E-Mails 📧

- +

Entries

2018

May 10

2017

+
A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes

by Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧
Jul 07 \ No newline at end of file diff --git a/web/authors/kolanski/index.html b/web/authors/kolanski/index.html --- a/web/authors/kolanski/index.html +++ b/web/authors/kolanski/index.html @@ -1,107 +1,107 @@ kolanski - Archive of Formal Proofs

Rafal Kolanski

E-Mails 📧

Entries

2016

2012

May 11
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Alexander Krauss

Homepages 🌐

Entries

2010

May 12
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Ondřej Kunčar

Homepages 🌐

Entries

2016

May 20
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Peter Lammich

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E-Mails 📧

Entries

2021

2020

2019

Jun 25
+
Priority Search Trees

by Peter Lammich 🌐 and Tobias Nipkow 🌐
Jun 25
Kruskal's Algorithm for Minimum Spanning Forest

by Maximilian P. L. Haslbeck 🌐, Peter Lammich 🌐 and Julian Biendarra
Feb 14
-
IMP2 – Simple Program Verification in Isabelle/HOL

by Peter Lammich 🌐 and Simon Wimmer 🌐
+
IMP2 – Simple Program Verification in Isabelle/HOL

by Peter Lammich 🌐 and Simon Wimmer 🌐 Jan 15

2018

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VerifyThis 2018 - Polished Isabelle Solutions

by Peter Lammich 🌐 and Simon Wimmer 🌐
+
VerifyThis 2018 - Polished Isabelle Solutions

by Peter Lammich 🌐 and Simon Wimmer 🌐 Apr 27

2017

The string search algorithm by Knuth, Morris and Pratt

by Fabian Hellauer 📧 and Peter Lammich 🌐
Dec 18
Formalizing Push-Relabel Algorithms

by Peter Lammich 🌐 and S. Reza Sefidgar
Jun 01
Flow Networks and the Min-Cut-Max-Flow Theorem

by Peter Lammich 🌐 and S. Reza Sefidgar
Jun 01
-
The Floyd-Warshall Algorithm for Shortest Paths

by Simon Wimmer 🌐 and Peter Lammich 🌐
+
The Floyd-Warshall Algorithm for Shortest Paths

by Simon Wimmer 🌐 and Peter Lammich 🌐 May 08

2016

Formalizing the Edmonds-Karp Algorithm

by Peter Lammich 📧 and S. Reza Sefidgar
Aug 12
The Imperative Refinement Framework

by Peter Lammich 🌐
Aug 08
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A Framework for Verifying Depth-First Search Algorithms

by Peter Lammich 🌐 and René Neumann 📧
+
A Framework for Verifying Depth-First Search Algorithms

by Peter Lammich 🌐 and René Neumann 📧 Jul 05
-
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐
+
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐 Apr 27

2014

Verified Efficient Implementation of Gabow's Strongly Connected Components Algorithm

by Peter Lammich 🌐
May 28
The CAVA Automata Library

by Peter Lammich 🌐
May 28
Converting Linear-Time Temporal Logic to Generalized Büchi Automata

by Alexander Schimpf 📧 and Peter Lammich 🌐
May 28
-
A Fully Verified Executable LTL Model Checker

by Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐
+
A Fully Verified Executable LTL Model Checker

by Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐 May 28
Bounded-Deducibility Security

by Andrei Popescu 🌐, Peter Lammich 🌐 and Thomas Bauereiss 📧
Apr 22
A shallow embedding of HyperCTL*

by Markus N. Rabe 🌐, Peter Lammich 🌐 and Andrei Popescu 🌐
Apr 16

2013

Automatic Data Refinement

by Peter Lammich 📧
Oct 02

2012

A Separation Logic Framework for Imperative HOL

by Peter Lammich 🌐 and Rene Meis 📧
Nov 14
Refinement for Monadic Programs

by Peter Lammich 🌐
Jan 30
Dijkstra's Shortest Path Algorithm

by Benedikt Nordhoff 📧 and Peter Lammich 🌐
Jan 30

2010

Finger Trees

by Benedikt Nordhoff 📧, Stefan Körner 📧 and Peter Lammich 🌐
Oct 28
Binomial Heaps and Skew Binomial Heaps

by Rene Meis 📧, Finn Nielsen 📧 and Peter Lammich 🌐
Oct 28

2009

Tree Automata

by Peter Lammich 🌐
Nov 25
Collections Framework

by Peter Lammich 🌐
Nov 25

2007

Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors

by Peter Lammich 🌐 and Markus Müller-Olm 🌐
Dec 14
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Bruno Langenstein

E-Mails 📧

Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/li/index.html b/web/authors/li/index.html --- a/web/authors/li/index.html +++ b/web/authors/li/index.html @@ -1,173 +1,173 @@ li - Archive of Formal Proofs

Wenda Li

Homepages 🌐

- +

Entries

2021

2020

2019

2018

May 23

2017

Oct 17
Oct 17

2014

Sep 19

2013

Jul 19
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Andreas Lochbihler

Homepages 🌐

- +

Entries

2021

Mar 17

2020

+
Authenticated Data Structures As Functors

by Andreas Lochbihler 🌐 and Ognjen Marić 📧
Apr 16

2019

-
Sigma Protocols and Commitment Schemes

by David Butler 🌐 and Andreas Lochbihler 🌐
+
Sigma Protocols and Commitment Schemes

by David Butler 🌐 and Andreas Lochbihler 🌐 Oct 07

2018

Constructive Cryptography in HOL

by Andreas Lochbihler 🌐 and S. Reza Sefidgar
Dec 17
-
Bounded Natural Functors with Covariance and Contravariance

by Andreas Lochbihler 🌐 and Joshua Schneider 📧
+
Bounded Natural Functors with Covariance and Contravariance

by Andreas Lochbihler 🌐 and Joshua Schneider 📧 Apr 24

2017

-
Probabilistic while loop

by Andreas Lochbihler 🌐
- - May 05 - -
-
-
-
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐
+
Probabilistic while loop

by Andreas Lochbihler 🌐 May 05
-
Game-based cryptography in HOL

by Andreas Lochbihler 🌐, S. Reza Sefidgar and Bhargav Bhatt 📧
+
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐 May 05
-
Effect polymorphism in higher-order logic

by Andreas Lochbihler 🌐
+
Game-based cryptography in HOL

by Andreas Lochbihler 🌐, S. Reza Sefidgar and Bhargav Bhatt 📧 May 05
-
CryptHOL

by Andreas Lochbihler 🌐
+
Effect polymorphism in higher-order logic

by Andreas Lochbihler 🌐 + + May 05 + +
+
+
+
CryptHOL

by Andreas Lochbihler 🌐
May 05

2016

-
A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks

by Andreas Lochbihler 🌐
+
A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks

by Andreas Lochbihler 🌐 May 09

2015

-
The Stern-Brocot Tree

by Peter Gammie 🌐 and Andreas Lochbihler 🌐
+
The Stern-Brocot Tree

by Peter Gammie 🌐 and Andreas Lochbihler 🌐 Dec 22
-
Applicative Lifting

by Andreas Lochbihler 🌐 and Joshua Schneider
+
Applicative Lifting

by Andreas Lochbihler 🌐 and Joshua Schneider Dec 22
-
A Zoo of Probabilistic Systems

by Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐
+
A Zoo of Probabilistic Systems

by Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐 May 27
-
Trie

by Andreas Lochbihler 🌐 and Tobias Nipkow 🌐
+
Trie

by Andreas Lochbihler 🌐 and Tobias Nipkow 🌐 Mar 30

2014

-
Stream Fusion in HOL with Code Generation

by Andreas Lochbihler 🌐 and Alexandra Maximova 📧
+
Stream Fusion in HOL with Code Generation

by Andreas Lochbihler 🌐 and Alexandra Maximova 📧 Oct 10

2013

-
Native Word

by Andreas Lochbihler 🌐
+
Native Word

by Andreas Lochbihler 🌐 Sep 17
-
Light-weight Containers

by Andreas Lochbihler 🌐
+
Light-weight Containers

by Andreas Lochbihler 🌐 Apr 15

2010

-
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧
+
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧 Aug 10
-
Coinductive

by Andreas Lochbihler 🌐
+
Coinductive

by Andreas Lochbihler 🌐 Feb 12

2009

-
Code Generation for Functions as Data

by Andreas Lochbihler 🌐
+
Code Generation for Functions as Data

by Andreas Lochbihler 🌐 May 06

2007

-
Jinja with Threads

by Andreas Lochbihler 🌐
+
Jinja with Threads

by Andreas Lochbihler 🌐 Dec 03
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Alexander Maletzky

Homepages 🌐

Entries

2019

2018

2016

May 02

2010

+
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧
Aug 10 \ No newline at end of file diff --git a/web/authors/mantel/index.html b/web/authors/mantel/index.html --- a/web/authors/mantel/index.html +++ b/web/authors/mantel/index.html @@ -1,121 +1,121 @@ mantel - Archive of Formal Proofs

Heiko Mantel

E-Mails 📧

Entries

2018

May 07

2014

Apr 23
Apr 23
Apr 23
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Ognjen Marić

E-Mails 📧

Entries

2020

Apr 16

2015

Mar 18
\ No newline at end of file diff --git a/web/authors/maricf/index.html b/web/authors/maricf/index.html --- a/web/authors/maricf/index.html +++ b/web/authors/maricf/index.html @@ -1,126 +1,126 @@ maricf - Archive of Formal Proofs

Filip Marić

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- +

E-Mails 📧

Entries

2019

2018

Aug 24

2008

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Formal Verification of Modern SAT Solvers

by Filip Marić 🌐
Jul 23 \ No newline at end of file diff --git a/web/authors/maximova/index.html b/web/authors/maximova/index.html --- a/web/authors/maximova/index.html +++ b/web/authors/maximova/index.html @@ -1,98 +1,98 @@ maximova - Archive of Formal Proofs

Alexandra Maximova

E-Mails 📧

Entries

2014

Oct 10
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Julius Michaelis

Homepages 🌐

- +

Entries

2021

2017

Jun 21

2016

+
LOFT — Verified Migration of Linux Firewalls to SDN

by Julius Michaelis 🌐 and Cornelius Diekmann 🌐
Oct 21
-
Routing

by Julius Michaelis 🌐 and Cornelius Diekmann 🌐
+
Routing

by Julius Michaelis 🌐 and Cornelius Diekmann 🌐 Aug 31
-
Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐
+
Simple Firewall

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐 Aug 24
-
IP Addresses

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐
+
IP Addresses

by Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐 Jun 28
-
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐
+
Algorithms for Reduced Ordered Binary Decision Diagrams

by Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐 Apr 27
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Bernhard Möller

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Entries

2020

Jan 31
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Dominic P. Mulligan

E-Mails 📧

Entries

2018

May 10

2017

Aug 16
+
A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes

by Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧
Jul 07 \ No newline at end of file diff --git a/web/authors/murray/index.html b/web/authors/murray/index.html --- a/web/authors/murray/index.html +++ b/web/authors/murray/index.html @@ -1,114 +1,114 @@ murray - Archive of Formal Proofs

Toby Murray

Homepages 🌐

- +

Entries

2020

2016

Jun 28
+
A Dependent Security Type System for Concurrent Imperative Programs

by Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐
Jun 25 \ No newline at end of file diff --git a/web/authors/naraschewski/index.html b/web/authors/naraschewski/index.html --- a/web/authors/naraschewski/index.html +++ b/web/authors/naraschewski/index.html @@ -1,95 +1,95 @@ naraschewski - Archive of Formal Proofs

Wolfgang Naraschewski

Entries

2004

Mar 19
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Yakoub Nemouchi

E-Mails 📧

Entries

2019

Feb 01

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18 \ No newline at end of file diff --git a/web/authors/neumann/index.html b/web/authors/neumann/index.html --- a/web/authors/neumann/index.html +++ b/web/authors/neumann/index.html @@ -1,123 +1,123 @@ neumann - Archive of Formal Proofs

René Neumann

E-Mails 📧

- +

Entries

2016

Jul 05

2014

May 28
+
A Fully Verified Executable LTL Model Checker

by Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐
May 28

2010

-
Functional Binomial Queues

by René Neumann 📧
+
Functional Binomial Queues

by René Neumann 📧 Oct 28
\ No newline at end of file diff --git a/web/authors/nipkow/index.html b/web/authors/nipkow/index.html --- a/web/authors/nipkow/index.html +++ b/web/authors/nipkow/index.html @@ -1,434 +1,434 @@ nipkow - Archive of Formal Proofs

Tobias Nipkow

Homepages 🌐

- +

Entries

2021

Dec 29
+
Isabelle's Metalogic: Formalization and Proof Checker

by Tobias Nipkow 🌐 and Simon Roßkopf 🌐
Apr 27

2020

-
Verified Approximation Algorithms

by Robin Eßmann 📧, Tobias Nipkow 🌐, Simon Robillard 🌐 and Ujkan Sulejmani
+
Verified Approximation Algorithms

by Robin Eßmann 📧, Tobias Nipkow 🌐, Simon Robillard 🌐 and Ujkan Sulejmani Jan 16
-
Closest Pair of Points Algorithms

by Martin Rau 📧 and Tobias Nipkow 🌐
+
Closest Pair of Points Algorithms

by Martin Rau 📧 and Tobias Nipkow 🌐 Jan 13

2019

-
Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra

by Peter Lammich 🌐 and Tobias Nipkow 🌐
+
Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra

by Peter Lammich 🌐 and Tobias Nipkow 🌐 Jun 25
-
Priority Search Trees

by Peter Lammich 🌐 and Tobias Nipkow 🌐
+
Priority Search Trees

by Peter Lammich 🌐 and Tobias Nipkow 🌐 Jun 25

2018

-
Optimal Binary Search Trees

by Tobias Nipkow 🌐 and Dániel Somogyi
+
Optimal Binary Search Trees

by Tobias Nipkow 🌐 and Dániel Somogyi May 27
-
Monadification, Memoization and Dynamic Programming

by Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐
+
Monadification, Memoization and Dynamic Programming

by Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐 May 22
-
Weight-Balanced Trees

by Tobias Nipkow 🌐 and Stefan Dirix
+
Weight-Balanced Trees

by Tobias Nipkow 🌐 and Stefan Dirix Mar 13
-
Hoare Logics for Time Bounds

by Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐
+
Hoare Logics for Time Bounds

by Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐 Feb 26
-
Treaps

by Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐
+
Treaps

by Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐 Feb 06

2017

-
Root-Balanced Tree

by Tobias Nipkow 🌐
+
Root-Balanced Tree

by Tobias Nipkow 🌐 Aug 20
-
Propositional Proof Systems

by Julius Michaelis 🌐 and Tobias Nipkow 🌐
+
Propositional Proof Systems

by Julius Michaelis 🌐 and Tobias Nipkow 🌐 Jun 21

2016

-
Abstract Interpretation of Annotated Commands

by Tobias Nipkow 🌐
+
Abstract Interpretation of Annotated Commands

by Tobias Nipkow 🌐 Nov 23
-
Pairing Heap

by Hauke Brinkop 📧 and Tobias Nipkow 🌐
+
Pairing Heap

by Hauke Brinkop 📧 and Tobias Nipkow 🌐 Jul 14
-
Analysis of List Update Algorithms

by Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐
+
Analysis of List Update Algorithms

by Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐 Feb 17

2015

-
Parameterized Dynamic Tables

by Tobias Nipkow 🌐
+
Parameterized Dynamic Tables

by Tobias Nipkow 🌐 Jun 07
-
Trie

by Andreas Lochbihler 🌐 and Tobias Nipkow 🌐
+
Trie

by Andreas Lochbihler 🌐 and Tobias Nipkow 🌐 Mar 30

2014

-
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐
+
A Verified Compiler for Probability Density Functions

by Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐 Oct 09
-
Priority Queues Based on Braun Trees

by Tobias Nipkow 🌐
+
Priority Queues Based on Braun Trees

by Tobias Nipkow 🌐 Sep 04
-
Skew Heap

by Tobias Nipkow 🌐
+
Skew Heap

by Tobias Nipkow 🌐 Aug 13
-
Splay Tree

by Tobias Nipkow 🌐
+
Splay Tree

by Tobias Nipkow 🌐 Aug 12
-
Amortized Complexity Verified

by Tobias Nipkow 🌐
+
Amortized Complexity Verified

by Tobias Nipkow 🌐 Jul 07
-
Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions

by Dmitriy Traytel 🌐 and Tobias Nipkow 🌐
+
Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions

by Dmitriy Traytel 🌐 and Tobias Nipkow 🌐 Jun 12
-
Boolean Expression Checkers

by Tobias Nipkow 🌐
+
Boolean Expression Checkers

by Tobias Nipkow 🌐 Jun 08
-
A Fully Verified Executable LTL Model Checker

by Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐
+
A Fully Verified Executable LTL Model Checker

by Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐 May 28
-
Unified Decision Procedures for Regular Expression Equivalence

by Tobias Nipkow 🌐 and Dmitriy Traytel 🌐
+
Unified Decision Procedures for Regular Expression Equivalence

by Tobias Nipkow 🌐 and Dmitriy Traytel 🌐 Jan 30

2012

-
Markov Models

by Johannes Hölzl 🌐 and Tobias Nipkow 🌐
+
Markov Models

by Johannes Hölzl 🌐 and Tobias Nipkow 🌐 Jan 03

2011

-
Gauss-Jordan Elimination for Matrices Represented as Functions

by Tobias Nipkow 🌐
+
Gauss-Jordan Elimination for Matrices Represented as Functions

by Tobias Nipkow 🌐 Aug 19

2010

-
Hall's Marriage Theorem

by Dongchen Jiang 📧 and Tobias Nipkow 🌐
+
Hall's Marriage Theorem

by Dongchen Jiang 📧 and Tobias Nipkow 🌐 Dec 17
-
Regular Sets and Expressions

by Alexander Krauss 🌐 and Tobias Nipkow 🌐
+
Regular Sets and Expressions

by Alexander Krauss 🌐 and Tobias Nipkow 🌐 May 12
-
List Index

by Tobias Nipkow 🌐
+
List Index

by Tobias Nipkow 🌐 Feb 20

2008

-
Fun With Tilings

by Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐
+
Fun With Tilings

by Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐 Nov 07
-
Arrow and Gibbard-Satterthwaite

by Tobias Nipkow 🌐
+
Arrow and Gibbard-Satterthwaite

by Tobias Nipkow 🌐 Sep 01
-
Fun With Functions

by Tobias Nipkow 🌐
+
Fun With Functions

by Tobias Nipkow 🌐 Aug 26
-
Normalization by Evaluation

by Klaus Aehlig 🌐 and Tobias Nipkow 🌐
+
Normalization by Evaluation

by Klaus Aehlig 🌐 and Tobias Nipkow 🌐 Feb 18
-
Quantifier Elimination for Linear Arithmetic

by Tobias Nipkow 🌐
+
Quantifier Elimination for Linear Arithmetic

by Tobias Nipkow 🌐 Jan 11

2006

-
Hotel Key Card System

by Tobias Nipkow 🌐
+
Hotel Key Card System

by Tobias Nipkow 🌐 Sep 09
-
Abstract Hoare Logics

by Tobias Nipkow 🌐
+
Abstract Hoare Logics

by Tobias Nipkow 🌐 Aug 08
-
Flyspeck I: Tame Graphs

by Gertrud Bauer and Tobias Nipkow 🌐
+
Flyspeck I: Tame Graphs

by Gertrud Bauer and Tobias Nipkow 🌐 May 22

2005

-
Jinja is not Java

by Gerwin Klein 🌐 and Tobias Nipkow 🌐
+
Jinja is not Java

by Gerwin Klein 🌐 and Tobias Nipkow 🌐 Jun 01

2004

-
Compiling Exceptions Correctly

by Tobias Nipkow 🌐
+
Compiling Exceptions Correctly

by Tobias Nipkow 🌐 Jul 09
-
Functional Automata

by Tobias Nipkow 🌐
+
Functional Automata

by Tobias Nipkow 🌐 Mar 30
-
Mini ML

by Wolfgang Naraschewski and Tobias Nipkow 🌐
+
Mini ML

by Wolfgang Naraschewski and Tobias Nipkow 🌐 Mar 19
-
AVL Trees

by Tobias Nipkow 🌐 and Cornelia Pusch
+
AVL Trees

by Tobias Nipkow 🌐 and Cornelia Pusch Mar 19
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Miguel Pagano

Homepages 🌐

Entries

2022

Mar 06
+
Transitive Models of Fragments of ZFC

by Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧
Mar 03

2020

-
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐
+
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐 May 06
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Julian Parsert

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E-Mails 📧

Entries

2019

Aug 06

2018

Jul 04

2017

Oct 14
Sep 01
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Lawrence C. Paulson

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- +

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Entries

2022

Mar 23
Feb 18
Jan 31
Jan 08

2021

Dec 28
Nov 05
Aug 13
Mar 29

2020

Aug 03
May 16

2019

Oct 24
Sep 06

2018

+
The Prime Number Theorem

by Manuel Eberl 🌐 and Lawrence C. Paulson 🌐
Sep 19
Quaternions

by Lawrence C. Paulson 🌐
Sep 05
-
An Isabelle/HOL formalisation of Green's Theorem

by Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐
+
An Isabelle/HOL formalisation of Green's Theorem

by Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐 Jan 11

2016

Source Coding Theorem

by Quentin Hibon 📧 and Lawrence C. Paulson 📧
Oct 19
-
The Cartan Fixed Point Theorems

by Lawrence C. Paulson 🌐
+
The Cartan Fixed Point Theorems

by Lawrence C. Paulson 🌐 Mar 08

2015

-
Finite Automata in Hereditarily Finite Set Theory

by Lawrence C. Paulson 🌐
+
Finite Automata in Hereditarily Finite Set Theory

by Lawrence C. Paulson 🌐 Feb 05

2014

-
Real-Valued Special Functions: Upper and Lower Bounds

by Lawrence C. Paulson 🌐
+
Real-Valued Special Functions: Upper and Lower Bounds

by Lawrence C. Paulson 🌐 Aug 29

2013

-
The Hereditarily Finite Sets

by Lawrence C. Paulson 🌐
+
The Hereditarily Finite Sets

by Lawrence C. Paulson 🌐 Nov 17
-
Gödel's Incompleteness Theorems

by Lawrence C. Paulson 🌐
+
Gödel's Incompleteness Theorems

by Lawrence C. Paulson 🌐 Nov 17

2012

-
Proving the Impossibility of Trisecting an Angle and Doubling the Cube

by Ralph Romanos 📧 and Lawrence C. Paulson 🌐
+
Proving the Impossibility of Trisecting an Angle and Doubling the Cube

by Ralph Romanos 📧 and Lawrence C. Paulson 🌐 Aug 05

2008

-
Fun With Tilings

by Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐
+
Fun With Tilings

by Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐 Nov 07
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Edward Pierzchalski

Entries

2016

Jun 28
+
A Dependent Security Type System for Concurrent Imperative Programs

by Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐
Jun 25 \ No newline at end of file diff --git a/web/authors/platzer/index.html b/web/authors/platzer/index.html --- a/web/authors/platzer/index.html +++ b/web/authors/platzer/index.html @@ -1,117 +1,117 @@ platzer - Archive of Formal Proofs

André Platzer

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- +

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Entries

2021

2019

Jun 03
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Andrei Popescu

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Entries

2021

2020

-
Sep 16
+
Robinson Arithmetic

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
Sep 16
-
From Abstract to Concrete Gödel's Incompleteness Theorems—Part I

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
From Abstract to Concrete Gödel's Incompleteness Theorems—Part II

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Sep 16
-
An Abstract Formalization of Gödel's Incompleteness Theorems

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
From Abstract to Concrete Gödel's Incompleteness Theorems—Part I

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐 + + Sep 16 + +
+
+
+
An Abstract Formalization of Gödel's Incompleteness Theorems

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
Sep 16

2019

A General Theory of Syntax with Bindings

by Lorenzo Gheri 📧 and Andrei Popescu 🌐
Apr 06

2017

-
Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Dec 19
-
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Feb 10

2014

Bounded-Deducibility Security

by Andrei Popescu 🌐, Peter Lammich 🌐 and Thomas Bauereiss 📧
Apr 22
-
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Apr 16
A shallow embedding of HyperCTL*

by Markus N. Rabe 🌐, Peter Lammich 🌐 and Andrei Popescu 🌐
Apr 16
-
Probabilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 🌐
+
Probabilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 🌐 Mar 11

2013

Sound and Complete Sort Encodings for First-Order Logic

by Jasmin Christian Blanchette 🌐 and Andrei Popescu 🌐
Jun 27

2012

Possibilistic Noninterference

by Andrei Popescu 🌐 and Johannes Hölzl 📧
Sep 10

2009

Ordinals and Cardinals

by Andrei Popescu 🌐
Sep 01
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Cornelia Pusch

Entries

2004

Mar 19
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Martin Raszyk

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Entries

2022

2020

Apr 09
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Martin Rau

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Entries

2020

Jan 13

2019

May 30
\ No newline at end of file diff --git a/web/authors/raya/index.html b/web/authors/raya/index.html --- a/web/authors/raya/index.html +++ b/web/authors/raya/index.html @@ -1,98 +1,98 @@ raya - Archive of Formal Proofs

Rodrigo Raya

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Entries

2019

Dec 10
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Alban Reynaud

Entries

2019

Jun 21
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Pedro Ribeiro

Entries

2019

Feb 01
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Albert Rizaldi

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Entries

2020

Jun 01
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Christine Rizkallah

Homepages 🌐

Entries

2016

Jun 28
+
A Dependent Security Type System for Concurrent Imperative Programs

by Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐
Jun 25

2013

An Axiomatic Characterization of the Single-Source Shortest Path Problem

by Christine Rizkallah 🌐
May 22

2011

Maximum Cardinality Matching

by Christine Rizkallah 🌐
Jul 21
\ No newline at end of file diff --git a/web/authors/robillard/index.html b/web/authors/robillard/index.html --- a/web/authors/robillard/index.html +++ b/web/authors/robillard/index.html @@ -1,98 +1,98 @@ robillard - Archive of Formal Proofs

Simon Robillard

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Entries

2020

Jan 16
\ No newline at end of file diff --git a/web/authors/romanos/index.html b/web/authors/romanos/index.html --- a/web/authors/romanos/index.html +++ b/web/authors/romanos/index.html @@ -1,98 +1,98 @@ romanos - Archive of Formal Proofs

Ralph Romanos

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Entries

2012

Aug 05
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Simon Roßkopf

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Entries

2021

Apr 27
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Christian Saile

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Entries

2018

Mar 22
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Maximilian Schäffeler

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Entries

2021

Dec 16
+
Markov Decision Processes with Rewards

by Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧
Dec 16 \ No newline at end of file diff --git a/web/authors/schimpf/index.html b/web/authors/schimpf/index.html --- a/web/authors/schimpf/index.html +++ b/web/authors/schimpf/index.html @@ -1,105 +1,105 @@ schimpf - Archive of Formal Proofs

Alexander Schimpf

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Entries

2014

May 28
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Anders Schlichtkrull

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Entries

2020

2018

Nov 23
+
Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧
Jan 18

2017

First-Order Logic According to Harrison

by Alexander Birch Jensen 🌐, Anders Schlichtkrull 🌐 and Jørgen Villadsen 🌐
Jan 01

2016

Paraconsistency

by Anders Schlichtkrull 🌐 and Jørgen Villadsen 🌐
Dec 07
The Resolution Calculus for First-Order Logic

by Anders Schlichtkrull 🌐
Jun 30
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Julien Schmaltz

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Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/schneider/index.html b/web/authors/schneider/index.html --- a/web/authors/schneider/index.html +++ b/web/authors/schneider/index.html @@ -1,141 +1,141 @@ schneider - Archive of Formal Proofs

Joshua Schneider

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Entries

2020

Apr 10
+
Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations

by Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐
Apr 09

2019

-
Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic

by Joshua Schneider 📧 and Dmitriy Traytel 🌐
+
Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic

by Joshua Schneider 📧 and Dmitriy Traytel 🌐 Jul 04

2018

-
Bounded Natural Functors with Covariance and Contravariance

by Andreas Lochbihler 🌐 and Joshua Schneider 📧
+
Bounded Natural Functors with Covariance and Contravariance

by Andreas Lochbihler 🌐 and Joshua Schneider 📧 Apr 24

2017

-
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐
+
Monad normalisation

by Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐 May 05

2015

-
Applicative Lifting

by Andreas Lochbihler 🌐 and Joshua Schneider
+
Applicative Lifting

by Andreas Lochbihler 🌐 and Joshua Schneider Dec 22
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S. Reza Sefidgar

Entries

2021

Mar 17

2018

Dec 17

2017

Jun 01
Jun 01
+
Game-based cryptography in HOL

by Andreas Lochbihler 🌐, S. Reza Sefidgar and Bhargav Bhatt 📧
May 05

2016

Formalizing the Edmonds-Karp Algorithm

by Peter Lammich 📧 and S. Reza Sefidgar
Aug 12
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Salomon Sickert

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- +

Entries

2020

2019

2016

2015

Sep 04
\ No newline at end of file diff --git a/web/authors/sison/index.html b/web/authors/sison/index.html --- a/web/authors/sison/index.html +++ b/web/authors/sison/index.html @@ -1,102 +1,102 @@ sison - Archive of Formal Proofs

Robert Sison

Entries

2016

Jun 28
+
A Dependent Security Type System for Concurrent Imperative Programs

by Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐
Jun 25 \ No newline at end of file diff --git a/web/authors/smaus/index.html b/web/authors/smaus/index.html --- a/web/authors/smaus/index.html +++ b/web/authors/smaus/index.html @@ -1,98 +1,98 @@ smaus - Archive of Formal Proofs

Jan-Georg Smaus

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Entries

2014

May 28
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Dániel Somogyi

Entries

2018

May 27
\ No newline at end of file diff --git a/web/authors/spasic/index.html b/web/authors/spasic/index.html --- a/web/authors/spasic/index.html +++ b/web/authors/spasic/index.html @@ -1,98 +1,98 @@ spasic - Archive of Formal Proofs

Mirko Spasić

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Entries

2018

Aug 24
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Matías Steinberg

E-Mails 📧

Entries

2022

Mar 06
+
Transitive Models of Fragments of ZFC

by Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧
Mar 03 \ No newline at end of file diff --git a/web/authors/stephan/index.html b/web/authors/stephan/index.html --- a/web/authors/stephan/index.html +++ b/web/authors/stephan/index.html @@ -1,98 +1,98 @@ stephan - Archive of Formal Proofs

Werner Stephan

E-Mails 📧

Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/sternagel/index.html b/web/authors/sternagel/index.html --- a/web/authors/sternagel/index.html +++ b/web/authors/sternagel/index.html @@ -1,245 +1,245 @@ sternagel - Archive of Formal Proofs

Christian Sternagel

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2021

2020

May 13

2018

Feb 06

2017

Oct 14
Jul 15

2016

Jun 30

2015

Mar 11

2014

Oct 03
Oct 03
Sep 25
Jul 29

2012

Nov 02
Apr 13

2011

Nov 09
Mar 14

2010

+
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧
Aug 10
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Executable Matrix Operations on Matrices of Arbitrary Dimensions

by Christian Sternagel 📧 and René Thiemann 🌐
+
Executable Matrix Operations on Matrices of Arbitrary Dimensions

by Christian Sternagel 📧 and René Thiemann 🌐 Jun 17
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Abstract Rewriting

by Christian Sternagel 📧 and René Thiemann 🌐
+
Abstract Rewriting

by Christian Sternagel 📧 and René Thiemann 🌐 Jun 14
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Christian Stricker

Homepages 🌐

Entries

2018

Mar 22
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Georg Struth

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Entries

2018

2017

2016

Apr 12

2015

+
Binary Multirelations

by Hitoshi Furusawa 🌐 and Georg Struth 🌐
Jun 11
Residuated Lattices

by Victor B. F. Gomes 📧 and Georg Struth 📧
Apr 15

2014

-
Regular Algebras

by Simon Foster 🌐 and Georg Struth 🌐
+
Regular Algebras

by Simon Foster 🌐 and Georg Struth 🌐 May 21
Relation Algebra

by Alasdair Armstrong, Simon Foster 📧, Georg Struth 🌐 and Tjark Weber 🌐
Jan 25
-
Kleene Algebra with Tests and Demonic Refinement Algebras

by Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐
+
Kleene Algebra with Tests and Demonic Refinement Algebras

by Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐 Jan 23

2013

Kleene Algebra

by Alasdair Armstrong, Georg Struth 🌐 and Tjark Weber 🌐
Jan 15
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Daniel Stüwe

Entries

2019

Feb 11
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Henning Sudbrock

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Entries

2018

May 07
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Ujkan Sulejmani

Entries

2020

Jan 16
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Safouan Taha

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Entries

2021

2020

2019

Apr 26
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Yong Kiam Tan

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Entries

2021

2019

Dec 18
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Markus Tasch

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Entries

2018

May 07
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Pedro Sánchez Terraf

Homepages 🌐

- +

Entries

2022

Mar 06
+
Transitive Models of Fragments of ZFC

by Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧
Mar 03

2020

Cofinality and the Delta System Lemma

by Pedro Sánchez Terraf 🌐
Dec 27
-
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐
+
Formalization of Forcing in Isabelle/ZF

by Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐 May 06
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René Thiemann

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Entries

2022

2021

Nov 08
Sep 16
Sep 03
Mar 12
Feb 25

2020

+
A Formalization of Knuth–Bendix Orders

by Christian Sternagel 📧 and René Thiemann 🌐
May 13

2019

-
Linear Inequalities

by Ralph Bottesch 🌐, Alban Reynaud and René Thiemann 🌐
+
Linear Inequalities

by Ralph Bottesch 🌐, Alban Reynaud and René Thiemann 🌐 Jun 21
-
Farkas' Lemma and Motzkin's Transposition Theorem

by Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐
+
Farkas' Lemma and Motzkin's Transposition Theorem

by Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐 Jan 17

2018

-
An Incremental Simplex Algorithm with Unsatisfiable Core Generation

by Filip Marić 📧, Mirko Spasić 📧 and René Thiemann 🌐
+
An Incremental Simplex Algorithm with Unsatisfiable Core Generation

by Filip Marić 📧, Mirko Spasić 📧 and René Thiemann 🌐 Aug 24
First-Order Terms

by Christian Sternagel 📧 and René Thiemann 🌐
Feb 06
-
A verified factorization algorithm for integer polynomials with polynomial complexity

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada 📧
+
A verified factorization algorithm for integer polynomials with polynomial complexity

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada 📧 Feb 06
-
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada Feb 02

2017

-
Stochastic Matrices and the Perron-Frobenius Theorem

by René Thiemann 🌐
+
Stochastic Matrices and the Perron-Frobenius Theorem

by René Thiemann 🌐 Nov 22
Subresultants

by Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
Apr 06

2016

-
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
+
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧 Oct 14
-
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧
+
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧 May 20
Polynomial Interpolation

by René Thiemann 📧 and Akihisa Yamada 📧
Jan 29
Polynomial Factorization

by René Thiemann 📧 and Akihisa Yamada 📧
Jan 29

2015

Algebraic Numbers in Isabelle/HOL

by René Thiemann 📧, Akihisa Yamada 📧 and Sebastiaan J. C. Joosten 📧
Dec 22
Matrices, Jordan Normal Forms, and Spectral Radius Theory

by René Thiemann 📧 and Akihisa Yamada 📧
Aug 21
Deriving class instances for datatypes

by Christian Sternagel 📧 and René Thiemann 📧
Mar 11

2014

Lifting Definition Option

by René Thiemann 📧
Oct 13
XML

by Christian Sternagel 📧 and René Thiemann 📧
Oct 03
Certification Monads

by Christian Sternagel 📧 and René Thiemann 📧
Oct 03
Haskell's Show Class in Isabelle/HOL

by Christian Sternagel 📧 and René Thiemann 📧
Jul 29
Mutually Recursive Partial Functions

by René Thiemann 📧
Feb 18
Implementing field extensions of the form Q[sqrt(b)]

by René Thiemann 📧
Feb 06

2013

Computing N-th Roots using the Babylonian Method

by René Thiemann 📧
Jan 03

2012

Generating linear orders for datatypes

by René Thiemann 📧
Aug 07
Executable Transitive Closures

by René Thiemann 📧
Feb 29

2011

Executable Transitive Closures of Finite Relations

by Christian Sternagel 📧 and René Thiemann 📧
Mar 14

2010

-
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧
+
Executable Multivariate Polynomials

by Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧 Aug 10
-
Executable Matrix Operations on Matrices of Arbitrary Dimensions

by Christian Sternagel 📧 and René Thiemann 🌐
+
Executable Matrix Operations on Matrices of Arbitrary Dimensions

by Christian Sternagel 📧 and René Thiemann 🌐 Jun 17
-
Abstract Rewriting

by Christian Sternagel 📧 and René Thiemann 🌐
+
Abstract Rewriting

by Christian Sternagel 📧 and René Thiemann 🌐 Jun 14
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Joseph Thommes

Entries

2021

Jul 07
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Sophie Tourret

Homepages 🌐

- +

Entries

2020

Aug 25
Apr 09
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Christoph Traut

Entries

2018

Jan 08
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Dmitriy Traytel

Homepages 🌐

- +

Entries

2021

2020

- -
Sep 16
- - Sep 16 - -
-
- +
Robinson Arithmetic

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
Sep 16
-
A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm

by Ben Fiedler 📧 and Dmitriy Traytel 🌐
+
From Abstract to Concrete Gödel's Incompleteness Theorems—Part II

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐 + + Sep 16 + +
+
+
+
From Abstract to Concrete Gödel's Incompleteness Theorems—Part I

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+ + Sep 16 + +
+
+
+
An Abstract Formalization of Gödel's Incompleteness Theorems

by Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+ + Sep 16 + +
+
+
+
A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm

by Ben Fiedler 📧 and Dmitriy Traytel 🌐
Jul 21
-
Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows

by Lukas Heimes, Dmitriy Traytel 🌐 and Joshua Schneider
+
Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows

by Lukas Heimes, Dmitriy Traytel 🌐 and Joshua Schneider Apr 10
-
Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations

by Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐
+
Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations

by Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐 Apr 09

2019

-
Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic

by Joshua Schneider 📧 and Dmitriy Traytel 🌐
+
Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic

by Joshua Schneider 📧 and Dmitriy Traytel 🌐 Jul 04
-
Formalization of Generic Authenticated Data Structures

by Matthias Brun and Dmitriy Traytel 🌐
+
Formalization of Generic Authenticated Data Structures

by Matthias Brun and Dmitriy Traytel 🌐 May 14

2018

-
A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧 and Dmitriy Traytel 🌐
+
A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧 and Dmitriy Traytel 🌐 Nov 23
-
Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧
+
Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

by Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧 Jan 18

2017

-
Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Operations on Bounded Natural Functors

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Dec 19
-
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Soundness

by Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Feb 10

2016

-
Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

by Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐
+
Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

by Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐 Nov 12

2015

-
Derivatives of Logical Formulas

by Dmitriy Traytel 🌐
+
Derivatives of Logical Formulas

by Dmitriy Traytel 🌐 May 28
-
A Zoo of Probabilistic Systems

by Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐
+
A Zoo of Probabilistic Systems

by Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐 May 27

2014

-
Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions

by Dmitriy Traytel 🌐 and Tobias Nipkow 🌐
+
Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions

by Dmitriy Traytel 🌐 and Tobias Nipkow 🌐 Jun 12
-
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐
+
Abstract Completeness

by Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 Apr 16
-
Unified Decision Procedures for Regular Expression Equivalence

by Tobias Nipkow 🌐 and Dmitriy Traytel 🌐
+
Unified Decision Procedures for Regular Expression Equivalence

by Tobias Nipkow 🌐 and Dmitriy Traytel 🌐 Jan 30

2013

-
A Codatatype of Formal Languages

by Dmitriy Traytel 🌐
+
A Codatatype of Formal Languages

by Dmitriy Traytel 🌐 Nov 15
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Frédéric Tuong

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E-Mails 📧

Entries

2019

2015

2014

Jan 16
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Sergey Tverdyshev

E-Mails 📧

Entries

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/unruh/index.html b/web/authors/unruh/index.html --- a/web/authors/unruh/index.html +++ b/web/authors/unruh/index.html @@ -1,117 +1,117 @@ unruh - Archive of Formal Proofs

Dominique Unruh

Homepages 🌐

- +

E-Mails 📧

Entries

2021

2020

May 02
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Christian Urban

Homepages 🌐

- +

Entries

2019

2016

May 24

2013

+
Nominal 2

by Christian Urban 🌐, Stefan Berghofer 🌐 and Cezary Kaliszyk 🌐
Feb 21

2011

-
The Myhill-Nerode Theorem Based on Regular Expressions

by Chunhan Wu, Xingyuan Zhang and Christian Urban 🌐
+
The Myhill-Nerode Theorem Based on Regular Expressions

by Chunhan Wu, Xingyuan Zhang and Christian Urban 🌐 Aug 26
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Freek Verbeek

E-Mails 📧

Entries

2021

2014

+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
Jul 18
\ No newline at end of file diff --git a/web/authors/voisin/index.html b/web/authors/voisin/index.html --- a/web/authors/voisin/index.html +++ b/web/authors/voisin/index.html @@ -1,95 +1,95 @@ voisin - Archive of Formal Proofs

Frederic Voisin

Entries

2016

Aug 18
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Uwe Waldmann

E-Mails 📧

- +

Entries

2018

Jan 18

2016

Nov 12
Sep 23
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Tjark Weber

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Entries

2016

Apr 12

2014

Jan 25

2013

Jan 15
\ No newline at end of file diff --git a/web/authors/wimmer/index.html b/web/authors/wimmer/index.html --- a/web/authors/wimmer/index.html +++ b/web/authors/wimmer/index.html @@ -1,172 +1,172 @@ wimmer - Archive of Formal Proofs

Simon Wimmer

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- +

E-Mails 📧

Entries

2019

Jan 15

2018

+
Hidden Markov Models

by Simon Wimmer 🌐
May 25
-
Probabilistic Timed Automata

by Simon Wimmer 🌐 and Johannes Hölzl 🌐
+
Probabilistic Timed Automata

by Simon Wimmer 🌐 and Johannes Hölzl 🌐 May 24
-
Monadification, Memoization and Dynamic Programming

by Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐
+
Monadification, Memoization and Dynamic Programming

by Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐 May 22
-
VerifyThis 2018 - Polished Isabelle Solutions

by Peter Lammich 🌐 and Simon Wimmer 🌐
+
VerifyThis 2018 - Polished Isabelle Solutions

by Peter Lammich 🌐 and Simon Wimmer 🌐 Apr 27

2017

-
The Floyd-Warshall Algorithm for Shortest Paths

by Simon Wimmer 🌐 and Peter Lammich 🌐
+
The Floyd-Warshall Algorithm for Shortest Paths

by Simon Wimmer 🌐 and Peter Lammich 🌐 May 08

2016

-
Timed Automata

by Simon Wimmer 🌐
+
Timed Automata

by Simon Wimmer 🌐 Mar 08

2013

Pratt's Primality Certificates

by Simon Wimmer 📧 and Lars Noschinski 🌐
Jul 22
Lehmer's Theorem

by Simon Wimmer 📧 and Lars Noschinski 🌐
Jul 22
\ No newline at end of file diff --git a/web/authors/wolff/index.html b/web/authors/wolff/index.html --- a/web/authors/wolff/index.html +++ b/web/authors/wolff/index.html @@ -1,204 +1,204 @@ wolff - Archive of Formal Proofs

Burkhart Wolff

Homepages 🌐

E-Mails 📧

- +

Entries

2020

2019

Apr 26
+
Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming

by Simon Foster 🌐, Frank Zeyda, Yakoub Nemouchi 📧, Pedro Ribeiro and Burkhart Wolff 📧
Feb 01

2017

-
Formal Network Models and Their Application to Firewall Policies

by Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐
+
Formal Network Models and Their Application to Firewall Policies

by Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐 Jan 08

2016

-
Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths

by Romain Aissat, Frederic Voisin and Burkhart Wolff 📧
+
Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths

by Romain Aissat, Frederic Voisin and Burkhart Wolff 📧 Aug 18

2015

A Meta-Model for the Isabelle API

by Frédéric Tuong 📧 and Burkhart Wolff 🌐
Sep 16

2014

-
The Unified Policy Framework (UPF)

by Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧
+
The Unified Policy Framework (UPF)

by Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧 Nov 28
-
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧
+
Formal Specification of a Generic Separation Kernel

by Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧 Jul 18
-
Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5

by Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧
+
Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5

by Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧 Jan 16

2012

-
Isabelle/Circus

by Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Marie-Claude Gaudel 📧
+
Isabelle/Circus

by Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Marie-Claude Gaudel 📧 May 27
\ No newline at end of file diff --git a/web/authors/wu/index.html b/web/authors/wu/index.html --- a/web/authors/wu/index.html +++ b/web/authors/wu/index.html @@ -1,95 +1,95 @@ wu - Archive of Formal Proofs

Chunhan Wu

Entries

2011

Aug 26
\ No newline at end of file diff --git a/web/authors/yamada/index.html b/web/authors/yamada/index.html --- a/web/authors/yamada/index.html +++ b/web/authors/yamada/index.html @@ -1,181 +1,181 @@ yamada - Archive of Formal Proofs

Akihisa Yamada

Homepages 🌐

E-Mails 📧

Entries

2021

2019

2018

Feb 06
+
A verified LLL algorithm

by Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada
Feb 02

2017

Subresultants

by Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
Apr 06

2016

-
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧
+
The Factorization Algorithm of Berlekamp and Zassenhaus

by Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧 Oct 14
-
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧
+
Perron-Frobenius Theorem for Spectral Radius Analysis

by Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧 May 20
Polynomial Interpolation

by René Thiemann 📧 and Akihisa Yamada 📧
Jan 29
Polynomial Factorization

by René Thiemann 📧 and Akihisa Yamada 📧
Jan 29

2015

Algebraic Numbers in Isabelle/HOL

by René Thiemann 📧, Akihisa Yamada 📧 and Sebastiaan J. C. Joosten 📧
Dec 22
Matrices, Jordan Normal Forms, and Spectral Radius Theory

by René Thiemann 📧 and Akihisa Yamada 📧
Aug 21
\ No newline at end of file diff --git a/web/authors/ye/index.html b/web/authors/ye/index.html --- a/web/authors/ye/index.html +++ b/web/authors/ye/index.html @@ -1,107 +1,107 @@ ye - Archive of Formal Proofs

Lina Ye

E-Mails 📧

Entries

2020

2019

Apr 26
\ No newline at end of file diff --git a/web/authors/zeyda/index.html b/web/authors/zeyda/index.html --- a/web/authors/zeyda/index.html +++ b/web/authors/zeyda/index.html @@ -1,107 +1,107 @@ zeyda - Archive of Formal Proofs

Frank Zeyda

E-Mails 📧

Entries

2019

Feb 01

2017

May 25
\ No newline at end of file diff --git a/web/authors/zhan/index.html b/web/authors/zhan/index.html --- a/web/authors/zhan/index.html +++ b/web/authors/zhan/index.html @@ -1,121 +1,121 @@ zhan - Archive of Formal Proofs

Bohua Zhan

Homepages 🌐

Entries

2019

2018

Oct 22
\ No newline at end of file diff --git a/web/authors/zhangx/index.html b/web/authors/zhangx/index.html --- a/web/authors/zhangx/index.html +++ b/web/authors/zhangx/index.html @@ -1,104 +1,104 @@ zhangx - Archive of Formal Proofs

Xingyuan Zhang

Entries

2019

2011

Aug 26
\ No newline at end of file diff --git a/web/entries/ADS_Functor.html b/web/entries/ADS_Functor.html --- a/web/entries/ADS_Functor.html +++ b/web/entries/ADS_Functor.html @@ -1,186 +1,186 @@ Authenticated Data Structures As Functors - Archive of Formal Proofs

Authenticated Data Structures as Functors

-

Andreas Lochbihler 🌐 and Ognjen Marić 📧 +

Andreas Lochbihler 🌐 and Ognjen Marić 📧

April 16, 2020

Abstract

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 Canton, 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.
BSD License

Topics

Theories of ADS_Functor

\ No newline at end of file diff --git a/web/entries/AVL-Trees.html b/web/entries/AVL-Trees.html --- a/web/entries/AVL-Trees.html +++ b/web/entries/AVL-Trees.html @@ -1,155 +1,155 @@ AVL Trees - Archive of Formal Proofs

AVL Trees

-

Tobias Nipkow 🌐 and Cornelia Pusch +

Tobias Nipkow 🌐 and Cornelia Pusch

March 19, 2004

Abstract

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 gerwin.klein@nicta.com.au.
BSD License

Change history

[2011-04-11] Ondrej Kuncar added delete function

Topics

Theories of AVL-Trees

\ No newline at end of file diff --git a/web/entries/Abs_Int_ITP2012.html b/web/entries/Abs_Int_ITP2012.html --- a/web/entries/Abs_Int_ITP2012.html +++ b/web/entries/Abs_Int_ITP2012.html @@ -1,186 +1,186 @@ Abstract Interpretation of Annotated Commands - Archive of Formal Proofs

Abstract Interpretation of Annotated Commands

-

Tobias Nipkow 🌐 +

Tobias Nipkow 🌐

November 23, 2016

Abstract

This is the Isabelle formalization of the material decribed in the eponymous ITP 2012 paper. 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 Concrete Semantics.
BSD License

Topics

Theories of Abs_Int_ITP2012

\ No newline at end of file diff --git a/web/entries/Abstract-Hoare-Logics.html b/web/entries/Abstract-Hoare-Logics.html --- a/web/entries/Abstract-Hoare-Logics.html +++ b/web/entries/Abstract-Hoare-Logics.html @@ -1,176 +1,176 @@ Abstract Hoare Logics - Archive of Formal Proofs

Abstract Hoare Logics

-

Tobias Nipkow 🌐 +

Tobias Nipkow 🌐

August 8, 2006

Abstract

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.
BSD License

Topics

Theories of Abstract-Hoare-Logics

\ No newline at end of file diff --git a/web/entries/Abstract-Rewriting.html b/web/entries/Abstract-Rewriting.html --- a/web/entries/Abstract-Rewriting.html +++ b/web/entries/Abstract-Rewriting.html @@ -1,190 +1,190 @@ Abstract Rewriting - Archive of Formal Proofs

Abstract Rewriting

-

Christian Sternagel 📧 and René Thiemann 🌐 +

Christian Sternagel 📧 and René Thiemann 🌐

June 14, 2010

Abstract

We present an Isabelle formalization of abstract rewriting (see, e.g., the book by Baader and Nipkow). First, we define standard relations like joinability, meetability, conversion, 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 CeTA (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.
GNU Lesser General Public License (LGPL)

Change history

[2010-09-17] Added theories defining several (ordered) semirings related to strong normalization and giving some standard instances.
[2013-10-16] Generalized delta-orders from rationals to Archimedean fields.

Topics

Theories of Abstract-Rewriting

\ No newline at end of file diff --git a/web/entries/Abstract_Completeness.html b/web/entries/Abstract_Completeness.html --- a/web/entries/Abstract_Completeness.html +++ b/web/entries/Abstract_Completeness.html @@ -1,173 +1,173 @@ Abstract Completeness - Archive of Formal Proofs

Abstract Completeness

-

Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

Jasmin Christian Blanchette 🌐, Andrei Popescu 🌐 and Dmitriy Traytel 🌐

April 16, 2014

Abstract

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].
BSD License

Topics

Theories of Abstract_Completeness

\ No newline at end of file diff --git a/web/entries/Abstract_Soundness.html b/web/entries/Abstract_Soundness.html --- a/web/entries/Abstract_Soundness.html +++ b/web/entries/Abstract_Soundness.html @@ -1,179 +1,179 @@ Abstract Soundness - Archive of Formal Proofs

Abstract Soundness

-

Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐

February 10, 2017

Abstract

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 Journal of Automated Reasoning. The abstract proof can be instantiated for various formalisms, including first-order logic with inductive predicates.
BSD License

Topics

Theories of Abstract_Soundness

\ No newline at end of file diff --git a/web/entries/Ackermanns_not_PR.html b/web/entries/Ackermanns_not_PR.html --- a/web/entries/Ackermanns_not_PR.html +++ b/web/entries/Ackermanns_not_PR.html @@ -1,168 +1,168 @@ Ackermann's Function Is Not Primitive Recursive - Archive of Formal Proofs

Ackermann's Function Is Not Primitive Recursive

-

Lawrence C. Paulson 🌐 +

Lawrence C. Paulson 🌐

March 23, 2022

Abstract

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.
BSD License

Topics

Theories of Ackermanns_not_PR

Related Entries

\ No newline at end of file diff --git a/web/entries/Affine_Arithmetic.html b/web/entries/Affine_Arithmetic.html --- a/web/entries/Affine_Arithmetic.html +++ b/web/entries/Affine_Arithmetic.html @@ -1,187 +1,187 @@ Affine Arithmetic - Archive of Formal Proofs

Affine Arithmetic

-

Fabian Immler 🌐 +

Fabian Immler 🌐

February 7, 2014

Abstract

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.
BSD License

Change history

[2015-01-31] added algorithm for zonotope/hyperplane intersection
[2017-09-20] linear approximations for all symbols from the floatarith data type

Topics

Theories of Affine_Arithmetic

\ No newline at end of file diff --git a/web/entries/Aggregation_Algebras.html b/web/entries/Aggregation_Algebras.html --- a/web/entries/Aggregation_Algebras.html +++ b/web/entries/Aggregation_Algebras.html @@ -1,167 +1,167 @@ Aggregation Algebras - Archive of Formal Proofs

Aggregation Algebras

-

Walter Guttmann 🌐 +

Walter Guttmann 🌐

September 15, 2018

Abstract

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.
BSD License

Topics

Theories of Aggregation_Algebras

\ No newline at end of file diff --git a/web/entries/Akra_Bazzi.html b/web/entries/Akra_Bazzi.html --- a/web/entries/Akra_Bazzi.html +++ b/web/entries/Akra_Bazzi.html @@ -1,188 +1,188 @@ The Akra-Bazzi theorem and the Master theorem - Archive of Formal Proofs

The Akra-Bazzi Theorem and the Master Theorem

-

Manuel Eberl 🌐 +

Manuel Eberl 🌐

July 14, 2015

Abstract

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.

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).

BSD License

Topics

Theories of Akra_Bazzi

\ No newline at end of file diff --git a/web/entries/Algebraic_Numbers.html b/web/entries/Algebraic_Numbers.html --- a/web/entries/Algebraic_Numbers.html +++ b/web/entries/Algebraic_Numbers.html @@ -1,196 +1,196 @@ Algebraic Numbers in Isabelle/HOL - Archive of Formal Proofs

Algebraic Numbers in Isabelle/HOL

René Thiemann 📧, Akihisa Yamada 📧 and Sebastiaan J. C. Joosten 📧 - with contributions from Manuel Eberl 🌐 + with contributions from Manuel Eberl 🌐

December 22, 2015

Abstract

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.

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.

BSD License

Change history

[2016-01-29] Split off Polynomial Interpolation and Polynomial Factorization
[2017-04-16] Use certified Berlekamp-Zassenhaus factorization, use subresultant algorithm for computing resultants, improved bisection algorithm

Topics

Theories of Algebraic_Numbers

\ No newline at end of file diff --git a/web/entries/Amortized_Complexity.html b/web/entries/Amortized_Complexity.html --- a/web/entries/Amortized_Complexity.html +++ b/web/entries/Amortized_Complexity.html @@ -1,201 +1,201 @@ Amortized Complexity Verified - Archive of Formal Proofs

Amortized Complexity Verified

-

Tobias Nipkow 🌐 +

Tobias Nipkow 🌐

July 7, 2014

Abstract

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.

A preliminary version of this work (without pairing heaps) is described in a paper published in the proceedings of the conference on Interactive Theorem Proving ITP 2015. An extended version of this publication is available here.

BSD License

Change history

[2015-03-17] Added pairing heaps by Hauke Brinkop.
[2016-07-12] Moved splay heaps from here to Splay_Tree
[2016-07-14] Moved pairing heaps from here to the new Pairing_Heap

Topics

Theories of Amortized_Complexity

\ No newline at end of file diff --git a/web/entries/AnselmGod.html b/web/entries/AnselmGod.html --- a/web/entries/AnselmGod.html +++ b/web/entries/AnselmGod.html @@ -1,170 +1,170 @@ Anselm's God in Isabelle/HOL - Archive of Formal Proofs

Anselm's God in Isabelle/HOL

-

Ben Blumson 🌐 +

Ben Blumson 🌐

September 6, 2017

Abstract

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.
BSD License

Topics

Theories of AnselmGod

\ No newline at end of file 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 @@ -1,200 +1,200 @@ Applicative Lifting - Archive of Formal Proofs

Applicative Lifting

-

Andreas Lochbihler 🌐 and Joshua Schneider +

Andreas Lochbihler 🌐 and Joshua Schneider

December 22, 2015

Abstract

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.

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.

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.

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.

BSD License

Change history

[2016-03-03] added formalisation of lifting with combinators

Topics

Theories of Applicative_Lifting

\ No newline at end of file diff --git a/web/entries/Approximation_Algorithms.html b/web/entries/Approximation_Algorithms.html --- a/web/entries/Approximation_Algorithms.html +++ b/web/entries/Approximation_Algorithms.html @@ -1,175 +1,175 @@ Verified Approximation Algorithms - Archive of Formal Proofs

Verified Approximation Algorithms

-

Robin Eßmann 📧, Tobias Nipkow 🌐, Simon Robillard 🌐 and Ujkan Sulejmani +

Robin Eßmann 📧, Tobias Nipkow 🌐, Simon Robillard 🌐 and Ujkan Sulejmani

January 16, 2020

Abstract

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. A detailed description of our work (excluding center selection) has been published in the proceedings of IJCAR 2020.
BSD License

Topics

Theories of Approximation_Algorithms

\ No newline at end of file diff --git a/web/entries/ArrowImpossibilityGS.html b/web/entries/ArrowImpossibilityGS.html --- a/web/entries/ArrowImpossibilityGS.html +++ b/web/entries/ArrowImpossibilityGS.html @@ -1,167 +1,167 @@ Arrow and Gibbard-Satterthwaite - Archive of Formal Proofs

Arrow and Gibbard-Satterthwaite

-

Tobias Nipkow 🌐 +

Tobias Nipkow 🌐

September 1, 2008

Abstract

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.

An article about these proofs is found here.
BSD License

Topics

Theories of ArrowImpossibilityGS

\ No newline at end of file diff --git a/web/entries/BNF_CC.html b/web/entries/BNF_CC.html --- a/web/entries/BNF_CC.html +++ b/web/entries/BNF_CC.html @@ -1,190 +1,190 @@ Bounded Natural Functors with Covariance and Contravariance - Archive of Formal Proofs

Bounded Natural Functors With Covariance and Contravariance

-

Andreas Lochbihler 🌐 and Joshua Schneider 📧 +

Andreas Lochbihler 🌐 and Joshua Schneider 📧

April 24, 2018

Abstract

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 BNFCC that extends the mapper and relator to covariant and contravariant parameters. We show that
  1. BNFCCs are closed under functor composition and least and greatest fixpoints,
  2. subtypes inherit the BNFCC structure under conditions that generalise those for the BNF case, and
  3. BNFCCs preserve quotients under mild conditions.
These proofs are carried out for abstract BNFCCs similar to the AFP entry BNF Operations. In addition, we apply the BNFCC theory to several concrete functors.
BSD License

Topics

Theories of BNF_CC

\ No newline at end of file diff --git a/web/entries/BNF_Operations.html b/web/entries/BNF_Operations.html --- a/web/entries/BNF_Operations.html +++ b/web/entries/BNF_Operations.html @@ -1,182 +1,182 @@ Operations on Bounded Natural Functors - Archive of Formal Proofs

Operations on Bounded Natural Functors

-

Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

Jasmin Christian Blanchette 📧, Andrei Popescu 🌐 and Dmitriy Traytel 🌐

December 19, 2017

Abstract

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.
BSD License

Topics

Theories of BNF_Operations

\ No newline at end of file diff --git a/web/entries/Banach_Steinhaus.html b/web/entries/Banach_Steinhaus.html --- a/web/entries/Banach_Steinhaus.html +++ b/web/entries/Banach_Steinhaus.html @@ -1,176 +1,176 @@ Banach-Steinhaus Theorem - Archive of Formal Proofs

Banach-Steinhaus Theorem

-

Dominique Unruh 🌐 📧 and José Manuel Rodríguez Caballero 🌐 📧 +

Dominique Unruh 🌐 📧 and José Manuel Rodríguez Caballero 🌐 📧

May 2, 2020

Abstract

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.
BSD License

Topics

Theories of Banach_Steinhaus

\ No newline at end of file diff --git a/web/entries/Berlekamp_Zassenhaus.html b/web/entries/Berlekamp_Zassenhaus.html --- a/web/entries/Berlekamp_Zassenhaus.html +++ b/web/entries/Berlekamp_Zassenhaus.html @@ -1,218 +1,218 @@ The Factorization Algorithm of Berlekamp and Zassenhaus - Archive of Formal Proofs

The Factorization Algorithm of Berlekamp and Zassenhaus

-

Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧 +

Jose Divasón 🌐, Sebastiaan J. C. Joosten 📧, René Thiemann 📧 and Akihisa Yamada 📧

October 14, 2016

Abstract

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.

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.

Through experiments we verify that our algorithm factors polynomials of degree 100 within seconds.

BSD License

Topics

Theories of Berlekamp_Zassenhaus

\ No newline at end of file diff --git a/web/entries/Bernoulli.html b/web/entries/Bernoulli.html --- a/web/entries/Bernoulli.html +++ b/web/entries/Bernoulli.html @@ -1,183 +1,183 @@ Bernoulli Numbers - Archive of Formal Proofs

Bernoulli Numbers

-

Lukas Bulwahn 📧 and Manuel Eberl 🌐 +

Lukas Bulwahn 📧 and Manuel Eberl 🌐

January 24, 2017

Abstract

Bernoulli numbers were first discovered in the closed-form expansion of the sum 1m + 2m + … + nm 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.

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.

We also prove the correctness of the Akiyama–Tanigawa algorithm for computing Bernoulli numbers with reasonable efficiency, and we define the periodic Bernoulli polynomials (which appear e.g. in the Euler–MacLaurin summation formula and the expansion of the log-Gamma function) and prove their basic properties.

BSD License

Topics

Theories of Bernoulli

\ No newline at end of file diff --git a/web/entries/Bertrands_Postulate.html b/web/entries/Bertrands_Postulate.html --- a/web/entries/Bertrands_Postulate.html +++ b/web/entries/Bertrands_Postulate.html @@ -1,178 +1,178 @@ Bertrand's postulate - Archive of Formal Proofs

Bertrand's Postulate

-

Julian Biendarra and Manuel Eberl 🌐 - with contributions from Lawrence C. Paulson 🌐 +

Julian Biendarra and Manuel Eberl 🌐 + with contributions from Lawrence C. Paulson 🌐

January 17, 2017

Abstract

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.

BSD License

Topics

Theories of Bertrands_Postulate

\ No newline at end of file diff --git a/web/entries/Binomial-Queues.html b/web/entries/Binomial-Queues.html --- a/web/entries/Binomial-Queues.html +++ b/web/entries/Binomial-Queues.html @@ -1,167 +1,167 @@ Functional Binomial Queues - Archive of Formal Proofs

Functional Binomial Queues

-

René Neumann 📧 +

René Neumann 📧

October 28, 2010

Abstract

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.
BSD License

Topics

Theories of Binomial-Queues

\ No newline at end of file diff --git a/web/entries/Boolean_Expression_Checkers.html b/web/entries/Boolean_Expression_Checkers.html --- a/web/entries/Boolean_Expression_Checkers.html +++ b/web/entries/Boolean_Expression_Checkers.html @@ -1,164 +1,164 @@ Boolean Expression Checkers - Archive of Formal Proofs

Boolean Expression Checkers

-

Tobias Nipkow 🌐 +

Tobias Nipkow 🌐

June 8, 2014

Abstract

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).
BSD License

Change history

[2015-09-23] 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.

Topics

Theories of Boolean_Expression_Checkers

Used by

\ No newline at end of file diff --git a/web/entries/Buffons_Needle.html b/web/entries/Buffons_Needle.html --- a/web/entries/Buffons_Needle.html +++ b/web/entries/Buffons_Needle.html @@ -1,164 +1,164 @@ Buffon's Needle Problem - Archive of Formal Proofs

Buffon's Needle Problem

-

Manuel Eberl 🌐 +

Manuel Eberl 🌐

June 6, 2017

Abstract

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.
BSD License

Topics

Theories of Buffons_Needle

\ No newline at end of file diff --git a/web/entries/CAVA_LTL_Modelchecker.html b/web/entries/CAVA_LTL_Modelchecker.html --- a/web/entries/CAVA_LTL_Modelchecker.html +++ b/web/entries/CAVA_LTL_Modelchecker.html @@ -1,227 +1,227 @@ A Fully Verified Executable LTL Model Checker - Archive of Formal Proofs

A Fully Verified Executable LTL Model Checker

-

Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐 +

Javier Esparza 🌐, Peter Lammich 🌐, René Neumann 📧, Tobias Nipkow 🌐, Alexander Schimpf 📧 and Jan-Georg Smaus 🌐

May 28, 2014

Abstract

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.

An early version of this model checker is described in the CAV 2013 paper with the same title.

BSD License

Topics

Theories of SM_Base

    Theories of SM

    Theories of CAVA_Setup

      Theories of CAVA_LTL_Modelchecker

      \ No newline at end of file diff --git a/web/entries/CISC-Kernel.html b/web/entries/CISC-Kernel.html --- a/web/entries/CISC-Kernel.html +++ b/web/entries/CISC-Kernel.html @@ -1,192 +1,192 @@ Formal Specification of a Generic Separation Kernel - Archive of Formal Proofs

      Formal Specification of a Generic Separation Kernel

      -

      Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧 +

      Freek Verbeek 📧, Sergey Tverdyshev 📧, Oto Havle 📧, Holger Blasum 📧, Bruno Langenstein 📧, Werner Stephan 📧, Yakoub Nemouchi 📧, Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Julien Schmaltz 📧

      July 18, 2014

      Abstract

      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.

      This document corresponds to the deliverable D31.1 of the EURO-MILS Project http://www.euromils.eu.

      BSD License

      Topics

      Theories of CISC-Kernel

      \ No newline at end of file diff --git a/web/entries/CRDT.html b/web/entries/CRDT.html --- a/web/entries/CRDT.html +++ b/web/entries/CRDT.html @@ -1,176 +1,176 @@ A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes - Archive of Formal Proofs

      A Framework for Establishing Strong Eventual Consistency for Conflict-Free Replicated Datatypes

      -

      Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧 +

      Victor B. F. Gomes 📧, Martin Kleppmann 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧

      July 7, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of CRDT

      Used by

      \ No newline at end of file diff --git a/web/entries/CYK.html b/web/entries/CYK.html --- a/web/entries/CYK.html +++ b/web/entries/CYK.html @@ -1,167 +1,167 @@ A formalisation of the Cocke-Younger-Kasami algorithm - Archive of Formal Proofs

      A Formalisation of the Cocke-Younger-Kasami Algorithm

      -

      Maksym Bortin 📧 +

      Maksym Bortin 📧

      April 27, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of CYK

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Cartan_FP.html b/web/entries/Cartan_FP.html --- a/web/entries/Cartan_FP.html +++ b/web/entries/Cartan_FP.html @@ -1,171 +1,171 @@ The Cartan Fixed Point Theorems - Archive of Formal Proofs

      The Cartan Fixed Point Theorems

      -

      Lawrence C. Paulson 🌐 +

      Lawrence C. Paulson 🌐

      March 8, 2016

      Abstract

      The Cartan fixed point theorems concern the group of holomorphic automorphisms on a connected open set of Cn. 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".
      BSD License

      Topics

      Theories of Cartan_FP

      \ No newline at end of file diff --git a/web/entries/Catalan_Numbers.html b/web/entries/Catalan_Numbers.html --- a/web/entries/Catalan_Numbers.html +++ b/web/entries/Catalan_Numbers.html @@ -1,168 +1,168 @@ Catalan Numbers - Archive of Formal Proofs

      Catalan Numbers

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      June 21, 2016

      Abstract

      In this work, we define the Catalan numbers Cn 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 n), prove the asymptotic growth approximation Cn ∼ 4n / (√π · n1.5), and provide reasonably efficient executable code to compute them.

      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.

      BSD License

      Topics

      Theories of Catalan_Numbers

      Depends On

      \ No newline at end of file diff --git a/web/entries/Chandy_Lamport.html b/web/entries/Chandy_Lamport.html --- a/web/entries/Chandy_Lamport.html +++ b/web/entries/Chandy_Lamport.html @@ -1,180 +1,180 @@ A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm - Archive of Formal Proofs

      A Formal Proof of the Chandy--Lamport Distributed Snapshot Algorithm

      -

      Ben Fiedler 📧 and Dmitriy Traytel 🌐 +

      Ben Fiedler 📧 and Dmitriy Traytel 🌐

      July 21, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Chandy_Lamport

      \ No newline at end of file diff --git a/web/entries/Circus.html b/web/entries/Circus.html --- a/web/entries/Circus.html +++ b/web/entries/Circus.html @@ -1,180 +1,180 @@ Isabelle/Circus - Archive of Formal Proofs

      Isabelle/Circus

      -

      Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Marie-Claude Gaudel 📧 +

      Abderrahmane Feliachi 📧, Burkhart Wolff 📧 and Marie-Claude Gaudel 📧 with contributions from Makarius Wenzel 📧

      May 27, 2012

      Abstract

      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).

      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.

      BSD License

      Change history

      [2014-06-05] More polishing, shorter proofs, added Circus syntax, added Makarius Wenzel as contributor.

      Topics

      Theories of Circus

      \ No newline at end of file diff --git a/web/entries/Closest_Pair_Points.html b/web/entries/Closest_Pair_Points.html --- a/web/entries/Closest_Pair_Points.html +++ b/web/entries/Closest_Pair_Points.html @@ -1,177 +1,177 @@ Closest Pair of Points Algorithms - Archive of Formal Proofs

      Closest Pair of Points Algorithms

      -

      Martin Rau 📧 and Tobias Nipkow 🌐 +

      Martin Rau 📧 and Tobias Nipkow 🌐

      January 13, 2020

      Abstract

      This entry provides two related verified divide-and-conquer algorithms solving the fundamental Closest Pair of Points problem in Computational Geometry. Functional correctness and the optimal running time of O(n log n) are proved. Executable code is generated which is empirically competitive with handwritten reference implementations.
      BSD License

      Change history

      [2020-04-14] Incorporate Time_Monad of the AFP entry Root_Balanced_Tree.

      Topics

      Theories of Closest_Pair_Points

      \ No newline at end of file diff --git a/web/entries/Coinductive.html b/web/entries/Coinductive.html --- a/web/entries/Coinductive.html +++ b/web/entries/Coinductive.html @@ -1,183 +1,183 @@ Coinductive - Archive of Formal Proofs

      Coinductive

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐 with contributions from Johannes Hölzl 📧

      February 12, 2010

      Abstract

      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.
      The initial theory was contributed by Paulson and Wenzel. Extensions and other coinductive formalisations of general interest are welcome.
      BSD License

      Topics

      Theories of Coinductive

      \ No newline at end of file diff --git a/web/entries/Coinductive_Languages.html b/web/entries/Coinductive_Languages.html --- a/web/entries/Coinductive_Languages.html +++ b/web/entries/Coinductive_Languages.html @@ -1,185 +1,185 @@ A Codatatype of Formal Languages - Archive of Formal Proofs

      A Codatatype of Formal Languages

      -

      Dmitriy Traytel 🌐 +

      Dmitriy Traytel 🌐

      November 15, 2013

      Abstract

      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.

      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.

      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.

      BSD License

      Topics

      Theories of Coinductive_Languages

      \ No newline at end of file diff --git a/web/entries/Collections.html b/web/entries/Collections.html --- a/web/entries/Collections.html +++ b/web/entries/Collections.html @@ -1,321 +1,321 @@ Collections Framework - Archive of Formal Proofs

      Collections Framework

      Peter Lammich 🌐 - with contributions from Andreas Lochbihler 🌐 and Thomas Tuerk + with contributions from Andreas Lochbihler 🌐 and Thomas Tuerk

      November 25, 2009

      Abstract

      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.
      BSD License

      Change history

      [2010-10-08] 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.
      [2010-12-01] New Interfaces: Priority Queues, Annotated Lists. Implemented by finger trees, (skew) binomial queues.
      [2011-10-10] 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
      [2012-04-25] New iterator foundation by Tuerk. Various maintenance changes.

      Topics

      Theories of Collections

      Theories of Collections_Examples

      \ No newline at end of file diff --git a/web/entries/Comparison_Sort_Lower_Bound.html b/web/entries/Comparison_Sort_Lower_Bound.html --- a/web/entries/Comparison_Sort_Lower_Bound.html +++ b/web/entries/Comparison_Sort_Lower_Bound.html @@ -1,183 +1,183 @@ Lower bound on comparison-based sorting algorithms - Archive of Formal Proofs

      Lower Bound on Comparison-Based Sorting Algorithms

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 15, 2017

      Abstract

      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 n is at least log2 (n!) in the worst case, i. e. Ω(n log n).

      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.

      BSD License

      Topics

      Theories of Comparison_Sort_Lower_Bound

      \ No newline at end of file diff --git a/web/entries/Compiling-Exceptions-Correctly.html b/web/entries/Compiling-Exceptions-Correctly.html --- a/web/entries/Compiling-Exceptions-Correctly.html +++ b/web/entries/Compiling-Exceptions-Correctly.html @@ -1,152 +1,152 @@ Compiling Exceptions Correctly - Archive of Formal Proofs

      Compiling Exceptions Correctly

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      July 9, 2004

      Abstract

      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 Hutton and Wright.
      BSD License

      Topics

      Theories of Compiling-Exceptions-Correctly

      \ No newline at end of file diff --git a/web/entries/Constructive_Cryptography_CM.html b/web/entries/Constructive_Cryptography_CM.html --- a/web/entries/Constructive_Cryptography_CM.html +++ b/web/entries/Constructive_Cryptography_CM.html @@ -1,195 +1,195 @@ Constructive Cryptography in HOL: the Communication Modeling Aspect - Archive of Formal Proofs

      Constructive Cryptography in HOL: The Communication Modeling Aspect

      -

      Andreas Lochbihler 🌐 and S. Reza Sefidgar +

      Andreas Lochbihler 🌐 and S. Reza Sefidgar

      March 17, 2021

      Abstract

      Constructive Cryptography (CC) [ICS 2011, TOSCA 2011, TCC 2016] 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 [Constructive_Cryptography, CSF 2019] 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 [CryptHOL, ESOP 2016, J Cryptol 2020]. This formalization is described in Abstract Modeling of Systems Communication in Constructive Cryptography using CryptHOL.
      BSD License

      Topics

      Theories of Constructive_Cryptography_CM

      \ No newline at end of file diff --git a/web/entries/Containers.html b/web/entries/Containers.html --- a/web/entries/Containers.html +++ b/web/entries/Containers.html @@ -1,224 +1,224 @@ Light-weight Containers - Archive of Formal Proofs

      Light-Weight Containers

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐 with contributions from René Thiemann 📧

      April 15, 2013

      Abstract

      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.

      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.

      BSD License

      Change history

      [2013-07-11] add pretty printing for sets (revision 7f3f52c5f5fa)
      [2014-07-08] add support for going from partial functions to mappings (revision 7a6fc957e8ed)
      [2018-03-05] add two application examples: depth-first search and 2SAT (revision e5e1a1da2411)

      Topics

      Theories of Containers

      Theories of Containers-Benchmarks

      \ No newline at end of file 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 @@ -1,214 +1,214 @@ The Safely Composable DOM - Archive of Formal Proofs

      The Safely Composable DOM

      -

      Achim D. Brucker 🌐 and Michael Herzberg 🌐 +

      Achim D. Brucker 🌐 and Michael Herzberg 🌐

      September 28, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Core_SC_DOM

      \ No newline at end of file diff --git a/web/entries/Cotangent_PFD_Formula.html b/web/entries/Cotangent_PFD_Formula.html --- a/web/entries/Cotangent_PFD_Formula.html +++ b/web/entries/Cotangent_PFD_Formula.html @@ -1,159 +1,159 @@ A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent - Archive of Formal Proofs

      A Proof From the BOOK: The Partial Fraction Expansion of the Cotangent

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 15, 2022

      Abstract

      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’:

      \[\pi \cot(\pi z) = \frac{1}{z} + \sum_{n=1}^\infty\left(\frac{1}{z+n} + \frac{1}{z-n}\right)\]

      The proof uses Herglotz's trick to show the real case and analytic continuation for the complex case.

      BSD License

      Topics

      Theories of Cotangent_PFD_Formula

      \ No newline at end of file diff --git a/web/entries/CryptHOL.html b/web/entries/CryptHOL.html --- a/web/entries/CryptHOL.html +++ b/web/entries/CryptHOL.html @@ -1,189 +1,189 @@ CryptHOL - Archive of Formal Proofs

      CryptHOL

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      May 5, 2017

      Abstract

      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.

      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.

      BSD License

      Topics

      Theories of CryptHOL

      \ No newline at end of file diff --git a/web/entries/DFS_Framework.html b/web/entries/DFS_Framework.html --- a/web/entries/DFS_Framework.html +++ b/web/entries/DFS_Framework.html @@ -1,195 +1,195 @@ A Framework for Verifying Depth-First Search Algorithms - Archive of Formal Proofs

      A Framework for Verifying Depth-First Search Algorithms

      -

      Peter Lammich 🌐 and René Neumann 📧 +

      Peter Lammich 🌐 and René Neumann 📧

      July 5, 2016

      Abstract

      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.

      [CPP-2015] Peter Lammich, René Neumann: A Framework for Verifying Depth-First Search Algorithms. CPP 2015: 137-146

      BSD License

      Topics

      Theories of DFS_Framework

      \ No newline at end of file diff --git a/web/entries/DOM_Components.html b/web/entries/DOM_Components.html --- a/web/entries/DOM_Components.html +++ b/web/entries/DOM_Components.html @@ -1,183 +1,183 @@ A Formalization of Web Components - Archive of Formal Proofs

      A Formalization of Web Components

      -

      Achim D. Brucker 🌐 and Michael Herzberg 🌐 +

      Achim D. Brucker 🌐 and Michael Herzberg 🌐

      September 28, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of DOM_Components

      \ No newline at end of file diff --git a/web/entries/Density_Compiler.html b/web/entries/Density_Compiler.html --- a/web/entries/Density_Compiler.html +++ b/web/entries/Density_Compiler.html @@ -1,188 +1,188 @@ A Verified Compiler for Probability Density Functions - Archive of Formal Proofs

      A Verified Compiler for Probability Density Functions

      -

      Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐 +

      Manuel Eberl 🌐, Johannes Hölzl 🌐 and Tobias Nipkow 🌐

      October 9, 2014

      Abstract

      Bhat et al. [TACAS 2013] 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.

      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.

      BSD License

      Topics

      Theories of Density_Compiler

      \ No newline at end of file diff --git a/web/entries/Dependent_SIFUM_Refinement.html b/web/entries/Dependent_SIFUM_Refinement.html --- a/web/entries/Dependent_SIFUM_Refinement.html +++ b/web/entries/Dependent_SIFUM_Refinement.html @@ -1,181 +1,181 @@ Compositional Security-Preserving Refinement for Concurrent Imperative Programs - Archive of Formal Proofs

      Compositional Security-Preserving Refinement for Concurrent Imperative Programs

      -

      Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐 +

      Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐

      June 28, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Dependent_SIFUM_Refinement

      \ No newline at end of file diff --git a/web/entries/Dependent_SIFUM_Type_Systems.html b/web/entries/Dependent_SIFUM_Type_Systems.html --- a/web/entries/Dependent_SIFUM_Type_Systems.html +++ b/web/entries/Dependent_SIFUM_Type_Systems.html @@ -1,187 +1,187 @@ A Dependent Security Type System for Concurrent Imperative Programs - Archive of Formal Proofs

      A Dependent Security Type System for Concurrent Imperative Programs

      -

      Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐 +

      Toby Murray 🌐, Robert Sison, Edward Pierzchalski and Christine Rizkallah 🌐

      June 25, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Dependent_SIFUM_Type_Systems

      \ No newline at end of file diff --git a/web/entries/Descartes_Sign_Rule.html b/web/entries/Descartes_Sign_Rule.html --- a/web/entries/Descartes_Sign_Rule.html +++ b/web/entries/Descartes_Sign_Rule.html @@ -1,174 +1,174 @@ Descartes' Rule of Signs - Archive of Formal Proofs

      Descartes' Rule of Signs

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 28, 2015

      Abstract

      Descartes' Rule of Signs relates the number of positive real roots of a polynomial with the number of sign changes in its coefficient sequence.

      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.

      BSD License

      Topics

      Theories of Descartes_Sign_Rule

      \ 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 @@ -1,186 +1,186 @@ Differential Game Logic - Archive of Formal Proofs

      Differential Game Logic

      -

      André Platzer 🌐 +

      André Platzer 🌐

      June 3, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Differential_Game_Logic

      \ No newline at end of file diff --git a/web/entries/Dirichlet_L.html b/web/entries/Dirichlet_L.html --- a/web/entries/Dirichlet_L.html +++ b/web/entries/Dirichlet_L.html @@ -1,186 +1,186 @@ Dirichlet L-Functions and Dirichlet's Theorem - Archive of Formal Proofs

      Dirichlet L-Functions and Dirichlet's Theorem

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 21, 2017

      Abstract

      This article provides a formalisation of Dirichlet characters and Dirichlet L-functions including proofs of their basic properties – most notably their analyticity, their areas of convergence, and their non-vanishing for ℜ(s) ≥ 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.

      This also leads to a relatively short proof of Dirichlet’s Theorem, which states that, if h and n are coprime, there are infinitely many primes p with ph (mod n).

      BSD License

      Topics

      Theories of Dirichlet_L

      \ No newline at end of file diff --git a/web/entries/Dirichlet_Series.html b/web/entries/Dirichlet_Series.html --- a/web/entries/Dirichlet_Series.html +++ b/web/entries/Dirichlet_Series.html @@ -1,201 +1,201 @@ Dirichlet Series - Archive of Formal Proofs

      Dirichlet Series

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      October 12, 2017

      Abstract

      This entry is a formalisation of much of Chapters 2, 3, and 11 of Apostol's “Introduction to Analytic Number Theory”. This includes:
      • Definitions and basic properties for several number-theoretic functions (Euler's φ, Möbius μ, Liouville's λ, the divisor function σ, von Mangoldt's Λ)
      • Executable code for most of these functions, the most efficient implementations using the factoring algorithm by Thiemann et al.
      • Dirichlet products and formal Dirichlet series
      • Analytic results connecting convergent formal Dirichlet series to complex functions
      • Euler product expansions
      • Asymptotic estimates of number-theoretic functions including the density of squarefree integers and the average number of divisors of a natural number
      These results are useful as a basis for developing more number-theoretic results, such as the Prime Number Theorem.
      BSD License

      Topics

      Theories of Dirichlet_Series

      \ No newline at end of file diff --git a/web/entries/DiscretePricing.html b/web/entries/DiscretePricing.html --- a/web/entries/DiscretePricing.html +++ b/web/entries/DiscretePricing.html @@ -1,165 +1,165 @@ Pricing in discrete financial models - Archive of Formal Proofs

      Pricing in Discrete Financial Models

      -

      Mnacho Echenim 🌐 +

      Mnacho Echenim 🌐

      July 16, 2018

      Abstract

      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 paper.
      BSD License

      Topics

      Theories of DiscretePricing

      \ No newline at end of file diff --git a/web/entries/Dynamic_Tables.html b/web/entries/Dynamic_Tables.html --- a/web/entries/Dynamic_Tables.html +++ b/web/entries/Dynamic_Tables.html @@ -1,172 +1,172 @@ Parameterized Dynamic Tables - Archive of Formal Proofs

      Parameterized Dynamic Tables

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      June 7, 2015

      Abstract

      This article formalizes the amortized analysis of dynamic tables parameterized with their minimal and maximal load factors and the expansion and contraction factors.

      A full description is found in a companion paper.

      BSD License

      Topics

      Theories of Dynamic_Tables

      \ No newline at end of file diff --git a/web/entries/E_Transcendental.html b/web/entries/E_Transcendental.html --- a/web/entries/E_Transcendental.html +++ b/web/entries/E_Transcendental.html @@ -1,159 +1,159 @@ The Transcendence of e - Archive of Formal Proofs

      The Transcendence of E

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      January 12, 2017

      Abstract

      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.

      This kind of approach can be found in many different sources; this formalisation mostly follows a PlanetMath article by Roger Lipsett.

      BSD License

      Topics

      Theories of E_Transcendental

      \ No newline at end of file diff --git a/web/entries/Echelon_Form.html b/web/entries/Echelon_Form.html --- a/web/entries/Echelon_Form.html +++ b/web/entries/Echelon_Form.html @@ -1,182 +1,182 @@ Echelon Form - Archive of Formal Proofs

      Echelon Form

      -

      Jose Divasón 🌐 and Jesús Aransay 🌐 +

      Jose Divasón 🌐 and Jesús Aransay 🌐

      February 12, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Echelon_Form

      \ No newline at end of file diff --git a/web/entries/Ergodic_Theory.html b/web/entries/Ergodic_Theory.html --- a/web/entries/Ergodic_Theory.html +++ b/web/entries/Ergodic_Theory.html @@ -1,180 +1,180 @@ Ergodic Theory - Archive of Formal Proofs

      Ergodic Theory

      Sebastien Gouezel 📧 - with contributions from Manuel Eberl 🌐 + with contributions from Manuel Eberl 🌐

      December 1, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Ergodic_Theory

      \ No newline at end of file diff --git a/web/entries/Error_Function.html b/web/entries/Error_Function.html --- a/web/entries/Error_Function.html +++ b/web/entries/Error_Function.html @@ -1,172 +1,172 @@ The Error Function - Archive of Formal Proofs

      The Error Function

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      February 6, 2018

      Abstract

      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.

      BSD License

      Topics

      Theories of Error_Function

      \ No newline at end of file diff --git a/web/entries/Euler_MacLaurin.html b/web/entries/Euler_MacLaurin.html --- a/web/entries/Euler_MacLaurin.html +++ b/web/entries/Euler_MacLaurin.html @@ -1,180 +1,180 @@ The Euler–MacLaurin Formula - Archive of Formal Proofs

      The Euler–MacLaurin Formula

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 10, 2017

      Abstract

      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.

      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 Concrete Mathematics that is more useful for deriving asymptotic estimates.

      As example applications, we use that formula to derive the full asymptotic expansion of the harmonic numbers and the sum of inverse squares.

      BSD License

      Topics

      Theories of Euler_MacLaurin

      \ No newline at end of file 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 @@ -1,193 +1,193 @@ Factorization of Polynomials with Algebraic Coefficients - Archive of Formal Proofs

      Factorization of Polynomials With Algebraic Coefficients

      -

      Manuel Eberl 🌐 and René Thiemann 📧 +

      Manuel Eberl 🌐 and René Thiemann 📧

      November 8, 2021

      Abstract

      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.
      BSD License

      Topics

      Theories of Factor_Algebraic_Polynomial

      \ No newline at end of file diff --git a/web/entries/Farkas.html b/web/entries/Farkas.html --- a/web/entries/Farkas.html +++ b/web/entries/Farkas.html @@ -1,182 +1,182 @@ Farkas' Lemma and Motzkin's Transposition Theorem - Archive of Formal Proofs

      Farkas' Lemma and Motzkin's Transposition Theorem

      -

      Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐 +

      Ralph Bottesch 🌐, Max W. Haslbeck 🌐 and René Thiemann 🌐

      January 17, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Farkas

      \ No newline at end of file diff --git a/web/entries/Featherweight_OCL.html b/web/entries/Featherweight_OCL.html --- a/web/entries/Featherweight_OCL.html +++ b/web/entries/Featherweight_OCL.html @@ -1,194 +1,194 @@ Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5 - Archive of Formal Proofs

      Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5

      -

      Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧 +

      Achim D. Brucker 📧, Frédéric Tuong 📧 and Burkhart Wolff 📧

      January 16, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of Featherweight_OCL

      \ 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 @@ -1,169 +1,169 @@ Code Generation for Functions as Data - Archive of Formal Proofs

      Code Generation for Functions as Data

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      May 6, 2009

      Abstract

      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.
      BSD License

      Topics

      Theories of FinFun

      \ No newline at end of file diff --git a/web/entries/Finite_Automata_HF.html b/web/entries/Finite_Automata_HF.html --- a/web/entries/Finite_Automata_HF.html +++ b/web/entries/Finite_Automata_HF.html @@ -1,173 +1,173 @@ Finite Automata in Hereditarily Finite Set Theory - Archive of Formal Proofs

      Finite Automata in Hereditarily Finite Set Theory

      -

      Lawrence C. Paulson 🌐 +

      Lawrence C. Paulson 🌐

      February 5, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Finite_Automata_HF

      \ No newline at end of file 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 +++ b/web/entries/Finitely_Generated_Abelian_Groups.html @@ -1,186 +1,186 @@ Finitely Generated Abelian Groups - Archive of Formal Proofs

      Finitely Generated Abelian Groups

      -

      Joseph Thommes and Manuel Eberl 🌐 +

      Joseph Thommes and Manuel Eberl 🌐

      July 7, 2021

      Abstract

      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.
      BSD License

      Topics

      Theories of Finitely_Generated_Abelian_Groups

      \ No newline at end of file diff --git a/web/entries/Fishburn_Impossibility.html b/web/entries/Fishburn_Impossibility.html --- a/web/entries/Fishburn_Impossibility.html +++ b/web/entries/Fishburn_Impossibility.html @@ -1,178 +1,178 @@ The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency - Archive of Formal Proofs

      The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency

      -

      Felix Brandt 🌐, Manuel Eberl 🌐, Christian Saile 🌐 and Christian Stricker 🌐 +

      Felix Brandt 🌐, Manuel Eberl 🌐, Christian Saile 🌐 and Christian Stricker 🌐

      March 22, 2018

      Abstract

      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 Brandt et al., 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.

      BSD License

      Topics

      Theories of Fishburn_Impossibility

      \ No newline at end of file diff --git a/web/entries/Fisher_Yates.html b/web/entries/Fisher_Yates.html --- a/web/entries/Fisher_Yates.html +++ b/web/entries/Fisher_Yates.html @@ -1,156 +1,156 @@ Fisher–Yates shuffle - Archive of Formal Proofs

      Fisher–Yates Shuffle

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      September 30, 2016

      Abstract

      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.

      BSD License

      Topics

      Theories of Fisher_Yates

      \ No newline at end of file diff --git a/web/entries/Floyd_Warshall.html b/web/entries/Floyd_Warshall.html --- a/web/entries/Floyd_Warshall.html +++ b/web/entries/Floyd_Warshall.html @@ -1,184 +1,184 @@ The Floyd-Warshall Algorithm for Shortest Paths - Archive of Formal Proofs

      The Floyd-Warshall Algorithm for Shortest Paths

      -

      Simon Wimmer 🌐 and Peter Lammich 🌐 +

      Simon Wimmer 🌐 and Peter Lammich 🌐

      May 8, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Floyd_Warshall

      \ No newline at end of file diff --git a/web/entries/Flyspeck-Tame.html b/web/entries/Flyspeck-Tame.html --- a/web/entries/Flyspeck-Tame.html +++ b/web/entries/Flyspeck-Tame.html @@ -1,212 +1,212 @@ Flyspeck I: Tame Graphs - Archive of Formal Proofs

      Flyspeck I: Tame Graphs

      -

      Gertrud Bauer and Tobias Nipkow 🌐 +

      Gertrud Bauer and Tobias Nipkow 🌐

      May 22, 2006

      Abstract

      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 Sphere Packings. A Blueprint for Formal Proofs. [CUP 2012]. The values of the constants in the definition of tameness are identical to those in the Flyspeck project. The IJCAR 2006 paper by Nipkow, Bauer and Schultz refers to the original version of Hales' proof, the ITP 2011 paper by Nipkow refers to the Blueprint version of the proof.
      BSD License

      Change history

      [2010-11-02] modified theories to reflect the modified definition of tameness in Hales' revised proof.
      [2014-07-03] modified constants in def of tameness and Archive according to the final state of the Flyspeck proof.

      Topics

      Theories of Flyspeck-Tame

      Theories of Flyspeck-Tame-Computation

      Depends On

      Used by

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Forcing.html b/web/entries/Forcing.html --- a/web/entries/Forcing.html +++ b/web/entries/Forcing.html @@ -1,203 +1,203 @@ Formalization of Forcing in Isabelle/ZF - Archive of Formal Proofs

      Formalization of Forcing in Isabelle/ZF

      -

      Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐 +

      Emmanuel Gunther 📧, Miguel Pagano 🌐 and Pedro Sánchez Terraf 🌐

      May 6, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Forcing

      \ No newline at end of file diff --git a/web/entries/Formal_Puiseux_Series.html b/web/entries/Formal_Puiseux_Series.html --- a/web/entries/Formal_Puiseux_Series.html +++ b/web/entries/Formal_Puiseux_Series.html @@ -1,179 +1,179 @@ Formal Puiseux Series - Archive of Formal Proofs

      Formal Puiseux Series

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      February 17, 2021

      Abstract

      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 N is an integer and d is a positive integer.

      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.

      BSD License

      Topics

      Theories of Formal_Puiseux_Series

      \ No newline at end of file diff --git a/web/entries/Formula_Derivatives.html b/web/entries/Formula_Derivatives.html --- a/web/entries/Formula_Derivatives.html +++ b/web/entries/Formula_Derivatives.html @@ -1,188 +1,188 @@ Derivatives of Logical Formulas - Archive of Formal Proofs

      Derivatives of Logical Formulas

      -

      Dmitriy Traytel 🌐 +

      Dmitriy Traytel 🌐

      May 28, 2015

      Abstract

      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 not 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).

      The WS1S instance is described in the draft paper A Coalgebraic Decision Procedure for WS1S by the author.

      BSD License

      Topics

      Theories of Formula_Derivatives

      Theories of Formula_Derivatives-Examples

      \ No newline at end of file diff --git a/web/entries/Free-Boolean-Algebra.html b/web/entries/Free-Boolean-Algebra.html --- a/web/entries/Free-Boolean-Algebra.html +++ b/web/entries/Free-Boolean-Algebra.html @@ -1,161 +1,161 @@ Free Boolean Algebra - Archive of Formal Proofs

      Free Boolean Algebra

      -

      Brian Huffman 🌐 +

      Brian Huffman 🌐

      March 29, 2010

      Abstract

      This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula 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.
      BSD License

      Topics

      Theories of Free-Boolean-Algebra

      Related Entries

      \ No newline at end of file diff --git a/web/entries/FunWithFunctions.html b/web/entries/FunWithFunctions.html --- a/web/entries/FunWithFunctions.html +++ b/web/entries/FunWithFunctions.html @@ -1,152 +1,152 @@ Fun With Functions - Archive of Formal Proofs

      Fun With Functions

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      August 26, 2008

      Abstract

      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!
      BSD License

      Topics

      Theories of FunWithFunctions

      \ No newline at end of file diff --git a/web/entries/FunWithTilings.html b/web/entries/FunWithTilings.html --- a/web/entries/FunWithTilings.html +++ b/web/entries/FunWithTilings.html @@ -1,161 +1,161 @@ Fun With Tilings - Archive of Formal Proofs

      Fun With Tilings

      -

      Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐 +

      Tobias Nipkow 🌐 and Lawrence C. Paulson 🌐

      November 7, 2008

      Abstract

      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!
      BSD License

      Topics

      Theories of FunWithTilings

      \ No newline at end of file diff --git a/web/entries/Functional-Automata.html b/web/entries/Functional-Automata.html --- a/web/entries/Functional-Automata.html +++ b/web/entries/Functional-Automata.html @@ -1,179 +1,179 @@ Functional Automata - Archive of Formal Proofs

      Functional Automata

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      March 30, 2004

      Abstract

      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.
      BSD License

      Topics

      Theories of Functional-Automata

      \ No newline at end of file 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 @@ -1,176 +1,176 @@ A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover - Archive of Formal Proofs

      A Verified Functional Implementation of Bachmair and Ganzinger's Ordered Resolution Prover

      -

      Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧 and Dmitriy Traytel 🌐 +

      Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧 and Dmitriy Traytel 🌐

      November 23, 2018

      Abstract

      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 Handbook of Automated Reasoning. The result is a functional implementation of a first-order prover.
      BSD License

      Topics

      Theories of Functional_Ordered_Resolution_Prover

      \ No newline at end of file diff --git a/web/entries/Furstenberg_Topology.html b/web/entries/Furstenberg_Topology.html --- a/web/entries/Furstenberg_Topology.html +++ b/web/entries/Furstenberg_Topology.html @@ -1,169 +1,169 @@ Furstenberg's topology and his proof of the infinitude of primes - Archive of Formal Proofs

      Furstenberg's Topology and His Proof of the Infinitude of Primes

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 22, 2020

      Abstract

      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.

      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.

      BSD License

      Topics

      Theories of Furstenberg_Topology

      Related Entries

      \ No newline at end of file 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 @@ -1,186 +1,186 @@ Gale-Stewart Games - Archive of Formal Proofs

      Gale-Stewart Games

      -

      Sebastiaan J. C. Joosten 🌐 +

      Sebastiaan J. C. Joosten 🌐

      April 23, 2021

      Abstract

      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.
      BSD License

      Topics

      Theories of GaleStewart_Games

      \ No newline at end of file diff --git a/web/entries/Gale_Shapley.html b/web/entries/Gale_Shapley.html --- a/web/entries/Gale_Shapley.html +++ b/web/entries/Gale_Shapley.html @@ -1,175 +1,175 @@ Gale-Shapley Algorithm - Archive of Formal Proofs

      Gale-Shapley Algorithm

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      December 29, 2021

      Abstract

      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 O(n2) where n is the cardinality of the two sets to be matched.
      BSD License

      Topics

      Theories of Gale_Shapley

      \ No newline at end of file diff --git a/web/entries/Game_Based_Crypto.html b/web/entries/Game_Based_Crypto.html --- a/web/entries/Game_Based_Crypto.html +++ b/web/entries/Game_Based_Crypto.html @@ -1,206 +1,206 @@ Game-based cryptography in HOL - Archive of Formal Proofs

      Game-Based Cryptography in HOL

      -

      Andreas Lochbihler 🌐, S. Reza Sefidgar and Bhargav Bhatt 📧 +

      Andreas Lochbihler 🌐, S. Reza Sefidgar and Bhargav Bhatt 📧

      May 5, 2017

      Abstract

      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.

      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.

      BSD License

      Topics

      Theories of Game_Based_Crypto

      \ No newline at end of file diff --git a/web/entries/Gauss-Jordan-Elim-Fun.html b/web/entries/Gauss-Jordan-Elim-Fun.html --- a/web/entries/Gauss-Jordan-Elim-Fun.html +++ b/web/entries/Gauss-Jordan-Elim-Fun.html @@ -1,164 +1,164 @@ Gauss-Jordan Elimination for Matrices Represented as Functions - Archive of Formal Proofs

      Gauss-Jordan Elimination for Matrices Represented as Functions

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      August 19, 2011

      Abstract

      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.
      BSD License

      Topics

      Theories of Gauss-Jordan-Elim-Fun

      Used by

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Gauss_Jordan.html b/web/entries/Gauss_Jordan.html --- a/web/entries/Gauss_Jordan.html +++ b/web/entries/Gauss_Jordan.html @@ -1,198 +1,198 @@ Gauss-Jordan Algorithm and Its Applications - Archive of Formal Proofs

      Gauss-Jordan Algorithm and Its Applications

      -

      Jose Divasón 🌐 and Jesús Aransay 🌐 +

      Jose Divasón 🌐 and Jesús Aransay 🌐

      September 3, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of Gauss_Jordan

      \ No newline at end of file diff --git a/web/entries/Gauss_Sums.html b/web/entries/Gauss_Sums.html --- a/web/entries/Gauss_Sums.html +++ b/web/entries/Gauss_Sums.html @@ -1,171 +1,171 @@ Gauss Sums and the Pólya–Vinogradov Inequality - Archive of Formal Proofs

      Gauss Sums and the Pólya–Vinogradov Inequality

      -

      Rodrigo Raya 🌐 and Manuel Eberl 🌐 +

      Rodrigo Raya 🌐 and Manuel Eberl 🌐

      December 10, 2019

      Abstract

      This article provides a full formalisation of Chapter 8 of Apostol's Introduction to Analytic Number Theory. Subjects that are covered are:

      • periodic arithmetic functions and their finite Fourier series
      • (generalised) Ramanujan sums
      • Gauss sums and separable characters
      • induced moduli and primitive characters
      • the Pólya—Vinogradov inequality
      BSD License

      Topics

      Theories of Gauss_Sums

      \ No newline at end of file diff --git a/web/entries/Gaussian_Integers.html b/web/entries/Gaussian_Integers.html --- a/web/entries/Gaussian_Integers.html +++ b/web/entries/Gaussian_Integers.html @@ -1,185 +1,185 @@ Gaussian Integers - Archive of Formal Proofs

      Gaussian Integers

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      April 24, 2020

      Abstract

      The Gaussian integers are the subring ℤ[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.

      Lastly, this Gaussian integer formalisation is used in two short applications:

      1. The characterisation of all positive integers that can be written as sums of two squares
      2. Euclid's formula for primitive Pythagorean triples

      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.

      BSD License

      Topics

      Theories of Gaussian_Integers

      \ No newline at end of file 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 @@ -1,178 +1,178 @@ From Abstract to Concrete Gödel's Incompleteness Theorems—Part I - Archive of Formal Proofs

      From Abstract to Concrete Gödel's Incompleteness Theorems—Part I

      -

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐

      September 16, 2020

      Abstract

      We validate an abstract formulation of Gödel's First and Second Incompleteness Theorems from a separate AFP entry by instantiating them to the case of finite sound extensions of the Hereditarily Finite (HF) Set theory, 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 AFP entry by Larry Paulson; our instantiation reuses the infrastructure developed in that entry.
      BSD License

      Topics

      Theories of Goedel_HFSet_Semantic

      \ No newline at end of file diff --git a/web/entries/Goedel_HFSet_Semanticless.html b/web/entries/Goedel_HFSet_Semanticless.html --- a/web/entries/Goedel_HFSet_Semanticless.html +++ b/web/entries/Goedel_HFSet_Semanticless.html @@ -1,195 +1,195 @@ From Abstract to Concrete Gödel's Incompleteness Theorems—Part II - Archive of Formal Proofs

      From Abstract to Concrete Gödel's Incompleteness Theorems—Part II

      -

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐

      September 16, 2020

      Abstract

      We validate an abstract formulation of Gödel's Second Incompleteness Theorem from a separate AFP entry by instantiating it to the case of finite consistent extensions of the Hereditarily Finite (HF) Set theory, 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 direct formalisation of the concrete result. It strengthens Paulson's formalization of Gödel's Second from that entry by not 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 Gödel's Second locale.
      BSD License

      Topics

      Theories of Goedel_HFSet_Semanticless

      \ No newline at end of file diff --git a/web/entries/Goedel_Incompleteness.html b/web/entries/Goedel_Incompleteness.html --- a/web/entries/Goedel_Incompleteness.html +++ b/web/entries/Goedel_Incompleteness.html @@ -1,204 +1,204 @@ An Abstract Formalization of Gödel's Incompleteness Theorems - Archive of Formal Proofs

      An Abstract Formalization of Gödel's Incompleteness Theorems

      -

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐

      September 16, 2020

      Abstract

      We present an abstract formalization of Gödel'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–Paulson semantics-based approach. This AFP entry is the main entry point to the results described in our CADE-27 paper A Formally Verified Abstract Account of Gödel's Incompleteness Theorems. As part of our abstract formalization's validation, we instantiate our locales twice in the separate AFP entries Goedel_HFSet_Semantic and Goedel_HFSet_Semanticless.
      BSD License

      Topics

      Theories of Goedel_Incompleteness

      \ No newline at end of file diff --git a/web/entries/Green.html b/web/entries/Green.html --- a/web/entries/Green.html +++ b/web/entries/Green.html @@ -1,182 +1,182 @@ An Isabelle/HOL formalisation of Green's Theorem - Archive of Formal Proofs

      An Isabelle/HOL Formalisation of Green's Theorem

      -

      Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐 +

      Mohammad Abdulaziz 🌐 and Lawrence C. Paulson 🌐

      January 11, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Green

      \ No newline at end of file diff --git a/web/entries/Groebner_Bases.html b/web/entries/Groebner_Bases.html --- a/web/entries/Groebner_Bases.html +++ b/web/entries/Groebner_Bases.html @@ -1,201 +1,201 @@ Gröbner Bases Theory - Archive of Formal Proofs

      Gröbner Bases Theory

      -

      Fabian Immler 🌐 and Alexander Maletzky 🌐 +

      Fabian Immler 🌐 and Alexander Maletzky 🌐

      May 2, 2016

      Abstract

      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.
      BSD License

      Change history

      [2019-04-18] Specialized Gröbner bases to less abstract representation of polynomials, where power-products are represented as polynomial mappings.

      Topics

      Theories of Groebner_Bases

      \ No newline at end of file diff --git a/web/entries/HOL-CSP.html b/web/entries/HOL-CSP.html --- a/web/entries/HOL-CSP.html +++ b/web/entries/HOL-CSP.html @@ -1,197 +1,197 @@ HOL-CSP Version 2.0 - Archive of Formal Proofs

      HOL-CSP Version 2.0

      -

      Safouan Taha 📧, Lina Ye 📧 and Burkhart Wolff 📧 +

      Safouan Taha 📧, Lina Ye 📧 and Burkhart Wolff 📧

      April 26, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of HOL-CSP

      \ No newline at end of file diff --git a/web/entries/HereditarilyFinite.html b/web/entries/HereditarilyFinite.html --- a/web/entries/HereditarilyFinite.html +++ b/web/entries/HereditarilyFinite.html @@ -1,183 +1,183 @@ The Hereditarily Finite Sets - Archive of Formal Proofs

      The Hereditarily Finite Sets

      -

      Lawrence C. Paulson 🌐 +

      Lawrence C. Paulson 🌐

      November 17, 2013

      Abstract

      The theory of hereditarily finite sets is formalised, following the development 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 formalised separately.
      BSD License

      Change history

      [2015-02-23] Added the theory "Finitary" defining the class of types that can be embedded in hf, including int, char, option, list, etc.

      Topics

      Theories of HereditarilyFinite

      \ No newline at end of file diff --git a/web/entries/Hermite.html b/web/entries/Hermite.html --- a/web/entries/Hermite.html +++ b/web/entries/Hermite.html @@ -1,172 +1,172 @@ Hermite Normal Form - Archive of Formal Proofs

      Hermite Normal Form

      -

      Jose Divasón 🌐 and Jesús Aransay 🌐 +

      Jose Divasón 🌐 and Jesús Aransay 🌐

      July 7, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Hermite

      \ No newline at end of file diff --git a/web/entries/Hermite_Lindemann.html b/web/entries/Hermite_Lindemann.html --- a/web/entries/Hermite_Lindemann.html +++ b/web/entries/Hermite_Lindemann.html @@ -1,202 +1,202 @@ The Hermite–Lindemann–Weierstraß Transcendence Theorem - Archive of Formal Proofs

      The Hermite–Lindemann–Weierstraß Transcendence Theorem

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 3, 2021

      Abstract

      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.

      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 $\mathbb{Q}$.

      Like the previous formalisation in Coq by Bernard, I proceeded by formalising Baker's version of the theorem and proof 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.

      This has a number of direct corollaries, e.g.:

      • $e$ and $\pi$ are transcendental
      • $e^z$, $\sin z$, $\tan z$, etc. are transcendental for algebraic $z\in\mathbb{C}\setminus\{0\}$
      • $\ln z$ is transcendental for algebraic $z\in\mathbb{C}\setminus\{0, 1\}$
      BSD License

      Topics

      Theories of Hermite_Lindemann

      \ No newline at end of file diff --git a/web/entries/Hidden_Markov_Models.html b/web/entries/Hidden_Markov_Models.html --- a/web/entries/Hidden_Markov_Models.html +++ b/web/entries/Hidden_Markov_Models.html @@ -1,178 +1,178 @@ Hidden Markov Models - Archive of Formal Proofs

      Hidden Markov Models

      -

      Simon Wimmer 🌐 +

      Simon Wimmer 🌐

      May 25, 2018

      Abstract

      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].
      BSD License

      Topics

      Theories of Hidden_Markov_Models

      \ No newline at end of file diff --git a/web/entries/Hoare_Time.html b/web/entries/Hoare_Time.html --- a/web/entries/Hoare_Time.html +++ b/web/entries/Hoare_Time.html @@ -1,207 +1,207 @@ Hoare Logics for Time Bounds - Archive of Formal Proofs

      Hoare Logics for Time Bounds

      -

      Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐 +

      Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐

      February 26, 2018

      Abstract

      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 et al. and a separation logic 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.
      BSD License

      Topics

      Theories of Hoare_Time

      \ No newline at end of file diff --git a/web/entries/HotelKeyCards.html b/web/entries/HotelKeyCards.html --- a/web/entries/HotelKeyCards.html +++ b/web/entries/HotelKeyCards.html @@ -1,157 +1,157 @@ Hotel Key Card System - Archive of Formal Proofs

      Hotel Key Card System

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      September 9, 2006

      Abstract

      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.
      BSD License

      Topics

      Theories of HotelKeyCards

      \ No newline at end of file diff --git a/web/entries/IEEE_Floating_Point.html b/web/entries/IEEE_Floating_Point.html --- a/web/entries/IEEE_Floating_Point.html +++ b/web/entries/IEEE_Floating_Point.html @@ -1,183 +1,183 @@ A Formal Model of IEEE Floating Point Arithmetic - Archive of Formal Proofs

      A Formal Model of IEEE Floating Point Arithmetic

      Lei Yu 📧 - with contributions from Fabian Hellauer 📧 and Fabian Immler 🌐 + with contributions from Fabian Hellauer 📧 and Fabian Immler 🌐

      July 27, 2013

      Abstract

      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.
      BSD License

      Change history

      [2017-09-25] Added conversions from and to software floating point numbers (by Fabian Hellauer and Fabian Immler).
      [2018-02-05] '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.

      Topics

      Theories of IEEE_Floating_Point

      \ No newline at end of file diff --git a/web/entries/IMO2019.html b/web/entries/IMO2019.html --- a/web/entries/IMO2019.html +++ b/web/entries/IMO2019.html @@ -1,174 +1,174 @@ Selected Problems from the International Mathematical Olympiad 2019 - Archive of Formal Proofs

      Selected Problems From the International Mathematical Olympiad 2019

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      August 5, 2019

      Abstract

      This entry contains formalisations of the answers to three of the six problem of the International Mathematical Olympiad 2019, namely Q1, Q4, and Q5.

      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.

      BSD License

      Topics

      Theories of IMO2019

      \ No newline at end of file diff --git a/web/entries/IMP2.html b/web/entries/IMP2.html --- a/web/entries/IMP2.html +++ b/web/entries/IMP2.html @@ -1,203 +1,203 @@ IMP2 – Simple Program Verification in Isabelle/HOL - Archive of Formal Proofs

      IMP2 – Simple Program Verification in Isabelle/HOL

      -

      Peter Lammich 🌐 and Simon Wimmer 🌐 +

      Peter Lammich 🌐 and Simon Wimmer 🌐

      January 15, 2019

      Abstract

      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:
      • Bisection Square Root,
      • Extended Euclid,
      • Exponentiation by Squaring,
      • Binary Search,
      • Insertion Sort,
      • Quicksort,
      • Depth First Search.
      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.
      BSD License

      Topics

      Theories of IMP2

      \ No newline at end of file diff --git a/web/entries/IP_Addresses.html b/web/entries/IP_Addresses.html --- a/web/entries/IP_Addresses.html +++ b/web/entries/IP_Addresses.html @@ -1,195 +1,195 @@ IP Addresses - Archive of Formal Proofs

      IP Addresses

      -

      Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐 +

      Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Lars Hupel 🌐

      June 28, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of IP_Addresses

      Depends On

      Used by

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Impossible_Geometry.html b/web/entries/Impossible_Geometry.html --- a/web/entries/Impossible_Geometry.html +++ b/web/entries/Impossible_Geometry.html @@ -1,165 +1,165 @@ Proving the Impossibility of Trisecting an Angle and Doubling the Cube - Archive of Formal Proofs

      Proving the Impossibility of Trisecting an Angle and Doubling the Cube

      -

      Ralph Romanos 📧 and Lawrence C. Paulson 🌐 +

      Ralph Romanos 📧 and Lawrence C. Paulson 🌐

      August 5, 2012

      Abstract

      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.
      BSD License

      Topics

      Theories of Impossible_Geometry

      \ No newline at end of file diff --git a/web/entries/Incompleteness.html b/web/entries/Incompleteness.html --- a/web/entries/Incompleteness.html +++ b/web/entries/Incompleteness.html @@ -1,185 +1,185 @@ Gödel's Incompleteness Theorems - Archive of Formal Proofs

      Gödel's Incompleteness Theorems

      -

      Lawrence C. Paulson 🌐 +

      Lawrence C. Paulson 🌐

      November 17, 2013

      Abstract

      Gödel's two incompleteness theorems are formalised, following a careful presentation by Swierczkowski, in the theory of hereditarily finite sets. 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.
      BSD License

      Topics

      Theories of Incompleteness

      \ No newline at end of file diff --git a/web/entries/Independence_CH.html b/web/entries/Independence_CH.html --- a/web/entries/Independence_CH.html +++ b/web/entries/Independence_CH.html @@ -1,208 +1,208 @@ The Independence of the Continuum Hypothesis in Isabelle/ZF - Archive of Formal Proofs

      The Independence of the Continuum Hypothesis in Isabelle/ZF

      -

      Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧 +

      Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧

      March 6, 2022

      Abstract

      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.
      BSD License

      Topics

      Theories of Independence_CH

      \ No newline at end of file diff --git a/web/entries/InfPathElimination.html b/web/entries/InfPathElimination.html --- a/web/entries/InfPathElimination.html +++ b/web/entries/InfPathElimination.html @@ -1,191 +1,191 @@ Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths - Archive of Formal Proofs

      Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths

      -

      Romain Aissat, Frederic Voisin and Burkhart Wolff 📧 +

      Romain Aissat, Frederic Voisin and Burkhart Wolff 📧

      August 18, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of InfPathElimination

      \ No newline at end of file diff --git a/web/entries/Irrationality_J_Hancl.html b/web/entries/Irrationality_J_Hancl.html --- a/web/entries/Irrationality_J_Hancl.html +++ b/web/entries/Irrationality_J_Hancl.html @@ -1,171 +1,171 @@ Irrational Rapidly Convergent Series - Archive of Formal Proofs

      Irrational Rapidly Convergent Series

      -

      Angeliki Koutsoukou-Argyraki 🌐 and Wenda Li 🌐 +

      Angeliki Koutsoukou-Argyraki 🌐 and Wenda Li 🌐

      May 23, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Irrationality_J_Hancl

      \ No newline at end of file diff --git a/web/entries/Jinja.html b/web/entries/Jinja.html --- a/web/entries/Jinja.html +++ b/web/entries/Jinja.html @@ -1,242 +1,242 @@ Jinja is not Java - Archive of Formal Proofs

      Jinja Is Not Java

      -

      Gerwin Klein 🌐 and Tobias Nipkow 🌐 +

      Gerwin Klein 🌐 and Tobias Nipkow 🌐

      June 1, 2005

      Abstract

      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.
      BSD License

      Topics

      Theories of Jinja

      \ No newline at end of file diff --git a/web/entries/JinjaThreads.html b/web/entries/JinjaThreads.html --- a/web/entries/JinjaThreads.html +++ b/web/entries/JinjaThreads.html @@ -1,331 +1,331 @@ Jinja with Threads - Archive of Formal Proofs

      Jinja With Threads

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      December 3, 2007

      Abstract

      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.
      BSD License

      Topics

      Theories of JinjaThreads

      \ No newline at end of file diff --git a/web/entries/KAD.html b/web/entries/KAD.html --- a/web/entries/KAD.html +++ b/web/entries/KAD.html @@ -1,188 +1,188 @@ Kleene Algebras with Domain - Archive of Formal Proofs

      Kleene Algebras With Domain

      -

      Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐 +

      Victor B. F. Gomes 🌐, Walter Guttmann 🌐, Peter Höfner 🌐, Georg Struth 🌐 and Tjark Weber 🌐

      April 12, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of KAD

      \ No newline at end of file diff --git a/web/entries/KAT_and_DRA.html b/web/entries/KAT_and_DRA.html --- a/web/entries/KAT_and_DRA.html +++ b/web/entries/KAT_and_DRA.html @@ -1,191 +1,191 @@ Kleene Algebra with Tests and Demonic Refinement Algebras - Archive of Formal Proofs

      Kleene Algebra With Tests and Demonic Refinement Algebras

      -

      Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐 +

      Alasdair Armstrong, Victor B. F. Gomes 🌐 and Georg Struth 🌐

      January 23, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of KAT_and_DRA

      \ No newline at end of file diff --git a/web/entries/Knuth_Bendix_Order.html b/web/entries/Knuth_Bendix_Order.html --- a/web/entries/Knuth_Bendix_Order.html +++ b/web/entries/Knuth_Bendix_Order.html @@ -1,181 +1,181 @@ A Formalization of Knuth–Bendix Orders - Archive of Formal Proofs

      A Formalization of Knuth–Bendix Orders

      -

      Christian Sternagel 📧 and René Thiemann 🌐 +

      Christian Sternagel 📧 and René Thiemann 🌐

      May 13, 2020

      Abstract

      We define a generalized version of Knuth–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.
      BSD License

      Topics

      Theories of Knuth_Bendix_Order

      \ No newline at end of file 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 @@ -1,202 +1,202 @@ A verified LLL algorithm - Archive of Formal Proofs

      A Verified LLL Algorithm

      -

      Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada +

      Ralph Bottesch, Jose Divasón 🌐, Max W. Haslbeck 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada

      February 2, 2018

      Abstract

      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.
      BSD License

      Change history

      [2018-04-16] Integrated formal complexity bounds (Haslbeck, Thiemann) [2018-05-25] Integrated much faster LLL implementation based on integer arithmetic (Bottesch, Haslbeck, Thiemann)

      Topics

      Theories of LLL_Basis_Reduction

      \ No newline at end of file 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 @@ -1,186 +1,186 @@ A verified factorization algorithm for integer polynomials with polynomial complexity - Archive of Formal Proofs

      A Verified Factorization Algorithm for Integer Polynomials With Polynomial Complexity

      -

      Jose Divasón 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada 📧 +

      Jose Divasón 🌐, Sebastiaan J. C. Joosten 🌐, René Thiemann 🌐 and Akihisa Yamada 📧

      February 6, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of LLL_Factorization

      \ No newline at end of file diff --git a/web/entries/LOFT.html b/web/entries/LOFT.html --- a/web/entries/LOFT.html +++ b/web/entries/LOFT.html @@ -1,173 +1,173 @@ LOFT — Verified Migration of Linux Firewalls to SDN - Archive of Formal Proofs

      LOFTVerified Migration of Linux Firewalls to SDN

      -

      Julius Michaelis 🌐 and Cornelius Diekmann 🌐 +

      Julius Michaelis 🌐 and Cornelius Diekmann 🌐

      October 21, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of LOFT

      Depends On

      \ No newline at end of file diff --git a/web/entries/LTL_to_DRA.html b/web/entries/LTL_to_DRA.html --- a/web/entries/LTL_to_DRA.html +++ b/web/entries/LTL_to_DRA.html @@ -1,178 +1,178 @@ Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata - Archive of Formal Proofs

      Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata

      -

      Salomon Sickert 📧 +

      Salomon Sickert 📧

      September 4, 2015

      Abstract

      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.
      BSD License

      Change history

      [2015-09-23] Enable code export for the eager unfolding optimisation and reduce running time of the generated tool. Moreover, add support for the mlton SML compiler.
      [2016-03-24] Make use of the LTL entry and include the simplifier.

      Topics

      Theories of LTL_to_DRA

      \ No newline at end of file diff --git a/web/entries/LambdaAuth.html b/web/entries/LambdaAuth.html --- a/web/entries/LambdaAuth.html +++ b/web/entries/LambdaAuth.html @@ -1,187 +1,187 @@ Formalization of Generic Authenticated Data Structures - Archive of Formal Proofs

      Formalization of Generic Authenticated Data Structures

      -

      Matthias Brun and Dmitriy Traytel 🌐 +

      Matthias Brun and Dmitriy Traytel 🌐

      May 14, 2019

      Abstract

      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. Miller et al. introduced λ• (pronounced lambda auth)—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 λ• 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 ITP'19 paper.
      BSD License

      Topics

      Theories of LambdaAuth

      \ No newline at end of file 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 @@ -1,173 +1,173 @@ The Lambert W Function on the Reals - Archive of Formal Proofs

      The Lambert W Function on the Reals

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      April 24, 2020

      Abstract

      The Lambert W function is a multi-valued function defined as the inverse function of xx ex. Besides numerous applications in combinatorics, physics, and engineering, it also frequently occurs when solving equations containing both ex and x, or both x and log x.

      This article provides a definition of the two real-valued branches W0(x) and W-1(x) and proves various properties such as basic identities and inequalities, monotonicity, differentiability, asymptotic expansions, and the MacLaurin series of W0(x) at x = 0.

      BSD License

      Topics

      Theories of Lambert_W

      \ No newline at end of file diff --git a/web/entries/Landau_Symbols.html b/web/entries/Landau_Symbols.html --- a/web/entries/Landau_Symbols.html +++ b/web/entries/Landau_Symbols.html @@ -1,169 +1,169 @@ Landau Symbols - Archive of Formal Proofs

      Landau Symbols

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      July 14, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Landau_Symbols

      \ No newline at end of file diff --git a/web/entries/Laws_of_Large_Numbers.html b/web/entries/Laws_of_Large_Numbers.html --- a/web/entries/Laws_of_Large_Numbers.html +++ b/web/entries/Laws_of_Large_Numbers.html @@ -1,187 +1,187 @@ The Laws of Large Numbers - Archive of Formal Proofs

      The Laws of Large Numbers

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      February 10, 2021

      Abstract

      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 $E[X]$.

      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:

      • 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 $\varepsilon > 0$.
      • The Strong Law of Large Numbers states that $\overline{X}_{n} \longrightarrow E[X_1]$ almost surely for $n\to\infty$, i.e. $\mathcal{P}(\overline{X}_{n} \longrightarrow E[X_1]) = 1$.

      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.

      BSD License

      Topics

      Theories of Laws_of_Large_Numbers

      \ No newline at end of file diff --git a/web/entries/LinearQuantifierElim.html b/web/entries/LinearQuantifierElim.html --- a/web/entries/LinearQuantifierElim.html +++ b/web/entries/LinearQuantifierElim.html @@ -1,179 +1,179 @@ Quantifier Elimination for Linear Arithmetic - Archive of Formal Proofs

      Quantifier Elimination for Linear Arithmetic

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      January 11, 2008

      Abstract

      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.
      BSD License

      Topics

      Theories of LinearQuantifierElim

      \ No newline at end of file diff --git a/web/entries/Linear_Inequalities.html b/web/entries/Linear_Inequalities.html --- a/web/entries/Linear_Inequalities.html +++ b/web/entries/Linear_Inequalities.html @@ -1,194 +1,194 @@ Linear Inequalities - Archive of Formal Proofs

      Linear Inequalities

      -

      Ralph Bottesch 🌐, Alban Reynaud and René Thiemann 🌐 +

      Ralph Bottesch 🌐, Alban Reynaud and René Thiemann 🌐

      June 21, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Linear_Inequalities

      \ No newline at end of file diff --git a/web/entries/Linear_Programming.html b/web/entries/Linear_Programming.html --- a/web/entries/Linear_Programming.html +++ b/web/entries/Linear_Programming.html @@ -1,178 +1,178 @@ Linear Programming - Archive of Formal Proofs

      Linear Programming

      -

      Julian Parsert 🌐 and Cezary Kaliszyk 🌐 +

      Julian Parsert 🌐 and Cezary Kaliszyk 🌐

      August 6, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Linear_Programming

      \ No newline at end of file diff --git a/web/entries/Linear_Recurrences.html b/web/entries/Linear_Recurrences.html --- a/web/entries/Linear_Recurrences.html +++ b/web/entries/Linear_Recurrences.html @@ -1,190 +1,190 @@ Linear Recurrences - Archive of Formal Proofs

      Linear Recurrences

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      October 12, 2017

      Abstract

      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 f(n) = f(n-1) + f(n - 2) and the quite non-obvious closed form (φn - (-φ)-n) / √5 where φ is the golden ratio.

      In this work, I build on existing tools in Isabelle – such as formal power series and polynomial factorisation algorithms – to develop a theory of these recurrences and derive a fully executable solver for them that can be exported to programming languages like Haskell.

      BSD License

      Topics

      Theories of Linear_Recurrences

      Theories of Linear_Recurrences_Solver

      \ No newline at end of file diff --git a/web/entries/Liouville_Numbers.html b/web/entries/Liouville_Numbers.html --- a/web/entries/Liouville_Numbers.html +++ b/web/entries/Liouville_Numbers.html @@ -1,175 +1,175 @@ Liouville numbers - Archive of Formal Proofs

      Liouville Numbers

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 28, 2015

      Abstract

      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.

      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.

      The proof is very elementary and requires only standard arithmetic, the Mean Value Theorem for polynomials, and the boundedness of polynomials on compact intervals.

      BSD License

      Topics

      Theories of Liouville_Numbers

      \ No newline at end of file diff --git a/web/entries/List-Index.html b/web/entries/List-Index.html --- a/web/entries/List-Index.html +++ b/web/entries/List-Index.html @@ -1,155 +1,155 @@ List Index - Archive of Formal Proofs

      List Index

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      February 20, 2010

      Abstract

      This theory provides functions for finding the index of an element in a list, by predicate and by value.
      BSD License

      Topics

      Theories of List-Index

      \ No newline at end of file diff --git a/web/entries/List_Inversions.html b/web/entries/List_Inversions.html --- a/web/entries/List_Inversions.html +++ b/web/entries/List_Inversions.html @@ -1,170 +1,170 @@ The Inversions of a List - Archive of Formal Proofs

      The Inversions of a List

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      February 1, 2019

      Abstract

      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 log n) divide-and-conquer algorithm to compute the number of inversions.

      BSD License

      Topics

      Theories of List_Inversions

      \ No newline at end of file diff --git a/web/entries/List_Update.html b/web/entries/List_Update.html --- a/web/entries/List_Update.html +++ b/web/entries/List_Update.html @@ -1,190 +1,190 @@ Analysis of List Update Algorithms - Archive of Formal Proofs

      Analysis of List Update Algorithms

      -

      Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐 +

      Maximilian P. L. Haslbeck 🌐 and Tobias Nipkow 🌐

      February 17, 2016

      Abstract

      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 Online Computation and Competitive Analysis by Borodin and El-Yaniv.

      For an informal description see the FSTTCS 2016 publication Verified Analysis of List Update Algorithms by Haslbeck and Nipkow.

      BSD License

      Topics

      Theories of List_Update

      \ No newline at end of file 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 @@ -1,182 +1,182 @@ Computer-assisted Reconstruction and Assessment of E. J. Lowe's Modal Ontological Argument - Archive of Formal Proofs

      Computer-Assisted Reconstruction and Assessment of E. J. Lowe's Modal Ontological Argument

      -

      David Fuenmayor 📧 and Christoph Benzmüller 🌐 +

      David Fuenmayor 📧 and Christoph Benzmüller 🌐

      September 21, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Lowe_Ontological_Argument

      \ No newline at end of file diff --git a/web/entries/MDP-Algorithms.html b/web/entries/MDP-Algorithms.html --- a/web/entries/MDP-Algorithms.html +++ b/web/entries/MDP-Algorithms.html @@ -1,195 +1,195 @@ Verified Algorithms for Solving Markov Decision Processes - Archive of Formal Proofs

      Verified Algorithms for Solving Markov Decision Processes

      -

      Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧 +

      Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧

      December 16, 2021

      Abstract

      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".
      BSD License

      Topics

      Theories of MDP-Algorithms

      \ No newline at end of file diff --git a/web/entries/MDP-Rewards.html b/web/entries/MDP-Rewards.html --- a/web/entries/MDP-Rewards.html +++ b/web/entries/MDP-Rewards.html @@ -1,186 +1,186 @@ Markov Decision Processes with Rewards - Archive of Formal Proofs

      Markov Decision Processes With Rewards

      -

      Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧 +

      Maximilian Schäffeler 📧 and Mohammad Abdulaziz 📧

      December 16, 2021

      Abstract

      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".
      BSD License

      Topics

      Theories of MDP-Rewards

      \ No newline at end of file diff --git a/web/entries/MFMC_Countable.html b/web/entries/MFMC_Countable.html --- a/web/entries/MFMC_Countable.html +++ b/web/entries/MFMC_Countable.html @@ -1,197 +1,197 @@ A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks - Archive of Formal Proofs

      A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      May 9, 2016

      Abstract

      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 The Max-Flow Min-Cut theorem for countable networks 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.
      BSD License

      Topics

      Theories of MFMC_Countable

      \ No newline at end of file diff --git a/web/entries/MFODL_Monitor_Optimized.html b/web/entries/MFODL_Monitor_Optimized.html --- a/web/entries/MFODL_Monitor_Optimized.html +++ b/web/entries/MFODL_Monitor_Optimized.html @@ -1,196 +1,196 @@ Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations - Archive of Formal Proofs

      Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic With Aggregations

      -

      Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐 +

      Thibault Dardinier, Lukas Heimes, Martin Raszyk 📧, Joshua Schneider 📧 and Dmitriy Traytel 🌐

      April 9, 2020

      Abstract

      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 forthcoming paper at IJCAR 2020, significantly extends previous work on a verified monitor for MFOTL. Apart from the addition of regular expressions and aggregations, we implemented multi-way joins and a specialized sliding window algorithm to further optimize the monitor.
      BSD License

      Change history

      [2021-10-19] corrected a mistake in the calculation of median aggregations (reported by Nicolas Kaletsch, revision 02b14c9bf3da)

      Topics

      Theories of MFODL_Monitor_Optimized

      \ No newline at end of file diff --git a/web/entries/MFOTL_Monitor.html b/web/entries/MFOTL_Monitor.html --- a/web/entries/MFOTL_Monitor.html +++ b/web/entries/MFOTL_Monitor.html @@ -1,192 +1,192 @@ Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic - Archive of Formal Proofs

      Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic

      -

      Joshua Schneider 📧 and Dmitriy Traytel 🌐 +

      Joshua Schneider 📧 and Dmitriy Traytel 🌐

      July 4, 2019

      Abstract

      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 RV 2019 paper, 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.
      BSD License

      Topics

      Theories of MFOTL_Monitor

      \ No newline at end of file diff --git a/web/entries/MSO_Regex_Equivalence.html b/web/entries/MSO_Regex_Equivalence.html --- a/web/entries/MSO_Regex_Equivalence.html +++ b/web/entries/MSO_Regex_Equivalence.html @@ -1,201 +1,201 @@ Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions - Archive of Formal Proofs

      Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions

      -

      Dmitriy Traytel 🌐 and Tobias Nipkow 🌐 +

      Dmitriy Traytel 🌐 and Tobias Nipkow 🌐

      June 12, 2014

      Abstract

      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.

      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.

      The formalization is described in this ICFP 2013 functional pearl.

      BSD License

      Topics

      Theories of MSO_Regex_Equivalence

      \ No newline at end of file diff --git a/web/entries/Markov_Models.html b/web/entries/Markov_Models.html --- a/web/entries/Markov_Models.html +++ b/web/entries/Markov_Models.html @@ -1,196 +1,196 @@ Markov Models - Archive of Formal Proofs

      Markov Models

      -

      Johannes Hölzl 🌐 and Tobias Nipkow 🌐 +

      Johannes Hölzl 🌐 and Tobias Nipkow 🌐

      January 3, 2012

      Abstract

      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.

      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. See here for the corresponding paper.

      BSD License

      Topics

      Theories of Markov_Models

      \ No newline at end of file diff --git a/web/entries/Marriage.html b/web/entries/Marriage.html --- a/web/entries/Marriage.html +++ b/web/entries/Marriage.html @@ -1,157 +1,157 @@ Hall's Marriage Theorem - Archive of Formal Proofs

      Hall's Marriage Theorem

      -

      Dongchen Jiang 📧 and Tobias Nipkow 🌐 +

      Dongchen Jiang 📧 and Tobias Nipkow 🌐

      December 17, 2010

      Abstract

      Two proofs of Hall's Marriage Theorem: one due to Halmos and Vaughan, one due to Rado.
      BSD License

      Change history

      [2011-09-09] Added Rado's proof

      Topics

      Theories of Marriage

      Used by

      \ No newline at end of file diff --git a/web/entries/Mason_Stothers.html b/web/entries/Mason_Stothers.html --- a/web/entries/Mason_Stothers.html +++ b/web/entries/Mason_Stothers.html @@ -1,182 +1,182 @@ The Mason–Stothers Theorem - Archive of Formal Proofs

      The Mason–Stothers Theorem

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 21, 2017

      Abstract

      This article provides a formalisation of Snyder’s simple and elegant proof of the Mason–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.

      In short, the statement of the theorem is that three non-zero coprime polynomials A, B, C over a field which sum to 0 and do not all have vanishing derivatives fulfil max{deg(A), deg(B), deg(C)} < deg(rad(ABC)) where the rad(P) denotes the radical of P, i. e. the product of all unique irreducible factors of P.

      This theorem also implies a kind of polynomial analogue of Fermat’s Last Theorem for polynomials: except for trivial cases, An + Bn + Cn = 0 implies n ≤ 2 for coprime polynomials A, B, C over a field.

      BSD License

      Topics

      Theories of Mason_Stothers

      \ No newline at end of file diff --git a/web/entries/Matrix.html b/web/entries/Matrix.html --- a/web/entries/Matrix.html +++ b/web/entries/Matrix.html @@ -1,182 +1,182 @@ Executable Matrix Operations on Matrices of Arbitrary Dimensions - Archive of Formal Proofs

      Executable Matrix Operations on Matrices of Arbitrary Dimensions

      -

      Christian Sternagel 📧 and René Thiemann 🌐 +

      Christian Sternagel 📧 and René Thiemann 🌐

      June 17, 2010

      Abstract

      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 CeTA system which contains several termination techniques. The provided theories have been essential to formalize matrix-interpretations and arctic interpretations.
      GNU Lesser General Public License (LGPL)

      Change history

      [2010-09-17] Moved theory on arbitrary (ordered) semirings to Abstract Rewriting.

      Topics

      Theories of Matrix

      \ No newline at end of file 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 @@ -1,173 +1,173 @@ The Median-of-Medians Selection Algorithm - Archive of Formal Proofs

      The Median-of-Medians Selection Algorithm

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 21, 2017

      Abstract

      This entry provides an executable functional implementation of the Median-of-Medians algorithm for selecting the k-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.

      BSD License

      Topics

      Theories of Median_Of_Medians_Selection

      \ No newline at end of file diff --git a/web/entries/Mersenne_Primes.html b/web/entries/Mersenne_Primes.html --- a/web/entries/Mersenne_Primes.html +++ b/web/entries/Mersenne_Primes.html @@ -1,177 +1,177 @@ Mersenne primes and the Lucas–Lehmer test - Archive of Formal Proofs

      Mersenne Primes and the Lucas–Lehmer Test

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      January 17, 2020

      Abstract

      This article provides formal proofs of basic properties of Mersenne numbers, i. e. numbers of the form 2n - 1, and especially of Mersenne primes.

      In particular, an efficient, verified, and executable version of the Lucas–Lehmer test is developed. This test decides primality for Mersenne numbers in time polynomial in n.

      BSD License

      Topics

      Theories of Mersenne_Primes

      \ No newline at end of file diff --git a/web/entries/Metalogic_ProofChecker.html b/web/entries/Metalogic_ProofChecker.html --- a/web/entries/Metalogic_ProofChecker.html +++ b/web/entries/Metalogic_ProofChecker.html @@ -1,194 +1,194 @@ Isabelle's Metalogic: Formalization and Proof Checker - Archive of Formal Proofs

      Isabelle's Metalogic: Formalization and Proof Checker

      -

      Tobias Nipkow 🌐 and Simon Roßkopf 🌐 +

      Tobias Nipkow 🌐 and Simon Roßkopf 🌐

      April 27, 2021

      Abstract

      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 CADE 28 paper.
      BSD License

      Topics

      Theories of Metalogic_ProofChecker

      \ No newline at end of file diff --git a/web/entries/MiniML.html b/web/entries/MiniML.html --- a/web/entries/MiniML.html +++ b/web/entries/MiniML.html @@ -1,166 +1,166 @@ Mini ML - Archive of Formal Proofs

      Mini ML

      -

      Wolfgang Naraschewski and Tobias Nipkow 🌐 +

      Wolfgang Naraschewski and Tobias Nipkow 🌐

      March 19, 2004

      Abstract

      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 the soundness and completeness of W w.r.t. the rules.
      BSD License

      Topics

      Theories of MiniML

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Minkowskis_Theorem.html b/web/entries/Minkowskis_Theorem.html --- a/web/entries/Minkowskis_Theorem.html +++ b/web/entries/Minkowskis_Theorem.html @@ -1,173 +1,173 @@ Minkowski's Theorem - Archive of Formal Proofs

      Minkowski's Theorem

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      July 13, 2017

      Abstract

      Minkowski's theorem relates a subset of ℝn, the Lebesgue measure, and the integer lattice ℤn: It states that any convex subset of ℝn with volume greater than 2n contains at least one lattice point from ℤn\{0}, i. e. a non-zero point with integer coefficients.

      A related theorem which directly implies this is Blichfeldt's theorem, which states that any subset of ℝn with a volume greater than 1 contains two different points whose difference vector has integer components.

      The entry contains a proof of both theorems.

      BSD License

      Topics

      Theories of Minkowskis_Theorem

      Related Entries

      \ 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 +++ b/web/entries/Modular_Assembly_Kit_Security.html @@ -1,190 +1,190 @@ An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties - Archive of Formal Proofs

      An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties

      -

      Oliver Bračevac 📧, Richard Gay 📧, Sylvia Grewe 📧, Heiko Mantel 📧, Henning Sudbrock 📧 and Markus Tasch 📧 +

      Oliver Bračevac 📧, Richard Gay 📧, Sylvia Grewe 📧, Heiko Mantel 📧, Henning Sudbrock 📧 and Markus Tasch 📧

      May 7, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Modular_Assembly_Kit_Security

      \ No newline at end of file diff --git a/web/entries/Monad_Memo_DP.html b/web/entries/Monad_Memo_DP.html --- a/web/entries/Monad_Memo_DP.html +++ b/web/entries/Monad_Memo_DP.html @@ -1,208 +1,208 @@ Monadification, Memoization and Dynamic Programming - Archive of Formal Proofs

      Monadification, Memoization and Dynamic Programming

      -

      Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐 +

      Simon Wimmer 🌐, Shuwei Hu 📧 and Tobias Nipkow 🌐

      May 22, 2018

      Abstract

      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].
      BSD License

      Topics

      Theories of Monad_Memo_DP

      \ No newline at end of file diff --git a/web/entries/Monad_Normalisation.html b/web/entries/Monad_Normalisation.html --- a/web/entries/Monad_Normalisation.html +++ b/web/entries/Monad_Normalisation.html @@ -1,176 +1,176 @@ Monad normalisation - Archive of Formal Proofs

      Monad Normalisation

      -

      Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐 +

      Joshua Schneider, Manuel Eberl 🌐 and Andreas Lochbihler 🌐

      May 5, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Monad_Normalisation

      \ No newline at end of file diff --git a/web/entries/Monomorphic_Monad.html b/web/entries/Monomorphic_Monad.html --- a/web/entries/Monomorphic_Monad.html +++ b/web/entries/Monomorphic_Monad.html @@ -1,181 +1,181 @@ Effect polymorphism in higher-order logic - Archive of Formal Proofs

      Effect Polymorphism in Higher-Order Logic

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      May 5, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Monomorphic_Monad

      \ No newline at end of file diff --git a/web/entries/Multirelations.html b/web/entries/Multirelations.html --- a/web/entries/Multirelations.html +++ b/web/entries/Multirelations.html @@ -1,176 +1,176 @@ Binary Multirelations - Archive of Formal Proofs

      Binary Multirelations

      -

      Hitoshi Furusawa 🌐 and Georg Struth 🌐 +

      Hitoshi Furusawa 🌐 and Georg Struth 🌐

      June 11, 2015

      Abstract

      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.
      BSD License

      Topics

      Theories of Multirelations

      \ No newline at end of file diff --git a/web/entries/Myhill-Nerode.html b/web/entries/Myhill-Nerode.html --- a/web/entries/Myhill-Nerode.html +++ b/web/entries/Myhill-Nerode.html @@ -1,175 +1,175 @@ The Myhill-Nerode Theorem Based on Regular Expressions - Archive of Formal Proofs

      The Myhill-Nerode Theorem Based on Regular Expressions

      -

      Chunhan Wu, Xingyuan Zhang and Christian Urban 🌐 - with contributions from Manuel Eberl 🌐 +

      Chunhan Wu, Xingyuan Zhang and Christian Urban 🌐 + with contributions from Manuel Eberl 🌐

      August 26, 2011

      Abstract

      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.
      BSD License

      Topics

      Theories of Myhill-Nerode

      \ No newline at end of file diff --git a/web/entries/Native_Word.html b/web/entries/Native_Word.html --- a/web/entries/Native_Word.html +++ b/web/entries/Native_Word.html @@ -1,199 +1,199 @@ Native Word - Archive of Formal Proofs

      Native Word

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐 with contributions from Peter Lammich 🌐

      September 17, 2013

      Abstract

      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.
      BSD License

      Topics

      Theories of Native_Word

      \ No newline at end of file diff --git a/web/entries/Nested_Multisets_Ordinals.html b/web/entries/Nested_Multisets_Ordinals.html --- a/web/entries/Nested_Multisets_Ordinals.html +++ b/web/entries/Nested_Multisets_Ordinals.html @@ -1,178 +1,178 @@ Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals - Archive of Formal Proofs

      Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

      -

      Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐 +

      Jasmin Christian Blanchette 📧, Mathias Fleury 📧 and Dmitriy Traytel 🌐

      November 12, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Nested_Multisets_Ordinals

      \ No newline at end of file diff --git a/web/entries/Nominal2.html b/web/entries/Nominal2.html --- a/web/entries/Nominal2.html +++ b/web/entries/Nominal2.html @@ -1,188 +1,188 @@ Nominal 2 - Archive of Formal Proofs

      Nominal 2

      -

      Christian Urban 🌐, Stefan Berghofer 🌐 and Cezary Kaliszyk 🌐 +

      Christian Urban 🌐, Stefan Berghofer 🌐 and Cezary Kaliszyk 🌐

      February 21, 2013

      Abstract

      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.

      This entry can be used as a more advanced replacement for HOL/Nominal in the Isabelle distribution.

      BSD License

      Topics

      Theories of Nominal2

      \ No newline at end of file diff --git a/web/entries/NormByEval.html b/web/entries/NormByEval.html --- a/web/entries/NormByEval.html +++ b/web/entries/NormByEval.html @@ -1,152 +1,152 @@ Normalization by Evaluation - Archive of Formal Proofs

      Normalization by Evaluation

      -

      Klaus Aehlig 🌐 and Tobias Nipkow 🌐 +

      Klaus Aehlig 🌐 and Tobias Nipkow 🌐

      February 18, 2008

      Abstract

      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.
      BSD License

      Topics

      Theories of NormByEval

      \ No newline at end of file diff --git a/web/entries/Octonions.html b/web/entries/Octonions.html --- a/web/entries/Octonions.html +++ b/web/entries/Octonions.html @@ -1,175 +1,175 @@ Octonions - Archive of Formal Proofs

      Octonions

      -

      Angeliki Koutsoukou-Argyraki 🌐 +

      Angeliki Koutsoukou-Argyraki 🌐

      September 14, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Octonions

      \ No newline at end of file diff --git a/web/entries/OpSets.html b/web/entries/OpSets.html --- a/web/entries/OpSets.html +++ b/web/entries/OpSets.html @@ -1,172 +1,172 @@ OpSets: Sequential Specifications for Replicated Datatypes - Archive of Formal Proofs

      OpSets: Sequential Specifications for Replicated Datatypes

      -

      Martin Kleppmann 📧, Victor B. F. Gomes 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧 +

      Martin Kleppmann 📧, Victor B. F. Gomes 📧, Dominic P. Mulligan 📧 and Alastair R. Beresford 📧

      May 10, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of OpSets

      \ No newline at end of file diff --git a/web/entries/Optimal_BST.html b/web/entries/Optimal_BST.html --- a/web/entries/Optimal_BST.html +++ b/web/entries/Optimal_BST.html @@ -1,175 +1,175 @@ Optimal Binary Search Trees - Archive of Formal Proofs

      Optimal Binary Search Trees

      -

      Tobias Nipkow 🌐 and Dániel Somogyi +

      Tobias Nipkow 🌐 and Dániel Somogyi

      May 27, 2018

      Abstract

      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 Monadification, Memoization and Dynamic Programming, thus yielding dynamic programming algorithms.
      BSD License

      Topics

      Theories of Optimal_BST

      Depends On

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Ordered_Resolution_Prover.html b/web/entries/Ordered_Resolution_Prover.html --- a/web/entries/Ordered_Resolution_Prover.html +++ b/web/entries/Ordered_Resolution_Prover.html @@ -1,190 +1,190 @@ Formalization of Bachmair and Ganzinger's Ordered Resolution Prover - Archive of Formal Proofs

      Formalization of Bachmair and Ganzinger's Ordered Resolution Prover

      -

      Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧 +

      Anders Schlichtkrull 🌐, Jasmin Christian Blanchette 📧, Dmitriy Traytel 🌐 and Uwe Waldmann 📧

      January 18, 2018

      Abstract

      This Isabelle/HOL formalization covers Sections 2 to 4 of Bachmair and Ganzinger's "Resolution Theorem Proving" chapter in the Handbook of Automated Reasoning. 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.
      BSD License

      Topics

      Theories of Ordered_Resolution_Prover

      \ No newline at end of file diff --git a/web/entries/Ordinal.html b/web/entries/Ordinal.html --- a/web/entries/Ordinal.html +++ b/web/entries/Ordinal.html @@ -1,173 +1,173 @@ Countable Ordinals - Archive of Formal Proofs

      Countable Ordinals

      -

      Brian Huffman 🌐 +

      Brian Huffman 🌐

      November 11, 2005

      Abstract

      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.
      BSD License

      Topics

      Theories of Ordinal

      Used by

      Related Entries

      \ No newline at end of file diff --git a/web/entries/Ordinary_Differential_Equations.html b/web/entries/Ordinary_Differential_Equations.html --- a/web/entries/Ordinary_Differential_Equations.html +++ b/web/entries/Ordinary_Differential_Equations.html @@ -1,267 +1,267 @@ Ordinary Differential Equations - Archive of Formal Proofs

      Ordinary Differential Equations

      -

      Fabian Immler 🌐 and Johannes Hölzl 🌐 +

      Fabian Immler 🌐 and Johannes Hölzl 🌐

      April 26, 2012

      Abstract

      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 flow of ODEs.

      Not in the generated document are the following sessions:

      • 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.
      • HOL-ODE-Examples: Applications of the numerical algorithms to concrete systems of ODEs.
      • Lorenz_C0, Lorenz_C1: Verified algorithms for checking C1-information according to Tucker's proof, computation of C0-information.

      BSD License

      Change history

      [2014-02-13] added an implementation of the Euler method based on affine arithmetic
      [2016-04-14] added flow and variational equation
      [2016-08-03] numerical algorithms for reachability analysis (using second-order Runge-Kutta methods, splitting, and reduction) implemented using Lammich's framework for automatic refinement
      [2017-09-20] 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.

      Topics

      Theories of Ordinary_Differential_Equations

      Theories of HOL-ODE-Numerics

      Theories of Lorenz_Approximation

      Theories of HOL-ODE-Examples

      Theories of HOL-ODE-ARCH-COMP

      Theories of Lorenz_C0

      Theories of Lorenz_C1

      \ No newline at end of file diff --git a/web/entries/Pairing_Heap.html b/web/entries/Pairing_Heap.html --- a/web/entries/Pairing_Heap.html +++ b/web/entries/Pairing_Heap.html @@ -1,178 +1,178 @@ Pairing Heap - Archive of Formal Proofs

      Pairing Heap

      -

      Hauke Brinkop 📧 and Tobias Nipkow 🌐 +

      Hauke Brinkop 📧 and Tobias Nipkow 🌐

      July 14, 2016

      Abstract

      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.

      The amortized complexity of pairing heaps is analyzed in the AFP article Amortized Complexity.

      BSD License

      Extra 0

      Origin: This library was extracted from Amortized Complexity and extended.

      Topics

      Theories of Pairing_Heap

      \ No newline at end of file diff --git a/web/entries/Pell.html b/web/entries/Pell.html --- a/web/entries/Pell.html +++ b/web/entries/Pell.html @@ -1,198 +1,198 @@ Pell's Equation - Archive of Formal Proofs

      Pell's Equation

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      June 23, 2018

      Abstract

      This article gives the basic theory of Pell's equation x2 = 1 + Dy2, where D ∈ ℕ is a parameter and x, y are integer variables.

      The main result that is proven is the following: If D is not a perfect square, then there exists a fundamental solution (x0, y0) that is not the trivial solution (1, 0) and which generates all other solutions (x, y) in the sense that there exists some n ∈ ℕ such that |x| + |y| √D = (x0 + y0 √D)n. This also implies that the set of solutions is infinite, and it gives us an explicit and executable characterisation of all the solutions.

      Based on this, simple executable algorithms for computing the fundamental solution and the infinite sequence of all non-negative solutions are also provided.

      BSD License

      Topics

      Theories of Pell

      \ No newline at end of file diff --git a/web/entries/Perron_Frobenius.html b/web/entries/Perron_Frobenius.html --- a/web/entries/Perron_Frobenius.html +++ b/web/entries/Perron_Frobenius.html @@ -1,200 +1,200 @@ Perron-Frobenius Theorem for Spectral Radius Analysis - Archive of Formal Proofs

      Perron-Frobenius Theorem for Spectral Radius Analysis

      -

      Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧 +

      Jose Divasón 🌐, Ondřej Kunčar 🌐, René Thiemann 📧 and Akihisa Yamada 📧

      May 20, 2016

      Abstract

      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 An 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 complex eigenvalues. In case A contains only non-negative real values, a simplification is possible with the help of the Perron–Frobenius theorem, which tells us that it suffices to consider only the real eigenvalues of A, i.e., applying Sturm's method can decide the polynomial growth of An.

      We formalize the Perron–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 An is polynomially bounded in n.

      BSD License

      Topics

      Theories of Perron_Frobenius

      \ No newline at end of file diff --git a/web/entries/Pi_Transcendental.html b/web/entries/Pi_Transcendental.html --- a/web/entries/Pi_Transcendental.html +++ b/web/entries/Pi_Transcendental.html @@ -1,177 +1,177 @@ The Transcendence of π - Archive of Formal Proofs

      The Transcendence of Π

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      September 28, 2018

      Abstract

      This entry shows the transcendence of π 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 e.

      BSD License

      Topics

      Theories of Pi_Transcendental

      \ No newline at end of file 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 @@ -1,174 +1,174 @@ The Poincaré-Bendixson Theorem - Archive of Formal Proofs

      The Poincaré-Bendixson Theorem

      -

      Fabian Immler 🌐 and Yong Kiam Tan 🌐 +

      Fabian Immler 🌐 and Yong Kiam Tan 🌐

      December 18, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Poincare_Bendixson

      Depends On

      \ No newline at end of file diff --git a/web/entries/Polynomials.html b/web/entries/Polynomials.html --- a/web/entries/Polynomials.html +++ b/web/entries/Polynomials.html @@ -1,217 +1,217 @@ Executable Multivariate Polynomials - Archive of Formal Proofs

      Executable Multivariate Polynomials

      -

      Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧 +

      Christian Sternagel 📧, René Thiemann 🌐, Alexander Maletzky 🌐, Fabian Immler 🌐, Florian Haftmann 🌐, Andreas Lochbihler 🌐 and Alexander Bentkamp 📧

      August 10, 2010

      Abstract

      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 IsaFoR/CeTA-system which contains several termination techniques. The provided theories have been essential to formalize polynomial interpretations.

      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].

      GNU Lesser General Public License (LGPL)

      Change history

      [2010-09-17] Moved theories on arbitrary (ordered) semirings to Abstract Rewriting.
      [2016-10-28] Added abstract representation of polynomials and authors Maletzky/Immler.
      [2018-01-23] Added authors Haftmann, Lochbihler after incorporating their formalization of multivariate polynomials based on Polynomial mappings. Moved material from Bentkamp's entry "Deep Learning".
      [2019-04-18] Added material about polynomials whose power-products are represented themselves by polynomial mappings.

      Topics

      Theories of Polynomials

      \ No newline at end of file diff --git a/web/entries/Posix-Lexing.html b/web/entries/Posix-Lexing.html --- a/web/entries/Posix-Lexing.html +++ b/web/entries/Posix-Lexing.html @@ -1,168 +1,168 @@ POSIX Lexing with Derivatives of Regular Expressions - Archive of Formal Proofs

      POSIX Lexing With Derivatives of Regular Expressions

      -

      Fahad Ausaf 🌐, Roy Dyckhoff 🌐 and Christian Urban 🌐 +

      Fahad Ausaf 🌐, Roy Dyckhoff 🌐 and Christian Urban 🌐

      May 24, 2016

      Abstract

      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. In this entry 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). We also prove the correctness of an optimised version of the POSIX matching algorithm.
      BSD License

      Topics

      Theories of Posix-Lexing

      Depends On

      \ No newline at end of file diff --git a/web/entries/Power_Sum_Polynomials.html b/web/entries/Power_Sum_Polynomials.html --- a/web/entries/Power_Sum_Polynomials.html +++ b/web/entries/Power_Sum_Polynomials.html @@ -1,211 +1,211 @@ Power Sum Polynomials - Archive of Formal Proofs

      Power Sum Polynomials

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      April 24, 2020

      Abstract

      This article provides a formalisation of the symmetric multivariate polynomials known as power sum polynomials. These are of the form pn(X1,…, Xk) = X1n + … + Xkn. A formal proof of the Girard–Newton Theorem is also given. This theorem relates the power sum polynomials to the elementary symmetric polynomials sk in the form of a recurrence relation (-1)k k sk = ∑i∈[0,k) (-1)i si pk-i .

      As an application, this is then used to solve a generalised form of a puzzle given as an exercise in Dummit and Foote's Abstract Algebra: For k complex unknowns x1, …, xk, define pj := x1j + … + xkj. Then for each vector a ∈ ℂk, show that there is exactly one solution to the system p1 = a1, …, pk = ak up to permutation of the xi and determine the value of pi for i>k.

      BSD License

      Topics

      Theories of Power_Sum_Polynomials

      \ No newline at end of file diff --git a/web/entries/Prim_Dijkstra_Simple.html b/web/entries/Prim_Dijkstra_Simple.html --- a/web/entries/Prim_Dijkstra_Simple.html +++ b/web/entries/Prim_Dijkstra_Simple.html @@ -1,185 +1,185 @@ Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra - Archive of Formal Proofs

      Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra

      -

      Peter Lammich 🌐 and Tobias Nipkow 🌐 +

      Peter Lammich 🌐 and Tobias Nipkow 🌐

      June 25, 2019

      Abstract

      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 Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra.
      BSD License

      Topics

      Theories of Prim_Dijkstra_Simple

      \ No newline at end of file diff --git a/web/entries/Prime_Distribution_Elementary.html b/web/entries/Prime_Distribution_Elementary.html --- a/web/entries/Prime_Distribution_Elementary.html +++ b/web/entries/Prime_Distribution_Elementary.html @@ -1,191 +1,191 @@ Elementary Facts About the Distribution of Primes - Archive of Formal Proofs

      Elementary Facts About the Distribution of Primes

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      February 21, 2019

      Abstract

      This entry is a formalisation of Chapter 4 (and parts of Chapter 3) of Apostol's Introduction to Analytic Number Theory. The main topics that are addressed are properties of the distribution of prime numbers that can be shown in an elementary way (i. 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 n, the divisor function d(n), Euler's totient function φ(n), and lcm(1,…,n).

      BSD License

      Topics

      Theories of Prime_Distribution_Elementary

      \ No newline at end of file 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 @@ -1,179 +1,179 @@ The Divergence of the Prime Harmonic Series - Archive of Formal Proofs

      The Divergence of the Prime Harmonic Series

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 28, 2015

      Abstract

      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 Harmonic Series ∑[p prime] · 1/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.

      BSD License

      Topics

      Theories of Prime_Harmonic_Series

      \ No newline at end of file diff --git a/web/entries/Prime_Number_Theorem.html b/web/entries/Prime_Number_Theorem.html --- a/web/entries/Prime_Number_Theorem.html +++ b/web/entries/Prime_Number_Theorem.html @@ -1,207 +1,207 @@ The Prime Number Theorem - Archive of Formal Proofs

      The Prime Number Theorem

      -

      Manuel Eberl 🌐 and Lawrence C. Paulson 🌐 +

      Manuel Eberl 🌐 and Lawrence C. Paulson 🌐

      September 19, 2018

      Abstract

      This article provides a short proof of the Prime Number Theorem in several equivalent forms, most notably π(x) ~ x/ln x where π(x) is the number of primes no larger than x. It also defines other basic number-theoretic functions related to primes like Chebyshev's functions ϑ and ψ and the “n-th prime number” function pn. We also show various bounds and relationship between these functions are shown. Lastly, we derive Mertens' First and Second Theorem, i. e. ∑px ln p/p = ln x + O(1) and ∑px 1/p = ln ln x + M + O(1/ln x). We also give explicit bounds for the remainder terms.

      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 ∑px ln p/p = ln x + c + o(1).

      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 et al. 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.

      BSD License

      Topics

      Theories of Prime_Number_Theorem

      \ No newline at end of file diff --git a/web/entries/Priority_Queue_Braun.html b/web/entries/Priority_Queue_Braun.html --- a/web/entries/Priority_Queue_Braun.html +++ b/web/entries/Priority_Queue_Braun.html @@ -1,160 +1,160 @@ Priority Queues Based on Braun Trees - Archive of Formal Proofs

      Priority Queues Based on Braun Trees

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      September 4, 2014

      Abstract

      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.
      BSD License

      Change history

      [2019-12-16] Added theory Priority_Queue_Braun2 with second version of del_min

      Topics

      Theories of Priority_Queue_Braun

      \ No newline at end of file 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 +1,179 @@ Priority Search Trees - Archive of Formal Proofs

      Priority Search Trees

      -

      Peter Lammich 🌐 and Tobias Nipkow 🌐 +

      Peter Lammich 🌐 and Tobias Nipkow 🌐

      June 25, 2019

      Abstract

      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 tree. 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 Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra.
      BSD License

      Topics

      Theories of Priority_Search_Trees

      \ No newline at end of file diff --git a/web/entries/Probabilistic_Noninterference.html b/web/entries/Probabilistic_Noninterference.html --- a/web/entries/Probabilistic_Noninterference.html +++ b/web/entries/Probabilistic_Noninterference.html @@ -1,170 +1,170 @@ Probabilistic Noninterference - Archive of Formal Proofs

      Probabilistic Noninterference

      -

      Andrei Popescu 🌐 and Johannes Hölzl 🌐 +

      Andrei Popescu 🌐 and Johannes Hölzl 🌐

      March 11, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of Probabilistic_Noninterference

      \ No newline at end of file diff --git a/web/entries/Probabilistic_Prime_Tests.html b/web/entries/Probabilistic_Prime_Tests.html --- a/web/entries/Probabilistic_Prime_Tests.html +++ b/web/entries/Probabilistic_Prime_Tests.html @@ -1,189 +1,189 @@ Probabilistic Primality Testing - Archive of Formal Proofs

      Probabilistic Primality Testing

      -

      Daniel Stüwe and Manuel Eberl 🌐 +

      Daniel Stüwe and Manuel Eberl 🌐

      February 11, 2019

      Abstract

      The most efficient known primality tests are probabilistic in the sense that they use randomness and may, with some probability, mistakenly classify a composite number as prime – but never a prime number as composite. Examples of this are the Miller–Rabin test, the Solovay–Strassen test, and (in most cases) Fermat's test.

      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.

      BSD License

      Topics

      Theories of Probabilistic_Prime_Tests

      \ No newline at end of file diff --git a/web/entries/Probabilistic_System_Zoo.html b/web/entries/Probabilistic_System_Zoo.html --- a/web/entries/Probabilistic_System_Zoo.html +++ b/web/entries/Probabilistic_System_Zoo.html @@ -1,164 +1,164 @@ A Zoo of Probabilistic Systems - Archive of Formal Proofs

      A Zoo of Probabilistic Systems

      -

      Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐 +

      Johannes Hölzl 🌐, Andreas Lochbihler 🌐 and Dmitriy Traytel 🌐

      May 27, 2015

      Abstract

      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.

      This work is described in detail in the ITP 2015 publication by the authors.

      BSD License

      Topics

      Theories of Probabilistic_System_Zoo

      \ No newline at end of file diff --git a/web/entries/Probabilistic_Timed_Automata.html b/web/entries/Probabilistic_Timed_Automata.html --- a/web/entries/Probabilistic_Timed_Automata.html +++ b/web/entries/Probabilistic_Timed_Automata.html @@ -1,187 +1,187 @@ Probabilistic Timed Automata - Archive of Formal Proofs

      Probabilistic Timed Automata

      -

      Simon Wimmer 🌐 and Johannes Hölzl 🌐 +

      Simon Wimmer 🌐 and Johannes Hölzl 🌐

      May 24, 2018

      Abstract

      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].
      BSD License

      Topics

      Theories of Probabilistic_Timed_Automata

      Depends On

      Related Entries

      \ No newline at end of file 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 @@ -1,169 +1,169 @@ Probabilistic while loop - Archive of Formal Proofs

      Probabilistic While Loop

      -

      Andreas Lochbihler 🌐 +

      Andreas Lochbihler 🌐

      May 5, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Probabilistic_While

      Depends On

      Used by

      \ No newline at end of file diff --git a/web/entries/Propositional_Proof_Systems.html b/web/entries/Propositional_Proof_Systems.html --- a/web/entries/Propositional_Proof_Systems.html +++ b/web/entries/Propositional_Proof_Systems.html @@ -1,221 +1,221 @@ Propositional Proof Systems - Archive of Formal Proofs

      Propositional Proof Systems

      -

      Julius Michaelis 🌐 and Tobias Nipkow 🌐 +

      Julius Michaelis 🌐 and Tobias Nipkow 🌐

      June 21, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Propositional_Proof_Systems

      \ No newline at end of file diff --git a/web/entries/QR_Decomposition.html b/web/entries/QR_Decomposition.html --- a/web/entries/QR_Decomposition.html +++ b/web/entries/QR_Decomposition.html @@ -1,184 +1,184 @@ QR Decomposition - Archive of Formal Proofs

      QR Decomposition

      -

      Jose Divasón 🌐 and Jesús Aransay 🌐 +

      Jose Divasón 🌐 and Jesús Aransay 🌐

      February 12, 2015

      Abstract

      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.
      BSD License

      Change history

      [2015-06-18] The second part of the Fundamental Theorem of Linear Algebra has been generalized to more general inner product spaces.

      Topics

      Theories of QR_Decomposition

      \ No newline at end of file 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 @@ -1,180 +1,180 @@ The number of comparisons in QuickSort - Archive of Formal Proofs

      The Number of Comparisons in QuickSort

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      March 15, 2017

      Abstract

      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. e. QuickSort with random pivot choice) is 2 (n+1) Hn - 4 n, which is asymptotically equivalent to 2 n ln n; second, the number of comparisons performed by the classic non-randomised QuickSort has the same distribution in the average case as the randomised one.

      BSD License

      Topics

      Theories of Quick_Sort_Cost

      \ No newline at end of file diff --git a/web/entries/ROBDD.html b/web/entries/ROBDD.html --- a/web/entries/ROBDD.html +++ b/web/entries/ROBDD.html @@ -1,190 +1,190 @@ Algorithms for Reduced Ordered Binary Decision Diagrams - Archive of Formal Proofs

      Algorithms for Reduced Ordered Binary Decision Diagrams

      -

      Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐 +

      Julius Michaelis 🌐, Max W. Haslbeck 🌐, Peter Lammich 🌐 and Lars Hupel 🌐

      April 27, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of ROBDD

      \ No newline at end of file diff --git a/web/entries/Random_BSTs.html b/web/entries/Random_BSTs.html --- a/web/entries/Random_BSTs.html +++ b/web/entries/Random_BSTs.html @@ -1,179 +1,179 @@ Expected Shape of Random Binary Search Trees - Archive of Formal Proofs

      Expected Shape of Random Binary Search Trees

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      April 4, 2017

      Abstract

      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. e. BSTs that are formed by taking an empty BST and inserting elements from a fixed set in random order.

      In particular, we prove a logarithmic upper bound on the expected height and the Θ(n log n) 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.

      BSD License

      Topics

      Theories of Random_BSTs

      \ No newline at end of file diff --git a/web/entries/Randomised_BSTs.html b/web/entries/Randomised_BSTs.html --- a/web/entries/Randomised_BSTs.html +++ b/web/entries/Randomised_BSTs.html @@ -1,171 +1,171 @@ Randomised Binary Search Trees - Archive of Formal Proofs

      Randomised Binary Search Trees

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      October 19, 2018

      Abstract

      This work is a formalisation of the Randomised Binary Search Trees introduced by Martínez and Roura, including definitions and correctness proofs.

      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.

      BSD License

      Topics

      Theories of Randomised_BSTs

      \ No newline at end of file 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 @@ -1,172 +1,172 @@ Rank-Nullity Theorem in Linear Algebra - Archive of Formal Proofs

      Rank-Nullity Theorem in Linear Algebra

      -

      Jose Divasón 🌐 and Jesús Aransay 🌐 +

      Jose Divasón 🌐 and Jesús Aransay 🌐

      January 16, 2013

      Abstract

      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 Linear Algebra Done Right. 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.
      BSD License

      Change history

      [2014-07-14] 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.

      Topics

      Theories of Rank_Nullity_Theorem

      \ No newline at end of file diff --git a/web/entries/Regex_Equivalence.html b/web/entries/Regex_Equivalence.html --- a/web/entries/Regex_Equivalence.html +++ b/web/entries/Regex_Equivalence.html @@ -1,185 +1,185 @@ Unified Decision Procedures for Regular Expression Equivalence - Archive of Formal Proofs

      Unified Decision Procedures for Regular Expression Equivalence

      -

      Tobias Nipkow 🌐 and Dmitriy Traytel 🌐 +

      Tobias Nipkow 🌐 and Dmitriy Traytel 🌐

      January 30, 2014

      Abstract

      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. The formalization is described in a paper of the same name presented at Interactive Theorem Proving 2014.
      BSD License

      Topics

      Theories of Regex_Equivalence

      \ No newline at end of file diff --git a/web/entries/Regular-Sets.html b/web/entries/Regular-Sets.html --- a/web/entries/Regular-Sets.html +++ b/web/entries/Regular-Sets.html @@ -1,183 +1,183 @@ Regular Sets and Expressions - Archive of Formal Proofs

      Regular Sets and Expressions

      -

      Alexander Krauss 🌐 and Tobias Nipkow 🌐 - with contributions from Manuel Eberl 🌐 +

      Alexander Krauss 🌐 and Tobias Nipkow 🌐 + with contributions from Manuel Eberl 🌐

      May 12, 2010

      Abstract

      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. 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.

      Extended regular expressions with complement and intersection are also defined and an equivalence checker is provided.

      BSD License

      Change history

      [2011-08-26] Christian Urban added a theory about derivatives and partial derivatives of regular expressions
      [2012-05-10] Tobias Nipkow added equivalence checking with partial derivatives

      Topics

      Theories of Regular-Sets

      \ No newline at end of file diff --git a/web/entries/Regular_Algebras.html b/web/entries/Regular_Algebras.html --- a/web/entries/Regular_Algebras.html +++ b/web/entries/Regular_Algebras.html @@ -1,180 +1,180 @@ Regular Algebras - Archive of Formal Proofs

      Regular Algebras

      -

      Simon Foster 🌐 and Georg Struth 🌐 +

      Simon Foster 🌐 and Georg Struth 🌐

      May 21, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of Regular_Algebras

      \ No newline at end of file diff --git a/web/entries/Relational_Disjoint_Set_Forests.html b/web/entries/Relational_Disjoint_Set_Forests.html --- a/web/entries/Relational_Disjoint_Set_Forests.html +++ b/web/entries/Relational_Disjoint_Set_Forests.html @@ -1,166 +1,166 @@ Relational Disjoint-Set Forests - Archive of Formal Proofs

      Relational Disjoint-Set Forests

      -

      Walter Guttmann 🌐 +

      Walter Guttmann 🌐

      August 26, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Relational_Disjoint_Set_Forests

      \ No newline at end of file diff --git a/web/entries/Relational_Minimum_Spanning_Trees.html b/web/entries/Relational_Minimum_Spanning_Trees.html --- a/web/entries/Relational_Minimum_Spanning_Trees.html +++ b/web/entries/Relational_Minimum_Spanning_Trees.html @@ -1,161 +1,161 @@ Relational Minimum Spanning Tree Algorithms - Archive of Formal Proofs

      Relational Minimum Spanning Tree Algorithms

      -

      Walter Guttmann 🌐 and Nicolas Robinson-O’Brien +

      Walter Guttmann 🌐 and Nicolas Robinson-O’Brien

      December 8, 2020

      Abstract

      We verify the correctness of Prim's, Kruskal's and Borůvka's minimum spanning tree algorithms based on algebras for aggregation and minimisation.
      BSD License

      Topics

      Theories of Relational_Minimum_Spanning_Trees

      \ No newline at end of file diff --git a/web/entries/Relational_Paths.html b/web/entries/Relational_Paths.html --- a/web/entries/Relational_Paths.html +++ b/web/entries/Relational_Paths.html @@ -1,185 +1,185 @@ Relational Characterisations of Paths - Archive of Formal Proofs

      Relational Characterisations of Paths

      -

      Walter Guttmann 🌐 and Peter Höfner 🌐 +

      Walter Guttmann 🌐 and Peter Höfner 🌐

      July 13, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Relational_Paths

      \ No newline at end of file diff --git a/web/entries/Robinson_Arithmetic.html b/web/entries/Robinson_Arithmetic.html --- a/web/entries/Robinson_Arithmetic.html +++ b/web/entries/Robinson_Arithmetic.html @@ -1,177 +1,177 @@ Robinson Arithmetic - Archive of Formal Proofs

      Robinson Arithmetic

      -

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐

      September 16, 2020

      Abstract

      We instantiate our syntax-independent logic infrastructure developed in a separate AFP entry to the FOL theory of Robinson arithmetic (also known as Q). The latter was formalised using Nominal Isabelle by adapting Larry Paulson’s formalization of the Hereditarily Finite Set theory.
      BSD License

      Topics

      Theories of Robinson_Arithmetic

      \ No newline at end of file diff --git a/web/entries/Root_Balanced_Tree.html b/web/entries/Root_Balanced_Tree.html --- a/web/entries/Root_Balanced_Tree.html +++ b/web/entries/Root_Balanced_Tree.html @@ -1,188 +1,188 @@ Root-Balanced Tree - Archive of Formal Proofs

      Root-Balanced Tree

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      August 20, 2017

      Abstract

      Andersson introduced general balanced trees, 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 root-balanced trees. Using a lightweight model of execution time, amortized logarithmic complexity is verified in the theorem prover Isabelle.

      This is the Isabelle formalization of the material decribed in the APLAS 2017 article Verified Root-Balanced Trees by the same author, which also presents experimental results that show competitiveness of root-balanced with AVL and red-black trees.

      BSD License

      Topics

      Theories of Root_Balanced_Tree

      \ No newline at end of file diff --git a/web/entries/Routing.html b/web/entries/Routing.html --- a/web/entries/Routing.html +++ b/web/entries/Routing.html @@ -1,170 +1,170 @@ Routing - Archive of Formal Proofs

      Routing

      -

      Julius Michaelis 🌐 and Cornelius Diekmann 🌐 +

      Julius Michaelis 🌐 and Cornelius Diekmann 🌐

      August 31, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Routing

      Depends On

      Used by

      \ No newline at end of file diff --git a/web/entries/SATSolverVerification.html b/web/entries/SATSolverVerification.html --- a/web/entries/SATSolverVerification.html +++ b/web/entries/SATSolverVerification.html @@ -1,179 +1,179 @@ Formal Verification of Modern SAT Solvers - Archive of Formal Proofs

      Formal Verification of Modern SAT Solvers

      -

      Filip Marić 🌐 +

      Filip Marić 🌐

      July 23, 2008

      Abstract

      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:
      • a solver based on classical DPLL procedure (using only a backtrack-search with unit propagation),
      • a very general solver with backjumping and learning (similar to the description given in (Nieuwenhuis et al., 2006)), and
      • a solver with a specific conflict analysis algorithm (similar to the description given in (Krstic et al., 2007)).
      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.
      BSD License

      Topics

      Theories of SATSolverVerification

      \ No newline at end of file diff --git a/web/entries/SC_DOM_Components.html b/web/entries/SC_DOM_Components.html --- a/web/entries/SC_DOM_Components.html +++ b/web/entries/SC_DOM_Components.html @@ -1,188 +1,188 @@ A Formalization of Safely Composable Web Components - Archive of Formal Proofs

      A Formalization of Safely Composable Web Components

      -

      Achim D. Brucker 🌐 and Michael Herzberg 🌐 +

      Achim D. Brucker 🌐 and Michael Herzberg 🌐

      September 28, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of SC_DOM_Components

      \ No newline at end of file diff --git a/web/entries/Safe_Distance.html b/web/entries/Safe_Distance.html --- a/web/entries/Safe_Distance.html +++ b/web/entries/Safe_Distance.html @@ -1,167 +1,167 @@ A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles - Archive of Formal Proofs

      A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

      -

      Albert Rizaldi 📧 and Fabian Immler 🌐 +

      Albert Rizaldi 📧 and Fabian Immler 🌐

      June 1, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Safe_Distance

      Depends On

      \ No newline at end of file diff --git a/web/entries/Saturation_Framework_Extensions.html b/web/entries/Saturation_Framework_Extensions.html --- a/web/entries/Saturation_Framework_Extensions.html +++ b/web/entries/Saturation_Framework_Extensions.html @@ -1,171 +1,171 @@ Extensions to the Comprehensive Framework for Saturation Theorem Proving - Archive of Formal Proofs

      Extensions to the Comprehensive Framework for Saturation Theorem Proving

      -

      Jasmin Christian Blanchette 🌐 and Sophie Tourret 🌐 +

      Jasmin Christian Blanchette 🌐 and Sophie Tourret 🌐

      August 25, 2020

      Abstract

      This Isabelle/HOL formalization extends the AFP entry Saturation_Framework with the following contributions:
      • 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 Ordered_Resultion_Prover;
      • 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;
      • alternative proofs of fairness (and hence saturation and ultimately refutational completeness) for the given clause procedures GC and LGC, based on invariance.
      BSD License

      Topics

      Theories of Saturation_Framework_Extensions

      \ No newline at end of file diff --git a/web/entries/Separation_Algebra.html b/web/entries/Separation_Algebra.html --- a/web/entries/Separation_Algebra.html +++ b/web/entries/Separation_Algebra.html @@ -1,179 +1,179 @@ Separation Algebra - Archive of Formal Proofs

      Separation Algebra

      -

      Gerwin Klein 📧, Rafal Kolanski 📧 and Andrew Boyton 📧 +

      Gerwin Klein 📧, Rafal Kolanski 📧 and Andrew Boyton 📧

      May 11, 2012

      Abstract

      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.

      The ex directory contains example instantiations that include structures such as a heap or virtual memory.

      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.

      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.

      BSD License

      Topics

      Theories of Separation_Algebra

      \ No newline at end of file diff --git a/web/entries/Shadow_DOM.html b/web/entries/Shadow_DOM.html --- a/web/entries/Shadow_DOM.html +++ b/web/entries/Shadow_DOM.html @@ -1,197 +1,197 @@ A Formal Model of the Document Object Model with Shadow Roots - Archive of Formal Proofs

      A Formal Model of the Document Object Model With Shadow Roots

      -

      Achim D. Brucker 🌐 and Michael Herzberg 🌐 +

      Achim D. Brucker 🌐 and Michael Herzberg 🌐

      September 28, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Shadow_DOM

      \ No newline at end of file diff --git a/web/entries/Shadow_SC_DOM.html b/web/entries/Shadow_SC_DOM.html --- a/web/entries/Shadow_SC_DOM.html +++ b/web/entries/Shadow_SC_DOM.html @@ -1,199 +1,199 @@ A Formal Model of the Safely Composable Document Object Model with Shadow Roots - Archive of Formal Proofs

      A Formal Model of the Safely Composable Document Object Model With Shadow Roots

      -

      Achim D. Brucker 🌐 and Michael Herzberg 🌐 +

      Achim D. Brucker 🌐 and Michael Herzberg 🌐

      September 28, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Shadow_SC_DOM

      \ No newline at end of file diff --git a/web/entries/Sigma_Commit_Crypto.html b/web/entries/Sigma_Commit_Crypto.html --- a/web/entries/Sigma_Commit_Crypto.html +++ b/web/entries/Sigma_Commit_Crypto.html @@ -1,186 +1,186 @@ Sigma Protocols and Commitment Schemes - Archive of Formal Proofs

      Sigma Protocols and Commitment Schemes

      -

      David Butler 🌐 and Andreas Lochbihler 🌐 +

      David Butler 🌐 and Andreas Lochbihler 🌐

      October 7, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of Sigma_Commit_Crypto

      \ No newline at end of file diff --git a/web/entries/Simple_Firewall.html b/web/entries/Simple_Firewall.html --- a/web/entries/Simple_Firewall.html +++ b/web/entries/Simple_Firewall.html @@ -1,201 +1,201 @@ Simple Firewall - Archive of Formal Proofs

      Simple Firewall

      -

      Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐 +

      Cornelius Diekmann 🌐, Julius Michaelis 🌐 and Max W. Haslbeck 🌐

      August 24, 2016

      Abstract

      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 Verified iptables Firewall Analysis, IFIP Networking 2016.
      BSD License

      Topics

      Theories of Simple_Firewall

      \ No newline at end of file diff --git a/web/entries/Simplex.html b/web/entries/Simplex.html --- a/web/entries/Simplex.html +++ b/web/entries/Simplex.html @@ -1,181 +1,181 @@ An Incremental Simplex Algorithm with Unsatisfiable Core Generation - Archive of Formal Proofs

      An Incremental Simplex Algorithm With Unsatisfiable Core Generation

      -

      Filip Marić 📧, Mirko Spasić 📧 and René Thiemann 🌐 +

      Filip Marić 📧, Mirko Spasić 📧 and René Thiemann 🌐

      August 24, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Simplex

      \ No newline at end of file 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 @@ -1,174 +1,174 @@ Skew Heap - Archive of Formal Proofs

      Skew Heap

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      August 13, 2014

      Abstract

      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.

      The amortized complexity of skew heaps is analyzed in the AFP entry Amortized Complexity.

      BSD License

      Topics

      Theories of Skew_Heap

      \ No newline at end of file diff --git a/web/entries/Sliding_Window_Algorithm.html b/web/entries/Sliding_Window_Algorithm.html --- a/web/entries/Sliding_Window_Algorithm.html +++ b/web/entries/Sliding_Window_Algorithm.html @@ -1,173 +1,173 @@ Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows - Archive of Formal Proofs

      Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows

      -

      Lukas Heimes, Dmitriy Traytel 🌐 and Joshua Schneider +

      Lukas Heimes, Dmitriy Traytel 🌐 and Joshua Schneider

      April 10, 2020

      Abstract

      Basin et al.'s sliding window algorithm (SWA) 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.
      BSD License

      Topics

      Theories of Sliding_Window_Algorithm

      \ No newline at end of file diff --git a/web/entries/Smooth_Manifolds.html b/web/entries/Smooth_Manifolds.html --- a/web/entries/Smooth_Manifolds.html +++ b/web/entries/Smooth_Manifolds.html @@ -1,184 +1,184 @@ Smooth Manifolds - Archive of Formal Proofs

      Smooth Manifolds

      -

      Fabian Immler 🌐 and Bohua Zhan 🌐 +

      Fabian Immler 🌐 and Bohua Zhan 🌐

      October 22, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Smooth_Manifolds

      \ No newline at end of file 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 @@ -1,157 +1,157 @@ The Sophomore's Dream - Archive of Formal Proofs

      The Sophomore's Dream

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      April 10, 2022

      Abstract

      This article provides a brief formalisation of the two equations known as the Sophomore's Dream, first discovered by Johann Bernoulli in 1697:

      \[\int_0^1 x^{-x}\,\text{d}x = \sum_{n=1}^\infty n^{-n} \quad\text{and}\quad \int_0^1 x^x\,\text{d}x = -\sum_{n=1}^\infty (-n)^{-n}\]
      BSD License

      Topics

      Theories of Sophomores_Dream

      \ No newline at end of file diff --git a/web/entries/Special_Function_Bounds.html b/web/entries/Special_Function_Bounds.html --- a/web/entries/Special_Function_Bounds.html +++ b/web/entries/Special_Function_Bounds.html @@ -1,169 +1,169 @@ Real-Valued Special Functions: Upper and Lower Bounds - Archive of Formal Proofs

      Real-Valued Special Functions: Upper and Lower Bounds

      -

      Lawrence C. Paulson 🌐 +

      Lawrence C. Paulson 🌐

      August 29, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of Special_Function_Bounds

      Depends On

      Related Entries

      \ 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 @@ -1,177 +1,177 @@ Splay Tree - Archive of Formal Proofs

      Splay Tree

      -

      Tobias Nipkow 🌐 +

      Tobias Nipkow 🌐

      August 12, 2014

      Abstract

      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).

      The amortized complexity of splay trees and heaps is analyzed in the AFP entry Amortized Complexity.

      BSD License

      Change history

      [2016-07-12] Moved splay heaps here from Amortized_Complexity

      Topics

      Theories of Splay_Tree

      \ No newline at end of file diff --git a/web/entries/Stern_Brocot.html b/web/entries/Stern_Brocot.html --- a/web/entries/Stern_Brocot.html +++ b/web/entries/Stern_Brocot.html @@ -1,161 +1,161 @@ The Stern-Brocot Tree - Archive of Formal Proofs

      The Stern-Brocot Tree

      -

      Peter Gammie 🌐 and Andreas Lochbihler 🌐 +

      Peter Gammie 🌐 and Andreas Lochbihler 🌐

      December 22, 2015

      Abstract

      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.

      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.

      BSD License

      Topics

      Theories of Stern_Brocot

      Depends On

      \ No newline at end of file diff --git a/web/entries/Stirling_Formula.html b/web/entries/Stirling_Formula.html --- a/web/entries/Stirling_Formula.html +++ b/web/entries/Stirling_Formula.html @@ -1,166 +1,166 @@ Stirling's formula - Archive of Formal Proofs

      Stirling's Formula

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      September 1, 2016

      Abstract

      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 Graham Jameson.

      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 Γ is also extended to complex arguments.

      BSD License

      Topics

      Theories of Stirling_Formula

      \ No newline at end of file diff --git a/web/entries/Stochastic_Matrices.html b/web/entries/Stochastic_Matrices.html --- a/web/entries/Stochastic_Matrices.html +++ b/web/entries/Stochastic_Matrices.html @@ -1,177 +1,177 @@ Stochastic Matrices and the Perron-Frobenius Theorem - Archive of Formal Proofs

      Stochastic Matrices and the Perron-Frobenius Theorem

      -

      René Thiemann 🌐 +

      René Thiemann 🌐

      November 22, 2017

      Abstract

      Stochastic matrices are a convenient way to model discrete-time and finite state Markov chains. The Perron–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–Frobenius theorem to prove that stationary distributions always exist, and they are unique if the stochastic matrix is irreducible.
      BSD License

      Topics

      Theories of Stochastic_Matrices

      \ No newline at end of file diff --git a/web/entries/Stone_Algebras.html b/web/entries/Stone_Algebras.html --- a/web/entries/Stone_Algebras.html +++ b/web/entries/Stone_Algebras.html @@ -1,167 +1,167 @@ Stone Algebras - Archive of Formal Proofs

      Stone Algebras

      -

      Walter Guttmann 🌐 +

      Walter Guttmann 🌐

      September 6, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Stone_Algebras

      \ No newline at end of file diff --git a/web/entries/Stone_Kleene_Relation_Algebras.html b/web/entries/Stone_Kleene_Relation_Algebras.html --- a/web/entries/Stone_Kleene_Relation_Algebras.html +++ b/web/entries/Stone_Kleene_Relation_Algebras.html @@ -1,185 +1,185 @@ Stone-Kleene Relation Algebras - Archive of Formal Proofs

      Stone-Kleene Relation Algebras

      -

      Walter Guttmann 🌐 +

      Walter Guttmann 🌐

      July 6, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Stone_Kleene_Relation_Algebras

      \ No newline at end of file diff --git a/web/entries/Stone_Relation_Algebras.html b/web/entries/Stone_Relation_Algebras.html --- a/web/entries/Stone_Relation_Algebras.html +++ b/web/entries/Stone_Relation_Algebras.html @@ -1,180 +1,180 @@ Stone Relation Algebras - Archive of Formal Proofs

      Stone Relation Algebras

      -

      Walter Guttmann 🌐 +

      Walter Guttmann 🌐

      February 7, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of Stone_Relation_Algebras

      \ No newline at end of file diff --git a/web/entries/Stream-Fusion.html b/web/entries/Stream-Fusion.html --- a/web/entries/Stream-Fusion.html +++ b/web/entries/Stream-Fusion.html @@ -1,167 +1,167 @@ Stream Fusion - Archive of Formal Proofs

      Stream Fusion

      -

      Brian Huffman 🌐 +

      Brian Huffman 🌐

      April 29, 2009

      Abstract

      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 online.)

      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.
      BSD License

      Topics

      Theories of Stream-Fusion

      \ No newline at end of file diff --git a/web/entries/Stream_Fusion_Code.html b/web/entries/Stream_Fusion_Code.html --- a/web/entries/Stream_Fusion_Code.html +++ b/web/entries/Stream_Fusion_Code.html @@ -1,171 +1,171 @@ Stream Fusion in HOL with Code Generation - Archive of Formal Proofs

      Stream Fusion in HOL With Code Generation

      -

      Andreas Lochbihler 🌐 and Alexandra Maximova 📧 +

      Andreas Lochbihler 🌐 and Alexandra Maximova 📧

      October 10, 2014

      Abstract

      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 AFP entry 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.]
      BSD License

      Topics

      Theories of Stream_Fusion_Code

      \ No newline at end of file diff --git a/web/entries/Sturm_Sequences.html b/web/entries/Sturm_Sequences.html --- a/web/entries/Sturm_Sequences.html +++ b/web/entries/Sturm_Sequences.html @@ -1,181 +1,181 @@ Sturm's Theorem - Archive of Formal Proofs

      Sturm's Theorem

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      January 11, 2014

      Abstract

      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 ∈ ℝ”.
      BSD License

      Topics

      Theories of Sturm_Sequences

      \ No newline at end of file diff --git a/web/entries/Subset_Boolean_Algebras.html b/web/entries/Subset_Boolean_Algebras.html --- a/web/entries/Subset_Boolean_Algebras.html +++ b/web/entries/Subset_Boolean_Algebras.html @@ -1,166 +1,166 @@ A Hierarchy of Algebras for Boolean Subsets - Archive of Formal Proofs

      A Hierarchy of Algebras for Boolean Subsets

      -

      Walter Guttmann 🌐 and Bernhard Möller 🌐 +

      Walter Guttmann 🌐 and Bernhard Möller 🌐

      January 31, 2020

      Abstract

      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.
      BSD License

      Topics

      Theories of Subset_Boolean_Algebras

      \ No newline at end of file diff --git a/web/entries/Symmetric_Polynomials.html b/web/entries/Symmetric_Polynomials.html --- a/web/entries/Symmetric_Polynomials.html +++ b/web/entries/Symmetric_Polynomials.html @@ -1,197 +1,197 @@ Symmetric Polynomials - Archive of Formal Proofs

      Symmetric Polynomials

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      September 25, 2018

      Abstract

      A symmetric polynomial is a polynomial in variables X1,…,Xn that does not discriminate between its variables, i. 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.

      This article provides a definition of symmetric polynomials and the elementary symmetric polynomials e1,…,en and proofs of their basic properties, including three notable ones:

      • Vieta's formula, which gives an explicit expression for the k-th coefficient of a univariate monic polynomial in terms of its roots x1,…,xn, namely ck = (-1)n-k en-k(x1,…,xn).
      • 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.
      • Third, as a corollary of the previous two, that given a polynomial over some ring R, any symmetric polynomial combination of its roots is also in R even when the roots are not.

      Both the symmetry property itself and the witness for the Fundamental Theorem are executable.

      BSD License

      Topics

      Theories of Symmetric_Polynomials

      \ No newline at end of file diff --git a/web/entries/Syntax_Independent_Logic.html b/web/entries/Syntax_Independent_Logic.html --- a/web/entries/Syntax_Independent_Logic.html +++ b/web/entries/Syntax_Independent_Logic.html @@ -1,197 +1,197 @@ Syntax-Independent Logic Infrastructure - Archive of Formal Proofs

      Syntax-Independent Logic Infrastructure

      -

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐 +

      Andrei Popescu 🌐 and Dmitriy Traytel 🌐

      September 16, 2020

      Abstract

      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 Robinson_Arithmetic and to hereditarily finite set theory in the AFP entries Goedel_HFSet_Semantic and Goedel_HFSet_Semanticless, which are part of our formalization of Gödel's Incompleteness Theorems described in our CADE-27 paper A Formally Verified Abstract Account of Gödel's Incompleteness Theorems.
      BSD License

      Topics

      Theories of Syntax_Independent_Logic

      \ No newline at end of file diff --git a/web/entries/Taylor_Models.html b/web/entries/Taylor_Models.html --- a/web/entries/Taylor_Models.html +++ b/web/entries/Taylor_Models.html @@ -1,184 +1,184 @@ Taylor Models - Archive of Formal Proofs

      Taylor Models

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      Christoph Traut and Fabian Immler 🌐 +

      Christoph Traut and Fabian Immler 🌐

      January 8, 2018

      Abstract

      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.
      BSD License

      Topics

      Theories of Taylor_Models

      \ No newline at end of file diff --git a/web/entries/Timed_Automata.html b/web/entries/Timed_Automata.html --- a/web/entries/Timed_Automata.html +++ b/web/entries/Timed_Automata.html @@ -1,203 +1,203 @@ Timed Automata - Archive of Formal Proofs

      Timed Automata

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      Simon Wimmer 🌐 +

      Simon Wimmer 🌐

      March 8, 2016

      Abstract

      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.
      BSD License

      Topics

      Theories of Timed_Automata

      \ No newline at end of file diff --git a/web/entries/Transitive_Models.html b/web/entries/Transitive_Models.html --- a/web/entries/Transitive_Models.html +++ b/web/entries/Transitive_Models.html @@ -1,206 +1,206 @@ Transitive Models of Fragments of ZFC - Archive of Formal Proofs

      Transitive Models of Fragments of ZFC

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      Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧 +

      Emmanuel Gunther 📧, Miguel Pagano 🌐, Pedro Sánchez Terraf 🌐 and Matías Steinberg 📧

      March 3, 2022

      Abstract

      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.
      BSD License

      Topics

      Theories of Transitive_Models

      \ No newline at end of file diff --git a/web/entries/Treaps.html b/web/entries/Treaps.html --- a/web/entries/Treaps.html +++ b/web/entries/Treaps.html @@ -1,187 +1,187 @@ Treaps - Archive of Formal Proofs

      Treaps

      -

      Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐 +

      Max W. Haslbeck 🌐, Manuel Eberl 🌐 and Tobias Nipkow 🌐

      February 6, 2018

      Abstract

      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.

      In particular, by choosing these priorities at random upon insertion of an element, we can pretend that we inserted the elements in random order, 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.

      BSD License

      Topics

      Theories of Treaps

      \ No newline at end of file diff --git a/web/entries/Triangle.html b/web/entries/Triangle.html --- a/web/entries/Triangle.html +++ b/web/entries/Triangle.html @@ -1,179 +1,179 @@ Basic Geometric Properties of Triangles - Archive of Formal Proofs

      Basic Geometric Properties of Triangles

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      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 28, 2015

      Abstract

      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.

      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.

      BSD License

      Topics

      Theories of Triangle

      \ No newline at end of file diff --git a/web/entries/Trie.html b/web/entries/Trie.html --- a/web/entries/Trie.html +++ b/web/entries/Trie.html @@ -1,174 +1,174 @@ Trie - Archive of Formal Proofs

      Trie

      -

      Andreas Lochbihler 🌐 and Tobias Nipkow 🌐 +

      Andreas Lochbihler 🌐 and Tobias Nipkow 🌐

      March 30, 2015

      Abstract

      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.
      BSD License

      Extra 0

      Origin: This article was extracted from existing articles by the authors.

      Topics

      Theories of Trie

      \ No newline at end of file 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 @@ -1,183 +1,183 @@ Types, Tableaus and Gödel’s God in Isabelle/HOL - Archive of Formal Proofs

      Types, Tableaus and Gödel’s God in Isabelle/HOL

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      David Fuenmayor 📧 and Christoph Benzmüller 🌐 +

      David Fuenmayor 📧 and Christoph Benzmüller 🌐

      May 1, 2017

      Abstract

      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''.)
      BSD License

      Topics

      Theories of Types_Tableaus_and_Goedels_God

      \ No newline at end of file diff --git a/web/entries/UPF.html b/web/entries/UPF.html --- a/web/entries/UPF.html +++ b/web/entries/UPF.html @@ -1,188 +1,188 @@ The Unified Policy Framework (UPF) - Archive of Formal Proofs

      The Unified Policy Framework (UPF)

      -

      Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧 +

      Achim D. Brucker 📧, Lukas Brügger 📧 and Burkhart Wolff 📧

      November 28, 2014

      Abstract

      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.
      BSD License

      Topics

      Theories of UPF

      \ No newline at end of file diff --git a/web/entries/UPF_Firewall.html b/web/entries/UPF_Firewall.html --- a/web/entries/UPF_Firewall.html +++ b/web/entries/UPF_Firewall.html @@ -1,218 +1,218 @@ Formal Network Models and Their Application to Firewall Policies - Archive of Formal Proofs

      Formal Network Models and Their Application to Firewall Policies

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      Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐 +

      Achim D. Brucker 🌐, Lukas Brügger and Burkhart Wolff 🌐

      January 8, 2017

      Abstract

      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.
      BSD License

      Topics

      Theories of UPF_Firewall

      \ No newline at end of file diff --git a/web/entries/UTP.html b/web/entries/UTP.html --- a/web/entries/UTP.html +++ b/web/entries/UTP.html @@ -1,228 +1,228 @@ Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming - Archive of Formal Proofs

      Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming

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      Simon Foster 🌐, Frank Zeyda, Yakoub Nemouchi 📧, Pedro Ribeiro and Burkhart Wolff 📧 +

      Simon Foster 🌐, Frank Zeyda, Yakoub Nemouchi 📧, Pedro Ribeiro and Burkhart Wolff 📧

      February 1, 2019

      Abstract

      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.
      BSD License

      Topics

      Theories of UTP-Toolkit

      Theories of UTP

      \ No newline at end of file diff --git a/web/entries/VerifyThis2018.html b/web/entries/VerifyThis2018.html --- a/web/entries/VerifyThis2018.html +++ b/web/entries/VerifyThis2018.html @@ -1,180 +1,180 @@ VerifyThis 2018 - Polished Isabelle Solutions - Archive of Formal Proofs

      VerifyThis 2018 - Polished Isabelle Solutions

      -

      Peter Lammich 🌐 and Simon Wimmer 🌐 +

      Peter Lammich 🌐 and Simon Wimmer 🌐

      April 27, 2018

      Abstract

      VerifyThis 2018 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.
      BSD License

      Topics

      Theories of VerifyThis2018

      \ No newline at end of file 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 @@ -1,173 +1,173 @@ Weight-Balanced Trees - Archive of Formal Proofs

      Weight-Balanced Trees

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      Tobias Nipkow 🌐 and Stefan Dirix +

      Tobias Nipkow 🌐 and Stefan Dirix

      March 13, 2018

      Abstract

      This theory provides a verified implementation of weight-balanced trees following the work of Hirai and Yamamoto 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.
      BSD License

      Topics

      Theories of Weight_Balanced_Trees

      \ No newline at end of file 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 @@ -1,161 +1,161 @@ The Irrationality of ζ(3) - Archive of Formal Proofs

      The Irrationality of Ζ(3)

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      December 27, 2019

      Abstract

      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 Filaseta's presentation of Beukers's proof.

      BSD License

      Topics

      Theories of Zeta_3_Irrational

      \ No newline at end of file diff --git a/web/entries/Zeta_Function.html b/web/entries/Zeta_Function.html --- a/web/entries/Zeta_Function.html +++ b/web/entries/Zeta_Function.html @@ -1,192 +1,192 @@ The Hurwitz and Riemann ζ Functions - Archive of Formal Proofs

      The Hurwitz and Riemann Ζ Functions

      -

      Manuel Eberl 🌐 +

      Manuel Eberl 🌐

      October 12, 2017

      Abstract

      This entry builds upon the results about formal and analytic Dirichlet series to define the Hurwitz ζ function ζ(a,s) and, based on that, the Riemann ζ function ζ(s). This is done by first defining them for ℜ(z) > 1 and then successively extending the domain to the left using the Euler–MacLaurin formula.

      Apart from the most basic facts such as analyticity, the following results are provided:

      • the Stieltjes constants and the Laurent expansion of ζ(s) at s = 1
      • the non-vanishing of ζ(s) for ℜ(z) ≥ 1
      • the relationship between ζ(a,s) and Γ
      • the special values at negative integers and positive even integers
      • Hurwitz's formula and the reflection formula for ζ(s)
      • the Hadjicostas–Chapman formula

      The entry also contains Euler's analytic proof of the infinitude of primes, based on the fact that ζ(s) has a pole at s = 1.

      BSD License

      Topics

      Theories of Zeta_Function

      \ No newline at end of file