diff --git a/metadata/authors.toml b/metadata/authors.toml
--- a/metadata/authors.toml
+++ b/metadata/authors.toml
@@ -1,7647 +1,7672 @@
 
 [abdulaziz]
 name = "Mohammad Abdulaziz"
 
 [abdulaziz.emails]
 
 [abdulaziz.emails.abdulaziz_email]
 user = [
   "mohammad",
   "abdulaziz",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [abdulaziz.emails.abdulaziz_email1]
 user = [
   "mohammad",
   "abdulaziz8",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [abdulaziz.homepages]
 abdulaziz_homepage = "http://home.in.tum.de/~mansour/"
 
 [adelsberger]
 name = "Stephan Adelsberger"
 
 [adelsberger.emails]
 
 [adelsberger.emails.adelsberger_email]
 user = [
   "stvienna",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [adelsberger.homepages]
 adelsberger_homepage = "http://nm.wu.ac.at/nm/sadelsbe"
 
 [aehlig]
 name = "Klaus Aehlig"
 
 [aehlig.emails]
 
 [aehlig.homepages]
 aehlig_homepage = "http://www.linta.de/~aehlig/"
 
 [aissat]
 name = "Romain Aissat"
 
 [aissat.emails]
 
 [aissat.homepages]
 
 [amani]
 name = "Sidney Amani"
 
 [amani.emails]
 
 [amani.emails.amani_email]
 user = [
   "sidney",
   "amani",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [amani.homepages]
 
 [ammer]
 name = "Thomas Ammer"
 
 [ammer.emails]
 
 [ammer.emails.ammer_email]
 user = [
   "thomas",
   "ammer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [ammer.homepages]
 
 [andreka]
 name = "Hajnal Andreka"
 
 [andreka.emails]
 
 [andreka.homepages]
 andreka_homepage = "https://renyi.hu/en/researchers/hajnal-andreka"
 
 [andronick]
 name = "June Andronick"
 
 [andronick.emails]
 
 [andronick.homepages]
 
 [aransay]
 name = "Jesús Aransay"
 
 [aransay.emails]
 
 [aransay.emails.aransay_email]
 user = [
   "jesus-maria",
   "aransay",
 ]
 host = [
   "unirioja",
   "es",
 ]
 
 [aransay.homepages]
 aransay_homepage = "https://www.unirioja.es/cu/jearansa"
 
 [argyraki]
 name = "Angeliki Koutsoukou-Argyraki"
 
 [argyraki.emails]
 
 [argyraki.emails.argyraki_email]
 user = [
   "ak2110",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [argyraki.homepages]
 argyraki_homepage = "https://www.cl.cam.ac.uk/~ak2110/"
 argyraki_homepage2 = "https://www.cst.cam.ac.uk/people/ak2110"
 
 [armstrong]
 name = "Alasdair Armstrong"
 
 [armstrong.emails]
 
 [armstrong.homepages]
 
 [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"
 
 [avigad]
 name = "Jeremy Avigad"
 
 [avigad.emails]
 
 [avigad.emails.avigad_email]
 user = [
   "avigad",
 ]
 host = [
   "cmu",
   "edu",
 ]
 
 [avigad.homepages]
 avigad_homepage = "http://www.andrew.cmu.edu/user/avigad/"
 
 [back]
 name = "Ralph-Johan Back"
 
 [back.emails]
 
 [back.homepages]
 back_homepage = "http://users.abo.fi/Ralph-Johan.Back/"
 
 [baksys]
 name = "Mantas Bakšys"
 
 [baksys.emails]
 
 [baksys.emails.baksys_email]
 user = [
   "mb2412",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [baksys.homepages]
 baksys_homepage = "https://github.com/MantasBaksys"
 
 [balbach]
 name = "Frank J. Balbach"
 
 [balbach.emails]
 
 [balbach.emails.balbach_email]
 user = [
   "frank-balbach",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [balbach.homepages]
 
 [ballarin]
 name = "Clemens Ballarin"
 
 [ballarin.emails]
 
 [ballarin.emails.ballarin_email]
 user = [
   "ballarin",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [ballarin.homepages]
 ballarin_homepage = "http://www21.in.tum.de/~ballarin/"
 
 [ballenghien]
 name = "Benoît Ballenghien"
 
 [ballenghien.emails]
 
 [ballenghien.emails.ballenghien_email]
 user = [
   "benoit",
   "ballenghien",
 ]
 host = [
   "universite-paris-saclay",
   "fr",
 ]
 
 [ballenghien.homepages]
 
 [barsotti]
 name = "Damián Barsotti"
 
 [barsotti.emails]
 
 [barsotti.homepages]
 barsotti_homepage = "http://www.cs.famaf.unc.edu.ar/~damian/"
 
 [bauer]
 name = "Gertrud Bauer"
 
 [bauer.emails]
 
 [bauer.homepages]
 
 [bauereiss]
 name = "Thomas Bauereiss"
 
 [bauereiss.emails]
 
 [bauereiss.emails.bauereiss_email]
 user = [
   "thomas",
 ]
 host = [
   "bauereiss",
   "name",
 ]
 
 [bauereiss.homepages]
 
 [bayer]
 name = "Jonas Bayer"
 
 [bayer.emails]
 
 [bayer.emails.bayer_email]
 user = [
   "jonas",
   "bayer999",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bayer.homepages]
 
 [becker]
 name = "Heiko Becker"
 
 [becker.emails]
 
 [becker.emails.becker_email]
 user = [
   "hbecker",
 ]
 host = [
   "mpi-sws",
   "org",
 ]
 
 [becker.homepages]
 
 [beeren]
 name = "Joel Beeren"
 
 [beeren.emails]
 
 [beeren.homepages]
 
 [bella]
 name = "Giampaolo Bella"
 
 [bella.emails]
 
 [bella.emails.bella_email]
 user = [
   "giamp",
 ]
 host = [
   "dmi",
   "unict",
   "it",
 ]
 
 [bella.homepages]
 bella_homepage = "http://www.dmi.unict.it/~giamp/"
 
 [bengtson]
 name = "Jesper Bengtson"
 
 [bengtson.emails]
 
 [bengtson.homepages]
 bengtson_homepage = "http://www.itu.dk/people/jebe"
 
 [bentkamp]
 name = "Alexander Bentkamp"
 
 [bentkamp.emails]
 
 [bentkamp.emails.bentkamp_email]
 user = [
   "bentkamp",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bentkamp.emails.bentkamp_email1]
 user = [
   "a",
   "bentkamp",
 ]
 host = [
   "vu",
   "nl",
 ]
 
 [bentkamp.homepages]
 bentkamp_homepage = "https://www.cs.vu.nl/~abp290/"
 
 [benzmueller]
 name = "Christoph Benzmüller"
 
 [benzmueller.emails]
 
 [benzmueller.emails.benzmueller_email]
 user = [
   "c",
   "benzmueller",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [benzmueller.emails.benzmueller_email1]
 user = [
   "c",
   "benzmueller",
 ]
 host = [
   "fu-berlin",
   "de",
 ]
 
 [benzmueller.homepages]
 benzmueller_homepage = "http://christoph-benzmueller.de"
 benzmueller_homepage1 = "http://page.mi.fu-berlin.de/cbenzmueller/"
 
 [beresford]
 name = "Alastair R. Beresford"
 
 [beresford.emails]
 
 [beresford.emails.beresford_email]
 user = [
   "arb33",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [beresford.homepages]
 
 [berghofer]
 name = "Stefan Berghofer"
 
 [berghofer.emails]
 
 [berghofer.emails.berghofer_email]
 user = [
   "berghofe",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [berghofer.homepages]
 berghofer_homepage = "http://www.in.tum.de/~berghofe"
 
 [bergstroem]
 name = "Axel Bergström"
 
 [bergstroem.emails]
 
 [bergstroem.emails.bergstroem_email]
 user = [
   "axel",
   "bergstrom00",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bergstroem.homepages]
 
 [beringer]
 name = "Lennart Beringer"
 
 [beringer.emails]
 
 [beringer.emails.beringer_email]
 user = [
   "lennart",
   "beringer",
 ]
 host = [
   "ifi",
   "lmu",
   "de",
 ]
 
 [beringer.homepages]
 
 [bharadwaj]
 name = "Abhijith Bharadwaj"
 
 [bharadwaj.emails]
 
 [bharadwaj.homepages]
 
 [bhatt]
 name = "Bhargav Bhatt"
 
 [bhatt.emails]
 
 [bhatt.emails.bhatt_email]
 user = [
   "bhargav",
   "bhatt",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [bhatt.homepages]
 
 [biendarra]
 name = "Julian Biendarra"
 
 [biendarra.emails]
 
 [biendarra.homepages]
 
 [bisping]
 name = "Benjamin Bisping"
 orcid = "0000-0002-0637-0171"
 
 [bisping.emails]
 
 [bisping.emails.bisping_email]
 user = [
   "benjamin",
   "bisping",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [bisping.homepages]
 bisping_homepage = "https://bbisping.de"
 
 [blanchette]
 name = "Jasmin Christian Blanchette"
 
 [blanchette.emails]
 
 [blanchette.emails.blanchette_email]
 user = [
   "jasmin",
   "blanchette",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [blanchette.emails.blanchette_email1]
 user = [
   "j",
   "c",
   "blanchette",
 ]
 host = [
   "vu",
   "nl",
 ]
 
 [blanchette.homepages]
 blanchette_homepage = "http://www21.in.tum.de/~blanchet"
 blanchette_homepage1 = "https://www.cs.vu.nl/~jbe248/"
 
 [blasum]
 name = "Holger Blasum"
 
 [blasum.emails]
 
 [blasum.emails.blasum_email]
 user = [
   "holger",
   "blasum",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [blasum.homepages]
 
 [blumson]
 name = "Ben Blumson"
 
 [blumson.emails]
 
 [blumson.emails.blumson_email]
 user = [
   "benblumson",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [blumson.homepages]
 blumson_homepage = "https://philpeople.org/profiles/ben-blumson"
 
 [bockenek]
 name = "Joshua Bockenek"
 
 [bockenek.emails]
 
 [bockenek.homepages]
 
 [boehme]
 name = "Sascha Böhme"
 
 [boehme.emails]
 
 [boehme.emails.boehme_email]
 user = [
   "boehmes",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [boehme.homepages]
 boehme_homepage = "http://www21.in.tum.de/~boehmes/"
 
 [bohrer]
 name = "Rose Bohrer"
 
 [bohrer.emails]
 
 [bohrer.emails.bohrer_email]
 user = [
   "rose",
   "bohrer",
   "cs",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bohrer.homepages]
 
 [bootle]
 name = "Jonathan Bootle"
 
 [bootle.emails]
 
 [bootle.emails.bootle_email]
 user = [
   "JBT",
 ]
 host = [
   "zurich",
   "ibm",
   "com",
 ]
 
 [bootle.homepages]
 
 [bordg]
 name = "Anthony Bordg"
 
 [bordg.emails]
 
 [bordg.emails.bordg_email]
 user = [
   "apdb3",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [bordg.homepages]
 bordg_homepage = "https://sites.google.com/site/anthonybordg/"
 
 [borgstroem]
 name = "Johannes Borgström"
 
 [borgstroem.emails]
 
 [borgstroem.emails.borgstroem_email]
 user = [
   "johannes",
   "borgstrom",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [borgstroem.homepages]
 
 [bortin]
 name = "Maksym Bortin"
 
 [bortin.emails]
 
 [bortin.emails.bortin_email]
 user = [
   "maksym",
   "bortin",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [bortin.emails.bortin_email1]
 user = [
   "mbortin",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bortin.homepages]
 
 [bottesch]
 name = "Ralph Bottesch"
 
 [bottesch.emails]
 
 [bottesch.emails.bottesch_email]
 user = [
   "ralph",
   "bottesch",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [bottesch.homepages]
 bottesch_homepage = "http://cl-informatik.uibk.ac.at/users/bottesch/"
 
 [boulanger]
 name = "Frédéric Boulanger"
 
 [boulanger.emails]
 
 [boulanger.emails.boulanger_email]
 user = [
   "frederic",
   "boulanger",
 ]
 host = [
   "centralesupelec",
   "fr",
 ]
 
 [boulanger.homepages]
 
 [bourke]
 name = "Timothy Bourke"
 
 [bourke.emails]
 
 [bourke.emails.bourke_email]
 user = [
   "tim",
 ]
 host = [
   "tbrk",
   "org",
 ]
 
 [bourke.homepages]
 bourke_homepage = "http://www.tbrk.org"
 
 [boutry]
 name = "Pierre Boutry"
 
 [boutry.emails]
 
 [boutry.emails.boutry_email]
 user = [
   "boutry",
 ]
 host = [
   "unistra",
   "fr",
 ]
 
 [boutry.homepages]
 
 [boyton]
 name = "Andrew Boyton"
 
 [boyton.emails]
 
 [boyton.emails.boyton_email]
 user = [
   "andrew",
   "boyton",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [boyton.homepages]
 
 [bracevac]
 name = "Oliver Bračevac"
 
 [bracevac.emails]
 
 [bracevac.emails.bracevac_email]
 user = [
   "bracevac",
 ]
 host = [
   "st",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [bracevac.homepages]
 
 [brandt]
 name = "Felix Brandt"
 
 [brandt.emails]
 
 [brandt.homepages]
 brandt_homepage = "http://dss.in.tum.de/staff/brandt.html"
 
 [breitner]
 name = "Joachim Breitner"
 
 [breitner.emails]
 
 [breitner.emails.breitner_email]
 user = [
   "mail",
 ]
 host = [
   "joachim-breitner",
   "de",
 ]
 
 [breitner.emails.breitner_email1]
 user = [
   "joachim",
 ]
 host = [
   "cis",
   "upenn",
   "edu",
 ]
 
 [breitner.homepages]
 breitner_homepage = "http://pp.ipd.kit.edu/~breitner"
 
 [brien]
 name = "Nicolas Robinson-O'Brien"
 
 [brien.emails]
 
 [brien.homepages]
 
 [brinkop]
 name = "Hauke Brinkop"
 
 [brinkop.emails]
 
 [brinkop.emails.brinkop_email]
 user = [
   "hauke",
   "brinkop",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [brinkop.homepages]
 
 [brodmann]
 name = "Paul-David Brodmann"
 
 [brodmann.emails]
 
 [brodmann.emails.brodmann_email]
 user = [
   "p",
   "brodmann",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [brodmann.homepages]
 
 [brucker]
 name = "Achim D. Brucker"
 
 [brucker.emails]
 
 [brucker.emails.brucker_email]
 user = [
   "a",
   "brucker",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [brucker.emails.brucker_email2]
 user = [
   "adbrucker",
 ]
 host = [
   "0x5f",
   "org",
 ]
 
 [brucker.homepages]
 brucker_homepage = "https://www.brucker.ch/"
 
 [bruegger]
 name = "Lukas Brügger"
 
 [bruegger.emails]
 
 [bruegger.emails.bruegger_email]
 user = [
   "lukas",
   "a",
   "bruegger",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bruegger.homepages]
 
 [brun]
 name = "Matthias Brun"
 
 [brun.emails]
 
 [brun.emails.brun_email]
 user = [
   "matthias",
   "brun",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [brun.homepages]
 
 [brunner]
 name = "Julian Brunner"
 
 [brunner.emails]
 
 [brunner.emails.brunner_email]
 user = [
   "brunnerj",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [brunner.homepages]
 brunner_homepage = "http://www21.in.tum.de/~brunnerj/"
 
 [bulwahn]
 name = "Lukas Bulwahn"
 
 [bulwahn.emails]
 
 [bulwahn.emails.bulwahn_email]
 user = [
   "lukas",
   "bulwahn",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bulwahn.homepages]
 
 [buss]
 name = "Sebastián Buss"
 
 [buss.emails]
 
 [buss.emails.buss_email]
 user = [
   "sbuss94",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [buss.homepages]
 
 [butler]
 name = "David Butler"
 
 [butler.emails]
 
 [butler.emails.butler_email]
 user = [
   "dbutler",
 ]
 host = [
   "turing",
   "ac",
   "uk",
 ]
 
 [butler.homepages]
 butler_homepage = "https://www.turing.ac.uk/people/doctoral-students/david-butler"
 
 [buyse]
 name = "Maxime Buyse"
 
 [buyse.emails]
 
 [buyse.emails.buyse_email]
 user = [
   "maxime",
   "buyse",
 ]
 host = [
   "polytechnique",
   "edu",
 ]
 
 [buyse.homepages]
 
 [caballero]
 name = "José Manuel Rodríguez Caballero"
 
 [caballero.emails]
 
 [caballero.emails.caballero_email]
 user = [
   "jose",
   "manuel",
   "rodriguez",
   "caballero",
 ]
 host = [
   "ut",
   "ee",
 ]
 
 [caballero.homepages]
 caballero_homepage = "https://josephcmac.github.io/"
 
 [calk]
 name = "Cameron Calk"
 
 [calk.emails]
 
 [calk.homepages]
 
 [caminati]
 name = "Marco B. Caminati"
 
 [caminati.emails]
 
 [caminati.homepages]
 
 [campo]
 name = "Alejandro del Campo"
 
 [campo.emails]
 
 [campo.emails.campo_email]
 user = [
   "alejandro",
   "del-campo",
 ]
 host = [
   "alum",
   "unirioja",
   "es",
 ]
 
 [campo.homepages]
 
 [chaieb]
 name = "Amine Chaieb"
 
 [chaieb.emails]
 
 [chaieb.homepages]
 
 [chapman]
 name = "Peter Chapman"
 
 [chapman.emails]
 
 [chapman.emails.chapman_email]
 user = [
   "pc",
 ]
 host = [
   "cs",
   "st-andrews",
   "ac",
   "uk",
 ]
 
 [chapman.homepages]
 
 [chen]
 name = "L. Chen"
 
 [chen.emails]
 
 [chen.homepages]
 
 [chenj]
 name = "Jamie Chen"
 orcid = "0009-0008-5396-6059"
 
 [chenj.emails]
 
 [chenj.emails.chenj_email]
 user = [
   "jamiechen",
 ]
 host = [
   "tutanota",
   "com",
 ]
 
 [chenj.homepages]
 chenj_homepage = "https://gitlab.com/Jamie-Chen"
 
 [chevalier]
 name = "Loïc Chevalier"
 
 [chevalier.emails]
 
 [chevalier.homepages]
 
 [christfort]
 name = "Axel Christfort"
 
 [christfort.emails]
 
 [christfort.emails.christfort_email]
 user = [
   "axel",
 ]
 host = [
   "di",
   "ku",
   "dk",
 ]
 
 [christfort.homepages]
 
 [clouston]
 name = "Ranald Clouston"
 
 [clouston.emails]
 
 [clouston.emails.clouston_email]
 user = [
   "ranald",
   "clouston",
 ]
 host = [
   "cs",
   "au",
   "dk",
 ]
 
 [clouston.homepages]
 
 [cock]
 name = "David Cock"
 
 [cock.emails]
 
 [cock.emails.cock_email]
 user = [
   "david",
   "cock",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [cock.homepages]
 
 [coghetto]
 name = "Roland Coghetto"
 
 [coghetto.emails]
 
 [coghetto.emails.coghetto_email]
 user = [
   "roland_coghetto",
 ]
 host = [
   "hotmail",
   "com",
 ]
 
 [coghetto.homepages]
 
 [coglio]
 name = "Alessandro Coglio"
 
 [coglio.emails]
 
 [coglio.emails.coglio_email]
 user = [
   "coglio",
 ]
 host = [
   "kestrel",
   "edu",
 ]
 
 [coglio.homepages]
 coglio_homepage = "http://www.kestrel.edu/~coglio"
 
 [cohen]
 name = "Ernie Cohen"
 
 [cohen.emails]
 
 [cohen.emails.cohen_email]
 user = [
   "ecohen",
 ]
 host = [
   "amazon",
   "com",
 ]
 
 [cohen.homepages]
 
 [cordwell]
 name = "Katherine Kosaian"
 
 [cordwell.emails]
 
 [cordwell.emails.cordwell_email]
 user = [
   "kcordwel",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [cordwell.homepages]
 cordwell_homepage = "https://www.cs.cmu.edu/~kcordwel/"
 
 [cousin]
 name = "Marie Cousin"
 
 [cousin.emails]
 
 [cousin.emails.cousin_email]
 user = [
   "marie",
   "cousin",
 ]
 host = [
   "grenoble-inp",
   "org",
 ]
 
 [cousin.homepages]
 
 [cremer]
 name = "Nils Cremer"
 
 [cremer.emails]
 
 [cremer.emails.cremer_email]
 user = [
   "nils",
   "cremer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [cremer.homepages]
 
 [crighton]
 name = "Aaron Crighton"
 
 [crighton.emails]
 
 [crighton.emails.crighton_email]
 user = [
   "crightoa",
 ]
 host = [
   "mcmaster",
   "ca",
 ]
 
 [crighton.homepages]
 
 [dalvit]
 name = "Christian Dalvit"
 
 [dalvit.emails]
 
 [dalvit.emails.dalvit_email]
 user = [
   "chris",
   "dalvit",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [dalvit.homepages]
 
 [danilkin]
 name = "Anton Danilkin"
 
 [danilkin.emails]
 
 [danilkin.emails.danilkin_email]
 user = [
   "anton",
   "danilkin",
 ]
 host = [
   "ens",
   "psl",
   "eu",
 ]
 
 [danilkin.homepages]
 
 [dardinier]
 name = "Thibault Dardinier"
 
 [dardinier.emails]
 
 [dardinier.emails.dardinier_email]
 user = [
   "thibault",
   "dardinier",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [dardinier.homepages]
 dardinier_homepage = "https://dardinier.me/"
 
 [david]
 name = "Marco David"
 
 [david.emails]
 
 [david.emails.david_email]
 user = [
   "marco",
   "david",
 ]
 host = [
   "hotmail",
   "de",
 ]
 
 [david.homepages]
 
 [debois]
 name = "Søren Debois"
 
 [debois.emails]
 
 [debois.homepages]
 
 [debrat]
 name = "Henri Debrat"
 
 [debrat.emails]
 
 [debrat.emails.debrat_email]
 user = [
   "henri",
   "debrat",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [debrat.homepages]
 
 [decova]
 name = "Sára Decova"
 
 [decova.emails]
 
 [decova.homepages]
 
 [delemazure]
 name = "Théo Delemazure"
 
 [delemazure.emails]
 
 [delemazure.homepages]
 delemazure_homepage = "https://theo.delemazure.fr/"
 
 [demeulemeester]
 name = "Tom Demeulemeester"
 
 [demeulemeester.emails]
 
 [demeulemeester.homepages]
 demeulemeester_homepage = "https://www.kuleuven.be/wieiswie/en/person/00131528"
 
 [derrick]
 name = "John Derrick"
 
 [derrick.emails]
 
 [derrick.emails.derrick_email]
 user = [
   "j",
   "derrick",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [derrick.homepages]
 
 [desharnais]
 name = "Martin Desharnais"
 
 [desharnais.emails]
 
 [desharnais.emails.desharnais_email]
 user = [
   "martin",
   "desharnais",
 ]
 host = [
   "unibw",
   "de",
 ]
 
 [desharnais.emails.desharnais_email1]
 user = [
   "desharnais",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [desharnais.homepages]
 desharnais_homepage = "https://martin.desharnais.me"
 
 [diaz]
 name = "Javier Díaz"
 
 [diaz.emails]
 
 [diaz.emails.diaz_email]
 user = [
   "javier",
   "diaz",
   "manzi",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [diaz.homepages]
 
 [diekmann]
 name = "Cornelius Diekmann"
 
 [diekmann.emails]
 
 [diekmann.emails.diekmann_email]
 user = [
   "diekmann",
 ]
 host = [
   "net",
   "in",
   "tum",
   "de",
 ]
 
 [diekmann.homepages]
 diekmann_homepage = "http://net.in.tum.de/~diekmann"
 
 [dirix]
 name = "Stefan Dirix"
 
 [dirix.emails]
 
 [dirix.homepages]
 
 [dittmann]
 name = "Christoph Dittmann"
 
 [dittmann.emails]
 
 [dittmann.emails.dittmann_email]
 user = [
   "isabelle",
 ]
 host = [
   "christoph-d",
   "de",
 ]
 
 [dittmann.homepages]
 dittmann_homepage = "http://logic.las.tu-berlin.de/Members/Dittmann/"
 
 [divason]
 name = "Jose Divasón"
 
 [divason.emails]
 
 [divason.emails.divason_email]
 user = [
   "jose",
   "divason",
 ]
 host = [
   "unirioja",
   "es",
 ]
 
 [divason.homepages]
 divason_homepage = "https://www.unirioja.es/cu/jodivaso/"
 
 [doczkal]
 name = "Christian Doczkal"
 
 [doczkal.emails]
 
 [doczkal.emails.doczkal_email]
 user = [
   "doczkal",
 ]
 host = [
   "ps",
   "uni-saarland",
   "de",
 ]
 
 [doczkal.homepages]
 
 [dongol]
 name = "Brijesh Dongol"
 
 [dongol.emails]
 
 [dongol.emails.dongol_email]
 user = [
   "brijesh",
   "dongol",
 ]
 host = [
   "brunel",
   "ac",
   "uk",
 ]
 
 [dongol.homepages]
 
 [doty]
 name = "Matthew Doty"
 
 [doty.emails]
 
 [doty.emails.doty_email]
 user = [
   "matt",
 ]
 host = [
   "w-d",
   "org",
 ]
 
 [doty.homepages]
 
 [dubut]
 name = "Jérémy Dubut"
 
 [dubut.emails]
 
 [dubut.emails.dubut_email]
 user = [
   "dubut",
 ]
 host = [
   "nii",
   "ac",
   "jp",
 ]
 
 [dubut.emails.dubut_email1]
 user = [
   "jeremy",
   "dubut",
 ]
 host = [
   "aist",
   "go",
   "jp",
 ]
 
 [dubut.homepages]
 dubut_homepage = "http://group-mmm.org/~dubut/"
 
 [dunaev]
 name = "Georgy Dunaev"
 
 [dunaev.emails]
 
 [dunaev.emails.dunaev_email]
 user = [
   "georgedunaev",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [dunaev.homepages]
 
 [dyckhoff]
 name = "Roy Dyckhoff"
 
 [dyckhoff.emails]
 
 [dyckhoff.homepages]
 dyckhoff_homepage = "https://rd.host.cs.st-andrews.ac.uk"
 
 [eberl]
 name = "Manuel Eberl"
 orcid = "0000-0002-4263-6571"
 
 [eberl.emails]
 
 [eberl.emails.eberl_email]
 user = [
   "manuel",
 ]
 host = [
   "pruvisto",
   "org",
 ]
 
 [eberl.emails.eberl_email1]
 user = [
   "manuel",
   "eberl",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [eberl.emails.eberl_email2]
 user = [
   "manuel",
   "eberl",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [eberl.homepages]
 eberl_homepage = "https://pruvisto.org/"
 eberl_homepage2 = "https://www.in.tum.de/~eberlm"
 
 [echenim]
 name = "Mnacho Echenim"
 
 [echenim.emails]
 
 [echenim.emails.echenim_email]
 user = [
   "mnacho",
   "echenim",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [echenim.homepages]
 echenim_homepage = "https://lig-membres.imag.fr/mechenim/"
 
 [edmonds]
 name = "Chelsea Edmonds"
 
 [edmonds.emails]
 
 [edmonds.emails.edmonds_email]
 user = [
   "cle47",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [edmonds.homepages]
 edmonds_homepage = "https://www.cst.cam.ac.uk/people/cle47"
 
 [engelhardt]
 name = "Kai Engelhardt"
 
 [engelhardt.emails]
 
 [engelhardt.homepages]
 
 [eriksson]
 name = "Lars-Henrik Eriksson"
 
 [eriksson.emails]
 
 [eriksson.emails.eriksson_email]
 user = [
   "lhe",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [eriksson.homepages]
 
 [esparza]
 name = "Javier Esparza"
 
 [esparza.emails]
 
 [esparza.homepages]
 esparza_homepage = "https://www7.in.tum.de/~esparza/"
 
 [essmann]
 name = "Robin Eßmann"
 
 [essmann.emails]
 
 [essmann.emails.essmann_email]
 user = [
   "robin",
   "essmann",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [essmann.homepages]
 
 [felgenhauer]
 name = "Bertram Felgenhauer"
 
 [felgenhauer.emails]
 
 [felgenhauer.emails.felgenhauer_email]
 user = [
   "bertram",
   "felgenhauer",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [felgenhauer.emails.felgenhauer_email1]
 user = [
   "int-e",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [felgenhauer.homepages]
 
 [feliachi]
 name = "Abderrahmane Feliachi"
 
 [feliachi.emails]
 
 [feliachi.emails.feliachi_email]
 user = [
   "abderrahmane",
   "feliachi",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [feliachi.homepages]
 
 [fell]
 name = "Julian Fell"
 
 [fell.emails]
 
 [fell.emails.fell_email]
 user = [
   "julian",
   "fell",
 ]
 host = [
   "uq",
   "net",
   "au",
 ]
 
 [fell.homepages]
 
 [fernandez]
 name = "Matthew Fernandez"
 
 [fernandez.emails]
 
 [fernandez.homepages]
 
 [fiedler]
 name = "Ben Fiedler"
 
 [fiedler.emails]
 
 [fiedler.emails.fiedler_email]
 user = [
   "ben",
   "fiedler",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [fiedler.homepages]
 
 [fleuriot]
 name = "Jacques D. Fleuriot"
 
 [fleuriot.emails]
 
 [fleuriot.emails.fleuriot_email]
 user = [
   "Jacques",
   "Fleuriot",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [fleuriot.emails.fleuriot_email1]
 user = [
   "jdf",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [fleuriot.homepages]
 fleuriot_homepage = "https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html"
 
 [fleury]
 name = "Mathias Fleury"
 
 [fleury.emails]
 
 [fleury.emails.fleury_email]
 user = [
   "fleury",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [fleury.emails.fleury_email1]
 user = [
   "mathias",
   "fleury",
 ]
 host = [
   "jku",
   "at",
 ]
 
 [fleury.homepages]
 fleury_homepage = "http://fmv.jku.at/fleury"
 
 [foster]
 name = "Michael Foster"
 
 [foster.emails]
 
 [foster.emails.foster_email]
 user = [
   "m",
   "foster",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [foster.homepages]
 
 [fosterj]
 name = "J. Nathan Foster"
 
 [fosterj.emails]
 
 [fosterj.homepages]
 fosterj_homepage = "http://www.cs.cornell.edu/~jnfoster/"
 
 [fosters]
 name = "Simon Foster"
 
 [fosters.emails]
 
 [fosters.emails.fosters_email]
 user = [
   "simon",
   "foster",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [fosters.homepages]
 fosters_homepage = "https://www-users.cs.york.ac.uk/~simonf/"
 
 [fouillard]
 name = "Valentin Fouillard"
 
 [fouillard.emails]
 
 [fouillard.emails.fouillard_email]
 user = [
   "valentin",
   "fouillard",
 ]
 host = [
   "limsi",
   "fr",
 ]
 
 [fouillard.homepages]
 
 [friedrich]
 name = "Stefan Friedrich"
 
 [friedrich.emails]
 
 [friedrich.homepages]
 
 [from]
 name = "Asta Halkjær From"
 
 [from.emails]
 
 [from.emails.from_email]
 user = [
   "ahfrom",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [from.homepages]
 from_homepage = "https://people.compute.dtu.dk/ahfrom/"
 
 [fuenmayor]
 name = "David Fuenmayor"
 
 [fuenmayor.emails]
 
 [fuenmayor.emails.fuenmayor_email]
 user = [
   "davfuenmayor",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [fuenmayor.homepages]
 
 [furusawa]
 name = "Hitoshi Furusawa"
 
 [furusawa.emails]
 
 [furusawa.homepages]
 furusawa_homepage = "http://www.sci.kagoshima-u.ac.jp/~furusawa/"
 
 [gammie]
 name = "Peter Gammie"
 
 [gammie.emails]
 
 [gammie.emails.gammie_email]
 user = [
   "peteg42",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gammie.homepages]
 gammie_homepage = "http://peteg.org"
 
 [gao]
 name = "Xin Gao"
 
 [gao.emails]
 
 [gao.homepages]
 
 [garvia]
 name = "Azucena Garvia"
 
 [garvia.emails]
 
 [garvia.emails.garvia_email]
 user = [
   "zucegb",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [garvia.homepages]
 
 [gaudel]
 name = "Marie-Claude Gaudel"
 
 [gaudel.emails]
 
 [gaudel.emails.gaudel_email]
 user = [
   "mcg",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [gaudel.homepages]
 
 [gay]
 name = "Richard Gay"
 
 [gay.emails]
 
 [gay.emails.gay_email]
 user = [
   "gay",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [gay.homepages]
 
 [georgescu]
 name = "George Georgescu"
 
 [georgescu.emails]
 
 [georgescu.homepages]
 
 [gheri]
 name = "Lorenzo Gheri"
 
 [gheri.emails]
 
 [gheri.emails.gheri_email]
 user = [
   "lor",
   "gheri",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gheri.homepages]
 
 [ghourabi]
 name = "Fadoua Ghourabi"
 
 [ghourabi.emails]
 
 [ghourabi.emails.ghourabi_email]
 user = [
   "fadouaghourabi",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ghourabi.homepages]
 
 [gioiosa]
 name = "Gianpaolo Gioiosa"
 
 [gioiosa.emails]
 
 [gioiosa.homepages]
 
 [glabbeek]
 name = "Rob van Glabbeek"
 
 [glabbeek.emails]
 
 [glabbeek.homepages]
 glabbeek_homepage = "http://theory.stanford.edu/~rvg/"
 
 [gomes]
 name = "Victor B. F. Gomes"
 
 [gomes.emails]
 
 [gomes.emails.gomes_email]
 user = [
   "victor",
   "gomes",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [gomes.emails.gomes_email2]
 user = [
   "victorborgesfg",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gomes.emails.gomes_email4]
 user = [
   "vborgesferreiragomes1",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [gomes.homepages]
 gomes_homepage = "http://www.dcs.shef.ac.uk/~victor"
 
 [gonzalez]
 name = "Edgar Gonzàlez"
 orcid = "0000-0002-9169-0769"
 
 [gonzalez.emails]
 
 [gonzalez.emails.gonzalez_email]
 user = [
   "edgargip",
 ]
 host = [
   "google",
   "com",
 ]
 
 [gonzalez.homepages]
 
 [gore]
 name = "Rajeev Gore"
 
 [gore.emails]
 
 [gore.emails.gore_email]
 user = [
   "rajeev",
   "gore",
 ]
 host = [
   "anu",
   "edu",
   "au",
 ]
 
 [gore.homepages]
 
 [gouezel]
 name = "Sebastien Gouezel"
 
 [gouezel.emails]
 
 [gouezel.emails.gouezel_email]
 user = [
   "sebastien",
   "gouezel",
 ]
 host = [
   "univ-rennes1",
   "fr",
 ]
 
 [gouezel.homepages]
 gouezel_homepage = "http://www.math.sciences.univ-nantes.fr/~gouezel/"
 
 [grechuk]
 name = "Bogdan Grechuk"
 
 [grechuk.emails]
 
 [grechuk.emails.grechuk_email]
 user = [
   "grechukbogdan",
 ]
 host = [
   "yandex",
   "ru",
 ]
 
 [grechuk.homepages]
 
 [grewe]
 name = "Sylvia Grewe"
 
 [grewe.emails]
 
 [grewe.emails.grewe_email]
 user = [
   "grewe",
 ]
 host = [
   "cs",
   "tu-darmstadt",
   "de",
 ]
 
 [grewe.homepages]
 
 [griebel]
 name = "Simon Griebel"
 
 [griebel.emails]
 
 [griebel.emails.griebel_email]
 user = [
   "s",
   "griebel",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [griebel.homepages]
 
 [grov]
 name = "Gudmund Grov"
 
 [grov.emails]
 
 [grov.emails.grov_email]
 user = [
   "ggrov",
 ]
 host = [
   "inf",
   "ed",
   "ac",
   "uk",
 ]
 
 [grov.homepages]
 grov_homepage = "http://homepages.inf.ed.ac.uk/ggrov"
 
 [guerraoui]
 name = "Rachid Guerraoui"
 
 [guerraoui.emails]
 
 [guerraoui.emails.guerraoui_email]
 user = [
   "rachid",
   "guerraoui",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [guerraoui.homepages]
 
 [guiol]
 name = "Hervé Guiol"
 
 [guiol.emails]
 
 [guiol.emails.guiol_email]
 user = [
   "herve",
   "guiol",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [guiol.homepages]
 
 [gunther]
 name = "Emmanuel Gunther"
 
 [gunther.emails]
 
 [gunther.emails.gunther_email]
 user = [
   "gunther",
 ]
 host = [
   "famaf",
   "unc",
   "edu",
   "ar",
 ]
 
 [gunther.homepages]
 
 [gutkovas]
 name = "Ramunas Gutkovas"
 
 [gutkovas.emails]
 
 [gutkovas.emails.gutkovas_email]
 user = [
   "ramunas",
   "gutkovas",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [gutkovas.homepages]
 
 [guttmann]
 name = "Walter Guttmann"
 
 [guttmann.emails]
 
 [guttmann.emails.guttmann_email]
 user = [
   "walter",
   "guttmann",
 ]
 host = [
   "canterbury",
   "ac",
   "nz",
 ]
 
 [guttmann.homepages]
 guttmann_homepage = "https://www.cosc.canterbury.ac.nz/walter.guttmann/"
 
 [guzman]
 name = "Laura P. Gamboa Guzman"
 
 [guzman.emails]
 
 [guzman.emails.guzman_email]
 user = [
   "lpgamboa",
 ]
 host = [
   "iastate",
   "edu",
 ]
 
 [guzman.homepages]
 guzman_homepage = "https://sites.google.com/view/lpgamboa/home"
 
 [haftmann]
 name = "Florian Haftmann"
 
 [haftmann.emails]
 
 [haftmann.emails.haftmann_email]
 user = [
   "florian",
   "haftmann",
 ]
 host = [
   "informatik",
   "tu-muenchen",
   "de",
 ]
 
 [haftmann.homepages]
 haftmann_homepage = "http://isabelle.in.tum.de/~haftmann"
 
 [haslbeck]
 name = "Max W. Haslbeck"
 
 [haslbeck.emails]
 
 [haslbeck.emails.haslbeck_email]
 user = [
   "maximilian",
   "haslbeck",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [haslbeck.emails.haslbeck_email1]
 user = [
   "haslbecm",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [haslbeck.emails.haslbeck_email2]
 user = [
   "max",
   "haslbeck",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [haslbeck.homepages]
 haslbeck_homepage = "http://cl-informatik.uibk.ac.at/users/mhaslbeck/"
 
 [haslbeckm]
 name = "Maximilian P. L. Haslbeck"
 
 [haslbeckm.emails]
 
 [haslbeckm.emails.haslbeckm_email]
 user = [
   "haslbema",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [haslbeckm.homepages]
 haslbeckm_homepage = "http://in.tum.de/~haslbema/"
 
 [havle]
 name = "Oto Havle"
 
 [havle.emails]
 
 [havle.emails.havle_email]
 user = [
   "oha",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [havle.homepages]
 
 [hayes]
 name = "Ian J. Hayes"
 
 [hayes.emails]
 
 [hayes.emails.hayes_email]
 user = [
   "ian",
   "hayes",
 ]
 host = [
   "itee",
   "uq",
   "edu",
   "au",
 ]
 
 [hayes.homepages]
 
 [he]
 name = "Yijun He"
 
 [he.emails]
 
 [he.emails.he_email]
 user = [
   "yh403",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [he.homepages]
 
 [heimes]
 name = "Lukas Heimes"
 
 [heimes.emails]
 
 [heimes.emails.heimes_email]
 user = [
   "heimesl",
 ]
 host = [
   "student",
   "ethz",
   "ch",
 ]
 
 [heimes.homepages]
 
 [helke]
 name = "Steffen Helke"
 
 [helke.emails]
 
 [helke.emails.helke_email]
 user = [
   "helke",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [helke.homepages]
 
 [hellauer]
 name = "Fabian Hellauer"
 
 [hellauer.emails]
 
 [hellauer.emails.hellauer_email]
 user = [
   "hellauer",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [hellauer.homepages]
 
 [heller]
 name = "Armin Heller"
 
 [heller.emails]
 
 [heller.homepages]
 
 [henrio]
 name = "Ludovic Henrio"
 
 [henrio.emails]
 
 [henrio.emails.henrio_email]
 user = [
   "Ludovic",
   "Henrio",
 ]
 host = [
   "sophia",
   "inria",
   "fr",
 ]
 
 [henrio.homepages]
 
 [herzberg]
 name = "Michael Herzberg"
 
 [herzberg.emails]
 
 [herzberg.emails.herzberg_email]
 user = [
   "mail",
 ]
 host = [
   "michael-herzberg",
   "de",
 ]
 
 [herzberg.homepages]
 herzberg_homepage = "http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg"
 
 [hess]
 name = "Andreas V. Hess"
 
 [hess.emails]
 
 [hess.emails.hess_email]
 user = [
   "avhe",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [hess.emails.hess_email1]
 user = [
   "andreasvhess",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [hess.homepages]
 
 [hetzl]
 name = "Stefan Hetzl"
 
 [hetzl.emails]
 
 [hetzl.emails.hetzl_email]
 user = [
   "hetzl",
 ]
 host = [
   "logic",
   "at",
 ]
 
 [hetzl.homepages]
 hetzl_homepage = "http://www.logic.at/people/hetzl/"
 
 [hibon]
 name = "Quentin Hibon"
 
 [hibon.emails]
 
 [hibon.emails.hibon_email]
 user = [
   "qh225",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [hibon.homepages]
 
 [higgins]
 name = "Edward Higgins"
 
 [higgins.emails]
 
 [higgins.homepages]
 
 [hirata]
 name = "Michikazu Hirata"
 
 [hirata.emails]
 
 [hirata.emails.hirata_email]
 user = [
   "hirata",
   "m",
   "ac",
 ]
 host = [
   "m",
   "titech",
   "ac",
   "jp",
 ]
 
 [hirata.homepages]
 
 [hoefner]
 name = "Peter Höfner"
 
 [hoefner.emails]
 
 [hoefner.emails.hoefner_email]
 user = [
   "peter",
 ]
 host = [
   "hoefner-online",
   "de",
 ]
 
 [hoefner.homepages]
 hoefner_homepage = "http://www.hoefner-online.de/"
 
 [hoelzl]
 name = "Johannes Hölzl"
 
 [hoelzl.emails]
 
 [hoelzl.emails.hoelzl_email]
 user = [
   "hoelzl",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [hoelzl.homepages]
 hoelzl_homepage = "http://home.in.tum.de/~hoelzl"
 
 [hofmann]
 name = "Martin Hofmann"
 
 [hofmann.emails]
 
 [hofmann.homepages]
 hofmann_homepage = "http://www.tcs.informatik.uni-muenchen.de/~mhofmann"
 
 [hofmeier]
 name = "Paul Hofmeier"
 
 [hofmeier.emails]
 
 [hofmeier.emails.hofmeier_email]
 user = [
   "paul",
   "hofmeier",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [hofmeier.homepages]
 
 [holub]
 name = "Štěpán Holub"
 
 [holub.emails]
 
 [holub.emails.holub_email]
 user = [
   "holub",
 ]
 host = [
   "karlin",
   "mff",
   "cuni",
   "cz",
 ]
 
 [holub.homepages]
 holub_homepage = "https://www2.karlin.mff.cuni.cz/~holub/"
 
 [hosking]
 name = "Tony Hosking"
 
 [hosking.emails]
 
 [hosking.homepages]
 hosking_homepage = "https://www.cs.purdue.edu/homes/hosking/"
 
 [hou]
 name = "Zhe Hou"
 
 [hou.emails]
 
 [hou.emails.hou_email]
 user = [
   "zhe",
   "hou",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [hou.homepages]
 
 [hu]
 name = "Shuwei Hu"
 
 [hu.emails]
 
 [hu.emails.hu_email]
 user = [
   "shuwei",
   "hu",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [hu.homepages]
 
 [huffman]
 name = "Brian Huffman"
 
 [huffman.emails]
 
 [huffman.emails.huffman_email]
 user = [
   "huffman",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [huffman.emails.huffman_email1]
 user = [
   "brianh",
 ]
 host = [
   "cs",
   "pdx",
   "edu",
 ]
 
 [huffman.homepages]
 huffman_homepage = "http://cs.pdx.edu/~brianh/"
 
 [hupel]
 name = "Lars Hupel"
 
 [hupel.emails]
 
 [hupel.emails.hupel_email]
 user = [
   "lars",
 ]
 host = [
   "hupel",
   "info",
 ]
 
 [hupel.homepages]
 hupel_homepage = "https://lars.hupel.info/"
 
 [ijbema]
 name = "Mark Ijbema"
 
 [ijbema.emails]
 
 [ijbema.emails.ijbema_email]
 user = [
   "ijbema",
 ]
 host = [
   "fmf",
   "nl",
 ]
 
 [ijbema.homepages]
 
 [immler]
 name = "Fabian Immler"
 
 [immler.emails]
 
 [immler.emails.immler_email]
 user = [
   "immler",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [immler.emails.immler_email1]
 user = [
   "fimmler",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [immler.homepages]
 immler_homepage = "https://home.in.tum.de/~immler/"
 
 [israel]
 name = "Jonas Israel"
 
 [israel.emails]
 
 [israel.homepages]
 israel_homepage = "https://www.algo.tu-berlin.de/menue/people/jonas_israel/"
 
 [ito]
 name = "Yosuke Ito"
 
 [ito.emails]
 
 [ito.emails.ito_email]
 user = [
   "glacier345",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ito.homepages]
 
 [iwama]
 name = "Fumiya Iwama"
 
 [iwama.emails]
 
 [iwama.emails.iwama_email]
 user = [
   "d1623001",
 ]
 host = [
   "s",
   "konan-u",
   "ac",
   "jp",
 ]
 
 [iwama.homepages]
 
 [jacobsen]
 name = "Frederik Krogsdal Jacobsen"
 
 [jacobsen.emails]
 
 [jacobsen.emails.jacobsen_email]
 user = [
   "fkjac",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [jacobsen.homepages]
 jacobsen_homepage = "http://people.compute.dtu.dk/fkjac/"
 
 [jaskelioff]
 name = "Mauro Jaskelioff"
 
 [jaskelioff.emails]
 
 [jaskelioff.homepages]
 jaskelioff_homepage = "http://www.fceia.unr.edu.ar/~mauro/"
 
 [jaskolka]
 name = "Jason Jaskolka"
 
 [jaskolka.emails]
 
 [jaskolka.emails.jaskolka_email]
 user = [
   "jason",
   "jaskolka",
 ]
 host = [
   "carleton",
   "ca",
 ]
 
 [jaskolka.homepages]
 jaskolka_homepage = "https://carleton.ca/jaskolka/"
 
 [jensen]
 name = "Alexander Birch Jensen"
 
 [jensen.emails]
 
 [jensen.emails.jensen_email]
 user = [
   "aleje",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [jensen.homepages]
 jensen_homepage = "https://people.compute.dtu.dk/aleje/"
 
 [jiang]
 name = "Nan Jiang"
 
 [jiang.emails]
 
 [jiang.emails.jiang_email]
 user = [
   "nanjiang",
 ]
 host = [
   "whu",
   "edu",
   "cn",
 ]
 
 [jiang.homepages]
 
 [jiangd]
 name = "Dongchen Jiang"
 
 [jiangd.emails]
 
 [jiangd.emails.jiangd_email]
 user = [
   "dongchenjiang",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [jiangd.homepages]
 
 [joosten]
 name = "Sebastiaan J. C. Joosten"
 
 [joosten.emails]
 
 [joosten.emails.joosten_email]
 user = [
   "sebastiaan",
   "joosten",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [joosten.emails.joosten_email1]
 user = [
   "sjcjoosten",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [joosten.emails.joosten_email2]
 user = [
   "s",
   "j",
   "c",
   "joosten",
 ]
 host = [
   "utwente",
   "nl",
 ]
 
 [joosten.homepages]
 joosten_homepage = "https://sjcjoosten.nl/"
 
 [jungnickel]
 name = "Tim Jungnickel"
 
 [jungnickel.emails]
 
 [jungnickel.emails.jungnickel_email]
 user = [
   "tim",
   "jungnickel",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [jungnickel.homepages]
 
 [kadzioka]
 name = "Maya Kądziołka"
 
 [kadzioka.emails]
 
 [kadzioka.emails.kadzioka_email]
 user = [
   "afp",
 ]
 host = [
   "compilercrim",
   "es",
 ]
 
 [kadzioka.homepages]
 
 [kaliszyk]
 name = "Cezary Kaliszyk"
 
 [kaliszyk.emails]
 
 [kaliszyk.emails.kaliszyk_email]
 user = [
   "cezary",
   "kaliszyk",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [kaliszyk.homepages]
 kaliszyk_homepage = "http://cl-informatik.uibk.ac.at/users/cek/"
 
 [kammueller]
 name = "Florian Kammüller"
 
 [kammueller.emails]
 
 [kammueller.emails.kammueller_email]
 user = [
   "flokam",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [kammueller.emails.kammueller_email1]
 user = [
   "florian",
   "kammuller",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [kammueller.homepages]
 kammueller_homepage = "http://www.cs.mdx.ac.uk/people/florian-kammueller/"
 
 [kappelmann]
 name = "Kevin Kappelmann"
 
 [kappelmann.emails]
 
 [kappelmann.emails.kappelmann_email]
 user = [
   "kevin",
   "kappelmann",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kappelmann.homepages]
 kappelmann_homepage = "https://www21.in.tum.de/team/kappelmk/"
 
 [karayel]
 name = "Emin Karayel"
 orcid = "0000-0003-3290-5034"
 
 [karayel.emails]
 
 [karayel.emails.karayel_email]
 user = [
   "me",
 ]
 host = [
   "eminkarayel",
   "de",
 ]
 
 [karayel.homepages]
 karayel_homepage = "https://orcid.org/0000-0003-3290-5034"
 
 [kastermans]
 name = "Bart Kastermans"
 
 [kastermans.emails]
 
 [kastermans.homepages]
 kastermans_homepage = "http://kasterma.net"
 
 [katovsky]
 name = "Alexander Katovsky"
 
 [katovsky.emails]
 
 [katovsky.emails.katovsky_email]
 user = [
   "apk32",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [katovsky.emails.katovsky_email1]
 user = [
   "alexander",
   "katovsky",
 ]
 host = [
   "cantab",
   "net",
 ]
 
 [katovsky.homepages]
 
 [kaufmann]
 name = "Daniela Kaufmann"
 
 [kaufmann.emails]
 
 [kaufmann.homepages]
 kaufmann_homepage = "http://fmv.jku.at/kaufmann"
 
 [keefe]
 name = "Greg O'Keefe"
 
 [keefe.emails]
 
 [keefe.homepages]
 keefe_homepage = "http://users.rsise.anu.edu.au/~okeefe/"
 
 [keinholz]
 name = "Jonas Keinholz"
 
 [keinholz.emails]
 
 [keinholz.homepages]
 
 [kerber]
 name = "Manfred Kerber"
 
 [kerber.emails]
 
 [kerber.emails.kerber_email]
 user = [
   "mnfrd",
   "krbr",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [kerber.homepages]
 kerber_homepage = "http://www.cs.bham.ac.uk/~mmk"
 
 [keskin]
 name = "Ata Keskin"
 orcid = "0000-0002-8296-1766"
 
 [keskin.emails]
 
 [keskin.emails.keskin_email]
 user = [
   "ata",
   "keskin",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [keskin.homepages]
 
 [ketland]
 name = "Jeffrey Ketland"
 
 [ketland.emails]
 
 [ketland.emails.ketland_email]
 user = [
   "jeffreyketland",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ketland.homepages]
 
 [kim]
 name = "Sunpill Kim"
 orcid = "0000-0002-7767-4084"
 
 [kim.emails]
 
 [kim.homepages]
 
 [kirchner]
 name = "Daniel Kirchner"
 
 [kirchner.emails]
 
 [kirchner.emails.kirchner_email]
 user = [
   "daniel",
 ]
 host = [
   "ekpyron",
   "org",
 ]
 
 [kirchner.homepages]
 
 [klein]
 name = "Gerwin Klein"
 
 [klein.emails]
 
 [klein.emails.klein_email]
 user = [
   "kleing",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [klein.homepages]
 klein_homepage = "http://www.cse.unsw.edu.au/~kleing/"
 
 [klenze]
 name = "Tobias Klenze"
 
 [klenze.emails]
 
 [klenze.emails.klenze_email]
 user = [
   "tobias",
   "klenze",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [klenze.homepages]
 
 [kleppmann]
 name = "Martin Kleppmann"
 
 [kleppmann.emails]
 
 [kleppmann.emails.kleppmann_email]
 user = [
   "martin",
   "kleppmann",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [kleppmann.homepages]
 
 [kobayashi]
 name = "Hidetsune Kobayashi"
 
 [kobayashi.emails]
 
 [kobayashi.homepages]
 
 [koerner]
 name = "Stefan Körner"
 
 [koerner.emails]
 
 [koerner.emails.koerner_email]
 user = [
   "s_koer03",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [koerner.homepages]
 
 [kolanski]
 name = "Rafal Kolanski"
 
 [kolanski.emails]
 
 [kolanski.emails.kolanski_email]
 user = [
   "rafal",
   "kolanski",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [kolanski.homepages]
 
 [koller]
 name = "Lukas Koller"
 
 [koller.emails]
 
 [koller.emails.koller_email]
 user = [
   "lukas",
   "koller",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [koller.homepages]
 
 [krauss]
 name = "Alexander Krauss"
 
 [krauss.emails]
 
 [krauss.emails.krauss_email]
 user = [
   "krauss",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [krauss.homepages]
 krauss_homepage = "http://www.in.tum.de/~krauss"
 
 [kreuzer]
 name = "Katharina Kreuzer"
 
 [kreuzer.emails]
 
 [kreuzer.emails.kreuzer_email]
 user = [
   "kreuzerk",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [kreuzer.emails.kreuzer_email1]
 user = [
   "k",
   "kreuzer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kreuzer.homepages]
 kreuzer_homepage = "https://www21.in.tum.de/team/kreuzer/"
 
 [kuncak]
 name = "Viktor Kuncak"
 
 [kuncak.emails]
 
 [kuncak.homepages]
 kuncak_homepage = "http://lara.epfl.ch/~kuncak/"
 
 [kuncar]
 name = "Ondřej Kunčar"
 
 [kuncar.emails]
 
 [kuncar.homepages]
 kuncar_homepage = "http://www21.in.tum.de/~kuncar/"
 
 [kurz]
 name = "Friedrich Kurz"
 
 [kurz.emails]
 
 [kurz.emails.kurz_email]
 user = [
   "friedrich",
   "kurz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kurz.homepages]
 
 [lachnitt]
 name = "Hanna Lachnitt"
 
 [lachnitt.emails]
 
 [lachnitt.emails.lachnitt_email]
 user = [
   "lachnitt",
 ]
 host = [
   "stanford",
   "edu",
 ]
 
 [lachnitt.homepages]
 
 [lallemand]
 name = "Joseph Lallemand"
 
 [lallemand.emails]
 
 [lallemand.emails.lallemand_email]
 user = [
   "joseph",
   "lallemand",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [lallemand.homepages]
 
 [lameris]
 name = "Cárolos Laméris"
 
 [lameris.emails]
 
 [lameris.emails.lameris_email]
 user = [
   "carolos",
   "lameris",
 ]
 host = [
   "ru",
   "nl",
 ]
 
 [lameris.homepages]
 
 [lammich]
 name = "Peter Lammich"
 
 [lammich.emails]
 
 [lammich.emails.lammich_email]
 user = [
   "lammich",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [lammich.emails.lammich_email1]
 user = [
   "peter",
   "lammich",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [lammich.homepages]
 lammich_homepage = "http://www21.in.tum.de/~lammich"
 
 [lange]
 name = "Christoph Lange"
 
 [lange.emails]
 
 [lange.emails.lange_email]
 user = [
   "math",
   "semantic",
   "web",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [lange.homepages]
 
 [langenstein]
 name = "Bruno Langenstein"
 
 [langenstein.emails]
 
 [langenstein.emails.langenstein_email]
 user = [
   "langenstein",
 ]
 host = [
   "dfki",
   "de",
 ]
 
 [langenstein.homepages]
 
 [lattuada]
 name = "Andrea Lattuada"
 
 [lattuada.emails]
 
 [lattuada.homepages]
 lattuada_homepage = "https://andrea.lattuada.me"
 
 [lauermann]
 name = "Nils Lauermann"
 
 [lauermann.emails]
 
 [lauermann.emails.lauermann_email]
 user = [
   "Nils",
   "Lauermann",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [lauermann.homepages]
 
 [laursen]
 name = "Christian Pardillo-Laursen"
 
 [laursen.emails]
 
 [laursen.emails.laursen_email]
 user = [
   "christian",
   "laursen",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [laursen.homepages]
 
 [lederer]
 name = "Patrick Lederer"
 
 [lederer.emails]
 
 [lederer.homepages]
 lederer_homepage = "https://www.cs.cit.tum.de/en/dss/members/patrick-lederer/"
 
 [lee]
 name = "Holden Lee"
 
 [lee.emails]
 
 [lee.emails.lee_email]
 user = [
   "holdenl",
 ]
 host = [
   "princeton",
   "edu",
 ]
 
 [lee.homepages]
 
 [leek]
 name = "Kevin Lee"
 
 [leek.emails]
 
 [leek.emails.leek_email]
 user = [
   "kfkl2",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [leek.homepages]
 
 [leustean]
 name = "Laurentiu Leustean"
 
 [leustean.emails]
 
 [leustean.homepages]
 
 [lewis]
 name = "Corey Lewis"
 
 [lewis.emails]
 
 [lewis.emails.lewis_email]
 user = [
   "corey",
   "lewis",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [lewis.homepages]
 
 [li]
 name = "Wenda Li"
 
 [li.emails]
 
 [li.emails.li_email]
 user = [
   "wl302",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [li.emails.li_email1]
 user = [
   "liwenda1990",
 ]
 host = [
   "hotmail",
   "com",
 ]
 
 [li.homepages]
 li_homepage = "https://www.cl.cam.ac.uk/~wl302/"
 
 [lim]
 name = "Japheth Lim"
 
 [lim.emails]
 
 [lim.homepages]
 
 [lindenberg]
 name = "Christina Lindenberg"
 
 [lindenberg.emails]
 
 [lindenberg.homepages]
 
 [linker]
 name = "Sven Linker"
 
 [linker.emails]
 
 [linker.emails.linker_email]
 user = [
   "s",
   "linker",
 ]
 host = [
   "liverpool",
   "ac",
   "uk",
 ]
 
 [linker.homepages]
 
 [liu]
 name = "Junyi Liu"
 
 [liu.emails]
 
 [liu.homepages]
 
 [liut]
 name = "Tao Liu"
 
 [liut.emails]
 
 [liut.homepages]
 
 [liuy]
 name = "Yang Liu"
 
 [liuy.emails]
 
 [liuy.emails.liuy_email]
 user = [
   "yangliu",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [liuy.homepages]
 
 [liy]
 name = "Yangjia Li"
 
 [liy.emails]
 
 [liy.homepages]
 
 [lochbihler]
 name = "Andreas Lochbihler"
 
 [lochbihler.emails]
 
 [lochbihler.emails.lochbihler_email1]
 user = [
   "mail",
 ]
 host = [
   "andreas-lochbihler",
   "de",
 ]
 
 [lochbihler.homepages]
 lochbihler_homepage = "http://www.andreas-lochbihler.de/"
 
 [lochmann]
 name = "Alexander Lochmann"
 
 [lochmann.emails]
 
 [lochmann.emails.lochmann_email]
 user = [
   "alexander",
   "lochmann",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [lochmann.homepages]
 
 [lohner]
 name = "Denis Lohner"
 
 [lohner.emails]
 
 [lohner.emails.lohner_email]
 user = [
   "denis",
   "lohner",
 ]
 host = [
   "kit",
   "edu",
 ]
 
 [lohner.homepages]
 lohner_homepage = "http://pp.ipd.kit.edu/person.php?id=88"
 
 [loibl]
 name = "Matthias Loibl"
 
 [loibl.emails]
 
 [loibl.homepages]
 
 [londono]
 name = "Alejandro Gómez-Londoño"
 
 [londono.emails]
 
 [londono.emails.londono_email]
 user = [
   "alejandro",
   "gomez",
 ]
 host = [
   "chalmers",
   "se",
 ]
 
 [londono.homepages]
 
 [losa]
 name = "Giuliano Losa"
 
 [losa.emails]
 
 [losa.emails.losa_email]
 user = [
   "giuliano",
   "losa",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [losa.emails.losa_email1]
 user = [
   "giuliano",
 ]
 host = [
   "galois",
   "com",
 ]
 
 [losa.emails.losa_email2]
 user = [
   "giuliano",
 ]
 host = [
   "losa",
   "fr",
 ]
 
 [losa.homepages]
 
 [lutz]
 name = "Bianca Lutz"
 
 [lutz.emails]
 
 [lutz.emails.lutz_email]
 user = [
   "sowilo",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [lutz.homepages]
 
 [lux]
 name = "Alexander Lux"
 
 [lux.emails]
 
 [lux.emails.lux_email]
 user = [
   "lux",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [lux.homepages]
 
 [madarasz]
 name = "Judit Madarasz"
 
 [madarasz.emails]
 
 [madarasz.homepages]
 madarasz_homepage = "https://users.renyi.hu/~madarasz/"
 
 [makarios]
 name = "T. J. M. Makarios"
 
 [makarios.emails]
 
 [makarios.emails.makarios_email]
 user = [
   "tjm1983",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [makarios.homepages]
 
 [maletzky]
 name = "Alexander Maletzky"
 
 [maletzky.emails]
 
 [maletzky.emails.maletzky_email]
 user = [
   "alexander",
   "maletzky",
 ]
 host = [
   "risc",
   "jku",
   "at",
 ]
 
 [maletzky.emails.maletzky_email1]
 user = [
   "alexander",
   "maletzky",
 ]
 host = [
   "risc-software",
   "at",
 ]
 
 [maletzky.homepages]
 maletzky_homepage = "https://risc.jku.at/m/alexander-maletzky/"
 
 [mansky]
 name = "Susannah Mansky"
 
 [mansky.emails]
 
 [mansky.emails.mansky_email]
 user = [
   "sjohnsn2",
 ]
 host = [
   "illinois",
   "edu",
 ]
 
 [mansky.emails.mansky_email1]
 user = [
   "susannahej",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [mansky.homepages]
 
 [mantel]
 name = "Heiko Mantel"
 
 [mantel.emails]
 
 [mantel.emails.mantel_email]
 user = [
   "mantel",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [mantel.homepages]
 
 [margetson]
 name = "James Margetson"
 
 [margetson.emails]
 
 [margetson.homepages]
 
 [maric]
 name = "Ognjen Marić"
 
 [maric.emails]
 
 [maric.emails.maric_email]
 user = [
   "ogi",
   "afp",
 ]
 host = [
   "mynosefroze",
   "com",
 ]
 
 [maric.homepages]
 
 [maricf]
 name = "Filip Marić"
 
 [maricf.emails]
 
 [maricf.emails.maricf_email]
 user = [
   "filip",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [maricf.homepages]
 maricf_homepage = "http://www.matf.bg.ac.rs/~filip"
 
 [marmsoler]
 name = "Diego Marmsoler"
 
 [marmsoler.emails]
 
 [marmsoler.emails.marmsoler_email]
 user = [
   "diego",
   "marmsoler",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [marmsoler.emails.marmsoler_email1]
 user = [
   "d",
   "marmsoler",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [marmsoler.homepages]
 marmsoler_homepage = "http://marmsoler.com"
 
 [massacrier]
 name = "Tanguy Massacrier"
 
 [massacrier.emails]
 
 [massacrier.homepages]
 
 [matache]
 name = "Cristina Matache"
 
 [matache.emails]
 
 [matache.emails.matache_email]
 user = [
   "cris",
   "matache",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [matache.homepages]
 
 [mateo]
 name = "Adrián Doña Mateo"
 
 [mateo.emails]
 
 [mateo.emails.mateo_email]
 user = [
   "adrian",
   "dona",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [mateo.homepages]
 
 [matichuk]
 name = "Daniel Matichuk"
 
 [matichuk.emails]
 
 [matichuk.homepages]
 
 [matiyasevich]
 name = "Yuri Matiyasevich"
 
 [matiyasevich.emails]
 
 [matiyasevich.homepages]
 
 [maximova]
 name = "Alexandra Maximova"
 
 [maximova.emails]
 
 [maximova.emails.maximova_email]
 user = [
   "amaximov",
 ]
 host = [
   "student",
   "ethz",
   "ch",
 ]
 
 [maximova.homepages]
 
 [meis]
 name = "Rene Meis"
 
 [meis.emails]
 
 [meis.emails.meis_email]
 user = [
   "rene",
   "meis",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [meis.emails.meis_email1]
 user = [
   "rene",
   "meis",
 ]
 host = [
   "uni-due",
   "de",
 ]
 
 [meis.homepages]
 
 [merz]
 name = "Stephan Merz"
 
 [merz.emails]
 
 [merz.emails.merz_email]
 user = [
   "Stephan",
   "Merz",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [merz.homepages]
 merz_homepage = "http://www.loria.fr/~merz"
 
 [messner]
 name = "Florian Messner"
 
 [messner.emails]
 
 [messner.emails.messner_email]
 user = [
   "florian",
   "g",
   "messner",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [messner.homepages]
 
 [mhalla]
 name = "Mehdi Mhalla"
 
 [mhalla.emails]
 
 [mhalla.emails.mhalla_email]
 user = [
   "mhallam",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [mhalla.homepages]
 
 [michaelis]
 name = "Julius Michaelis"
 
 [michaelis.emails]
 
 [michaelis.emails.michaelis_email]
 user = [
   "isabelleopenflow",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email1]
 user = [
   "maintainafpppt",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email2]
 user = [
   "bdd",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email3]
 user = [
   "afp",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.homepages]
 michaelis_homepage = "http://liftm.de/"
 
 [milehins]
 name = "Mihails Milehins"
 
 [milehins.emails]
 
 [milehins.emails.milehins_email]
 user = [
   "mihailsmilehins",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [milehins.homepages]
 
 [minamide]
 name = "Yasuhiko Minamide"
 
 [minamide.emails]
 
 [minamide.emails.minamide_email]
 user = [
   "minamide",
 ]
 host = [
   "is",
   "titech",
   "ac",
   "jp",
 ]
 
 [minamide.homepages]
 minamide_homepage = "https://sv.c.titech.ac.jp/minamide/index.en.html"
 
 [mitchell]
 name = "Neil Mitchell"
 
 [mitchell.emails]
 
 [mitchell.homepages]
 
 [mitsch]
 name = "Stefan Mitsch"
 
 [mitsch.emails]
 
 [mitsch.emails.mitsch_email]
 user = [
   "smitsch",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [mitsch.homepages]
 
 [moedersheim]
 name = "Sebastian Mödersheim"
 
 [moedersheim.emails]
 
 [moedersheim.emails.moedersheim_email]
 user = [
   "samo",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [moedersheim.homepages]
 moedersheim_homepage = "https://people.compute.dtu.dk/samo/"
 
 [moeller]
 name = "Bernhard Möller"
 
 [moeller.emails]
 
 [moeller.homepages]
 moeller_homepage = "https://www.informatik.uni-augsburg.de/en/chairs/dbis/pmi/staff/moeller/"
 
 [montanari]
 name = "Luisa Montanari"
 orcid = "0000-0002-5270-0290"
 
 [montanari.emails]
 
 [montanari.homepages]
 
 [mori]
 name = "Coraline Mori"
 
 [mori.emails]
 
 [mori.emails.mori_email]
 user = [
   "coraline",
   "mori",
 ]
 host = [
   "grenoble-inp",
   "org",
 ]
 
 [mori.homepages]
 
 [muendler]
 name = "Niels Mündler"
 
 [muendler.emails]
 
 [muendler.emails.muendler_email]
 user = [
   "n",
   "muendler",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [muendler.homepages]
 
 [mulligan]
 name = "Dominic P. Mulligan"
 
 [mulligan.emails]
 
 [mulligan.emails.mulligan_email]
 user = [
   "dominic",
   "p",
   "mulligan",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [mulligan.emails.mulligan_email1]
 user = [
   "Dominic",
   "Mulligan",
 ]
 host = [
   "arm",
   "com",
 ]
 
 [mulligan.homepages]
 
 [munive]
 name = "Jonathan Julian Huerta y Munive"
 
 [munive.emails]
 
 [munive.emails.munive_email]
 user = [
   "jjhuertaymunive1",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [munive.emails.munive_email1]
 user = [
   "jonjulian23",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [munive.homepages]
 
 [murao]
 name = "H. Murao"
 
 [murao.emails]
 
 [murao.homepages]
 
 [murray]
 name = "Toby Murray"
 
 [murray.emails]
 
 [murray.emails.murray_email]
 user = [
   "toby",
   "murray",
 ]
 host = [
   "unimelb",
   "edu",
   "au",
 ]
 
 [murray.homepages]
 murray_homepage = "https://people.eng.unimelb.edu.au/tobym/"
 
 [myreen]
 name = "Magnus O. Myreen"
 orcid = "0000-0002-9504-4107"
 
 [myreen.emails]
 
 [myreen.emails.myreen_email]
 user = [
   "myreen",
 ]
 host = [
   "chalmers",
   "se",
 ]
 
 [myreen.homepages]
 
 [nagashima]
 name = "Yutaka Nagashima"
 
 [nagashima.emails]
 
 [nagashima.emails.nagashima_email]
 user = [
   "Yutaka",
   "Nagashima",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [nagashima.homepages]
 
 [nagele]
 name = "Julian Nagele"
 
 [nagele.emails]
 
 [nagele.emails.nagele_email]
 user = [
   "julian",
   "nagele",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [nagele.homepages]
 
 [naraschewski]
 name = "Wolfgang Naraschewski"
 
 [naraschewski.emails]
 
 [naraschewski.homepages]
 
 [nedzelsky]
 name = "Michael Nedzelsky"
 
 [nedzelsky.emails]
 
 [nedzelsky.emails.nedzelsky_email]
 user = [
   "MichaelNedzelsky",
 ]
 host = [
   "yandex",
   "ru",
 ]
 
 [nedzelsky.homepages]
 
 [nemeti]
 name = "István Németi"
 
 [nemeti.emails]
 
 [nemeti.homepages]
 nemeti_homepage = "http://www.renyi.hu/~nemeti/"
 
 [nemouchi]
 name = "Yakoub Nemouchi"
 
 [nemouchi.emails]
 
 [nemouchi.emails.nemouchi_email]
 user = [
   "nemouchi",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [nemouchi.emails.nemouchi_email1]
 user = [
   "yakoub",
   "nemouchi",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [nemouchi.homepages]
 
 [nestmann]
 name = "Uwe Nestmann"
 
 [nestmann.emails]
 
 [nestmann.homepages]
 nestmann_homepage = "https://www.mtv.tu-berlin.de/nestmann/"
 
 [neumann]
 name = "René Neumann"
 
 [neumann.emails]
 
 [neumann.emails.neumann_email]
 user = [
   "rene",
   "neumann",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [neumann.homepages]
 
 [nielsen]
 name = "Finn Nielsen"
 
 [nielsen.emails]
 
 [nielsen.emails.nielsen_email]
 user = [
   "finn",
   "nielsen",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [nielsen.homepages]
 
 [nikiforov]
 name = "Denis Nikiforov"
 
 [nikiforov.emails]
 
 [nikiforov.emails.nikiforov_email]
 user = [
   "denis",
   "nikif",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [nikiforov.homepages]
 
 [nipkow]
 name = "Tobias Nipkow"
 orcid = "0000-0003-0730-515X"
 
 [nipkow.emails]
 
 [nipkow.emails.nipkow_email]
 user = [
   "nipkow",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [nipkow.homepages]
 nipkow_homepage = "https://www.in.tum.de/~nipkow/"
 
 [nishihara]
 name = "Toshiaki Nishihara"
 
 [nishihara.emails]
 
 [nishihara.homepages]
 
 [noce]
 name = "Pasquale Noce"
 
 [noce.emails]
 
 [noce.emails.noce_email]
 user = [
   "pasquale",
   "noce",
   "lavoro",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [noce.homepages]
 
 [nordhoff]
 name = "Benedikt Nordhoff"
 
 [nordhoff.emails]
 
 [nordhoff.emails.nordhoff_email]
 user = [
   "b",
   "n",
 ]
 host = [
   "wwu",
   "de",
 ]
 
 [nordhoff.emails.nordhoff_email1]
 user = [
   "b_nord01",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [nordhoff.homepages]
 
 [noschinski]
 name = "Lars Noschinski"
 
 [noschinski.emails]
 
 [noschinski.emails.noschinski_email]
 user = [
   "noschinl",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [noschinski.homepages]
 noschinski_homepage = "http://www21.in.tum.de/~noschinl/"
 
 [obua]
 name = "Steven Obua"
 
 [obua.emails]
 
 [obua.emails.obua_email]
 user = [
   "steven",
 ]
 host = [
   "recursivemind",
   "com",
 ]
 
 [obua.homepages]
 
 [ogawa]
 name = "Mizuhito Ogawa"
 
 [ogawa.emails]
 
 [ogawa.homepages]
 
 [oldenburg]
 name = "Lennart Oldenburg"
 
 [oldenburg.emails]
 
 [oldenburg.homepages]
 
 [olm]
 name = "Markus Müller-Olm"
 
 [olm.emails]
 
 [olm.homepages]
 olm_homepage = "http://cs.uni-muenster.de/u/mmo/"
 
 [oosterhuis]
 name = "Roelof Oosterhuis"
 
 [oosterhuis.emails]
 
 [oosterhuis.emails.oosterhuis_email]
 user = [
   "roelofoosterhuis",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [oosterhuis.homepages]
 
 [oostrom]
 name = "Vincent van Oostrom"
 
 [oostrom.emails]
 
 [oostrom.homepages]
 
 [ortner]
 name = "Veronika Ortner"
 
 [ortner.emails]
 
 [ortner.homepages]
 
 [overbeek]
 name = "Roy Overbeek"
 
 [overbeek.emails]
 
 [overbeek.emails.overbeek_email]
 user = [
   "Roy",
   "Overbeek",
 ]
 host = [
   "cwi",
   "nl",
 ]
 
 [overbeek.homepages]
 
 [pagano]
 name = "Miguel Pagano"
 
 [pagano.emails]
 
 [pagano.emails.pagano_email]
 user = [
   "miguel",
   "pagano",
 ]
 host = [
   "unc",
   "edu",
   "ar",
 ]
 
 [pagano.homepages]
 pagano_homepage = "https://cs.famaf.unc.edu.ar/~mpagano/"
 
 [pal]
 name = "Abhik Pal"
 
 [pal.emails]
 
 [pal.homepages]
 
 [paleo]
 name = "Bruno Woltzenlogel Paleo"
 
 [paleo.emails]
 
 [paleo.homepages]
 paleo_homepage = "http://www.logic.at/staff/bruno/"
 
 [palmer]
 name = "Jake Palmer"
 
 [palmer.emails]
 
 [palmer.emails.palmer_email]
 user = [
   "jake",
   "palmer",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [palmer.homepages]
 
 [park]
 name = "Seung Hoon Park"
 orcid = "0000-0001-7165-6857"
 
 [park.emails]
 
 [park.emails.park_email]
 user = [
   "seunghoon",
   "park",
 ]
 host = [
   "cs",
   "ox",
   "ac",
   "uk",
 ]
 
 [park.homepages]
 park_homepage = "https://www.cs.ox.ac.uk/people/simon.park/"
 
 [parkinson]
 name = "Matthew Parkinson"
 
 [parkinson.emails]
 
 [parkinson.homepages]
 parkinson_homepage = "http://research.microsoft.com/people/mattpark/"
 
 [parrow]
 name = "Joachim Parrow"
 
 [parrow.emails]
 
 [parrow.emails.parrow_email]
 user = [
   "joachim",
   "parrow",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [parrow.homepages]
 
 [parsert]
 name = "Julian Parsert"
 
 [parsert.emails]
 
 [parsert.emails.parsert_email]
 user = [
   "julian",
   "parsert",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [parsert.emails.parsert_email1]
 user = [
   "julian",
   "parsert",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [parsert.homepages]
 parsert_homepage = "http://www.parsert.com/"
 
 [paulson]
 name = "Lawrence C. Paulson"
 
 [paulson.emails]
 
 [paulson.emails.paulson_email]
 user = [
   "lp15",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [paulson.homepages]
 paulson_homepage = "https://www.cl.cam.ac.uk/~lp15/"
 
 [peltier]
 name = "Nicolas Peltier"
 
 [peltier.emails]
 
 [peltier.emails.peltier_email]
 user = [
   "Nicolas",
   "Peltier",
 ]
 host = [
   "imag",
   "fr",
 ]
 
 [peltier.homepages]
 peltier_homepage = "http://membres-lig.imag.fr/peltier/"
 
 [peters]
 name = "Kirstin Peters"
 
 [peters.emails]
 
 [peters.emails.peters_email]
 user = [
   "kirstin",
   "peters",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [peters.homepages]
 
 [petrovic]
 name = "Danijela Petrovic"
 
 [petrovic.emails]
 
 [petrovic.homepages]
 petrovic_homepage = "http://www.matf.bg.ac.rs/~danijela"
 
 [pierzchalski]
 name = "Edward Pierzchalski"
 
 [pierzchalski.emails]
 
 [pierzchalski.homepages]
 
 [platzer]
 name = "André Platzer"
 
 [platzer.emails]
 
 [platzer.emails.platzer_email]
 user = [
   "aplatzer",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [platzer.homepages]
 platzer_homepage = "https://www.cs.cmu.edu/~aplatzer/"
 
 [pohjola]
 name = "Johannes Åman Pohjola"
 
 [pohjola.emails]
 
 [pohjola.emails.pohjola_email]
 user = [
   "j",
   "amanpohjola",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [pohjola.homepages]
 
 [pollak]
 name = "Florian Pollak"
 
 [pollak.emails]
 
 [pollak.emails.pollak_email]
 user = [
   "florian",
   "pollak",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [pollak.homepages]
 
 [popescu]
 name = "Andrei Popescu"
 
 [popescu.emails]
 
 [popescu.emails.popescu_email]
 user = [
   "a",
   "popescu",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [popescu.emails.popescu_email1]
 user = [
   "uuomul",
 ]
 host = [
   "yahoo",
   "com",
 ]
 
 [popescu.emails.popescu_email2]
 user = [
   "a",
   "popescu",
 ]
 host = [
   "mdx",
   "ac",
   "uk",
 ]
 
 [popescu.homepages]
 popescu_homepage = "https://www.andreipopescu.uk"
 
 [porter]
 name = "Benjamin Porter"
 
 [porter.emails]
 
 [porter.homepages]
 
 [prathamesh]
 name = "T.V.H. Prathamesh"
 
 [prathamesh.emails]
 
 [prathamesh.emails.prathamesh_email]
 user = [
   "prathamesh",
 ]
 host = [
   "imsc",
   "res",
   "in",
 ]
 
 [prathamesh.homepages]
 
 [preoteasa]
 name = "Viorel Preoteasa"
 
 [preoteasa.emails]
 
 [preoteasa.emails.preoteasa_email]
 user = [
   "viorel",
   "preoteasa",
 ]
 host = [
   "aalto",
   "fi",
 ]
 
 [preoteasa.homepages]
 preoteasa_homepage = "http://users.abo.fi/vpreotea/"
 
 [pusch]
 name = "Cornelia Pusch"
 
 [pusch.emails]
 
 [pusch.homepages]
 
 [qiu]
 name = "Qi Qiu"
 
 [qiu.emails]
 
 [qiu.emails.qiu_email]
 user = [
   "qi",
   "qiu",
 ]
 host = [
   "univ-lyon1",
   "fr",
 ]
 
 [qiu.homepages]
 
 [rabe]
 name = "Markus N. Rabe"
 
 [rabe.emails]
 
 [rabe.homepages]
 rabe_homepage = "http://www.react.uni-saarland.de/people/rabe.html"
 
 [rabing]
 name = "Mathias Schack Rabing"
 
 [rabing.emails]
 
 [rabing.emails.rabing_email]
 user = [
   "mathiasrabing",
 ]
 host = [
   "outlook",
   "com",
 ]
 
 [rabing.homepages]
 
 [raedle]
 name = "Jonas Rädle"
 
 [raedle.emails]
 
 [raedle.emails.raedle_email]
 user = [
   "jonas",
   "raedle",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [raedle.emails.raedle_email1]
 user = [
   "jonas",
   "raedle",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [raedle.homepages]
 
 [raska]
 name = "Martin Raška"
 
 [raska.emails]
 
 [raska.homepages]
 
 [raszyk]
 name = "Martin Raszyk"
 
 [raszyk.emails]
 
 [raszyk.emails.raszyk_email]
 user = [
   "martin",
   "raszyk",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [raszyk.emails.raszyk_email1]
 user = [
   "m",
   "raszyk",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [raszyk.homepages]
 
 [rau]
 name = "Martin Rau"
 
 [rau.emails]
 
 [rau.emails.rau_email]
 user = [
   "martin",
   "rau",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [rau.emails.rau_email1]
 user = [
   "mrtnrau",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [rau.homepages]
 
 [rauch]
 name = "Nicole Rauch"
 
 [rauch.emails]
 
 [rauch.emails.rauch_email]
 user = [
   "rauch",
 ]
 host = [
   "informatik",
   "uni-kl",
   "de",
 ]
 
 [rauch.homepages]
 
 [raumer]
 name = "Jakob von Raumer"
 
 [raumer.emails]
 
 [raumer.emails.raumer_email]
 user = [
   "psxjv4",
 ]
 host = [
   "nottingham",
   "ac",
   "uk",
 ]
 
 [raumer.homepages]
 
 [ravindran]
 name = "Binoy Ravindran"
 
 [ravindran.emails]
 
 [ravindran.homepages]
 
 [rawson]
 name = "Michael Rawson"
 
 [rawson.emails]
 
 [rawson.emails.rawson_email]
 user = [
   "michaelrawson76",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [rawson.homepages]
 
 [raya]
 name = "Rodrigo Raya"
 
 [raya.emails]
 
 [raya.emails.raya_email]
 user = [
   "rodrigo",
   "raya",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [raya.homepages]
 raya_homepage = "https://people.epfl.ch/rodrigo.raya"
 
 [regensburger]
 name = "Franz Regensburger"
 
 [regensburger.emails]
 
 [regensburger.emails.regensburger_email]
 user = [
   "Franz",
   "Regensburger",
 ]
 host = [
   "thi",
   "de",
 ]
 
 [regensburger.homepages]
 regensburger_homepage = "https://www.thi.de/suche/mitarbeiter/prof-dr-rer-nat-franz-regensburger"
 
 [reiche]
 name = "Sebastian Reiche"
 
 [reiche.emails]
 
 [reiche.homepages]
 reiche_homepage = "https://www.linkedin.com/in/sebastian-reiche-0b2093178"
 
 [reiter]
 name = "Markus Reiter"
 
 [reiter.emails]
 
 [reiter.homepages]
 
 [reynaud]
 name = "Alban Reynaud"
 
 [reynaud.emails]
 
 [reynaud.homepages]
 
 [ribeiro]
 name = "Pedro Ribeiro"
 
 [ribeiro.emails]
 
 [ribeiro.homepages]
 
 [richter]
 name = "Stefan Richter"
 
 [richter.emails]
 
 [richter.emails.richter_email]
 user = [
   "richter",
 ]
 host = [
   "informatik",
   "rwth-aachen",
   "de",
 ]
 
 [richter.homepages]
 richter_homepage = "http://www-lti.informatik.rwth-aachen.de/~richter/"
 
 [rickmann]
 name = "Christina Rickmann"
 
 [rickmann.emails]
 
 [rickmann.emails.rickmann_email]
 user = [
   "c",
   "rickmann",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [rickmann.homepages]
 
 [ridge]
 name = "Tom Ridge"
 
 [ridge.emails]
 
 [ridge.homepages]
 
 [rizaldi]
 name = "Albert Rizaldi"
 
 [rizaldi.emails]
 
 [rizaldi.emails.rizaldi_email]
 user = [
   "albert",
   "rizaldi",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [rizaldi.homepages]
 
 [rizkallah]
 name = "Christine Rizkallah"
 
 [rizkallah.emails]
 
 [rizkallah.homepages]
 rizkallah_homepage = "https://www.mpi-inf.mpg.de/~crizkall/"
 
 [robillard]
 name = "Simon Robillard"
 
 [robillard.emails]
 
 [robillard.homepages]
 robillard_homepage = "https://simon-robillard.net/"
 
 [roessle]
 name = "Ian Roessle"
 
 [roessle.emails]
 
 [roessle.homepages]
 
 [romanos]
 name = "Ralph Romanos"
 
 [romanos.emails]
 
 [romanos.emails.romanos_email]
 user = [
   "ralph",
   "romanos",
 ]
 host = [
   "student",
   "ecp",
   "fr",
 ]
 
 [romanos.homepages]
 
 [rosskopf]
 name = "Simon Roßkopf"
 
 [rosskopf.emails]
 
 [rosskopf.emails.rosskopf_email]
 user = [
   "rosskops",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [rosskopf.homepages]
 rosskopf_homepage = "http://www21.in.tum.de/~rosskops"
 
 [rowat]
 name = "Colin Rowat"
 
 [rowat.emails]
 
 [rowat.emails.rowat_email]
 user = [
   "c",
   "rowat",
 ]
 host = [
   "bham",
   "ac",
   "uk",
 ]
 
 [rowat.homepages]
 
 [sabouret]
 name = "Nicolas Sabouret"
 
 [sabouret.emails]
 
 [sabouret.homepages]
 
 [sachtleben]
 name = "Robert Sachtleben"
 
 [sachtleben.emails]
 
 [sachtleben.emails.sachtleben_email]
 user = [
   "rob_sac",
 ]
 host = [
   "uni-bremen",
   "de",
 ]
 
 [sachtleben.homepages]
 
 [saile]
 name = "Christian Saile"
 
 [saile.emails]
 
 [saile.homepages]
 saile_homepage = "http://dss.in.tum.de/staff/christian-saile.html"
 
 [sanan]
 name = "David Sanan"
 
 [sanan.emails]
 
 [sanan.emails.sanan_email]
 user = [
   "sanan",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [sanan.homepages]
 
 [sato]
 name = "Tetsuya Sato"
 
 [sato.emails]
 
 [sato.emails.sato_email]
 user = [
   "tsato",
 ]
 host = [
   "c",
   "titech",
   "ac",
   "jp",
 ]
 
 [sato.homepages]
 sato_homepage = "https://sites.google.com/view/tetsuyasato/"
 
 [sauer]
 name = "Jens Sauer"
 
 [sauer.emails]
 
 [sauer.emails.sauer_email]
 user = [
   "sauer",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [sauer.homepages]
 
 [schaeffeler]
 name = "Maximilian Schäffeler"
 
 [schaeffeler.emails]
 
 [schaeffeler.emails.schaeffeler_email]
 user = [
   "schaeffm",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [schaeffeler.homepages]
 
 [scharager]
 name = "Matias Scharager"
 
 [scharager.emails]
 
 [scharager.emails.scharager_email]
 user = [
   "mscharag",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [scharager.homepages]
 
 [schimpf]
 name = "Alexander Schimpf"
 
 [schimpf.emails]
 
 [schimpf.emails.schimpf_email]
 user = [
   "schimpfa",
 ]
 host = [
   "informatik",
   "uni-freiburg",
   "de",
 ]
 
 [schimpf.homepages]
 
 [schirmer]
 name = "Norbert Schirmer"
 
 [schirmer.emails]
 
 [schirmer.emails.schirmer_email]
 user = [
   "norbert",
   "schirmer",
 ]
 host = [
   "web",
   "de",
 ]
 
 [schirmer.homepages]
 
 [schleicher]
 name = "Dierk Schleicher"
 
 [schleicher.emails]
 
 [schleicher.homepages]
 
 [schlichtkrull]
 name = "Anders Schlichtkrull"
 
 [schlichtkrull.emails]
 
 [schlichtkrull.emails.schlichtkrull_email]
 user = [
   "andschl",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [schlichtkrull.homepages]
 schlichtkrull_homepage = "https://people.compute.dtu.dk/andschl/"
 
 [schmaltz]
 name = "Julien Schmaltz"
 
 [schmaltz.emails]
 
 [schmaltz.emails.schmaltz_email]
 user = [
   "Julien",
   "Schmaltz",
 ]
 host = [
   "ou",
   "nl",
 ]
 
 [schmaltz.homepages]
 
 [schmidinger]
 name = "Lukas Schmidinger"
 
 [schmidinger.emails]
 
 [schmidinger.homepages]
 
 [schmoetten]
 name = "Richard Schmoetten"
 
 [schmoetten.emails]
 
 [schmoetten.emails.schmoetten_email]
 user = [
   "s1311325",
 ]
 host = [
   "sms",
   "ed",
   "ac",
   "uk",
 ]
 
 [schmoetten.homepages]
 
 [schneider]
 name = "Joshua Schneider"
 
 [schneider.emails]
 
 [schneider.emails.schneider_email]
 user = [
   "joshua",
   "schneider",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [schneider.homepages]
 
 [schoepe]
 name = "Daniel Schoepe"
 
 [schoepe.emails]
 
 [schoepe.emails.schoepe_email]
 user = [
   "daniel",
 ]
 host = [
   "schoepe",
   "org",
 ]
 
 [schoepe.homepages]
 
 [schoepf]
 name = "Jonas Schöpf"
 
 [schoepf.emails]
 
 [schoepf.emails.schoepf_email]
 user = [
   "jonas",
   "schoepf",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [schoepf.homepages]
 
 [schou]
 name = "Morten Konggaard Schou"
 orcid = "0000-0002-5970-4294"
 
 [schou.emails]
 
 [schou.emails.schou_email]
 user = [
   "mksc",
 ]
 host = [
   "cs",
   "aau",
   "dk",
 ]
 
 [schou.homepages]
 
 [schulz]
 name = "Jakob Schulz"
 
 [schulz.emails]
 
 [schulz.emails.schulz_email]
 user = [
   "jakob",
   "schulz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [schulz.homepages]
 
 [scott]
 name = "Dana Scott"
 
 [scott.emails]
 
 [scott.homepages]
 scott_homepage = "http://www.cs.cmu.edu/~scott/"
 
 [sefidgar]
 name = "S. Reza Sefidgar"
 
 [sefidgar.emails]
 
 [sefidgar.emails.sefidgar_email]
 user = [
   "reza",
   "sefidgar",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [sefidgar.homepages]
 
 [seidl]
 name = "Benedikt Seidl"
 
 [seidl.emails]
 
 [seidl.emails.seidl_email]
 user = [
   "benedikt",
   "seidl",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [seidl.homepages]
 
 [seidler]
 name = "Henning Seidler"
 
 [seidler.emails]
 
 [seidler.emails.seidler_email]
 user = [
   "henning",
   "seidler",
 ]
 host = [
   "mailbox",
   "tu-berlin",
   "de",
 ]
 
 [seidler.homepages]
 
 [sewell]
 name = "Thomas Sewell"
 
 [sewell.emails]
 
 [sewell.homepages]
 
 [sickert]
 name = "Salomon Sickert"
 
 [sickert.emails]
 
 [sickert.emails.sickert_email]
 user = [
   "s",
   "sickert",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [sickert.homepages]
 sickert_homepage = "https://www7.in.tum.de/~sickert"
 
 [siek]
 name = "Jeremy Siek"
 
 [siek.emails]
 
 [siek.emails.siek_email]
 user = [
   "jsiek",
 ]
 host = [
   "indiana",
   "edu",
 ]
 
 [siek.homepages]
 siek_homepage = "http://homes.soic.indiana.edu/jsiek/"
 
 [simic]
 name = "Danijela Simić"
 
 [simic.emails]
 
 [simic.emails.simic_email]
 user = [
   "danijela",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [simic.homepages]
 simic_homepage = "http://poincare.matf.bg.ac.rs/~danijela"
 
 [sison]
 name = "Robert Sison"
 
 [sison.emails]
 
 [sison.homepages]
 
 [smaus]
 name = "Jan-Georg Smaus"
 
 [smaus.emails]
 
 [smaus.homepages]
 smaus_homepage = "http://www.irit.fr/~Jan-Georg.Smaus"
 
 [smola]
 name = "Filip Smola"
 
 [smola.emails]
 
 [smola.emails.smola_email]
 user = [
   "f",
   "smola",
 ]
 host = [
   "sms",
   "ed",
   "ac",
   "uk",
 ]
 
 [smola.homepages]
 
 [snelting]
 name = "Gregor Snelting"
 
 [snelting.emails]
 
 [snelting.homepages]
 snelting_homepage = "http://pp.info.uni-karlsruhe.de/personhp/gregor_snelting.php"
 
 [somaini]
 name = "Ivano Somaini"
 
 [somaini.emails]
 
 [somaini.homepages]
 
 [somogyi]
 name = "Dániel Somogyi"
 
 [somogyi.emails]
 
 [somogyi.homepages]
 
 [spasic]
 name = "Mirko Spasić"
 
 [spasic.emails]
 
 [spasic.emails.spasic_email]
 user = [
   "mirko",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [spasic.homepages]
 
 [spichkova]
 name = "Maria Spichkova"
 
 [spichkova.emails]
 
 [spichkova.emails.spichkova_email]
 user = [
   "maria",
   "spichkova",
 ]
 host = [
   "rmit",
   "edu",
   "au",
 ]
 
 [spichkova.homepages]
 
 [spitz]
 name = "Maximilian Spitz"
 
 [spitz.emails]
 
 [spitz.emails.spitz_email]
 user = [
   "maximilian",
   "spitz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [spitz.homepages]
 
 [sprenger]
 name = "Christoph Sprenger"
 
 [sprenger.emails]
 
 [sprenger.emails.sprenger_email]
 user = [
   "sprenger",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [sprenger.homepages]
 
 [springsklee]
 name = "Valentin Springsklee"
 
 [springsklee.emails]
 
 [springsklee.emails.springsklee_email]
 user = [
   "uidpn>",
 ]
 host = [
   "student",
   "kit",
   "edu",
 ]
 
 [springsklee.homepages]
 
 [srba]
 name = "Jiří Srba"
 orcid = "0000-0001-5551-6547"
 
 [srba.emails]
 
 [srba.homepages]
 srba_homepage = "https://homes.cs.aau.dk/~srba/"
 
 [staats]
 name = "Charles Staats"
 
 [staats.emails]
 
 [staats.emails.staats_email]
 user = [
   "cstaats",
 ]
 host = [
   "google",
   "com",
 ]
 
 [staats.emails.staats_email1]
 user = [
   "charles",
   "staats",
   "iii",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [staats.homepages]
 
 [stannett]
 name = "Mike Stannett"
 
 [stannett.emails]
 
 [stannett.emails.stannett_email]
 user = [
   "m",
   "stannett",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [stannett.homepages]
 
 [stark]
 name = "Eugene W. Stark"
 
 [stark.emails]
 
 [stark.emails.stark_email]
 user = [
   "stark",
 ]
 host = [
   "cs",
   "stonybrook",
   "edu",
 ]
 
 [stark.homepages]
 
 [starosta]
 name = "Štěpán Starosta"
 
 [starosta.emails]
 
 [starosta.emails.starosta_email]
 user = [
   "stepan",
   "starosta",
 ]
 host = [
   "fit",
   "cvut",
   "cz",
 ]
 
 [starosta.homepages]
 starosta_homepage = "https://staroste.pages.fit/"
 
 [steen]
 name = "Alexander Steen"
 
 [steen.emails]
 
 [steen.homepages]
 
 [steinberg]
 name = "Matías Steinberg"
 
 [steinberg.emails]
 
 [steinberg.emails.steinberg_email]
 user = [
   "matias",
   "steinberg",
 ]
 host = [
   "mi",
   "unc",
   "edu",
   "ar",
 ]
 
 [steinberg.homepages]
 
 [stell]
 name = "Amy Stell"
 orcid = "0000-0003-0714-3269"
 
 [stell.emails]
 
 [stell.emails.stell_email]
 user = [
   "as1343",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [stell.homepages]
 stell_homepage = "https://computerscience.exeter.ac.uk/staff/as1343?sm=as1343"
 
 [stephan]
 name = "Werner Stephan"
 
 [stephan.emails]
 
 [stephan.emails.stephan_email]
 user = [
   "stephan",
 ]
 host = [
   "dfki",
   "de",
 ]
 
 [stephan.homepages]
 
 [sternagel]
 name = "Christian Sternagel"
 
 [sternagel.emails]
 
 [sternagel.emails.sternagel_email]
 user = [
   "c",
   "sternagel",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [sternagel.emails.sternagel_email1]
 user = [
   "christian",
   "sternagel",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [sternagel.homepages]
 sternagel_homepage = "http://cl-informatik.uibk.ac.at/users/griff/"
 
 [sternagelt]
 name = "Thomas Sternagel"
 
 [sternagelt.emails]
 
 [sternagelt.homepages]
 
 [stevens]
 name = "Lukas Stevens"
 
 [stevens.emails]
 
 [stevens.emails.stevens_email]
 user = [
   "lukas",
   "stevens",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [stevens.homepages]
 stevens_homepage = "https://www21.in.tum.de/team/stevensl"
 
 [stock]
 name = "Benedikt Stock"
 
 [stock.emails]
 
 [stock.emails.stock_email]
 user = [
   "benedikt1999",
 ]
 host = [
   "freenet",
   "de",
 ]
 
 [stock.homepages]
 
 [stoeckl]
 name = "Bernhard Stöckl"
 
 [stoeckl.emails]
 
 [stoeckl.emails.stoeckl_email]
 user = [
   "stoeckl",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [stoeckl.homepages]
 
 [stricker]
 name = "Christian Stricker"
 
 [stricker.emails]
 
 [stricker.homepages]
 stricker_homepage = "http://dss.in.tum.de/staff/christian-stricker.html"
 
 [strnisa]
 name = "Rok Strniša"
 
 [strnisa.emails]
 
 [strnisa.emails.strnisa_email]
 user = [
   "rok",
 ]
 host = [
   "strnisa",
   "com",
 ]
 
 [strnisa.homepages]
 strnisa_homepage = "http://rok.strnisa.com/lj/"
 
 [struth]
 name = "Georg Struth"
 
 [struth.emails]
 
 [struth.emails.struth_email]
 user = [
   "g",
   "struth",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [struth.homepages]
 struth_homepage = "http://staffwww.dcs.shef.ac.uk/people/G.Struth/"
 
 [stueber]
 name = "Anke Stüber"
 
 [stueber.emails]
 
 [stueber.emails.stueber_email]
 user = [
   "anke",
   "stueber",
 ]
 host = [
   "campus",
   "tu-berlin",
   "de",
 ]
 
 [stueber.homepages]
 
+[stuebinger]
+name = "Terru Stübinger"
+orcid = "0009-0006-7411-2533"
+
+[stuebinger.emails]
+
+[stuebinger.homepages]
+stuebinger_homepage = "https://stuebinm.eu/"
+
 [stuewe]
 name = "Daniel Stüwe"
 
 [stuewe.emails]
 
 [stuewe.homepages]
 
 [sudbrock]
 name = "Henning Sudbrock"
 
 [sudbrock.emails]
 
 [sudbrock.emails.sudbrock_email]
 user = [
   "sudbrock",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [sudbrock.homepages]
 
 [sudhof]
 name = "Henry Sudhof"
 
 [sudhof.emails]
 
 [sudhof.emails.sudhof_email]
 user = [
   "hsudhof",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [sudhof.homepages]
 
 [sulejmani]
 name = "Ujkan Sulejmani"
 
 [sulejmani.emails]
 
 [sulejmani.emails.sulejmani_email]
 user = [
   "ujkan",
   "sulejmani",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [sulejmani.emails.sulejmani_email1]
 user = [
   "ujkan99",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [sulejmani.homepages]
 
 [sutcliffe]
 name = "Geoff Sutcliffe"
 
 [sutcliffe.emails]
 
 [sutcliffe.homepages]
 
 [sylvestre]
 name = "Jeremy Sylvestre"
 
 [sylvestre.emails]
 
 [sylvestre.emails.sylvestre_email]
 user = [
   "jeremy",
   "sylvestre",
 ]
 host = [
   "ualberta",
   "ca",
 ]
 
 [sylvestre.emails.sylvestre_email1]
 user = [
   "jsylvest",
 ]
 host = [
   "ualberta",
   "ca",
 ]
 
 [sylvestre.homepages]
 sylvestre_homepage = "http://ualberta.ca/~jsylvest/"
 
 [szekely]
 name = "Gergely Szekely"
 
 [szekely.emails]
 
 [szekely.homepages]
 szekely_homepage = "https://users.renyi.hu/~turms/"
 
 [taha]
 name = "Safouan Taha"
 
 [taha.emails]
 
 [taha.emails.taha_email]
 user = [
   "safouan",
   "taha",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [taha.homepages]
 
 [tan]
 name = "Yong Kiam Tan"
 
 [tan.emails]
 
 [tan.emails.tan_email]
 user = [
   "yongkiat",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [tan.homepages]
 tan_homepage = "https://www.cs.cmu.edu/~yongkiat/"
 
 [tanaka]
 name = "Miki Tanaka"
 
 [tanaka.emails]
 
 [tanaka.emails.tanaka_email]
 user = [
   "miki",
   "tanaka",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [tanaka.homepages]
 
 [tasch]
 name = "Markus Tasch"
 
 [tasch.emails]
 
 [tasch.emails.tasch_email]
 user = [
   "tasch",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [tasch.homepages]
 
 [taylor]
 name = "Ramsay G. Taylor"
 
 [taylor.emails]
 
 [taylor.emails.taylor_email]
 user = [
   "r",
   "g",
   "taylor",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [taylor.homepages]
 
 [terraf]
 name = "Pedro Sánchez Terraf"
 
 [terraf.emails]
 
 [terraf.emails.terraf_email]
 user = [
   "psterraf",
 ]
 host = [
   "unc",
   "edu",
   "ar",
 ]
 
 [terraf.homepages]
 terraf_homepage = "https://cs.famaf.unc.edu.ar/~pedro/home_en.html"
 
 [thiemann]
 name = "René Thiemann"
 
 [thiemann.emails]
 
 [thiemann.emails.thiemann_email]
 user = [
   "rene",
   "thiemann",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [thiemann.homepages]
 thiemann_homepage = "http://cl-informatik.uibk.ac.at/users/thiemann/"
 
 [thommes]
 name = "Joseph Thommes"
 
 [thommes.emails]
 
 [thommes.emails.thommes_email]
 user = [
   "joseph-thommes",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [thommes.homepages]
 
 [thomson]
 name = "Fox Thomson"
 
 [thomson.emails]
 
 [thomson.emails.thomson_email]
 user = [
   "foxthomson0",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [thomson.homepages]
 
 [tiu]
 name = "Alwen Tiu"
 
 [tiu.emails]
 
 [tiu.emails.tiu_email]
 user = [
   "ATiu",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [tiu.homepages]
 tiu_homepage = "http://users.cecs.anu.edu.au/~tiu/"
 
 [toth]
 name = "Balazs Toth"
 
 [toth.emails]
 
 [toth.emails.toth_email]
 user = [
   "balazs",
   "toth",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [toth.homepages]
 
 [tourret]
 name = "Sophie Tourret"
 
 [tourret.emails]
 
 [tourret.emails.tourret_email]
 user = [
   "stourret",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [tourret.homepages]
 tourret_homepage = "https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret/"
 
 [trachtenherz]
 name = "David Trachtenherz"
 
 [trachtenherz.emails]
 
 [trachtenherz.homepages]
 
 [traut]
 name = "Christoph Traut"
 
 [traut.emails]
 
 [traut.homepages]
 
 [traytel]
 name = "Dmitriy Traytel"
 
 [traytel.emails]
 
 [traytel.emails.traytel_email]
 user = [
   "traytel",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [traytel.emails.traytel_email1]
 user = [
   "traytel",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [traytel.emails.traytel_email2]
 user = [
   "traytel",
 ]
 host = [
   "di",
   "ku",
   "dk",
 ]
 
 [traytel.homepages]
 traytel_homepage = "https://traytel.bitbucket.io/"
 
 [trelat]
 name = "Vincent Trélat"
 
 [trelat.emails]
 
 [trelat.emails.trelat_email]
 user = [
   "vincent",
   "trelat",
 ]
 host = [
   "depinfonancy",
   "net",
 ]
 
 [trelat.homepages]
 
 [tuerk]
 name = "Thomas Tuerk"
 
 [tuerk.emails]
 
 [tuerk.homepages]
 
 [tuong]
 name = "Frédéric Tuong"
 
 [tuong.emails]
 
 [tuong.emails.tuong_email]
 user = [
   "tuong",
 ]
 host = [
   "users",
   "gforge",
   "inria",
   "fr",
 ]
 
 [tuong.emails.tuong_email1]
 user = [
   "ftuong",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [tuong.homepages]
 tuong_homepage = "https://www.lri.fr/~ftuong/"
 
 [tuongj]
 name = "Joseph Tuong"
 
 [tuongj.emails]
 
 [tuongj.homepages]
 
 [tverdyshev]
 name = "Sergey Tverdyshev"
 
 [tverdyshev.emails]
 
 [tverdyshev.emails.tverdyshev_email]
 user = [
   "stv",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [tverdyshev.homepages]
 
 [ullrich]
 name = "Sebastian Ullrich"
 
 [ullrich.emails]
 
 [ullrich.emails.ullrich_email]
 user = [
   "sebasti",
 ]
 host = [
   "nullri",
   "ch",
 ]
 
 [ullrich.homepages]
 
 [unruh]
 name = "Dominique Unruh"
 
 [unruh.emails]
 
 [unruh.emails.unruh_email]
 user = [
   "unruh",
 ]
 host = [
   "ut",
   "ee",
 ]
 
 [unruh.homepages]
 unruh_homepage = "https://www.ut.ee/~unruh/"
 
 [urban]
 name = "Christian Urban"
 
 [urban.emails]
 
 [urban.emails.urban_email]
 user = [
   "christian",
   "urban",
 ]
 host = [
   "kcl",
   "ac",
   "uk",
 ]
 
 [urban.homepages]
 urban_homepage = "https://nms.kcl.ac.uk/christian.urban/"
 
 [van]
 name = "Hai Nguyen Van"
 
 [van.emails]
 
 [van.emails.van_email]
 user = [
   "hai",
   "nguyenvan",
   "phie",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [van.homepages]
 
 [velykis]
 name = "Andrius Velykis"
 
 [velykis.emails]
 
 [velykis.homepages]
 velykis_homepage = "http://andrius.velykis.lt"
 
 [verbeek]
 name = "Freek Verbeek"
 
 [verbeek.emails]
 
 [verbeek.emails.verbeek_email]
 user = [
   "Freek",
   "Verbeek",
 ]
 host = [
   "ou",
   "nl",
 ]
 
 [verbeek.emails.verbeek_email1]
 user = [
   "freek",
 ]
 host = [
   "vt",
   "edu",
 ]
 
 [verbeek.homepages]
 
 [villadsen]
 name = "Jørgen Villadsen"
 
 [villadsen.emails]
 
 [villadsen.emails.villadsen_email]
 user = [
   "jovi",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [villadsen.homepages]
 villadsen_homepage = "https://people.compute.dtu.dk/jovi/"
 
 [voisin]
 name = "Frederic Voisin"
 
 [voisin.emails]
 
 [voisin.homepages]
 
 [vytiniotis]
 name = "Dimitrios Vytiniotis"
 
 [vytiniotis.emails]
 
 [vytiniotis.homepages]
 vytiniotis_homepage = "http://research.microsoft.com/en-us/people/dimitris/"
 
 [wagner]
 name = "Max Wagner"
 
 [wagner.emails]
 
 [wagner.emails.wagner_email]
 user = [
   "max",
 ]
 host = [
   "trollbu",
   "de",
 ]
 
 [wagner.homepages]
 
 [waldmann]
 name = "Uwe Waldmann"
 
 [waldmann.emails]
 
 [waldmann.emails.waldmann_email]
 user = [
   "waldmann",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [waldmann.homepages]
 
 [wand]
 name = "Daniel Wand"
 
 [wand.emails]
 
 [wand.emails.wand_email]
 user = [
   "dwand",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [wand.homepages]
 
 [wang]
 name = "Shuling Wang"
 
 [wang.emails]
 
 [wang.homepages]
 
 [wassell]
 name = "Mark Wassell"
 
 [wassell.emails]
 
 [wassell.emails.wassell_email]
 user = [
   "mpwassell",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [wassell.homepages]
 
 [wasserrab]
 name = "Daniel Wasserrab"
 
 [wasserrab.emails]
 
 [wasserrab.homepages]
 wasserrab_homepage = "http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php"
 
 [watt]
 name = "Conrad Watt"
 
 [watt.emails]
 
 [watt.emails.watt_email]
 user = [
   "caw77",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [watt.homepages]
 watt_homepage = "http://www.cl.cam.ac.uk/~caw77/"
 
 [weber]
 name = "Tjark Weber"
 
 [weber.emails]
 
 [weber.emails.weber_email]
 user = [
   "tjark",
   "weber",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [weber.homepages]
 weber_homepage = "http://user.it.uu.se/~tjawe125/"
 
 [weerwag]
 name = "Timmy Weerwag"
 
 [weerwag.emails]
 
 [weerwag.homepages]
 
 [weidner]
 name = "Arno Wilhelm-Weidner"
 
 [weidner.emails]
 
 [weidner.emails.weidner_email]
 user = [
   "arno",
   "wilhelm-weidner",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [weidner.homepages]
 
 [wenninger]
 name = "Elias Wenninger"
 
 [wenninger.emails]
 
 [wenninger.homepages]
 
 [wenzel]
 name = "Makarius Wenzel"
 
 [wenzel.emails]
 
 [wenzel.emails.wenzel_email]
 user = [
   "makarius",
 ]
 host = [
   "sketis",
   "net",
 ]
 
 [wenzel.homepages]
 
 [whitley]
 name = "A Whitley"
 
 [whitley.emails]
 
 [whitley.emails.whitley_email]
 user = [
   "awhitley",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [whitley.homepages]
 
 [wickerson]
 name = "John Wickerson"
 
 [wickerson.emails]
 
 [wickerson.homepages]
 wickerson_homepage = "http://www.doc.ic.ac.uk/~jpw48"
 
 [willenbrink]
 name = "Sebastian Willenbrink"
 
 [willenbrink.emails]
 
 [willenbrink.emails.willenbrink_email]
 user = [
   "sebastian",
   "willenbrink",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [willenbrink.homepages]
 
 [wimmer]
 name = "Simon Wimmer"
 
 [wimmer.emails]
 
 [wimmer.emails.wimmer_email]
 user = [
   "simon",
   "wimmer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [wimmer.homepages]
 wimmer_homepage = "http://home.in.tum.de/~wimmers/"
 
 [wirt]
 name = "Kai Wirt"
 
 [wirt.emails]
 
 [wirt.homepages]
 
 [wolff]
 name = "Burkhart Wolff"
 
 [wolff.emails]
 
 [wolff.emails.wolff_email]
 user = [
   "burkhart",
   "wolff",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [wolff.homepages]
 wolff_homepage = "https://www.lri.fr/~wolff/"
 
 [wu]
 name = "Chunhan Wu"
 
 [wu.emails]
 
 [wu.homepages]
 
 [xu]
 name = "Jian Xu"
 
 [xu.emails]
 
 [xu.homepages]
 
 [yamada]
 name = "Akihisa Yamada"
 
 [yamada.emails]
 
 [yamada.emails.yamada_email]
 user = [
   "akihisa",
   "yamada",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [yamada.emails.yamada_email1]
 user = [
   "ayamada",
 ]
 host = [
   "trs",
   "cm",
   "is",
   "nagoya-u",
   "ac",
   "jp",
 ]
 
 [yamada.emails.yamada_email2]
 user = [
   "akihisa",
   "yamada",
 ]
 host = [
   "aist",
   "go",
   "jp",
 ]
 
 [yamada.emails.yamada_email3]
 user = [
   "akihisayamada",
 ]
 host = [
   "nii",
   "ac",
   "jp",
 ]
 
 [yamada.homepages]
 yamada_homepage = "http://group-mmm.org/~ayamada/"
 
+[yang]
+name = "Jiong Yang"
+
+[yang.emails]
+
+[yang.emails.yang_email]
+user = [
+  "jiongyangcobe",
+]
+host = [
+  "gmail",
+  "com",
+]
+
+[yang.homepages]
+
 [ye]
 name = "Lina Ye"
 
 [ye.emails]
 
 [ye.emails.ye_email]
 user = [
   "lina",
   "ye",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [ye.homepages]
 
 [yez]
 name = "Zhengkun Ye"
 
 [yez.emails]
 
 [yez.emails.yez_email]
 user = [
   "zy307",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [yez.homepages]
 
 [ying]
 name = "Shenggang Ying"
 
 [ying.emails]
 
 [ying.homepages]
 
 [yingm]
 name = "Mingsheng Ying"
 
 [yingm.emails]
 
 [yingm.homepages]
 
 [yu]
 name = "Lei Yu"
 
 [yu.emails]
 
 [yu.emails.yu_email]
 user = [
   "yulei0603",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [yu.homepages]
 
 [zankl]
 name = "Harald Zankl"
 
 [zankl.emails]
 
 [zankl.emails.zankl_email]
 user = [
   "Harald",
   "Zankl",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [zankl.homepages]
 zankl_homepage = "http://cl-informatik.uibk.ac.at/users/hzankl"
 
 [zee]
 name = "Karen Zee"
 
 [zee.emails]
 
 [zee.emails.zee_email]
 user = [
   "kkz",
 ]
 host = [
   "mit",
   "edu",
 ]
 
 [zee.homepages]
 zee_homepage = "http://www.mit.edu/~kkz/"
 
 [zeller]
 name = "Peter Zeller"
 
 [zeller.emails]
 
 [zeller.emails.zeller_email]
 user = [
   "p_zeller",
 ]
 host = [
   "cs",
   "uni-kl",
   "de",
 ]
 
 [zeller.homepages]
 
 [zeyda]
 name = "Frank Zeyda"
 
 [zeyda.emails]
 
 [zeyda.emails.zeyda_email]
 user = [
   "frank",
   "zeyda",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [zeyda.homepages]
 
 [zhan]
 name = "Bohua Zhan"
 
 [zhan.emails]
 
 [zhan.emails.zhan_email]
 user = [
   "bzhan",
 ]
 host = [
   "ios",
   "ac",
   "cn",
 ]
 
 [zhan.homepages]
 zhan_homepage = "http://lcs.ios.ac.cn/~bzhan/"
 
 [zhang]
 name = "Yu Zhang"
 
 [zhang.emails]
 
 [zhang.homepages]
 
 [zhangx]
 name = "Xingyuan Zhang"
 
 [zhangx.emails]
 
 [zhangx.homepages]
 
 [zhann]
 name = "Naijun Zhan"
 
 [zhann.emails]
 
 [zhann.homepages]
diff --git a/metadata/authors.toml.orig b/metadata/authors.toml.orig
--- a/metadata/authors.toml.orig
+++ b/metadata/authors.toml.orig
@@ -1,7629 +1,7656 @@
 
 [abdulaziz]
 name = "Mohammad Abdulaziz"
 
 [abdulaziz.emails]
 
 [abdulaziz.emails.abdulaziz_email]
 user = [
   "mohammad",
   "abdulaziz",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [abdulaziz.emails.abdulaziz_email1]
 user = [
   "mohammad",
   "abdulaziz8",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [abdulaziz.homepages]
 abdulaziz_homepage = "http://home.in.tum.de/~mansour/"
 
 [adelsberger]
 name = "Stephan Adelsberger"
 
 [adelsberger.emails]
 
 [adelsberger.emails.adelsberger_email]
 user = [
   "stvienna",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [adelsberger.homepages]
 adelsberger_homepage = "http://nm.wu.ac.at/nm/sadelsbe"
 
 [aehlig]
 name = "Klaus Aehlig"
 
 [aehlig.emails]
 
 [aehlig.homepages]
 aehlig_homepage = "http://www.linta.de/~aehlig/"
 
 [aissat]
 name = "Romain Aissat"
 
 [aissat.emails]
 
 [aissat.homepages]
 
 [amani]
 name = "Sidney Amani"
 
 [amani.emails]
 
 [amani.emails.amani_email]
 user = [
   "sidney",
   "amani",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [amani.homepages]
 
 [ammer]
 name = "Thomas Ammer"
 
 [ammer.emails]
 
 [ammer.emails.ammer_email]
 user = [
   "thomas",
   "ammer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [ammer.homepages]
 
 [andreka]
 name = "Hajnal Andreka"
 
 [andreka.emails]
 
 [andreka.homepages]
 andreka_homepage = "https://renyi.hu/en/researchers/hajnal-andreka"
 
 [andronick]
 name = "June Andronick"
 
 [andronick.emails]
 
 [andronick.homepages]
 
 [aransay]
 name = "Jesús Aransay"
 
 [aransay.emails]
 
 [aransay.emails.aransay_email]
 user = [
   "jesus-maria",
   "aransay",
 ]
 host = [
   "unirioja",
   "es",
 ]
 
 [aransay.homepages]
 aransay_homepage = "https://www.unirioja.es/cu/jearansa"
 
 [argyraki]
 name = "Angeliki Koutsoukou-Argyraki"
 
 [argyraki.emails]
 
 [argyraki.emails.argyraki_email]
 user = [
   "ak2110",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [argyraki.homepages]
 argyraki_homepage = "https://www.cl.cam.ac.uk/~ak2110/"
 argyraki_homepage2 = "https://www.cst.cam.ac.uk/people/ak2110"
 
 [armstrong]
 name = "Alasdair Armstrong"
 
 [armstrong.emails]
 
 [armstrong.homepages]
 
 [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"
 
 [avigad]
 name = "Jeremy Avigad"
 
 [avigad.emails]
 
 [avigad.emails.avigad_email]
 user = [
   "avigad",
 ]
 host = [
   "cmu",
   "edu",
 ]
 
 [avigad.homepages]
 avigad_homepage = "http://www.andrew.cmu.edu/user/avigad/"
 
 [back]
 name = "Ralph-Johan Back"
 
 [back.emails]
 
 [back.homepages]
 back_homepage = "http://users.abo.fi/Ralph-Johan.Back/"
 
 [baksys]
 name = "Mantas Bakšys"
 
 [baksys.emails]
 
 [baksys.emails.baksys_email]
 user = [
   "mb2412",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [baksys.homepages]
 baksys_homepage = "https://github.com/MantasBaksys"
 
 [balbach]
 name = "Frank J. Balbach"
 
 [balbach.emails]
 
 [balbach.emails.balbach_email]
 user = [
   "frank-balbach",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [balbach.homepages]
 
 [ballarin]
 name = "Clemens Ballarin"
 
 [ballarin.emails]
 
 [ballarin.emails.ballarin_email]
 user = [
   "ballarin",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [ballarin.homepages]
 ballarin_homepage = "http://www21.in.tum.de/~ballarin/"
 
 [ballenghien]
 name = "Benoît Ballenghien"
 
 [ballenghien.emails]
 
 [ballenghien.emails.ballenghien_email]
 user = [
   "benoit",
   "ballenghien",
 ]
 host = [
   "universite-paris-saclay",
   "fr",
 ]
 
 [ballenghien.homepages]
 
 [barsotti]
 name = "Damián Barsotti"
 
 [barsotti.emails]
 
 [barsotti.homepages]
 barsotti_homepage = "http://www.cs.famaf.unc.edu.ar/~damian/"
 
 [bauer]
 name = "Gertrud Bauer"
 
 [bauer.emails]
 
 [bauer.homepages]
 
 [bauereiss]
 name = "Thomas Bauereiss"
 
 [bauereiss.emails]
 
 [bauereiss.emails.bauereiss_email]
 user = [
   "thomas",
 ]
 host = [
   "bauereiss",
   "name",
 ]
 
 [bauereiss.homepages]
 
 [bayer]
 name = "Jonas Bayer"
 
 [bayer.emails]
 
 [bayer.emails.bayer_email]
 user = [
   "jonas",
   "bayer999",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bayer.homepages]
 
 [becker]
 name = "Heiko Becker"
 
 [becker.emails]
 
 [becker.emails.becker_email]
 user = [
   "hbecker",
 ]
 host = [
   "mpi-sws",
   "org",
 ]
 
 [becker.homepages]
 
 [beeren]
 name = "Joel Beeren"
 
 [beeren.emails]
 
 [beeren.homepages]
 
 [bella]
 name = "Giampaolo Bella"
 
 [bella.emails]
 
 [bella.emails.bella_email]
 user = [
   "giamp",
 ]
 host = [
   "dmi",
   "unict",
   "it",
 ]
 
 [bella.homepages]
 bella_homepage = "http://www.dmi.unict.it/~giamp/"
 
 [bengtson]
 name = "Jesper Bengtson"
 
 [bengtson.emails]
 
 [bengtson.homepages]
 bengtson_homepage = "http://www.itu.dk/people/jebe"
 
 [bentkamp]
 name = "Alexander Bentkamp"
 
 [bentkamp.emails]
 
 [bentkamp.emails.bentkamp_email]
 user = [
   "bentkamp",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bentkamp.emails.bentkamp_email1]
 user = [
   "a",
   "bentkamp",
 ]
 host = [
   "vu",
   "nl",
 ]
 
 [bentkamp.homepages]
 bentkamp_homepage = "https://www.cs.vu.nl/~abp290/"
 
 [benzmueller]
 name = "Christoph Benzmüller"
 
 [benzmueller.emails]
 
 [benzmueller.emails.benzmueller_email]
 user = [
   "c",
   "benzmueller",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [benzmueller.emails.benzmueller_email1]
 user = [
   "c",
   "benzmueller",
 ]
 host = [
   "fu-berlin",
   "de",
 ]
 
 [benzmueller.homepages]
 benzmueller_homepage = "http://christoph-benzmueller.de"
 benzmueller_homepage1 = "http://page.mi.fu-berlin.de/cbenzmueller/"
 
 [beresford]
 name = "Alastair R. Beresford"
 
 [beresford.emails]
 
 [beresford.emails.beresford_email]
 user = [
   "arb33",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [beresford.homepages]
 
 [berghofer]
 name = "Stefan Berghofer"
 
 [berghofer.emails]
 
 [berghofer.emails.berghofer_email]
 user = [
   "berghofe",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [berghofer.homepages]
 berghofer_homepage = "http://www.in.tum.de/~berghofe"
 
 [bergstroem]
 name = "Axel Bergström"
 
 [bergstroem.emails]
 
 [bergstroem.emails.bergstroem_email]
 user = [
   "axel",
   "bergstrom00",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bergstroem.homepages]
 
 [beringer]
 name = "Lennart Beringer"
 
 [beringer.emails]
 
 [beringer.emails.beringer_email]
 user = [
   "lennart",
   "beringer",
 ]
 host = [
   "ifi",
   "lmu",
   "de",
 ]
 
 [beringer.homepages]
 
 [bharadwaj]
 name = "Abhijith Bharadwaj"
 
 [bharadwaj.emails]
 
 [bharadwaj.homepages]
 
 [bhatt]
 name = "Bhargav Bhatt"
 
 [bhatt.emails]
 
 [bhatt.emails.bhatt_email]
 user = [
   "bhargav",
   "bhatt",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [bhatt.homepages]
 
 [biendarra]
 name = "Julian Biendarra"
 
 [biendarra.emails]
 
 [biendarra.homepages]
 
 [bisping]
 name = "Benjamin Bisping"
 orcid = "0000-0002-0637-0171"
 
 [bisping.emails]
 
 [bisping.emails.bisping_email]
 user = [
   "benjamin",
   "bisping",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [bisping.homepages]
 bisping_homepage = "https://bbisping.de"
 
 [blanchette]
 name = "Jasmin Christian Blanchette"
 
 [blanchette.emails]
 
 [blanchette.emails.blanchette_email]
 user = [
   "jasmin",
   "blanchette",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [blanchette.emails.blanchette_email1]
 user = [
   "j",
   "c",
   "blanchette",
 ]
 host = [
   "vu",
   "nl",
 ]
 
 [blanchette.homepages]
 blanchette_homepage = "http://www21.in.tum.de/~blanchet"
 blanchette_homepage1 = "https://www.cs.vu.nl/~jbe248/"
 
 [blasum]
 name = "Holger Blasum"
 
 [blasum.emails]
 
 [blasum.emails.blasum_email]
 user = [
   "holger",
   "blasum",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [blasum.homepages]
 
 [blumson]
 name = "Ben Blumson"
 
 [blumson.emails]
 
 [blumson.emails.blumson_email]
 user = [
   "benblumson",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [blumson.homepages]
 blumson_homepage = "https://philpeople.org/profiles/ben-blumson"
 
 [bockenek]
 name = "Joshua Bockenek"
 
 [bockenek.emails]
 
 [bockenek.homepages]
 
 [boehme]
 name = "Sascha Böhme"
 
 [boehme.emails]
 
 [boehme.emails.boehme_email]
 user = [
   "boehmes",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [boehme.homepages]
 boehme_homepage = "http://www21.in.tum.de/~boehmes/"
 
 [bohrer]
 name = "Rose Bohrer"
 
 [bohrer.emails]
 
 [bohrer.emails.bohrer_email]
 user = [
   "rose",
   "bohrer",
   "cs",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bohrer.homepages]
 
 [bootle]
 name = "Jonathan Bootle"
 
 [bootle.emails]
 
 [bootle.emails.bootle_email]
 user = [
   "JBT",
 ]
 host = [
   "zurich",
   "ibm",
   "com",
 ]
 
 [bootle.homepages]
 
 [bordg]
 name = "Anthony Bordg"
 
 [bordg.emails]
 
 [bordg.emails.bordg_email]
 user = [
   "apdb3",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [bordg.homepages]
 bordg_homepage = "https://sites.google.com/site/anthonybordg/"
 
 [borgstroem]
 name = "Johannes Borgström"
 
 [borgstroem.emails]
 
 [borgstroem.emails.borgstroem_email]
 user = [
   "johannes",
   "borgstrom",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [borgstroem.homepages]
 
 [bortin]
 name = "Maksym Bortin"
 
 [bortin.emails]
 
 [bortin.emails.bortin_email]
 user = [
   "maksym",
   "bortin",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [bortin.emails.bortin_email1]
 user = [
   "mbortin",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bortin.homepages]
 
 [bottesch]
 name = "Ralph Bottesch"
 
 [bottesch.emails]
 
 [bottesch.emails.bottesch_email]
 user = [
   "ralph",
   "bottesch",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [bottesch.homepages]
 bottesch_homepage = "http://cl-informatik.uibk.ac.at/users/bottesch/"
 
 [boulanger]
 name = "Frédéric Boulanger"
 
 [boulanger.emails]
 
 [boulanger.emails.boulanger_email]
 user = [
   "frederic",
   "boulanger",
 ]
 host = [
   "centralesupelec",
   "fr",
 ]
 
 [boulanger.homepages]
 
 [bourke]
 name = "Timothy Bourke"
 
 [bourke.emails]
 
 [bourke.emails.bourke_email]
 user = [
   "tim",
 ]
 host = [
   "tbrk",
   "org",
 ]
 
 [bourke.homepages]
 bourke_homepage = "http://www.tbrk.org"
 
 [boutry]
 name = "Pierre Boutry"
 
 [boutry.emails]
 
 [boutry.emails.boutry_email]
 user = [
   "boutry",
 ]
 host = [
   "unistra",
   "fr",
 ]
 
 [boutry.homepages]
 
 [boyton]
 name = "Andrew Boyton"
 
 [boyton.emails]
 
 [boyton.emails.boyton_email]
 user = [
   "andrew",
   "boyton",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [boyton.homepages]
 
 [bracevac]
 name = "Oliver Bračevac"
 
 [bracevac.emails]
 
 [bracevac.emails.bracevac_email]
 user = [
   "bracevac",
 ]
 host = [
   "st",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [bracevac.homepages]
 
 [brandt]
 name = "Felix Brandt"
 
 [brandt.emails]
 
 [brandt.homepages]
 brandt_homepage = "http://dss.in.tum.de/staff/brandt.html"
 
 [breitner]
 name = "Joachim Breitner"
 
 [breitner.emails]
 
 [breitner.emails.breitner_email]
 user = [
   "mail",
 ]
 host = [
   "joachim-breitner",
   "de",
 ]
 
 [breitner.emails.breitner_email1]
 user = [
   "joachim",
 ]
 host = [
   "cis",
   "upenn",
   "edu",
 ]
 
 [breitner.homepages]
 breitner_homepage = "http://pp.ipd.kit.edu/~breitner"
 
 [brien]
 name = "Nicolas Robinson-O'Brien"
 
 [brien.emails]
 
 [brien.homepages]
 
 [brinkop]
 name = "Hauke Brinkop"
 
 [brinkop.emails]
 
 [brinkop.emails.brinkop_email]
 user = [
   "hauke",
   "brinkop",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [brinkop.homepages]
 
 [brodmann]
 name = "Paul-David Brodmann"
 
 [brodmann.emails]
 
 [brodmann.emails.brodmann_email]
 user = [
   "p",
   "brodmann",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [brodmann.homepages]
 
 [brucker]
 name = "Achim D. Brucker"
 
 [brucker.emails]
 
 [brucker.emails.brucker_email]
 user = [
   "a",
   "brucker",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [brucker.emails.brucker_email2]
 user = [
   "adbrucker",
 ]
 host = [
   "0x5f",
   "org",
 ]
 
 [brucker.homepages]
 brucker_homepage = "https://www.brucker.ch/"
 
 [bruegger]
 name = "Lukas Brügger"
 
 [bruegger.emails]
 
 [bruegger.emails.bruegger_email]
 user = [
   "lukas",
   "a",
   "bruegger",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bruegger.homepages]
 
 [brun]
 name = "Matthias Brun"
 
 [brun.emails]
 
 [brun.emails.brun_email]
 user = [
   "matthias",
   "brun",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [brun.homepages]
 
 [brunner]
 name = "Julian Brunner"
 
 [brunner.emails]
 
 [brunner.emails.brunner_email]
 user = [
   "brunnerj",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [brunner.homepages]
 brunner_homepage = "http://www21.in.tum.de/~brunnerj/"
 
 [bulwahn]
 name = "Lukas Bulwahn"
 
 [bulwahn.emails]
 
 [bulwahn.emails.bulwahn_email]
 user = [
   "lukas",
   "bulwahn",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [bulwahn.homepages]
 
 [buss]
 name = "Sebastián Buss"
 
 [buss.emails]
 
 [buss.emails.buss_email]
 user = [
   "sbuss94",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [buss.homepages]
 
 [butler]
 name = "David Butler"
 
 [butler.emails]
 
 [butler.emails.butler_email]
 user = [
   "dbutler",
 ]
 host = [
   "turing",
   "ac",
   "uk",
 ]
 
 [butler.homepages]
 butler_homepage = "https://www.turing.ac.uk/people/doctoral-students/david-butler"
 
 [buyse]
 name = "Maxime Buyse"
 
 [buyse.emails]
 
 [buyse.emails.buyse_email]
 user = [
   "maxime",
   "buyse",
 ]
 host = [
   "polytechnique",
   "edu",
 ]
 
 [buyse.homepages]
 
 [caballero]
 name = "José Manuel Rodríguez Caballero"
 
 [caballero.emails]
 
 [caballero.emails.caballero_email]
 user = [
   "jose",
   "manuel",
   "rodriguez",
   "caballero",
 ]
 host = [
   "ut",
   "ee",
 ]
 
 [caballero.homepages]
 caballero_homepage = "https://josephcmac.github.io/"
 
 [calk]
 name = "Cameron Calk"
 
 [calk.emails]
 
 [calk.homepages]
 
 [caminati]
 name = "Marco B. Caminati"
 
 [caminati.emails]
 
 [caminati.homepages]
 
 [campo]
 name = "Alejandro del Campo"
 
 [campo.emails]
 
 [campo.emails.campo_email]
 user = [
   "alejandro",
   "del-campo",
 ]
 host = [
   "alum",
   "unirioja",
   "es",
 ]
 
 [campo.homepages]
 
 [chaieb]
 name = "Amine Chaieb"
 
 [chaieb.emails]
 
 [chaieb.homepages]
 
 [chapman]
 name = "Peter Chapman"
 
 [chapman.emails]
 
 [chapman.emails.chapman_email]
 user = [
   "pc",
 ]
 host = [
   "cs",
   "st-andrews",
   "ac",
   "uk",
 ]
 
 [chapman.homepages]
 
 [chen]
 name = "L. Chen"
 
 [chen.emails]
 
 [chen.homepages]
 
+[chenj]
+name = "Jamie Chen"
+orcid = "0009-0008-5396-6059"
+
+[chenj.emails]
+
+[chenj.emails.chenj_email]
+user = [
+  "jamiechen",
+]
+host = [
+  "tutanota",
+  "com",
+]
+
+[chenj.homepages]
+chenj_homepage = "https://gitlab.com/Jamie-Chen"
+
 [chevalier]
 name = "Loïc Chevalier"
 
 [chevalier.emails]
 
 [chevalier.homepages]
 
 [christfort]
 name = "Axel Christfort"
 
 [christfort.emails]
 
 [christfort.emails.christfort_email]
 user = [
   "axel",
 ]
 host = [
   "di",
   "ku",
   "dk",
 ]
 
 [christfort.homepages]
 
 [clouston]
 name = "Ranald Clouston"
 
 [clouston.emails]
 
 [clouston.emails.clouston_email]
 user = [
   "ranald",
   "clouston",
 ]
 host = [
   "cs",
   "au",
   "dk",
 ]
 
 [clouston.homepages]
 
 [cock]
 name = "David Cock"
 
 [cock.emails]
 
 [cock.emails.cock_email]
 user = [
   "david",
   "cock",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [cock.homepages]
 
 [coghetto]
 name = "Roland Coghetto"
 
 [coghetto.emails]
 
 [coghetto.emails.coghetto_email]
 user = [
   "roland_coghetto",
 ]
 host = [
   "hotmail",
   "com",
 ]
 
 [coghetto.homepages]
 
 [coglio]
 name = "Alessandro Coglio"
 
 [coglio.emails]
 
 [coglio.emails.coglio_email]
 user = [
   "coglio",
 ]
 host = [
   "kestrel",
   "edu",
 ]
 
 [coglio.homepages]
 coglio_homepage = "http://www.kestrel.edu/~coglio"
 
 [cohen]
 name = "Ernie Cohen"
 
 [cohen.emails]
 
 [cohen.emails.cohen_email]
 user = [
   "ecohen",
 ]
 host = [
   "amazon",
   "com",
 ]
 
 [cohen.homepages]
 
 [cordwell]
 name = "Katherine Kosaian"
 
 [cordwell.emails]
 
 [cordwell.emails.cordwell_email]
 user = [
   "kcordwel",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [cordwell.homepages]
 cordwell_homepage = "https://www.cs.cmu.edu/~kcordwel/"
 
 [cousin]
 name = "Marie Cousin"
 
 [cousin.emails]
 
 [cousin.emails.cousin_email]
 user = [
   "marie",
   "cousin",
 ]
 host = [
   "grenoble-inp",
   "org",
 ]
 
 [cousin.homepages]
 
 [cremer]
 name = "Nils Cremer"
 
 [cremer.emails]
 
 [cremer.emails.cremer_email]
 user = [
   "nils",
   "cremer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [cremer.homepages]
 
 [crighton]
 name = "Aaron Crighton"
 
 [crighton.emails]
 
 [crighton.emails.crighton_email]
 user = [
   "crightoa",
 ]
 host = [
   "mcmaster",
   "ca",
 ]
 
 [crighton.homepages]
 
 [dalvit]
 name = "Christian Dalvit"
 
 [dalvit.emails]
 
 [dalvit.emails.dalvit_email]
 user = [
   "chris",
   "dalvit",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [dalvit.homepages]
 
 [danilkin]
 name = "Anton Danilkin"
 
 [danilkin.emails]
 
 [danilkin.emails.danilkin_email]
 user = [
   "anton",
   "danilkin",
 ]
 host = [
   "ens",
   "psl",
   "eu",
 ]
 
 [danilkin.homepages]
 
 [dardinier]
 name = "Thibault Dardinier"
 
 [dardinier.emails]
 
 [dardinier.emails.dardinier_email]
 user = [
   "thibault",
   "dardinier",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [dardinier.homepages]
 dardinier_homepage = "https://dardinier.me/"
 
 [david]
 name = "Marco David"
 
 [david.emails]
 
 [david.emails.david_email]
 user = [
   "marco",
   "david",
 ]
 host = [
   "hotmail",
   "de",
 ]
 
 [david.homepages]
 
 [debois]
 name = "Søren Debois"
 
 [debois.emails]
 
 [debois.homepages]
 
 [debrat]
 name = "Henri Debrat"
 
 [debrat.emails]
 
 [debrat.emails.debrat_email]
 user = [
   "henri",
   "debrat",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [debrat.homepages]
 
 [decova]
 name = "Sára Decova"
 
 [decova.emails]
 
 [decova.homepages]
 
 [delemazure]
 name = "Théo Delemazure"
 
 [delemazure.emails]
 
 [delemazure.homepages]
 delemazure_homepage = "https://theo.delemazure.fr/"
 
 [demeulemeester]
 name = "Tom Demeulemeester"
 
 [demeulemeester.emails]
 
 [demeulemeester.homepages]
 demeulemeester_homepage = "https://www.kuleuven.be/wieiswie/en/person/00131528"
 
 [derrick]
 name = "John Derrick"
 
 [derrick.emails]
 
 [derrick.emails.derrick_email]
 user = [
   "j",
   "derrick",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [derrick.homepages]
 
 [desharnais]
 name = "Martin Desharnais"
 
 [desharnais.emails]
 
 [desharnais.emails.desharnais_email]
 user = [
   "martin",
   "desharnais",
 ]
 host = [
   "unibw",
   "de",
 ]
 
 [desharnais.emails.desharnais_email1]
 user = [
   "desharnais",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [desharnais.homepages]
 desharnais_homepage = "https://martin.desharnais.me"
 
 [diaz]
 name = "Javier Díaz"
 
 [diaz.emails]
 
 [diaz.emails.diaz_email]
 user = [
   "javier",
   "diaz",
   "manzi",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [diaz.homepages]
 
 [diekmann]
 name = "Cornelius Diekmann"
 
 [diekmann.emails]
 
 [diekmann.emails.diekmann_email]
 user = [
   "diekmann",
 ]
 host = [
   "net",
   "in",
   "tum",
   "de",
 ]
 
 [diekmann.homepages]
 diekmann_homepage = "http://net.in.tum.de/~diekmann"
 
 [dirix]
 name = "Stefan Dirix"
 
 [dirix.emails]
 
 [dirix.homepages]
 
 [dittmann]
 name = "Christoph Dittmann"
 
 [dittmann.emails]
 
 [dittmann.emails.dittmann_email]
 user = [
   "isabelle",
 ]
 host = [
   "christoph-d",
   "de",
 ]
 
 [dittmann.homepages]
 dittmann_homepage = "http://logic.las.tu-berlin.de/Members/Dittmann/"
 
 [divason]
 name = "Jose Divasón"
 
 [divason.emails]
 
 [divason.emails.divason_email]
 user = [
   "jose",
   "divason",
 ]
 host = [
   "unirioja",
   "es",
 ]
 
 [divason.homepages]
 divason_homepage = "https://www.unirioja.es/cu/jodivaso/"
 
 [doczkal]
 name = "Christian Doczkal"
 
 [doczkal.emails]
 
 [doczkal.emails.doczkal_email]
 user = [
   "doczkal",
 ]
 host = [
   "ps",
   "uni-saarland",
   "de",
 ]
 
 [doczkal.homepages]
 
 [dongol]
 name = "Brijesh Dongol"
 
 [dongol.emails]
 
 [dongol.emails.dongol_email]
 user = [
   "brijesh",
   "dongol",
 ]
 host = [
   "brunel",
   "ac",
   "uk",
 ]
 
 [dongol.homepages]
 
 [doty]
 name = "Matthew Doty"
 
 [doty.emails]
 
 [doty.emails.doty_email]
 user = [
   "matt",
 ]
 host = [
   "w-d",
   "org",
 ]
 
 [doty.homepages]
 
 [dubut]
 name = "Jérémy Dubut"
 
 [dubut.emails]
 
 [dubut.emails.dubut_email]
 user = [
   "dubut",
 ]
 host = [
   "nii",
   "ac",
   "jp",
 ]
 
 [dubut.emails.dubut_email1]
 user = [
   "jeremy",
   "dubut",
 ]
 host = [
   "aist",
   "go",
   "jp",
 ]
 
 [dubut.homepages]
 dubut_homepage = "http://group-mmm.org/~dubut/"
 
 [dunaev]
 name = "Georgy Dunaev"
 
 [dunaev.emails]
 
 [dunaev.emails.dunaev_email]
 user = [
   "georgedunaev",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [dunaev.homepages]
 
 [dyckhoff]
 name = "Roy Dyckhoff"
 
 [dyckhoff.emails]
 
 [dyckhoff.homepages]
 dyckhoff_homepage = "https://rd.host.cs.st-andrews.ac.uk"
 
 [eberl]
 name = "Manuel Eberl"
 orcid = "0000-0002-4263-6571"
 
 [eberl.emails]
 
 [eberl.emails.eberl_email]
 user = [
   "manuel",
 ]
 host = [
   "pruvisto",
   "org",
 ]
 
 [eberl.emails.eberl_email1]
 user = [
   "manuel",
   "eberl",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [eberl.emails.eberl_email2]
 user = [
   "manuel",
   "eberl",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [eberl.homepages]
 eberl_homepage = "https://pruvisto.org/"
 eberl_homepage2 = "https://www.in.tum.de/~eberlm"
 
 [echenim]
 name = "Mnacho Echenim"
 
 [echenim.emails]
 
 [echenim.emails.echenim_email]
 user = [
   "mnacho",
   "echenim",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [echenim.homepages]
 echenim_homepage = "https://lig-membres.imag.fr/mechenim/"
 
 [edmonds]
 name = "Chelsea Edmonds"
 
 [edmonds.emails]
 
 [edmonds.emails.edmonds_email]
 user = [
   "cle47",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [edmonds.homepages]
 edmonds_homepage = "https://www.cst.cam.ac.uk/people/cle47"
 
 [engelhardt]
 name = "Kai Engelhardt"
 
 [engelhardt.emails]
 
 [engelhardt.homepages]
 
 [eriksson]
 name = "Lars-Henrik Eriksson"
 
 [eriksson.emails]
 
 [eriksson.emails.eriksson_email]
 user = [
   "lhe",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [eriksson.homepages]
 
 [esparza]
 name = "Javier Esparza"
 
 [esparza.emails]
 
 [esparza.homepages]
 esparza_homepage = "https://www7.in.tum.de/~esparza/"
 
 [essmann]
 name = "Robin Eßmann"
 
 [essmann.emails]
 
 [essmann.emails.essmann_email]
 user = [
   "robin",
   "essmann",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [essmann.homepages]
 
 [felgenhauer]
 name = "Bertram Felgenhauer"
 
 [felgenhauer.emails]
 
 [felgenhauer.emails.felgenhauer_email]
 user = [
   "bertram",
   "felgenhauer",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [felgenhauer.emails.felgenhauer_email1]
 user = [
   "int-e",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [felgenhauer.homepages]
 
 [feliachi]
 name = "Abderrahmane Feliachi"
 
 [feliachi.emails]
 
 [feliachi.emails.feliachi_email]
 user = [
   "abderrahmane",
   "feliachi",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [feliachi.homepages]
 
 [fell]
 name = "Julian Fell"
 
 [fell.emails]
 
 [fell.emails.fell_email]
 user = [
   "julian",
   "fell",
 ]
 host = [
   "uq",
   "net",
   "au",
 ]
 
 [fell.homepages]
 
 [fernandez]
 name = "Matthew Fernandez"
 
 [fernandez.emails]
 
 [fernandez.homepages]
 
 [fiedler]
 name = "Ben Fiedler"
 
 [fiedler.emails]
 
 [fiedler.emails.fiedler_email]
 user = [
   "ben",
   "fiedler",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [fiedler.homepages]
 
 [fleuriot]
 name = "Jacques D. Fleuriot"
 
 [fleuriot.emails]
 
 [fleuriot.emails.fleuriot_email]
 user = [
   "Jacques",
   "Fleuriot",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [fleuriot.emails.fleuriot_email1]
 user = [
   "jdf",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [fleuriot.homepages]
 fleuriot_homepage = "https://www.inf.ed.ac.uk/people/staff/Jacques_Fleuriot.html"
 
 [fleury]
 name = "Mathias Fleury"
 
 [fleury.emails]
 
 [fleury.emails.fleury_email]
 user = [
   "fleury",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [fleury.emails.fleury_email1]
 user = [
   "mathias",
   "fleury",
 ]
 host = [
   "jku",
   "at",
 ]
 
 [fleury.homepages]
 fleury_homepage = "http://fmv.jku.at/fleury"
 
 [foster]
 name = "Michael Foster"
 
 [foster.emails]
 
 [foster.emails.foster_email]
 user = [
   "m",
   "foster",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [foster.homepages]
 
 [fosterj]
 name = "J. Nathan Foster"
 
 [fosterj.emails]
 
 [fosterj.homepages]
 fosterj_homepage = "http://www.cs.cornell.edu/~jnfoster/"
 
 [fosters]
 name = "Simon Foster"
 
 [fosters.emails]
 
 [fosters.emails.fosters_email]
 user = [
   "simon",
   "foster",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [fosters.homepages]
 fosters_homepage = "https://www-users.cs.york.ac.uk/~simonf/"
 
 [fouillard]
 name = "Valentin Fouillard"
 
 [fouillard.emails]
 
 [fouillard.emails.fouillard_email]
 user = [
   "valentin",
   "fouillard",
 ]
 host = [
   "limsi",
   "fr",
 ]
 
 [fouillard.homepages]
 
 [friedrich]
 name = "Stefan Friedrich"
 
 [friedrich.emails]
 
 [friedrich.homepages]
 
 [from]
 name = "Asta Halkjær From"
 
 [from.emails]
 
 [from.emails.from_email]
 user = [
   "ahfrom",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [from.homepages]
 from_homepage = "https://people.compute.dtu.dk/ahfrom/"
 
 [fuenmayor]
 name = "David Fuenmayor"
 
 [fuenmayor.emails]
 
 [fuenmayor.emails.fuenmayor_email]
 user = [
   "davfuenmayor",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [fuenmayor.homepages]
 
 [furusawa]
 name = "Hitoshi Furusawa"
 
 [furusawa.emails]
 
 [furusawa.homepages]
 furusawa_homepage = "http://www.sci.kagoshima-u.ac.jp/~furusawa/"
 
 [gammie]
 name = "Peter Gammie"
 
 [gammie.emails]
 
 [gammie.emails.gammie_email]
 user = [
   "peteg42",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gammie.homepages]
 gammie_homepage = "http://peteg.org"
 
 [gao]
 name = "Xin Gao"
 
 [gao.emails]
 
 [gao.homepages]
 
 [garvia]
 name = "Azucena Garvia"
 
 [garvia.emails]
 
 [garvia.emails.garvia_email]
 user = [
   "zucegb",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [garvia.homepages]
 
 [gaudel]
 name = "Marie-Claude Gaudel"
 
 [gaudel.emails]
 
 [gaudel.emails.gaudel_email]
 user = [
   "mcg",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [gaudel.homepages]
 
 [gay]
 name = "Richard Gay"
 
 [gay.emails]
 
 [gay.emails.gay_email]
 user = [
   "gay",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [gay.homepages]
 
 [georgescu]
 name = "George Georgescu"
 
 [georgescu.emails]
 
 [georgescu.homepages]
 
 [gheri]
 name = "Lorenzo Gheri"
 
 [gheri.emails]
 
 [gheri.emails.gheri_email]
 user = [
   "lor",
   "gheri",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gheri.homepages]
 
 [ghourabi]
 name = "Fadoua Ghourabi"
 
 [ghourabi.emails]
 
 [ghourabi.emails.ghourabi_email]
 user = [
   "fadouaghourabi",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ghourabi.homepages]
 
 [gioiosa]
 name = "Gianpaolo Gioiosa"
 
 [gioiosa.emails]
 
 [gioiosa.homepages]
 
 [glabbeek]
 name = "Rob van Glabbeek"
 
 [glabbeek.emails]
 
 [glabbeek.homepages]
 glabbeek_homepage = "http://theory.stanford.edu/~rvg/"
 
 [gomes]
 name = "Victor B. F. Gomes"
 
 [gomes.emails]
 
 [gomes.emails.gomes_email]
 user = [
   "victor",
   "gomes",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [gomes.emails.gomes_email2]
 user = [
   "victorborgesfg",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [gomes.emails.gomes_email4]
 user = [
   "vborgesferreiragomes1",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [gomes.homepages]
 gomes_homepage = "http://www.dcs.shef.ac.uk/~victor"
 
 [gonzalez]
 name = "Edgar Gonzàlez"
 orcid = "0000-0002-9169-0769"
 
 [gonzalez.emails]
 
 [gonzalez.emails.gonzalez_email]
 user = [
   "edgargip",
 ]
 host = [
   "google",
   "com",
 ]
 
 [gonzalez.homepages]
 
 [gore]
 name = "Rajeev Gore"
 
 [gore.emails]
 
 [gore.emails.gore_email]
 user = [
   "rajeev",
   "gore",
 ]
 host = [
   "anu",
   "edu",
   "au",
 ]
 
 [gore.homepages]
 
 [gouezel]
 name = "Sebastien Gouezel"
 
 [gouezel.emails]
 
 [gouezel.emails.gouezel_email]
 user = [
   "sebastien",
   "gouezel",
 ]
 host = [
   "univ-rennes1",
   "fr",
 ]
 
 [gouezel.homepages]
 gouezel_homepage = "http://www.math.sciences.univ-nantes.fr/~gouezel/"
 
 [grechuk]
 name = "Bogdan Grechuk"
 
 [grechuk.emails]
 
 [grechuk.emails.grechuk_email]
 user = [
   "grechukbogdan",
 ]
 host = [
   "yandex",
   "ru",
 ]
 
 [grechuk.homepages]
 
 [grewe]
 name = "Sylvia Grewe"
 
 [grewe.emails]
 
 [grewe.emails.grewe_email]
 user = [
   "grewe",
 ]
 host = [
   "cs",
   "tu-darmstadt",
   "de",
 ]
 
 [grewe.homepages]
 
 [griebel]
 name = "Simon Griebel"
 
 [griebel.emails]
 
 [griebel.emails.griebel_email]
 user = [
   "s",
   "griebel",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [griebel.homepages]
 
 [grov]
 name = "Gudmund Grov"
 
 [grov.emails]
 
 [grov.emails.grov_email]
 user = [
   "ggrov",
 ]
 host = [
   "inf",
   "ed",
   "ac",
   "uk",
 ]
 
 [grov.homepages]
 grov_homepage = "http://homepages.inf.ed.ac.uk/ggrov"
 
 [guerraoui]
 name = "Rachid Guerraoui"
 
 [guerraoui.emails]
 
 [guerraoui.emails.guerraoui_email]
 user = [
   "rachid",
   "guerraoui",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [guerraoui.homepages]
 
 [guiol]
 name = "Hervé Guiol"
 
 [guiol.emails]
 
 [guiol.emails.guiol_email]
 user = [
   "herve",
   "guiol",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [guiol.homepages]
 
 [gunther]
 name = "Emmanuel Gunther"
 
 [gunther.emails]
 
 [gunther.emails.gunther_email]
 user = [
   "gunther",
 ]
 host = [
   "famaf",
   "unc",
   "edu",
   "ar",
 ]
 
 [gunther.homepages]
 
 [gutkovas]
 name = "Ramunas Gutkovas"
 
 [gutkovas.emails]
 
 [gutkovas.emails.gutkovas_email]
 user = [
   "ramunas",
   "gutkovas",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [gutkovas.homepages]
 
 [guttmann]
 name = "Walter Guttmann"
 
 [guttmann.emails]
 
 [guttmann.emails.guttmann_email]
 user = [
   "walter",
   "guttmann",
 ]
 host = [
   "canterbury",
   "ac",
   "nz",
 ]
 
 [guttmann.homepages]
 guttmann_homepage = "https://www.cosc.canterbury.ac.nz/walter.guttmann/"
 
 [guzman]
 name = "Laura P. Gamboa Guzman"
 
 [guzman.emails]
 
 [guzman.emails.guzman_email]
 user = [
   "lpgamboa",
 ]
 host = [
   "iastate",
   "edu",
 ]
 
 [guzman.homepages]
 guzman_homepage = "https://sites.google.com/view/lpgamboa/home"
 
 [haftmann]
 name = "Florian Haftmann"
 
 [haftmann.emails]
 
 [haftmann.emails.haftmann_email]
 user = [
   "florian",
   "haftmann",
 ]
 host = [
   "informatik",
   "tu-muenchen",
   "de",
 ]
 
 [haftmann.homepages]
 haftmann_homepage = "http://isabelle.in.tum.de/~haftmann"
 
 [haslbeck]
 name = "Max W. Haslbeck"
 
 [haslbeck.emails]
 
 [haslbeck.emails.haslbeck_email]
 user = [
   "maximilian",
   "haslbeck",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [haslbeck.emails.haslbeck_email1]
 user = [
   "haslbecm",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [haslbeck.emails.haslbeck_email2]
 user = [
   "max",
   "haslbeck",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [haslbeck.homepages]
 haslbeck_homepage = "http://cl-informatik.uibk.ac.at/users/mhaslbeck/"
 
 [haslbeckm]
 name = "Maximilian P. L. Haslbeck"
 
 [haslbeckm.emails]
 
 [haslbeckm.emails.haslbeckm_email]
 user = [
   "haslbema",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [haslbeckm.homepages]
 haslbeckm_homepage = "http://in.tum.de/~haslbema/"
 
 [havle]
 name = "Oto Havle"
 
 [havle.emails]
 
 [havle.emails.havle_email]
 user = [
   "oha",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [havle.homepages]
 
 [hayes]
 name = "Ian J. Hayes"
 
 [hayes.emails]
 
 [hayes.emails.hayes_email]
 user = [
   "ian",
   "hayes",
 ]
 host = [
   "itee",
   "uq",
   "edu",
   "au",
 ]
 
 [hayes.homepages]
 
 [he]
 name = "Yijun He"
 
 [he.emails]
 
 [he.emails.he_email]
 user = [
   "yh403",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [he.homepages]
 
 [heimes]
 name = "Lukas Heimes"
 
 [heimes.emails]
 
 [heimes.emails.heimes_email]
 user = [
   "heimesl",
 ]
 host = [
   "student",
   "ethz",
   "ch",
 ]
 
 [heimes.homepages]
 
 [helke]
 name = "Steffen Helke"
 
 [helke.emails]
 
 [helke.emails.helke_email]
 user = [
   "helke",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [helke.homepages]
 
 [hellauer]
 name = "Fabian Hellauer"
 
 [hellauer.emails]
 
 [hellauer.emails.hellauer_email]
 user = [
   "hellauer",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [hellauer.homepages]
 
 [heller]
 name = "Armin Heller"
 
 [heller.emails]
 
 [heller.homepages]
 
 [henrio]
 name = "Ludovic Henrio"
 
 [henrio.emails]
 
 [henrio.emails.henrio_email]
 user = [
   "Ludovic",
   "Henrio",
 ]
 host = [
   "sophia",
   "inria",
   "fr",
 ]
 
 [henrio.homepages]
 
 [herzberg]
 name = "Michael Herzberg"
 
 [herzberg.emails]
 
 [herzberg.emails.herzberg_email]
 user = [
   "mail",
 ]
 host = [
   "michael-herzberg",
   "de",
 ]
 
 [herzberg.homepages]
 herzberg_homepage = "http://www.dcs.shef.ac.uk/cgi-bin/makeperson?M.Herzberg"
 
 [hess]
 name = "Andreas V. Hess"
 
 [hess.emails]
 
 [hess.emails.hess_email]
 user = [
   "avhe",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [hess.emails.hess_email1]
 user = [
   "andreasvhess",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [hess.homepages]
 
 [hetzl]
 name = "Stefan Hetzl"
 
 [hetzl.emails]
 
 [hetzl.emails.hetzl_email]
 user = [
   "hetzl",
 ]
 host = [
   "logic",
   "at",
 ]
 
 [hetzl.homepages]
 hetzl_homepage = "http://www.logic.at/people/hetzl/"
 
 [hibon]
 name = "Quentin Hibon"
 
 [hibon.emails]
 
 [hibon.emails.hibon_email]
 user = [
   "qh225",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [hibon.homepages]
 
 [higgins]
 name = "Edward Higgins"
 
 [higgins.emails]
 
 [higgins.homepages]
 
 [hirata]
 name = "Michikazu Hirata"
 
 [hirata.emails]
 
 [hirata.emails.hirata_email]
 user = [
   "hirata",
   "m",
   "ac",
 ]
 host = [
   "m",
   "titech",
   "ac",
   "jp",
 ]
 
 [hirata.homepages]
 
 [hoefner]
 name = "Peter Höfner"
 
 [hoefner.emails]
 
 [hoefner.emails.hoefner_email]
 user = [
   "peter",
 ]
 host = [
   "hoefner-online",
   "de",
 ]
 
 [hoefner.homepages]
 hoefner_homepage = "http://www.hoefner-online.de/"
 
 [hoelzl]
 name = "Johannes Hölzl"
 
 [hoelzl.emails]
 
 [hoelzl.emails.hoelzl_email]
 user = [
   "hoelzl",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [hoelzl.homepages]
 hoelzl_homepage = "http://home.in.tum.de/~hoelzl"
 
 [hofmann]
 name = "Martin Hofmann"
 
 [hofmann.emails]
 
 [hofmann.homepages]
 hofmann_homepage = "http://www.tcs.informatik.uni-muenchen.de/~mhofmann"
 
 [hofmeier]
 name = "Paul Hofmeier"
 
 [hofmeier.emails]
 
 [hofmeier.emails.hofmeier_email]
 user = [
   "paul",
   "hofmeier",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [hofmeier.homepages]
 
 [holub]
 name = "Štěpán Holub"
 
 [holub.emails]
 
 [holub.emails.holub_email]
 user = [
   "holub",
 ]
 host = [
   "karlin",
   "mff",
   "cuni",
   "cz",
 ]
 
 [holub.homepages]
 holub_homepage = "https://www2.karlin.mff.cuni.cz/~holub/"
 
 [hosking]
 name = "Tony Hosking"
 
 [hosking.emails]
 
 [hosking.homepages]
 hosking_homepage = "https://www.cs.purdue.edu/homes/hosking/"
 
 [hou]
 name = "Zhe Hou"
 
 [hou.emails]
 
 [hou.emails.hou_email]
 user = [
   "zhe",
   "hou",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [hou.homepages]
 
 [hu]
 name = "Shuwei Hu"
 
 [hu.emails]
 
 [hu.emails.hu_email]
 user = [
   "shuwei",
   "hu",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [hu.homepages]
 
 [huffman]
 name = "Brian Huffman"
 
 [huffman.emails]
 
 [huffman.emails.huffman_email]
 user = [
   "huffman",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [huffman.emails.huffman_email1]
 user = [
   "brianh",
 ]
 host = [
   "cs",
   "pdx",
   "edu",
 ]
 
 [huffman.homepages]
 huffman_homepage = "http://cs.pdx.edu/~brianh/"
 
 [hupel]
 name = "Lars Hupel"
 
 [hupel.emails]
 
 [hupel.emails.hupel_email]
 user = [
   "lars",
 ]
 host = [
   "hupel",
   "info",
 ]
 
 [hupel.homepages]
 hupel_homepage = "https://lars.hupel.info/"
 
 [ijbema]
 name = "Mark Ijbema"
 
 [ijbema.emails]
 
 [ijbema.emails.ijbema_email]
 user = [
   "ijbema",
 ]
 host = [
   "fmf",
   "nl",
 ]
 
 [ijbema.homepages]
 
 [immler]
 name = "Fabian Immler"
 
 [immler.emails]
 
 [immler.emails.immler_email]
 user = [
   "immler",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [immler.emails.immler_email1]
 user = [
   "fimmler",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [immler.homepages]
 immler_homepage = "https://home.in.tum.de/~immler/"
 
 [israel]
 name = "Jonas Israel"
 
 [israel.emails]
 
 [israel.homepages]
 israel_homepage = "https://www.algo.tu-berlin.de/menue/people/jonas_israel/"
 
 [ito]
 name = "Yosuke Ito"
 
 [ito.emails]
 
 [ito.emails.ito_email]
 user = [
   "glacier345",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ito.homepages]
 
 [iwama]
 name = "Fumiya Iwama"
 
 [iwama.emails]
 
 [iwama.emails.iwama_email]
 user = [
   "d1623001",
 ]
 host = [
   "s",
   "konan-u",
   "ac",
   "jp",
 ]
 
 [iwama.homepages]
 
 [jacobsen]
 name = "Frederik Krogsdal Jacobsen"
 
 [jacobsen.emails]
 
 [jacobsen.emails.jacobsen_email]
 user = [
   "fkjac",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [jacobsen.homepages]
 jacobsen_homepage = "http://people.compute.dtu.dk/fkjac/"
 
 [jaskelioff]
 name = "Mauro Jaskelioff"
 
 [jaskelioff.emails]
 
 [jaskelioff.homepages]
 jaskelioff_homepage = "http://www.fceia.unr.edu.ar/~mauro/"
 
 [jaskolka]
 name = "Jason Jaskolka"
 
 [jaskolka.emails]
 
 [jaskolka.emails.jaskolka_email]
 user = [
   "jason",
   "jaskolka",
 ]
 host = [
   "carleton",
   "ca",
 ]
 
 [jaskolka.homepages]
 jaskolka_homepage = "https://carleton.ca/jaskolka/"
 
 [jensen]
 name = "Alexander Birch Jensen"
 
 [jensen.emails]
 
 [jensen.emails.jensen_email]
 user = [
   "aleje",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [jensen.homepages]
 jensen_homepage = "https://people.compute.dtu.dk/aleje/"
 
 [jiang]
 name = "Nan Jiang"
 
 [jiang.emails]
 
 [jiang.emails.jiang_email]
 user = [
   "nanjiang",
 ]
 host = [
   "whu",
   "edu",
   "cn",
 ]
 
 [jiang.homepages]
 
 [jiangd]
 name = "Dongchen Jiang"
 
 [jiangd.emails]
 
 [jiangd.emails.jiangd_email]
 user = [
   "dongchenjiang",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [jiangd.homepages]
 
 [joosten]
 name = "Sebastiaan J. C. Joosten"
 
 [joosten.emails]
 
 [joosten.emails.joosten_email]
 user = [
   "sebastiaan",
   "joosten",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [joosten.emails.joosten_email1]
 user = [
   "sjcjoosten",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [joosten.emails.joosten_email2]
 user = [
   "s",
   "j",
   "c",
   "joosten",
 ]
 host = [
   "utwente",
   "nl",
 ]
 
 [joosten.homepages]
 joosten_homepage = "https://sjcjoosten.nl/"
 
 [jungnickel]
 name = "Tim Jungnickel"
 
 [jungnickel.emails]
 
 [jungnickel.emails.jungnickel_email]
 user = [
   "tim",
   "jungnickel",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [jungnickel.homepages]
 
 [kadzioka]
 name = "Maya Kądziołka"
 
 [kadzioka.emails]
 
 [kadzioka.emails.kadzioka_email]
 user = [
   "afp",
 ]
 host = [
   "compilercrim",
   "es",
 ]
 
 [kadzioka.homepages]
 
 [kaliszyk]
 name = "Cezary Kaliszyk"
 
 [kaliszyk.emails]
 
 [kaliszyk.emails.kaliszyk_email]
 user = [
   "cezary",
   "kaliszyk",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [kaliszyk.homepages]
 kaliszyk_homepage = "http://cl-informatik.uibk.ac.at/users/cek/"
 
 [kammueller]
 name = "Florian Kammüller"
 
 [kammueller.emails]
 
 [kammueller.emails.kammueller_email]
 user = [
   "flokam",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [kammueller.emails.kammueller_email1]
 user = [
   "florian",
   "kammuller",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [kammueller.homepages]
 kammueller_homepage = "http://www.cs.mdx.ac.uk/people/florian-kammueller/"
 
 [kappelmann]
 name = "Kevin Kappelmann"
 
 [kappelmann.emails]
 
 [kappelmann.emails.kappelmann_email]
 user = [
   "kevin",
   "kappelmann",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kappelmann.homepages]
 kappelmann_homepage = "https://www21.in.tum.de/team/kappelmk/"
 
 [karayel]
 name = "Emin Karayel"
 orcid = "0000-0003-3290-5034"
 
 [karayel.emails]
 
 [karayel.emails.karayel_email]
 user = [
   "me",
 ]
 host = [
   "eminkarayel",
   "de",
 ]
 
 [karayel.homepages]
 karayel_homepage = "https://orcid.org/0000-0003-3290-5034"
 
 [kastermans]
 name = "Bart Kastermans"
 
 [kastermans.emails]
 
 [kastermans.homepages]
 kastermans_homepage = "http://kasterma.net"
 
 [katovsky]
 name = "Alexander Katovsky"
 
 [katovsky.emails]
 
 [katovsky.emails.katovsky_email]
 user = [
   "apk32",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [katovsky.emails.katovsky_email1]
 user = [
   "alexander",
   "katovsky",
 ]
 host = [
   "cantab",
   "net",
 ]
 
 [katovsky.homepages]
 
 [kaufmann]
 name = "Daniela Kaufmann"
 
 [kaufmann.emails]
 
 [kaufmann.homepages]
 kaufmann_homepage = "http://fmv.jku.at/kaufmann"
 
 [keefe]
 name = "Greg O'Keefe"
 
 [keefe.emails]
 
 [keefe.homepages]
 keefe_homepage = "http://users.rsise.anu.edu.au/~okeefe/"
 
 [keinholz]
 name = "Jonas Keinholz"
 
 [keinholz.emails]
 
 [keinholz.homepages]
 
 [kerber]
 name = "Manfred Kerber"
 
 [kerber.emails]
 
 [kerber.emails.kerber_email]
 user = [
   "mnfrd",
   "krbr",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [kerber.homepages]
 kerber_homepage = "http://www.cs.bham.ac.uk/~mmk"
 
 [keskin]
 name = "Ata Keskin"
 orcid = "0000-0002-8296-1766"
 
 [keskin.emails]
 
 [keskin.emails.keskin_email]
 user = [
   "ata",
   "keskin",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [keskin.homepages]
 
 [ketland]
 name = "Jeffrey Ketland"
 
 [ketland.emails]
 
 [ketland.emails.ketland_email]
 user = [
   "jeffreyketland",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [ketland.homepages]
 
 [kim]
 name = "Sunpill Kim"
 orcid = "0000-0002-7767-4084"
 
 [kim.emails]
 
 [kim.homepages]
 
 [kirchner]
 name = "Daniel Kirchner"
 
 [kirchner.emails]
 
 [kirchner.emails.kirchner_email]
 user = [
   "daniel",
 ]
 host = [
   "ekpyron",
   "org",
 ]
 
 [kirchner.homepages]
 
 [klein]
 name = "Gerwin Klein"
 
 [klein.emails]
 
 [klein.emails.klein_email]
 user = [
   "kleing",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [klein.homepages]
 klein_homepage = "http://www.cse.unsw.edu.au/~kleing/"
 
 [klenze]
 name = "Tobias Klenze"
 
 [klenze.emails]
 
 [klenze.emails.klenze_email]
 user = [
   "tobias",
   "klenze",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [klenze.homepages]
 
 [kleppmann]
 name = "Martin Kleppmann"
 
 [kleppmann.emails]
 
 [kleppmann.emails.kleppmann_email]
 user = [
   "martin",
   "kleppmann",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [kleppmann.homepages]
 
 [kobayashi]
 name = "Hidetsune Kobayashi"
 
 [kobayashi.emails]
 
 [kobayashi.homepages]
 
 [koerner]
 name = "Stefan Körner"
 
 [koerner.emails]
 
 [koerner.emails.koerner_email]
 user = [
   "s_koer03",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [koerner.homepages]
 
 [kolanski]
 name = "Rafal Kolanski"
 
 [kolanski.emails]
 
 [kolanski.emails.kolanski_email]
 user = [
   "rafal",
   "kolanski",
 ]
 host = [
   "nicta",
   "com",
   "au",
 ]
 
 [kolanski.homepages]
 
 [koller]
 name = "Lukas Koller"
 
 [koller.emails]
 
 [koller.emails.koller_email]
 user = [
   "lukas",
   "koller",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [koller.homepages]
 
 [krauss]
 name = "Alexander Krauss"
 
 [krauss.emails]
 
 [krauss.emails.krauss_email]
 user = [
   "krauss",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [krauss.homepages]
 krauss_homepage = "http://www.in.tum.de/~krauss"
 
 [kreuzer]
 name = "Katharina Kreuzer"
 
 [kreuzer.emails]
 
 [kreuzer.emails.kreuzer_email]
 user = [
   "kreuzerk",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [kreuzer.emails.kreuzer_email1]
 user = [
   "k",
   "kreuzer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kreuzer.homepages]
 kreuzer_homepage = "https://www21.in.tum.de/team/kreuzer/"
 
 [kuncak]
 name = "Viktor Kuncak"
 
 [kuncak.emails]
 
 [kuncak.homepages]
 kuncak_homepage = "http://lara.epfl.ch/~kuncak/"
 
 [kuncar]
 name = "Ondřej Kunčar"
 
 [kuncar.emails]
 
 [kuncar.homepages]
 kuncar_homepage = "http://www21.in.tum.de/~kuncar/"
 
 [kurz]
 name = "Friedrich Kurz"
 
 [kurz.emails]
 
 [kurz.emails.kurz_email]
 user = [
   "friedrich",
   "kurz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [kurz.homepages]
 
 [lachnitt]
 name = "Hanna Lachnitt"
 
 [lachnitt.emails]
 
 [lachnitt.emails.lachnitt_email]
 user = [
   "lachnitt",
 ]
 host = [
   "stanford",
   "edu",
 ]
 
 [lachnitt.homepages]
 
 [lallemand]
 name = "Joseph Lallemand"
 
 [lallemand.emails]
 
 [lallemand.emails.lallemand_email]
 user = [
   "joseph",
   "lallemand",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [lallemand.homepages]
 
 [lameris]
 name = "Cárolos Laméris"
 
 [lameris.emails]
 
 [lameris.emails.lameris_email]
 user = [
   "carolos",
   "lameris",
 ]
 host = [
   "ru",
   "nl",
 ]
 
 [lameris.homepages]
 
 [lammich]
 name = "Peter Lammich"
 
 [lammich.emails]
 
 [lammich.emails.lammich_email]
 user = [
   "lammich",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [lammich.emails.lammich_email1]
 user = [
   "peter",
   "lammich",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [lammich.homepages]
 lammich_homepage = "http://www21.in.tum.de/~lammich"
 
 [lange]
 name = "Christoph Lange"
 
 [lange.emails]
 
 [lange.emails.lange_email]
 user = [
   "math",
   "semantic",
   "web",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [lange.homepages]
 
 [langenstein]
 name = "Bruno Langenstein"
 
 [langenstein.emails]
 
 [langenstein.emails.langenstein_email]
 user = [
   "langenstein",
 ]
 host = [
   "dfki",
   "de",
 ]
 
 [langenstein.homepages]
 
 [lattuada]
 name = "Andrea Lattuada"
 
 [lattuada.emails]
 
 [lattuada.homepages]
 lattuada_homepage = "https://andrea.lattuada.me"
 
 [lauermann]
 name = "Nils Lauermann"
 
 [lauermann.emails]
 
 [lauermann.emails.lauermann_email]
 user = [
   "Nils",
   "Lauermann",
 ]
 host = [
   "cl",
   "cam",
   "ac",
   "uk",
 ]
 
 [lauermann.homepages]
 
 [laursen]
 name = "Christian Pardillo-Laursen"
 
 [laursen.emails]
 
 [laursen.emails.laursen_email]
 user = [
   "christian",
   "laursen",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [laursen.homepages]
 
 [lederer]
 name = "Patrick Lederer"
 
 [lederer.emails]
 
 [lederer.homepages]
 lederer_homepage = "https://www.cs.cit.tum.de/en/dss/members/patrick-lederer/"
 
 [lee]
 name = "Holden Lee"
 
 [lee.emails]
 
 [lee.emails.lee_email]
 user = [
   "holdenl",
 ]
 host = [
   "princeton",
   "edu",
 ]
 
 [lee.homepages]
 
 [leek]
 name = "Kevin Lee"
 
 [leek.emails]
 
 [leek.emails.leek_email]
 user = [
   "kfkl2",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [leek.homepages]
 
 [leustean]
 name = "Laurentiu Leustean"
 
 [leustean.emails]
 
 [leustean.homepages]
 
 [lewis]
 name = "Corey Lewis"
 
 [lewis.emails]
 
 [lewis.emails.lewis_email]
 user = [
   "corey",
   "lewis",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [lewis.homepages]
 
 [li]
 name = "Wenda Li"
 
 [li.emails]
 
 [li.emails.li_email]
 user = [
   "wl302",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [li.emails.li_email1]
 user = [
   "liwenda1990",
 ]
 host = [
   "hotmail",
   "com",
 ]
 
 [li.homepages]
 li_homepage = "https://www.cl.cam.ac.uk/~wl302/"
 
 [lim]
 name = "Japheth Lim"
 
 [lim.emails]
 
 [lim.homepages]
 
 [lindenberg]
 name = "Christina Lindenberg"
 
 [lindenberg.emails]
 
 [lindenberg.homepages]
 
 [linker]
 name = "Sven Linker"
 
 [linker.emails]
 
 [linker.emails.linker_email]
 user = [
   "s",
   "linker",
 ]
 host = [
   "liverpool",
   "ac",
   "uk",
 ]
 
 [linker.homepages]
 
 [liu]
 name = "Junyi Liu"
 
 [liu.emails]
 
 [liu.homepages]
 
 [liut]
 name = "Tao Liu"
 
 [liut.emails]
 
 [liut.homepages]
 
 [liuy]
 name = "Yang Liu"
 
 [liuy.emails]
 
 [liuy.emails.liuy_email]
 user = [
   "yangliu",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [liuy.homepages]
 
 [liy]
 name = "Yangjia Li"
 
 [liy.emails]
 
 [liy.homepages]
 
 [lochbihler]
 name = "Andreas Lochbihler"
 
 [lochbihler.emails]
 
 [lochbihler.emails.lochbihler_email1]
 user = [
   "mail",
 ]
 host = [
   "andreas-lochbihler",
   "de",
 ]
 
 [lochbihler.homepages]
 lochbihler_homepage = "http://www.andreas-lochbihler.de/"
 
 [lochmann]
 name = "Alexander Lochmann"
 
 [lochmann.emails]
 
 [lochmann.emails.lochmann_email]
 user = [
   "alexander",
   "lochmann",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [lochmann.homepages]
 
 [lohner]
 name = "Denis Lohner"
 
 [lohner.emails]
 
 [lohner.emails.lohner_email]
 user = [
   "denis",
   "lohner",
 ]
 host = [
   "kit",
   "edu",
 ]
 
 [lohner.homepages]
 lohner_homepage = "http://pp.ipd.kit.edu/person.php?id=88"
 
 [loibl]
 name = "Matthias Loibl"
 
 [loibl.emails]
 
 [loibl.homepages]
 
 [londono]
 name = "Alejandro Gómez-Londoño"
 
 [londono.emails]
 
 [londono.emails.londono_email]
 user = [
   "alejandro",
   "gomez",
 ]
 host = [
   "chalmers",
   "se",
 ]
 
 [londono.homepages]
 
 [losa]
 name = "Giuliano Losa"
 
 [losa.emails]
 
 [losa.emails.losa_email]
 user = [
   "giuliano",
   "losa",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [losa.emails.losa_email1]
 user = [
   "giuliano",
 ]
 host = [
   "galois",
   "com",
 ]
 
 [losa.emails.losa_email2]
 user = [
   "giuliano",
 ]
 host = [
   "losa",
   "fr",
 ]
 
 [losa.homepages]
 
 [lutz]
 name = "Bianca Lutz"
 
 [lutz.emails]
 
 [lutz.emails.lutz_email]
 user = [
   "sowilo",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [lutz.homepages]
 
 [lux]
 name = "Alexander Lux"
 
 [lux.emails]
 
 [lux.emails.lux_email]
 user = [
   "lux",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [lux.homepages]
 
 [madarasz]
 name = "Judit Madarasz"
 
 [madarasz.emails]
 
 [madarasz.homepages]
 madarasz_homepage = "https://users.renyi.hu/~madarasz/"
 
 [makarios]
 name = "T. J. M. Makarios"
 
 [makarios.emails]
 
 [makarios.emails.makarios_email]
 user = [
   "tjm1983",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [makarios.homepages]
 
 [maletzky]
 name = "Alexander Maletzky"
 
 [maletzky.emails]
 
 [maletzky.emails.maletzky_email]
 user = [
   "alexander",
   "maletzky",
 ]
 host = [
   "risc",
   "jku",
   "at",
 ]
 
 [maletzky.emails.maletzky_email1]
 user = [
   "alexander",
   "maletzky",
 ]
 host = [
   "risc-software",
   "at",
 ]
 
 [maletzky.homepages]
 maletzky_homepage = "https://risc.jku.at/m/alexander-maletzky/"
 
 [mansky]
 name = "Susannah Mansky"
 
 [mansky.emails]
 
 [mansky.emails.mansky_email]
 user = [
   "sjohnsn2",
 ]
 host = [
   "illinois",
   "edu",
 ]
 
 [mansky.emails.mansky_email1]
 user = [
   "susannahej",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [mansky.homepages]
 
 [mantel]
 name = "Heiko Mantel"
 
 [mantel.emails]
 
 [mantel.emails.mantel_email]
 user = [
   "mantel",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [mantel.homepages]
 
 [margetson]
 name = "James Margetson"
 
 [margetson.emails]
 
 [margetson.homepages]
 
 [maric]
 name = "Ognjen Marić"
 
 [maric.emails]
 
 [maric.emails.maric_email]
 user = [
   "ogi",
   "afp",
 ]
 host = [
   "mynosefroze",
   "com",
 ]
 
 [maric.homepages]
 
 [maricf]
 name = "Filip Marić"
 
 [maricf.emails]
 
 [maricf.emails.maricf_email]
 user = [
   "filip",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [maricf.homepages]
 maricf_homepage = "http://www.matf.bg.ac.rs/~filip"
 
 [marmsoler]
 name = "Diego Marmsoler"
 
 [marmsoler.emails]
 
 [marmsoler.emails.marmsoler_email]
 user = [
   "diego",
   "marmsoler",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [marmsoler.emails.marmsoler_email1]
 user = [
   "d",
   "marmsoler",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [marmsoler.homepages]
 marmsoler_homepage = "http://marmsoler.com"
 
 [massacrier]
 name = "Tanguy Massacrier"
 
 [massacrier.emails]
 
 [massacrier.homepages]
 
 [matache]
 name = "Cristina Matache"
 
 [matache.emails]
 
 [matache.emails.matache_email]
 user = [
   "cris",
   "matache",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [matache.homepages]
 
 [mateo]
 name = "Adrián Doña Mateo"
 
 [mateo.emails]
 
 [mateo.emails.mateo_email]
 user = [
   "adrian",
   "dona",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [mateo.homepages]
 
 [matichuk]
 name = "Daniel Matichuk"
 
 [matichuk.emails]
 
 [matichuk.homepages]
 
 [matiyasevich]
 name = "Yuri Matiyasevich"
 
 [matiyasevich.emails]
 
 [matiyasevich.homepages]
 
 [maximova]
 name = "Alexandra Maximova"
 
 [maximova.emails]
 
 [maximova.emails.maximova_email]
 user = [
   "amaximov",
 ]
 host = [
   "student",
   "ethz",
   "ch",
 ]
 
 [maximova.homepages]
 
 [meis]
 name = "Rene Meis"
 
 [meis.emails]
 
 [meis.emails.meis_email]
 user = [
   "rene",
   "meis",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [meis.emails.meis_email1]
 user = [
   "rene",
   "meis",
 ]
 host = [
   "uni-due",
   "de",
 ]
 
 [meis.homepages]
 
 [merz]
 name = "Stephan Merz"
 
 [merz.emails]
 
 [merz.emails.merz_email]
 user = [
   "Stephan",
   "Merz",
 ]
 host = [
   "loria",
   "fr",
 ]
 
 [merz.homepages]
 merz_homepage = "http://www.loria.fr/~merz"
 
 [messner]
 name = "Florian Messner"
 
 [messner.emails]
 
 [messner.emails.messner_email]
 user = [
   "florian",
   "g",
   "messner",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [messner.homepages]
 
 [mhalla]
 name = "Mehdi Mhalla"
 
 [mhalla.emails]
 
 [mhalla.emails.mhalla_email]
 user = [
   "mhallam",
 ]
 host = [
   "univ-grenoble-alpes",
   "fr",
 ]
 
 [mhalla.homepages]
 
 [michaelis]
 name = "Julius Michaelis"
 
 [michaelis.emails]
 
 [michaelis.emails.michaelis_email]
 user = [
   "isabelleopenflow",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email1]
 user = [
   "maintainafpppt",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email2]
 user = [
   "bdd",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.emails.michaelis_email3]
 user = [
   "afp",
 ]
 host = [
   "liftm",
   "de",
 ]
 
 [michaelis.homepages]
 michaelis_homepage = "http://liftm.de/"
 
 [milehins]
 name = "Mihails Milehins"
 
 [milehins.emails]
 
 [milehins.emails.milehins_email]
 user = [
   "mihailsmilehins",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [milehins.homepages]
 
 [minamide]
 name = "Yasuhiko Minamide"
 
 [minamide.emails]
 
 [minamide.emails.minamide_email]
 user = [
   "minamide",
 ]
 host = [
   "is",
   "titech",
   "ac",
   "jp",
 ]
 
 [minamide.homepages]
 minamide_homepage = "https://sv.c.titech.ac.jp/minamide/index.en.html"
 
 [mitchell]
 name = "Neil Mitchell"
 
 [mitchell.emails]
 
 [mitchell.homepages]
 
 [mitsch]
 name = "Stefan Mitsch"
 
 [mitsch.emails]
 
 [mitsch.emails.mitsch_email]
 user = [
   "smitsch",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [mitsch.homepages]
 
 [moedersheim]
 name = "Sebastian Mödersheim"
 
 [moedersheim.emails]
 
 [moedersheim.emails.moedersheim_email]
 user = [
   "samo",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [moedersheim.homepages]
 moedersheim_homepage = "https://people.compute.dtu.dk/samo/"
 
 [moeller]
 name = "Bernhard Möller"
 
 [moeller.emails]
 
 [moeller.homepages]
 moeller_homepage = "https://www.informatik.uni-augsburg.de/en/chairs/dbis/pmi/staff/moeller/"
 
 [montanari]
 name = "Luisa Montanari"
 orcid = "0000-0002-5270-0290"
 
 [montanari.emails]
 
 [montanari.homepages]
 
 [mori]
 name = "Coraline Mori"
 
 [mori.emails]
 
 [mori.emails.mori_email]
 user = [
   "coraline",
   "mori",
 ]
 host = [
   "grenoble-inp",
   "org",
 ]
 
 [mori.homepages]
 
 [muendler]
 name = "Niels Mündler"
 
 [muendler.emails]
 
 [muendler.emails.muendler_email]
 user = [
   "n",
   "muendler",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [muendler.homepages]
 
 [mulligan]
 name = "Dominic P. Mulligan"
 
 [mulligan.emails]
 
 [mulligan.emails.mulligan_email]
 user = [
   "dominic",
   "p",
   "mulligan",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [mulligan.emails.mulligan_email1]
 user = [
   "Dominic",
   "Mulligan",
 ]
 host = [
   "arm",
   "com",
 ]
 
 [mulligan.homepages]
 
 [munive]
 name = "Jonathan Julian Huerta y Munive"
 
 [munive.emails]
 
 [munive.emails.munive_email]
 user = [
   "jjhuertaymunive1",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [munive.emails.munive_email1]
 user = [
   "jonjulian23",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [munive.homepages]
 
 [murao]
 name = "H. Murao"
 
 [murao.emails]
 
 [murao.homepages]
 
 [murray]
 name = "Toby Murray"
 
 [murray.emails]
 
 [murray.emails.murray_email]
 user = [
   "toby",
   "murray",
 ]
 host = [
   "unimelb",
   "edu",
   "au",
 ]
 
 [murray.homepages]
 murray_homepage = "https://people.eng.unimelb.edu.au/tobym/"
 
 [myreen]
 name = "Magnus O. Myreen"
 orcid = "0000-0002-9504-4107"
 
 [myreen.emails]
 
 [myreen.emails.myreen_email]
 user = [
   "myreen",
 ]
 host = [
   "chalmers",
   "se",
 ]
 
 [myreen.homepages]
 
 [nagashima]
 name = "Yutaka Nagashima"
 
 [nagashima.emails]
 
 [nagashima.emails.nagashima_email]
 user = [
   "Yutaka",
   "Nagashima",
 ]
 host = [
   "data61",
   "csiro",
   "au",
 ]
 
 [nagashima.homepages]
 
 [nagele]
 name = "Julian Nagele"
 
 [nagele.emails]
 
 [nagele.emails.nagele_email]
 user = [
   "julian",
   "nagele",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [nagele.homepages]
 
 [naraschewski]
 name = "Wolfgang Naraschewski"
 
 [naraschewski.emails]
 
 [naraschewski.homepages]
 
 [nedzelsky]
 name = "Michael Nedzelsky"
 
 [nedzelsky.emails]
 
 [nedzelsky.emails.nedzelsky_email]
 user = [
   "MichaelNedzelsky",
 ]
 host = [
   "yandex",
   "ru",
 ]
 
 [nedzelsky.homepages]
 
 [nemeti]
 name = "István Németi"
 
 [nemeti.emails]
 
 [nemeti.homepages]
 nemeti_homepage = "http://www.renyi.hu/~nemeti/"
 
 [nemouchi]
 name = "Yakoub Nemouchi"
 
 [nemouchi.emails]
 
 [nemouchi.emails.nemouchi_email]
 user = [
   "nemouchi",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [nemouchi.emails.nemouchi_email1]
 user = [
   "yakoub",
   "nemouchi",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [nemouchi.homepages]
 
 [nestmann]
 name = "Uwe Nestmann"
 
 [nestmann.emails]
 
 [nestmann.homepages]
 nestmann_homepage = "https://www.mtv.tu-berlin.de/nestmann/"
 
 [neumann]
 name = "René Neumann"
 
 [neumann.emails]
 
 [neumann.emails.neumann_email]
 user = [
   "rene",
   "neumann",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [neumann.homepages]
 
 [nielsen]
 name = "Finn Nielsen"
 
 [nielsen.emails]
 
 [nielsen.emails.nielsen_email]
 user = [
   "finn",
   "nielsen",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [nielsen.homepages]
 
 [nikiforov]
 name = "Denis Nikiforov"
 
 [nikiforov.emails]
 
 [nikiforov.emails.nikiforov_email]
 user = [
   "denis",
   "nikif",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [nikiforov.homepages]
 
 [nipkow]
 name = "Tobias Nipkow"
 orcid = "0000-0003-0730-515X"
 
 [nipkow.emails]
 
 [nipkow.emails.nipkow_email]
 user = [
   "nipkow",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [nipkow.homepages]
 nipkow_homepage = "https://www.in.tum.de/~nipkow/"
 
 [nishihara]
 name = "Toshiaki Nishihara"
 
 [nishihara.emails]
 
 [nishihara.homepages]
 
 [noce]
 name = "Pasquale Noce"
 
 [noce.emails]
 
 [noce.emails.noce_email]
 user = [
   "pasquale",
   "noce",
   "lavoro",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [noce.homepages]
 
 [nordhoff]
 name = "Benedikt Nordhoff"
 
 [nordhoff.emails]
 
 [nordhoff.emails.nordhoff_email]
 user = [
   "b",
   "n",
 ]
 host = [
   "wwu",
   "de",
 ]
 
 [nordhoff.emails.nordhoff_email1]
 user = [
   "b_nord01",
 ]
 host = [
   "uni-muenster",
   "de",
 ]
 
 [nordhoff.homepages]
 
 [noschinski]
 name = "Lars Noschinski"
 
 [noschinski.emails]
 
 [noschinski.emails.noschinski_email]
 user = [
   "noschinl",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [noschinski.homepages]
 noschinski_homepage = "http://www21.in.tum.de/~noschinl/"
 
 [obua]
 name = "Steven Obua"
 
 [obua.emails]
 
 [obua.emails.obua_email]
 user = [
   "steven",
 ]
 host = [
   "recursivemind",
   "com",
 ]
 
 [obua.homepages]
 
 [ogawa]
 name = "Mizuhito Ogawa"
 
 [ogawa.emails]
 
 [ogawa.homepages]
 
 [oldenburg]
 name = "Lennart Oldenburg"
 
 [oldenburg.emails]
 
 [oldenburg.homepages]
 
 [olm]
 name = "Markus Müller-Olm"
 
 [olm.emails]
 
 [olm.homepages]
 olm_homepage = "http://cs.uni-muenster.de/u/mmo/"
 
 [oosterhuis]
 name = "Roelof Oosterhuis"
 
 [oosterhuis.emails]
 
 [oosterhuis.emails.oosterhuis_email]
 user = [
   "roelofoosterhuis",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [oosterhuis.homepages]
 
 [oostrom]
 name = "Vincent van Oostrom"
 
 [oostrom.emails]
 
 [oostrom.homepages]
 
 [ortner]
 name = "Veronika Ortner"
 
 [ortner.emails]
 
 [ortner.homepages]
 
 [overbeek]
 name = "Roy Overbeek"
 
 [overbeek.emails]
 
 [overbeek.emails.overbeek_email]
 user = [
   "Roy",
   "Overbeek",
 ]
 host = [
   "cwi",
   "nl",
 ]
 
 [overbeek.homepages]
 
 [pagano]
 name = "Miguel Pagano"
 
 [pagano.emails]
 
 [pagano.emails.pagano_email]
 user = [
   "miguel",
   "pagano",
 ]
 host = [
   "unc",
   "edu",
   "ar",
 ]
 
 [pagano.homepages]
 pagano_homepage = "https://cs.famaf.unc.edu.ar/~mpagano/"
 
 [pal]
 name = "Abhik Pal"
 
 [pal.emails]
 
 [pal.homepages]
 
 [paleo]
 name = "Bruno Woltzenlogel Paleo"
 
 [paleo.emails]
 
 [paleo.homepages]
 paleo_homepage = "http://www.logic.at/staff/bruno/"
 
 [palmer]
 name = "Jake Palmer"
 
 [palmer.emails]
 
 [palmer.emails.palmer_email]
 user = [
   "jake",
   "palmer",
 ]
 host = [
   "ed",
   "ac",
   "uk",
 ]
 
 [palmer.homepages]
 
 [park]
 name = "Seung Hoon Park"
 orcid = "0000-0001-7165-6857"
 
 [park.emails]
 
 [park.emails.park_email]
 user = [
   "seunghoon",
   "park",
 ]
 host = [
   "cs",
   "ox",
   "ac",
   "uk",
 ]
 
 [park.homepages]
 park_homepage = "https://www.cs.ox.ac.uk/people/simon.park/"
 
 [parkinson]
 name = "Matthew Parkinson"
 
 [parkinson.emails]
 
 [parkinson.homepages]
 parkinson_homepage = "http://research.microsoft.com/people/mattpark/"
 
 [parrow]
 name = "Joachim Parrow"
 
 [parrow.emails]
 
 [parrow.emails.parrow_email]
 user = [
   "joachim",
   "parrow",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [parrow.homepages]
 
 [parsert]
 name = "Julian Parsert"
 
 [parsert.emails]
 
 [parsert.emails.parsert_email]
 user = [
   "julian",
   "parsert",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [parsert.emails.parsert_email1]
 user = [
   "julian",
   "parsert",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [parsert.homepages]
 parsert_homepage = "http://www.parsert.com/"
 
 [paulson]
 name = "Lawrence C. Paulson"
 
 [paulson.emails]
 
 [paulson.emails.paulson_email]
 user = [
   "lp15",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [paulson.homepages]
 paulson_homepage = "https://www.cl.cam.ac.uk/~lp15/"
 
 [peltier]
 name = "Nicolas Peltier"
 
 [peltier.emails]
 
 [peltier.emails.peltier_email]
 user = [
   "Nicolas",
   "Peltier",
 ]
 host = [
   "imag",
   "fr",
 ]
 
 [peltier.homepages]
 peltier_homepage = "http://membres-lig.imag.fr/peltier/"
 
 [peters]
 name = "Kirstin Peters"
 
 [peters.emails]
 
 [peters.emails.peters_email]
 user = [
   "kirstin",
   "peters",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [peters.homepages]
 
 [petrovic]
 name = "Danijela Petrovic"
 
 [petrovic.emails]
 
 [petrovic.homepages]
 petrovic_homepage = "http://www.matf.bg.ac.rs/~danijela"
 
 [pierzchalski]
 name = "Edward Pierzchalski"
 
 [pierzchalski.emails]
 
 [pierzchalski.homepages]
 
 [platzer]
 name = "André Platzer"
 
 [platzer.emails]
 
 [platzer.emails.platzer_email]
 user = [
   "aplatzer",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [platzer.homepages]
 platzer_homepage = "https://www.cs.cmu.edu/~aplatzer/"
 
 [pohjola]
 name = "Johannes Åman Pohjola"
 
 [pohjola.emails]
 
 [pohjola.emails.pohjola_email]
 user = [
   "j",
   "amanpohjola",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [pohjola.homepages]
 
 [pollak]
 name = "Florian Pollak"
 
 [pollak.emails]
 
 [pollak.emails.pollak_email]
 user = [
   "florian",
   "pollak",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [pollak.homepages]
 
 [popescu]
 name = "Andrei Popescu"
 
 [popescu.emails]
 
 [popescu.emails.popescu_email]
 user = [
   "a",
   "popescu",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [popescu.emails.popescu_email1]
 user = [
   "uuomul",
 ]
 host = [
   "yahoo",
   "com",
 ]
 
 [popescu.emails.popescu_email2]
 user = [
   "a",
   "popescu",
 ]
 host = [
   "mdx",
   "ac",
   "uk",
 ]
 
 [popescu.homepages]
 popescu_homepage = "https://www.andreipopescu.uk"
 
 [porter]
 name = "Benjamin Porter"
 
 [porter.emails]
 
 [porter.homepages]
 
 [prathamesh]
 name = "T.V.H. Prathamesh"
 
 [prathamesh.emails]
 
 [prathamesh.emails.prathamesh_email]
 user = [
   "prathamesh",
 ]
 host = [
   "imsc",
   "res",
   "in",
 ]
 
 [prathamesh.homepages]
 
 [preoteasa]
 name = "Viorel Preoteasa"
 
 [preoteasa.emails]
 
 [preoteasa.emails.preoteasa_email]
 user = [
   "viorel",
   "preoteasa",
 ]
 host = [
   "aalto",
   "fi",
 ]
 
 [preoteasa.homepages]
 preoteasa_homepage = "http://users.abo.fi/vpreotea/"
 
 [pusch]
 name = "Cornelia Pusch"
 
 [pusch.emails]
 
 [pusch.homepages]
 
 [qiu]
 name = "Qi Qiu"
 
 [qiu.emails]
 
 [qiu.emails.qiu_email]
 user = [
   "qi",
   "qiu",
 ]
 host = [
   "univ-lyon1",
   "fr",
 ]
 
 [qiu.homepages]
 
 [rabe]
 name = "Markus N. Rabe"
 
 [rabe.emails]
 
 [rabe.homepages]
 rabe_homepage = "http://www.react.uni-saarland.de/people/rabe.html"
 
 [rabing]
 name = "Mathias Schack Rabing"
 
 [rabing.emails]
 
 [rabing.emails.rabing_email]
 user = [
   "mathiasrabing",
 ]
 host = [
   "outlook",
   "com",
 ]
 
 [rabing.homepages]
 
 [raedle]
 name = "Jonas Rädle"
 
 [raedle.emails]
 
 [raedle.emails.raedle_email]
 user = [
   "jonas",
   "raedle",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [raedle.emails.raedle_email1]
 user = [
   "jonas",
   "raedle",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [raedle.homepages]
 
 [raska]
 name = "Martin Raška"
 
 [raska.emails]
 
 [raska.homepages]
 
 [raszyk]
 name = "Martin Raszyk"
 
 [raszyk.emails]
 
 [raszyk.emails.raszyk_email]
 user = [
   "martin",
   "raszyk",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [raszyk.emails.raszyk_email1]
 user = [
   "m",
   "raszyk",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [raszyk.homepages]
 
 [rau]
 name = "Martin Rau"
 
 [rau.emails]
 
 [rau.emails.rau_email]
 user = [
   "martin",
   "rau",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [rau.emails.rau_email1]
 user = [
   "mrtnrau",
 ]
 host = [
   "googlemail",
   "com",
 ]
 
 [rau.homepages]
 
 [rauch]
 name = "Nicole Rauch"
 
 [rauch.emails]
 
 [rauch.emails.rauch_email]
 user = [
   "rauch",
 ]
 host = [
   "informatik",
   "uni-kl",
   "de",
 ]
 
 [rauch.homepages]
 
 [raumer]
 name = "Jakob von Raumer"
 
 [raumer.emails]
 
 [raumer.emails.raumer_email]
 user = [
   "psxjv4",
 ]
 host = [
   "nottingham",
   "ac",
   "uk",
 ]
 
 [raumer.homepages]
 
 [ravindran]
 name = "Binoy Ravindran"
 
 [ravindran.emails]
 
 [ravindran.homepages]
 
 [rawson]
 name = "Michael Rawson"
 
 [rawson.emails]
 
 [rawson.emails.rawson_email]
 user = [
   "michaelrawson76",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [rawson.homepages]
 
 [raya]
 name = "Rodrigo Raya"
 
 [raya.emails]
 
 [raya.emails.raya_email]
 user = [
   "rodrigo",
   "raya",
 ]
 host = [
   "epfl",
   "ch",
 ]
 
 [raya.homepages]
 raya_homepage = "https://people.epfl.ch/rodrigo.raya"
 
 [regensburger]
 name = "Franz Regensburger"
 
 [regensburger.emails]
 
 [regensburger.emails.regensburger_email]
 user = [
   "Franz",
   "Regensburger",
 ]
 host = [
   "thi",
   "de",
 ]
 
 [regensburger.homepages]
 regensburger_homepage = "https://www.thi.de/suche/mitarbeiter/prof-dr-rer-nat-franz-regensburger"
 
 [reiche]
 name = "Sebastian Reiche"
 
 [reiche.emails]
 
 [reiche.homepages]
 reiche_homepage = "https://www.linkedin.com/in/sebastian-reiche-0b2093178"
 
 [reiter]
 name = "Markus Reiter"
 
 [reiter.emails]
 
 [reiter.homepages]
 
 [reynaud]
 name = "Alban Reynaud"
 
 [reynaud.emails]
 
 [reynaud.homepages]
 
 [ribeiro]
 name = "Pedro Ribeiro"
 
 [ribeiro.emails]
 
 [ribeiro.homepages]
 
 [richter]
 name = "Stefan Richter"
 
 [richter.emails]
 
 [richter.emails.richter_email]
 user = [
   "richter",
 ]
 host = [
   "informatik",
   "rwth-aachen",
   "de",
 ]
 
 [richter.homepages]
 richter_homepage = "http://www-lti.informatik.rwth-aachen.de/~richter/"
 
 [rickmann]
 name = "Christina Rickmann"
 
 [rickmann.emails]
 
 [rickmann.emails.rickmann_email]
 user = [
   "c",
   "rickmann",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [rickmann.homepages]
 
 [ridge]
 name = "Tom Ridge"
 
 [ridge.emails]
 
 [ridge.homepages]
 
 [rizaldi]
 name = "Albert Rizaldi"
 
 [rizaldi.emails]
 
 [rizaldi.emails.rizaldi_email]
 user = [
   "albert",
   "rizaldi",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [rizaldi.homepages]
 
 [rizkallah]
 name = "Christine Rizkallah"
 
 [rizkallah.emails]
 
 [rizkallah.homepages]
 rizkallah_homepage = "https://www.mpi-inf.mpg.de/~crizkall/"
 
 [robillard]
 name = "Simon Robillard"
 
 [robillard.emails]
 
 [robillard.homepages]
 robillard_homepage = "https://simon-robillard.net/"
 
 [roessle]
 name = "Ian Roessle"
 
 [roessle.emails]
 
 [roessle.homepages]
 
 [romanos]
 name = "Ralph Romanos"
 
 [romanos.emails]
 
 [romanos.emails.romanos_email]
 user = [
   "ralph",
   "romanos",
 ]
 host = [
   "student",
   "ecp",
   "fr",
 ]
 
 [romanos.homepages]
 
 [rosskopf]
 name = "Simon Roßkopf"
 
 [rosskopf.emails]
 
 [rosskopf.emails.rosskopf_email]
 user = [
   "rosskops",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [rosskopf.homepages]
 rosskopf_homepage = "http://www21.in.tum.de/~rosskops"
 
 [rowat]
 name = "Colin Rowat"
 
 [rowat.emails]
 
 [rowat.emails.rowat_email]
 user = [
   "c",
   "rowat",
 ]
 host = [
   "bham",
   "ac",
   "uk",
 ]
 
 [rowat.homepages]
 
 [sabouret]
 name = "Nicolas Sabouret"
 
 [sabouret.emails]
 
 [sabouret.homepages]
 
 [sachtleben]
 name = "Robert Sachtleben"
 
 [sachtleben.emails]
 
 [sachtleben.emails.sachtleben_email]
 user = [
   "rob_sac",
 ]
 host = [
   "uni-bremen",
   "de",
 ]
 
 [sachtleben.homepages]
 
 [saile]
 name = "Christian Saile"
 
 [saile.emails]
 
 [saile.homepages]
 saile_homepage = "http://dss.in.tum.de/staff/christian-saile.html"
 
 [sanan]
 name = "David Sanan"
 
 [sanan.emails]
 
 [sanan.emails.sanan_email]
 user = [
   "sanan",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [sanan.homepages]
 
 [sato]
 name = "Tetsuya Sato"
 
 [sato.emails]
 
 [sato.emails.sato_email]
 user = [
   "tsato",
 ]
 host = [
   "c",
   "titech",
   "ac",
   "jp",
 ]
 
 [sato.homepages]
 sato_homepage = "https://sites.google.com/view/tetsuyasato/"
 
 [sauer]
 name = "Jens Sauer"
 
 [sauer.emails]
 
 [sauer.emails.sauer_email]
 user = [
   "sauer",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [sauer.homepages]
 
 [schaeffeler]
 name = "Maximilian Schäffeler"
 
 [schaeffeler.emails]
 
 [schaeffeler.emails.schaeffeler_email]
 user = [
   "schaeffm",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [schaeffeler.homepages]
 
 [scharager]
 name = "Matias Scharager"
 
 [scharager.emails]
 
 [scharager.emails.scharager_email]
 user = [
   "mscharag",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [scharager.homepages]
 
 [schimpf]
 name = "Alexander Schimpf"
 
 [schimpf.emails]
 
 [schimpf.emails.schimpf_email]
 user = [
   "schimpfa",
 ]
 host = [
   "informatik",
   "uni-freiburg",
   "de",
 ]
 
 [schimpf.homepages]
 
 [schirmer]
 name = "Norbert Schirmer"
 
 [schirmer.emails]
 
 [schirmer.emails.schirmer_email]
 user = [
   "norbert",
   "schirmer",
 ]
 host = [
   "web",
   "de",
 ]
 
 [schirmer.homepages]
 
 [schleicher]
 name = "Dierk Schleicher"
 
 [schleicher.emails]
 
 [schleicher.homepages]
 
 [schlichtkrull]
 name = "Anders Schlichtkrull"
 
 [schlichtkrull.emails]
 
 [schlichtkrull.emails.schlichtkrull_email]
 user = [
   "andschl",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [schlichtkrull.homepages]
 schlichtkrull_homepage = "https://people.compute.dtu.dk/andschl/"
 
 [schmaltz]
 name = "Julien Schmaltz"
 
 [schmaltz.emails]
 
 [schmaltz.emails.schmaltz_email]
 user = [
   "Julien",
   "Schmaltz",
 ]
 host = [
   "ou",
   "nl",
 ]
 
 [schmaltz.homepages]
 
 [schmidinger]
 name = "Lukas Schmidinger"
 
 [schmidinger.emails]
 
 [schmidinger.homepages]
 
 [schmoetten]
 name = "Richard Schmoetten"
 
 [schmoetten.emails]
 
 [schmoetten.emails.schmoetten_email]
 user = [
   "s1311325",
 ]
 host = [
   "sms",
   "ed",
   "ac",
   "uk",
 ]
 
 [schmoetten.homepages]
 
 [schneider]
 name = "Joshua Schneider"
 
 [schneider.emails]
 
 [schneider.emails.schneider_email]
 user = [
   "joshua",
   "schneider",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [schneider.homepages]
 
 [schoepe]
 name = "Daniel Schoepe"
 
 [schoepe.emails]
 
 [schoepe.emails.schoepe_email]
 user = [
   "daniel",
 ]
 host = [
   "schoepe",
   "org",
 ]
 
 [schoepe.homepages]
 
 [schoepf]
 name = "Jonas Schöpf"
 
 [schoepf.emails]
 
 [schoepf.emails.schoepf_email]
 user = [
   "jonas",
   "schoepf",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [schoepf.homepages]
 
 [schou]
 name = "Morten Konggaard Schou"
 orcid = "0000-0002-5970-4294"
 
 [schou.emails]
 
 [schou.emails.schou_email]
 user = [
   "mksc",
 ]
 host = [
   "cs",
   "aau",
   "dk",
 ]
 
 [schou.homepages]
 
 [schulz]
 name = "Jakob Schulz"
 
 [schulz.emails]
 
 [schulz.emails.schulz_email]
 user = [
   "jakob",
   "schulz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [schulz.homepages]
 
 [scott]
 name = "Dana Scott"
 
 [scott.emails]
 
 [scott.homepages]
 scott_homepage = "http://www.cs.cmu.edu/~scott/"
 
 [sefidgar]
 name = "S. Reza Sefidgar"
 
 [sefidgar.emails]
 
 [sefidgar.emails.sefidgar_email]
 user = [
   "reza",
   "sefidgar",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [sefidgar.homepages]
 
 [seidl]
 name = "Benedikt Seidl"
 
 [seidl.emails]
 
 [seidl.emails.seidl_email]
 user = [
   "benedikt",
   "seidl",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [seidl.homepages]
 
 [seidler]
 name = "Henning Seidler"
 
 [seidler.emails]
 
 [seidler.emails.seidler_email]
 user = [
   "henning",
   "seidler",
 ]
 host = [
   "mailbox",
   "tu-berlin",
   "de",
 ]
 
 [seidler.homepages]
 
 [sewell]
 name = "Thomas Sewell"
 
 [sewell.emails]
 
 [sewell.homepages]
 
 [sickert]
 name = "Salomon Sickert"
 
 [sickert.emails]
 
 [sickert.emails.sickert_email]
 user = [
   "s",
   "sickert",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [sickert.homepages]
 sickert_homepage = "https://www7.in.tum.de/~sickert"
 
 [siek]
 name = "Jeremy Siek"
 
 [siek.emails]
 
 [siek.emails.siek_email]
 user = [
   "jsiek",
 ]
 host = [
   "indiana",
   "edu",
 ]
 
 [siek.homepages]
 siek_homepage = "http://homes.soic.indiana.edu/jsiek/"
 
 [simic]
 name = "Danijela Simić"
 
 [simic.emails]
 
 [simic.emails.simic_email]
 user = [
   "danijela",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [simic.homepages]
 simic_homepage = "http://poincare.matf.bg.ac.rs/~danijela"
 
 [sison]
 name = "Robert Sison"
 
 [sison.emails]
 
 [sison.homepages]
 
 [smaus]
 name = "Jan-Georg Smaus"
 
 [smaus.emails]
 
 [smaus.homepages]
 smaus_homepage = "http://www.irit.fr/~Jan-Georg.Smaus"
 
 [smola]
 name = "Filip Smola"
 
 [smola.emails]
 
 [smola.emails.smola_email]
 user = [
   "f",
   "smola",
 ]
 host = [
   "sms",
   "ed",
   "ac",
   "uk",
 ]
 
 [smola.homepages]
 
 [snelting]
 name = "Gregor Snelting"
 
 [snelting.emails]
 
 [snelting.homepages]
 snelting_homepage = "http://pp.info.uni-karlsruhe.de/personhp/gregor_snelting.php"
 
 [somaini]
 name = "Ivano Somaini"
 
 [somaini.emails]
 
 [somaini.homepages]
 
 [somogyi]
 name = "Dániel Somogyi"
 
 [somogyi.emails]
 
 [somogyi.homepages]
 
 [spasic]
 name = "Mirko Spasić"
 
 [spasic.emails]
 
 [spasic.emails.spasic_email]
 user = [
   "mirko",
 ]
 host = [
   "matf",
   "bg",
   "ac",
   "rs",
 ]
 
 [spasic.homepages]
 
 [spichkova]
 name = "Maria Spichkova"
 
 [spichkova.emails]
 
 [spichkova.emails.spichkova_email]
 user = [
   "maria",
   "spichkova",
 ]
 host = [
   "rmit",
   "edu",
   "au",
 ]
 
 [spichkova.homepages]
 
 [spitz]
 name = "Maximilian Spitz"
 
 [spitz.emails]
 
 [spitz.emails.spitz_email]
 user = [
   "maximilian",
   "spitz",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [spitz.homepages]
 
 [sprenger]
 name = "Christoph Sprenger"
 
 [sprenger.emails]
 
 [sprenger.emails.sprenger_email]
 user = [
   "sprenger",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [sprenger.homepages]
 
 [springsklee]
 name = "Valentin Springsklee"
 
 [springsklee.emails]
 
 [springsklee.emails.springsklee_email]
 user = [
   "uidpn>",
 ]
 host = [
   "student",
   "kit",
   "edu",
 ]
 
 [springsklee.homepages]
 
 [srba]
 name = "Jiří Srba"
 orcid = "0000-0001-5551-6547"
 
 [srba.emails]
 
 [srba.homepages]
 srba_homepage = "https://homes.cs.aau.dk/~srba/"
 
 [staats]
 name = "Charles Staats"
 
 [staats.emails]
 
 [staats.emails.staats_email]
 user = [
   "cstaats",
 ]
 host = [
   "google",
   "com",
 ]
 
 [staats.emails.staats_email1]
 user = [
   "charles",
   "staats",
   "iii",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [staats.homepages]
 
 [stannett]
 name = "Mike Stannett"
 
 [stannett.emails]
 
 [stannett.emails.stannett_email]
 user = [
   "m",
   "stannett",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [stannett.homepages]
 
 [stark]
 name = "Eugene W. Stark"
 
 [stark.emails]
 
 [stark.emails.stark_email]
 user = [
   "stark",
 ]
 host = [
   "cs",
   "stonybrook",
   "edu",
 ]
 
 [stark.homepages]
 
 [starosta]
 name = "Štěpán Starosta"
 
 [starosta.emails]
 
 [starosta.emails.starosta_email]
 user = [
   "stepan",
   "starosta",
 ]
 host = [
   "fit",
   "cvut",
   "cz",
 ]
 
 [starosta.homepages]
 starosta_homepage = "https://staroste.pages.fit/"
 
 [steen]
 name = "Alexander Steen"
 
 [steen.emails]
 
 [steen.homepages]
 
 [steinberg]
 name = "Matías Steinberg"
 
 [steinberg.emails]
 
 [steinberg.emails.steinberg_email]
 user = [
   "matias",
   "steinberg",
 ]
 host = [
   "mi",
   "unc",
   "edu",
   "ar",
 ]
 
 [steinberg.homepages]
 
 [stell]
 name = "Amy Stell"
 orcid = "0000-0003-0714-3269"
 
 [stell.emails]
 
 [stell.emails.stell_email]
 user = [
   "as1343",
 ]
 host = [
   "exeter",
   "ac",
   "uk",
 ]
 
 [stell.homepages]
 stell_homepage = "https://computerscience.exeter.ac.uk/staff/as1343?sm=as1343"
 
 [stephan]
 name = "Werner Stephan"
 
 [stephan.emails]
 
 [stephan.emails.stephan_email]
 user = [
   "stephan",
 ]
 host = [
   "dfki",
   "de",
 ]
 
 [stephan.homepages]
 
 [sternagel]
 name = "Christian Sternagel"
 
 [sternagel.emails]
 
 [sternagel.emails.sternagel_email]
 user = [
   "c",
   "sternagel",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [sternagel.emails.sternagel_email1]
 user = [
   "christian",
   "sternagel",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [sternagel.homepages]
 sternagel_homepage = "http://cl-informatik.uibk.ac.at/users/griff/"
 
 [sternagelt]
 name = "Thomas Sternagel"
 
 [sternagelt.emails]
 
 [sternagelt.homepages]
 
 [stevens]
 name = "Lukas Stevens"
 
 [stevens.emails]
 
 [stevens.emails.stevens_email]
 user = [
   "lukas",
   "stevens",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [stevens.homepages]
 stevens_homepage = "https://www21.in.tum.de/team/stevensl"
 
 [stock]
 name = "Benedikt Stock"
 
 [stock.emails]
 
 [stock.emails.stock_email]
 user = [
   "benedikt1999",
 ]
 host = [
   "freenet",
   "de",
 ]
 
 [stock.homepages]
 
 [stoeckl]
 name = "Bernhard Stöckl"
 
 [stoeckl.emails]
 
 [stoeckl.emails.stoeckl_email]
 user = [
   "stoeckl",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [stoeckl.homepages]
 
 [stricker]
 name = "Christian Stricker"
 
 [stricker.emails]
 
 [stricker.homepages]
 stricker_homepage = "http://dss.in.tum.de/staff/christian-stricker.html"
 
 [strnisa]
 name = "Rok Strniša"
 
 [strnisa.emails]
 
 [strnisa.emails.strnisa_email]
 user = [
   "rok",
 ]
 host = [
   "strnisa",
   "com",
 ]
 
 [strnisa.homepages]
 strnisa_homepage = "http://rok.strnisa.com/lj/"
 
 [struth]
 name = "Georg Struth"
 
 [struth.emails]
 
 [struth.emails.struth_email]
 user = [
   "g",
   "struth",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [struth.homepages]
 struth_homepage = "http://staffwww.dcs.shef.ac.uk/people/G.Struth/"
 
 [stueber]
 name = "Anke Stüber"
 
 [stueber.emails]
 
 [stueber.emails.stueber_email]
 user = [
   "anke",
   "stueber",
 ]
 host = [
   "campus",
   "tu-berlin",
   "de",
 ]
 
 [stueber.homepages]
 
+[stuebinger]
+name = "Terru Stübinger"
+orcid = "0009-0006-7411-2533"
+
+[stuebinger.emails]
+
+[stuebinger.homepages]
+stuebinger_homepage = "https://stuebinm.eu/"
+
 [stuewe]
 name = "Daniel Stüwe"
 
 [stuewe.emails]
 
 [stuewe.homepages]
 
 [sudbrock]
 name = "Henning Sudbrock"
 
 [sudbrock.emails]
 
 [sudbrock.emails.sudbrock_email]
 user = [
   "sudbrock",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [sudbrock.homepages]
 
 [sudhof]
 name = "Henry Sudhof"
 
 [sudhof.emails]
 
 [sudhof.emails.sudhof_email]
 user = [
   "hsudhof",
 ]
 host = [
   "cs",
   "tu-berlin",
   "de",
 ]
 
 [sudhof.homepages]
 
 [sulejmani]
 name = "Ujkan Sulejmani"
 
 [sulejmani.emails]
 
 [sulejmani.emails.sulejmani_email]
 user = [
   "ujkan",
   "sulejmani",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [sulejmani.emails.sulejmani_email1]
 user = [
   "ujkan99",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [sulejmani.homepages]
 
 [sutcliffe]
 name = "Geoff Sutcliffe"
 
 [sutcliffe.emails]
 
 [sutcliffe.homepages]
 
 [sylvestre]
 name = "Jeremy Sylvestre"
 
 [sylvestre.emails]
 
 [sylvestre.emails.sylvestre_email]
 user = [
   "jeremy",
   "sylvestre",
 ]
 host = [
   "ualberta",
   "ca",
 ]
 
 [sylvestre.emails.sylvestre_email1]
 user = [
   "jsylvest",
 ]
 host = [
   "ualberta",
   "ca",
 ]
 
 [sylvestre.homepages]
 sylvestre_homepage = "http://ualberta.ca/~jsylvest/"
 
 [szekely]
 name = "Gergely Szekely"
 
 [szekely.emails]
 
 [szekely.homepages]
 szekely_homepage = "https://users.renyi.hu/~turms/"
 
 [taha]
 name = "Safouan Taha"
 
 [taha.emails]
 
 [taha.emails.taha_email]
 user = [
   "safouan",
   "taha",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [taha.homepages]
 
 [tan]
 name = "Yong Kiam Tan"
 
 [tan.emails]
 
 [tan.emails.tan_email]
 user = [
   "yongkiat",
 ]
 host = [
   "cs",
   "cmu",
   "edu",
 ]
 
 [tan.homepages]
 tan_homepage = "https://www.cs.cmu.edu/~yongkiat/"
 
 [tanaka]
 name = "Miki Tanaka"
 
 [tanaka.emails]
 
 [tanaka.emails.tanaka_email]
 user = [
   "miki",
   "tanaka",
 ]
 host = [
   "unsw",
   "edu",
   "au",
 ]
 
 [tanaka.homepages]
 
 [tasch]
 name = "Markus Tasch"
 
 [tasch.emails]
 
 [tasch.emails.tasch_email]
 user = [
   "tasch",
 ]
 host = [
   "mais",
   "informatik",
   "tu-darmstadt",
   "de",
 ]
 
 [tasch.homepages]
 
 [taylor]
 name = "Ramsay G. Taylor"
 
 [taylor.emails]
 
 [taylor.emails.taylor_email]
 user = [
   "r",
   "g",
   "taylor",
 ]
 host = [
   "sheffield",
   "ac",
   "uk",
 ]
 
 [taylor.homepages]
 
 [terraf]
 name = "Pedro Sánchez Terraf"
 
 [terraf.emails]
 
 [terraf.emails.terraf_email]
 user = [
   "psterraf",
 ]
 host = [
   "unc",
   "edu",
   "ar",
 ]
 
 [terraf.homepages]
 terraf_homepage = "https://cs.famaf.unc.edu.ar/~pedro/home_en.html"
 
 [thiemann]
 name = "René Thiemann"
 
 [thiemann.emails]
 
 [thiemann.emails.thiemann_email]
 user = [
   "rene",
   "thiemann",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [thiemann.homepages]
 thiemann_homepage = "http://cl-informatik.uibk.ac.at/users/thiemann/"
 
 [thommes]
 name = "Joseph Thommes"
 
 [thommes.emails]
 
 [thommes.emails.thommes_email]
 user = [
   "joseph-thommes",
 ]
 host = [
   "gmx",
   "de",
 ]
 
 [thommes.homepages]
 
 [thomson]
 name = "Fox Thomson"
 
 [thomson.emails]
 
 [thomson.emails.thomson_email]
 user = [
   "foxthomson0",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [thomson.homepages]
 
 [tiu]
 name = "Alwen Tiu"
 
 [tiu.emails]
 
 [tiu.emails.tiu_email]
 user = [
   "ATiu",
 ]
 host = [
   "ntu",
   "edu",
   "sg",
 ]
 
 [tiu.homepages]
 tiu_homepage = "http://users.cecs.anu.edu.au/~tiu/"
 
 [toth]
 name = "Balazs Toth"
 
 [toth.emails]
 
 [toth.emails.toth_email]
 user = [
   "balazs",
   "toth",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [toth.homepages]
 
 [tourret]
 name = "Sophie Tourret"
 
 [tourret.emails]
 
 [tourret.emails.tourret_email]
 user = [
   "stourret",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [tourret.homepages]
 tourret_homepage = "https://www.mpi-inf.mpg.de/departments/automation-of-logic/people/sophie-tourret/"
 
 [trachtenherz]
 name = "David Trachtenherz"
 
 [trachtenherz.emails]
 
 [trachtenherz.homepages]
 
 [traut]
 name = "Christoph Traut"
 
 [traut.emails]
 
 [traut.homepages]
 
 [traytel]
 name = "Dmitriy Traytel"
 
 [traytel.emails]
 
 [traytel.emails.traytel_email]
 user = [
   "traytel",
 ]
 host = [
   "in",
   "tum",
   "de",
 ]
 
 [traytel.emails.traytel_email1]
 user = [
   "traytel",
 ]
 host = [
   "inf",
   "ethz",
   "ch",
 ]
 
 [traytel.emails.traytel_email2]
 user = [
   "traytel",
 ]
 host = [
   "di",
   "ku",
   "dk",
 ]
 
 [traytel.homepages]
 traytel_homepage = "https://traytel.bitbucket.io/"
 
 [trelat]
 name = "Vincent Trélat"
 
 [trelat.emails]
 
 [trelat.emails.trelat_email]
 user = [
   "vincent",
   "trelat",
 ]
 host = [
   "depinfonancy",
   "net",
 ]
 
 [trelat.homepages]
 
 [tuerk]
 name = "Thomas Tuerk"
 
 [tuerk.emails]
 
 [tuerk.homepages]
 
 [tuong]
 name = "Frédéric Tuong"
 
 [tuong.emails]
 
 [tuong.emails.tuong_email]
 user = [
   "tuong",
 ]
 host = [
   "users",
   "gforge",
   "inria",
   "fr",
 ]
 
 [tuong.emails.tuong_email1]
 user = [
   "ftuong",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [tuong.homepages]
 tuong_homepage = "https://www.lri.fr/~ftuong/"
 
 [tuongj]
 name = "Joseph Tuong"
 
 [tuongj.emails]
 
 [tuongj.homepages]
 
 [tverdyshev]
 name = "Sergey Tverdyshev"
 
 [tverdyshev.emails]
 
 [tverdyshev.emails.tverdyshev_email]
 user = [
   "stv",
 ]
 host = [
   "sysgo",
   "com",
 ]
 
 [tverdyshev.homepages]
 
 [ullrich]
 name = "Sebastian Ullrich"
 
 [ullrich.emails]
 
 [ullrich.emails.ullrich_email]
 user = [
   "sebasti",
 ]
 host = [
   "nullri",
   "ch",
 ]
 
 [ullrich.homepages]
 
 [unruh]
 name = "Dominique Unruh"
 
 [unruh.emails]
 
 [unruh.emails.unruh_email]
 user = [
   "unruh",
 ]
 host = [
   "ut",
   "ee",
 ]
 
 [unruh.homepages]
 unruh_homepage = "https://www.ut.ee/~unruh/"
 
 [urban]
 name = "Christian Urban"
 
 [urban.emails]
 
 [urban.emails.urban_email]
 user = [
   "christian",
   "urban",
 ]
 host = [
   "kcl",
   "ac",
   "uk",
 ]
 
 [urban.homepages]
 urban_homepage = "https://nms.kcl.ac.uk/christian.urban/"
 
 [van]
 name = "Hai Nguyen Van"
 
 [van.emails]
 
 [van.emails.van_email]
 user = [
   "hai",
   "nguyenvan",
   "phie",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [van.homepages]
 
 [velykis]
 name = "Andrius Velykis"
 
 [velykis.emails]
 
 [velykis.homepages]
 velykis_homepage = "http://andrius.velykis.lt"
 
 [verbeek]
 name = "Freek Verbeek"
 
 [verbeek.emails]
 
 [verbeek.emails.verbeek_email]
 user = [
   "Freek",
   "Verbeek",
 ]
 host = [
   "ou",
   "nl",
 ]
 
 [verbeek.emails.verbeek_email1]
 user = [
   "freek",
 ]
 host = [
   "vt",
   "edu",
 ]
 
 [verbeek.homepages]
 
 [villadsen]
 name = "Jørgen Villadsen"
 
 [villadsen.emails]
 
 [villadsen.emails.villadsen_email]
 user = [
   "jovi",
 ]
 host = [
   "dtu",
   "dk",
 ]
 
 [villadsen.homepages]
 villadsen_homepage = "https://people.compute.dtu.dk/jovi/"
 
 [voisin]
 name = "Frederic Voisin"
 
 [voisin.emails]
 
 [voisin.homepages]
 
 [vytiniotis]
 name = "Dimitrios Vytiniotis"
 
 [vytiniotis.emails]
 
 [vytiniotis.homepages]
 vytiniotis_homepage = "http://research.microsoft.com/en-us/people/dimitris/"
 
 [wagner]
 name = "Max Wagner"
 
 [wagner.emails]
 
 [wagner.emails.wagner_email]
 user = [
   "max",
 ]
 host = [
   "trollbu",
   "de",
 ]
 
 [wagner.homepages]
 
 [waldmann]
 name = "Uwe Waldmann"
 
 [waldmann.emails]
 
 [waldmann.emails.waldmann_email]
 user = [
   "waldmann",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [waldmann.homepages]
 
 [wand]
 name = "Daniel Wand"
 
 [wand.emails]
 
 [wand.emails.wand_email]
 user = [
   "dwand",
 ]
 host = [
   "mpi-inf",
   "mpg",
   "de",
 ]
 
 [wand.homepages]
 
 [wang]
 name = "Shuling Wang"
 
 [wang.emails]
 
 [wang.homepages]
 
 [wassell]
 name = "Mark Wassell"
 
 [wassell.emails]
 
 [wassell.emails.wassell_email]
 user = [
   "mpwassell",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [wassell.homepages]
 
 [wasserrab]
 name = "Daniel Wasserrab"
 
 [wasserrab.emails]
 
 [wasserrab.homepages]
 wasserrab_homepage = "http://pp.info.uni-karlsruhe.de/personhp/daniel_wasserrab.php"
 
 [watt]
 name = "Conrad Watt"
 
 [watt.emails]
 
 [watt.emails.watt_email]
 user = [
   "caw77",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [watt.homepages]
 watt_homepage = "http://www.cl.cam.ac.uk/~caw77/"
 
 [weber]
 name = "Tjark Weber"
 
 [weber.emails]
 
 [weber.emails.weber_email]
 user = [
   "tjark",
   "weber",
 ]
 host = [
   "it",
   "uu",
   "se",
 ]
 
 [weber.homepages]
 weber_homepage = "http://user.it.uu.se/~tjawe125/"
 
 [weerwag]
 name = "Timmy Weerwag"
 
 [weerwag.emails]
 
 [weerwag.homepages]
 
 [weidner]
 name = "Arno Wilhelm-Weidner"
 
 [weidner.emails]
 
 [weidner.emails.weidner_email]
 user = [
   "arno",
   "wilhelm-weidner",
 ]
 host = [
   "tu-berlin",
   "de",
 ]
 
 [weidner.homepages]
 
 [wenninger]
 name = "Elias Wenninger"
 
 [wenninger.emails]
 
 [wenninger.homepages]
 
 [wenzel]
 name = "Makarius Wenzel"
 
 [wenzel.emails]
 
 [wenzel.emails.wenzel_email]
 user = [
   "makarius",
 ]
 host = [
   "sketis",
   "net",
 ]
 
 [wenzel.homepages]
 
 [whitley]
 name = "A Whitley"
 
 [whitley.emails]
 
 [whitley.emails.whitley_email]
 user = [
   "awhitley",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [whitley.homepages]
 
 [wickerson]
 name = "John Wickerson"
 
 [wickerson.emails]
 
 [wickerson.homepages]
 wickerson_homepage = "http://www.doc.ic.ac.uk/~jpw48"
 
 [willenbrink]
 name = "Sebastian Willenbrink"
 
 [willenbrink.emails]
 
 [willenbrink.emails.willenbrink_email]
 user = [
   "sebastian",
   "willenbrink",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [willenbrink.homepages]
 
 [wimmer]
 name = "Simon Wimmer"
 
 [wimmer.emails]
 
 [wimmer.emails.wimmer_email]
 user = [
   "simon",
   "wimmer",
 ]
 host = [
   "tum",
   "de",
 ]
 
 [wimmer.homepages]
 wimmer_homepage = "http://home.in.tum.de/~wimmers/"
 
 [wirt]
 name = "Kai Wirt"
 
 [wirt.emails]
 
 [wirt.homepages]
 
 [wolff]
 name = "Burkhart Wolff"
 
 [wolff.emails]
 
 [wolff.emails.wolff_email]
 user = [
   "burkhart",
   "wolff",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [wolff.homepages]
 wolff_homepage = "https://www.lri.fr/~wolff/"
 
 [wu]
 name = "Chunhan Wu"
 
 [wu.emails]
 
 [wu.homepages]
 
 [xu]
 name = "Jian Xu"
 
 [xu.emails]
 
 [xu.homepages]
 
 [yamada]
 name = "Akihisa Yamada"
 
 [yamada.emails]
 
 [yamada.emails.yamada_email]
 user = [
   "akihisa",
   "yamada",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [yamada.emails.yamada_email1]
 user = [
   "ayamada",
 ]
 host = [
   "trs",
   "cm",
   "is",
   "nagoya-u",
   "ac",
   "jp",
 ]
 
 [yamada.emails.yamada_email2]
 user = [
   "akihisa",
   "yamada",
 ]
 host = [
   "aist",
   "go",
   "jp",
 ]
 
 [yamada.emails.yamada_email3]
 user = [
   "akihisayamada",
 ]
 host = [
   "nii",
   "ac",
   "jp",
 ]
 
 [yamada.homepages]
 yamada_homepage = "http://group-mmm.org/~ayamada/"
 
 [ye]
 name = "Lina Ye"
 
 [ye.emails]
 
 [ye.emails.ye_email]
 user = [
   "lina",
   "ye",
 ]
 host = [
   "lri",
   "fr",
 ]
 
 [ye.homepages]
 
 [yez]
 name = "Zhengkun Ye"
 
 [yez.emails]
 
 [yez.emails.yez_email]
 user = [
   "zy307",
 ]
 host = [
   "cam",
   "ac",
   "uk",
 ]
 
 [yez.homepages]
 
 [ying]
 name = "Shenggang Ying"
 
 [ying.emails]
 
 [ying.homepages]
 
 [yingm]
 name = "Mingsheng Ying"
 
 [yingm.emails]
 
 [yingm.homepages]
 
 [yu]
 name = "Lei Yu"
 
 [yu.emails]
 
 [yu.emails.yu_email]
 user = [
   "yulei0603",
 ]
 host = [
   "gmail",
   "com",
 ]
 
 [yu.homepages]
 
 [zankl]
 name = "Harald Zankl"
 
 [zankl.emails]
 
 [zankl.emails.zankl_email]
 user = [
   "Harald",
   "Zankl",
 ]
 host = [
   "uibk",
   "ac",
   "at",
 ]
 
 [zankl.homepages]
 zankl_homepage = "http://cl-informatik.uibk.ac.at/users/hzankl"
 
 [zee]
 name = "Karen Zee"
 
 [zee.emails]
 
 [zee.emails.zee_email]
 user = [
   "kkz",
 ]
 host = [
   "mit",
   "edu",
 ]
 
 [zee.homepages]
 zee_homepage = "http://www.mit.edu/~kkz/"
 
 [zeller]
 name = "Peter Zeller"
 
 [zeller.emails]
 
 [zeller.emails.zeller_email]
 user = [
   "p_zeller",
 ]
 host = [
   "cs",
   "uni-kl",
   "de",
 ]
 
 [zeller.homepages]
 
 [zeyda]
 name = "Frank Zeyda"
 
 [zeyda.emails]
 
 [zeyda.emails.zeyda_email]
 user = [
   "frank",
   "zeyda",
 ]
 host = [
   "york",
   "ac",
   "uk",
 ]
 
 [zeyda.homepages]
 
 [zhan]
 name = "Bohua Zhan"
 
 [zhan.emails]
 
 [zhan.emails.zhan_email]
 user = [
   "bzhan",
 ]
 host = [
   "ios",
   "ac",
   "cn",
 ]
 
 [zhan.homepages]
 zhan_homepage = "http://lcs.ios.ac.cn/~bzhan/"
 
 [zhang]
 name = "Yu Zhang"
 
 [zhang.emails]
 
 [zhang.homepages]
 
 [zhangx]
 name = "Xingyuan Zhang"
 
 [zhangx.emails]
 
 [zhangx.homepages]
 
 [zhann]
 name = "Naijun Zhan"
 
 [zhann.emails]
 
 [zhann.homepages]
diff --git a/metadata/entries/Approximate_Model_Counting.toml b/metadata/entries/Approximate_Model_Counting.toml
new file mode 100644
--- /dev/null
+++ b/metadata/entries/Approximate_Model_Counting.toml
@@ -0,0 +1,40 @@
+title = "Approximate Model Counting"
+date = 2024-03-15
+topics = [
+  "Computer science/Algorithms/Approximation",
+  "Computer science/Algorithms/Randomized",
+]
+abstract = """
+Approximate model counting is the task of approximating the number of solutions
+to an input formula.  This entry formalizes $\\mathsf{ApproxMC}$, an algorithm
+due to Chakraborty et al. with a
+probably approximately correct (PAC) guarantee, i.e., $\\mathsf{ApproxMC}$
+returns a multiplicative $(1+\\varepsilon)$-factor approximation of the model
+count with probability at least $1 - \\delta$, where $\\varepsilon > 0$ and $0 <
+\\delta \\leq 1$.  The algorithmic specification is further refined to a verified
+certificate checker that can be used to validate the results of untrusted
+$\\mathsf{ApproxMC}$ implementations (assuming access to trusted randomness)."""
+license = "bsd"
+note = ""
+
+[authors]
+
+[authors.tan]
+email = "tan_email"
+
+[authors.yang]
+email = "yang_email"
+
+[contributors]
+
+[notify]
+tan = "tan_email"
+yang = "yang_email"
+
+[history]
+
+[extra]
+
+[related]
+dois = []
+pubs = []
diff --git a/metadata/entries/Continued_Fractions.toml b/metadata/entries/Continued_Fractions.toml
new file mode 100644
--- /dev/null
+++ b/metadata/entries/Continued_Fractions.toml
@@ -0,0 +1,41 @@
+title = "Continued Fractions"
+date = 2024-03-20
+topics = [
+  "Mathematics/Analysis",
+]
+abstract = """
+<p>This article provides a formalisation of continued fractions of real numbers and their basic properties.
+It also contains a proof of the classic result that the irrational numbers with periodic continued
+ fraction expansions are precisely the quadratic irrationals, i.e. real numbers that fulfil a non-trivial quadratic equation $a x^2 + b x + c = 0$ with integer coefficients.</p>
+<p>
+Particular attention is given to the continued fraction expansion of $\\sqrt{D}$ for a non-square
+ natural number $D$. Basic results about the length and structure of its period are provided,
+ along with an executable algorithm to compute the period (and from it, the entire expansion).</p>
+<p>
+This is then also used to provide a fairly efficient, executable, and fully formalised algorithm to
+compute solutions to Pell's equation $x^2 - D y^2 = 1$. The performance is sufficiently good to
+find the solution to Archimedes's cattle problem in less than a second on a typical computer.
+This involves the value $D = 410286423278424$, for which the solution has over 200000 decimals.</p>
+<p>
+Lastly, a derivation of the continued fraction expansions of Euler's number $e$ and an executable
+function to compute continued fraction expansions using interval arithmetic is also provided.</p>"""
+license = "bsd"
+note = ""
+
+[authors]
+
+[authors.eberl]
+email = "eberl_email"
+
+[contributors]
+
+[notify]
+eberl = "eberl_email"
+
+[history]
+
+[extra]
+
+[related]
+dois = []
+pubs = []
diff --git a/metadata/entries/Go.toml b/metadata/entries/Go.toml
new file mode 100644
--- /dev/null
+++ b/metadata/entries/Go.toml
@@ -0,0 +1,35 @@
+title = "Go Code Generation for Isabelle"
+date = 2024-01-22
+topics = [
+  "Tools",
+]
+abstract = """
+This entry contains a standalone code generation target for the Go programming language.
+Unlike the previous targets, Go is not a functional language and encourages code in an imperative style, thus many of the features of Isabelle's language (particularly data types, pattern matching, and type classes) have to be emulated using imperative language constructs in Go.
+To generate Go code, users can simply import this entry, which makes the Go target available."""
+license = "bsd"
+note = ""
+
+[authors]
+
+[authors.stuebinger]
+homepage = "stuebinger_homepage"
+
+[authors.hupel]
+homepage = "hupel_homepage"
+
+[contributors]
+
+[notify]
+hupel = "hupel_email"
+
+[history]
+
+[extra]
+
+[related]
+dois = [
+  "10.48550/arXiv.2310.02704",
+  "10.5281/zenodo.8401392",
+]
+pubs = []
diff --git a/thys/Approximate_Model_Counting/ApproxMCAnalysis.thy b/thys/Approximate_Model_Counting/ApproxMCAnalysis.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/ApproxMCAnalysis.thy
@@ -0,0 +1,764 @@
+section \<open> ApproxMC definition and analysis \<close>
+
+text \<open>
+  This section puts together preceding results to formalize the
+  PAC guarantee of ApproxMC.
+\<close>
+
+theory ApproxMCAnalysis imports
+  ApproxMCCoreAnalysis
+  RandomXORHashFamily
+  Median_Method.Median
+begin
+
+lemma replicate_pmf_Pi_pmf:
+  assumes "distinct ls"
+  shows "replicate_pmf (length ls) P =
+    map_pmf (\<lambda>f. map f ls)
+      (Pi_pmf (set ls) def (\<lambda>_. P))"
+  using assms
+proof (induction ls)
+  case Nil
+  then show ?case
+  by auto
+next
+  case (Cons x xs)
+  then show ?case
+    by (auto intro!: bind_pmf_cong simp add: Pi_pmf_insert' map_bind_pmf bind_map_pmf)
+qed
+
+lemma replicate_pmf_Pi_pmf':
+  assumes "finite V"
+  shows "replicate_pmf (card V) P =
+    map_pmf (\<lambda>f. map f (sorted_list_of_set V))
+      (Pi_pmf V def (\<lambda>_. P))"
+proof -
+  have *:"card V = length (sorted_list_of_set V)"
+    using assms by auto
+  show ?thesis
+    unfolding *
+    apply (subst replicate_pmf_Pi_pmf)
+    using assms by auto
+qed
+
+definition map_of_default::"('a \<times> 'b) list \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'b"
+where "map_of_default ls def =
+  (let m = map_of ls in
+  (\<lambda>x. case m x of None \<Rightarrow> def | Some v \<Rightarrow> v))"
+
+lemma Pi_pmf_replicate_pmf:
+  assumes "finite V"
+  shows
+    "(Pi_pmf V def (\<lambda>_. p)) =
+    map_pmf (\<lambda>bs.
+      map_of_default (zip (sorted_list_of_set V) bs) def)
+      (replicate_pmf (card V) p)"
+proof -
+  show ?thesis
+   apply (subst replicate_pmf_Pi_pmf'[OF assms, where def="def"])
+  unfolding map_pmf_comp
+   apply (intro map_pmf_idI[symmetric])
+   unfolding map_of_default_def Let_def fun_eq_iff map_of_zip_map
+   by (smt (verit, del_insts) assms option.case(1) option.case(2) pmf_Pi pmf_eq_0_set_pmf sorted_list_of_set.set_sorted_key_list_of_set)
+qed
+
+lemma proj_inter_neutral:
+  assumes "\<And>w. w \<in> B \<longleftrightarrow> restr S w \<in> C"
+  shows "proj S (A \<inter> B) = proj S A \<inter> C"
+  unfolding ApproxMCCore.proj_def
+  using assms by auto
+
+text \<open>
+  An abstract spec of ApproxMC for any Boolean theory.
+  This locale must be instantiated with a theory implementing the two
+  the functions below (and satisfying the assumption linking them).
+\<close>
+locale ApproxMC =
+  fixes sols :: "'fml \<Rightarrow> ('a \<Rightarrow> bool) set"
+  fixes enc_xor :: "'a set \<times> bool \<Rightarrow> 'fml \<Rightarrow> 'fml"
+  assumes sols_enc_xor:
+    "\<And>F xor. finite (fst xor) \<Longrightarrow>
+      sols (enc_xor xor F) =
+      sols F \<inter> {\<omega>. satisfies_xor xor {x. \<omega> x}}"
+begin
+
+definition compute_thresh :: "real \<Rightarrow> nat"
+  where "compute_thresh \<epsilon> =
+  nat \<lceil>1 + 9.84 * (1 + \<epsilon> / (1 + \<epsilon>)) * (1 + 1 / \<epsilon>)^2\<rceil>"
+
+definition fix_t :: "real \<Rightarrow> nat"
+  where "fix_t \<delta> =
+  nat \<lceil>ln (1 / \<delta>) /(2 * (0.5-0.36)^2)\<rceil>"
+
+definition raw_median_bound :: "real \<Rightarrow> nat \<Rightarrow> real"
+  where "raw_median_bound \<alpha> t =
+  (\<Sum>i = 0..t div 2.
+    (t choose i) * (1 / 2 + \<alpha>) ^ i * (1 / 2 - \<alpha>) ^ (t - i))"
+
+definition compute_t :: "real \<Rightarrow> nat \<Rightarrow> nat"
+  where "compute_t \<delta> n =
+  (if raw_median_bound 0.14 n < \<delta> then n
+  else fix_t \<delta>)"
+
+(* The size of the projected solution set after adding i XORs*)
+definition size_xor ::"
+  'fml \<Rightarrow> 'a set \<Rightarrow>
+  (nat \<Rightarrow> ('a set \<times> bool) option) \<Rightarrow>
+  nat \<Rightarrow> nat"
+  where "size_xor F S xorsf i = (
+    let xors = map (the \<circ> xorsf) [0..<i] in
+    let Fenc = fold enc_xor xors F in
+      card (proj S (sols Fenc))
+    )"
+
+definition check_xor ::"
+  'fml \<Rightarrow> 'a set \<Rightarrow>
+  nat \<Rightarrow>
+  (nat \<Rightarrow> ('a set \<times> bool) option) \<Rightarrow>
+  nat \<Rightarrow> bool"
+  where "check_xor F S thresh xorsf i =
+  (size_xor F S xorsf i < thresh)"
+
+definition approxcore_xors :: "
+  'fml \<Rightarrow> 'a set \<Rightarrow>
+  nat \<Rightarrow>
+  (nat \<Rightarrow> ('a set \<times> bool) option) \<Rightarrow>
+  nat"
+  where "
+    approxcore_xors F S thresh xorsf =
+    (case List.find
+      (check_xor F S thresh xorsf) [1..<card S] of
+      None \<Rightarrow> 2 ^ card S
+    | Some m \<Rightarrow>
+      (2 ^ m * size_xor F S xorsf m))"
+
+definition approxmccore :: "'fml \<Rightarrow> 'a set \<Rightarrow> nat \<Rightarrow> nat pmf"
+where "approxmccore F S thresh =
+  map_pmf (approxcore_xors F S thresh) (random_xors S (card S - 1))"
+
+definition approxmc :: "'fml \<Rightarrow> 'a set \<Rightarrow> real \<Rightarrow> real \<Rightarrow> nat \<Rightarrow> nat pmf"
+  where "approxmc F S \<epsilon> \<delta> n = (
+    let thresh = compute_thresh \<epsilon> in
+    if card (proj S (sols F)) < thresh then
+      return_pmf (card (proj S (sols F)))
+    else
+      let t = compute_t \<delta> n in
+      map_pmf (median t)
+        (prod_pmf {0..<t::nat} (\<lambda>i. approxmccore F S thresh))
+  )"
+
+lemma median_commute:
+  assumes "t \<ge> 1"
+  shows "(real \<circ> median t) = (\<lambda>w::nat \<Rightarrow> nat. median t (real \<circ> w))"
+  unfolding median_def map_map[symmetric]
+  apply (subst Median.map_sort[where f = "\<lambda>x. real x"])
+  subgoal by (clarsimp simp add:mono_def)
+  apply (subst nth_map)
+  using assms by auto
+
+lemma median_default:
+  shows "median t y = median t (\<lambda>x. if x < t then y x else def)"
+  unfolding median_def
+  by (auto intro!: arg_cong[where f = "\<lambda>ls. sort ls ! (t div 2)"])
+
+definition default_\<alpha>::"'a set \<Rightarrow> nat assg"
+  where "default_\<alpha> S i = (if i < card S - 1 then Some True else None)"
+
+lemma dom_default_\<alpha>:
+  "dom (default_\<alpha> S) = {0..<card S -1}"
+  by (auto simp add:default_\<alpha>_def split: if_splits)
+
+lemma compute_thresh_bound_4:
+  assumes "\<epsilon> > 0"
+  shows"4 < compute_thresh \<epsilon>"
+proof -
+  have 1: "(1 + \<epsilon> / (1 + \<epsilon>)) > 1"
+    using assms
+    by simp
+  have 2: "(1 + 1 / \<epsilon>)^2 > 1"
+    using assms by simp
+
+  define a where "a = (1 + \<epsilon> / (1 + \<epsilon>)) * (1 + 1 / \<epsilon>)\<^sup>2"
+  have "a > 1" unfolding a_def
+    using 1 2
+    using less_1_mult by blast
+  then have "(984 / 10\<^sup>2) * a \<ge> 4"
+    by auto
+
+  thus ?thesis
+    unfolding compute_thresh_def
+    by (smt (verit) a_def arith_special(2) arithmetic_simps(1) more_arith_simps(11) nat_less_real_le numeral_Bit0 of_nat_numeral real_nat_ceiling_ge)
+qed
+
+lemma satisfies_xor_with_domain:
+  assumes "fst x \<subseteq> S"
+  shows "satisfies_xor x {x. w x} \<longleftrightarrow>
+    satisfies_xor x ({x. w x} \<inter> S)"
+  using assms
+  apply (cases x)
+  by (simp add: Int_assoc inf.absorb_iff2)
+
+(* The main step, where we instantiate the ApproxMCCore locale *)
+lemma approxcore_xors_eq:
+  assumes thresh:
+    "thresh = compute_thresh \<epsilon>"
+    "thresh \<le> card (proj S (sols F))"
+  assumes \<epsilon>: "\<epsilon> > (0::real)" "\<epsilon> \<le> 1"
+  assumes S: "finite S"
+  shows "measure_pmf.prob (random_xors S (card S - 1))
+       {xors. real (approxcore_xors F S thresh xors) \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+        (1 + \<epsilon>) * real (card (proj S (sols F)))}} \<ge> 0.64"
+proof -
+
+  have "ApproxMCCore (sols F) S \<epsilon> (default_\<alpha> S) thresh"
+    apply unfold_locales
+    subgoal using dom_default_\<alpha> by simp
+    subgoal using \<epsilon> by simp
+    subgoal using thresh assms(3) compute_thresh_bound_4 by blast
+    using thresh S by auto
+  then interpret amc: ApproxMCCore "sols F" _ _ "(default_\<alpha> S)" .
+
+  have "
+    m < card S \<Longrightarrow>
+    {0..<m} \<subseteq> dom xors \<Longrightarrow>
+    (\<And>i. i < m \<Longrightarrow> fst (the (xors i)) \<subseteq> S) \<Longrightarrow>
+    (proj S
+       (sols (fold enc_xor (map (the \<circ> xors) [0..<m]) F))) =
+     proj S (sols F) \<inter>
+        {w. hslice m (\<lambda>\<omega>. xor_hash \<omega> xors) w =
+          aslice m (default_\<alpha> S)}" for m xors
+  proof (induction m)
+    case 0
+    then show ?case
+      unfolding hslice_def aslice_def
+      by auto
+  next
+    case (Suc m)
+    have m: "m \<in> dom xors"
+      by (meson Set.basic_monos(7) Suc(3) atLeastLessThan_iff le0 lessI)
+    have sp: "fst (the (xors m)) \<subseteq> S"
+      by (simp add: Suc(4))
+
+    then obtain xor where x: "xors m = Some xor"
+      using m by blast
+
+    have eq: "{w. xor_hash w xors m = Some True} =
+        {\<omega>. satisfies_xor xor {x. \<omega> x = Some True}}"
+      unfolding xor_hash_def
+      by (clarsimp simp add: x)
+
+    have neut: "\<And>w.
+      w \<in> {\<omega>. satisfies_xor xor {x. \<omega> x}} \<longleftrightarrow>
+      restr S w \<in> {\<omega>. satisfies_xor xor {x. \<omega> x = Some True}}"
+      using sp unfolding restr_def
+      by (smt (verit, ccfv_SIG) Collect_cong Int_def mem_Collect_eq option.sel satisfies_xor_with_domain x)
+
+    have lhs: "
+      proj S
+       (sols (fold enc_xor (map (the \<circ> xors) [0..<Suc m]) F)) =
+      proj S (sols (fold enc_xor (map (the \<circ> xors) [0..<m]) F)) \<inter>
+        {w. xor_hash w xors m = Some True}"
+      apply clarsimp
+      apply (subst sols_enc_xor)
+      subgoal using assms(5) rev_finite_subset sp by blast
+      apply (subst proj_inter_neutral)
+      using eq neut x by auto
+
+    have rhs1:" hslice (Suc m) (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice (Suc m) (default_\<alpha> S) \<Longrightarrow>
+      hslice m (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice m (default_\<alpha> S)" for w
+      unfolding hslice_def aslice_def fun_eq_iff
+      by (auto simp add:lessThan_Suc restrict_map_def split: if_splits)
+
+    have rhs2:"hslice (Suc m) (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice (Suc m) (default_\<alpha> S) \<Longrightarrow>
+      xor_hash w xors m = Some True" for w
+      unfolding hslice_def aslice_def fun_eq_iff
+      apply (clarsimp simp add:lessThan_Suc restrict_map_def )
+      by (metis default_\<alpha>_def domIff m xor_hash_eq_dom)
+
+    have rhs3: "hslice m (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice m (default_\<alpha> S) \<Longrightarrow>
+      xor_hash w xors m = Some True \<Longrightarrow>
+      hslice (Suc m) (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice (Suc m) (default_\<alpha> S)" for w
+      unfolding hslice_def aslice_def fun_eq_iff
+      apply (clarsimp simp add:lessThan_Suc restrict_map_def )
+      by (metis One_nat_def Suc.prems(1) Suc_lessD Suc_less_eq Suc_pred default_\<alpha>_def gr_zeroI zero_less_diff)
+
+    have rhs: "{w. hslice (Suc m) (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice (Suc m) (default_\<alpha> S)} =
+      {w. hslice m (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice m (default_\<alpha> S)} \<inter>
+      {w. xor_hash w xors m = Some True}"
+      by (auto simp add: rhs1 rhs2 rhs3)
+
+    have ih: "proj S (sols (fold enc_xor (map (the \<circ> xors) [0..<m]) F)) =
+      proj S (sols F) \<inter>
+      {w. hslice m (\<lambda>\<omega>. xor_hash \<omega> xors) w = aslice m (default_\<alpha> S)}"
+      apply (intro Suc(1))
+      using Suc(2) Suc_lessD apply blast
+      using Suc(3) atLeast0_lessThan_Suc apply blast
+      using Suc(4) less_SucI by blast
+
+    show ?case
+      unfolding lhs rhs
+      by (simp add: Int_ac(1) ih)
+  qed
+  then have *: "
+    m < card S \<Longrightarrow>
+    {0..<m} \<subseteq> dom xors \<Longrightarrow>
+    (\<And>i. i < m \<Longrightarrow> fst (the (xors i)) \<subseteq> S) \<Longrightarrow>
+     size_xor F S xors m =
+     amc.card_slice (\<lambda>\<omega>. xor_hash \<omega> xors) m" for m xors
+    unfolding size_xor_def amc.card_slice_def
+    by auto
+
+  have **: "
+   {0..<card S - 1} \<subseteq> dom xors \<Longrightarrow>
+   (\<And>i. i < card S - 1 \<Longrightarrow> fst (the (xors i)) \<subseteq> S) \<Longrightarrow>
+   find (check_xor F S thresh xors) [1..<card S] =
+   find (\<lambda>i. (\<lambda>\<omega>. xor_hash \<omega> xors) \<in> amc.T i) [1..<card S]" for xors
+    apply (intro find_cong)
+    unfolding check_xor_def amc.T_def
+    subgoal by simp
+    apply (subst *)
+      subgoal by clarsimp
+      subgoal by (clarsimp simp add: domIff subset_iff)
+    by auto
+
+  have rw: "
+    {0..<card S - 1} \<subseteq> dom xors \<Longrightarrow>
+    (\<And>i. i < card S - 1 \<Longrightarrow> fst (the (xors i)) \<subseteq> S) \<Longrightarrow>
+    approxcore_xors F S thresh xors =
+      (\<lambda>(a,b). a*b) (amc.approxcore (\<lambda>\<omega>. xor_hash \<omega> xors))" for  xors
+    apply (subst amc.approxcore_def)
+    unfolding approxcore_xors_def
+    apply (subst **)
+      subgoal by clarsimp
+      subgoal by clarsimp
+    apply (clarsimp split: option.split)
+    apply (subst *)
+    subgoal by (auto simp add: find_Some_iff domIff subset_iff)
+    subgoal by (auto simp add: find_Some_iff domIff subset_iff)
+    subgoal
+      using \<open>\<And>x2. \<lbrakk>{0..<card S - Suc 0} \<subseteq> dom xors; \<And>i. i < card S - Suc 0 \<Longrightarrow> fst (the (xors i)) \<subseteq> S; find (\<lambda>i. (\<lambda>\<omega>. xor_hash \<omega> xors) \<in> amc.T i) [Suc 0..<card S] = Some x2\<rbrakk> \<Longrightarrow> x2 < card S\<close> by auto 
+    by auto
+
+  from xor_hash_family_2_universal[OF S]
+  have univ:"prob_space.k_universal (measure_pmf (random_xors S (card S - 1))) 2
+   xor_hash {\<alpha>. dom \<alpha> = S} {\<alpha>. dom \<alpha> = {0..<card S - 1}}" .
+
+  have "measure_pmf.prob
+   (map_pmf (\<lambda>s w. xor_hash w s) (random_xors S (card S - 1)))
+   amc.approxcore_fail \<le> 0.36"
+    apply (intro amc.analysis_3[OF _ _ univ])
+    apply (smt (verit, ccfv_SIG) Groups.mult_ac(3) amc.pivot_def assms(1) compute_thresh_def more_arith_simps(11) real_nat_ceiling_ge)
+    using S finite_random_xors_set_pmf apply blast
+    using \<epsilon> by auto
+
+  then have b: "measure_pmf.prob
+    (random_xors S (card S - 1))
+    {xors.
+      (real ((\<lambda>(a,b). a*b) (amc.approxcore (\<lambda>\<omega>. xor_hash \<omega> xors))))
+      \<notin>
+      {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+        (1 + \<epsilon>) * real (card (proj S (sols F)))}} \<le> 0.36"
+    unfolding amc.approxcore_fail_def
+    by (auto simp add: case_prod_unfold Let_def)
+
+  have 1: "x \<in> set_pmf (random_xors S (card S - Suc 0)) \<Longrightarrow>
+    {0..<card S - 1} \<subseteq> dom x" for x
+    by (auto simp add:random_xors_set_pmf[OF S])
+  have 2: "x \<in> set_pmf (random_xors S (card S - Suc 0)) \<Longrightarrow>
+    (\<forall>i. i < card S - 1 \<longrightarrow> fst (the (x i)) \<subseteq> S)" for x
+  proof -
+    assume x: "x \<in> set_pmf (random_xors S (card S - Suc 0))"
+    moreover {
+      fix i
+      assume i: "i < card S - 1"
+      from random_xors_set_pmf[OF S]
+      have xx: "dom x = {..<(card S - Suc 0)}" "ran x \<subseteq> Pow S \<times> UNIV"
+        using x by auto
+      obtain xi where xi: "x i = Some xi"
+        using xx i apply clarsimp
+        by (metis atLeast0LessThan atLeastLessThan_iff bot_nat_0.extremum domIff option.exhaust surj_pair)
+      then have "fst xi \<subseteq> S" using xx(2)
+        unfolding ran_def apply (clarsimp simp add: subset_iff)
+        by (metis prod.collapse)
+      then have "fst (the (x i)) \<subseteq> S" by (simp add: xi)
+    }
+    thus "(\<forall>i. i < card S - 1 \<longrightarrow> fst (the (x i)) \<subseteq> S)" by auto
+  qed
+
+  have "measure_pmf.prob (random_xors S (card S - 1))
+       {xors. real (approxcore_xors F S thresh xors) \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+        (1 + \<epsilon>) * real (card (proj S (sols F)))}} =
+    measure_pmf.prob
+    (random_xors S (card S - 1))
+    {xors.
+      (real ((\<lambda>(a,b). a*b) (amc.approxcore (\<lambda>\<omega>. xor_hash \<omega> xors))))
+      \<in>
+      {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+        (1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+    apply (intro measure_pmf.measure_pmf_eq[where p = "(random_xors S (card S - 1))"])
+    subgoal by auto
+    apply clarsimp
+    apply (frule 1)
+    apply (drule 2)
+    apply (frule rw)
+    by auto
+
+  moreover have "... =
+     1 - measure_pmf.prob
+      (random_xors S (card S - 1))
+      {xors.
+        (real ((\<lambda>(a,b). a*b) (amc.approxcore (\<lambda>\<omega>. xor_hash \<omega> xors))))
+        \<notin>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+    apply (subst measure_pmf.prob_compl[symmetric])
+    by (auto intro!: measure_pmf.measure_pmf_eq)
+  moreover have "... \<ge> 0.64"
+    using b
+    by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma compute_t_ge1:
+  assumes "0 < \<delta>" "\<delta> < 1"
+  shows"compute_t \<delta> n \<ge> 1"
+proof -
+  have "ln (1 / \<delta>) > 0"
+    by (simp add: assms)
+  then have fix_t: "1 \<le> fix_t \<delta>"
+    unfolding fix_t_def
+    by (simp add: Suc_leI)
+
+  show ?thesis
+  unfolding compute_t_def
+  using fix_t
+  apply (cases n)
+  unfolding raw_median_bound_def
+  using assms by auto
+qed
+
+lemma success_arith_bound:
+  assumes "s \<le> (f ::nat)"
+  assumes "p \<le> (1::real)" "q \<le> p" "1 /2 \<le> q"
+  shows "p ^ s * (1 - p) ^ f \<le> q ^ s * (1 - q) ^ f"
+proof -
+  have ple: "p * (1-p) \<le> q * (1-q)"
+    using assms(2-4)
+    by (sos "(((A<0 * R<1) + ((R<1 * (R<1 * [p + ~1*q]^2)) + ((A<=1 * (A<=2 * R<1)) * (R<2 * [1]^2)))))")
+
+  have feq:"f = (f-s)+s"
+    using Nat.le_imp_diff_is_add assms(1) by blast
+  then have "(1-p)^f = (1-p)^s * (1-p)^(f-s)"
+    by (metis add.commute power_add)
+  then have "p ^ s * (1 - p) ^ f =
+    (p * (1-p)) ^ s * (1 - p) ^ (f-s)"
+    by (simp add: power_mult_distrib)
+  moreover have "... \<le>
+    (q * (1-q)) ^ s * (1 - p) ^ (f-s)"
+    by (smt (verit) assms(1) assms(2) assms(3) assms(4) diff_self_eq_0 divide_nonneg_nonneg mult_nonneg_nonneg mult_right_mono order_le_less ple power_0 power_eq_0_iff power_mono zero_less_diff zero_less_power)
+  moreover have "... \<le>
+    (q * (1-q)) ^ s * (1 - q) ^ (f-s)"
+    by (smt (verit, ccfv_SIG) assms(2) assms(3) assms(4) divide_eq_0_iff divide_nonneg_nonneg mult_left_mono mult_pos_pos power_mono zero_less_power)
+  moreover have "... = q ^ s * (1 - q) ^ f"
+    by (smt (verit) feq mult.assoc mult.commute power_add power_mult_distrib)
+  ultimately show ?thesis by auto
+qed
+
+lemma prob_binomial_pmf_upto_mono:
+  assumes "1/2 \<le> q" "q \<le> p" "p \<le> 1"
+  shows "
+  measure_pmf.prob (binomial_pmf n p) {..n div 2} \<le>
+  measure_pmf.prob (binomial_pmf n q) {..n div 2}"
+proof -
+  have i: "i \<le> n div 2 \<Longrightarrow>
+    p ^ i * (1 - p) ^ (n - i) \<le> q ^ i * (1 - q) ^ (n - i)" for i
+    using assms by(auto intro!: success_arith_bound)
+
+  show ?thesis
+    apply (subst prob_binomial_pmf_upto)
+    subgoal using assms by auto
+    subgoal using assms by auto
+    apply (subst prob_binomial_pmf_upto)
+    subgoal using assms by auto
+    subgoal using assms by auto
+    by (auto intro!: sum_mono simp add: i ab_semigroup_mult_class.mult_ac(1) mult_left_mono)
+qed
+
+(* The main result *)
+theorem approxmc_sound:
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0" "\<epsilon> \<le> 1"
+  assumes S: "finite S"
+  shows "measure_pmf.prob (approxmc F S \<epsilon> \<delta> n)
+      {c. real c \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj S (sols F)))}}
+      \<ge> 1 - \<delta>"
+proof -
+  define thresh where "thresh = compute_thresh \<epsilon>"
+  define t where "t = compute_t \<delta> n"
+  then have t1: "1 \<le> t"
+    using compute_t_ge1[OF \<delta>] by auto
+
+  have "card (proj S (sols F)) < thresh \<or>
+      card (proj S (sols F)) \<ge> thresh" by auto
+  moreover {
+    assume "card (proj S (sols F)) < thresh"
+    then have "approxmc F S \<epsilon> \<delta> n =
+      return_pmf (card (proj S (sols F)))"
+      unfolding approxmc_def Let_def thresh_def
+      by auto
+    then have "?thesis"
+      unfolding indicator_def of_bool_def
+      using assms \<epsilon>
+      by (auto simp add: mult_le_cancel_left1 mult_le_cancel_right1 divide_le_eq)
+  }
+  moreover {
+    assume a: "card (proj S (sols F)) \<ge> thresh"
+    define Xf where "Xf = (\<lambda>(i::nat) xs.
+      approxcore_xors F S thresh (xs i))"
+
+    then have *: "approxmc F S \<epsilon> \<delta> n =
+      map_pmf (median t)
+      (prod_pmf {0..<t} (\<lambda>i. approxmccore F S thresh))"
+      using a
+      unfolding approxmc_def Let_def thresh_def t_def
+      by auto
+
+    have **: "map_pmf (real \<circ> median t)
+      (Pi_pmf {0..<t} (approxcore_xors F S thresh undefined)
+       (\<lambda>i. approxmccore F S thresh)) =
+       map_pmf (\<lambda>\<omega>. median t (\<lambda>i. real (Xf i \<omega>)))
+      (prod_pmf {0..<t} (\<lambda>i. random_xors S (card S - 1)))"
+      apply (subst median_commute)
+      subgoal using t1 by simp
+      unfolding approxmccore_def
+       apply (subst Pi_pmf_map)
+      unfolding Xf_def by (auto simp add: pmf.map_comp o_def)
+
+    define \<alpha> where "\<alpha> = (0.14 ::real)"
+    then have \<alpha>: "\<alpha> > 0" by auto
+
+    have indep:"prob_space.indep_vars
+     (measure_pmf
+       (prod_pmf {0..<t} (\<lambda>i. random_xors S (card S - 1))))
+      (\<lambda>_. borel) (\<lambda>x xa. real (Xf x xa)) {0..<t}"
+      unfolding Xf_def
+      apply (intro indep_vars_restrict_intro')
+      by (auto simp add: restrict_dfl_def)
+
+    have d: "\<delta> \<in> {0<..<1}" using \<delta> by auto
+
+    from approxcore_xors_eq[OF thresh_def a \<epsilon> S]
+    have b1: "1 / 2 + \<alpha> \<le>
+     measure_pmf.prob (random_xors S (card S - 1))
+      {xors.
+       real (approxcore_xors F S thresh xors)
+       \<in> {real (card (proj S (sols F))) /
+           (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+      unfolding \<alpha>_def by auto
+    then have b2: "i < t \<Longrightarrow>
+      1 / 2 + \<alpha> \<le>
+      measure_pmf.prob
+         (prod_pmf {0..<t}
+           (\<lambda>i. random_xors S (card S - 1)))
+         {\<omega> \<in> space
+                (measure_pmf
+                  (prod_pmf {0..<t}
+                    (\<lambda>i. random_xors S (card S - 1)))).
+          real (Xf i \<omega>)
+          \<in> {real (card (proj S (sols F))) /(1 + \<epsilon>)..
+              (1 + \<epsilon>) *real (card (proj S (sols F)))}}" for i
+    unfolding Xf_def apply clarsimp
+    apply (subst prob_prod_pmf_slice)
+    by auto
+
+    have ***: "1 - \<delta>
+      \<le> measure_pmf.prob (prod_pmf {0..<t} (\<lambda>i. random_xors S (card S - 1)))
+      {\<omega>.
+       median t (\<lambda>i. real (Xf i \<omega>))
+       \<in> {real (card (proj S (sols F))) /
+           (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+    proof -
+      have "t = fix_t \<delta> \<or> t = n \<and> raw_median_bound \<alpha> n < \<delta>"
+      unfolding t_def compute_t_def \<alpha>_def by auto
+      moreover {
+        assume "t = fix_t \<delta>"
+        then have tb:"- ln \<delta> / (2 * \<alpha>\<^sup>2) \<le> real t"
+        unfolding fix_t_def \<alpha>_def
+        apply clarsimp
+        by (metis assms(1) divide_minus_left inverse_eq_divide ln_inverse real_nat_ceiling_ge)
+
+        from measure_pmf.median_bound_1[OF \<alpha> d indep tb]
+        have ?thesis using b2 by auto
+      }
+      moreover {
+        assume *: "t = n" "raw_median_bound \<alpha> n < \<delta>"
+        have s: "1 / 2 - \<alpha> = 1 - (1 /2 + \<alpha>)"
+          by auto
+
+        have d1: "0 < t" using t1 by linarith
+        have d2: "1 / 2 + \<alpha> \<ge> 0" using \<alpha> by auto
+        have d3: "interval{x..y::real}" for x y
+          unfolding interval_def by auto
+
+        from prob_space.median_bound_raw[OF _ d1 d2 d3 indep b2]
+        have "1 -
+          measure_pmf.prob (binomial_pmf t (1 / 2 + \<alpha>)) {..t div 2}
+          \<le> measure_pmf.prob
+              (prod_pmf {0..<t}
+                (\<lambda>i. random_xors S (card S - 1)))
+              {\<omega>.
+               median t (\<lambda>i. real (Xf i \<omega>))
+               \<in> {real (card (proj S (sols F))) /
+                   (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+          by (auto simp add: prob_space_measure_pmf)
+
+        moreover have "measure_pmf.prob (binomial_pmf t (1 / 2 + \<alpha>)) {..t div 2} \<le> \<delta>"
+          by (smt (verit, ccfv_SIG) * b1 d2 measure_pmf.prob_le_1 prob_binomial_pmf_upto raw_median_bound_def s sum.cong)
+
+        ultimately have ?thesis by auto
+      }
+      ultimately show ?thesis by auto
+    qed
+
+    have "measure_pmf.prob (approxmc F S \<epsilon> \<delta> n)
+        {c. real c
+            \<in> {real (card (proj S (sols F))) /
+                (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}} =
+      measure_pmf.prob (map_pmf (real \<circ> median t)
+        (prod_pmf {0..<t}
+         (\<lambda>i. approxmccore F S thresh)))
+          {c. c \<in> {real (card (proj S (sols F))) /
+                  (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+      using * by auto
+    moreover have "... =
+      measure_pmf.prob (map_pmf (real \<circ> median t)
+      (map_pmf (\<lambda>f x. if x \<in> {0..<t} then f x else undefined) (Pi_pmf {0..<t} (approxcore_xors F S thresh undefined)
+       (\<lambda>i. approxmccore F S thresh))))
+      {c. c \<in> {real (card (proj S (sols F))) /
+                (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+      apply (subst Pi_pmf_default_swap)
+      by auto
+    moreover have "... =
+      measure_pmf.prob (map_pmf (real \<circ> median t)
+      (Pi_pmf {0..<t} (approxcore_xors F S thresh undefined)
+       (\<lambda>i. approxmccore F S thresh)))
+      {c. c \<in> {real (card (proj S (sols F))) /
+                (1 + \<epsilon>)..(1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+      by (clarsimp simp add: median_default[symmetric])
+    moreover have "... \<ge> 1 - \<delta>"
+      unfolding **
+      using ***
+      by auto
+    ultimately have ?thesis by auto
+  }
+  ultimately show ?thesis by auto
+qed
+
+text \<open> To simplify further analyses, we can remove the (required) upper bound on epsilon. \<close>
+
+definition mk_eps :: "real \<Rightarrow> real"
+  where "mk_eps \<epsilon> = (if \<epsilon> > 1 then 1 else \<epsilon>)"
+
+definition approxmc'::"
+  'fml \<Rightarrow> 'a set \<Rightarrow>
+  real \<Rightarrow> real \<Rightarrow> nat \<Rightarrow> nat pmf"
+  where "approxmc' F S \<epsilon> \<delta> n =
+    approxmc F S (mk_eps \<epsilon>) \<delta> n"
+
+corollary approxmc'_sound:
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes S: "finite S"
+  shows "prob_space.prob (approxmc' F S \<epsilon> \<delta> n)
+      {c. real c \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj S (sols F)))}}
+      \<ge> 1 - \<delta>"
+proof -
+  define \<epsilon>' where "\<epsilon>' = (if \<epsilon> > 1 then 1 else \<epsilon>)"
+  have \<epsilon>': "0 < \<epsilon>'" "\<epsilon>' \<le> 1"
+    unfolding \<epsilon>'_def using \<epsilon> by auto
+
+  from approxmc_sound[OF \<delta> \<epsilon>' S]
+  have *: "prob_space.prob (approxmc F S \<epsilon>' \<delta> n)
+      {c. real c \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>')..
+          (1 + \<epsilon>') * real (card (proj S (sols F)))}}
+      \<ge> 1 - \<delta>" .
+
+  have **: "
+    {c. real c \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>')..
+          (1 + \<epsilon>') * real (card (proj S (sols F)))}}
+    \<subseteq>
+    {c. real c \<in>
+        {real (card (proj S (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj S (sols F)))}}"
+    unfolding \<epsilon>'_def
+    apply clarsimp
+    apply (rule conjI)
+    apply (smt (verit) field_sum_of_halves frac_less2 zero_less_divide_iff)
+    by (metis (no_types, opaque_lifting) add_le_cancel_left arith_special(3) dual_order.trans less_eq_real_def mult_right_mono of_nat_0_le_iff)
+
+  show ?thesis
+    apply (intro order.trans[OF *])
+    unfolding approxmc'_def \<epsilon>'_def mk_eps_def
+    apply (intro measure_pmf.finite_measure_mono)
+    using **[unfolded  \<epsilon>'_def]
+    by auto
+qed
+
+text \<open> This shows we can lift all randomness to the top-level (i.e., eagerly sample it). \<close>
+
+definition approxmc_map::"
+  'fml \<Rightarrow> 'a set \<Rightarrow>
+  real \<Rightarrow> real \<Rightarrow> nat \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> ('a set \<times> bool) option) \<Rightarrow>
+  nat"
+  where "approxmc_map F S \<epsilon> \<delta> n xorsFs = (
+    let \<epsilon> = mk_eps \<epsilon> in
+    let thresh = compute_thresh \<epsilon> in
+    if card (proj S (sols F)) < thresh then
+      card (proj S (sols F))
+    else
+      let t = compute_t \<delta> n in
+      median t (approxcore_xors F S thresh \<circ> xorsFs))"
+
+lemma approxmc_map_eq:
+  shows "
+    map_pmf (approxmc_map F S \<epsilon> \<delta> n)
+      (Pi_pmf {0..<compute_t \<delta> n} def
+         (\<lambda>i. random_xors S (card S - 1))) =
+    approxmc' F S \<epsilon> \<delta> n"
+proof -
+  define def' where "def' = approxcore_xors F S (compute_thresh (mk_eps \<epsilon>)) def"
+
+  have *: "
+     map_pmf (median (compute_t \<delta> n))
+     (prod_pmf {0..<compute_t \<delta> n}
+       (\<lambda>i. map_pmf
+              (approxcore_xors F S
+                (compute_thresh (mk_eps \<epsilon>)))
+              (random_xors S (card S - Suc 0)))) =
+     map_pmf (median (compute_t \<delta> n))
+     (Pi_pmf {0..<compute_t \<delta> n} def'
+       (\<lambda>i. map_pmf
+              (approxcore_xors F S
+                (compute_thresh (mk_eps \<epsilon>)))
+              (random_xors S (card S - Suc 0))))"
+    apply (subst Pi_pmf_default_swap[symmetric, where dflt ="undefined", where dflt'="def'"])
+    by (auto simp add: map_pmf_comp median_default[symmetric])
+
+  show ?thesis
+  unfolding approxmc'_def approxmc_map_def approxmc_def Let_def approxmccore_def
+  using def'_def
+  by (auto simp add: map_pmf_comp  Pi_pmf_map[of _ _ def] *)
+qed
+
+end
+
+end
diff --git a/thys/Approximate_Model_Counting/ApproxMCCore.thy b/thys/Approximate_Model_Counting/ApproxMCCore.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/ApproxMCCore.thy
@@ -0,0 +1,570 @@
+section \<open> ApproxMCCore definitions \<close>
+
+text \<open>
+  This section defines the ApproxMCCore locale and various failure events to be used in its probabilistic analysis.
+  The definitions closely follow Section 4.2 of Chakraborty et al.~\cite{DBLP:conf/ijcai/ChakrabortyMV16}.
+  Some non-probabilistic properties of the events are proved, most notably, the event inclusions of Lemma 3~\cite{DBLP:conf/ijcai/ChakrabortyMV16}.
+  Note that ``events'' here refer to subsets of hash functions.
+\<close>
+
+theory ApproxMCCore imports
+  ApproxMCPreliminaries
+begin
+
+(* An 'a assg is a finite map from 'a to bool
+  It is useful to think of 'a as the type of (projected) variables *)
+type_synonym 'a assg = "'a \<rightharpoonup> bool"
+
+(* Restrict function to a domain (analogous to restrict_map) *)
+definition restr :: "'a set \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a assg"
+  where "restr S w = (\<lambda>x. if x \<in> S then Some (w x) else None)"
+
+lemma restrict_eq_mono:
+  assumes "x \<subseteq> y"
+  assumes "f |` y = g |` y"
+  shows "f |` x = g |` x"
+  using assms
+  by (metis Map.restrict_restrict inf.absorb_iff2)
+
+(* Projection of a solution set W onto variables S *)
+definition proj :: "'a set \<Rightarrow> ('a \<Rightarrow> bool) set \<Rightarrow> 'a assg set"
+  where "proj S W = restr S ` W"
+
+lemma card_proj:
+  assumes "finite S"
+  shows "finite (proj S W)" "card (proj S W) \<le> 2 ^ card S"
+proof -
+  have *: "proj S W \<subseteq> {w. dom w = S}"
+    unfolding proj_def restr_def
+    by (auto split: if_splits)
+  also have 1: "{w. dom w = S} = {w. dom w = S \<and> ran w \<subseteq> {True,False}}"
+    by auto
+  have f: "finite  {w. dom w = S \<and> ran w \<subseteq> {True,False}}"
+    by (simp add: assms finite_set_of_finite_maps)
+  thus "finite (proj S W)"
+    using * 1
+    by (metis finite_subset)
+
+  have 2:"card {w. dom w = S \<and> ran w \<subseteq> {True,False}} = (card {True,False}) ^ card S"
+    apply (intro card_dom_ran)
+    using assms by auto
+
+  show "card (proj S W) \<le> 2 ^ card S"
+    using * 1 2
+    by (metis (no_types, lifting) f card.empty card_insert_disjoint card_mono finite.emptyI finite.insertI insert_absorb insert_not_empty numeral_2_eq_2 singleton_insert_inj_eq)
+qed
+
+lemma proj_mono:
+  assumes "x \<subseteq> y"
+  shows "proj w x \<subseteq> proj w y"
+  unfolding proj_def
+  using assms by blast
+
+(* We can view nat assg as bit vectors, and take the i-th prefix slices *)
+definition aslice :: "nat \<Rightarrow> nat assg \<Rightarrow> nat assg"
+  where "aslice i a = a |` {..<i}"
+
+lemma aslice_eq:
+  assumes "i \<ge> n"
+  assumes "dom a = {..<n}"
+  shows "aslice i a = aslice n a"
+  using assms
+  unfolding aslice_def restrict_map_def dom_def
+  by fastforce
+
+(*  Prefix slice after hashing *)
+definition hslice :: "nat \<Rightarrow>
+  ('a assg \<Rightarrow> nat assg) \<Rightarrow> ('a assg \<Rightarrow> nat assg)"
+  where "hslice i h = aslice i \<circ> h"
+
+(* Convenient grouping of assumptions and parameters *)
+locale ApproxMCCore =
+  fixes W :: "('a \<Rightarrow> bool) set"
+  fixes S :: "'a set"
+  fixes \<epsilon> :: "real"
+  fixes \<alpha> :: "nat assg"
+  fixes thresh :: "nat"
+  assumes \<alpha>: "dom \<alpha> = {0..<card S - 1}"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes thresh:
+    "thresh > 4"
+    "card (proj S W) \<ge> thresh"
+  assumes S: "finite S"
+begin
+
+lemma finite_proj_S:
+  shows "finite (proj S W)"
+  using S by (auto intro!: card_proj)
+
+definition \<mu> :: "nat \<Rightarrow> real"
+  where "\<mu> i = card (proj S W) / 2 ^ i"
+
+(* A frequently used expression for the number of projected
+   witnesses w whose i-th slices match the target *)
+definition card_slice ::"
+  ('a assg \<Rightarrow> nat assg) \<Rightarrow>
+  nat \<Rightarrow> nat"
+  where "card_slice h i =
+    card (proj S W \<inter> {w. hslice i h w = aslice i \<alpha>})"
+
+lemma card_slice_anti_mono:
+  assumes "i \<le> j"
+  shows "card_slice h j \<le> card_slice h i"
+proof -
+  have *: "{..<i} \<subseteq> {..<j}" using assms by auto
+  have "{w. hslice j h w = aslice j \<alpha>}
+    \<subseteq> {w. hslice i h w = aslice i \<alpha>}"
+    by (auto intro: restrict_eq_mono[OF *] simp add: hslice_def aslice_def)
+  thus ?thesis
+    unfolding card_slice_def
+    apply (intro card_mono)
+    subgoal using finite_proj_S by blast
+    by (auto intro!: proj_mono)
+qed
+
+lemma hslice_eq:
+  assumes "n \<le> i"
+  assumes "\<And>w. dom (h w) = {..<n}"
+  shows "hslice i h = hslice n h"
+  using assms aslice_eq
+  unfolding hslice_def by auto
+
+lemma card_slice_lim:
+  assumes "card S - 1 \<le> i"
+  assumes "\<And>w. dom (h w) = {..<(card S - 1)}"
+  shows "card_slice h i = card_slice h (card S - 1)"
+  unfolding card_slice_def
+  apply(subst aslice_eq[OF assms(1)])
+  subgoal using \<alpha> by auto
+  apply(subst hslice_eq[OF assms(1)])
+  using assms by auto
+
+(* Defining the various events with respect to a fixed h *)
+definition T :: "nat \<Rightarrow>
+  ('a assg \<Rightarrow> nat assg) set"
+  where "T i = {h. card_slice h i < thresh}"
+
+lemma T_mono:
+  assumes "i \<le> j"
+  shows "T i \<subseteq> T j"
+  unfolding T_def
+  using card_slice_anti_mono[OF assms]
+    dual_order.strict_trans2
+    of_nat_mono
+  by blast
+
+lemma \<mu>_anti_mono:
+  assumes "i \<le> j"
+  shows "\<mu> i \<ge> \<mu> j"
+proof -
+  have "2^ i \<le> (2::real) ^ j"
+    by (simp add: assms)
+  then show ?thesis unfolding \<mu>_def
+    by (simp add: frac_le)
+qed
+
+lemma card_proj_witnesses:
+  "card (proj S W) > 0"
+  using thresh by linarith
+
+lemma \<mu>_strict_anti_mono:
+  assumes "i < j"
+  shows "\<mu> i > \<mu> j"
+proof -
+  have "2^ i < (2::real) ^ j"
+    by (simp add: assms)
+  then show ?thesis unfolding \<mu>_def
+    using card_proj_witnesses
+    by (simp add: frac_less2)
+qed
+
+lemma \<mu>_gt_zero:
+  shows "\<mu> i > 0"
+  unfolding \<mu>_def
+  using card_proj_witnesses
+  by auto
+
+definition L :: "nat \<Rightarrow>
+  ('a assg \<Rightarrow> nat assg) set"
+  where "
+    L i =
+    {h. real (card_slice h i) < \<mu> i / (1 + \<epsilon>)}"
+
+definition U :: "nat \<Rightarrow>
+  ('a assg \<Rightarrow> nat assg) set"
+  where "
+    U i =
+    {h. real (card_slice h i) \<ge> \<mu> i * (1 + \<epsilon> / (1 + \<epsilon>))}"
+
+(* Model of ApproxMC core without random choice of h *)
+definition approxcore :: "
+  ('a assg \<Rightarrow> nat assg) \<Rightarrow>
+  nat \<times> nat"
+  where "
+    approxcore h =
+    (case List.find
+      (\<lambda>i. h \<in> T i) [1..<card S] of
+      None \<Rightarrow> (2 ^ card S, 1)
+    | Some m \<Rightarrow>
+      (2 ^ m, card_slice h m))"
+
+(* The failure event as a set over hashes *)
+definition approxcore_fail :: "
+  ('a assg \<Rightarrow> nat assg) set"
+  where "approxcore_fail  =
+    {h.
+      let (cells,sols) = approxcore h in
+      cells * sols \<notin>
+      { card (proj S W) / (1 + \<epsilon>) ..
+        (1 + \<epsilon>::real) * card (proj S W)}
+    }"
+
+(* This is a global assumption of the locale *)
+lemma T0_empty:
+  shows "T 0 = {}"
+  unfolding T_def card_slice_def
+    hslice_def aslice_def
+  using thresh(2) by auto
+
+lemma L0_empty:
+  shows "L 0 = {}"
+proof -
+  have "0 < \<epsilon> \<Longrightarrow>
+    real (card (proj S W))
+    < real (card (proj S W)) / (1 + \<epsilon>) \<Longrightarrow>
+    False"
+    by (smt (z3) card_proj_witnesses divide_minus1 frac_less2 nonzero_minus_divide_right of_nat_0_less_iff)
+  thus ?thesis
+  unfolding L_def card_slice_def
+  hslice_def aslice_def \<mu>_def
+  using \<epsilon> by clarsimp
+qed
+
+lemma U0_empty:
+  shows "U 0 = {}"
+proof -
+  have *: "(1 + \<epsilon> / (1 + \<epsilon>)) > 1"
+    using \<epsilon> by auto
+  have **: "U 0 = {}"
+    unfolding U_def card_slice_def
+      hslice_def aslice_def \<mu>_def
+    using *
+    by (simp add: card_proj_witnesses)
+  thus ?thesis using ** by auto
+qed
+
+lemma real_divide_pos_left:
+  assumes "(0::real) < a"
+  assumes "a * b < c"
+  shows "b < c / a"
+  using assms
+  by (simp add: mult.commute mult_imp_less_div_pos)
+
+lemma real_divide_pos_right:
+  assumes "a > (0::real)"
+  assumes "b < a * c"
+  shows "b / a < c"
+  using assms
+  by (simp add: mult.commute mult_imp_div_pos_less)
+
+(* The first inclusion used in the upper bound of Lemma 3 *)
+lemma failure_imp:
+  shows "approxcore_fail \<subseteq>
+    (\<Union>i\<in>{1..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<union>
+    -T (card S - 1)"
+proof standard
+  fix h
+  assume "h \<in> approxcore_fail"
+  then obtain cells sols where
+    h: "approxcore h = (cells, sols)"
+    "cells * sols \<notin>
+      { card (proj S W) / (1 + \<epsilon>) ..
+        (1 + \<epsilon>::real) * card (proj S W)}" (is "_ \<notin> {?lower..?upper}")
+    unfolding approxcore_fail_def
+    by auto
+
+  have "List.find (\<lambda>i. h \<in> T i) [1..<card S] = None \<or>
+    List.find (\<lambda>i. h \<in> T i) [1..<card S] \<noteq> None" by auto
+  moreover {
+    assume "List.find (\<lambda>i. h \<in> T i) [1..<card S] = None"
+    then have "h \<notin> T (card S - 1)"
+      unfolding find_None_iff
+      by (metis T0_empty atLeastLessThan_iff diff_is_0_eq' diff_less empty_iff gr_zeroI leI less_one not_less_zero set_upt)
+  }
+  moreover {
+    assume "List.find (\<lambda>i. h \<in> T i) [1..<card S] \<noteq> None"
+    then obtain m where
+      findm: "List.find (\<lambda>i. h \<in> T i) [1..<card S] = Some m" by auto
+    then have
+      m: "1 \<le> m" "m < card S"
+      "h \<in> T m"
+      "\<forall>i. 1 \<le> i \<and> i < m \<longrightarrow> h \<notin> T i"
+      unfolding find_Some_iff
+      using less_Suc_eq_0_disj by auto
+
+    then have 1: "h \<notin> T (m - 1)"
+      by (metis T0_empty bot_nat_0.not_eq_extremum diff_is_0_eq diff_less empty_iff less_one)
+
+    have "2 ^ m * card_slice h m < ?lower \<or>
+       2 ^ m * card_slice h m > ?upper"
+      using h unfolding approxcore_def findm by auto
+    moreover {
+      assume "2 ^ m * card_slice h m < ?lower"
+      then have "card_slice h m < ?lower / 2 ^ m"
+        using real_divide_pos_left
+        by (metis numeral_power_eq_of_nat_cancel_iff of_nat_mult zero_less_numeral zero_less_power)
+
+      then have "h \<in> L m" unfolding L_def
+        by (simp add: \<mu>_def mult.commute)
+    }
+    moreover {
+      assume *: "?upper < 2 ^ m * card_slice h m"
+      have "1 / (1 + \<epsilon>) <  1"
+        using \<epsilon> divide_less_eq_1 by fastforce
+      then have "\<epsilon> / (1 + \<epsilon>) <  \<epsilon>"
+        using \<epsilon>
+        by (metis (no_types, opaque_lifting) add_cancel_left_right div_by_1 divide_divide_eq_left divide_less_eq_1_pos mult.commute nonzero_divide_mult_cancel_left)
+      then have "card (proj S W) * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> ?upper"
+        using linorder_not_less not_less_iff_gr_or_eq by fastforce
+      then have "(card (proj S W) * (1 + \<epsilon> / (1 + \<epsilon>))) / 2 ^ m < card_slice h m"
+        apply (intro real_divide_pos_right)
+        using * by auto
+      then have "h \<in> U m" unfolding U_def
+        by (simp add: \<mu>_def)
+    }
+    ultimately have "h \<in> L m \<or> h \<in> U m" by blast
+    then have "\<forall>m\<in>{Suc 0..<card S}.
+            h \<in> T m \<longrightarrow>
+            h \<in> T (m - Suc 0) \<or>
+            h \<notin> L m \<and> h \<notin> U m \<Longrightarrow>
+         h \<in> T (card S - Suc 0) \<Longrightarrow> False"
+      using m 1 by auto
+  }
+  ultimately show
+      "h \<in> (\<Union>i\<in>{1..<card S}.
+                  (T i - T (i - 1)) \<inter> (L i \<union> U i)) \<union>
+              - T (card S - 1)"
+    by auto
+qed
+
+(* technically not smallest, but doesn't matter for our use *)
+lemma smallest_nat_exists:
+  assumes "P i" "\<not>P (0::nat)"
+  obtains m where "m \<le> i" "P m" "\<not>P (m-1)"
+  using assms
+proof (induction i)
+  case 0
+  then show ?case by auto
+next
+  case (Suc i)
+  then show ?case
+    by (metis diff_Suc_1 le_Suc_eq)
+qed
+
+lemma mstar_non_zero:
+  shows "\<not> \<mu> 0 * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> thresh"
+proof -
+  have "\<mu> 0 \<ge> thresh"
+    unfolding \<mu>_def
+    by (auto simp add: thresh(2))
+  thus ?thesis
+    by (smt (verit, best) \<epsilon> \<mu>_gt_zero divide_pos_pos mult_le_cancel_left2)
+qed
+
+lemma real_div_less:
+  assumes "c > 0"
+  assumes "a \<le> b * (c::nat)"
+  shows "real a / real c \<le> b"
+  by (metis assms(1) assms(2) divide_le_eq of_nat_0_less_iff of_nat_mono of_nat_mult)
+
+(* Instead of giving mstar explicitly, we'll select it implicitly by the properties below *)
+lemma mstar_exists:
+  obtains m where
+    "\<mu> (m - 1) * (1 + \<epsilon> / (1 + \<epsilon>)) > thresh"
+    "\<mu> m * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> thresh"
+    "m \<le> card S - 1"
+proof -
+  have e1:"1 + \<epsilon> / (1 + \<epsilon>) > 1"
+    by (simp add: \<epsilon> add_nonneg_pos)
+  have e2:"1 + \<epsilon> / (1 + \<epsilon>) < 2"
+    by (simp add: \<epsilon> add_nonneg_pos)
+  have "thresh  \<ge> (4::real)"
+    using thresh(1) by linarith
+  then have up:"thresh / (1 + \<epsilon> / (1 + \<epsilon>)) > 2"
+    by (smt (verit) e1 e2 field_sum_of_halves frac_less2)
+
+  have "card (proj S W) \<le> 2 * 2 ^ (card S - Suc 0)"
+    by (metis One_nat_def S Suc_diff_Suc card.empty card_gt_0_iff card_proj(2) diff_zero less_one order_less_le_trans plus_1_eq_Suc power_0 power_Suc0_right power_add thresh(1) thresh(2) zero_neq_numeral)
+
+  then have low:"\<mu> (card S - 1) \<le> 2"
+    unfolding \<mu>_def
+    using real_div_less
+    by (smt (verit) Num.of_nat_simps(2) Num.of_nat_simps(4) Suc_1 nat_zero_less_power_iff numeral_nat(7) of_nat_power plus_1_eq_Suc pos2)
+
+  have pi: "\<mu> (card S - 1) * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> thresh"
+    using up low
+    by (smt (verit, ccfv_SIG) divide_le_eq e1)
+
+  from smallest_nat_exists[OF pi mstar_non_zero]
+  show ?thesis
+    by (metis linorder_not_less that)
+qed
+
+definition mstar :: "nat"
+  where "mstar = (@m.
+    \<mu> (m - 1) * (1 + \<epsilon> / (1 + \<epsilon>)) > thresh \<and>
+    \<mu> m * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> thresh \<and>
+    m \<le> card S - 1)"
+
+(* The main inequalities we need from mstar *)
+lemma mstar_prop:
+  shows
+    "\<mu> (mstar - 1) * (1 + \<epsilon> / (1 + \<epsilon>)) > thresh"
+    "\<mu> mstar * (1 + \<epsilon> / (1 + \<epsilon>)) \<le> thresh"
+    "mstar \<le> card S - 1"
+  unfolding mstar_def
+  by (smt (verit) some_eq_ex mstar_exists)+
+
+lemma O1_lem:
+  assumes "i \<le> m"
+  shows "(T i - T (i-1)) \<inter> (L i \<union> U i) \<subseteq> T m"
+  using T_mono assms by blast
+
+lemma O1:
+  shows "(\<Union>i\<in>{1..mstar-3}.
+    (T i - T (i-1)) \<inter> (L i \<union> U i)) \<subseteq> T (mstar-3)"
+  using T_mono by force
+
+lemma T_anti_mono_neg:
+  assumes "i \<le> j"
+  shows "- T j \<subseteq> - T i"
+  by (simp add: Diff_mono T_mono assms)
+
+lemma O2_lem:
+  assumes "mstar < i"
+  shows "(T i - T (i-1)) \<inter> (L i \<union> U i) \<subseteq> -T mstar"
+proof -
+  have "(T i - T (i-1)) \<inter> (L i \<union> U i) \<subseteq> -T (i-1)"
+    by blast
+  thus ?thesis
+    by (smt (verit) T_mono ApproxMCCore_axioms One_nat_def Suc_diff_Suc Suc_le_eq assms compl_mono diff_is_0_eq' diff_less_mono leI minus_nat.diff_0 subset_trans)
+qed
+
+lemma O2:
+  shows "(\<Union>i\<in>{mstar..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<union>
+    -T (card S - 1) \<subseteq> L mstar \<union> U mstar"
+proof -
+  have 0: "(\<Union>i\<in>{mstar..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<subseteq>
+    (T mstar - T (mstar-1)) \<inter> (L mstar \<union> U mstar) \<union>
+    (\<Union>i\<in>{mstar+1..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i))"
+    apply (intro subsetI)
+    apply clarsimp
+    by (metis Suc_le_eq atLeastLessThan_iff basic_trans_rules(18))
+
+  have 1: "(\<Union>i\<in>{mstar+1..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<subseteq> -T mstar"
+    apply clarsimp
+    by (metis (no_types, lifting) ApproxMCCore.T_mono ApproxMCCore_axioms One_nat_def diff_Suc_1 diff_le_mono subsetD)
+
+  have 2: "-T (card S - 1) \<subseteq> - T mstar"
+    using T_anti_mono_neg mstar_prop(3) by presburger
+
+  (* Note that the strict inequality is needed here *)
+  have "thresh \<ge> \<mu> mstar * (1 + \<epsilon> / (1 + \<epsilon>))"
+    using mstar_prop(2) thresh by linarith
+
+  then have *: "- T mstar \<subseteq> U mstar"
+    unfolding T_def U_def
+    by auto
+
+  have "(\<Union>i\<in>{mstar..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<union>
+    -T (card S - 1) \<subseteq>
+    ((T mstar - T (mstar-1)) \<inter> (L mstar \<union> U mstar)) \<union> -T mstar"
+    using 0 1 2 by (smt (z3) Un_iff subset_iff)
+
+  moreover have "... \<subseteq> L mstar \<union> U mstar"
+    using *
+    by blast
+  ultimately show ?thesis by auto
+qed
+
+lemma O3:
+  assumes "i \<le> mstar - 1"
+  shows "(T i - T (i-1)) \<inter> (L i \<union> U i) \<subseteq> L i"
+proof -
+  have *: "\<mu> i * (1 + \<epsilon> / (1 + \<epsilon>)) > thresh"
+    by (smt (verit, ccfv_SIG) \<epsilon> \<mu>_anti_mono assms divide_nonneg_nonneg mstar_prop(1) mult_right_mono)
+
+  have "x \<in> T i \<and> x \<in> U i \<Longrightarrow> False" for x
+      unfolding T_def U_def
+      using * by auto
+  thus ?thesis
+    by blast
+qed
+
+lemma union_split_lem:
+  assumes x: "x \<in> (\<Union>i\<in>{1..<n::nat}. P i)"
+  shows "x \<in> (\<Union>i\<in>{1..m-3}. P i) \<union>
+    P (m-2) \<union>
+    P (m-1) \<union>
+    (\<Union>i\<in>{m..<n}. P i)"
+proof -
+  obtain i where i: "i \<in> {1..<n}"
+    "x \<in> P i" using x by auto
+  have "i \<in> {1..m-3} \<or> i = m-2 \<or> i = m-1 \<or> i \<in> {m..<n}"
+    using i(1)
+    by auto
+  thus ?thesis using i
+    by blast
+qed
+
+lemma union_split:
+  "(\<Union>i\<in>{1..<n::nat}. P i) \<subseteq>
+   (\<Union>i\<in>{1..m-3}. P i) \<union>
+    P (m-2) \<union>
+    P (m-1) \<union>
+    (\<Union>i\<in>{m..<n}. P i)"
+  using union_split_lem
+  by (metis subsetI)
+
+lemma failure_bound:
+  shows "approxcore_fail \<subseteq>
+  T (mstar-3) \<union>
+  L (mstar-2) \<union>
+  L (mstar-1) \<union>
+  (L mstar \<union> U mstar)"
+proof -
+
+  have *: "approxcore_fail \<subseteq>
+    (\<Union>i\<in>{1..<card S}.
+      (T i - T (i-1)) \<inter> (L i \<union> U i)) \<union> -T (card S - 1)" (is "_ \<subseteq> (\<Union>i\<in>{1..<card S}. ?P i) \<union> _")
+    using failure_imp .
+
+  moreover have "... \<subseteq>
+    (\<Union>i\<in>{1..mstar - 3}. ?P i) \<union>
+    ?P (mstar - 2) \<union>
+    ?P (mstar - 1) \<union>
+    ((\<Union>i\<in>{mstar..<card S}. ?P i) \<union> -T (card S - 1))"
+    using
+    union_split[of "\<lambda>i. ?P i" "card S" "mstar"]
+    by blast
+  moreover have "... \<subseteq>
+    T (mstar - 3) \<union>
+    L (mstar - 2) \<union>
+    L (mstar - 1) \<union>
+    (L mstar \<union> U mstar)
+  "
+    using O1 O2 O3
+    by (metis (no_types, lifting) One_nat_def Un_mono diff_Suc_eq_diff_pred diff_le_self nat_1_add_1 plus_1_eq_Suc)
+  ultimately show ?thesis
+    by (meson order_trans)
+qed
+
+end
+
+end
diff --git a/thys/Approximate_Model_Counting/ApproxMCCoreAnalysis.thy b/thys/Approximate_Model_Counting/ApproxMCCoreAnalysis.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/ApproxMCCoreAnalysis.thy
@@ -0,0 +1,1273 @@
+section \<open> ApproxMCCore analysis \<close>
+
+text \<open>
+  This section analyzes ApproxMCCore with respect to a universal hash family.
+  The proof follows Lemmas 1 and 2 from Chakraborty et al.~\cite{DBLP:conf/ijcai/ChakrabortyMV16}.
+  \<close>
+theory ApproxMCCoreAnalysis imports
+  ApproxMCCore
+begin
+
+(* Slicing after a family *)
+definition Hslice :: "nat \<Rightarrow>
+  ('a assg \<Rightarrow> 'b \<Rightarrow> nat assg) \<Rightarrow> ('a assg \<Rightarrow> 'b \<Rightarrow> nat assg)"
+  where "Hslice i H = (\<lambda>w s. aslice i (H w s))"
+
+context prob_space
+begin
+
+lemma indep_vars_prefix:
+  assumes "indep_vars (\<lambda>_. count_space UNIV) H J"
+  shows "indep_vars (\<lambda>_. count_space UNIV) (Hslice i H) J"
+proof -
+  have "indep_vars (\<lambda>_. count_space UNIV) (\<lambda>y. (\<lambda>x. aslice i x) \<circ> H y) J"
+    by (auto intro!: indep_vars_compose[OF assms(1)])
+  thus ?thesis
+    unfolding o_def Hslice_def
+    by auto
+qed
+
+lemma assg_nonempty_dom:
+  shows "
+  (\<lambda>x. if x < i then Some True else None) \<in>
+    {\<alpha>::nat assg. dom \<alpha> = {0..<i}}"
+  by (auto split: if_splits)
+
+lemma card_dom_ran_nat_assg:
+  shows "card {\<alpha>::nat assg. dom \<alpha> = {0..<n}} = 2^n"
+proof -
+  have *: " {\<alpha>::nat assg. dom \<alpha> = {0..<n}} =
+    {w. dom w = {0..<n} \<and> ran w \<subseteq> {True,False}}"
+    by auto
+  have "finite {0..<n}" by auto
+  from card_dom_ran[OF this]
+  have "card {w. dom w = {0..<n} \<and> ran w \<subseteq> {True,False}} =
+    card {True,False} ^ card {0..<n}" .
+  thus ?thesis
+    unfolding *
+    by (auto simp add: numeral_2_eq_2)
+qed
+
+lemma card_nat_assg_le:
+  assumes "i \<le> n"
+  shows "card {\<alpha>::nat assg. dom \<alpha> = {0..<n}} =
+    2^(n-i) * card {\<alpha>::nat assg. dom \<alpha> = {0..<i}}"
+  unfolding card_dom_ran_nat_assg
+  by (metis assms le_add_diff_inverse mult.commute power_add)
+
+lemma empty_nat_assg_slice_notin:
+  assumes "i \<le> n"
+  assumes "dom \<beta> \<noteq> {0..<i}"
+  shows"{\<alpha>::nat assg. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>} = {}"
+proof (intro equals0I)
+  fix x
+  assume "x \<in> {\<alpha>. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>}"
+  then have "dom \<beta> = {0..<i}"
+    unfolding aslice_def
+    using assms(1) by force
+  thus False using assms(2) by blast
+qed
+
+lemma restrict_map_dom:
+  shows "\<alpha> |` dom \<alpha> = \<alpha>"
+  unfolding restrict_map_def fun_eq_iff
+  by (simp add: domIff)
+
+lemma aslice_refl:
+  assumes "dom \<alpha> = {..<i}"
+  shows "aslice i \<alpha> = \<alpha>"
+  unfolding aslice_def assms[symmetric]
+  using restrict_map_dom by auto
+
+lemma bij_betw_with_inverse:
+  assumes "f ` A \<subseteq> B"
+  assumes "\<And>x. x \<in> A \<Longrightarrow> g (f x) = x"
+  assumes "g ` B \<subseteq> A"
+  assumes "\<And>x. x \<in> B \<Longrightarrow> f (g x) = x"
+  shows "bij_betw f A B"
+proof -
+  have "inj_on f A"
+    by (metis assms(2) inj_onI)
+
+  thus ?thesis
+    unfolding bij_betw_def
+    using assms
+    by (metis image_subset_iff subsetI subset_antisym)
+qed
+
+lemma card_nat_assg_slice:
+  assumes "i \<le> n"
+  assumes "dom \<beta> = {0..<i}"
+  shows"card {\<alpha>::nat assg. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>} =
+    2 ^ (n-i)"
+proof -
+  have "dom \<alpha> = {0..<i} \<and> aslice i \<alpha> = \<beta> \<longleftrightarrow> \<alpha> = \<beta>" for \<alpha>
+    using aslice_refl
+    by (metis assms(2) lessThan_atLeast0)
+  then have r2:
+    "{\<alpha>::nat assg. dom \<alpha> = {0..<i} \<and> aslice i \<alpha> = \<beta>} = {\<beta>}"
+    by simp
+
+  define f where "f =
+    (\<lambda>(\<alpha>::nat assg,\<beta>::nat assg) j.
+    if j < i then \<beta> j else \<alpha> (j-i))"
+  let ?lhs = "({\<alpha>. dom \<alpha> = {0..<n - i}} \<times>
+      {\<alpha>. dom \<alpha> = {0..<i} \<and> aslice i \<alpha> = \<beta>})"
+  let ?rhs = "{\<alpha>::nat assg. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>}"
+
+  define finv where "finv =
+    (\<lambda>fab::nat assg.
+      ((\<lambda>j. fab (j + i)),
+        fab |` {..<i})
+    )"
+  have 11: "\<And>x. dom (f x) = {j. if j < i then j \<in> dom (snd x) else j - i \<in> dom (fst x)}"
+    unfolding f_def
+      by (auto simp add: fun_eq_iff split: if_splits)
+  have 1: " f ` ?lhs  \<subseteq> ?rhs"
+  proof standard
+    fix x
+    assume x: "x \<in> f ` ({\<alpha>. dom \<alpha> = {0..<n - i}} \<times> {\<alpha>. dom \<alpha> = {0..<i} \<and> aslice i \<alpha> = \<beta>})"
+    obtain a b where ab: "dom a = {0..<n - i}" "dom b = {0..<i}"
+      "x = f (a,b)"
+      using x by blast
+    have 1: "dom x = {0..<n}"
+      unfolding ab 11 using assms(1)
+      by (auto simp add: ab)
+    have 2: "aslice i x = \<beta>"
+      using x unfolding f_def
+      by (auto simp add: aslice_def restrict_map_def split: if_splits)
+    show " x \<in> {\<alpha>. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>}"
+      using 1 2 by blast
+  qed
+
+  have " dom a = {0..<n - i} \<Longrightarrow>
+       dom b = {0..<i} \<Longrightarrow>
+       \<forall>x. aslice i b x = \<beta> x \<Longrightarrow>
+       \<not> x < i \<Longrightarrow> None = b x" for a b :: "nat assg" and x
+    by (metis atLeastLessThan_iff domIff)
+  then have 2: "\<And>x. x \<in> ?lhs \<Longrightarrow> finv (f x) = x"
+    unfolding finv_def f_def
+    by (clarsimp simp add: fun_eq_iff restrict_map_def)
+
+  have 31: "\<And>fab x y.
+       dom fab = {0..<n} \<Longrightarrow>
+       \<beta> = aslice i fab \<Longrightarrow>
+       fab (x + i) = Some y \<Longrightarrow>
+       x < n - i" 
+    by (metis atLeastLessThan_iff domI less_diff_conv)
+  also have "\<And>fab x.
+       dom fab = {0..<n} \<Longrightarrow>
+       \<beta> = aslice i fab \<Longrightarrow>
+       x < i \<Longrightarrow> \<exists>y. fab x = Some y"
+    by (metis assms(1) domD dual_order.trans lessThan_atLeast0 lessThan_iff linorder_not_less)
+  ultimately have 3: "finv ` ?rhs \<subseteq> ?lhs"
+    unfolding finv_def
+    by (auto simp add: aslice_def split: if_splits)
+
+  have 4: "\<And>x. x \<in> ?rhs \<Longrightarrow> f (finv x) = x"
+    unfolding finv_def f_def
+    by (auto simp add: fun_eq_iff restrict_map_def)
+
+  have "bij_betw f ?lhs ?rhs"
+    by (auto intro: bij_betw_with_inverse[OF 1 2 3 4])
+
+  from bij_betw_same_card[OF this]
+  have
+  "card {\<alpha>::nat assg. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>} =
+   card ({\<alpha>::nat assg. dom \<alpha> = {0..<n-i}} \<times>
+        {\<alpha>::nat assg. dom \<alpha> = {0..<i} \<and> aslice i \<alpha> = \<beta>})"
+    by auto
+  moreover have "... = 2^(n-i)"
+    using r2 card_dom_ran_nat_assg
+    by (simp add: card_cartesian_product)
+
+  ultimately show ?thesis by auto
+qed
+
+lemma finite_dom:
+  assumes "finite V"
+  shows "finite {w :: 'a \<rightharpoonup> bool. dom w = V}"
+proof -
+  have *: "{w :: 'a \<rightharpoonup> bool. dom w = V} =
+    {w. dom w = V \<and> ran w \<subseteq> {True,False}}"
+    by auto
+  show ?thesis unfolding *
+    apply (intro finite_set_of_finite_maps)
+    using assms by auto
+qed
+
+(* TODO: generalizable to any finite output alphabet instead of just booleans *)
+lemma universal_prefix_family_from_hash:
+  assumes M: "M = measure_pmf p"
+  assumes kH: "k_universal k H D {\<alpha>::nat assg. dom \<alpha> = {0..<n}}"
+  assumes i: "i \<le> n"
+  shows "k_universal k (Hslice i H) D {\<alpha>. dom \<alpha> = {0..<i}}"
+proof -
+  have "k_wise_indep_vars k (\<lambda>_. count_space UNIV) H D"
+    using kH unfolding k_universal_def
+    by auto
+  then have 1: "k_wise_indep_vars k (\<lambda>_. count_space UNIV) (Hslice i H) D"
+    unfolding k_wise_indep_vars_def
+    using indep_vars_prefix
+    by auto
+
+  have fdom: "finite {\<alpha>::nat assg. dom \<alpha> = {0..<i}}"
+    using measure_pmf.finite_dom by blast
+  have nempty: "{\<alpha>::nat assg. dom \<alpha> = {0..<i}} \<noteq> {}"
+    using assg_nonempty_dom
+    by (metis empty_iff)
+  have 2: "x \<in> D \<Longrightarrow>
+    uniform_on (Hslice i H x) {\<alpha>. dom \<alpha> = {0..<i}}" for x
+  proof -
+    assume "x \<in> D"
+    then have unif: "uniform_on (H x) {\<alpha>. dom \<alpha> = {0..<n}}"
+      by (metis kH k_universal_def)
+    show "uniform_on (Hslice i H x) {\<alpha>. dom \<alpha> = {0..<i}}"
+    proof (intro uniform_onI[OF M fdom nempty])
+      fix \<beta>
+      have *: "{\<omega> \<in> space M. H x \<omega> \<in> {\<alpha>. aslice i \<alpha> = \<beta>}} =
+        {\<omega>. Hslice i H x \<omega> = \<beta>}"
+        unfolding Hslice_def
+        by (auto simp add: M)
+
+      have "{\<alpha>::nat assg. dom \<alpha> = {0..<n}} \<inter> {\<alpha>.  aslice i \<alpha> = \<beta>} =
+        {\<alpha>::nat assg. dom \<alpha> = {0..<n} \<and> aslice i \<alpha> = \<beta>}"
+        by auto
+
+      then have "(card ({\<alpha>::nat assg. dom \<alpha> = {0..<n}} \<inter> {\<alpha>.  aslice i \<alpha> = \<beta>}))
+        = (if dom \<beta> = {0..<i} then 2^(n-i) else 0)"
+       using card_nat_assg_slice[OF i]
+       by (simp add: empty_nat_assg_slice_notin i)
+
+     then have **: "real (card ({\<alpha>::nat assg. dom \<alpha> = {0..<n}} \<inter> {\<alpha>.  aslice i \<alpha> = \<beta>}))
+        = indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta>  * 2^(n-i)"
+       by simp
+
+      from uniform_onD[OF unif, of "{\<alpha>. aslice i \<alpha> = \<beta>}"]
+      have "prob {\<omega>. Hslice i H x \<omega> = \<beta>} =
+        real (card ({\<alpha>. dom \<alpha> = {0..<n}} \<inter> {\<alpha>. aslice i \<alpha> = \<beta>})) /
+        real (card {\<alpha>::nat assg. dom \<alpha> = {0..<n}})"
+        unfolding * by auto
+      moreover have "... =
+        indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta>  * 2^(n-i) /
+        real (card {\<alpha>::nat assg. dom \<alpha> = {0..<n}})"
+        unfolding ** by auto
+      moreover have "... = indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta> * 2^(n-i) / 2^n"
+        by (simp add: card_dom_ran_nat_assg)
+      moreover have "... = indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta> / 2^i"
+        by (simp add: i power_diff)
+      moreover have "... =  indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta> / real ((2^i)::nat)" by auto
+      moreover have "... =  indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta> / real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}})"
+        using card_dom_ran_nat_assg
+        by auto
+      ultimately show "prob {\<omega>. Hslice i H x \<omega> = \<beta>} =
+         indicat_real {\<alpha>. dom \<alpha> = {0..<i}} \<beta> /
+         real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}})"
+        by presburger
+    qed
+  qed
+  show ?thesis
+    unfolding k_universal_def
+    using 1 2
+    by blast
+qed
+
+end
+
+context ApproxMCCore
+begin
+
+definition pivot :: "real"
+  where "pivot = 9.84 * ( 1 + 1 / \<epsilon> )^2"
+
+context
+  assumes thresh: "thresh \<ge> (1 + \<epsilon> / (1 + \<epsilon>)) * pivot"
+begin
+
+lemma aux_1:
+  assumes fin:"finite (set_pmf p)"
+  assumes \<sigma>: "\<sigma> > 0"
+  assumes exp: "\<mu> i = measure_pmf.expectation p Y"
+  assumes var: "\<sigma>^2 = measure_pmf.variance p Y"
+  assumes var_bound: "\<sigma>^2 \<le> \<mu> i"
+  shows "
+    measure_pmf.prob p {y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> i }
+    \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> i) "
+proof -
+  have pvar: "measure_pmf.variance p Y > 0"
+    using var \<sigma>
+    by (metis zero_less_power)
+  have kmu: "\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>) > 0"
+    using \<sigma> pvar var var_bound
+    using \<epsilon> by auto
+  have mupos: "\<mu> i > 0"
+    using pvar var var_bound by linarith
+  from spec_chebyshev_inequality [OF fin pvar kmu]
+  have "measure_pmf.prob p
+    {y. (Y y - measure_pmf.expectation p Y)^2 \<ge>
+       (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2 * measure_pmf.variance p Y} \<le> 1 / (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2"
+    by simp
+  then have ineq1:"measure_pmf.prob p
+    {y. (Y y - \<mu> i)^2 \<ge>
+       (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2 * \<sigma>^2} \<le> 1 / (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2"
+    using exp var by simp
+  have "(\<lambda>y. (Y y - \<mu> i)^2 \<ge> (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2 * \<sigma>^2)
+        = (\<lambda>y. (Y y - \<mu> i)^2 \<ge> (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>) * \<sigma> )^2)"
+    by (metis power_mult_distrib)
+  moreover have "... = (\<lambda>y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>) * \<sigma>)"
+  proof -
+    have "0 \<le> \<epsilon> * \<mu> i / (1 + \<epsilon>)"
+      by (simp add: \<epsilon> less_eq_real_def mupos zero_compare_simps(1))
+    then show ?thesis
+      apply clarsimp
+      by (metis abs_le_square_iff abs_of_nonneg)
+  qed
+  moreover have "... = (\<lambda>y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> * (\<mu> i) / (1 + \<epsilon>))"
+    using \<sigma> by auto
+  ultimately have simp1:"(\<lambda>y. (Y y - \<mu> i)^2 \<ge> (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2 * \<sigma>^2)
+                  = (\<lambda>y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * (\<mu> i))"
+    by auto
+
+  have "\<sigma>^2/(\<mu> i)^2 \<le> (\<mu> i)/(\<mu> i)^2"
+    using var_bound \<mu>_gt_zero
+    by (simp add: divide_right_mono)
+  moreover have "... = 1 / (\<mu> i)"
+    by (simp add: power2_eq_square)
+  ultimately have simp2: "\<sigma>^2/(\<mu> i)^2 \<le> 1 / (\<mu> i)" by auto
+
+  have "measure_pmf.prob p {y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * (\<mu> i)}
+        \<le> 1 / (\<epsilon> * (\<mu> i) / ((1 + \<epsilon>) * \<sigma>))^2"
+    using ineq1 simp1
+    by auto
+  moreover have "... = (1 + \<epsilon>)^2 / \<epsilon>^2 * \<sigma>^2/(\<mu> i)^2"
+    by (simp add: power_divide power_mult_distrib)
+  moreover have "... \<le> (1 + \<epsilon>)^2 / \<epsilon>^2 * (1 / (\<mu> i))"
+    using simp2
+    by (smt (verit, best) \<epsilon> divide_pos_pos mult_left_mono times_divide_eq_right zero_less_power)
+  ultimately have "measure_pmf.prob p {y. \<bar> Y y - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * (\<mu> i)}
+                    \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * (\<mu> i))"
+    by auto
+  thus ?thesis by auto
+qed
+
+(* Lem 1.1 in IJCAI'16 paper *)
+lemma analysis_1_1:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  assumes i: "i \<le> card S - 1"
+  shows "
+    measure_pmf.prob p
+    {s. \<bar> card_slice ((\<lambda>w. H w s)) i - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> i}
+    \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> i)"
+proof -
+
+  (* The variance for i-th slice *)
+  define var where "var =
+      (\<lambda>i. measure_pmf.variance p
+        (\<lambda>s. real (card (proj S W \<inter>
+          {w. Hslice i H w s = aslice i \<alpha>}))))"
+
+  from prob_space.universal_prefix_family_from_hash[OF _ _ ind]
+  have hf: "prob_space.k_universal (measure_pmf p) 2
+   (Hslice i H) {\<alpha>::'a assg. dom \<alpha> = S} {\<alpha>. dom \<alpha> = {0..<i}}"
+    using prob_space_measure_pmf
+    using i ind prob_space.universal_prefix_family_from_hash
+    by blast
+
+  have pSW: "proj S W \<subseteq> {\<alpha>. dom \<alpha> = S}"
+    unfolding proj_def restr_def by (auto split:if_splits)
+
+  have ain: "aslice i \<alpha> \<in> {\<alpha>. dom \<alpha> = {0..<i}}" using \<alpha>
+    unfolding aslice_def using i by auto
+
+  from k_universal_expectation_eq[OF p hf finite_proj_S pSW ain]
+  have exp:"measure_pmf.expectation p
+   (\<lambda>s. real (card (proj S W \<inter>
+                     {w. Hslice i H w s = aslice i \<alpha>}))) =
+    real (card (proj S W)) /
+    real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}})" .
+
+  have exp_mu:"real (card (proj S W)) /
+    real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}}) = \<mu> i"
+    unfolding \<mu>_def
+    by (simp add: measure_pmf.card_dom_ran_nat_assg)
+
+  have "proj S W \<inter>
+               {w. Hslice i H w s = aslice i \<alpha>} =
+    proj S W \<inter> {w. hslice i (\<lambda>w. H w s) w =  aslice i \<alpha>}" for s
+    unfolding proj_def Hslice_def hslice_def
+    by auto
+  then have extend_card_slice:
+    "\<And>s. (card (proj S W \<inter> {w. Hslice i H w s = aslice i \<alpha>})) =
+    card_slice ((\<lambda>w. H w s)) i"
+    unfolding card_slice_def by auto
+
+  have mu_exp:" \<mu> i = measure_pmf.expectation p
+   (\<lambda>s. real (card (proj S W \<inter> {w. Hslice i H w s = aslice i \<alpha>})))"
+    using exp exp_mu by auto
+
+  from two_universal_variance_bound[OF p hf finite_proj_S pSW ain]
+  have "
+    var i \<le>
+    measure_pmf.expectation p
+      (\<lambda>s. real (card (proj S W \<inter>
+                        {w. Hslice i H w s = aslice i \<alpha>})))"
+    unfolding var_def  .
+  then have var_bound: "var i \<le> \<mu> i" using exp exp_mu
+    by linarith
+
+  have "var i \<ge> 0" unfolding var_def by auto
+  then have "var i > 0 \<or>  var i = 0" by auto
+  moreover {
+    assume "var i = 0"
+
+    then have 1: "
+      measure_pmf.expectation p
+        (\<lambda>s. (card_slice (\<lambda>w. H w s) i - \<mu> i)^2) = 0"
+      unfolding var_def extend_card_slice mu_exp by auto
+
+    have 2: "measure_pmf.expectation p
+        (\<lambda>s. (card_slice (\<lambda>w. H w s) i - \<mu> i)^2) =
+      sum (\<lambda>s. (card_slice (\<lambda>w. H w s) i - \<mu> i)^2 * pmf p s) (set_pmf p)"
+      using assms by (auto intro!: integral_measure_pmf_real)
+
+    have "\<forall>x \<in> set_pmf p. (card_slice (\<lambda>w. H w x) i - \<mu> i)^2 * pmf p x = 0"
+      apply (subst sum_nonneg_eq_0_iff[symmetric])
+      using 1 2 p by auto
+    then have *: "\<And>x. x \<in> set_pmf p \<Longrightarrow> (card_slice (\<lambda>w. H w x) i - \<mu> i)^2 = 0"
+      by (meson mult_eq_0_iff set_pmf_iff)
+
+    have **: "(1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> i) > 0"
+      using \<mu>_gt_zero \<epsilon> by auto
+    have "\<epsilon> / (1 + \<epsilon>) * \<mu> i > 0"
+      using \<mu>_gt_zero \<epsilon> by auto
+    then have "\<And>s. s \<in> set_pmf p \<Longrightarrow> \<bar> card_slice ((\<lambda>w. H w s)) i - \<mu> i \<bar> < \<epsilon> / (1 + \<epsilon>) * \<mu> i"
+      using * by auto
+    then have "
+    measure_pmf.prob p
+    {s. \<bar> card_slice ((\<lambda>w. H w s)) i - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> i } = 0"
+      apply (subst measure_pmf_zero_iff)
+      using linorder_not_less by auto
+    then have "
+    measure_pmf.prob p
+      {s. \<bar> card_slice ((\<lambda>w. H w s)) i - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> i }
+      \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> i)"
+      using ** by auto
+  }
+  moreover {
+    define sigma where "sigma = sqrt(var i)"
+    assume "var i > 0"
+
+    then have sigma_gt_0: "sigma > 0"
+      unfolding sigma_def by simp
+
+    have extend_sigma: "sigma^2 = measure_pmf.variance p
+        (\<lambda>s. real (card (proj S W \<inter>
+        {w. Hslice i H w s = aslice i \<alpha>})))"
+      unfolding sigma_def var_def
+      using less_eq_real_def local.var_def real_sqrt_pow2 sigma_def sigma_gt_0
+      by fastforce
+
+    have sigma_bound: "sigma^2 \<le> \<mu> i"
+      using var_bound sigma_gt_0
+      using sigma_def by force
+
+    from aux_1[OF p sigma_gt_0 mu_exp extend_sigma sigma_bound]
+    have "
+      measure_pmf.prob p
+      {s. \<bar> card_slice ((\<lambda>w. H w s)) i - \<mu> i \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> i }
+      \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> i)"
+      using extend_card_slice by auto
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Lem 1.2 in IJCAI'16 paper *)
+lemma analysis_1_2:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  assumes i: "i \<le> card S - 1"
+  assumes \<beta>: "\<beta> \<le> 1"
+  shows "measure_pmf.prob p
+    {s. real(card_slice ((\<lambda>w. H w s)) i) \<le> \<beta> * \<mu> i }
+    \<le> 1 / (1 + (1 - \<beta>)^2 * \<mu> i)"
+proof -
+  have *: "(\<And>s. (0::real) \<le> card_slice ((\<lambda>w. H w s)) i)"
+    by simp
+  from spec_paley_zygmund_inequality[OF p * \<beta>]
+  have paley_zigmund:
+    "(measure_pmf.variance p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) )
+    + (1-\<beta>)^2 * (measure_pmf.expectation p (\<lambda>s. card_slice ((\<lambda>w. H w s)) i))^2) *
+    measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) )} \<ge>
+    (1-\<beta>)^2 * (measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) ))^2"
+    by auto
+  define var where "var = (\<lambda>i. measure_pmf.variance p
+      (\<lambda>s. real (card (proj S W \<inter>
+      {w. Hslice i H w s = aslice i \<alpha>}))))"
+
+  from prob_space.universal_prefix_family_from_hash[OF _ _ ind]
+  have hf: "prob_space.k_universal (measure_pmf p) 2
+   (Hslice i H) {\<alpha>::'a assg. dom \<alpha> = S} {\<alpha>. dom \<alpha> = {0..<i}}"
+    using prob_space_measure_pmf
+    using i ind prob_space.universal_prefix_family_from_hash
+    by blast
+
+  have pSW: "proj S W \<subseteq> {\<alpha>. dom \<alpha> = S}"
+    unfolding proj_def restr_def
+    by (auto split:if_splits)
+
+  have ain: "aslice i \<alpha> \<in> {\<alpha>. dom \<alpha> = {0..<i}}" using \<alpha>
+    unfolding aslice_def using i by auto
+
+  from k_universal_expectation_eq[OF p hf finite_proj_S pSW ain]
+  have exp:"measure_pmf.expectation p
+   (\<lambda>s. real (card (proj S W \<inter>
+                     {w. Hslice i H w s = aslice i \<alpha>}))) =
+    real (card (proj S W)) /
+    real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}})" .
+
+  have exp_mu:"real (card (proj S W)) /
+    real (card {\<alpha>::nat assg. dom \<alpha> = {0..<i}}) = \<mu> i"
+    unfolding \<mu>_def
+    by (simp add: measure_pmf.card_dom_ran_nat_assg)
+
+  have "proj S W \<inter>
+               {w. Hslice i H w s = aslice i \<alpha>} =
+    proj S W \<inter> {w. hslice i (\<lambda>w. H w s) w =  aslice i \<alpha>}" for s
+    unfolding proj_def Hslice_def hslice_def
+    by auto
+
+  then have extend_card_slice:"\<And>s. (card (proj S W \<inter>
+                     {w. Hslice i H w s = aslice i \<alpha>})) =
+    card_slice ((\<lambda>w. H w s)) i"
+    unfolding card_slice_def by auto
+
+  have mu_exp:" \<mu> i = measure_pmf.expectation p
+   (\<lambda>s. real (card (proj S W \<inter>
+                     {w. Hslice i H w s = aslice i \<alpha>})))"
+    using exp exp_mu by auto
+
+  from two_universal_variance_bound[OF p hf finite_proj_S pSW ain]
+  have "
+    var i \<le>
+    measure_pmf.expectation p
+      (\<lambda>s. real (card (proj S W \<inter>
+                        {w. Hslice i H w s = aslice i \<alpha>})))"
+    unfolding var_def  .
+  then have var_bound: "var i \<le> \<mu> i" using exp exp_mu
+    by linarith
+
+  have pos_mu: "\<mu> i > 0"
+    unfolding \<mu>_def
+    by (simp add: card_proj_witnesses)
+
+  have comp: "measure_pmf.prob p
+      {s. \<beta> * \<mu> i < real (card_slice (\<lambda>w. H w s) i)} =
+    (1 - measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) \<le> \<beta> * \<mu> i})"
+    apply (subst measure_pmf.prob_compl[symmetric])
+    by (auto intro!: arg_cong[where f = "measure_pmf.prob p"])
+
+  have extend_var_bound: "measure_pmf.variance p (\<lambda>s. card_slice ((\<lambda>w. H w s)) i) \<le> \<mu> i"
+    using var_bound
+    unfolding var_def
+    by (simp add: extend_card_slice)
+  then have
+    "(measure_pmf.variance p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i))
+      + (1-\<beta>)^2 * (measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) ) )^2)
+      * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) )} \<le>
+    (\<mu> i + (1-\<beta>)^2 * (measure_pmf.expectation p ( \<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) ) )^2)
+    * measure_pmf.prob p
+          {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) )}"
+    by (auto intro!: mult_right_mono)
+  moreover have
+    "... \<le> (\<mu> i + (1-\<beta>)^2 * (measure_pmf.expectation p ( \<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) ) )^2)
+    * measure_pmf.prob p
+          {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * measure_pmf.expectation p (\<lambda>s. real(card_slice ((\<lambda>w. H w s)) i) )}"
+    by fastforce
+  ultimately have
+    "(\<mu> i + (1-\<beta>)^2 * (\<mu> i)^2) * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * \<mu> i} \<ge> (1-\<beta>)^2 * (\<mu> i)^2"
+    unfolding mu_exp extend_card_slice
+    using paley_zigmund by linarith
+  then have
+    "(1 + (1-\<beta>)^2 * (\<mu> i)) * (\<mu> i) * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * \<mu> i} \<ge> (1-\<beta>)^2 * (\<mu> i) * (\<mu> i)"
+    by (smt (verit) left_diff_distrib' more_arith_simps(11) mult_cancel_right mult_cancel_right2 power2_eq_square)
+  then have
+    "(1 + (1-\<beta>)^2 * (\<mu> i)) * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) > \<beta> * \<mu> i} \<ge> (1-\<beta>)^2 * (\<mu> i)"
+    using pos_mu by force
+  then have
+    "(1 + (1-\<beta>)^2 * (\<mu> i)) * (1 - measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) \<le> \<beta> * \<mu> i}) \<ge> (1-\<beta>)^2 * (\<mu> i)"
+    using comp by auto
+  then have
+    "(1 + (1-\<beta>)^2 * (\<mu> i)) - (1 + (1-\<beta>)^2 * (\<mu> i)) * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) \<le> \<beta> * \<mu> i} \<ge> (1-\<beta>)^2 * (\<mu> i)"
+    by (simp add: right_diff_distrib)
+  then have
+    "(1 + (1-\<beta>)^2 * (\<mu> i)) * measure_pmf.prob p {s. real(card_slice ((\<lambda>w. H w s)) i) \<le> \<beta> * \<mu> i} \<le> 1"
+    by simp
+  thus ?thesis by (smt (verit, best) mult_nonneg_nonneg nonzero_mult_div_cancel_left pos_mu real_divide_pos_left zero_le_power2)
+qed
+
+lemma shift_\<mu>:
+  assumes "k \<le> i"
+  shows"\<mu> i * 2^k = \<mu> (i-k)"
+  unfolding \<mu>_def
+  by (auto simp add: assms power_diff)
+
+(* Lem 2.1 in IJCAI'16 paper *)
+lemma analysis_2_1:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  assumes \<epsilon>_up: "\<epsilon> \<le> 1"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+      \<le> 1 / 62.5"
+proof -
+  have "1 + 1 / \<epsilon> > 0"
+    by (simp add: \<epsilon> pos_add_strict)
+  then have pos_pivot: "pivot > 0"
+    unfolding pivot_def
+    by simp
+
+  have "mstar \<ge> 4 \<or> mstar < 4" by auto
+  moreover {
+    assume "mstar < 4"
+    then have " measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+      \<le> 1 / 62.5"
+      by (auto simp add: T0_empty)
+  }
+  moreover {
+    assume lo_mstar: "mstar \<ge> 4"
+
+    have extend_mu3: "\<mu> (mstar-1) * 2^2 = \<mu> (mstar-3)"
+      apply (subst shift_\<mu>)
+      subgoal using lo_mstar by linarith
+      using numeral_3_eq_3
+      using Suc_1 diff_Suc_eq_diff_pred numeral_nat(7) by presburger
+
+    have ******: "1 + \<epsilon> / (1 + \<epsilon>) \<le> 3 / 2"
+      using \<epsilon> assms(3) by auto
+    have mu_mstar_3_gt_zero: "\<mu> (mstar - 3) / 4 > 0"
+      using \<mu>_gt_zero by simp
+
+    from mstar_prop(1)
+    have "thresh < \<mu> (mstar - 1) *2^2 / 4 * (1 + \<epsilon> / (1 + \<epsilon>))"
+      by auto
+    also have "... = \<mu> (mstar - 3) / 4 * (1 + \<epsilon> / (1 + \<epsilon>))"
+      unfolding extend_mu3 by auto
+    also have "... \<le> \<mu> (mstar - 3) / 4 * (3 / 2)"
+      apply (intro mult_left_mono)
+      using ****** mu_mstar_3_gt_zero by auto
+    also have "... = 3 / 8 * \<mu> (mstar - 3)"
+      by auto
+    finally have thresh2mu: "thresh < 3 / 8 * \<mu> (mstar - 3)" .
+
+    have "1 + \<epsilon> / (1 + \<epsilon>) > 0"
+      by (simp add: add_nonneg_pos \<epsilon>)
+    then have "\<mu> (mstar-1) > pivot" (* pivot = thresh / (1 + \<epsilon>/(1+\<epsilon>)) *)
+      using mstar_prop(1) thresh
+      by (smt (verit) nonzero_mult_div_cancel_right real_divide_pos_left)
+    then have lo_mu_mstar_3: "\<mu> (mstar-3) > 4*pivot"
+      using extend_mu3
+      by simp
+
+    have mstar_3: "mstar-3 \<le> card S - 1"
+      using lo_mstar
+      using diff_le_self dual_order.trans mstar_prop(3) by blast
+
+    have *: "(5 / 8)^2 = ((25 / 64)::real)"
+      by (auto simp add: field_simps)
+    have **: " 1 + 25/64 * 4*pivot \<le> 1+ 25 / 64 * \<mu> (mstar - 3) "
+      using lo_mu_mstar_3
+      by auto
+
+    have "1 + 1/\<epsilon> \<ge> 2"
+      by (simp add: \<epsilon> assms(3))
+    then have "(1 + 1/\<epsilon>)^2 \<ge> 2^2"
+      by (smt (verit) power_mono)
+    then have ***: " 1 + 25/64 * 4 * 4*9.84 \<le> 1+ 25 / 64 * 4*pivot"
+      unfolding pivot_def
+      by auto
+    have ****: "1 + 25/64 * 4 * 4*9.84 > (0::real)"
+      by simp
+
+    have "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le>
+        3 / 8 * \<mu> (mstar - 3)}
+      \<le> 1 / (1 + (1 - 3 / 8)\<^sup>2 * \<mu> (mstar - 3))"
+      apply(intro analysis_1_2[OF p ind mstar_3])
+      by auto
+    also have "... = 1 / (1 + (5 / 8)^2 * \<mu> (mstar-3))"
+      by simp
+    also have "... = 1 / (1 + 25 / 64 * \<mu> (mstar-3))"
+      unfolding * by auto
+    also have "... \<le> 1 / (1+ 25/64 * 4*pivot)"
+      using **
+      by (metis Groups.add_ac(2) add_sign_intros(3) divide_nonneg_nonneg frac_le mult_right_mono mult_zero_left of_nat_0_le_iff of_nat_numeral order_le_less pos_pivot zero_less_one)
+    also have "... \<le> 1 / (1+ 25/64 * 4 * 4*9.84)"
+      using *** ****
+      by (smt (verit) frac_le)
+    also have "... \<le> 1 / 62.5"
+      by simp
+    finally have *****: "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le> 3 / 8 * \<mu> (mstar - 3)} \<le> 1 / 62.5"
+      by auto
+
+    have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+        = measure_pmf.prob p {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) < thresh}"
+      unfolding T_def
+      by auto
+    also have "... \<le> measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le> 3 / 8 * \<mu> (mstar - 3)}"
+      using thresh2mu by (auto intro!: measure_pmf.finite_measure_mono)
+    also have "... \<le> 1 / 62.5"
+      using *****
+      by auto
+    finally have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3)) \<le> 1 / 62.5" .
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Alternative Lem 2.1 in IJCAI'16 paper without bound on epsilon *)
+lemma analysis_2_1':
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+      \<le> 1 / 10.84"
+proof -
+  have "1 + 1 / \<epsilon> > 0"
+    by (simp add: \<epsilon> pos_add_strict)
+  then have pos_pivot: "pivot > 0"
+    unfolding pivot_def
+    by simp
+
+  have "mstar \<ge> 4 \<or> mstar < 4" by auto
+  moreover {
+    assume "mstar < 4"
+    then have " measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+      \<le> 1 / 10.84"
+      by (auto simp add: T0_empty)
+  }
+  moreover {
+    assume lo_mstar: "mstar \<ge> 4"
+
+    have extend_mu3: "\<mu> (mstar-1) * 2^2 = \<mu> (mstar-3)"
+      apply (subst shift_\<mu>)
+      subgoal using lo_mstar semiring_norm(87) by linarith
+      using diff_Suc_eq_diff_pred eval_nat_numeral(3) by presburger
+
+    have "\<epsilon> / (1 + \<epsilon>) < 1"
+      using \<epsilon> by auto
+    then have ******: "1 + \<epsilon> / (1 + \<epsilon>) < 2"
+      using \<epsilon> by auto
+    have mu_mstar_3_gt_zero: "\<mu> (mstar - 3) / 4 > 0"
+      using \<mu>_gt_zero by simp
+
+    from mstar_prop(1)
+    have "thresh < \<mu> (mstar - 1) * (1 + \<epsilon> / (1 + \<epsilon>))"
+      by auto
+    also have "... = \<mu> (mstar - 1) *2^2 / 4 * (1 + \<epsilon> / (1 + \<epsilon>))"
+      by auto
+    also have "... = \<mu> (mstar - 3) / 4 * (1 + \<epsilon> / (1 + \<epsilon>))"
+      unfolding extend_mu3 by auto
+    also have "... < \<mu> (mstar - 3) / 4 * 2"
+      apply (intro mult_strict_left_mono)
+      using ****** mu_mstar_3_gt_zero by auto
+    also have "... = 1 / 2 * \<mu> (mstar - 3)"
+      by auto
+    finally have thresh2mu: "thresh < 1 / 2 * \<mu> (mstar - 3)" .
+
+    have "1 + \<epsilon> / (1 + \<epsilon>) > 0"
+      by (simp add: add_nonneg_pos \<epsilon>)
+    then have "\<mu> (mstar-1) * 4 > 4*pivot"
+      using mstar_prop(1) thresh
+      by (smt (verit) nonzero_mult_div_cancel_right real_divide_pos_left)
+    then have lo_mu_mstar_3: "\<mu> (mstar-3) > 4*pivot"
+      using extend_mu3
+      by simp
+
+    have mstar_3: "mstar-3 \<le> card S - 1"
+      using lo_mstar
+      using diff_le_self dual_order.trans mstar_prop(3) by blast
+
+    have *: "(1 / 2)^2 = ((1 / 4)::real)"
+      by (auto simp add: field_simps)
+    have **: " 1 + 1/4 * 4*pivot \<le> 1+ 1/4 * \<mu> (mstar - 3) "
+      using lo_mu_mstar_3
+      by auto
+
+    have "(1 + 1/\<epsilon>)^2 > 1^2"
+      by (simp add: \<epsilon>)
+    then have ***: " 1 + 1/4 * 4*9.84 \<le> 1+ 1/4 * 4 *pivot"
+      unfolding pivot_def by auto
+    have ****: "1 + 1/4 * 4 * 9.84 > (0::real)"
+      by simp
+
+    have "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le>
+        1 / 2 * \<mu> (mstar - 3)}
+      \<le> 1 / (1 + (1 - 1 / 2)\<^sup>2 * \<mu> (mstar - 3))"
+      apply(intro analysis_1_2[OF p ind mstar_3])
+      by auto
+    also have "... = 1 / (1 + 1 / 4 * \<mu> (mstar-3))"
+      using * by force
+    also have "... \<le> 1 / (1+ 1/4 * 4*pivot)"
+      using **
+      by (simp add: add_nonneg_pos frac_le pos_pivot)
+    also have "... \<le> 1 / (1+ 1/4 * 4 *9.84)"
+      using *** ****
+      by (smt (verit) frac_le)
+    also have "... \<le> 1 / 10.84"
+      by simp
+    finally have *****: "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le> 1/2 * \<mu> (mstar - 3)} \<le> 1 / 10.84" .
+
+    have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+        = measure_pmf.prob p {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) < thresh}"
+      unfolding T_def
+      by auto
+    also have "... \<le> measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 3)) \<le> 1 / 2 * \<mu> (mstar - 3)}"
+      using thresh2mu by (auto intro!: measure_pmf.finite_measure_mono)
+    also have "... \<le> 1 /  10.84"
+      using *****
+      by auto
+    finally have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3)) \<le> 1 /  10.84" .
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Lem 2.2 in IJCAI'16 paper *)
+lemma analysis_2_2:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2)) \<le> 1 / 20.68"
+proof -
+  have epos: "1 + 1 / \<epsilon> > 0"
+    by (simp add: \<epsilon> pos_add_strict)
+  then have pos_pivot: "pivot > 0"
+    unfolding pivot_def
+    by simp
+
+  have "mstar \<ge> 3 \<or> mstar < 3" by auto
+  moreover {
+    assume "mstar < 3"
+    then have " measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2))
+          \<le> 1 / 20.68"
+      by (auto simp add: L0_empty)
+  }
+  moreover {
+    assume lo_mstar: "mstar \<ge> 3"
+
+    have extend_mu2: "\<mu> (mstar-1) * 2^1 = \<mu> (mstar-2)"
+      apply (subst shift_\<mu>)
+      subgoal using lo_mstar by linarith
+      by (metis diff_diff_left one_add_one)
+
+    have "1 + \<epsilon> / (1 + \<epsilon>) > 0"
+      by (simp add: add_nonneg_pos \<epsilon>)
+    then have "\<mu> (mstar-1) > pivot"
+      using mstar_prop(1) thresh
+      by (smt (verit) nonzero_mult_div_cancel_right real_divide_pos_left)
+    then have lo_mu_mstar_2: "\<mu> (mstar-2) > 2*pivot"
+      using extend_mu2
+      by simp
+
+    have mstar_2: "mstar-2 \<le> card S - 1"
+      using lo_mstar
+      using diff_le_self dual_order.trans mstar_prop(3) by blast
+
+    have beta:"1/(1+\<epsilon>) \<le> (1::real)"
+      using \<epsilon> by auto
+    have pos: "(1 / (1 + 1/\<epsilon>))\<^sup>2 > 0"
+      using epos by auto
+    then have *: "1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 2*pivot \<le> 1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * \<mu> (mstar - 2)"
+      using lo_mu_mstar_2
+      by auto
+
+    have "1 - 1/(1+\<epsilon>) = 1 / (1 + 1/\<epsilon>)"
+      by (smt (verit, ccfv_threshold) \<epsilon> conjugate_exponent_def conjugate_exponent_real(1))
+    then have **: "(1 - 1/(1+\<epsilon>))^2 = (1 / (1 + 1/\<epsilon>))^2"
+      by simp
+    have ***: "1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 2 * 9.84 * ( 1 + 1/\<epsilon> )^2
+            = 1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * ( 1 + 1/\<epsilon> )^2 *  2 * 9.84"
+      by (simp add: mult.commute)
+    have ****: "(1 / (1 + 1/\<epsilon>))\<^sup>2 * ( 1 + 1/\<epsilon> )^2 = 1"
+      using pos
+      by (simp add: power_one_over)
+
+    from analysis_1_2[OF p ind mstar_2 beta]
+    have "measure_pmf.prob p
+      {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 2)}
+        \<le> 1 / (1 + (1 - 1/(1+\<epsilon>))\<^sup>2 * \<mu> (mstar - 2))"
+      by auto
+    also have "... = 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * \<mu> (mstar - 2))"
+      unfolding ** by auto
+    also have "... \<le> 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 2 * pivot)"
+      using *
+      by (smt (verit) epos divide_pos_pos frac_le pivot_def pos_prod_le zero_less_power)
+    also have "... = 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 2 * 9.84 * ( 1 + 1/\<epsilon> )^2)"
+      unfolding pivot_def by auto
+    also have "... = 1 / 20.68"
+      unfolding *** **** by auto
+    finally have *****: "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 2)} \<le> 1 / 20.68" .
+
+    have "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) < 1/(1+\<epsilon>) * \<mu> (mstar - 2)}
+        \<le> measure_pmf.prob p {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 2)}"
+      by (auto intro!: measure_pmf.finite_measure_mono)
+    then have ******: "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) < 1/(1+\<epsilon>) * \<mu> (mstar - 2)}
+          \<le> 1 / 20.68"
+      using ***** by auto
+
+    have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2))
+        = measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 2)) < 1/(1+\<epsilon>) * \<mu> (mstar - 2)}"
+      unfolding L_def
+      by auto
+    also have "... \<le> 1 / 20.68"
+      using ****** by auto
+    finally have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2)) \<le> 1 / 20.68" .
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Lem 2.3 in IJCAI'16 paper *)
+lemma analysis_2_3:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  shows "
+    measure_pmf.prob
+    (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1)) \<le> 1 / 10.84"
+proof -
+  have epos: "1 + 1 / \<epsilon> > 0"
+    by (simp add: \<epsilon> pos_add_strict)
+  then have pos_pivot: "pivot > 0"
+    unfolding pivot_def
+    by simp
+
+  have "mstar \<ge> 2 \<or> mstar < 2" by auto
+  moreover {
+    assume "mstar < 2"
+    then have " measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2))
+          \<le> 1 / 10.84"
+      by (auto simp add: L0_empty)
+  }
+  moreover {
+    assume lo_mstar: "mstar \<ge> 2"
+
+    have "1 + \<epsilon> / (1 + \<epsilon>) > 0"
+      by (simp add: add_nonneg_pos \<epsilon>)
+    then have lo_mu_mstar_1: "\<mu> (mstar-1) > pivot"
+      using mstar_prop(1) using thresh
+      by (smt (verit) nonzero_mult_div_cancel_right real_divide_pos_left)
+
+    have mstar_1: "mstar-1 \<le> card S - 1"
+      using lo_mstar diff_le_self dual_order.trans mstar_prop(3) by blast
+
+    have beta: "1/(1+\<epsilon>) \<le> (1::real)"
+      using \<epsilon> by auto
+    have "(1 / (1 + 1/\<epsilon>))\<^sup>2 > 0"
+      using epos by auto
+    then have *: "1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * pivot \<le> 1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * \<mu> (mstar - 1)"
+      using lo_mu_mstar_1
+      by auto
+
+    have "1 - 1/(1+\<epsilon>) = 1 / (1 + 1/\<epsilon>)"
+      by (smt (verit, ccfv_threshold) \<epsilon> conjugate_exponent_def conjugate_exponent_real(1))
+    then have **: "(1 - 1/(1+\<epsilon>))^2 = (1 / (1 + 1/\<epsilon>))^2"
+      by simp
+    have ***: "1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 9.84 * ( 1 + 1/\<epsilon> )^2
+            = 1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * ( 1 + 1/\<epsilon> )^2 * 9.84"
+      by (simp add: mult.commute)
+    have ****: "(1 / (1 + 1/\<epsilon>))\<^sup>2 * ( 1 + 1/\<epsilon> )^2 = 1"
+      by (metis (mono_tags, opaque_lifting) \<open>0 < 1 + 1 / \<epsilon>\<close> div_by_1 divide_divide_eq_right divide_self_if less_irrefl mult.commute power_mult_distrib power_one)
+
+    from analysis_1_2[OF p ind mstar_1 beta]
+    have "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 1)}
+    \<le> 1 / (1 + (1 - 1/(1+\<epsilon>))\<^sup>2 * \<mu> (mstar - 1))"
+      by auto
+    moreover have "... = 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * \<mu> (mstar - 1))"
+      unfolding ** by auto
+    moreover have "... \<le> 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * pivot)"
+      using *
+      by (smt (verit) \<open>0 < (1 / (1 + 1 / \<epsilon>))\<^sup>2\<close> frac_le pos_pivot zero_le_mult_iff)
+    moreover have "... = 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * 9.84 * ( 1 + 1/\<epsilon> )^2)"
+      unfolding pivot_def by auto
+    moreover have "... = 1 / (1 + (1 / (1 + 1/\<epsilon>))\<^sup>2 * ( 1 + 1/\<epsilon> )^2 * 9.84)"
+      unfolding *** by auto
+    moreover have "... = 1 / (1 + 9.84)"
+      unfolding **** by auto
+    moreover have "... = 1 / 10.84"
+      by auto
+    ultimately have *****: "measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 1)} \<le> 1 / 10.84"
+      by linarith
+    have "measure_pmf.prob p
+      {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) < 1/(1+\<epsilon>) * \<mu> (mstar - 1)}
+        \<le> measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) \<le> 1/(1+\<epsilon>) * \<mu> (mstar - 1)}"
+      by (auto intro!: measure_pmf.finite_measure_mono)
+    then have ******: "measure_pmf.prob p
+      {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) < 1/(1+\<epsilon>) * \<mu> (mstar - 1)}
+          \<le> 1 / 10.84"
+      using ***** by auto
+
+    have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1))
+        = measure_pmf.prob p
+     {s. real (card_slice (\<lambda>w. H w s) (mstar - 1)) < 1/(1+\<epsilon>) * \<mu> (mstar - 1)}"
+      unfolding L_def
+      by auto
+    moreover have "... \<le> 1 / 10.84"
+      using ****** by auto
+    ultimately have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1)) \<le> 1 / 10.84"
+      by auto
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Lem 2.4 in IJCAI'16 paper *)
+lemma analysis_2_4:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar) \<le> 1 / 4.92"
+proof -
+  have "1 + 1 / \<epsilon> > 0"
+    by (simp add: \<epsilon> pos_add_strict)
+  then have pos_pivot: "pivot > 0"
+    unfolding pivot_def
+    by simp
+
+  have "mstar \<ge> 1 \<or> mstar < 1" by auto
+  moreover {
+    assume "mstar < 1"
+    have LU0_empty: "L mstar \<union> U mstar = {}"
+      using L0_empty U0_empty
+      using \<open>mstar < 1\<close> less_one by auto
+    then have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)
+          \<le> 1 / 4.92"
+      by auto
+  }
+  moreover {
+    assume lo_mstar: "mstar \<ge> 1"
+    have extend_mu: "\<mu> mstar * 2^1 = \<mu> (mstar-1)"
+      using lo_mstar
+      apply (subst shift_\<mu>)
+      by auto
+
+    have "1 + \<epsilon> / (1 + \<epsilon>) > 0"
+      by (simp add: add_nonneg_pos \<epsilon>)
+    then have "\<mu> (mstar-1) > pivot"
+      using mstar_prop(1) thresh
+      by (smt (verit) nonzero_mult_div_cancel_right real_divide_pos_left)
+    then have lo_mu_star: "\<mu> mstar > pivot / 2"
+      using extend_mu
+      by auto
+
+    have mstar: "mstar \<le> card S - 1"
+      using lo_mstar
+      using diff_le_self dual_order.trans mstar_prop(3) by blast
+
+    have "\<epsilon>*(1+1/\<epsilon>) = 1+\<epsilon>"
+      by (smt (verit) \<epsilon> add_divide_eq_if_simps(1) divide_cancel_right divide_self_if nonzero_mult_div_cancel_left)
+    then have *: "9.84 * \<epsilon>^2*(1+1/\<epsilon>)^2 / 2 = 9.84 * (1+\<epsilon>)^2 / 2"
+      by (metis (mono_tags, opaque_lifting) more_arith_simps(11) power_mult_distrib)
+
+    have "\<epsilon>^2 * \<mu> mstar \<ge> \<epsilon>^2 * pivot / 2"
+      using lo_mu_star
+      by (metis less_eq_real_def ordered_comm_semiring_class.comm_mult_left_mono times_divide_eq_right zero_le_power2)
+    then have **: "\<epsilon>^2 * \<mu> mstar \<ge> 9.84 * (1+\<epsilon>)^2 / 2"
+      unfolding pivot_def using * by auto
+
+    from analysis_1_1[OF p ind mstar]
+    have "measure_pmf.prob p
+      {s. \<bar> card_slice ((\<lambda>w. H w s)) mstar - \<mu> mstar \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> mstar }
+          \<le> (1 + \<epsilon>)^2 / (\<epsilon>^2 * \<mu> mstar)"
+      by auto
+    also have "... \<le> (1 + \<epsilon>)^2 / (9.84 * (1+\<epsilon>)^2 / 2)"
+      using **
+      by (smt (verit) divide_cancel_left divide_le_0_iff frac_le pos_prod_le power2_less_0 zero_eq_power2)
+    also have "... = (1 + \<epsilon>)^2 / (4.92 * (1+\<epsilon>)^2)"
+      by simp
+    also have "... = 1 / 4.92"
+      using \<epsilon> by simp
+    finally have *******: "measure_pmf.prob p
+      {s. \<bar> card_slice ((\<lambda>w. H w s)) mstar - \<mu> mstar \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> mstar }
+          \<le> 1 / 4.92" .
+
+    have "\<mu> mstar / (1 + \<epsilon>) - \<mu> mstar = \<mu> mstar * (1 / (1+\<epsilon>) - 1)"
+      by (simp add: right_diff_distrib')
+    also have "... = \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))"
+      by (smt (verit) \<epsilon> add_divide_distrib div_self minus_divide_left)
+    finally have ***: "\<mu> mstar / (1 + \<epsilon>) - \<mu> mstar = \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))" .
+
+    have "{h. real (card_slice h mstar) \<le> \<mu> mstar / (1 + \<epsilon>)}
+        = {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar / (1 + \<epsilon>) - \<mu> mstar}"
+      by auto
+    also have "... = {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))}"
+      using *** by auto
+    finally have ****: "
+      {h. real (card_slice h mstar) \<le> \<mu> mstar / (1 + \<epsilon>)} =
+      {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))}" .
+
+    have "L mstar
+            = {h. real (card_slice h mstar) < \<mu> mstar / (1 + \<epsilon>)}"
+      unfolding L_def by auto
+    also have "...\<subseteq> {h. real (card_slice h mstar) \<le> \<mu> mstar / (1 + \<epsilon>)}"
+      by auto
+    also have "... = {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))}"
+      unfolding **** by auto
+    finally have extend_L: "L mstar \<subseteq> {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))}" .
+
+    have *****: "\<mu> mstar * (1 + \<epsilon> / (1+\<epsilon>)) - \<mu> mstar = \<mu> mstar * (\<epsilon> / (1+\<epsilon>))"
+      by (metis (no_types, opaque_lifting) add.commute diff_add_cancel group_cancel.sub1 mult.right_neutral right_diff_distrib')
+
+    have ******: "U mstar = {h. real (card_slice h mstar) \<ge> \<mu> mstar * (1 + \<epsilon> / (1+\<epsilon>))}"
+      unfolding U_def by auto
+    have "{h. real (card_slice h mstar) \<ge> \<mu> mstar * (1 + \<epsilon> / (1+\<epsilon>))}
+          = {h. real (card_slice h mstar) - \<mu> mstar \<ge> \<mu> mstar * (1 + \<epsilon> / (1+\<epsilon>)) - \<mu> mstar}"
+      by auto
+    also have "... = {h. real (card_slice h mstar) - \<mu> mstar \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}"
+      unfolding ***** by auto
+    finally have extend_U: "U mstar = {h. real (card_slice h mstar) - \<mu> mstar \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}"
+      using ****** by auto
+
+    have "L mstar \<union> U mstar \<subseteq>
+                    {h. real (card_slice h mstar) - \<mu> mstar \<le> \<mu> mstar * (- \<epsilon> / (1+\<epsilon>))}
+                  \<union> {h. real (card_slice h mstar) - \<mu> mstar \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}"
+      unfolding extend_U
+      using extend_L
+      by auto
+    also have "... = {h. \<bar> real (card_slice h mstar) - \<mu> mstar \<bar> \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}"
+      by auto
+    finally have extend_LU: "L mstar \<union> U mstar \<subseteq> {h. \<bar> real (card_slice h mstar) - \<mu> mstar \<bar> \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}" .
+
+    have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)
+        \<le> measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) {h. \<bar> real (card_slice h mstar) - \<mu> mstar \<bar> \<ge> \<mu> mstar * (\<epsilon> / (1+\<epsilon>))}"
+      using extend_LU
+      by (auto intro!: measure_pmf.finite_measure_mono)
+    also have "... = measure_pmf.prob p
+      {s. \<bar> real (card_slice (\<lambda>w. H w s) mstar) - \<mu> mstar \<bar> \<ge> \<epsilon> / (1 + \<epsilon>) * \<mu> mstar }"
+      by (simp add: mult.commute)
+    also have "... \<le> 1 / 4.92"
+      using ******* by auto
+    finally have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar) \<le> 1 / 4.92" .
+  }
+
+  ultimately show ?thesis by auto
+qed
+
+(* Lem 3 in IJCAI'16 paper *)
+lemma analysis_3:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  assumes \<epsilon>_up: "\<epsilon> \<le> 1"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p)
+    approxcore_fail \<le> 0.36"
+proof -
+  have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) approxcore_fail
+    \<le> measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p)
+   (T (mstar-3) \<union>
+    L (mstar-2) \<union>
+    L (mstar-1) \<union>
+    (L mstar \<union> U mstar))"
+    using failure_bound
+    by (auto intro!: measure_pmf.finite_measure_mono)
+
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3) \<union> L (mstar-2) \<union> L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3) \<union> L (mstar-2))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le> 1/62.5 + 1/20.68 + 1/10.84 + 1/4.92"
+    using analysis_2_1[OF p ind \<epsilon>_up]
+    using analysis_2_2[OF p ind]
+    using analysis_2_3[OF p ind]
+    using analysis_2_4[OF p ind]
+    by auto
+  ultimately show ?thesis by force
+qed
+
+(* Alternative Lem 3 in IJCAI'16 paper without bound on epsilon *)
+lemma analysis_3':
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H
+    {\<alpha>::'a assg. dom \<alpha> = S}
+    {\<alpha>::nat assg. dom \<alpha> = {0..<card S - 1}}"
+  shows "
+    measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p)
+    approxcore_fail \<le> 0.44"
+proof -
+  have "measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) approxcore_fail
+    \<le> measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p)
+   (T (mstar-3) \<union>
+    L (mstar-2) \<union>
+    L (mstar-1) \<union>
+    (L mstar \<union> U mstar))"
+    using failure_bound
+    by (auto intro!: measure_pmf.finite_measure_mono)
+
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3) \<union> L (mstar-2) \<union> L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3) \<union> L (mstar-2))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le>
+      measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (T (mstar-3))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-2))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L (mstar-1))
+    + measure_pmf.prob (map_pmf (\<lambda>s w. H w s) p) (L mstar \<union> U mstar)"
+    by (auto intro!: measure_pmf.finite_measure_subadditive)
+  moreover have "... \<le> 1/10.84 + 1/20.68 + 1/10.84 + 1/4.92"
+    using analysis_2_1'[OF p ind]
+    using analysis_2_2[OF p ind]
+    using analysis_2_3[OF p ind]
+    using analysis_2_4[OF p ind]
+    by auto
+  ultimately show ?thesis by auto
+qed
+end
+
+end
+
+end
diff --git a/thys/Approximate_Model_Counting/ApproxMCPreliminaries.thy b/thys/Approximate_Model_Counting/ApproxMCPreliminaries.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/ApproxMCPreliminaries.thy
@@ -0,0 +1,342 @@
+section \<open>Preliminary probability/UHF lemmas\<close>
+
+text \<open> This section proves some simplified/specialized forms of lemmas
+  that will be used in the algorithm's analysis later. \<close>
+
+theory ApproxMCPreliminaries imports
+  Frequency_Moments.Probability_Ext
+  Concentration_Inequalities.Paley_Zygmund_Inequality
+begin
+
+lemma card_inter_sum_indicat_real:
+  assumes "finite A"
+  shows "card (A \<inter> B) = sum (indicat_real B) A"
+  by (simp add: assms indicator_def)
+
+(* Counting number of finite maps *)
+lemma card_dom_ran:
+  assumes "finite D"
+  shows "card {w. dom w = D \<and> ran w \<subseteq> R} = card R ^ card D"
+  using assms
+proof (induct rule: finite_induct)
+  case empty
+  have "{w::'a \<Rightarrow> 'b option. w = Map.empty \<and> ran w \<subseteq> R} = {Map.empty}"
+    by auto
+  then show ?case
+    by auto
+next
+  case (insert a A)
+  have 1: "inj_on (\<lambda>(w, r). w(a \<mapsto> r))
+     ({w. dom w = A \<and> ran w \<subseteq> R} \<times> R)"
+    unfolding inj_on_def
+    by (smt (verit, del_insts) CollectD SigmaE fun_upd_None_if_notin_dom local.insert(2) map_upd_eqD1 prod.simps(2) restrict_complement_singleton_eq restrict_upd_same)
+  have 21: "(\<lambda>(w, r). w(a \<mapsto> r)) `
+    ({w. dom w = A \<and> ran w \<subseteq> R} \<times> R) \<subseteq>
+    {w. dom w = insert a A \<and> ran w \<subseteq> R}"
+    unfolding image_def
+    using CollectD local.insert(2) by force
+
+  have "\<And>x. dom x = insert a A \<Longrightarrow>
+         ran x \<subseteq> R \<Longrightarrow>
+         \<exists>xa. dom xa = A \<and>
+              ran xa \<subseteq> R \<and> (\<exists>y\<in>R. x = xa(a \<mapsto> y))"
+    by (smt (verit, del_insts) Diff_insert_absorb domD dom_fun_upd fun_upd_triv fun_upd_upd insert.hyps(2) insertCI insert_subset ran_map_upd)
+  then have 22: "
+    {w. dom w = insert a A \<and> ran w \<subseteq> R} \<subseteq>
+    (\<lambda>(w, r). w(a \<mapsto> r)) `
+    ({w. dom w = A \<and> ran w \<subseteq> R} \<times> R)"
+    by (clarsimp simp add: image_def)
+
+  have "bij_betw (\<lambda>(w,r). w(a\<mapsto>r))
+    ({w. dom w = A \<and> ran w \<subseteq> R} \<times> R)
+    {w. dom w = insert a A \<and> ran w \<subseteq> R} "
+    unfolding bij_betw_def
+    using 1 21 22 by clarsimp
+
+  then have "card {w. dom w = insert a A \<and> ran w \<subseteq> R} = card ({w. dom w = A \<and> ran w \<subseteq> R} \<times> R)"
+    by (auto simp add: bij_betw_same_card 1 21 22)
+
+  moreover have "... = card R ^ card A * card R"
+    by(subst card_cartesian_product) (use insert.hyps(3) in auto)
+
+  ultimately show ?case
+    using insert.hyps by (auto simp add: card_insert_if)
+qed
+
+lemma finite_set_pmf_expectation_sum:
+  fixes f :: "'a \<Rightarrow> 'c \<Rightarrow> 'b::{banach, second_countable_topology}"
+  assumes "finite (set_pmf A)"
+  shows "measure_pmf.expectation A (\<lambda>x. sum (f x) T) =
+    (\<Sum>i\<in>T. measure_pmf.expectation A (\<lambda>x. f x i))"
+  apply (intro Bochner_Integration.integral_sum integrable_measure_pmf_finite)
+  using assms by auto
+
+lemma (in prob_space) k_universal_prob_unif:
+  assumes "k_universal k H D R"
+  assumes "w \<in> D" "\<alpha> \<in> R"
+  shows "prob {s \<in> space M. H w s = \<alpha>} = 1 / card R"
+proof -
+  have "uniform_on (H w) R"
+    using assms unfolding k_universal_def
+    by auto
+
+  from uniform_onD[OF this]
+  have "prob
+   {\<omega> \<in> space M.  H w \<omega> \<in> {\<alpha>}} =
+    real (card (R \<inter> {\<alpha>})) / real (card R)" .
+
+  thus ?thesis
+    using assms by auto
+qed
+
+(* For h: D \<rightarrow> R, k-universal, S \<subseteq> D.
+   E( | {w \<in> S. h w = \<alpha>} | ) = |S| / |R| *)
+lemma k_universal_expectation_eq:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal p k H D R"
+  assumes S: "finite S" "S \<subseteq> D"
+  assumes a: "\<alpha> \<in> R"
+  shows
+    "prob_space.expectation p
+      (\<lambda>s. real (card (S \<inter> {w. H w s = \<alpha>}))) =
+    real (card S) / card R"
+proof -
+  have 1: "prob_space (measure_pmf p)"
+    by (simp add: prob_space_measure_pmf)
+  have 2: "space (measure_pmf p) = UNIV" by auto
+  from prob_space.k_universal_prob_unif[OF 1 ind _ a]
+  have *: "\<And>w. w \<in> S \<Longrightarrow>
+   prob_space.prob p {s. H w s = \<alpha>} = 1 / real (card R)"
+    using S(2) by auto
+
+  have "measure_pmf.expectation p
+    (\<lambda>s. real (card (S \<inter> {w. H w s = \<alpha>}))) =
+    measure_pmf.expectation p
+    (\<lambda>s. sum (indicat_real {w. H w s = \<alpha>}) S)"
+    unfolding card_inter_sum_indicat_real[OF S(1)]
+    by presburger
+
+  moreover have "... =
+    (\<Sum>i\<in>S.
+       measure_pmf.expectation p
+        (indicat_real {s. H i s = \<alpha>}))"
+    apply (subst finite_set_pmf_expectation_sum)
+    using assms unfolding indicator_def by auto
+
+  moreover have " ... =
+    (\<Sum>i\<in> S.
+       measure_pmf.prob p {s. H i s = \<alpha>})"
+    by auto
+
+  moreover have "... = (\<Sum>i\<in>S. 1 / card R)"
+    using * by auto
+
+  ultimately show ?thesis by auto
+qed
+
+lemma (in prob_space) two_universal_indep_var:
+  assumes "k_universal 2 H D R"
+  assumes "w \<in> D" "w' \<in> D" "w \<noteq> w'"
+  shows "indep_var
+      borel
+      (\<lambda>x. indicat_real {w. H w x = \<alpha>} w)
+      borel
+      (\<lambda>x. indicat_real {w. H w x = \<alpha>} w')"
+proof -
+  have Y: "(\<lambda>z. (of_bool (z = \<alpha>))::real) \<in> (count_space UNIV) \<rightarrow>\<^sub>M borel"
+    by auto
+
+  have "k_wise_indep_vars  2
+     (\<lambda>_. count_space UNIV)
+     H D"
+    using assms
+    unfolding k_universal_def
+    by auto
+
+  then have "indep_vars (\<lambda>_. count_space UNIV) H {w, w'}"
+    unfolding k_wise_indep_vars_def
+    by (metis UNIV_bool assms(2) assms(3) card.empty card.insert card_UNIV_bool card_insert_le empty_iff empty_subsetI finite.emptyI finite.insertI insert_subset order.refl singletonD singleton_insert_inj_eq')
+
+  from indep_var_from_indep_vars[OF assms(4) this]
+  have "indep_var
+    (count_space UNIV) (H w)
+    (count_space UNIV) (H w')" .
+
+  from indep_var_compose[OF this Y Y]
+  show ?thesis
+    unfolding indicator_def
+    by (auto simp add: o_def)
+qed
+
+(* For h: D \<rightarrow> R, 2-universal, S \<subseteq> D.
+   V( | {w \<in> S. h w = \<alpha>} | ) \<le>  E( | {w \<in> S. h w = \<alpha>} | ) *)
+lemma two_universal_variance_bound:
+  assumes p: "finite (set_pmf p)"
+  assumes ind: "prob_space.k_universal (measure_pmf p) 2 H D R"
+  assumes S: "finite S" "S \<subseteq> D"
+  assumes a: "\<alpha> \<in> R"
+  shows
+  "measure_pmf.variance p
+    (\<lambda>s. real (card (S \<inter> {w. H w s = \<alpha>}))) \<le>
+  measure_pmf.expectation p
+    (\<lambda>s. real (card (S \<inter> {w. H w s = \<alpha>})))"
+proof -
+  have vb: "measure_pmf.variance p
+        (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)) \<le>
+    measure_pmf.expectation p
+        (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i))" for i
+  proof -
+    have "measure_pmf.variance p
+        (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)) =
+     measure_pmf.expectation p
+     (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)\<^sup>2) -
+    (measure_pmf.expectation p
+      (\<lambda>x. indicat_real {w. H w x = \<alpha>} i))\<^sup>2"
+      apply (subst measure_pmf.variance_eq)
+      by (auto simp add: p integrable_measure_pmf_finite)
+    moreover have "... \<le> measure_pmf.expectation p
+     (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)\<^sup>2)"
+      by simp
+    moreover have "... = measure_pmf.expectation p
+     (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i))"
+      by (metis (mono_tags, lifting) indicator_simps(1) indicator_simps(2) power2_eq_1_iff zero_eq_power2)
+    ultimately show ?thesis by linarith
+  qed
+
+  have "measure_pmf.variance p
+    (\<lambda>s. real (card (S \<inter> {w. H w s = \<alpha>}))) =
+    measure_pmf.variance p
+    (\<lambda>s. sum (indicat_real {w. H w s = \<alpha>}) S)"
+    unfolding card_inter_sum_indicat_real[OF S(1)]
+    by presburger
+
+  then have "... = (\<Sum>i\<in>S.
+       measure_pmf.variance p
+        (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)))"
+    apply (subst measure_pmf.var_sum_pairwise_indep)
+    using S prob_space_measure_pmf
+    by (auto intro!: prob_space.two_universal_indep_var[OF _ ind] simp add: p integrable_measure_pmf_finite)
+
+  moreover have "... \<le> (\<Sum>i\<in>S.
+       measure_pmf.expectation p
+        (\<lambda>x. (indicat_real {w. H w x = \<alpha>} i)))"
+    by (simp add: sum_mono vb)
+  moreover have "... = measure_pmf.expectation p
+    (\<lambda>s. sum (indicat_real {w. H w s = \<alpha>}) S)"
+    apply (subst finite_set_pmf_expectation_sum)
+    using assms by auto
+  ultimately show ?thesis
+    by (simp add: assms(3) card_inter_sum_indicat_real)
+qed
+
+lemma (in prob_space) k_universal_mono:
+  assumes "k' \<le> k"
+  assumes"k_universal k H D R"
+  shows"k_universal k' H D R"
+  using assms
+  unfolding k_universal_def k_wise_indep_vars_def
+  by auto
+
+lemma finite_set_pmf_expectation_add:
+  assumes "finite (set_pmf S)"
+  shows "measure_pmf.expectation S (\<lambda>x. ((f x)::real) + g x) =
+    measure_pmf.expectation S f + measure_pmf.expectation S g"
+  by (auto intro: Bochner_Integration.integral_add simp add: assms integrable_measure_pmf_finite)
+
+lemma finite_set_pmf_expectation_add_const:
+  assumes "finite (set_pmf S)"
+  shows "measure_pmf.expectation S (\<lambda>x. ((f x)::real) + g) =
+    measure_pmf.expectation S f + g"
+proof -
+  have "g = measure_pmf.expectation S (\<lambda>x. g)"
+    by simp
+  thus ?thesis
+    by (simp add: assms finite_set_pmf_expectation_add)
+qed
+
+lemma finite_set_pmf_expectation_diff:
+  assumes "finite (set_pmf S)"
+  shows "measure_pmf.expectation S (\<lambda>x. ((f x)::real) - g x) =
+    measure_pmf.expectation S f - measure_pmf.expectation S g"
+  by (auto intro: Bochner_Integration.integral_diff simp add: assms integrable_measure_pmf_finite)
+
+(* convenient forms of library inequalities *)
+lemma spec_paley_zygmund_inequality:
+  assumes fin: "finite (set_pmf p)"
+  assumes Zpos: "\<And>z. Z z \<ge> 0"
+  assumes t: "\<theta> \<le> 1"
+  shows "
+    (measure_pmf.variance p Z + (1-\<theta>)^2 * (measure_pmf.expectation p Z)^2) *
+    measure_pmf.prob p {z. Z z > \<theta> * measure_pmf.expectation p Z} \<ge>
+    (1-\<theta>)^2 * (measure_pmf.expectation p Z)^2"
+proof -
+  have "prob_space (measure_pmf p)" by (auto simp add: prob_space_measure_pmf)
+
+  from prob_space.paley_zygmund_inequality[OF this _ integrable_measure_pmf_finite[OF fin] t]
+  show ?thesis
+    using Zpos by auto
+qed
+
+lemma spec_chebyshev_inequality:
+  assumes fin: "finite (set_pmf p)"
+  assumes pvar: "measure_pmf.variance p Y > 0"
+  assumes k: "k > 0"
+  shows "
+    measure_pmf.prob p
+    {y. (Y y - measure_pmf.expectation p Y)^2 \<ge>
+       k^2 * measure_pmf.variance p Y} \<le> 1 / k^2"
+proof -
+  define f where
+    "f x = Y x / sqrt(measure_pmf.variance p Y)" for x
+  have 1:
+    "measure_pmf.random_variable p borel f"
+    by auto
+  have *: "(\<lambda>x. (f x)\<^sup>2) = (\<lambda>x. (Y x)\<^sup>2/ measure_pmf.variance p Y)"
+    unfolding f_def
+    by (simp add: power_divide)
+  have 2:
+    "integrable p (\<lambda>x. (f x)\<^sup>2)"
+    unfolding *
+    by (intro integrable_measure_pmf_finite[OF fin])
+  from
+    measure_pmf.Chebyshev_inequality[OF 1 2 k]
+  have ineq1:"measure_pmf.prob p
+   {x . k \<le> \<bar>f x - measure_pmf.expectation p f\<bar>}
+    \<le> measure_pmf.expectation p
+    (\<lambda>x. (f x - measure_pmf.expectation p f)\<^sup>2) / k\<^sup>2" by auto
+
+  have "(\<lambda>x. (f x - measure_pmf.expectation p f)\<^sup>2) =
+    (\<lambda>x. ((Y x - measure_pmf.expectation p Y) / sqrt(measure_pmf.variance p Y))\<^sup>2)"
+    unfolding f_def
+    by (simp add: diff_divide_distrib)
+
+  moreover have "... =  (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 / (sqrt(measure_pmf.variance p Y))^2)"
+    by (simp add: power_divide)
+  moreover have "... =  (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 / measure_pmf.variance p Y)"
+    by simp
+  ultimately have unfold:"(\<lambda>x. (f x - measure_pmf.expectation p f)\<^sup>2)
+                = (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 / measure_pmf.variance p Y)"
+    by auto
+  then have "measure_pmf.expectation p (\<lambda>x. (f x - measure_pmf.expectation p f)\<^sup>2) / k\<^sup>2
+    =  measure_pmf.expectation p (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 / measure_pmf.variance p Y) / k\<^sup>2"
+    by auto
+  moreover have "... = measure_pmf.variance p Y / measure_pmf.variance p Y / k\<^sup>2"
+    by simp
+  moreover have "... = 1 / k\<^sup>2"
+    using pvar by force
+  ultimately have eq1:"measure_pmf.expectation p (\<lambda>x. (f x - measure_pmf.expectation p f)\<^sup>2) / k\<^sup>2 = 1 / k\<^sup>2"
+    by auto
+  have "(\<lambda>x. k \<le> \<bar>f x - measure_pmf.expectation p f\<bar>) = (\<lambda>x. k\<^sup>2 \<le> (f x - measure_pmf.expectation p f)\<^sup>2)"
+    by (metis (no_types, opaque_lifting) abs_of_nonneg k less_le real_le_rsqrt real_sqrt_abs sqrt_ge_absD)
+  moreover have "... = (\<lambda>x. k\<^sup>2 \<le> ((Y x - measure_pmf.expectation p Y)^2 / measure_pmf.variance p Y))"
+    by (metis unfold)
+  moreover have "... = (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 \<ge> k\<^sup>2 * measure_pmf.variance p Y)"
+    by (simp add: pos_le_divide_eq pvar)
+  ultimately have cond:"(\<lambda>x. k \<le> \<bar>f x - measure_pmf.expectation p f\<bar>)
+                 = (\<lambda>x. (Y x - measure_pmf.expectation p Y)^2 \<ge> k\<^sup>2 * measure_pmf.variance p Y)"
+    by auto
+  show "?thesis" using ineq1 cond eq1
+    by auto
+qed
+
+end
diff --git a/thys/Approximate_Model_Counting/CertCheck.thy b/thys/Approximate_Model_Counting/CertCheck.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/CertCheck.thy
@@ -0,0 +1,1159 @@
+section \<open> Certificate-based ApproxMC \<close>
+
+text \<open> This turns the randomized algorithm into an
+  executable certificate checker \<close>
+
+theory CertCheck
+imports ApproxMCAnalysis
+
+begin
+
+subsection \<open> ApproxMC with lists instead of sets \<close>
+
+type_synonym 'a xor = "'a list \<times> bool"
+
+definition satisfies_xorL :: "'a xor \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"
+  where "satisfies_xorL xb \<omega> =
+    even (sum_list (map (of_bool \<circ> \<omega>) (fst xb)) +
+      of_bool (snd xb)::nat)"
+
+(* Extract a sublist based on bits *)
+definition sublist_bits::"'a list \<Rightarrow> bool list \<Rightarrow> 'a list"
+  where "sublist_bits ls bs =
+    map fst (filter snd (zip ls bs))"
+
+definition xor_from_bits::
+  "'a list \<Rightarrow> bool list \<times> bool \<Rightarrow> 'a xor"
+  where "xor_from_bits V xsb =
+    (sublist_bits V (fst xsb), snd xsb)"
+
+locale ApproxMCL =
+  fixes sols :: "'fml \<Rightarrow> ('a \<Rightarrow> bool) set"
+  fixes enc_xor :: "'a xor \<Rightarrow> 'fml \<Rightarrow> 'fml"
+  assumes sols_enc_xor:
+    "\<And>F xor.
+      sols (enc_xor xor F) =
+      sols F \<inter> {\<omega>. satisfies_xorL xor \<omega>}"
+begin
+
+definition list_of_set ::"'a set \<Rightarrow> 'a list"
+where "list_of_set x = (@ls. set ls = x \<and> distinct ls)"
+
+definition xor_conc :: "'a set \<times> bool \<Rightarrow> 'a xor"
+  where "xor_conc xsb = (list_of_set (fst xsb), snd xsb)"
+
+definition enc_xor_conc :: "'a set \<times> bool \<Rightarrow> 'fml \<Rightarrow> 'fml"
+  where "enc_xor_conc = enc_xor \<circ> xor_conc"
+
+lemma distinct_count_list:
+  assumes "distinct ls"
+  shows "count_list ls x = of_bool (x \<in> set ls)"
+  using assms
+  apply (induction ls)
+  by auto
+
+lemma list_of_set:
+  assumes "finite x"
+  shows "distinct (list_of_set x)" "set (list_of_set x) = x"
+  unfolding list_of_set_def
+  by (metis (mono_tags, lifting) assms finite_distinct_list someI_ex)+
+
+lemma count_list_list_of_set:
+  assumes "finite x"
+  shows "count_list (list_of_set x) y = of_bool (y \<in> x)"
+  apply (subst distinct_count_list)
+  using list_of_set[OF assms]
+  by auto
+
+lemma satisfies_xorL_xor_conc:
+  assumes "finite x"
+  shows"satisfies_xorL (xor_conc (x,b)) \<omega> \<longleftrightarrow> satisfies_xor (x,b) {x. \<omega> x}"
+  unfolding satisfies_xorL_def xor_conc_def
+  using list_of_set[OF assms]
+  by (auto simp add: sum_list_map_eq_sum_count count_list_list_of_set[OF assms] Int_ac(3) assms)
+
+sublocale appmc: ApproxMC sols enc_xor_conc
+  apply unfold_locales
+  unfolding enc_xor_conc_def o_def
+  apply (subst sols_enc_xor)
+  using satisfies_xorL_xor_conc by fastforce
+
+definition size_xorL ::"
+  'fml \<Rightarrow> 'a list \<Rightarrow>
+  (nat \<Rightarrow> bool list \<times> bool) \<Rightarrow>
+  nat \<Rightarrow> nat"
+  where "size_xorL F S xorsl i = (
+    let xors = map (xor_from_bits S \<circ> xorsl) [0..<i] in
+    let Fenc = fold enc_xor xors F in
+      card (proj (set S) (sols Fenc)))"
+
+definition check_xorL ::"
+  'fml \<Rightarrow> 'a list \<Rightarrow>
+  nat \<Rightarrow>
+  (nat \<Rightarrow> bool list \<times> bool) \<Rightarrow>
+  nat \<Rightarrow> bool"
+  where "check_xorL F S thresh xorsl i =
+  (size_xorL F S xorsl i < thresh)"
+
+definition approxcore_xorsL :: "
+  'fml \<Rightarrow> 'a list \<Rightarrow>
+  nat \<Rightarrow>
+  (nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow>
+  nat"
+  where "
+    approxcore_xorsL F S thresh xorsl =
+    (case List.find
+      (check_xorL F S thresh xorsl) [1..<length S] of
+      None \<Rightarrow> 2 ^ length S
+    | Some m \<Rightarrow>
+      (2 ^ m * size_xorL F S xorsl m))"
+
+definition xor_abs :: "'a xor \<Rightarrow> 'a set \<times> bool"
+  where "xor_abs xsb = (set (fst xsb), snd xsb)"
+
+lemma sols_fold_enc_xor:
+  assumes "list_all2 (\<lambda>x y.
+    \<forall>w. satisfies_xorL x w = satisfies_xorL y w) xs ys"
+  assumes "sols F = sols G"
+  shows "sols (fold enc_xor xs F) = sols (fold enc_xor ys G)"
+  using assms
+proof (induction xs arbitrary: ys F G)
+  case Nil
+  then show ?case
+    by auto
+  next
+  case (Cons x xss)
+  then obtain y yss where ys: "ys = y#yss"
+  by (meson list_all2_Cons1)
+  have all2: "\<forall>w. satisfies_xorL x w = satisfies_xorL y w"
+    using Cons.prems(1) ys by blast
+  have *: "sols (enc_xor x F) = sols (enc_xor y G)"
+    apply (subst sols_enc_xor)
+    using all2 local.Cons(3) sols_enc_xor by presburger
+  then show ?case unfolding ys
+  using "*" Cons.IH Cons.prems(2) local.Cons(2) local.Cons(3) ys by auto
+qed
+
+lemma satisfies_xor_xor_abs:
+  assumes "distinct x"
+  shows"satisfies_xor (xor_abs (x,b)) {x. \<omega> x} \<longleftrightarrow> satisfies_xorL (x,b) \<omega>"
+  unfolding satisfies_xorL_def xor_abs_def
+  apply (clarsimp simp add: sum_list_map_eq_sum_count)
+  by (smt (verit, ccfv_SIG) IntD1 Int_commute assms card_eq_sum distinct_count_list of_bool_eq(2) sum.cong)
+
+lemma xor_conc_xor_abs_rel:
+  assumes "distinct (fst x)"
+  shows"satisfies_xorL (xor_conc (xor_abs x)) w \<longleftrightarrow>
+    satisfies_xorL x w"
+  unfolding xor_abs_def
+  apply (subst satisfies_xorL_xor_conc)
+  subgoal by (simp add: xor_abs_def[symmetric])
+  using assms satisfies_xor_xor_abs xor_abs_def by auto
+
+lemma sorted_sublist_bits:
+  assumes "sorted V"
+  shows"sorted (sublist_bits V bs)"
+  unfolding sublist_bits_def
+  using assms
+  by (auto intro!: sorted_filter sorted_wrt_take simp add: map_fst_zip_take)
+
+lemma distinct_sublist_bits:
+  assumes "distinct V"
+  shows"distinct (sublist_bits V bs)"
+  unfolding sublist_bits_def
+  using assms
+  by (auto intro!: distinct_map_filter simp add: map_fst_zip_take)
+
+lemma distinct_fst_xor_from_bits:
+  assumes "distinct V"
+  shows"distinct (fst (xor_from_bits V bs))"
+  unfolding xor_from_bits_def
+  using distinct_sublist_bits[OF assms]
+  by auto
+
+lemma size_xorL:
+  assumes "\<And>j. j < i \<Longrightarrow>
+    xorsf j =
+    Some (xor_abs (xor_from_bits S (xorsl j)))"
+  assumes "distinct S"
+  shows "size_xorL F S xorsl i =
+    appmc.size_xor F (set S) xorsf i"
+  unfolding appmc.size_xor_def size_xorL_def
+  apply (clarsimp simp add: enc_xor_conc_def fold_map[symmetric])
+  apply (intro arg_cong[where f = "(\<lambda>x. card (proj (set S) x))"])
+  apply (intro sols_fold_enc_xor)
+  by (auto simp add: list_all2_map1 list_all2_map2 list_all2_same assms(1) assms(2) distinct_fst_xor_from_bits xor_conc_xor_abs_rel)
+
+lemma fold_enc_xor_more:
+  assumes "x \<in> sols (fold enc_xor (xs @ rev ys) F)"
+  shows "x \<in> sols (fold enc_xor xs F)"
+  using assms
+proof (induction ys arbitrary: F)
+  case Nil
+  then show ?case
+    by auto
+next
+  case ih: (Cons y ys)
+  show ?case
+    using ih by (auto simp add: ih.prems(1) sols_enc_xor)
+qed
+
+lemma size_xorL_anti_mono:
+  assumes "x \<le> y" "distinct S"
+  shows "size_xorL F S xorsl x \<ge> size_xorL F S xorsl y"
+proof -
+  obtain ys where ys: "[0..<y] = [0..<x] @ ys" "distinct ys"
+  by (metis assms(1) bot_nat_0.extremum distinct_upt ordered_cancel_comm_monoid_diff_class.add_diff_inverse upt_add_eq_append)
+
+  define rys where"rys = (rev (map (xor_from_bits S \<circ> xorsl) ys))"
+  have *: "\<And>y. y \<in> set rys \<Longrightarrow> distinct (fst y)"
+    unfolding rys_def
+    using assms(2) distinct_fst_xor_from_bits
+    by (metis (no_types, opaque_lifting) ex_map_conv o_apply set_rev)
+
+  show ?thesis
+    unfolding size_xorL_def Let_def
+  apply (intro card_mono proj_mono)
+  subgoal using card_proj(1) by blast
+  unfolding ys
+  by (metis fold_enc_xor_more map_append rev_rev_ident subsetI)
+qed
+
+lemma find_upto_SomeI:
+  assumes "\<And>i. a \<le> i \<Longrightarrow> i < x \<Longrightarrow> \<not>P i"
+  assumes "P x" "a \<le> x" "x < b"
+  shows "find P [a..<b] = Some x"
+proof -
+  have x: "[a..<b] ! (x-a) = x"
+    by (simp add: assms(3) assms(4))
+  have j: "\<And>j. j<x-a \<Longrightarrow> \<not> P ([a..<b] ! j)"
+    using assms(1) assms(4) by auto
+  show ?thesis
+  unfolding find_Some_iff
+  using x j
+  by (metis assms(2) assms(3) assms(4) diff_less_mono length_upt)
+qed
+
+lemma check_xorL:
+  assumes "\<And>j. j < i \<Longrightarrow>
+    xorsf j =
+    Some (xor_abs (xor_from_bits S (xorsl j)))"
+  assumes "distinct S"
+  shows "check_xorL F S thresh xorsl i =
+    appmc.check_xor F (set S) thresh xorsf i"
+  unfolding appmc.check_xor_def check_xorL_def
+  using size_xorL[OF assms] by presburger
+
+lemma approxcore_xorsL:
+  assumes "\<And>j. j < length S - 1  \<Longrightarrow>
+    xorsf j =
+    Some (xor_abs (xor_from_bits S (xorsl j)))"
+  assumes S: "distinct S"
+  shows "approxcore_xorsL F S thresh xorsl =
+    appmc.approxcore_xors F (set S) thresh xorsf"
+proof -
+  have c:"card (set S) = length S" using S
+  by (simp add: distinct_card)
+
+  have *: "find (check_xorL F S thresh xorsl) [1..<length S] =
+   find (appmc.check_xor F (set S) thresh xorsf) [1..<card (set S)]"
+    unfolding c
+    by (auto intro!: find_cong check_xorL[OF assms(1) S])
+
+  have **: "find (appmc.check_xor F
+                  (set S) thresh xorsf)
+            [Suc 0..<length S] =
+           Some a \<Longrightarrow>
+           j < a \<Longrightarrow>
+           xorsf j =
+           Some
+            (xor_abs
+              (xor_from_bits S
+                (xorsl j)))" for a j
+    unfolding find_Some_iff
+    by (auto simp add: assms(1))
+  show ?thesis
+  unfolding appmc.approxcore_xors_def approxcore_xorsL_def * c
+  apply (cases "find (appmc.check_xor F (set S) thresh xorsf)
+           [Suc 0..<length S]")
+  subgoal by clarsimp
+  by (auto intro!: ApproxMCL.size_xorL simp add: ApproxMCL_axioms assms **)
+qed
+
+definition approxmc_mapL::"
+  'fml \<Rightarrow> 'a list \<Rightarrow>
+  real \<Rightarrow> real \<Rightarrow> nat \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow>
+  nat"
+  where "approxmc_mapL F S \<epsilon> \<delta> n xorsLs = (
+    let \<epsilon> = appmc.mk_eps \<epsilon> in
+    let thresh = appmc.compute_thresh \<epsilon> in
+    if card (proj (set S) (sols F)) < thresh then
+      card (proj (set S) (sols F))
+    else
+      let t = appmc.compute_t \<delta> n in
+      median t (approxcore_xorsL F S thresh \<circ> xorsLs))"
+
+definition random_xorB :: "nat \<Rightarrow> (bool list \<times> bool) pmf"
+  where "random_xorB n =
+    pair_pmf
+      (replicate_pmf n (bernoulli_pmf (1/2)))
+      (bernoulli_pmf (1/2))"
+
+(* Actually, we can restrict i too *)
+lemma approxmc_mapL:
+  assumes "\<And>i j. j < length S - 1 \<Longrightarrow>
+    xorsFs i j =
+    Some (xor_abs (xor_from_bits S (xorsLs i j)))"
+  assumes S: "distinct S"
+  shows "
+    approxmc_mapL F S \<epsilon> \<delta> n xorsLs =
+    appmc.approxmc_map F (set S) \<epsilon> \<delta> n xorsFs"
+proof -
+  show ?thesis
+    unfolding approxmc_mapL_def appmc.approxmc_map_def Let_def
+    using assms by (auto intro!: median_cong approxcore_xorsL)
+qed
+
+lemma approxmc_mapL':
+  assumes S: "distinct S"
+  shows "
+    approxmc_mapL F S \<epsilon> \<delta> n xorsLs =
+    appmc.approxmc_map F (set S) \<epsilon> \<delta> n
+      (\<lambda>i j. if j < length S - 1
+         then Some (xor_abs (xor_from_bits S (xorsLs i j)))
+         else None)"
+  apply (intro approxmc_mapL)
+  using assms by auto
+
+lemma bits_to_random_xor:
+  assumes "distinct S"
+  shows "map_pmf
+    (\<lambda>x. xor_abs (xor_from_bits S x))
+    (random_xorB (length S)) =
+    random_xor (set S)"
+proof -
+  have "xor_abs (xor_from_bits S (a,b)) = apfst (set \<circ> sublist_bits S) (a,b)" for a b
+   using xor_abs_def by (auto simp add: xor_from_bits_def)
+
+  then have *: "(\<lambda>x. xor_abs (xor_from_bits S x)) = apfst (set \<circ> sublist_bits S)"
+    by auto
+
+  have "\<And>x. x \<in> set S \<Longrightarrow>
+         z x \<Longrightarrow>
+         \<exists>b. (\<exists>n. S ! n = x \<and>
+                  map z S ! n = b \<and>
+                  n < length S) \<and> b" for z
+    by (metis assms distinct_Ex1 nth_map)
+
+  then have " set (map fst
+               (filter snd
+                 (zip S (map z S)))) =
+         {x \<in> set S. Some (z x) = Some True}" for z
+    by (auto elim: in_set_zipE simp add: in_set_zip image_def )
+
+  then have **: "map_pmf (set \<circ> sublist_bits S)
+       (replicate_pmf (length S) (bernoulli_pmf (1 / 2))) =
+    map_pmf (\<lambda>b. {x \<in> set S. b x = Some True})
+       (Pi_pmf (set S) (Some undefined)
+         (\<lambda>_. map_pmf Some (bernoulli_pmf (1 / 2))))"
+    apply (subst replicate_pmf_Pi_pmf[OF assms, where def = "undefined"])
+    apply (subst Pi_pmf_map[of _  _ "undefined"])
+    subgoal by (auto intro!: pmf.map_cong0 simp add: map_pmf_comp sublist_bits_def)
+    subgoal by (meson set_zip_leftD)
+    unfolding map_pmf_comp sublist_bits_def o_def
+    by (auto intro!: pmf.map_cong0)
+
+  show ?thesis
+    unfolding random_xorB_def
+    apply (subst random_xor_from_bits)
+    by (auto simp add: * ** pair_map_pmf1[symmetric])
+qed
+
+lemma Pi_pmf_map_pmf_Some:
+  assumes "finite S"
+  shows "Pi_pmf S None (\<lambda>_. map_pmf Some p) =
+    map_pmf (\<lambda>f v. if v \<in> S then Some (f v) else None)
+    (Pi_pmf S def (\<lambda>_. p))"
+proof -
+  have *: "Pi_pmf S None (\<lambda>_. map_pmf Some p) =
+    map_pmf (\<lambda>f x. if x \<in> S then f x else None)
+    (Pi_pmf S (Some def) (\<lambda>_. map_pmf Some p))"
+    apply (subst Pi_pmf_default_swap[OF assms])
+      by auto
+
+  show ?thesis unfolding *
+    apply (subst Pi_pmf_map[OF assms, of  _ def])
+    subgoal by simp
+    apply (simp add: map_pmf_comp o_def )
+    by (metis comp_eq_dest_lhs)
+qed
+
+lemma bits_to_random_xors:
+  assumes "distinct S"
+  shows "
+    map_pmf
+    (\<lambda>f j.
+      if j < n
+      then Some (xor_abs (xor_from_bits S (f j)))
+      else None)
+    (Pi_pmf {..<(n::nat)} def (\<lambda>_. random_xorB (length S))) =
+    random_xors (set S) n"
+  unfolding random_xors_def
+  apply (subst Pi_pmf_map_pmf_Some)
+  subgoal using assms by simp
+  apply (subst bits_to_random_xor[symmetric, OF assms])
+  apply (subst Pi_pmf_map[where dflt = "def", where dflt'="xor_abs (xor_from_bits S def)"])
+  subgoal by simp
+  subgoal by simp
+  apply (clarsimp simp add: map_pmf_comp o_def)
+  by (metis o_apply)
+
+lemma bits_to_all_random_xors:
+  assumes "distinct S"
+  assumes "(\<lambda>j. if j < n
+          then Some (xor_abs (xor_from_bits S (def1 j)))
+          else None) = def"
+  shows "
+    map_pmf
+    ((\<circ>) (\<lambda>f j. if j < n
+                 then Some (xor_abs (xor_from_bits S (f j)))
+                 else None))
+    (Pi_pmf {0..<(m::nat)} def1
+      (\<lambda>_.
+        Pi_pmf {..<(n::nat)} def2 (\<lambda>_. random_xorB (length S)))) =
+    Pi_pmf {0..<m} def
+         (\<lambda>i. random_xors (set S) n)"
+  apply (subst bits_to_random_xors[symmetric, OF assms(1), of _ "def2"])
+  apply (subst Pi_pmf_map[OF _])
+  using assms(2) by auto
+
+(* Sample t * (l-1) * l XORs *)
+definition random_seed_xors::"nat \<Rightarrow> nat \<Rightarrow> (nat \<Rightarrow> nat \<Rightarrow> bool list \<times> bool) pmf"
+  where "random_seed_xors t l =
+    (prod_pmf {0..<t}
+      (\<lambda>_. prod_pmf {..<l-1} (\<lambda>_. random_xorB l)))"
+
+lemma approxmcL_sound:
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes S: "distinct S"
+  shows "
+    prob_space.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (random_seed_xors (appmc.compute_t \<delta> n) (length S)))
+      {c. real c \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}}
+      \<ge> 1 - \<delta>"
+proof -
+  define def where "def =
+      (\<lambda>j. if j < degree S
+          then Some (xor_abs (xor_from_bits S (undefined j)))
+          else None)"
+  have *: "(map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (Pi_pmf {0..<appmc.compute_t \<delta> n} undefined
+           (\<lambda>_. Pi_pmf {..<length S - 1} undefined
+            (\<lambda>_. random_xorB (length S))))) =
+     (map_pmf (appmc.approxmc_map F (set S) \<epsilon> \<delta> n)
+      (map_pmf ((\<circ>) (\<lambda>f.
+          (\<lambda>j. if j < length S - 1
+                 then Some (xor_abs (xor_from_bits S (f j)))
+                 else None)))
+       (Pi_pmf {0..<appmc.compute_t \<delta> n} undefined
+         (\<lambda>_. Pi_pmf {..<length S - 1} undefined
+                (\<lambda>_. random_xorB (length S))))))"
+    unfolding approxmc_mapL'[OF S]
+    by (simp add: map_pmf_comp o_def)
+  have **: "
+    (map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (Pi_pmf {0..<appmc.compute_t \<delta> n} undefined
+           (\<lambda>_. Pi_pmf {..<length S - 1} undefined
+            (\<lambda>_. random_xorB (length S))))) =
+    map_pmf (appmc.approxmc_map F (set S) \<epsilon> \<delta> n)
+     (Pi_pmf {0..<appmc.compute_t \<delta> n} def
+       (\<lambda>i. random_xors (set S) (card (set S) - 1)))"
+    unfolding *
+    apply (subst bits_to_all_random_xors[OF S])
+    using def_def
+    by (auto simp add: assms(4) distinct_card)
+  show ?thesis
+    unfolding ** appmc.approxmc_map_eq random_seed_xors_def
+    using \<delta>(2) \<epsilon> appmc.approxmc'_sound assms(1) by blast
+qed
+
+(* This is more convenient for stating what happens when
+  certification returns the "wrong" result *)
+lemma approxmcL_sound':
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes S: "distinct S"
+  shows "
+    prob_space.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (random_seed_xors (appmc.compute_t \<delta> n) (length S)))
+      {c. real c \<notin>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<le> \<delta>"
+proof -
+  have "prob_space.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (Pi_pmf {0..<appmc.compute_t \<delta> n} undefined
+           (\<lambda>_. Pi_pmf {..<length S - 1} undefined
+            (\<lambda>_. random_xorB (length S)))))
+      {c. real c \<notin>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} =
+    1 - prob_space.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> n)
+        (Pi_pmf {0..<appmc.compute_t \<delta> n} undefined
+           (\<lambda>_. Pi_pmf {..<length S - 1} undefined
+            (\<lambda>_. random_xorB (length S)))))
+      {c. real c \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}}"
+    apply (subst measure_pmf.prob_compl[symmetric])
+    by (auto simp add: vimage_def)
+  thus ?thesis using approxmcL_sound[OF assms, of "F" "n"] \<delta>
+    unfolding random_seed_xors_def
+    by linarith
+qed
+
+end
+
+subsection \<open> ApproxMC certificate checker \<close>
+
+(* Helper functions *)
+definition str_of_bool :: "bool \<Rightarrow> String.literal"
+  where "str_of_bool b = (
+  if b then STR ''true'' else STR ''false'')"
+
+fun str_of_nat_aux :: "nat \<Rightarrow> char list \<Rightarrow> char list"
+  where "str_of_nat_aux n acc = (
+  let c = char_of_integer (of_nat (48 + n mod 10)) in
+  if n < 10 then c # acc
+  else str_of_nat_aux (n div 10) (c # acc))"
+
+definition str_of_nat :: "nat \<Rightarrow> String.literal"
+  where "str_of_nat n = String.implode (str_of_nat_aux n [])"
+
+type_synonym 'a sol = "('a \<times> bool) list"
+
+(* The canonical assignment specified by a list *)
+definition canon_map_of :: "('a \<times> bool) list \<Rightarrow> ('a \<Rightarrow> bool)"
+  where "canon_map_of ls =
+    (let m = map_of ls in
+    (\<lambda>x. case m x of None \<Rightarrow> False | Some b \<Rightarrow> b))"
+
+(* The canonical assignment specified by a list *)
+lemma canon_map_of[code]:
+  shows "canon_map_of ls =
+    (let m = Mapping.of_alist ls in
+     Mapping.lookup_default False m)"
+  unfolding canon_map_of_def lookup_default_def
+  by (auto simp add: lookup_of_alist)
+
+definition proj_sol :: "'a list \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool list"
+  where "proj_sol S w = map w S"
+
+text \<open> The following extended locale assumes
+  additional support for syntactically working with solutions \<close>
+locale CertCheck = ApproxMCL sols enc_xor
+  for sols :: "'fml \<Rightarrow> ('a \<Rightarrow> bool) set"
+  and enc_xor :: "'a list \<times> bool \<Rightarrow> 'fml \<Rightarrow> 'fml" +
+  fixes check_sol :: "'fml \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool"
+  fixes ban_sol :: "'a sol \<Rightarrow> 'fml \<Rightarrow> 'fml"
+  assumes sols_ban_sol:
+    "\<And>F vs.
+      sols (ban_sol vs F) =
+      sols F \<inter> {\<omega>. map \<omega> (map fst vs) \<noteq> map snd vs}"
+  assumes check_sol:
+    "\<And>F w. check_sol F w \<longleftrightarrow> w \<in> sols F"
+begin
+
+text \<open> Assuming parameter access to an UNSAT checking oracle \<close>
+context
+  fixes check_unsat :: "'fml \<Rightarrow> bool"
+begin
+
+text \<open> Throughout this checker, INL indicates error, INR indicates success \<close>
+
+definition check_BSAT_sols::"
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow> ('a \<Rightarrow> bool) list \<Rightarrow> String.literal + unit"
+where "check_BSAT_sols F S thresh cms = (
+  let ps = map (proj_sol S) cms in
+  let b1 = list_all (check_sol F) cms in
+  let b2 = distinct ps in
+  let b3 =
+    (length cms < thresh \<longrightarrow>
+      check_unsat (fold ban_sol (map (zip S) ps) F)) in
+    if b1 \<and> b2 \<and> b3 then Inr ()
+    else Inl (STR  ''checks ---'' +
+      STR '' all valid sols: '' + str_of_bool b1 +
+      STR '', all distinct sols: '' + str_of_bool b2 +
+      STR '', unsat check (< thresh sols): '' + str_of_bool b3)
+  )"
+
+definition BSAT ::"
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow> ('a \<Rightarrow> bool) list \<Rightarrow> String.literal + nat"
+where "BSAT F S thresh xs = (
+  case check_BSAT_sols F S thresh xs of
+    Inl err \<Rightarrow> Inl err
+  | Inr _ \<Rightarrow> Inr (length xs)
+)"
+
+(* A size certificate is simply a list of solutions*)
+definition size_xorL_cert :: "
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow>
+  (nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow> nat \<Rightarrow>
+  (('a \<Rightarrow> bool) list) \<Rightarrow> String.literal + nat"
+  where "size_xorL_cert F S thresh xorsl i xs = (
+    let xors = map (xor_from_bits S \<circ> xorsl) [0..<i]  in
+    let Fenc = fold enc_xor xors F in
+    BSAT Fenc S thresh xs
+  )"
+
+(* Checks whether the value of m is an appropriate value
+  Especially in the case where 1 \<le> m \<le> |S|-1 *)
+fun approxcore_xorsL_cert :: "
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow>
+  nat \<times> ('a \<Rightarrow> bool) list \<times> ('a \<Rightarrow> bool) list \<Rightarrow>
+  (nat \<Rightarrow> (bool list \<times> bool))
+  \<Rightarrow> String.literal + nat"
+where "approxcore_xorsL_cert F S thresh (m,cert1,cert2) xorsl = (
+  if 1 \<le> m \<and> m \<le> length S
+  then
+    case size_xorL_cert F S thresh xorsl (m-1) cert1 of
+      Inl err \<Rightarrow> Inl (STR ''cert1 '' + err)
+    | Inr n \<Rightarrow>
+    if n \<ge> thresh
+    then
+      if m = length S
+      then Inr (2 ^ length S)
+      else
+        case size_xorL_cert F S thresh xorsl m cert2 of
+          Inl err \<Rightarrow> Inl (STR ''cert2 '' + err)
+        | Inr c \<Rightarrow>
+          if c < thresh then Inr (2 ^ m * c)
+          else Inl (STR ''too many solutions at m added XORs'')
+    else Inl (STR ''too few solutions at m-1 added XORs'')
+  else
+     Inl (STR ''invalid value of m, need 1 <= m <= |S|''))"
+
+(* Compute the correct choice of n up to a bound arbitrarily set to 256 for now *)
+definition find_t :: "real \<Rightarrow> nat"
+where "find_t \<delta> = (
+  case find (\<lambda>i. appmc.raw_median_bound 0.14 i < \<delta>) [0..<256] of
+    Some m \<Rightarrow> m
+  | None \<Rightarrow> appmc.fix_t \<delta>
+  )"
+
+fun fold_approxcore_xorsL_cert:: "
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow>
+  nat \<Rightarrow> nat \<Rightarrow>
+  (nat \<Rightarrow> (nat \<times> ('a \<Rightarrow> bool) list \<times> ('a \<Rightarrow> bool) list)) \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> (bool list \<times> bool))
+  \<Rightarrow> String.literal + (nat list)"
+  where
+  "fold_approxcore_xorsL_cert F S thresh t 0 cs xorsLs = Inr []"
+| "fold_approxcore_xorsL_cert F S thresh t (Suc i) cs xorsLs = (
+    let it = t - Suc i in
+    case approxcore_xorsL_cert F S thresh (cs it) (xorsLs it) of
+      Inl err \<Rightarrow> Inl (STR ''round '' + str_of_nat it + STR '' '' + err)
+    | Inr n \<Rightarrow>
+      (case fold_approxcore_xorsL_cert F S thresh t i cs xorsLs of
+          Inl err \<Rightarrow> Inl err
+        | Inr ns \<Rightarrow> Inr (n # ns)))"
+
+definition calc_median::"
+  'fml \<Rightarrow> 'a list \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow>
+  (nat \<Rightarrow> (nat \<times> ('a \<Rightarrow> bool) list \<times> ('a \<Rightarrow> bool) list)) \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow>
+  String.literal + nat"
+  where "calc_median F S thresh t ms xorsLs = (
+      case fold_approxcore_xorsL_cert F S thresh t t ms xorsLs of
+        Inl err \<Rightarrow> Inl err
+      | Inr ls \<Rightarrow> Inr (sort ls ! (t div 2))
+  )"
+
+fun certcheck::"
+  'fml \<Rightarrow> 'a list \<Rightarrow>
+  real \<Rightarrow> real \<Rightarrow>
+  (('a \<Rightarrow> bool) list \<times>
+  (nat \<Rightarrow> (nat \<times> ('a \<Rightarrow> bool) list \<times> ('a \<Rightarrow> bool) list))) \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow>
+  String.literal + nat"
+  where "certcheck F S \<epsilon> \<delta> (m0,ms) xorsLs = (
+    let \<epsilon> = appmc.mk_eps \<epsilon> in
+    let thresh = appmc.compute_thresh \<epsilon> in
+    case BSAT F S thresh m0 of Inl err \<Rightarrow> Inl err
+    | Inr Y \<Rightarrow>
+    if Y < thresh then Inr Y
+    else
+      let t = find_t \<delta> in
+      calc_median F S thresh t ms xorsLs)"
+
+(* The correctness property for BSAT oracle calls that
+   will be certified externally through proof logging *)
+context
+  assumes check_unsat: "\<And>F. check_unsat F \<Longrightarrow> sols F = {}"
+begin
+
+lemma sols_fold_ban_sol:
+  shows"sols (fold ban_sol ls F) =
+  sols F \<inter> {\<omega>. (\<forall>vs \<in> set ls. map \<omega> (map fst vs) \<noteq> map snd vs)}"
+proof (induction ls arbitrary: F)
+  case Nil
+  then show ?case by auto
+next
+  case (Cons vs ls)
+  show ?case
+    using Cons(1) sols_ban_sol
+    by auto
+qed
+
+lemma inter_cong_right:
+  assumes "\<And>x. x \<in> A \<Longrightarrow> x \<in> B \<longleftrightarrow> x \<in> C"
+  shows "A \<inter> B = A \<inter> C"
+  using assms by auto
+
+lemma proj_sol_canon_map_of:
+  assumes "distinct S" "length S = length w"
+  shows "proj_sol S (canon_map_of (zip S w)) = w"
+  using assms
+  unfolding proj_sol_def canon_map_of_def
+proof (induction w arbitrary: S)
+  case Nil
+  then show ?case
+    by auto
+next
+  case (Cons a w)
+  obtain s ss where ss: "S = s # ss"
+    by (metis Cons.prems(2) Suc_le_length_iff order.refl)
+  then show ?case
+    apply clarsimp
+    by (smt (z3) Cons.IH Cons.prems(2) add.right_neutral add_Suc_right distinct.simps(2) list.size(4) local.Cons(2) map_eq_conv nat.inject)
+qed
+
+lemma proj_sol_cong:
+  assumes "restr (set S) A = restr (set S) B"
+  shows "proj_sol S A = proj_sol S B"
+  using assms
+  unfolding proj_sol_def restr_def map_eq_conv
+  by (metis option.simps(1))
+
+lemma canon_map_of_map_of:
+  assumes "length S = length x"
+  assumes "canon_map_of (zip S x) \<in> A"
+  shows "map_of (zip S x) \<in> proj (set S) A"
+proof -
+  define f where "f = (\<lambda>xa. case map_of (zip S x) xa of
+           None \<Rightarrow> False | Some b \<Rightarrow> b)"
+  have "map_of (zip S x) =
+       (\<lambda>y. if y \<in> set S then Some (f y) else None)"
+    unfolding f_def fun_eq_iff
+    using map_of_zip_is_Some[OF assms(1)]
+    by (metis option.case_eq_if option.distinct(1) option.exhaust option.sel)
+  thus ?thesis
+  using assms unfolding canon_map_of_def ApproxMCCore.proj_def restr_def image_def
+  using f_def by auto
+qed
+
+lemma proj_proj_sol_map_of_zip_1:
+  assumes "distinct S" "length S = length w"
+  assumes w: "w \<in> rdb"
+  shows "
+    map_of (zip S w) \<in>
+    proj (set S) {\<omega>. proj_sol S \<omega> \<in> rdb}"
+  apply (intro canon_map_of_map_of[OF assms(2)])
+  using proj_sol_canon_map_of[OF assms(1-2)] w by auto
+
+lemma proj_proj_sol_map_of_zip_2:
+  assumes "\<And>bs. bs \<in> rdb \<Longrightarrow> length bs = length S"
+  assumes w: "w \<in> proj (set S) {\<omega>. proj_sol S \<omega> \<in> rdb}"
+  shows "
+    w \<in> (map_of \<circ> zip S) ` rdb"
+proof -
+  obtain ww where ww: "proj_sol S ww \<in> rdb" "w = restr (set S) ww"
+  using w unfolding ApproxMCCore.proj_def
+  by auto
+
+  have "w = map_of (zip S (proj_sol S ww))"
+    unfolding ww restr_def proj_sol_def map_of_zip_map
+    by auto
+
+  thus ?thesis using ww
+  by (auto simp add: image_def)
+qed
+
+lemma proj_proj_sol_map_of_zip:
+  assumes "distinct S"
+  assumes "\<And>bs. bs \<in> rdb \<Longrightarrow> length bs = length S"
+  shows "
+    proj (set S) {\<omega>. proj_sol S \<omega> \<in> rdb} =
+    (map_of \<circ> zip S) ` rdb"
+  apply (rule antisym)
+  subgoal
+    using proj_proj_sol_map_of_zip_2[OF assms(2)]
+    by blast
+  using assms(2)
+  by (auto intro!: proj_proj_sol_map_of_zip_1[OF assms(1)])
+
+definition ban_proj_sol ::"'a list \<Rightarrow> ('a \<Rightarrow> bool) list \<Rightarrow> 'fml \<Rightarrow> 'fml"
+where "ban_proj_sol S xs F =
+    fold ban_sol (map (zip S \<circ> proj_sol S) xs) F"
+
+lemma check_sol_imp_proj:
+  assumes "w \<in> sols F"
+  shows "map_of (zip S (proj_sol S w)) \<in> proj (set S) (sols F)"
+  unfolding proj_sol_def map_of_zip_map ApproxMCCore.proj_def image_def restr_def
+  using assms by auto
+
+lemma checked_BSAT_lower:
+  assumes S: "distinct S"
+  assumes "check_BSAT_sols F S thresh xs = Inr ()"
+  shows "length xs \<le> card (proj (set S) (sols F))"
+  "length xs < thresh \<Longrightarrow>
+    card (proj (set S) (sols F)) = length xs"
+proof -
+  define Sxs where "Sxs = map (proj_sol S) xs"
+  have dSxs: "distinct Sxs"
+    using assms unfolding Sxs_def check_BSAT_sols_def Let_def
+    by (auto split: if_splits)
+
+  have lSxs: "\<And>x. x \<in> set Sxs \<Longrightarrow> length x = length S"
+    unfolding Sxs_def proj_sol_def by auto
+  define SSxs where "SSxs = map (zip S) Sxs"
+  have dSSxs: "distinct (map map_of SSxs)"
+    unfolding SSxs_def
+    using dSxs unfolding inj_on_def distinct_map
+    by (smt (verit) assms(1) imageE lSxs list.set_map map_of_zip_inject)
+
+  have *: "set (map map_of SSxs) \<subseteq> proj (set S) (sols F)"
+    unfolding Sxs_def SSxs_def
+    using assms unfolding check_BSAT_sols_def Let_def
+    by (auto intro!: check_sol_imp_proj split: if_splits simp add: check_sol list_all_iff)
+  have "length xs = card (set (map map_of SSxs))"
+    by (metis SSxs_def Sxs_def dSSxs length_map length_remdups_card_conv remdups_id_iff_distinct)
+
+  thus "length xs \<le> card (proj (set S) (sols F))"
+    by (metis * List.finite_set card_mono card_proj(1))
+
+  have frr1: "(\<forall>vs \<in> set SSxs. map \<omega> (map fst vs) \<noteq> map snd vs) \<Longrightarrow>
+    (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)" for \<omega>
+    apply (clarsimp simp add: proj_sol_def SSxs_def)
+    by (metis (mono_tags, lifting) in_set_zip nth_map)
+  have frr2: "(\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs) \<Longrightarrow>
+    (vs \<in> set SSxs \<Longrightarrow> map \<omega> (map fst vs) \<noteq> map snd vs)" for vs \<omega>
+    apply (clarsimp simp add: proj_sol_def SSxs_def)
+    by (smt (z3) Sxs_def assms(1) length_map length_map length_map map_eq_conv map_fst_zip map_of_zip_inject mem_Collect_eq nth_map nth_map nth_map proj_sol_def set_conv_nth set_conv_nth zip_map_fst_snd)
+
+  have frr: "{\<omega>. (\<forall>vs \<in> set SSxs. map \<omega> (map fst vs) \<noteq> map snd vs)} =
+    {\<omega>. (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)}"
+    using frr1 frr2 by auto
+
+  moreover {
+    assume "length xs < thresh"
+    then have "sols (ban_proj_sol S xs F) = {}"
+      apply (intro check_unsat)
+      using assms(2) unfolding check_BSAT_sols_def Let_def
+      by (auto simp add:ban_proj_sol_def o_assoc split: if_splits)
+
+    then have "sols F \<inter> {\<omega>. (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)} = {}"
+      unfolding ban_proj_sol_def sols_fold_ban_sol
+      frr[symmetric]
+      by (auto simp add: SSxs_def Sxs_def)
+    then have 1:"proj (set S) (sols F) \<inter>
+      proj (set S)
+       {\<omega>. \<forall>vs\<in>set Sxs. proj_sol S \<omega> \<noteq> vs} = {}"
+      unfolding ApproxMCCore.proj_def
+      using proj_sol_cong
+      by (smt (verit, del_insts) disjoint_iff_not_equal image_iff mem_Collect_eq)
+
+    have 2: "proj (set S) (sols F) \<inter> -proj (set S) {\<omega>. (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)} =
+      proj (set S) (sols F) \<inter> proj (set S)  {\<omega>. proj_sol S \<omega> \<in> set Sxs}"
+      apply (intro inter_cong_right)
+      by (auto intro!: proj_sol_cong simp add: ApproxMCCore.proj_def ) 
+      
+    have 3: "proj (set S)  {\<omega>. proj_sol S \<omega> \<in> set Sxs} = (map_of \<circ> zip S) ` (set Sxs)"
+      apply (intro proj_proj_sol_map_of_zip[OF S])
+      using lSxs by auto
+
+    have 4: " proj (set S) (sols F) \<inter> (map_of \<circ> zip S) ` (set Sxs) =
+      (map_of \<circ> zip S) ` (set Sxs)"
+      using "*" SSxs_def by auto
+
+    have **:"proj (set S) (sols F) =
+      proj (set S) (sols F) \<inter> proj (set S) {\<omega>. (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)} \<union>
+      proj (set S) (sols F) \<inter> -proj (set S) {\<omega>. (\<forall>vs \<in> set Sxs. proj_sol S \<omega> \<noteq> vs)}"
+      by auto
+
+    have "card (proj (set S) (sols F)) =
+      card ((map_of \<circ> zip S) ` (set Sxs))"
+      apply (subst **)
+      apply (subst card_Un_disjoint)
+      using 1 2 3 4 by (auto simp add: card_proj(1))
+
+    then have "card (proj (set S) (sols F)) = length xs"
+      by (simp add: SSxs_def \<open>length xs = card (set (map map_of SSxs))\<close>)
+  }
+  thus "length xs < thresh \<Longrightarrow> card (proj (set S) (sols F)) = length xs"
+  by auto
+qed
+
+lemma good_BSAT:
+  assumes "distinct S"
+  assumes "BSAT F S thresh xs = Inr n"
+  shows "n \<le> card (proj (set S) (sols F))"
+    "n < thresh \<Longrightarrow>
+      card (proj (set S) (sols F)) = n"
+  using checked_BSAT_lower[OF assms(1)] assms(2)
+  by (auto simp add: BSAT_def split: if_splits sum.splits)
+
+lemma size_xorL_cert:
+  assumes "distinct S"
+  assumes "size_xorL_cert F S thresh xorsl i xs = Inr n"
+  shows
+    "size_xorL F S xorsl i \<ge> n"
+    "n < thresh \<longrightarrow> size_xorL F S xorsl i = n"
+  using assms unfolding size_xorL_def size_xorL_cert_def
+  using good_BSAT by auto
+
+lemma approxcore_xorsL_cert:
+  assumes S: "distinct S"
+  assumes "approxcore_xorsL_cert F S thresh mc xorsl = Inr n"
+  shows "approxcore_xorsL F S thresh xorsl = n"
+proof -
+  obtain m cert1 cert2 where mc: "mc = (m,cert1,cert2)"
+    using prod_cases3 by blast
+  obtain nn1 where
+    nn1:"size_xorL_cert F S thresh xorsl (m-1) cert1 = Inr nn1"
+    using assms unfolding mc
+    by (auto split: if_splits sum.splits)
+
+  from  size_xorL_cert[OF S this]
+  have nn1l:
+    "nn1 \<le> size_xorL F S xorsl (m - 1)"
+    "nn1 < thresh \<longrightarrow> size_xorL F S xorsl (m - 1) = nn1" by auto
+
+  have m: "1 \<le> m" "m \<le> length S"
+    "nn1 \<ge> thresh" and
+    ms: "m = length S \<and> n = 2 ^ length S \<or>
+      m < length S"
+    using nn1 assms unfolding mc
+    by (auto split: if_splits simp add: Let_def)
+
+  have bnd: "\<And>i. 1 \<le> i \<Longrightarrow> i \<le> m -1 \<Longrightarrow>
+      size_xorL F S xorsl i \<ge> thresh"
+    using nn1l m(3)
+    by (meson assms(1) dual_order.trans size_xorL_anti_mono)
+
+  note ms
+  moreover {
+    assume *: "m = length S"
+    then have "find (check_xorL F S thresh xorsl) [1..<length S] = None"
+      unfolding find_None_iff check_xorL_def
+      by (auto simp add: bnd leD)
+    then have ?thesis
+      unfolding approxcore_xorsL_def
+      using * ms by force
+  }
+  moreover {
+    assume *: "m < length S"
+
+    obtain nn2 where
+      nn2:"size_xorL_cert F S thresh xorsl m cert2 = Inr nn2"
+        "nn2 < thresh"
+        "n = 2 ^ m * nn2"
+      using assms * unfolding mc
+      by (auto split: if_splits sum.splits)
+
+    from size_xorL_cert[OF S nn2(1)]
+    have nn2l:
+      "size_xorL F S xorsl m = nn2"
+      using nn2(2) by blast
+
+    then have "find (check_xorL F S thresh xorsl) [Suc 0..<length S] = Some m"
+      apply (intro find_upto_SomeI)
+      subgoal by (auto  simp add: m * bnd check_xorL_def leD)
+      subgoal 
+        using "*" calculation(1) size_xorL_cert(2) nn2
+        by (auto  simp add: m * bnd check_xorL_def leD) 
+      subgoal using m(1) by linarith
+      by (auto  simp add: m * bnd check_xorL_def leD)
+
+    then have ?thesis
+      unfolding approxcore_xorsL_def using nn2 nn2l
+      by auto
+  }
+  ultimately show ?thesis by auto
+qed
+
+lemma fold_approxcore_xorsL_cert:
+  assumes S: "distinct S"
+  assumes "i \<le> t"
+  assumes "fold_approxcore_xorsL_cert F S thresh t i cs xorsLs = Inr ns"
+  shows "map (approxcore_xorsL F S thresh \<circ> xorsLs) [t-i..<t] = ns "
+  using assms(2-3)
+proof (induction i arbitrary: ns)
+  case 0
+  then show ?case
+    by auto
+next
+  case c:(Suc i)
+  from c(3)
+  obtain n nss where *:"ns = n # nss"
+     "fold_approxcore_xorsL_cert F S thresh t i cs xorsLs = Inr nss"
+     "approxcore_xorsL_cert F S thresh (cs (t-Suc i)) (xorsLs (t-Suc i)) = Inr n"
+    by (auto simp add: Let_def split: sum.splits)
+
+  have "i \<le> t" using c by auto
+  from c(1)[OF this *(2)]
+  have 2: "nss =
+    map (approxcore_xorsL F S thresh \<circ> xorsLs) [t - i..<t]"
+    by auto
+
+  have i:"[t - Suc i..<t] = (t - Suc i) # [t - i..<t]"
+    apply (subst upt_rec)
+    using c(2)
+    using Suc_diff_Suc Suc_le_lessD by presburger
+
+  show ?case
+    unfolding i *
+    apply (clarsimp simp add: 2 )
+    using  2 "*"(3) approxcore_xorsL_cert assms(1) by blast
+qed
+
+lemma calc_median:
+  assumes S: "distinct S"
+  assumes "calc_median F S thresh t ms xorsLs = Inr n"
+  shows "median t (approxcore_xorsL F S thresh \<circ> xorsLs) = n"
+  using assms
+  unfolding calc_median_def  median_def
+  apply (clarsimp simp add: assms split: if_splits sum.splits)
+  using  fold_approxcore_xorsL_cert[OF S]
+  by (metis diff_is_0_eq' dual_order.refl)
+
+lemma compute_t_find_t[simp]:
+  shows "appmc.compute_t \<delta> (find_t \<delta>) = find_t \<delta>"
+  unfolding find_t_def appmc.compute_t_def
+  apply (clarsimp simp add: option.case_eq_if)
+  unfolding find_Some_iff
+  by auto
+
+lemma certcheck:
+  assumes "distinct S"
+  assumes "certcheck F S \<epsilon> \<delta> (m0,ms) xorsLs = Inr n"
+  shows "approxmc_mapL F S \<epsilon> \<delta> (find_t \<delta>) xorsLs = n"
+  using assms(2)
+  unfolding approxmc_mapL_def
+  using good_BSAT apply (clarsimp split: sum.splits if_splits simp add: Let_def)
+  subgoal using order_le_less_trans assms by blast
+  using assms order.strict_trans1
+  by (meson assms(1) calc_median)
+
+lemma certcheck':
+  assumes "distinct S"
+  assumes "\<not>isl (certcheck F S \<epsilon> \<delta> m xorsLs)"
+  shows "projr (certcheck F S \<epsilon> \<delta> m xorsLs) =
+    approxmc_mapL F S \<epsilon> \<delta> (find_t \<delta>) xorsLs"
+  by (metis certcheck assms(1) assms(2) sum.collapse(2) surj_pair)
+
+(* For any function f mapping randomness to certificates,
+  The probability that the certificate accepts (\<not>isl)
+  With output c not in the interval is at most \<delta> *)
+lemma certcheck_sound:
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes S: "distinct S"
+  shows "
+    measure_pmf.prob
+      (map_pmf (\<lambda>r. certcheck F S \<epsilon> \<delta> (f r) r)
+        (random_seed_xors (find_t \<delta>) (length S)))
+      {c. \<not>isl c \<and>
+        real (projr c) \<notin>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<le> \<delta>"
+proof -
+  have "measure_pmf.prob
+      (map_pmf (\<lambda>r. certcheck F S \<epsilon> \<delta> (f r) r)
+        (random_seed_xors (find_t \<delta>) (length S)))
+      {c. \<not>isl c \<and>
+        real (projr c) \<notin>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<le>
+   prob_space.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> (find_t \<delta>))
+        (random_seed_xors (appmc.compute_t \<delta> (find_t \<delta>)) (length S)))
+      {c. real c \<notin>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}}"
+    unfolding measure_map_pmf compute_t_find_t
+    by (auto intro!: measure_pmf.finite_measure_mono simp add: certcheck'[OF S])
+  also have "... \<le> \<delta>"
+    by (intro approxmcL_sound'[OF assms])
+  finally show ?thesis by auto
+qed
+
+(* A completeness theorem for the checker in the face of probabilistic guarantees
+  It is stated with a "promise"-style guarantee:
+  For any function f mapping randomness to certificates,
+  If the checker accepts (\<not>isl) the output of f on any randomness
+  Then the output c is in the interval with high probability (1 - \<delta>) *)
+lemma certcheck_promise_complete:
+  assumes \<delta>: "\<delta> > 0" "\<delta> < 1"
+  assumes \<epsilon>: "\<epsilon> > 0"
+  assumes S: "distinct S"
+  assumes r: "\<And>r.
+    r \<in> set_pmf (random_seed_xors (find_t \<delta>) (length S)) \<Longrightarrow>
+    \<not>isl (certcheck F S \<epsilon> \<delta> (f r) r)"
+  shows "
+    measure_pmf.prob
+      (map_pmf (\<lambda>r. certcheck F S \<epsilon> \<delta> (f r) r)
+        (random_seed_xors (find_t \<delta>) (length S)))
+      {c. real (projr c) \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<ge> 1 - \<delta>"
+proof -
+  have "
+   measure_pmf.prob
+      (map_pmf (\<lambda>r. certcheck F S \<epsilon> \<delta> (f r) r)
+        (random_seed_xors (find_t \<delta>) (length S)))
+      {c. real (projr c) \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} =
+   measure_pmf.prob
+      (map_pmf (approxmc_mapL F S \<epsilon> \<delta> (find_t \<delta>))
+        (random_seed_xors (appmc.compute_t \<delta> (find_t \<delta>)) (length S)))
+      {c. real c \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}}"
+    unfolding measure_map_pmf compute_t_find_t
+    by (auto intro!: measure_pmf.measure_pmf_eq simp add: certcheck'[OF S] r)
+  also have "... \<ge> 1 -  \<delta>"
+    by (intro approxmcL_sound[OF assms(1-4)])
+  finally show ?thesis by auto
+qed
+
+end
+
+lemma certcheck_code[code]:
+   "certcheck F S \<epsilon> \<delta> (m0,ms) xorsLs = (
+    if \<delta> > 0 \<and> \<delta> < 1 \<and> \<epsilon> > 0 \<and> distinct S then
+      (let \<epsilon> = appmc.mk_eps \<epsilon> in
+      let thresh = appmc.compute_thresh \<epsilon> in
+      case BSAT F S thresh m0 of Inl err \<Rightarrow> Inl err
+      | Inr Y \<Rightarrow>
+      if Y < thresh then Inr Y
+      else
+        let t = find_t \<delta> in
+        calc_median F S thresh t ms xorsLs)
+     else Code.abort (STR ''invalid inputs'')
+        (\<lambda>_. certcheck F S \<epsilon> \<delta> (m0,ms) xorsLs))"
+  by auto
+
+end
+
+end
+
+end
diff --git a/thys/Approximate_Model_Counting/CertCheck_CNF_XOR.thy b/thys/Approximate_Model_Counting/CertCheck_CNF_XOR.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/CertCheck_CNF_XOR.thy
@@ -0,0 +1,670 @@
+section \<open> ApproxMC certification for CNF-XOR \<close>
+
+text \<open>
+  This concretely instantiates the locales with a syntax and
+  semantics for CNF-XOR, giving us a certificate checker for
+  approximate counting in this theory.
+\<close>
+
+theory CertCheck_CNF_XOR imports
+  ApproxMCAnalysis
+  CertCheck
+  HOL.String "HOL-Library.Code_Target_Numeral"
+  Show.Show_Real
+begin
+
+text \<open>
+  This follows CryptoMiniSAT's CNF-XOR formula syntax.
+  A clause is a list of literals (one of which must be satisfied).
+  An XOR constraint has the form $l_1 + l_2 + \dots + l_n = 1$ where addition is taken over $F_2$.
+  Syntactically, they are specified by the list of LHS literals.
+  Variables are natural numbers (in practice, variable 0 is never used)
+\<close>
+
+datatype lit = Pos nat | Neg nat
+type_synonym clause = "lit list"
+type_synonym cmsxor = "lit list"
+type_synonym fml = "clause list \<times> cmsxor list"
+
+type_synonym assignment = "nat \<Rightarrow> bool"
+
+definition sat_lit :: "assignment \<Rightarrow> lit \<Rightarrow> bool" where
+  "sat_lit w l = (case l of Pos x \<Rightarrow> w x | Neg x \<Rightarrow> \<not>w x)"
+
+definition sat_clause :: "assignment \<Rightarrow> clause \<Rightarrow> bool" where
+  "sat_clause w C = (\<exists>l \<in> set C. sat_lit w l)"
+
+definition sat_cmsxor :: "assignment \<Rightarrow> cmsxor \<Rightarrow> bool" where
+  "sat_cmsxor w C = odd ((sum_list (map (of_bool \<circ> (sat_lit w)) C))::nat)"
+
+definition sat_fml :: "assignment \<Rightarrow> fml \<Rightarrow> bool"
+  where
+  "sat_fml w f = (
+    (\<forall>C \<in> set (fst f). sat_clause w C) \<and>
+    (\<forall>C \<in> set (snd f). sat_cmsxor w C))"
+
+(* The solution set *)
+definition sols :: "fml \<Rightarrow> assignment set"
+  where "sols f = {w. sat_fml w f}"
+
+lemma sat_fml_cons[simp]:
+  shows
+  "sat_fml w (FC, x # FX) \<longleftrightarrow>
+  sat_fml w (FC,FX) \<and> sat_cmsxor w x"
+  "sat_fml w (c # FC, FX) \<longleftrightarrow>
+  sat_fml w (FC,FX) \<and> sat_clause w c"
+  unfolding sat_fml_def by auto
+
+(* Construct clauses for a given XOR *)
+fun enc_xor :: "nat xor \<Rightarrow> fml \<Rightarrow> fml"
+  where
+    "enc_xor (x,b) (FC,FX) = (
+    if b then (FC, map Pos x # FX)
+    else
+      case x of
+        [] \<Rightarrow> (FC,FX)
+      | (v#vs) \<Rightarrow> (FC, (Neg v # map Pos vs) # FX))"
+
+lemma sols_enc_xor:
+  shows "sols (enc_xor (x,b) (FC,FX)) =
+       sols (FC,FX) \<inter> {\<omega>. satisfies_xorL (x,b) \<omega>}"
+  unfolding sols_def
+  by (cases x; auto simp add: satisfies_xorL_def sat_cmsxor_def o_def sat_lit_def list.case_eq_if)
+
+(* Solution checking *)
+definition check_sol :: "fml \<Rightarrow> (nat \<Rightarrow> bool) \<Rightarrow> bool"
+  where "check_sol fml w = (
+  list_all (list_ex (sat_lit w)) (fst fml) \<and>
+  list_all (sat_cmsxor w) (snd fml))"
+
+definition ban_sol :: "(nat \<times> bool) list \<Rightarrow> fml \<Rightarrow> fml"
+  where "ban_sol vs fml =
+    ((map (\<lambda>(v,b). if b then Neg v else Pos v) vs)#fst fml, snd fml)"
+
+lemma check_sol_sol:
+  shows "w \<in> sols F \<longleftrightarrow>
+  check_sol F w"
+  unfolding check_sol_def sols_def sat_fml_def
+  apply clarsimp
+  by (metis Ball_set_list_all Bex_set_list_ex sat_clause_def)
+
+lemma ban_sat_clause:
+  shows "sat_clause w (map (\<lambda>(v, b). if b then Neg v else Pos v) vs) \<longleftrightarrow>
+    map w (map fst vs) \<noteq> map snd vs"
+  unfolding sat_clause_def
+  by (force simp add: sat_lit_def split: if_splits)
+
+lemma sols_ban_sol:
+  shows"sols (ban_sol vs F) =
+       sols F \<inter>
+       {\<omega>. map \<omega> (map fst vs) \<noteq> map snd vs}"
+  unfolding ban_sol_def sols_def
+  by (auto simp add: ban_sat_clause)
+
+(* Globally interpret the ApproxMC locale to make
+    ApproxMC certification available for CNF-XOR *)
+global_interpretation CertCheck_CNF_XOR :
+  CertCheck "sols" "enc_xor" "check_sol" "ban_sol"
+  defines
+    random_seed_xors = CertCheck_CNF_XOR.random_seed_xors and
+    fix_t = CertCheck_CNF_XOR.appmc.fix_t and
+    find_t = CertCheck_CNF_XOR.find_t and
+    BSAT = CertCheck_CNF_XOR.BSAT and
+    check_BSAT_sols = CertCheck_CNF_XOR.check_BSAT_sols and
+    size_xorL_cert = CertCheck_CNF_XOR.size_xorL_cert and
+    approxcore_xorsL = CertCheck_CNF_XOR.approxcore_xorsL and
+    fold_approxcore_xorsL_cert = CertCheck_CNF_XOR.fold_approxcore_xorsL_cert and
+    approxcore_xorsL_cert = CertCheck_CNF_XOR.approxcore_xorsL_cert and
+    calc_median = CertCheck_CNF_XOR.calc_median and
+    certcheck = CertCheck_CNF_XOR.certcheck
+  apply unfold_locales
+  subgoal by (metis sols_enc_xor surj_pair)
+  subgoal by (metis sols_ban_sol)
+  by (metis check_sol_sol)
+
+(* Note that we automatically get the associated theorems
+thm CertCheck_CNF_XOR.certcheck_sound
+
+thm CertCheck_CNF_XOR.certcheck_promise_complete
+*)
+
+subsection \<open> Blasting XOR constraints to CNF \<close>
+
+text \<open>
+  This formalizes the usual linear conversion from CNF-XOR into CNF.
+  It is not necessary to use this conversion for solvers that support
+  CNF-XOR formulas natively.
+\<close>
+
+definition negate_lit :: "lit \<Rightarrow> lit"
+  where "negate_lit l = (case l of Pos x \<Rightarrow> Neg x | Neg x \<Rightarrow> Pos x)"
+
+(* Naive direct encoding XOR *)
+fun xor_clauses :: "cmsxor \<Rightarrow> bool \<Rightarrow> clause list"
+  where
+    "xor_clauses [] b = (if b then [[]] else [])"
+  | "xor_clauses (x#xs) b =
+    (let p_x = xor_clauses xs b in
+     let n_x = xor_clauses xs (\<not>b) in
+       map (\<lambda>c. x # c) p_x @ map (\<lambda>c. negate_lit x # c) n_x)"
+
+lemma sat_cmsxor_nil[simp]:
+  shows"\<not> (sat_cmsxor w [])"
+  unfolding sat_cmsxor_def
+  by auto
+
+lemma sat_cmsxor_cons:
+  shows "sat_cmsxor w (x # xs) =
+    (if sat_lit w x then \<not> (sat_cmsxor w xs) else sat_cmsxor w xs)"
+  unfolding sat_cmsxor_def
+  by auto
+
+lemma sat_cmsxor_append:
+  shows "sat_cmsxor w (xs @ ys) =
+    (if sat_cmsxor w xs then \<not> (sat_cmsxor w ys) else sat_cmsxor w ys)"
+proof (induction xs)
+  case Nil
+  then show ?case
+    by (auto simp add: sat_cmsxor_def)
+next
+  case (Cons x xs)
+  then show ?case
+    by (auto simp add: sat_cmsxor_cons)
+qed
+
+definition sat_clauses:: "assignment \<Rightarrow> clause list \<Rightarrow> bool"
+  where "sat_clauses w cs = (\<forall>c \<in> set cs. sat_clause w c)"
+
+lemma sat_clauses_append:
+  shows "sat_clauses w (xs @ ys) =
+    (sat_clauses w xs \<and> sat_clauses w ys)"
+  unfolding sat_clauses_def by auto
+
+lemma sat_clauses_map:
+  shows "sat_clauses w (map ((#) x) cs) =
+    (sat_lit w x \<or> sat_clauses w cs)"
+  unfolding sat_clauses_def sat_clause_def by auto
+
+lemma sat_lit_negate_lit[simp]:
+  "sat_lit w (negate_lit l) = (\<not>sat_lit w l)"
+  apply (cases l)
+  by (auto simp add: negate_lit_def sat_lit_def)
+
+lemma sols_xor_clauses:
+  shows "
+    sat_clauses w (xor_clauses xs b) \<longleftrightarrow>
+    (sat_cmsxor w xs = b)"
+proof (induction xs arbitrary: b)
+  case Nil
+  then show ?case
+    by (auto simp add: sat_cmsxor_def sat_clauses_def sat_clause_def)
+next
+  case (Cons x xs b)
+  have *: "(sat_cmsxor w (x # xs) = b) =
+    (if sat_lit w x
+     then (sat_cmsxor w xs = (\<not>b))
+     else (sat_cmsxor w xs = b))" unfolding sat_cmsxor_cons
+    by auto
+
+  have "sat_clauses w (xor_clauses (x # xs) b) \<longleftrightarrow>
+    ((sat_lit w x \<or> sat_clauses w (xor_clauses xs b)) \<and>
+     (\<not>(sat_lit w x) \<or> sat_clauses w (xor_clauses xs (\<not> b))))"
+    unfolding xor_clauses.simps Let_def sat_clauses_append sat_clauses_map
+    by auto
+  moreover have "... = (
+     (sat_lit w x \<or> (sat_cmsxor w xs = b)) \<and>
+     (\<not>(sat_lit w x) \<or> (sat_cmsxor w xs = (\<not> b))))"
+    using Cons.IH by auto
+  moreover have "... = (sat_cmsxor w (x # xs) = b)"
+    unfolding * by auto
+  ultimately show ?case
+    by auto
+qed
+
+(* This can be done more generally with freshness *)
+definition var_lit :: "lit \<Rightarrow> nat"
+  where "var_lit l = (case l of Pos x \<Rightarrow> x  | Neg x \<Rightarrow> x)"
+
+definition var_lits :: "lit list \<Rightarrow> nat"
+  where "var_lits ls = fold max (map var_lit ls) 0"
+
+lemma sat_lit_same:
+  assumes "\<And>x. x \<le> var_lit l \<Longrightarrow> w x = w' x"
+  shows "sat_lit w l = sat_lit w' l"
+  using assms
+  apply (cases l)
+  by (auto simp add: sat_lit_def var_lit_def)
+
+lemma var_lits_eq:
+  "var_lits ls = Max (set (0 # map var_lit ls))"
+  unfolding var_lits_def Max.set_eq_fold
+  by auto
+
+lemma sat_lits_same:
+  assumes "\<And>x. x \<le> var_lits c \<Longrightarrow> w x = w' x"
+  shows "sat_clause w c = sat_clause w' c"
+  using assms
+  unfolding sat_clause_def var_lits_eq sat_lit_same
+  by (smt (verit) List.finite_set Max_ge dual_order.trans image_subset_iff list.set_map sat_lit_same set_subset_Cons)
+
+lemma le_var_lits_in:
+  assumes "y \<in> set ys" "v \<le> var_lit y"
+  shows "v \<le> var_lits ys"
+  using assms unfolding var_lits_eq
+  by (metis List.finite_set Max_ge dual_order.trans imageI insertCI list.set(2) list.set_map)
+
+lemma sat_cmsxor_same:
+  assumes "\<And>x. x \<le> var_lits xs \<Longrightarrow> w x = w' x"
+  shows "sat_cmsxor w xs = sat_cmsxor w' xs"
+  using assms
+proof (induction xs)
+  case Nil
+  then show ?case
+    unfolding sat_cmsxor_def
+    by auto
+next
+  case ih:(Cons x xs)
+  have 1: "sat_lit w x = sat_lit w' x"
+    apply (intro sat_lit_same)
+    using ih(2)
+    by (metis le_var_lits_in list.set_intros(1))
+  have 2: "sat_cmsxor w xs = sat_cmsxor w' xs"
+    apply (intro ih(1))
+    using ih(2)
+    by (smt (verit) List.finite_set Max_ge_iff empty_not_insert insert_iff list.set(2) list.simps(9) var_lits_eq)
+  show ?case
+    unfolding sat_cmsxor_cons
+    using 1 2 by presburger
+qed
+
+(* linear *)
+lemma sat_cmsxor_split:
+  assumes u: "var_lits xs < u" "var_lits ys < u"
+  assumes w': "w' = (\<lambda>x. if x = u then \<not> sat_cmsxor w xs else w x)"
+  shows "
+   (sat_cmsxor w (xs @ ys) =
+    (sat_cmsxor w' (Pos u # xs) \<and>
+    sat_cmsxor w' (Neg u # ys)))"
+proof -
+  have xs: "sat_cmsxor w' xs = sat_cmsxor w xs"
+    apply (intro sat_cmsxor_same)
+    using u unfolding w' by auto
+  have ys: "sat_cmsxor w' ys = sat_cmsxor w ys"
+    apply (intro sat_cmsxor_same)
+    using u unfolding w' by auto
+
+  show ?thesis
+    unfolding sat_cmsxor_append sat_cmsxor_cons xs ys
+    unfolding w' by (auto simp add: sat_lit_def)
+qed
+
+(* split an XOR constraint into chunks of at most k+3 literals *)
+fun split_xor ::"nat \<Rightarrow> cmsxor \<Rightarrow> cmsxor list \<times> nat \<Rightarrow> cmsxor list \<times> nat"
+  where "split_xor k xs (acc,u) = (
+    if length xs \<le> k + 3 then (xs # acc, u)
+    else (
+      let xs1 = take (k + 2) xs in
+      let xs2 = drop (k + 2) xs in
+      split_xor k (Neg u # xs2) ((Pos u # xs1) # acc, u+1)
+    )
+  )"
+
+declare split_xor.simps[simp del]
+
+lemma split_xor_bound:
+  assumes "split_xor k xs (acc,u) = (acc',u')"
+  shows  "u \<le> u'"
+  using assms
+proof (induction "length xs" arbitrary: xs acc u acc' u' rule: less_induct)
+  case less
+  have " length xs \<le> k + 3 \<or> \<not> ( length xs \<le> k + 3)" by auto
+  moreover {
+    assume "length xs \<le> k + 3"
+    then have "u \<le> u'"
+      using less(2) split_xor.simps by auto
+  }
+  moreover {
+    assume s: "\<not> ( length xs \<le> k + 3)"
+    then have l: "length (Neg u # drop (Suc (Suc k)) xs) < length xs"
+      by auto
+    have "Suc u \<le> u'"
+      using s less(2)
+      unfolding split_xor.simps[of k xs]
+      using less(1)[OF l] by auto
+    then have "u \<le> u'" by auto
+  }
+  ultimately show ?case by auto
+qed
+
+lemma var_lits_append:
+  shows "var_lits xs \<le> var_lits (xs @ ys)"
+    "var_lits ys \<le> var_lits (xs @ ys)"
+  unfolding var_lits_eq
+  by auto
+
+lemma fold_max_eq:
+  assumes "i \<le> u"
+  shows "fold max ls u = max u (fold max ls (i::nat))"
+  using assms
+  apply (induction ls arbitrary: i)
+  subgoal by clarsimp
+  apply clarsimp
+  by (smt (verit) List.finite_set Max.set_eq_fold Max_ge_iff empty_iff insert_iff list.set(2) max.orderI max_def pre_arith_simps(3))
+
+(* We can be more precise here that the number of solutions
+  is preserved exactly, but for UNSAT this is not needed *)
+lemma split_xor_sound:
+  assumes "sat_cmsxor w xs" "\<And>x. x \<in> set acc \<Longrightarrow> sat_cmsxor w x"
+  assumes u: "var_lits xs < u" "\<And>x. x \<in> set acc \<Longrightarrow> var_lits x < u"
+  assumes "split_xor k xs (acc,u) = (acc',u')"
+  obtains w' where
+    "\<And>x. x < u \<Longrightarrow> w x = w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> sat_cmsxor w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> var_lits x < u'"
+  using assms
+proof (induction "length xs" arbitrary: w xs acc u acc' u' thesis rule: less_induct)
+  case less
+  have " length xs \<le> k + 3 \<or> \<not> ( length xs \<le> k + 3)" by auto
+  moreover {
+    assume "length xs \<le> k + 3"
+    then have *: "acc' = xs # acc"
+      using less(7) split_xor.simps
+      by auto
+    then have
+    "\<And>x. x < u \<Longrightarrow> w x = w x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> sat_cmsxor w x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> var_lits x < u'"
+      subgoal by meson
+      subgoal using less
+        by (metis * set_ConsD)
+      using less
+      by (metis "*" order_trans_rules(22) set_ConsD split_xor_bound)
+  }
+  moreover {
+    assume s: "\<not> (length xs \<le> k + 3)"
+    define xs1 where xs1:"xs1 = take (k + 2) xs"
+    define xs2 where xs2:"xs2 = drop (k + 2) xs"
+    have sp: "split_xor k (Neg u # xs2) ((Pos u # xs1) # acc, u+1) = (acc',u')"
+      by (metis less(7) s split_xor.simps xs1 xs2)
+    have l: "length (Neg u # xs2) < length xs"
+      using s xs2 by auto
+
+    have xs: "xs = xs1 @ xs2" by (simp add: xs1 xs2)
+
+    define w' where w': "w' =
+    (\<lambda>x. if x = u then \<not> sat_cmsxor w xs1 else w x)"
+
+    have vl: "var_lits xs1 < u" "var_lits xs2 < u"
+      apply (metis less(5) order_trans_rules(21) var_lits_append(1) xs)
+      by (metis less(5) order_trans_rules(21) var_lits_append(2) xs)
+
+    from sat_cmsxor_split[OF this w']
+    have satws1: "sat_cmsxor w' (Pos u # xs1)"
+     and satws2: "sat_cmsxor w' (Neg u # xs2)"
+      using less(3) xs by auto
+
+    have satacc: "\<And>x. x \<in> set ((Pos u # xs1) # acc) \<Longrightarrow>
+        sat_cmsxor w' x"
+      by (metis less(4) less(6) not_less sat_cmsxor_same satws1 set_ConsD w')
+
+    have v1: "var_lits (Neg u # xs2) < u + 1"
+      unfolding var_lits_def
+      apply (simp add: var_lit_def)
+      using vl var_lits_def fold_max_eq
+      by (metis le_add2 le_add_same_cancel2 less_Suc_eq max.absorb3)
+
+    have "fold max (map var_lit xs1) u < Suc u"
+      using vl var_lits_def
+      by (smt (verit, best) List.finite_set Max.set_eq_fold Max_ge_iff dual_order.trans empty_iff insert_iff lessI less_or_eq_imp_le list.set(2) not_less)
+    moreover have "\<And>x. x \<in> set acc \<Longrightarrow>
+         fold max (map var_lit x) 0 < Suc u"
+      by (metis less(6) less_SucI var_lits_def)
+    ultimately have v2:"\<And>x. x \<in> set ((Pos u # xs1) # acc) \<Longrightarrow> var_lits x < u + 1"
+      unfolding var_lits_def
+      by (auto simp add: var_lit_def)
+
+    obtain w'' where
+    w'': "\<And>x. x < u + 1 \<Longrightarrow> w' x = w'' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> sat_cmsxor w'' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> var_lits x < u'"
+      using less(1)[OF l _ satws2 satacc v1 v2 sp]
+      by auto
+
+    have "\<And>x. x < u \<Longrightarrow> w x = w'' x"
+      using w''(1)
+      unfolding w'
+      using less_Suc_eq by fastforce
+
+    then have "\<exists>w''. (
+         (\<forall>x. x < u \<longrightarrow> w x = w'' x) \<and>
+          (\<forall>x. x \<in> set acc' \<longrightarrow> sat_cmsxor w'' x) \<and>
+          (\<forall>x. x \<in> set acc' \<longrightarrow> var_lits x < u'))"
+      using w''(2-3) by auto
+  }
+  ultimately show ?case
+    using less(2)
+    by (metis (mono_tags, lifting))
+qed
+
+definition split_xors ::"nat \<Rightarrow> nat \<Rightarrow> cmsxor list \<Rightarrow> cmsxor list"
+where "split_xors k u xs = fst (fold (split_xor k) xs ([],u))"
+
+lemma split_xors_sound:
+  assumes "\<And>x. x \<in> set xs \<Longrightarrow> sat_cmsxor w x"
+          "\<And>x. x \<in> set acc \<Longrightarrow> sat_cmsxor w x"
+  assumes u: "\<And>x. x \<in> set xs \<Longrightarrow> var_lits x < u"
+      "\<And>x. x \<in> set acc \<Longrightarrow> var_lits x < u"
+  assumes "fold (split_xor k) xs (acc,u) = (acc',u')"
+  obtains w' where
+    "\<And>x. x < u \<Longrightarrow> w x = w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> sat_cmsxor w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> var_lits x < u'"
+  using assms
+proof (induction xs arbitrary: w acc u acc' u')
+  case Nil
+  then show ?case
+    by auto
+next
+  case ih:(Cons x xs)
+  obtain acc'' u'' where x: "split_xor k x (acc, u) = (acc'',u'')"
+    by fastforce
+  from split_xor_sound[OF _ _ _ _ this]
+  obtain w'' where
+    w'': "\<And>x. x < u \<Longrightarrow> w x = w'' x"
+    "\<And>x. x \<in> set acc'' \<Longrightarrow> sat_cmsxor w'' x"
+    "\<And>x. x \<in> set acc'' \<Longrightarrow> var_lits x < u''"
+    by (smt (verit, del_insts) ih(4) ih(5) ih(6) ih.prems(2) list.set_intros(1))
+  have rw: "fold (split_xor k) xs (acc'',u'') = (acc', u')"
+    using ih(7) x by auto
+  have 1: "\<And>x. x \<in> set xs \<Longrightarrow>sat_cmsxor w'' x"
+    by (metis basic_trans_rules(22) ih(3) ih(5) list.set_intros(2) not_less sat_cmsxor_same w''(1))
+  have 2: "\<And>x. x \<in> set xs \<Longrightarrow> var_lits x < u''"
+    by (meson ih(5) list.set_intros(2) order_trans_rules(22) split_xor_bound x)
+  show ?case
+    using ih(1)[OF _ 1 w''(2) 2 w''(3) rw]
+    by (smt (verit, best) basic_trans_rules(22) ih(2) split_xor_bound w''(1) x)
+qed
+
+(* maximum variable occuring in the whole formula *)
+definition var_fml :: "fml \<Rightarrow> nat"
+  where "var_fml f =
+  max (fold max (map var_lits (fst f)) 0)
+      (fold max (map var_lits (snd f)) 0)"
+
+lemma var_fml_eq:
+  "var_fml f =
+    max (Max (set (0 # map var_lits (fst f))))
+    (Max (set (0 # map var_lits (snd f))))"
+  unfolding var_fml_def Max.set_eq_fold
+  by auto
+
+definition split_fml ::" nat \<Rightarrow> fml \<Rightarrow> fml"
+  where "split_fml k f = (
+  let u = var_fml f + 1 in
+    (fst f, (split_xors k u (snd f)))
+  )"
+
+lemma var_lits_var_fml:
+  shows "\<And>x. x \<in> set (snd F) \<Longrightarrow> var_lits x \<le> var_fml F"
+  "\<And>x. x \<in> set (fst F) \<Longrightarrow> var_lits x \<le> var_fml F"
+  unfolding var_fml_eq
+  subgoal
+    apply clarsimp
+    by (meson List.finite_set Max_ge finite_imageI finite_insert image_subset_iff max.coboundedI2 subset_insertI)
+  apply clarsimp
+  by (meson List.finite_set Max_ge finite_imageI finite_insert image_subset_iff max.coboundedI1 subset_insertI)
+
+lemma split_fml_satisfies:
+  assumes "sat_fml w F"
+  obtains w' where "sat_fml w' (split_fml k F)"
+proof -
+  obtain acc' u' where
+    *: "fold (split_xor k) (snd F) ([], var_fml F + 1) = (acc',u')"
+    by fastforce
+  have 1:"\<And>x. x \<in> set (snd F) \<Longrightarrow> sat_cmsxor w x"
+    using assms unfolding sat_fml_def by auto
+  have 2:"\<And>x. x \<in> set (snd F) \<Longrightarrow> var_lits x < var_fml F + 1"
+    using var_lits_var_fml
+    by (meson less_add_one order_le_less_trans)
+  from split_xors_sound[OF 1 _ _ 2 *]
+  obtain w' where
+    w': "\<And>x. x < var_fml F + 1 \<Longrightarrow> w x = w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> sat_cmsxor w' x"
+    "\<And>x. x \<in> set acc' \<Longrightarrow> var_lits x < u'"
+    using "2" by auto
+  have "\<And>x. x \<in> set (fst F) \<Longrightarrow> sat_clause w' x"
+    by (metis assms less_add_one order_trans_rules(21) sat_fml_def sat_lits_same var_lits_var_fml(2) w'(1))
+
+  then have "sat_fml w' (split_fml k F)"
+    unfolding split_fml_def Let_def split_xors_def *
+    by (auto simp add: sat_fml_def w'(2))
+  thus ?thesis
+    using that by auto
+qed
+
+lemma split_fml_sols:
+  assumes "sols (split_fml k F) = {}"
+  shows "sols F = {}"
+  using assms
+  using split_fml_satisfies unfolding sols_def
+  by (metis Collect_empty_eq)
+
+definition blast_xors :: "cmsxor list \<Rightarrow> clause list"
+  where "blast_xors xors =  concat (map (\<lambda>x. xor_clauses x True) xors)"
+
+definition blast_fml :: "fml \<Rightarrow> clause list"
+  where "blast_fml f =
+    fst f @ blast_xors (snd f)"
+
+lemma sat_clauses_concat:
+  "sat_clauses w (concat xs) \<longleftrightarrow>
+  (\<forall>x \<in> set xs. sat_clauses w x)"
+  unfolding sat_clauses_def
+  by auto
+
+lemma blast_xors_sound:
+  assumes "(\<And>x. x \<in> set xors \<Longrightarrow> sat_cmsxor w x)"
+  shows "sat_clauses w (blast_xors xors)"
+  unfolding blast_xors_def sat_clauses_concat
+  by (auto simp add: assms sols_xor_clauses)
+
+lemma blast_fml_sound:
+  assumes "sat_fml w F"
+  shows "sat_fml w (blast_fml F,[])"
+  unfolding blast_fml_def sat_fml_def
+  apply clarsimp
+  using assms blast_xors_sound sat_clauses_def sat_fml_def by blast
+
+definition blast_split_fml :: "fml \<Rightarrow> clause list"
+  where "blast_split_fml f = blast_fml (split_fml 1 f)"
+
+lemma blast_split_fml_sols:
+  assumes "sols (blast_split_fml F,[]) = {}"
+  shows "sols F = {}"
+  by (metis Collect_empty_eq assms blast_fml_sound blast_split_fml_def sols_def split_fml_sols)
+
+definition certcheck_blast::"
+  (clause list \<Rightarrow> bool) \<Rightarrow>
+  fml \<Rightarrow> nat list \<Rightarrow>
+  real \<Rightarrow> real \<Rightarrow>
+  ((nat \<Rightarrow> bool) list \<times>
+    (nat \<Rightarrow> (nat \<times> (nat \<Rightarrow> bool) list \<times> (nat \<Rightarrow> bool) list))) \<Rightarrow>
+  (nat \<Rightarrow> nat \<Rightarrow> (bool list \<times> bool)) \<Rightarrow>
+  String.literal + nat"
+  where "certcheck_blast check_unsat F S \<epsilon> \<delta> m0ms =
+   certcheck (check_unsat \<circ> blast_split_fml) F S \<epsilon> \<delta> m0ms"
+
+(* Just for completeness, we re-state the main theorems *)
+corollary certcheck_blast_sound:
+  assumes "\<And>F. check_unsat F \<Longrightarrow> sols (F, []) = {}"
+  assumes "0 < \<delta>" "\<delta> < 1"
+  assumes "0 < \<epsilon>"
+  assumes "distinct S"
+  shows "
+  measure_pmf.prob
+    (map_pmf (\<lambda>r. certcheck_blast check_unsat F S \<epsilon> \<delta> (f r) r)
+      (random_seed_xors (find_t \<delta>) (length S)))
+  {c. \<not> isl c \<and>
+     real (projr c) \<notin>
+      {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+        (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<le> \<delta>"
+  unfolding certcheck_blast_def
+  apply (intro CertCheck_CNF_XOR.certcheck_sound[OF _ assms(2-5)])
+  using assms(1) unfolding Let_def
+  using blast_split_fml_sols by auto
+
+corollary certcheck_blast_promise_complete:
+  assumes "\<And>F. check_unsat F \<Longrightarrow> sols (F, []) = {}"
+  assumes "0 < \<delta>" "\<delta> < 1"
+  assumes "0 < \<epsilon>"
+  assumes "distinct S"
+  assumes r: "\<And>r.
+    r \<in> set_pmf (random_seed_xors (find_t \<delta>) (length S)) \<Longrightarrow>
+    \<not>isl (certcheck_blast check_unsat F S \<epsilon> \<delta> (f r) r)"
+  shows "
+    measure_pmf.prob
+      (map_pmf (\<lambda>r. certcheck_blast check_unsat F S \<epsilon> \<delta> (f r) r)
+        (random_seed_xors (find_t \<delta>) (length S)))
+      {c. real (projr c) \<in>
+        {real (card (proj (set S) (sols F))) / (1 + \<epsilon>)..
+          (1 + \<epsilon>) * real (card (proj (set S) (sols F)))}} \<ge> 1 - \<delta>"
+  unfolding certcheck_blast_def
+  apply (intro CertCheck_CNF_XOR.certcheck_promise_complete[OF _ assms(2-5)])
+  using assms(1) unfolding Let_def
+  using blast_split_fml_sols assms(6) unfolding certcheck_blast_def by auto
+
+subsection \<open> Export code for a SML implementation. \<close>
+
+definition real_of_int :: "integer \<Rightarrow> real"
+  where "real_of_int n = real (nat_of_integer n)"
+
+definition real_mult :: "real \<Rightarrow> real \<Rightarrow> real"
+  where "real_mult n m = n * m"
+
+definition real_div :: "real \<Rightarrow> real \<Rightarrow> real"
+  where "real_div n m = n / m"
+
+definition real_plus :: "real \<Rightarrow> real \<Rightarrow> real"
+  where "real_plus n m = n + m"
+
+definition real_minus :: "real \<Rightarrow> real \<Rightarrow> real"
+  where "real_minus n m = n - m"
+
+declare [[code abort: fix_t]]
+
+(* Sample code export.
+  Helper Isabelle converters, followed by exporting the actual code *)
+export_code
+  length
+  nat_of_integer int_of_integer
+  integer_of_nat integer_of_int
+  real_of_int real_mult real_div real_plus real_minus
+  quotient_of
+
+  Pos Neg
+  CertCheck_CNF_XOR.appmc.compute_thresh
+  find_t certcheck
+  certcheck_blast
+  in SML
+
+end
diff --git a/thys/Approximate_Model_Counting/ROOT b/thys/Approximate_Model_Counting/ROOT
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/ROOT
@@ -0,0 +1,18 @@
+chapter AFP
+
+session Approximate_Model_Counting = Frequency_Moments +
+  options [timeout = 600]
+  sessions
+    Concentration_Inequalities
+    Monad_Normalisation
+  theories
+    ApproxMCPreliminaries
+    RandomXOR
+    RandomXORHashFamily
+    ApproxMCCore
+    ApproxMCCoreAnalysis
+    CertCheck
+    CertCheck_CNF_XOR
+  document_files
+    "root.tex"
+    "root.bib"
diff --git a/thys/Approximate_Model_Counting/RandomXOR.thy b/thys/Approximate_Model_Counting/RandomXOR.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/RandomXOR.thy
@@ -0,0 +1,1634 @@
+section \<open>Random XORs\<close>
+
+text \<open>The goal of this section is to prove that,
+  for a randomly sampled XOR $X$ from a set of variables $V$:
+  \begin{enumerate}
+  \item the probability of an assignment $w$ satisfying $X$ is $\frac{1}{2}$;
+  \item for any distinct assignments $w$, $w'$ the probability of both satisfying $X$ is equal to $\frac{1}{4}$ (2-wise independence); and
+  \item for any distinct assignments $w$, $w'$, $w''$ the probability of all three
+     satisfying $X$ is equal to $\frac{1}{8}$ (3-wise independence).
+  \end{enumerate}
+  \<close>
+
+theory RandomXOR imports
+  ApproxMCPreliminaries
+  Frequency_Moments.Product_PMF_Ext
+  Monad_Normalisation.Monad_Normalisation
+begin
+
+
+text \<open>A random XOR constraint is modeled
+  as a random subset of variables and a randomly chosen RHS bit. \<close>
+definition random_xor :: "'a set \<Rightarrow> ('a set \<times> bool) pmf"
+  where "random_xor V =
+    pair_pmf (pmf_of_set (Pow V)) (bernoulli_pmf (1/2))"
+
+lemma pmf_of_set_Pow_fin_map:
+  assumes V:"finite V"
+  shows "pmf_of_set (Pow V) =
+    map_pmf (\<lambda>b. {x \<in> V. b x = Some True})
+     (Pi_pmf V def (\<lambda>_. map_pmf Some (bernoulli_pmf (1 / 2))))"
+proof -
+  have *: "Pi_pmf V def (\<lambda>_. map_pmf Some (bernoulli_pmf (1 / 2))) =
+    map_pmf (\<lambda>f x. if x \<in> V then f x else def)
+    (Pi_pmf V (Some False) (\<lambda>_. map_pmf Some (bernoulli_pmf (1 / 2))))"
+    unfolding Pi_pmf_default_swap[OF V] by auto
+
+  have **: "pmf_of_set (Pow V) =
+    map_pmf
+     (\<lambda>x. {xa. (xa \<in> V \<longrightarrow> x xa) \<and> xa \<in> V})
+     (Pi_pmf V False  (\<lambda>_. bernoulli_pmf (1 / 2)))"
+    by (smt (verit, ccfv_SIG) Collect_cong pmf_of_set_Pow_conv_bernoulli V pmf.map_cong)
+  show ?thesis
+    unfolding *
+    apply (subst Pi_pmf_map[OF V, of _ "False"])
+    using ** by (auto simp add: pmf.map_comp o_def)
+qed
+
+(* A random XOR can also be sampled as a
+  map |V| \<Rightarrow> bool + a coin flip *)
+lemma random_xor_from_bits:
+  assumes V:"finite V"
+  shows "random_xor V =
+    pair_pmf
+      (map_pmf (\<lambda>b. {x \<in> V. b x = Some True})
+        (Pi_pmf V def (\<lambda>_. map_pmf Some (bernoulli_pmf (1/2)))))
+      (bernoulli_pmf (1/2))"
+  unfolding random_xor_def
+  using V pmf_of_set_Pow_fin_map by fastforce
+
+(* An assignment is a subset \<omega> of V
+   i.e., those variables assigned to true *)
+fun satisfies_xor :: "('a set \<times> bool) \<Rightarrow> 'a set \<Rightarrow> bool"
+  where "satisfies_xor (x,b) \<omega> =
+     even (card (\<omega> \<inter> x) + of_bool b) "
+
+(*
+(* x_0 \<oplus> x_1 \<oplus> x_2 = 0 *)
+value "satisfies_xor ({0,1,2},False) {0::nat}"
+(* x_0 \<oplus> x_1 \<oplus> x_2 = 1 *)
+value "satisfies_xor ({0,1,2},True) {0::nat}"
+*)
+
+lemma satisfies_xor_inter:
+  shows "satisfies_xor ( \<omega> \<inter> x ,b) \<omega> = satisfies_xor (x,b) \<omega>"
+  by (auto simp add: Int_commute)
+
+lemma prob_bernoulli_bind_pmf:
+  assumes "0 \<le> p" "p \<le> 1"
+  assumes "finite E"
+  shows "measure_pmf.prob
+   (bernoulli_pmf p \<bind> x) E =
+  p * (measure_pmf.prob (x True) E) +
+  (1 - p) * (measure_pmf.prob (x False) E) "
+  using assms
+  by (auto simp add: pmf_bind measure_measure_pmf_finite[OF assms(3)] vector_space_over_itself.scale_sum_right comm_monoid_add_class.sum.distrib mult.commute)
+
+lemma set_pmf_random_xor:
+  assumes V: "finite V"
+  shows "set_pmf (random_xor V) = (Pow V) \<times> UNIV"
+  unfolding random_xor_def
+  using assms by (auto simp add: Pow_not_empty Set.basic_monos(7))
+
+lemma pmf_of_set_prod:
+  assumes "P \<noteq> {}" "Q \<noteq> {}"
+  assumes "finite P" "finite Q"
+  shows "pmf_of_set (P \<times> Q) = pair_pmf (pmf_of_set P) (pmf_of_set Q)"
+  by (auto intro!: pmf_eqI simp add: indicator_def pmf_pair assms)
+
+lemma random_xor_pmf_of_set:
+  assumes V:"finite V"
+  shows "random_xor V  = pmf_of_set ((Pow V) \<times> UNIV)"
+  unfolding random_xor_def
+  apply (subst pmf_of_set_prod)
+  using V bernoulli_pmf_half_conv_pmf_of_set by auto
+
+lemma prob_random_xor_with_set_pmf:
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V) {c. P c} =
+    prob_space.prob (random_xor V) {c. fst c \<subseteq> V \<and> P c}"
+  by (smt (verit, best) PowD assms measure_pmf.measure_pmf_eq mem_Collect_eq mem_Sigma_iff prod.collapse set_pmf_random_xor)
+
+lemma prob_set_parity:
+  assumes "measure_pmf.prob M
+    {c. P c} = q"
+  shows "measure_pmf.prob M
+    {c. P c = b} = (if b then q else 1 - q)"
+proof -
+  {
+    assume b:"b"
+    have ?thesis using assms
+      using b by presburger
+  }
+  moreover {
+    assume b:"\<not>b"
+    have "{c. P c} \<in> measure_pmf.events M" by auto
+    from measure_pmf.prob_compl[OF this]
+    have "1 - q = measure_pmf.prob M (UNIV - {c. P c})"
+      using assms by auto
+    moreover have " ... =
+      prob_space.prob M
+      {c. P c = b}"
+      by (simp add: b measure_pmf.measure_pmf_eq)
+    ultimately have ?thesis
+      using b by presburger
+  }
+  ultimately show ?thesis by auto
+qed
+
+lemma satisfies_random_xor:
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega>} = 1 / 2"
+proof -
+  have eq: "{(c::'a set \<times> bool). fst c \<subseteq> V} = {c. c \<subseteq> V} \<times> UNIV"
+    by auto
+  then have "finite {(c::'a set \<times> bool). fst c \<subseteq> V}"
+    using assms by auto
+
+  then have *: "
+    x \<subseteq> V \<Longrightarrow>
+    measure_pmf.prob (bernoulli_pmf (1 / 2) \<bind> (\<lambda>y. return_pmf (x, y)))
+        {c. fst c \<subseteq> V \<and> satisfies_xor c \<omega>} = 1 / 2" for x
+    apply (subst prob_bernoulli_bind_pmf)
+    by (auto simp add: indicator_def)
+
+  have "prob_space.prob (random_xor V) {c. satisfies_xor c \<omega>} =
+    prob_space.prob (random_xor V) {c. fst c \<subseteq> V \<and> satisfies_xor c \<omega>}"
+    using prob_random_xor_with_set_pmf[OF V] by auto
+  also have "... =
+    prob_space.expectation (random_xor V)
+    (indicat_real {c. fst c \<subseteq> V \<and> satisfies_xor c \<omega>})"
+    by auto
+  also have "... = (\<Sum>a\<in>Pow V.
+       inverse (real (card (Pow V))) *
+       measure_pmf.prob
+        (bernoulli_pmf (1 / 2) \<bind>
+         (\<lambda>y. return_pmf (a, y)))
+        {c. fst c \<subseteq> V \<and> satisfies_xor c \<omega>})"
+    unfolding random_xor_def pair_pmf_def
+    apply (subst pmf_expectation_bind_pmf_of_set)
+    using assms by auto
+  also have "... = (\<Sum>a\<in>Pow V.
+       inverse (real (card (Pow V))) * (1/2))"
+    by (simp add: *)
+  also have "... =
+       inverse (real (card (Pow V))) * (1/2) * (\<Sum>a\<in>Pow V. 1)"
+    using * by force
+  also have "... = 1/2"
+    by (metis One_nat_def Suc_leI assms card_Pow divide_real_def inverse_inverse_eq inverse_nonzero_iff_nonzero nat_one_le_power nonzero_mult_div_cancel_left not_one_le_zero of_nat_eq_0_iff pos2 real_of_card)
+  finally show ?thesis
+    by presburger
+qed
+
+lemma satisfies_random_xor_parity:
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega> = b} = 1 / 2"
+  using prob_set_parity[OF satisfies_random_xor[OF V]]
+    by auto
+
+subsection "Independence properties of random XORs"
+
+lemma pmf_of_set_powerset_split:
+  assumes "S \<subseteq> V" "finite V"
+  shows "
+    map_pmf (\<lambda>(x,y). x \<union> y)
+    (pmf_of_set (Pow S \<times> Pow (V - S))) =
+  pmf_of_set (Pow V)"
+proof -
+  have spmfS: "set_pmf (pmf_of_set (Pow S)) = Pow S"
+    using assms
+    by (auto intro!: set_pmf_of_set simp add: rev_finite_subset)
+  have spmfVS: "set_pmf (pmf_of_set (Pow (V-S))) = Pow (V-S)"
+    using assms by (auto intro!: set_pmf_of_set)
+
+  have xsub: "x \<subseteq> V \<Longrightarrow>
+         \<exists>xa\<in>Pow S.
+            \<exists>y\<in>Pow (V - S). x = xa \<union> y" for x 
+    by (metis Diff_subset_conv Pow_iff Un_Diff_Int basic_trans_rules(23) inf_le2 sup_commute)
+
+  have inj: "inj_on (\<lambda>(x, y). x \<union> y)
+     (Pow S \<times> Pow (V - S))"
+    unfolding inj_on_def
+    by auto
+  then have bij: "bij_betw (\<lambda>(x, y). x \<union> y)
+     ((Pow S) \<times> Pow (V - S))
+     (Pow V)"
+    unfolding bij_betw_def
+    using assms(1) xsub by (auto simp add: image_def)
+
+  have "map_pmf (\<lambda>(x, y). x \<union> y)
+     (pmf_of_set (Pow S \<times> Pow (V - S))) =
+    pmf_of_set (Pow V)"
+    apply (subst map_pmf_of_set_inj[OF inj])
+    subgoal by (auto simp add: image_def)
+    subgoal using bij assms(2) bij_betw_finite by blast
+    apply (intro arg_cong[where f = "pmf_of_set"])
+    using assms(1) xsub by (auto  simp add: image_def)
+
+  thus ?thesis
+    unfolding spmfS spmfVS
+    by auto
+qed
+
+lemma pmf_of_set_Pow_sing:
+  shows"pmf_of_set (Pow {x}) =
+     bernoulli_pmf (1 / 2) \<bind>
+     (\<lambda>b. return_pmf (if b then {x} else {}))"
+  apply (intro pmf_eqI)
+  apply (subst pmf_of_set)
+  by (auto simp add: pmf_bind card_Pow indicator_def subset_singleton_iff)
+
+lemma pmf_of_set_sing_coin_flip:
+  assumes "finite V"
+  shows "pmf_of_set (Pow {x} \<times> Pow V) =
+    map_pmf (\<lambda>(r,c). (if c then {x} else {}, r)) (random_xor V)"
+proof -
+  have *: "pmf_of_set (Pow {x} \<times> Pow V) =
+    pair_pmf (pmf_of_set (Pow {x})) (pmf_of_set (Pow V))"
+    apply(intro pmf_of_set_prod)
+    using assms by auto
+  show ?thesis
+    unfolding *
+    apply (intro pmf_eqI)
+    including monad_normalisation
+    by (auto simp add: map_pmf_def pair_pmf_def random_xor_def pmf_of_set_Pow_sing)
+qed
+
+(* TODO: there is a more general version below *)
+lemma measure_pmf_prob_dependent_product_bound_eq:
+  assumes "countable A" "\<And>i. countable (B i)"
+  assumes "\<And>a. a \<in> A \<Longrightarrow> measure_pmf.prob N (B a) = r"
+  shows "measure_pmf.prob (pair_pmf M N) (Sigma A B) =
+    measure_pmf.prob M A * r"
+proof -
+  have "measure_pmf.prob (pair_pmf M N) (Sigma A B) =
+    (\<Sum>\<^sub>a(a, b) \<in> Sigma A B. pmf M a * pmf N b)"
+    by (auto intro!: infsetsum_cong simp add: measure_pmf_conv_infsetsum pmf_pair)
+  also have "... = (\<Sum>\<^sub>aa\<in>A. \<Sum>\<^sub>ab\<in>B a. pmf M a * pmf N b)"
+    apply (subst infsetsum_Sigma[OF assms(1-2)])
+    subgoal by (metis (no_types, lifting) SigmaE abs_summable_on_cong case_prod_conv pmf_abs_summable pmf_pair)
+    by (auto simp add: assms case_prod_unfold)
+
+  also have "... = (\<Sum>\<^sub>aa\<in>A. pmf M a * (measure_pmf.prob N (B a)))"
+    by (simp add: infsetsum_cmult_right measure_pmf_conv_infsetsum pmf_abs_summable)
+  also have "... = (\<Sum>\<^sub>aa\<in>A. pmf M a * r)"
+    using assms(3) by force
+  also have"... = measure_pmf.prob M A * r"
+    by (simp add: infsetsum_cmult_left pmf_abs_summable measure_pmf_conv_infsetsum)
+  finally show ?thesis
+    by linarith
+qed
+
+(* TODO: duplicated in Schwartz_Zippel, but
+  we don't want to pull in the multivariate polynomials library *)
+lemma measure_pmf_prob_dependent_product_bound_eq':
+  assumes "countable (A \<inter> set_pmf M)" "\<And>i. countable (B i \<inter> set_pmf N)"
+  assumes "\<And>a. a \<in> A \<inter> set_pmf M \<Longrightarrow> measure_pmf.prob N (B a \<inter> set_pmf N) = r"
+  shows "measure_pmf.prob (pair_pmf M N) (Sigma A B) = measure_pmf.prob M A * r"
+proof -
+  have *: "Sigma A B \<inter> (set_pmf M \<times> set_pmf N) =
+    Sigma (A \<inter> set_pmf M) (\<lambda>i. B i \<inter> set_pmf N)"
+    by auto
+
+  have "measure_pmf.prob (pair_pmf M N) (Sigma A B) =
+    measure_pmf.prob (pair_pmf M N) (Sigma (A \<inter> set_pmf M) (\<lambda>i. B i \<inter> set_pmf N))"
+    by (metis * measure_Int_set_pmf set_pair_pmf)
+  moreover have "... =
+    measure_pmf.prob M (A \<inter> set_pmf M) * r"
+    using measure_pmf_prob_dependent_product_bound_eq[OF assms(1-3)]
+    by auto
+  moreover have "... = measure_pmf.prob M A * r"
+    by (simp add: measure_Int_set_pmf)
+  ultimately show ?thesis by linarith
+qed
+
+lemma single_var_parity_coin_flip:
+  assumes "x \<in> \<omega>" "finite \<omega>"
+  assumes "finite a" "x \<notin> a"
+  shows "measure_pmf.prob (pmf_of_set (Pow {x}))
+          {y. even (card ((a \<union> y) \<inter> \<omega>)) = b}  = 1/2"
+proof -
+  have "insert x a \<inter> \<omega> = insert x (a \<inter> \<omega>)"
+    using assms by auto
+  then have *: "card (insert x a \<inter> \<omega>) = 1 + card (a \<inter> \<omega>)"
+    by (simp add: assms(2) assms(4))
+
+  have "measure_pmf.prob (pmf_of_set (Pow {x}))
+          {y. even (card ((a \<union> y) \<inter> \<omega>)) = b} =
+    measure_pmf.prob (bernoulli_pmf (1/2))
+          {odd (card (a \<inter> \<omega>)) = b}"
+    unfolding pmf_of_set_Pow_sing map_pmf_def[symmetric]
+    by (auto intro!: measure_prob_cong_0 simp add:image_def * )
+  moreover have "... = 1/2"
+    by (simp add: measure_pmf_single)
+  ultimately show ?thesis by auto
+qed
+
+(*
+  Fix any event E that does not touch x
+  Then we can sample that event separately
+*)
+lemma prob_pmf_of_set_nonempty_parity:
+  assumes V: "finite V"
+  assumes "x \<in> \<omega>" "\<omega> \<subseteq> V"
+  assumes "\<And>c. c \<in> E \<longleftrightarrow> c - {x} \<in> E"
+  shows "prob_space.prob (pmf_of_set (Pow V))
+    (E \<inter> {c. even (card (c \<inter> \<omega>)) = b}) =
+    1 / 2 * prob_space.prob (pmf_of_set (Pow (V - {x}))) E"
+proof -
+  have 1: "set_pmf (pmf_of_set (Pow {x})) = Pow {x}"
+    by (simp add: Pow_not_empty)
+  have 2: "set_pmf (pmf_of_set (Pow (V-{x}))) = Pow (V-{x})"
+    by (simp add: Pow_not_empty assms(1))
+  have 3: "set_pmf (pmf_of_set (Pow {x} \<times> Pow (V - {x}))) = Pow {x} \<times> Pow (V - {x})"
+    by (simp add: Pow_not_empty assms(1))
+
+  have "{x} \<subseteq> V" using assms by auto
+  from pmf_of_set_powerset_split[OF this assms(1)]
+  have e: "map_pmf (\<lambda>(x, y). x \<union> y)
+     (pmf_of_set (Pow {x} \<times> Pow (V - {x}))) =
+    pmf_of_set (Pow V)" using 1 2 by auto
+  have "map_pmf (\<lambda>(x, y). x \<union> y)
+     (pair_pmf (pmf_of_set (Pow {x}))
+       (pmf_of_set (Pow (V - {x})))) =
+    map_pmf (\<lambda>(x, y). x \<union> y)
+     (pair_pmf (pmf_of_set (Pow (V - {x})))
+       (pmf_of_set (Pow {x})))"
+    apply (subst pair_commute_pmf)
+    by (auto simp add: pmf.map_comp o_def case_prod_unfold Un_commute)
+  then have *: "pmf_of_set (Pow V) =
+    map_pmf (\<lambda>(x, y). x \<union> y)
+     (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x})))"
+    unfolding e[symmetric]
+    apply (subst pmf_of_set_prod)
+    using V by auto
+
+  have **: "((\<lambda>(x, y). x \<union> y) -` (E \<inter> S)) \<inter> (Pow (V - {x}) \<times> Pow{x}) =
+    Sigma E (\<lambda>x. {y. (x \<union> y) \<in> S}) \<inter> (Pow (V - {x}) \<times> Pow{x})" for S
+  proof -
+    have 11: "\<And>a b. a \<union> b \<in> E \<Longrightarrow>
+           a \<union> b \<in> S \<Longrightarrow>
+           a \<subseteq> V - {x} \<Longrightarrow>
+           b \<subseteq> {x} \<Longrightarrow> a \<in> E"
+      by (metis Diff_insert_absorb Un_insert_right assms(4) boolean_algebra_cancel.sup0 subset_Diff_insert subset_singleton_iff)
+
+    have 21: " \<And>a b. a \<in> E \<Longrightarrow>
+           a \<union> b \<in> S \<Longrightarrow>
+           a \<subseteq> V - {x} \<Longrightarrow>
+           b \<subseteq> {x} \<Longrightarrow> a \<union> b \<in> E"
+      by (metis Diff_cancel Un_Diff Un_empty_left assms(4) inf_sup_aci(5) subset_singletonD)
+
+    have 1: "
+      \<And>ab.  ab \<in> ((\<lambda>(x, y). x \<union> y) -` (E \<inter> S)) \<inter> (Pow (V - {x}) \<times> Pow{x}) \<Longrightarrow>
+        ab \<in> Sigma E (\<lambda>x. {y. (x \<union> y) \<in> S}) \<inter> (Pow (V - {x}) \<times> Pow{x})"
+        using 11 by clarsimp
+
+    also have 2: "
+      \<And>ab. ab \<in> Sigma E (\<lambda>x. {y. (x \<union> y) \<in> S}) \<inter> (Pow (V - {x}) \<times> Pow{x}) \<Longrightarrow>
+         ab \<in> ((\<lambda>(x, y). x \<union> y) -` (E \<inter> S)) \<inter> (Pow (V - {x}) \<times> Pow{x})"
+      using 21 by clarsimp
+    ultimately show ?thesis
+      apply (intro antisym)
+      by (meson subsetI)+
+  qed
+
+  have eR: "\<And>a. a \<in> E \<inter> set_pmf (pmf_of_set (Pow (V - {x}))) \<Longrightarrow>
+   measure_pmf.prob (pmf_of_set (Pow {x}))
+    ({y. even (card ((a \<union> y) \<inter> \<omega>)) = b} \<inter>
+     set_pmf (pmf_of_set (Pow {x}))) = 1/2 "
+    apply (subst measure_Int_set_pmf)
+    apply (intro single_var_parity_coin_flip)
+    subgoal using assms by clarsimp
+    subgoal using assms rev_finite_subset by blast
+    subgoal by (metis 2 IntD2 PowD assms(1) finite_Diff rev_finite_subset)
+    using 2 by blast
+
+  have "
+    prob_space.prob (pmf_of_set (Pow V))
+      (E \<inter> {c. even (card (c \<inter> \<omega>)) = b}) =
+    prob_space.prob (map_pmf (\<lambda>(x, y). x \<union> y)
+       (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x}))))
+      (E \<inter> {c. even (card (c \<inter> \<omega>)) = b})" unfolding * by auto
+  moreover have "... =
+    prob_space.prob (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x})))
+      ((\<lambda>(x, y). x \<union> y) -` (E \<inter> {c. even (card (c \<inter> \<omega>)) = b}))"
+    by auto
+  moreover have "... =
+   prob_space.prob (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x})))
+    ((\<lambda>(x, y). x \<union> y) -` (E \<inter> {c. even (card (c \<inter> \<omega>)) = b}) \<inter> (Pow (V - {x}) \<times> Pow{x}))"
+    by (smt (verit) "1" "2" Int_iff Sigma_cong measure_pmf.measure_pmf_eq set_pair_pmf)
+  moreover have "... =
+   prob_space.prob (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x})))
+    (Sigma E (\<lambda>x. {y. even (card ((x \<union> y) \<inter> \<omega>)) = b}) \<inter> (Pow (V - {x}) \<times> Pow{x}))"
+    unfolding ** by auto
+  moreover have "... =
+   prob_space.prob (pair_pmf (pmf_of_set (Pow (V - {x}))) (pmf_of_set (Pow {x})))
+    (Sigma E (\<lambda>x. {y. even (card ((x \<union> y) \<inter> \<omega>)) = b}))"
+    by (smt (verit, best) 1 2 Int_iff Sigma_cong measure_pmf.measure_pmf_eq set_pair_pmf)
+  moreover have "... =
+    measure_pmf.prob (pmf_of_set (Pow (V - {x}))) E *
+    (1 / 2)"
+    apply (subst measure_pmf_prob_dependent_product_bound_eq'[OF _ _ eR])
+    by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma prob_random_xor_split:
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V) E =
+    1 / 2 * prob_space.prob (pmf_of_set (Pow V)) {e. (e,True) \<in> E} +
+    1 / 2 * prob_space.prob (pmf_of_set (Pow V)) {e. (e,False) \<in> E}"
+proof -
+  have fin: "finite (set_pmf (random_xor V))"
+    by (simp add: V set_pmf_random_xor)
+
+  have fin2: "finite ((\<lambda>(x, y). (y, x)) -` set_pmf (random_xor V))"
+    by(auto intro!: finite_vimageI[OF fin] simp add: inj_def)
+
+  have rw: "{x. (x, b) \<in> E \<and> (x, b) \<in> set_pmf (random_xor V)} =
+    {x. (x,b) \<in> E} \<inter> set_pmf (pmf_of_set (Pow V))" for b
+    by (auto simp add: V set_pmf_random_xor Pow_not_empty)
+
+  have "prob_space.prob (random_xor V) E =
+    prob_space.prob (random_xor V) (E \<inter> set_pmf (random_xor V))"
+    by (simp add: measure_Int_set_pmf)
+
+  moreover have "... =
+     measure_pmf.prob
+     (pair_pmf (bernoulli_pmf (1 / 2))
+       (pmf_of_set (Pow V)))
+     ((\<lambda>(x, y). (y, x)) -` (E \<inter> set_pmf (random_xor V)))"
+    unfolding random_xor_def
+    apply (subst pair_commute_pmf)
+    by simp
+  moreover have "... =
+    1 / 2 *
+      measure_pmf.prob (pmf_of_set (Pow V)) {x. (x, True) \<in> E} +
+    1 / 2 *
+      measure_pmf.prob (pmf_of_set (Pow V)) {x. (x, False) \<in> E}"
+    unfolding pair_pmf_def
+    apply (subst prob_bernoulli_bind_pmf)
+    using fin2
+    unfolding map_pmf_def[symmetric] measure_map_pmf
+    by (auto simp add: vimage_def rw simp add: measure_Int_set_pmf)
+  ultimately show ?thesis by auto
+qed
+
+lemma prob_random_xor_nonempty_parity:
+  assumes V: "finite V"
+  assumes \<omega>: "x \<in> \<omega>" "\<omega> \<subseteq> V"
+  assumes E: "\<And>c. c \<in> E \<longleftrightarrow> (fst c - {x},snd c) \<in> E"
+  shows "prob_space.prob (random_xor V)
+    (E \<inter> {c. satisfies_xor c \<omega> = b}) =
+    1 / 2 * prob_space.prob (random_xor (V - {x})) E"
+proof -
+  have *: "{e. (e, b') \<in> E \<inter> {c. satisfies_xor c \<omega> = b}} =
+    {e. (e, b') \<in> E} \<inter> {c. even (card (c \<inter> \<omega>)) = (b \<noteq> b')}" for b'
+    by (auto simp add: Int_commute)
+
+  have "prob_space.prob (random_xor V)
+    (E \<inter> {c. satisfies_xor c \<omega> = b})  =
+    1 / 2 *
+    measure_pmf.prob (pmf_of_set (Pow V))
+     {e. (e, True) \<in> E \<inter> {c. satisfies_xor c \<omega> = b}} +
+    1 / 2 *
+    measure_pmf.prob (pmf_of_set (Pow V))
+     {e. (e, False) \<in> E \<inter> {c. satisfies_xor c \<omega> = b}}"
+    unfolding prob_random_xor_split[OF V] by auto
+  also have "... =
+    1 / 2 *
+    measure_pmf.prob (pmf_of_set (Pow V))
+     ({e. (e, True) \<in> E} \<inter> {c. even (card (c \<inter> \<omega>)) = (b \<noteq> True)}) +
+    1 / 2 *
+    measure_pmf.prob (pmf_of_set (Pow V))
+     ({e. (e, False) \<in> E} \<inter> {c. even (card (c \<inter> \<omega>)) = (b \<noteq> False)})"
+    unfolding * by auto
+  also have "... =
+    1 / 2 *
+    (1 / 2 *
+     measure_pmf.prob (pmf_of_set (Pow (V - {x})))
+      {e. (e, True) \<in> E} +
+     1 / 2 *
+     measure_pmf.prob (pmf_of_set (Pow (V - {x})))
+      {e. (e, False) \<in> E})"
+    apply (subst prob_pmf_of_set_nonempty_parity[OF V \<omega>])
+    subgoal using E by clarsimp
+    apply (subst prob_pmf_of_set_nonempty_parity[OF V \<omega>])
+    using E by auto
+  also have "... =
+    1 / 2 * measure_pmf.prob (random_xor (V - {x})) E"
+    apply (subst prob_random_xor_split[symmetric])
+    using V by auto
+  finally show ?thesis by auto
+qed
+
+lemma pair_satisfies_random_xor_parity_1:
+  assumes V:"finite V"
+  assumes x: "x \<notin> \<omega>" "x \<in> \<omega>'"
+  assumes \<omega>: "\<omega> \<subseteq> V" "\<omega>' \<subseteq> V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b'} = 1 / 4"
+proof -
+  have wa: "\<omega> \<inter> (a - {x}) = \<omega> \<inter> a" for a
+    using x
+    by blast
+  have "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b'} =
+    prob_space.prob (random_xor V)
+    ({c. satisfies_xor c \<omega> = b} \<inter> {c. satisfies_xor c \<omega>' = b'})"
+    by (simp add: Collect_conj_eq)
+  also have "... =
+    1 / 2 *
+    measure_pmf.prob (random_xor (V - {x})) {c. satisfies_xor c \<omega> = b}"
+    apply (subst prob_random_xor_nonempty_parity[OF V x(2) \<omega>(2)])
+    by (auto simp add: wa)
+  also have "... = 1/4"
+    apply (subst satisfies_random_xor_parity)
+    using V by auto
+  finally show ?thesis by auto
+qed
+
+lemma pair_satisfies_random_xor_parity:
+  assumes V:"finite V"
+  assumes \<omega>: "\<omega> \<noteq> \<omega>'" "\<omega> \<subseteq> V" "\<omega>' \<subseteq> V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b'} = 1 / 4"
+proof -
+  obtain x where "x \<notin> \<omega> \<and> x \<in> \<omega>' \<or> x \<notin> \<omega>' \<and> x \<in> \<omega>"
+    using \<omega>
+    by blast
+  moreover {
+    assume x: "x \<notin> \<omega>" "x \<in> \<omega>'"
+    have ?thesis using pair_satisfies_random_xor_parity_1[OF V x \<omega>(2-3)]
+      by blast
+  }
+  moreover {
+    assume x: "x \<notin> \<omega>'" "x \<in> \<omega>"
+    then have ?thesis using pair_satisfies_random_xor_parity_1[OF V x \<omega>(3) \<omega>(2)]
+      by (simp add: Collect_conj_eq Int_commute)
+  }
+  ultimately show ?thesis by auto
+qed
+
+lemma prob_pmf_of_set_nonempty_parity_UNIV:
+  assumes "finite V"
+  assumes "x \<in> \<omega>" "\<omega> \<subseteq> V"
+  shows "prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (c \<inter> \<omega>)) = b} = 1 / 2"
+  using prob_pmf_of_set_nonempty_parity[OF assms, of UNIV]
+  by auto
+
+lemma prob_Pow_split:
+  assumes "\<omega> \<subseteq> V" "finite V"
+  shows "prob_space.prob (pmf_of_set (Pow V))
+    {x. P (\<omega> \<inter> x) \<and> Q ((V - \<omega>) \<inter> x)} =
+  prob_space.prob (pmf_of_set (Pow \<omega>))
+    {x. P x} *
+  prob_space.prob (pmf_of_set (Pow (V - \<omega>)))
+    {x. Q x}"
+proof -
+  have 1: "set_pmf (pmf_of_set (Pow \<omega>)) = Pow \<omega>"
+    by (meson Pow_not_empty assms(1) assms(2) finite_Pow_iff finite_subset set_pmf_of_set)
+  have 2: "set_pmf
+         (pmf_of_set (Pow (V - \<omega>))) = Pow (V - \<omega> )"
+    by (simp add: Pow_not_empty assms(2))
+
+  have *: "(pmf_of_set (Pow \<omega> \<times> Pow (V - \<omega>))) =
+     (pair_pmf (pmf_of_set (Pow \<omega>)) (pmf_of_set (Pow (V - \<omega>))))"
+    unfolding 1 2
+    apply (subst pmf_of_set_prod)
+    using assms rev_finite_subset by auto
+  have **: "(((\<lambda>(x, y). x \<union> y) -`
+      {x. P (\<omega> \<inter> x) \<and> Q ((V - \<omega>) \<inter> x)}) \<inter> ((Pow \<omega>) \<times> (Pow (V - \<omega>)))) =
+    ({x. P x} \<inter> Pow \<omega>) \<times> ({x. Q x} \<inter> Pow (V - \<omega>))"
+    apply (rule antisym)
+    subgoal
+      apply clarsimp
+      by (smt (verit) Diff_disjoint Int_Un_eq(4) inf.orderE inf_commute inf_sup_distrib1 sup_bot.right_neutral sup_commute)
+    apply (intro subsetI)
+    apply clarsimp
+    by (smt (verit, ccfv_threshold) Diff_Int Diff_disjoint Diff_empty Diff_eq_empty_iff Un_Int_assoc_eq Un_commute sup_bot.left_neutral)
+
+  have "prob_space.prob (pmf_of_set (Pow V))
+    {x. P (\<omega> \<inter> x) \<and> Q ((V - \<omega>) \<inter> x)} =
+    prob_space.prob (map_pmf (\<lambda>(x,y). x \<union> y)
+      (pmf_of_set (Pow \<omega> \<times> Pow (V - \<omega>))))
+    {x. P (\<omega> \<inter> x) \<and>  Q ((V - \<omega>) \<inter> x)}"
+    apply (subst pmf_of_set_powerset_split[symmetric, OF assms(1-2)])
+    by auto
+  moreover have "... =
+    measure_pmf.prob
+     (pair_pmf (pmf_of_set (Pow \<omega>)) (pmf_of_set (Pow (V - \<omega>))))
+     ((\<lambda>(x, y). x \<union> y) -`
+      {x. P (\<omega> \<inter> x) \<and> Q ((V - \<omega>) \<inter> x)})"
+    unfolding measure_map_pmf
+    using *
+    by presburger
+  moreover have "... =
+    measure_pmf.prob
+     (pair_pmf (pmf_of_set (Pow \<omega>)) (pmf_of_set (Pow (V - \<omega>))))
+     (((\<lambda>(x, y). x \<union> y) -`
+      {x. P (\<omega> \<inter> x) \<and> Q ((V - \<omega>) \<inter> x)}) \<inter> ((Pow \<omega>) \<times> (Pow (V - \<omega>))))"
+    using 1 2
+    by (smt (verit) Int_Collect Int_def Sigma_cong inf_idem measure_pmf.measure_pmf_eq set_pair_pmf)
+  moreover have "... =
+     measure_pmf.prob
+     (pair_pmf (pmf_of_set (Pow \<omega>)) (pmf_of_set (Pow (V - \<omega>))))
+      (({x. P x} \<inter> Pow \<omega>) \<times> ({x. Q x} \<inter> Pow (V - \<omega>)))"
+    unfolding **
+    by auto
+  moreover have "... =
+     measure_pmf.prob
+     (pmf_of_set (Pow \<omega>)) ({x. P x} \<inter> Pow \<omega>) *
+     measure_pmf.prob
+     (pmf_of_set (Pow (V - \<omega>))) ({x. Q x} \<inter> Pow (V - \<omega>))"
+    apply (intro measure_pmf_prob_product)
+    subgoal by (meson assms(1) assms(2) countable_finite finite_Int finite_Pow_iff rev_finite_subset)
+    by (simp add: assms(2) countable_finite)
+  moreover have "... =
+     measure_pmf.prob
+     (pmf_of_set (Pow \<omega>)) {x. P x} *
+     measure_pmf.prob
+     (pmf_of_set (Pow (V - \<omega>))) {x. Q x}"
+    by (metis "1" "2" measure_Int_set_pmf)
+  ultimately show ?thesis by auto
+qed
+
+(* Split probability for two disjoint non-empty sets *)
+lemma disjoint_prob_pmf_of_set_nonempty:
+  assumes \<omega>: "x \<in> \<omega>" "\<omega> \<subseteq> V"
+  assumes \<omega>': "x' \<in> \<omega>'" "\<omega>' \<subseteq> V"
+  assumes "\<omega> \<inter> \<omega>' = {}"
+  assumes V: "finite V"
+  shows "prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and> even (card (\<omega>' \<inter> c)) = b'} = 1 / 4"
+proof -
+  have "prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and> even (card (\<omega>' \<inter> c)) = b'} =
+    prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and> even (card (((V - \<omega>) \<inter> c) \<inter> \<omega>')) = b'}"
+    by (smt (verit) Collect_cong Diff_Diff_Int Diff_eq_empty_iff Int_Diff Int_commute \<omega>'(2) assms(5) inf.orderE)
+
+  moreover have "... =
+    measure_pmf.prob (pmf_of_set (Pow \<omega>))
+     {x. even (card x) = b} *
+    measure_pmf.prob (pmf_of_set (Pow (V - \<omega>)))
+     {x. even (card (x \<inter> \<omega>')) = b'}"
+    apply (subst prob_Pow_split)
+    using assms by auto
+  moreover have "... =
+    measure_pmf.prob (pmf_of_set (Pow \<omega>))
+     {x. even (card (x \<inter> \<omega>)) = b} *
+    measure_pmf.prob (pmf_of_set (Pow (V - \<omega>)))
+     {x. even (card (x \<inter> \<omega>')) = b'} "
+    by (smt (verit, best) PowD Pow_not_empty \<omega>(2) assms(6) finite_Pow_iff inf.orderE measure_pmf.measure_pmf_eq mem_Collect_eq rev_finite_subset set_pmf_of_set)
+
+   moreover have "... = 1/4"
+    apply (subst prob_pmf_of_set_nonempty_parity_UNIV[OF _ \<omega>(1)])
+     subgoal using assms rev_finite_subset by blast
+     subgoal by simp
+    apply (subst prob_pmf_of_set_nonempty_parity_UNIV)
+    using assms by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma measure_pmf_prob_product_finite_set_pmf:
+  assumes "finite (set_pmf M)" "finite (set_pmf N)"
+  shows "measure_pmf.prob (pair_pmf M N) (A \<times> B) =
+  measure_pmf.prob M A * measure_pmf.prob N B"
+proof -
+  have A: "measure_pmf.prob M A = measure_pmf.prob M (A \<inter> set_pmf M)"
+    by (simp add: measure_Int_set_pmf)
+  have B: "measure_pmf.prob N B = measure_pmf.prob N (B \<inter> set_pmf N)"
+    by (simp add: measure_Int_set_pmf)
+  have "measure_pmf.prob M A * measure_pmf.prob N B =
+    measure_pmf.prob M (A \<inter> set_pmf M) *  measure_pmf.prob N (B \<inter> set_pmf N)"
+    using A B by auto
+  moreover have "... = measure_pmf.prob (pair_pmf M N)
+     ((A \<inter> set_pmf M) \<times> (B \<inter> set_pmf N))"
+    apply (subst measure_pmf_prob_product[symmetric])
+    by auto
+  moreover have "... = measure_pmf.prob (pair_pmf M N)
+     ((A \<times> B) \<inter> set_pmf (pair_pmf M N))"
+    by (simp add: Times_Int_Times)
+  moreover have "... = measure_pmf.prob (pair_pmf M N)
+     ((A \<times> B) )"
+    using measure_Int_set_pmf by blast
+  ultimately show ?thesis by auto
+qed
+
+lemma prob_random_xor_split_space:
+  assumes "\<omega> \<subseteq> V" "finite V"
+  shows "prob_space.prob (random_xor V)
+    {(x,b). P (\<omega> \<inter> x) b \<and> Q ((V - \<omega>) \<inter> x)} =
+  prob_space.prob (random_xor \<omega>)
+    {(x,b). P x b} *
+  prob_space.prob (pmf_of_set (Pow (V - \<omega>)))
+    {x. Q x}"
+proof -
+  have d1: "set_pmf (random_xor \<omega>) = Pow \<omega> \<times> UNIV"
+    by (metis assms(1) assms(2) infinite_super set_pmf_random_xor)
+  have d2: "set_pmf (pmf_of_set (Pow (V - \<omega>))) = Pow (V- \<omega>)"
+    by (simp add: Pow_not_empty assms(2))
+  have rhs: "prob_space.prob (random_xor \<omega>)
+    {(x,b). P x b} *
+  prob_space.prob (pmf_of_set (Pow (V - \<omega>)))
+    {x. Q x} =
+  prob_space.prob (pair_pmf (random_xor \<omega>) (pmf_of_set (Pow (V - \<omega>))))
+    ({(x,b). P x b} \<times> {x. Q x})"
+    apply (subst measure_pmf_prob_product_finite_set_pmf)
+    subgoal by (metis Pow_def assms(1) assms(2) finite_Collect_subsets finite_SigmaI finite_code rev_finite_subset set_pmf_random_xor)
+    using assms by (auto simp add: Pow_not_empty)
+
+  from pmf_of_set_powerset_split[OF assms]
+  have *: "pmf_of_set (Pow V) =
+    map_pmf (\<lambda>(x, y). x \<union> y)
+   (pair_pmf (pmf_of_set (Pow \<omega>)) (pmf_of_set (Pow (V - \<omega>))))"
+    by (metis Pow_not_empty assms(1) assms(2) finite_Diff finite_Pow_iff pmf_of_set_prod rev_finite_subset)
+
+  have **: "random_xor V =
+    map_pmf (\<lambda>((x,b),y). (x \<union> y,b)) (pair_pmf (random_xor \<omega>) (pmf_of_set (Pow (V - \<omega>))))"
+    unfolding random_xor_def *
+    including monad_normalisation
+    by (auto simp add: pair_pmf_def map_pmf_def case_prod_unfold)
+
+  have "prob_space.prob (random_xor V) {(x,b). P (\<omega> \<inter> x) b \<and> Q ((V - \<omega>) \<inter> x)} =
+    measure_pmf.prob
+     (pair_pmf (random_xor \<omega>) (pmf_of_set (Pow (V - \<omega>))))
+     {y. P (\<omega> \<inter> (fst (fst y) \<union> snd y)) (snd (fst y)) \<and>
+         Q ((V - \<omega>) \<inter> (fst (fst y) \<union> snd y))}"
+    unfolding **
+    by (auto simp add:case_prod_unfold)
+
+  moreover have "... =
+  prob_space.prob (pair_pmf (random_xor \<omega>) (pmf_of_set (Pow (V - \<omega>))))
+    ({(x,b). P x b} \<times> {x. Q x})"
+    apply (intro measure_pmf.measure_pmf_eq[where p ="pair_pmf (random_xor \<omega>)
+       (pmf_of_set (Pow (V - \<omega>)))"])
+    subgoal by simp
+    apply (clarsimp simp add: d1 d2)
+    by (smt (verit, del_insts) Diff_disjoint Int_Diff boolean_algebra_cancel.sup0 inf.orderE inf_commute inf_sup_distrib1 sup_bot.left_neutral)
+  ultimately show ?thesis using rhs
+    by simp
+qed
+
+lemma three_disjoint_prob_random_xor_nonempty:
+  assumes \<omega>: "\<omega> \<noteq> {}" "\<omega> \<subseteq> V"
+  assumes \<omega>': "\<omega>' \<noteq> {}" "\<omega>' \<subseteq> V"
+  assumes I: "I \<subseteq> V"
+  assumes int: "I \<inter> \<omega> = {}" "I \<inter> \<omega>' = {}" "\<omega> \<inter> \<omega>' = {}"
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c I = b \<and>
+      even (card (\<omega> \<inter> fst c)) = b' \<and>
+      even (card (\<omega>' \<inter> fst c)) = b''} = 1 / 8"
+proof -
+  have finI: "finite I"
+    using V I
+    using rev_finite_subset by blast
+  have finVI: "finite (V - I)"
+    using V I
+    using rev_finite_subset by blast
+  obtain x x' where x: "x \<in> \<omega>" "x' \<in> \<omega>'" using \<omega> \<omega>'
+    by blast
+
+  have rw1:"\<omega> \<inter> ((V - I) \<inter> xx) = \<omega> \<inter>  xx " for xx
+    by (metis Diff_Int_distrib2 Diff_empty \<omega>(2) assms(6) inf.absorb_iff2 inf_assoc inf_left_commute)
+
+  have rw2:"\<omega>' \<inter> ((V - I) \<inter> xx)= \<omega>' \<inter>  xx" for xx
+    by (metis Diff_Int_distrib2 Diff_empty \<omega>'(2) assms(7) inf.absorb_iff2 inf_assoc inf_left_commute)
+
+  have "prob_space.prob (random_xor V)
+    {c. satisfies_xor c I = b \<and>
+      even (card ( \<omega> \<inter> fst c )) = b' \<and>
+      even (card (\<omega>' \<inter>  fst c )) = b''} =
+    prob_space.prob (random_xor V)
+    {(x,bb). satisfies_xor (I \<inter> x, bb) I = b \<and>
+      even (card (\<omega> \<inter> ((V - I) \<inter> x))) = b' \<and>
+      even (card ( \<omega>' \<inter> ((V - I) \<inter> x))) = b''}"
+    apply (intro arg_cong[where f = "prob_space.prob (random_xor V)"])
+    unfolding rw1 rw2 satisfies_xor_inter
+    by (smt (verit) Collect_cong prod.collapse split_conv)
+
+  moreover have "... =
+    measure_pmf.prob (random_xor I)
+     {c. satisfies_xor c I = b} *
+    measure_pmf.prob (pmf_of_set (Pow (V - I)))
+     {x. even (card (\<omega> \<inter> x)) = b' \<and>
+         even (card (\<omega>' \<inter> x)) = b''}"
+    apply (subst prob_random_xor_split_space[OF I V])
+    by (metis (no_types, lifting) Collect_cong case_prodE case_prodI2)
+  moreover have "... = 1 / 8"
+    apply (subst satisfies_random_xor_parity[OF finI])
+    apply (subst disjoint_prob_pmf_of_set_nonempty)
+    using x \<omega> \<omega>' int finVI by auto
+  ultimately show ?thesis by auto
+qed
+
+(* Split probability for three disjoint non-empty sets *)
+lemma three_disjoint_prob_pmf_of_set_nonempty:
+  assumes \<omega>: "x \<in> \<omega>" "\<omega> \<subseteq> V"
+  assumes \<omega>': "x' \<in> \<omega>'" "\<omega>' \<subseteq> V"
+  assumes \<omega>'': "x'' \<in> \<omega>''" "\<omega>'' \<subseteq> V"
+  assumes int: "\<omega> \<inter> \<omega>' = {}" "\<omega>' \<inter> \<omega>'' = {}" "\<omega>'' \<inter> \<omega> = {}"
+  assumes V: "finite V"
+  shows "prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and> even (card (\<omega>' \<inter> c)) = b' \<and> even (card (\<omega>'' \<inter> c)) = b''} = 1 / 8"
+proof -
+  have "prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and> even (card (\<omega>' \<inter> c)) = b' \<and> even (card (\<omega>'' \<inter> c)) = b''} =
+    prob_space.prob (pmf_of_set (Pow V))
+    {c. even (card (\<omega> \<inter> c)) = b \<and>
+        even (card (((V - \<omega>) \<inter> c) \<inter> \<omega>')) = b' \<and>
+        even (card (((V - \<omega>) \<inter> c) \<inter> \<omega>'')) = b''}"
+    by (smt (verit,best) Collect_cong Diff_Diff_Int Diff_eq_empty_iff Int_Diff Int_commute \<omega>' \<omega>'' int inf.orderE)
+
+  moreover have "... =
+    measure_pmf.prob (pmf_of_set (Pow \<omega>))
+     {x. even (card x) = b} *
+    measure_pmf.prob (pmf_of_set (Pow (V - \<omega>)))
+     {x. even (card (\<omega>' \<inter> x)) = b' \<and> even (card (\<omega>'' \<inter> x)) = b''}"
+    apply (subst prob_Pow_split)
+    using assms by (auto simp add: inf.commute)
+  moreover have "... =
+    measure_pmf.prob (pmf_of_set (Pow \<omega>))
+     {x. even (card (x \<inter> \<omega>)) = b} *
+    measure_pmf.prob (pmf_of_set (Pow (V - \<omega>)))
+     {x. even (card (\<omega>' \<inter> x)) = b'\<and> even (card (\<omega>'' \<inter> x)) = b''} "
+    by (smt (verit, best) PowD Pow_not_empty \<omega> V finite_Pow_iff inf.orderE measure_pmf.measure_pmf_eq mem_Collect_eq rev_finite_subset set_pmf_of_set)
+
+   moreover have "... = 1/8"
+    apply (subst prob_pmf_of_set_nonempty_parity_UNIV[OF _ \<omega>(1)])
+     subgoal using \<omega>(2) V rev_finite_subset by blast
+     subgoal by simp
+     apply (subst disjoint_prob_pmf_of_set_nonempty)
+     using assms by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma four_disjoint_prob_random_xor_nonempty:
+  assumes \<omega>: "\<omega> \<noteq> {}" "\<omega> \<subseteq> V"
+  assumes \<omega>': "\<omega>' \<noteq> {}" "\<omega>' \<subseteq> V"
+  assumes \<omega>'': "\<omega>'' \<noteq> {}" "\<omega>'' \<subseteq> V"
+  assumes I: "I \<subseteq> V"
+  assumes int: "I \<inter> \<omega> = {}" "I \<inter> \<omega>' = {}" "I \<inter> \<omega>'' = {}"
+    "\<omega> \<inter> \<omega>' = {}" "\<omega>' \<inter> \<omega>'' = {}" "\<omega>'' \<inter> \<omega> = {}"
+  assumes V: "finite V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c I = b0 \<and>
+      even (card (\<omega> \<inter> fst c)) = b \<and>
+      even (card (\<omega>' \<inter> fst c)) = b' \<and>
+      even (card (\<omega>'' \<inter> fst c)) = b''} = 1 / 16"
+proof -
+  have finI: "finite I"
+    using V I
+    using rev_finite_subset by blast
+  have finVI: "finite (V - I)"
+    using V I
+    using rev_finite_subset by blast
+  obtain x x' x'' where x: "x \<in> \<omega>" "x' \<in> \<omega>'" "x'' \<in> \<omega>''"
+    using \<omega> \<omega>' \<omega>''
+    by blast
+
+  have rw1:"\<omega> \<inter> ((V - I) \<inter> xx) = \<omega> \<inter>  xx " for xx
+    by (metis Diff_Int_distrib2 Diff_empty \<omega>(2) int(1) inf.absorb_iff2 inf_assoc inf_left_commute)
+
+  have rw2:"\<omega>' \<inter> ((V - I) \<inter> xx)= \<omega>' \<inter>  xx" for xx
+    by (metis Diff_Int_distrib2 Diff_empty \<omega>'(2) int(2) inf.absorb_iff2 inf_assoc inf_left_commute)
+
+  have rw3:"\<omega>'' \<inter> ((V - I) \<inter> xx)= \<omega>'' \<inter>  xx" for xx
+    by (metis Diff_Int_distrib2 Diff_empty \<omega>''(2) int(3) inf.absorb_iff2 inf_assoc inf_left_commute)
+
+  have "prob_space.prob (random_xor V)
+    {c. satisfies_xor c I = b0 \<and>
+      even (card (\<omega> \<inter> fst c)) = b \<and>
+      even (card (\<omega>' \<inter>  fst c)) = b' \<and>
+      even (card (\<omega>'' \<inter>  fst c)) = b''} =
+    prob_space.prob (random_xor V)
+    {(x,bb). satisfies_xor (I \<inter> x, bb) I = b0 \<and>
+      even (card (\<omega> \<inter> ((V - I) \<inter> x))) = b \<and>
+      even (card (\<omega>' \<inter> ((V - I) \<inter> x))) = b' \<and>
+      even (card (\<omega>'' \<inter> ((V - I) \<inter> x))) = b''}"
+    apply (intro arg_cong[where f = "prob_space.prob (random_xor V)"])
+    unfolding rw1 rw2 rw3 satisfies_xor_inter
+    by (smt (verit) Collect_cong prod.collapse split_conv)
+
+  moreover have "... =
+    measure_pmf.prob (random_xor I)
+     {c. satisfies_xor c I = b0} *
+    measure_pmf.prob (pmf_of_set (Pow (V - I)))
+     {x. even (card (\<omega> \<inter> x)) = b \<and>
+         even (card (\<omega>' \<inter> x)) = b' \<and>
+         even (card (\<omega>'' \<inter> x)) = b''}"
+    apply (subst prob_random_xor_split_space[OF I V])
+    by (metis (no_types, lifting) Collect_cong case_prodE case_prodI2)
+  moreover have "... = 1 / 16"
+    apply(subst satisfies_random_xor_parity[OF finI])
+    apply (subst three_disjoint_prob_pmf_of_set_nonempty)
+    using x \<omega> \<omega>' \<omega>'' int finVI by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma three_satisfies_random_xor_parity_1:
+  assumes V:"finite V"
+  assumes \<omega>: "\<omega> \<subseteq> V" "\<omega>' \<subseteq> V" "\<omega>'' \<subseteq> V"
+  assumes x: "x \<notin> \<omega>" "x \<notin> \<omega>'" "x \<in> \<omega>''"
+  assumes d: "\<omega> \<noteq> \<omega>'"
+  shows "prob_space.prob (random_xor V)
+    {c.
+    satisfies_xor c \<omega> = b \<and>
+    satisfies_xor c \<omega>' = b' \<and>
+    satisfies_xor c \<omega>'' = b''} = 1 / 8"
+proof -
+  have wa: "\<omega> \<inter> (a - {x}) = \<omega> \<inter> a" for a
+    using x
+    by blast
+  have wa': "\<omega>' \<inter> (a - {x}) = \<omega>' \<inter> a" for a
+    using x
+    by blast
+  have "prob_space.prob (random_xor V)
+    {c.
+      satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b' \<and>
+      satisfies_xor c \<omega>'' = b''} =
+    prob_space.prob (random_xor V)
+    ({c. satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b'} \<inter>
+      {c. satisfies_xor c \<omega>'' = b''})"
+    by (simp add: Collect_conj_eq inf_assoc)
+  moreover have "... =
+    1 / 2 *
+    measure_pmf.prob (random_xor (V - {x}))
+      {c. satisfies_xor c \<omega> = b \<and> satisfies_xor c \<omega>' = b'}"
+    apply (subst prob_random_xor_nonempty_parity[OF V x(3) \<omega>(3)])
+    by (auto simp add: wa wa')
+  moreover have "... = 1/8"
+    apply (subst pair_satisfies_random_xor_parity)
+    using V \<omega> x d by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma split_boolean_eq:
+  shows"(A \<longleftrightarrow> B) = (b \<longleftrightarrow> I) \<and>
+    (B \<longleftrightarrow> C) = (b' \<longleftrightarrow>  I) \<and>
+    (C \<longleftrightarrow> A) = (b'' \<longleftrightarrow> I)
+  \<longleftrightarrow>
+    I = odd(of_bool b + of_bool b' + of_bool b'') \<and>
+     (A = True \<and>
+      B = (b'=b'') \<and>
+      C = (b = b') \<or>
+      A = False \<and>
+      B = (b' \<noteq> b'') \<and>
+      C = (b \<noteq> b'))"
+  by auto
+
+lemma three_satisfies_random_xor_parity:
+  assumes V:"finite V"
+  assumes \<omega>:
+      "\<omega> \<noteq> \<omega>'" "\<omega> \<noteq> \<omega>''" "\<omega>' \<noteq> \<omega>''"
+      "\<omega> \<subseteq> V" "\<omega>' \<subseteq> V" "\<omega>'' \<subseteq> V"
+  shows "prob_space.prob (random_xor V)
+    {c. satisfies_xor c \<omega> = b \<and>
+        satisfies_xor c \<omega>' = b' \<and>
+        satisfies_xor c \<omega>'' = b''} = 1 / 8"
+proof -
+  have "(\<exists>x.
+    x \<in> \<omega> \<and> x \<notin> \<omega>' \<and> x \<notin> \<omega>'' \<or>
+    x \<in> \<omega>' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>'' \<or>
+    x \<in> \<omega>'' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>') \<or>
+    \<omega> - (\<omega>' \<union> \<omega>'') = {} \<and>
+    \<omega>' - (\<omega> \<union> \<omega>'') = {} \<and>
+    \<omega>'' - (\<omega> \<union> \<omega>') = {}"
+    by blast
+  moreover {
+    assume "(\<exists>x.
+    x \<in> \<omega> \<and> x \<notin> \<omega>' \<and> x \<notin> \<omega>'' \<or>
+    x \<in> \<omega>' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>'' \<or>
+    x \<in> \<omega>'' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>')"
+    then obtain x where "
+      x \<in> \<omega> \<and> x \<notin> \<omega>' \<and> x \<notin> \<omega>'' \<or>
+      x \<in> \<omega>' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>'' \<or>
+      x \<in> \<omega>'' \<and> x \<notin> \<omega> \<and> x \<notin> \<omega>'" by auto
+    moreover {
+      assume x: "x \<notin> \<omega>'" "x \<notin> \<omega>''" "x \<in> \<omega>"
+      have "measure_pmf.prob (random_xor V)
+       {c. satisfies_xor c \<omega>' = b' \<and>
+           satisfies_xor c \<omega>'' = b'' \<and>
+           satisfies_xor c \<omega> = b} = 1 / 8"
+        apply (intro three_satisfies_random_xor_parity_1[OF V _ _ _ x])
+        using \<omega> by auto
+      then have ?thesis
+        by (smt (verit, ccfv_SIG) Collect_cong)
+    }
+    moreover {
+      assume x: "x \<notin> \<omega>" "x \<notin> \<omega>''" "x \<in> \<omega>'"
+      have "measure_pmf.prob (random_xor V)
+       {c. satisfies_xor c \<omega> = b \<and>
+           satisfies_xor c \<omega>'' = b'' \<and>
+           satisfies_xor c \<omega>' = b'} = 1 / 8"
+        apply (intro three_satisfies_random_xor_parity_1[OF V _ _ _ x])
+        using \<omega> by auto
+      then have ?thesis
+        by (smt (verit, ccfv_SIG) Collect_cong)
+    }
+    moreover {
+      assume x: "x \<notin> \<omega>" "x \<notin> \<omega>'" "x \<in> \<omega>''"
+      have "measure_pmf.prob (random_xor V)
+       {c. satisfies_xor c \<omega> = b \<and>
+           satisfies_xor c \<omega>' = b' \<and>
+           satisfies_xor c \<omega>'' = b''} = 1 / 8"
+        apply (intro three_satisfies_random_xor_parity_1[OF V _ _ _ x])
+        using \<omega> by auto
+      then have ?thesis
+        by (smt (verit, ccfv_SIG) Collect_cong)
+    }
+    ultimately have ?thesis by auto
+  }
+  moreover {
+    assume dis: "\<omega> - (\<omega>' \<union> \<omega>'') = {} \<and>
+      \<omega>' - (\<omega> \<union> \<omega>'') = {} \<and>
+      \<omega>'' - (\<omega> \<union> \<omega>') = {}"
+
+    define A where "A = (\<omega> \<inter> \<omega>'') - \<omega>'"
+    define B where "B = (\<omega> \<inter> \<omega>') - \<omega>''"
+    define C where "C = (\<omega>' \<inter> \<omega>'') - \<omega>"
+    define I where "I = \<omega> \<inter> \<omega>' \<inter> \<omega>''"
+
+    have f: "finite A" "finite B" "finite C" "finite I"
+      unfolding A_def B_def C_def I_def
+      by (meson V \<omega> finite_Diff finite_Int rev_finite_subset)+
+
+    have s: "A \<subseteq> V" "B \<subseteq> V" "C \<subseteq> V" "I \<subseteq> V"
+      unfolding A_def B_def C_def I_def
+      using \<omega> by auto
+
+    have i: "I \<inter> A = {}" "I \<inter> B = {}" "I \<inter> C = {}"
+        "B \<inter> C = {}" "C \<inter> A = {}" "A \<inter> B = {}"
+      unfolding A_def B_def C_def I_def
+      by blast +
+
+    have s1: "\<omega> = A \<union> B \<union> I"
+      unfolding A_def B_def I_def
+      using dis by auto
+    have sx1: "satisfies_xor (xx,bb) \<omega> = b \<longleftrightarrow>
+      even (card (A \<inter> xx)) = even (card (B \<inter> xx)) = (b \<longleftrightarrow> satisfies_xor(xx,bb) I)" for xx bb
+      unfolding s1 satisfies_xor.simps Int_Un_distrib2
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using A_def B_def I_def by blast
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using A_def B_def I_def by blast
+      by auto
+
+    have s2: "\<omega>' = B \<union> C \<union> I"
+      unfolding B_def C_def I_def
+      using dis by auto
+    have sx2: "satisfies_xor (xx,bb) \<omega>' = b' \<longleftrightarrow>
+      even (card (B \<inter> xx)) = even (card (C \<inter> xx)) = (b' \<longleftrightarrow> satisfies_xor(xx,bb) I)" for xx bb
+      unfolding s2 satisfies_xor.simps Int_Un_distrib2
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using B_def C_def I_def by blast
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using B_def C_def I_def by blast
+      by auto
+
+    have s3: "\<omega>'' = A \<union> C \<union> I"
+      unfolding A_def C_def I_def
+      using dis by auto
+    have sx3: "satisfies_xor (xx,bb) \<omega>'' = b'' \<longleftrightarrow>
+      even (card (C \<inter> xx)) = even (card (A \<inter> xx)) = (b'' \<longleftrightarrow> satisfies_xor(xx,bb) I)" for xx bb
+      unfolding s3 satisfies_xor.simps Int_Un_distrib2
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using A_def B_def C_def I_def by blast
+      apply (subst card_Un_disjoint)
+      subgoal using f by auto
+      subgoal using f by auto
+      subgoal using A_def B_def C_def I_def by blast
+      by auto
+
+    have "A = {} \<and> B \<noteq> {} \<and> C \<noteq> {} \<or>
+      A \<noteq> {} \<and> B = {} \<and> C \<noteq> {} \<or>
+      A \<noteq> {} \<and> B \<noteq> {} \<and> C = {} \<or>
+      A \<noteq> {} \<and> B \<noteq> {} \<and> C \<noteq> {}"
+      by (metis Un_commute \<omega>(1) \<omega>(2) \<omega>(3) s1 s2 s3)
+
+    moreover {
+      assume as: "A = {}" "B \<noteq> {}" "C \<noteq> {}"
+      have "satisfies_xor (xx,bb) \<omega> = b
+        \<and> satisfies_xor (xx,bb) \<omega>' = b'
+        \<and> satisfies_xor (xx,bb) \<omega>'' = b'' \<longleftrightarrow>
+      (satisfies_xor (xx, bb) I =
+       odd (of_bool b + of_bool b' + of_bool b'') \<and>
+       (even (card (B \<inter> xx)) = (b' = b'') \<and>
+        even (card (C \<inter> xx)) = (b = b')))" for xx bb
+        unfolding sx1 sx2 sx3
+        apply(subst split_boolean_eq)
+        using as by simp
+      then have *: "{c. satisfies_xor c \<omega> = b
+        \<and> satisfies_xor c \<omega>' = b'
+        \<and> satisfies_xor c \<omega>'' = b''} =
+      {c. satisfies_xor c I =
+       odd (of_bool b + of_bool b' + of_bool b'') \<and>
+       even (card (B \<inter> fst c)) = (b' = b'') \<and>
+       even (card (C \<inter> fst c)) = (b = b')}"
+        by (smt (verit,best) Collect_cong prod.collapse)
+      have ?thesis
+        apply (subst *)
+        apply (intro three_disjoint_prob_random_xor_nonempty)
+        using as s i V by auto
+    }
+
+    moreover {
+      assume as: "A \<noteq> {}" "B \<noteq> {}" "C = {}"
+      have "satisfies_xor (xx,bb) \<omega>'' = b''
+        \<and> satisfies_xor (xx,bb) \<omega> = b
+        \<and> satisfies_xor (xx,bb) \<omega>' = b' \<longleftrightarrow>
+      (satisfies_xor (xx, bb) I =
+       odd (of_bool b'' + of_bool b + of_bool b') \<and>
+       (even (card (A \<inter> xx)) = (b = b') \<and>
+        even (card (B \<inter> xx)) = (b'' = b)))" for xx bb
+        unfolding sx1 sx2 sx3
+        apply(subst split_boolean_eq)
+        using as by simp
+      then have *: "{c. satisfies_xor c \<omega> = b
+        \<and> satisfies_xor c \<omega>' = b'
+        \<and> satisfies_xor c \<omega>'' = b''} =
+      {c. satisfies_xor c I =
+       odd (of_bool b'' + of_bool b + of_bool b') \<and>
+       (even (card (A \<inter> fst c)) = (b = b') \<and>
+        even (card (B \<inter> fst c)) = (b'' = b))}"
+        by (smt (verit,best) Collect_cong prod.collapse)
+      have ?thesis
+        apply (subst *)
+        apply (intro three_disjoint_prob_random_xor_nonempty)
+        using as s i V by auto
+    }
+
+    moreover {
+      assume as: "A \<noteq> {}" "B = {}" "C \<noteq> {}"
+      have "satisfies_xor (xx,bb) \<omega>' = b'
+        \<and> satisfies_xor (xx,bb) \<omega>'' = b''
+        \<and> satisfies_xor (xx,bb) \<omega> = b \<longleftrightarrow>
+      (satisfies_xor (xx, bb) I =
+       odd (of_bool b' + of_bool b'' + of_bool b) \<and>
+       (even (card (C \<inter> xx)) = (b'' = b) \<and>
+        even (card (A \<inter> xx)) = (b' = b'')))" for xx bb
+        unfolding sx1 sx2 sx3
+        apply(subst split_boolean_eq)
+        using as by simp
+      then have *: "{c. satisfies_xor c \<omega> = b
+        \<and> satisfies_xor c \<omega>' = b'
+        \<and> satisfies_xor c \<omega>'' = b''} =
+      {c. satisfies_xor c I =
+       odd (of_bool b' + of_bool b'' + of_bool b) \<and>
+       (even (card (C \<inter> fst c)) = (b'' = b) \<and>
+        even (card (A \<inter> fst c)) = (b' = b''))}"
+        by (smt (verit,best) Collect_cong prod.collapse)
+      have ?thesis
+        apply (subst *)
+        apply (intro three_disjoint_prob_random_xor_nonempty)
+        using as s i V by auto
+    }
+
+    moreover {
+      assume as: "A \<noteq> {}" "B \<noteq> {}" "C \<noteq> {}"
+      have 1: "satisfies_xor (xx,bb) \<omega> = b
+        \<and> satisfies_xor (xx,bb) \<omega>' = b'
+        \<and> satisfies_xor (xx,bb) \<omega>'' = b'' \<longleftrightarrow>
+      (satisfies_xor (xx, bb) I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> xx)) = True \<and>
+        even (card (B \<inter> xx)) = (b' = b'') \<and>
+        even (card (C \<inter> xx)) = (b = b') \<or>
+       satisfies_xor (xx, bb) I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> xx)) = False \<and>
+        even (card (B \<inter> xx)) = (b' \<noteq> b'') \<and>
+        even (card (C \<inter> xx)) = (b \<noteq> b'))" for xx bb
+        unfolding sx1 sx2 sx3
+        apply(subst split_boolean_eq)
+        by auto
+      have 2: "satisfies_xor c \<omega> = b
+        \<and> satisfies_xor c \<omega>' = b'
+        \<and> satisfies_xor c \<omega>'' = b'' \<longleftrightarrow>
+      (satisfies_xor c I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> fst c)) = True \<and>
+        even (card (B \<inter> fst c)) = (b' = b'') \<and>
+        even (card (C \<inter> fst c)) = (b = b') \<or>
+       satisfies_xor c I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> fst c)) = False \<and>
+        even (card (B \<inter> fst c)) = (b' \<noteq> b'') \<and>
+        even (card (C \<inter> fst c)) = (b \<noteq> b'))" for c
+      proof -
+        obtain xx bb where c:"c = (xx,bb)" by fastforce
+        show ?thesis unfolding c
+          apply (subst 1)
+          by auto
+      qed
+      have *: "{c. satisfies_xor c \<omega> = b
+        \<and> satisfies_xor c \<omega>' = b'
+        \<and> satisfies_xor c \<omega>'' = b''} =
+      {c. satisfies_xor c I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> fst c)) = True \<and>
+        even (card (B \<inter> fst c)) = (b' = b'') \<and>
+        even (card (C \<inter> fst c)) = (b = b')} \<union>
+      {c. satisfies_xor c I =
+        odd (of_bool b + of_bool b' + of_bool b'') \<and>
+        even (card (A \<inter> fst c)) = False \<and>
+        even (card (B \<inter> fst c)) = (b' \<noteq> b'') \<and>
+        even (card (C \<inter> fst c)) = (b \<noteq> b')}"
+        apply (subst Un_def)
+        apply (intro Collect_cong)
+        apply (subst 2)
+        by simp
+
+      have **: "1 / 16 +
+        measure_pmf.prob (random_xor V)
+         {c. satisfies_xor c I =
+             odd (of_bool b + of_bool b' +
+                  of_bool b'') \<and>
+             even (card (A \<inter> fst c)) =
+             False \<and>
+             even (card (B \<inter> fst c)) =
+             (b' \<noteq> b'') \<and>
+             even (card (C \<inter> fst c)) =
+             (b \<noteq> b')} =
+        1 / 8" 
+        apply (subst four_disjoint_prob_random_xor_nonempty)
+        using as s i V by auto
+      have ?thesis
+        apply (subst *)
+        apply (subst measure_pmf.finite_measure_Union)
+        subgoal by simp
+        subgoal by simp
+        subgoal by auto
+        apply (subst four_disjoint_prob_random_xor_nonempty)
+        using as s i V ** by auto
+    }
+
+    ultimately have ?thesis by auto
+  }
+  ultimately show ?thesis by auto
+qed
+
+subsection "Independence for repeated XORs"
+
+text \<open> We can lift the previous result to a list of independent sampled XORs. \<close>
+
+definition random_xors :: "'a set \<Rightarrow> nat \<Rightarrow>
+    (nat \<rightharpoonup> 'a set \<times> bool) pmf"
+  where "random_xors V n =
+    Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V))"
+
+(* The set of random XORs expressed in various ways*)
+lemma random_xors_set:
+  assumes V:"finite V"
+  shows
+    "PiE_dflt {..<n} None
+      (set_pmf \<circ> (\<lambda>_. map_pmf Some (random_xor V))) =
+     {xors. dom xors = {..<n} \<and>
+        ran xors \<subseteq> (Pow V) \<times> UNIV}" (is "?lhs = ?rhs")
+proof -
+  have "?lhs =
+    {f. dom f = {..<n} \<and>
+        (\<forall>x \<in> {..<n}. f x \<in> Some ` (Pow V \<times> UNIV))}"
+    unfolding PiE_dflt_def o_def set_map_pmf set_pmf_random_xor[OF V]
+    by force
+
+  also have "... = ?rhs"
+    apply (rule antisym)
+    subgoal
+      apply clarsimp
+      by (smt (z3) PowD domI image_iff mem_Collect_eq mem_Sigma_iff option.simps(1) ran_def subsetD)
+    apply clarsimp
+    by (smt (verit, ccfv_threshold) domD image_iff lessThan_iff ranI subsetD)
+  finally show ?thesis .
+qed
+
+lemma random_xors_eq:
+  assumes V:"finite V"
+  shows"random_xors V n =
+    pmf_of_set
+    {xors. dom xors = {..<n} \<and> ran xors \<subseteq> (Pow V) \<times> UNIV}"
+proof -
+  have "pmf_of_set
+    {xors. dom xors = {..<n} \<and>
+        ran xors \<subseteq> (Pow V) \<times> UNIV} =
+    pmf_of_set
+      (PiE_dflt {..<n} None
+      (set_pmf \<circ> (\<lambda>_. map_pmf Some (random_xor V))))"
+    unfolding random_xors_set[OF V] by auto
+  also have "... =
+    Pi_pmf {..<n} None
+     (\<lambda>x. pmf_of_set
+            ((set_pmf \<circ>
+              (\<lambda>_. map_pmf Some (random_xor V))) x))"
+    apply (subst Pi_pmf_of_set[symmetric])
+    by (auto simp add:set_pmf_random_xor[OF V] V)
+  also have "... = random_xors V n"
+    unfolding random_xors_def o_def set_map_pmf
+    apply (subst map_pmf_of_set_inj[symmetric])
+    subgoal by (auto simp add:set_pmf_random_xor[OF V] V)
+    subgoal by (auto simp add:set_pmf_random_xor[OF V] V)
+    subgoal by (auto simp add:set_pmf_random_xor[OF V] V)
+    by (metis V random_xor_pmf_of_set set_pmf_random_xor)
+  ultimately show ?thesis by auto
+qed
+
+(* The XOR hash function from a mapping nat \<rightharpoonup> XOR *)
+definition xor_hash ::
+  "('a \<rightharpoonup> bool) \<Rightarrow>
+   (nat \<rightharpoonup> ('a set \<times> bool)) \<Rightarrow>
+   (nat \<rightharpoonup> bool)"
+  where "xor_hash \<omega> xors =
+      (map_option
+        (\<lambda>xor. satisfies_xor xor {x. \<omega> x = Some True}) \<circ> xors)"
+
+lemma finite_map_set_nonempty:
+  assumes "R \<noteq> {}"
+  shows "
+    {xors.
+      dom xors = D \<and> ran xors \<subseteq> R} \<noteq> {}"
+proof -
+  obtain r where "r \<in> R"
+    using assms by blast
+  then have "(\<lambda>x. if x \<in> D then Some r else None) \<in>
+    {xors. dom xors = D \<and> ran xors \<subseteq> R}"
+    by (auto split:if_splits simp:ran_def)
+  thus ?thesis by auto
+qed
+
+lemma random_xors_set_pmf:
+  assumes V: "finite V"
+  shows "
+    set_pmf (random_xors V n) =
+      {xors. dom xors = {..<n} \<and>
+        ran xors \<subseteq> (Pow V) \<times> UNIV}"
+  unfolding random_xors_eq[OF V]
+  apply (intro set_pmf_of_set)
+  subgoal
+    apply (intro finite_map_set_nonempty)
+    by blast
+  apply (intro finite_set_of_finite_maps)
+  by (auto simp add: V)
+
+lemma finite_random_xors_set_pmf:
+  assumes V: "finite V"
+  shows "
+    finite (set_pmf (random_xors V n))"
+  unfolding random_xors_set_pmf[OF V]
+  by (auto intro!: finite_set_of_finite_maps simp add: V)
+
+lemma map_eq_1:
+  assumes "dom f = dom g"
+  assumes "\<And>x. x \<in> dom f \<Longrightarrow> the (f x) = the (g x)"
+  shows "f = g"
+  by (metis assms(1) assms(2) domIff map_le_antisym map_le_def option.expand)
+
+lemma xor_hash_eq_iff:
+  assumes "dom \<alpha> = {..<n}"
+  shows"xor_hash \<omega> x = \<alpha> \<longleftrightarrow>
+  (dom x = {..<n} \<and>
+  (\<forall>i. i < n \<longrightarrow>
+    (\<exists>xor. x i = Some xor \<and>
+    satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i))
+  ))"
+proof -
+  have 1: "xor_hash \<omega> x = \<alpha> \<longleftrightarrow>
+    (dom (xor_hash \<omega> x) = dom \<alpha>) \<and>
+    (\<forall>i \<in> dom \<alpha>. the (xor_hash \<omega> x i) = the (\<alpha> i))"
+    using map_eq_1 by fastforce
+  have 2: "dom (xor_hash \<omega> x) = dom x"
+    unfolding xor_hash_def
+    by auto
+  have 3: "\<And>i. i \<in> dom x \<Longrightarrow>
+    xor_hash \<omega> x i = Some (satisfies_xor (the (x i)) {x. \<omega> x = Some True})"
+    unfolding xor_hash_def
+    by fastforce
+  show ?thesis 
+    unfolding 1 assms 2
+    using 3
+    by (smt (verit, best) domD lessThan_iff option.sel)
+qed
+
+lemma xor_hash_eq_PiE_dflt:
+  assumes "dom \<alpha> = {..<n}"
+  shows
+    "{xors. xor_hash \<omega> xors = \<alpha>} =
+    PiE_dflt {..<n} None
+      (\<lambda>i. Some `
+        {xor. satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i)})"
+proof -
+  have *: "\<And>x xa a b.
+       (\<not> xa < n \<longrightarrow> x xa = None) \<Longrightarrow>
+       x xa = Some (a, b) \<Longrightarrow> xa < n"
+  by (metis option.distinct(2))
+  show ?thesis
+  unfolding PiE_dflt_def
+  unfolding xor_hash_eq_iff[OF assms]
+  by (auto intro: * simp del: satisfies_xor.simps)
+qed
+
+lemma prob_random_xors_xor_hash:
+  assumes V: "finite V"
+  assumes \<alpha>: "dom \<alpha> = {..<n}"
+  shows "
+  measure_pmf.prob (random_xors V n)
+    {xors. xor_hash \<omega> xors = \<alpha>} = 1 / 2  ^ n"
+proof -
+  have "measure_pmf.prob (random_xors V n)
+    {xors. xor_hash \<omega> xors = \<alpha>} =
+    measure_pmf.prob
+    (Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V)))
+    (PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i)}))"
+    unfolding random_xors_def xor_hash_eq_PiE_dflt[OF \<alpha>]
+    by auto
+  also have "... =
+    (\<Prod>x<n. measure_pmf.prob (random_xor V)
+             ({xor.
+               satisfies_xor xor {x. \<omega> x = Some True} =
+               the (\<alpha> x)}))"
+    by (subst measure_Pi_pmf_PiE_dflt)
+     (auto simp add: inj_vimage_image_eq)
+  also have "... = (\<Prod>x<n. 1/2)"
+    by (simp add: assms(1) satisfies_random_xor_parity)
+  also have "... = 1/ 2 ^ n"
+    by (simp add: power_one_over)
+  finally show ?thesis by auto
+qed
+
+lemma PiE_dflt_inter:
+  shows"PiE_dflt A dflt B \<inter> PiE_dflt A dflt B' =
+    PiE_dflt A dflt (\<lambda>b. B b \<inter> B' b)"
+  unfolding PiE_dflt_def
+  by auto
+
+lemma random_xors_xor_hash_pair:
+  assumes V: "finite V"
+  assumes \<alpha>: "dom \<alpha> = {..<n}"
+  assumes \<alpha>': "dom \<alpha>' = {..<n}"
+  assumes \<omega>: "dom \<omega> = V"
+  assumes \<omega>': "dom \<omega>' = V"
+  assumes neq: "\<omega> \<noteq> \<omega>'"
+  shows "
+  measure_pmf.prob (random_xors V n)
+    {xors. xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>'} =
+    1 / 4  ^ n"
+proof -
+  obtain y where "\<omega> y \<noteq> \<omega>' y"
+    using neq
+    by blast
+  then have neq:"{x. \<omega> x = Some True} \<noteq> {x. \<omega>' x = Some True}"
+    by (smt (verit, ccfv_threshold) assms(4) assms(5) domD domIff mem_Collect_eq)
+  have "measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>'} =
+    measure_pmf.prob (random_xors V n)
+      ({xors. xor_hash \<omega> xors = \<alpha>} \<inter>
+        {xors. xor_hash \<omega>' xors = \<alpha>'})"
+    by (simp add: Collect_conj_eq)
+  also have "... =
+    measure_pmf.prob
+    (Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V)))
+    (PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i)})
+    \<inter>
+    PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' i)}))"
+    unfolding random_xors_def xor_hash_eq_PiE_dflt[OF \<alpha>] xor_hash_eq_PiE_dflt[OF \<alpha>']
+    by auto
+  also have "... =
+    measure_pmf.prob
+    (Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V)))
+    (PiE_dflt {..<n} None
+      (\<lambda>i.
+      Some ` {xor.
+        satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i) \<and>
+        satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' i)}))"
+    unfolding PiE_dflt_inter
+    apply (subst image_Int[symmetric])
+    by (auto simp add: Collect_conj_eq)
+
+  also have "... =
+    (\<Prod>x<n. measure_pmf.prob (random_xor V)
+       ({xor.
+         satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> x) \<and>
+         satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' x)}))"
+    by (subst measure_Pi_pmf_PiE_dflt)
+     (auto simp add: inj_vimage_image_eq)
+  also have "... = (\<Prod>x<n. 1/4)"
+    apply (subst pair_satisfies_random_xor_parity)
+    using assms neq by auto
+  also have "... = 1/ 4 ^ n"
+    by (simp add: power_one_over)
+  finally show ?thesis by auto
+qed
+
+lemma random_xors_xor_hash_three:
+  assumes V: "finite V"
+  assumes \<alpha>: "dom \<alpha> = {..<n}"
+  assumes \<alpha>': "dom \<alpha>' = {..<n}"
+  assumes \<alpha>'': "dom \<alpha>'' = {..<n}"
+  assumes \<omega>: "dom \<omega> = V"
+  assumes \<omega>': "dom \<omega>' = V"
+  assumes \<omega>': "dom \<omega>'' = V"
+  assumes neq: "\<omega> \<noteq> \<omega>'" "\<omega>' \<noteq> \<omega>''" "\<omega>'' \<noteq> \<omega>"
+  shows "
+  measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>
+      \<and> xor_hash \<omega>' xors = \<alpha>'
+      \<and> xor_hash \<omega>'' xors = \<alpha>''} =
+    1 / 8  ^ n"
+proof -
+  obtain x y z where "\<omega> x \<noteq> \<omega>' x" "\<omega>' y \<noteq> \<omega>'' y" "\<omega>'' z \<noteq> \<omega> z"
+    using neq
+    by blast
+  then have neq:
+    "{x. \<omega> x = Some True} \<noteq> {x. \<omega>' x = Some True}"
+    "{x. \<omega>' x = Some True} \<noteq> {x. \<omega>'' x = Some True}"
+    "{x. \<omega>'' x = Some True} \<noteq> {x. \<omega> x = Some True}"
+    by (smt (verit, ccfv_threshold) assms domD domIff mem_Collect_eq)+
+  have "measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>' \<and> xor_hash \<omega>'' xors = \<alpha>''} =
+    measure_pmf.prob (random_xors V n)
+      ({xors. xor_hash \<omega> xors = \<alpha>} \<inter>
+      {xors. xor_hash \<omega>' xors = \<alpha>'} \<inter>
+      {xors. xor_hash \<omega>'' xors = \<alpha>''})"
+    by (simp add: measure_pmf.measure_pmf_eq)
+  moreover have "... =
+    measure_pmf.prob
+    (Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V)))
+    (PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i)})
+    \<inter>
+    PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' i)})
+    \<inter>
+    PiE_dflt {..<n} None
+      (\<lambda>i. Some ` {xor. satisfies_xor xor {x. \<omega>'' x = Some True} = the (\<alpha>'' i)}))"
+    unfolding random_xors_def xor_hash_eq_PiE_dflt[OF \<alpha>] xor_hash_eq_PiE_dflt[OF \<alpha>'] xor_hash_eq_PiE_dflt[OF \<alpha>'']
+    by auto
+  moreover have "... =
+    measure_pmf.prob
+    (Pi_pmf {..<(n::nat)} None
+      (\<lambda>_. map_pmf Some (random_xor V)))
+    (PiE_dflt {..<n} None
+      (\<lambda>i.
+      Some ` {xor.
+        satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> i) \<and>
+        satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' i) \<and>
+        satisfies_xor xor {x. \<omega>'' x = Some True} = the (\<alpha>'' i)}))
+    "
+    unfolding PiE_dflt_inter
+    apply (subst image_Int[symmetric])
+    subgoal by simp
+    apply (intro arg_cong[where f="measure_pmf.prob
+     (Pi_pmf {..<n} None
+       (\<lambda>_. map_pmf Some (random_xor V)))"])
+    apply (intro arg_cong[where f="PiE_dflt {..<n} None"])
+    by auto
+
+  moreover have "... =
+    (\<Prod>x<n. measure_pmf.prob (random_xor V)
+       ({xor.
+         satisfies_xor xor {x. \<omega> x = Some True} = the (\<alpha> x) \<and>
+         satisfies_xor xor {x. \<omega>' x = Some True} = the (\<alpha>' x)\<and>
+         satisfies_xor xor {x. \<omega>'' x = Some True} = the (\<alpha>'' x)}))"
+     apply (subst measure_Pi_pmf_PiE_dflt)
+     by (auto simp add: inj_vimage_image_eq)
+  moreover have "... = (\<Prod>x<n. 1/8)"
+    apply (subst three_satisfies_random_xor_parity)
+    subgoal using assms neq by clarsimp
+    subgoal using assms neq by clarsimp
+    subgoal using assms neq by clarsimp
+    subgoal using assms neq by clarsimp
+    subgoal using assms(5) by blast
+    subgoal using assms(6) by blast
+    subgoal using assms(7) by blast
+    by auto
+  moreover have "... = 1/ 8 ^ n"
+    by (simp add: power_one_over)
+  ultimately show ?thesis by auto
+qed
+
+end
diff --git a/thys/Approximate_Model_Counting/RandomXORHashFamily.thy b/thys/Approximate_Model_Counting/RandomXORHashFamily.thy
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/RandomXORHashFamily.thy
@@ -0,0 +1,302 @@
+section \<open>Random XOR hash family\<close>
+
+text \<open>This section defines a hash family based on random XORs and proves
+  that this hash family is 3-universal. \<close>
+
+theory RandomXORHashFamily imports
+  RandomXOR
+begin
+
+lemma finite_dom:
+  assumes "finite V"
+  shows "finite {w :: 'a \<rightharpoonup> bool. dom w = V}"
+proof -
+  have *: "{w :: 'a \<rightharpoonup> bool. dom w = V} =
+    {w. dom w = V \<and> ran w \<subseteq> {True,False}}"
+    by auto
+  show ?thesis unfolding *
+    apply (intro finite_set_of_finite_maps)
+    using assms by auto
+qed
+
+lemma xor_hash_eq_dom:
+  assumes "xor_hash \<omega> xors = \<alpha>"
+  shows "dom xors = dom \<alpha>"
+  using assms unfolding xor_hash_def
+  by auto
+
+lemma prob_random_xors_xor_hash_indicat_real:
+  assumes V: "finite V"
+  shows"
+  measure_pmf.prob (random_xors V n)
+    {xors. xor_hash \<omega> xors = \<alpha>} =
+     indicat_real {\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}} \<alpha> /
+     real (card {\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}})"
+proof -
+  have *: "{\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}} =
+     {\<alpha>. dom \<alpha> = {0..<n} \<and> ran \<alpha> \<subseteq> {True, False}}"
+    by auto
+  have **: "card {\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}} = 2^n"
+    unfolding *
+    apply (subst card_dom_ran)
+    by (auto simp add: numerals(2))
+  have "dom \<alpha> = {..<n} \<or> dom \<alpha> \<noteq> {..<n}"
+    by auto
+  moreover {
+    assume "dom \<alpha> = {..<n}"
+    from prob_random_xors_xor_hash[OF V this]
+    have ?thesis
+      unfolding **
+      by (simp add: \<open>dom \<alpha> = {..<n}\<close> atLeast0LessThan)
+  }
+  moreover {
+    assume *:"dom \<alpha> \<noteq> {..<n}"
+    then have "x \<in> set_pmf (random_xors V n) \<Longrightarrow>
+         \<alpha> \<noteq> xor_hash \<omega> x" for x
+      by (metis (mono_tags, lifting) V mem_Collect_eq random_xors_set_pmf xor_hash_eq_dom)
+    then have "measure_pmf.prob (random_xors V n)
+     {xors. xor_hash \<omega> xors = \<alpha>} = 0"
+      apply (intro measure_pmf.measure_exclude[where A = "set_pmf ((random_xors V n))"])
+      by (auto simp add: Sigma_Algebra.measure_def emeasure_pmf xor_hash_eq_dom)
+    then have ?thesis
+      by (simp add: * atLeast0LessThan)
+  }
+  ultimately show ?thesis
+    by auto
+qed
+
+lemma xor_hash_family_uniform:
+  assumes V: "finite V"
+  assumes "dom \<omega> = V"
+  shows "prob_space.uniform_on
+         (random_xors V n)
+         (xor_hash i) {\<alpha>. dom \<alpha> = {0..<n}}"
+  apply (intro measure_pmf.uniform_onI[where p = "random_xors V n"])
+  subgoal by clarsimp
+  subgoal  using finite_dom by blast
+  using prob_random_xors_xor_hash_indicat_real[OF V]
+  by (auto intro!: exI[where x = "(\<lambda>i. if i < n then Some True else None)"] split:if_splits)
+
+lemma random_xors_xor_hash_pair_indicat:
+  assumes V: "finite V"
+  assumes \<omega>: "dom \<omega> = V"
+  assumes \<omega>': "dom \<omega>' = V"
+  assumes neq: "\<omega> \<noteq> \<omega>'"
+  shows "
+  measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>'} =
+  (measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>} *
+   measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega>' xors = \<alpha>'})"
+proof -
+  have "dom \<alpha> = {..<n} \<and> dom \<alpha>' = {..<n} \<or>
+    \<not>(dom \<alpha> = {..<n} \<and> dom \<alpha>' = {..<n})" by auto
+  moreover {
+    assume *: "dom \<alpha> = {..<n}" "dom \<alpha>' = {..<n}"
+    have "measure_pmf.prob (random_xors V n)
+     {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>'} = 1 / 4 ^n"
+      by (simp add: "*"(1) "*"(2) assms(1) assms(2) assms(3) assms(4) random_xors_xor_hash_pair)
+    moreover have "
+    measure_pmf.prob (random_xors V n)
+      {xors.  xor_hash \<omega> xors = \<alpha>} = 1/2^n"
+      by (simp add: "*"(1) assms(1) prob_random_xors_xor_hash)
+    moreover have "
+    measure_pmf.prob (random_xors V n)
+      {xors.  xor_hash \<omega>' xors = \<alpha>'} = 1/2^n"
+      by (simp add: "*"(2) assms(1) prob_random_xors_xor_hash)
+    ultimately have ?thesis
+      by (metis (full_types) Groups.mult_ac(2) four_x_squared power2_eq_square power_mult power_one_over verit_prod_simplify(2))
+  }
+  moreover {
+    assume *: "dom \<alpha> \<noteq> {..<n} \<or> dom \<alpha>' \<noteq> {..<n}"
+    then have **: "x \<in> set_pmf (random_xors V n) \<Longrightarrow>
+         \<alpha> = xor_hash \<omega> x \<Longrightarrow>
+         \<alpha>' = xor_hash \<omega>' x \<Longrightarrow> False" for x
+      by (metis (mono_tags, lifting) CollectD assms(1) random_xors_set_pmf xor_hash_eq_dom)
+    have "measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>} = 0 \<or>
+     measure_pmf.prob (random_xors V n)
+      {xors.
+        xor_hash \<omega>' xors = \<alpha>'} = 0"
+      unfolding prob_random_xors_xor_hash_indicat_real[OF V]
+      by (metis (full_types) * atLeast0LessThan div_0 indicator_simps(2) mem_Collect_eq)
+    moreover have "
+    measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>'} = 0"
+      apply (intro measure_pmf.measure_exclude[where A = "set_pmf ((random_xors V n))"])
+      using ** by (auto simp add: Sigma_Algebra.measure_def emeasure_pmf)
+    ultimately have ?thesis by auto
+  }
+  ultimately show ?thesis by auto
+qed
+
+lemma prod_3_expand:
+  assumes "a \<noteq> b" "b \<noteq> c" "c \<noteq> a"
+  shows"(\<Prod>\<omega>\<in>{a, b, c}. f \<omega>) = f a * (f b * f c)"
+  using assms by auto
+
+lemma random_xors_xor_hash_three_indicat:
+  assumes V: "finite V"
+  assumes \<omega>: "dom \<omega> = V"
+  assumes \<omega>': "dom \<omega>' = V"
+  assumes \<omega>'': "dom \<omega>'' = V"
+  assumes neq: "\<omega> \<noteq> \<omega>'" "\<omega>' \<noteq> \<omega>''" "\<omega>'' \<noteq> \<omega>"
+  shows "
+  measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>
+    \<and> xor_hash \<omega>' xors = \<alpha>'
+    \<and> xor_hash \<omega>'' xors = \<alpha>''} =
+  (measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>} *
+   measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega>' xors = \<alpha>'} *
+   measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega>'' xors = \<alpha>''})"
+proof -
+  have "dom \<alpha> = {..<n} \<and> dom \<alpha>' = {..<n} \<and> dom \<alpha>'' = {..<n} \<or>
+    \<not>(dom \<alpha> = {..<n} \<and> dom \<alpha>' = {..<n} \<and> dom \<alpha>'' = {..<n})" by auto
+  moreover {
+    assume *: "dom \<alpha> = {..<n}" "dom \<alpha>' = {..<n}" "dom \<alpha>'' = {..<n}"
+    have 1:"measure_pmf.prob (random_xors V n)
+     {xors.
+      xor_hash \<omega> xors = \<alpha> \<and>
+      xor_hash \<omega>' xors = \<alpha>' \<and>
+      xor_hash \<omega>'' xors = \<alpha>''} = 1 / 8 ^n"
+      apply (intro random_xors_xor_hash_three)
+      using V * \<omega> \<omega>' \<omega>'' neq by auto
+    have 2:"
+    measure_pmf.prob (random_xors V n)
+      {xors.  xor_hash \<omega> xors = \<alpha>} = 1/2^n"
+      by (simp add: "*"(1) assms(1) prob_random_xors_xor_hash)
+    have 3:"
+    measure_pmf.prob (random_xors V n)
+      {xors.  xor_hash \<omega>' xors = \<alpha>'} = 1/2^n"
+      by (simp add: "*"(2) assms(1) prob_random_xors_xor_hash)
+    have 4: "
+    measure_pmf.prob (random_xors V n)
+      {xors.  xor_hash \<omega>'' xors = \<alpha>''} = 1/2^n"
+      by (simp add: "*"(3) assms(1) prob_random_xors_xor_hash)
+    have ?thesis
+      unfolding 1 2 3 4
+      by (metis (mono_tags, opaque_lifting) arith_simps(11) arith_simps(12) arith_simps(58) divide_divide_eq_left mult.right_neutral power_mult_distrib times_divide_eq_right)
+  }
+  moreover {
+    assume *: "dom \<alpha> \<noteq> {..<n} \<or> dom \<alpha>' \<noteq> {..<n} \<or> dom \<alpha>'' \<noteq> {..<n}"
+    then have **: "x \<in> set_pmf (random_xors V n) \<Longrightarrow>
+         \<alpha> = xor_hash \<omega> x \<Longrightarrow>
+         \<alpha>' = xor_hash \<omega>' x \<Longrightarrow>
+         \<alpha>'' = xor_hash \<omega>'' x \<Longrightarrow> False" for x
+      by (metis (mono_tags, lifting) CollectD assms(1) random_xors_set_pmf xor_hash_eq_dom)
+    have "measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha>} = 0 \<or>
+     measure_pmf.prob (random_xors V n)
+      {xors.
+        xor_hash \<omega>' xors = \<alpha>'} = 0 \<or>
+     measure_pmf.prob (random_xors V n)
+      {xors.
+        xor_hash \<omega>'' xors = \<alpha>''} = 0"
+      unfolding prob_random_xors_xor_hash_indicat_real[OF V]
+      by (metis (full_types) * atLeast0LessThan div_0 indicator_simps(2) mem_Collect_eq)
+    moreover have "
+    measure_pmf.prob (random_xors V n)
+    {xors.
+      xor_hash \<omega> xors = \<alpha> \<and> xor_hash \<omega>' xors = \<alpha>' \<and> xor_hash \<omega>'' xors = \<alpha>''} = 0"
+      apply (intro measure_pmf.measure_exclude[where A = "set_pmf ((random_xors V n))"])
+      using ** by (auto simp add: Sigma_Algebra.measure_def emeasure_pmf)
+    ultimately have ?thesis by auto
+  }
+  ultimately show ?thesis
+    by fastforce
+qed
+
+lemma xor_hash_3_indep:
+  assumes V: "finite V"
+  assumes J: "card J \<le> 3" "J \<subseteq> {\<alpha>. dom \<alpha> = V}"
+  shows "
+    measure_pmf.prob (random_xors V n)
+      {xors. \<forall>\<omega>\<in>J. xor_hash \<omega> xors = f \<omega>} =
+       (\<Prod>\<omega>\<in>J.
+          measure_pmf.prob (random_xors V n)
+           {xors. xor_hash \<omega> xors = f \<omega>})"
+proof -
+  have "card J = 0 \<or> card J = 1 \<or> card J = 2 \<or> card J = 3"
+    using assms by auto
+  moreover {
+    assume" card J = 0"
+    then have "J = {}"
+      by (meson assms(1) assms(3) card_eq_0_iff finite_dom finite_subset)
+    then have ?thesis
+      by clarsimp
+  }
+  moreover {
+    assume "card J = 1"
+    then obtain x where "J = {x}"
+      using card_1_singletonE by blast
+    then have ?thesis
+      by auto
+  }
+  moreover {
+    assume "card J = 2"
+    then obtain \<omega> \<omega>' where J:"J = {\<omega>, \<omega>'}" and
+      \<omega>: "\<omega> \<noteq> \<omega>'" "dom \<omega> = V" "dom \<omega>' = V"
+      unfolding card_2_iff
+      using J
+      by force
+    have ?thesis unfolding J
+      by (auto simp add: random_xors_xor_hash_pair_indicat V \<omega>)
+  }
+  moreover {
+    assume "card J = 3"
+    then obtain \<omega> \<omega>' \<omega>'' where J:"J = {\<omega>, \<omega>', \<omega>''}" and
+      \<omega>: "\<omega> \<noteq> \<omega>'" "\<omega>' \<noteq> \<omega>''" "\<omega>'' \<noteq> \<omega>"
+        "dom \<omega> = V" "dom \<omega>' = V" "dom \<omega>'' = V"
+      unfolding card_3_iff
+      using J
+      by force
+    have ?thesis unfolding J
+      by (auto simp add: random_xors_xor_hash_three_indicat V \<omega>  prod_3_expand[OF \<omega>(1-3)])
+  }
+  ultimately show ?thesis by auto
+qed
+
+lemma xor_hash_3_wise_indep:
+  assumes "finite V"
+  shows "prob_space.k_wise_indep_vars
+     (random_xors V n) 3
+     (\<lambda>_. Universal_Hash_Families_More_Independent_Families.discrete) xor_hash
+     {\<alpha>. dom \<alpha> = V}"
+  apply (subst prob_space.k_wise_indep_vars_def)
+  by (auto intro!: measure_pmf.indep_vars_pmf xor_hash_3_indep simp add: measure_pmf.prob_space_axioms assms card_mono dual_order.trans)
+
+theorem xor_hash_family_3_universal:
+  assumes "finite V"
+  shows"prob_space.k_universal
+    (random_xors V n) 3 xor_hash
+    {\<alpha>::'a \<rightharpoonup> bool. dom \<alpha> = V}
+    {\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}}"
+  apply (subst prob_space.k_universal_def)
+  subgoal by (clarsimp simp add: measure_pmf.prob_space_axioms )
+  using xor_hash_3_wise_indep assms xor_hash_family_uniform assms by blast
+
+corollary xor_hash_family_2_universal:
+  assumes "finite V"
+  shows"prob_space.k_universal
+    (random_xors V n) 2 xor_hash
+    {\<alpha>::'a \<rightharpoonup> bool. dom \<alpha> = V}
+    {\<alpha>::nat \<rightharpoonup> bool. dom \<alpha> = {0..<n}}"
+  using assms
+  by (auto intro!: prob_space.k_universal_mono[OF _ _ xor_hash_family_3_universal] measure_pmf.prob_space_axioms)
+
+end
diff --git a/thys/Approximate_Model_Counting/document/root.bib b/thys/Approximate_Model_Counting/document/root.bib
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/document/root.bib
@@ -0,0 +1,16 @@
+@inproceedings{DBLP:conf/ijcai/ChakrabortyMV16,
+  author       = {Supratik Chakraborty and
+                  Kuldeep S. Meel and
+                  Moshe Y. Vardi},
+  editor       = {Subbarao Kambhampati},
+  title        = {Algorithmic Improvements in Approximate Counting for Probabilistic
+                  Inference: From Linear to Logarithmic {SAT} Calls},
+  booktitle    = {IJCAI},
+  pages        = {3569--3576},
+  publisher    = {{IJCAI/AAAI} Press},
+  year         = {2016},
+  url          = {http://www.ijcai.org/Abstract/16/503},
+  timestamp    = {Tue, 20 Aug 2019 16:19:10 +0200},
+  biburl       = {https://dblp.org/rec/conf/ijcai/ChakrabortyMV16.bib},
+  bibsource    = {dblp computer science bibliography, https://dblp.org}
+}
diff --git a/thys/Approximate_Model_Counting/document/root.tex b/thys/Approximate_Model_Counting/document/root.tex
new file mode 100644
--- /dev/null
+++ b/thys/Approximate_Model_Counting/document/root.tex
@@ -0,0 +1,36 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage[T1]{fontenc}
+\usepackage{isabelle,isabellesym}
+\usepackage{pdfsetup}
+\urlstyle{rm}
+\isabellestyle{it}
+\begin{document}
+
+\title{Approximate Model Counting}
+\author{Yong Kiam Tan and Jiong Yang}
+
+\maketitle
+
+\abstract{
+Approximate model counting is the task of approximating the number of solutions
+to an input formula.  This entry formalizes {$\mathsf{ApproxMC}$}, an algorithm
+due to Chakraborty et al.~\cite{DBLP:conf/ijcai/ChakrabortyMV16} with a
+probably approximately correct (PAC) guarantee, i.e., {$\mathsf{ApproxMC}$}
+returns a multiplicative $(1+\varepsilon)$-factor approximation of the model
+count with probability at least $1 - \delta$, where $\varepsilon > 0$ and $0 <
+\delta \leq 1$.  The algorithmic specification is further refined to a verified
+certificate checker that can be used to validate the results of untrusted
+{$\mathsf{ApproxMC}$} implementations (assuming access to trusted randomness).
+}
+
+\tableofcontents
+
+% sane default for proof documents
+\parindent 0pt\parskip 0.5ex
+
+\input{session}
+
+\bibliographystyle{abbrv}
+\bibliography{root}
+
+\end{document}
diff --git a/thys/Continued_Fractions/Continued_Fraction_Approximation.thy b/thys/Continued_Fractions/Continued_Fraction_Approximation.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Continued_Fraction_Approximation.thy
@@ -0,0 +1,190 @@
+(*
+  File:     Continued_Fractions/Continued_Fraction_Approximation.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Computing continued fraction expansions through interval arithmetic\<close>
+theory Continued_Fraction_Approximation
+imports
+  Complex_Main
+  "HOL-Decision_Procs.Approximation"
+  "Coinductive.Coinductive_List"
+  "HOL-Library.Code_Lazy"
+  "HOL-Library.Code_Target_Numeral"
+  Continued_Fractions
+keywords "approximate_cfrac" :: diag
+begin
+
+text \<open>
+  The approximation package allows us to compute an enclosing interval for a given
+  real constant. From this, we are able to compute an initial fragment of the continued
+  fraction expansion of the number.
+
+  The algorithm essentially works by computing the continued fraction expansion of the lower
+  and upper bound simultaneously and stopping when the results start to diverge.
+
+  This algorithm terminates because the lower and upper bounds, being rational numbers, have
+  a finite continued fraction expansion.
+\<close>
+
+definition float_to_rat :: "float \<Rightarrow> int \<times> int" where
+  "float_to_rat f = (if exponent f \<ge> 0 then
+     (mantissa f * 2 ^ nat (exponent f), 1) else (mantissa f, 2 ^ nat (-exponent f)))"
+
+lemma float_to_rat: "fst (float_to_rat f) / snd (float_to_rat f) = real_of_float f"
+  by (auto simp: float_to_rat_def mantissa_exponent powr_int)
+
+lemma snd_float_to_rat_pos [simp]: "snd (float_to_rat f) > 0"
+  by (simp add: float_to_rat_def)
+
+
+function cfrac_from_approx :: "int \<times> int \<Rightarrow> int \<times> int \<Rightarrow> int list" where
+  "cfrac_from_approx (nl, dl) (nu, du) =
+     (if nl = 0 \<or> nu = 0 \<or> dl = 0 \<or> du = 0 then []
+      else let l = nl div dl; u = nu div du
+           in  if l \<noteq> u then []
+               else l # (let m = nl mod dl in if m = 0 then [] else
+                           cfrac_from_approx (du, nu mod du) (dl, m)))"
+  by auto
+termination proof (relation "measure (\<lambda>((nl, dl), (nu, du)). nat (abs dl + abs du))", goal_cases)
+  case (2 nl dl nu du)
+  hence "\<bar>nl mod dl\<bar> + \<bar>nu mod du\<bar> < \<bar>dl\<bar> + \<bar>du\<bar>"
+    by (intro add_strict_mono) (auto simp: abs_mod_less)
+  thus ?case using 2 by simp
+qed auto
+
+lemmas [simp del] = cfrac_from_approx.simps
+
+lemma cfrac_from_approx_correct:
+  assumes "x \<in> {fst l / snd l..fst u / snd u}" and "snd l > 0" and "snd u > 0"
+  assumes "i < length (cfrac_from_approx l u)"
+  shows   "cfrac_nth (cfrac_of_real x) i = cfrac_from_approx l u ! i"
+  using assms
+proof (induction l u arbitrary: i x rule: cfrac_from_approx.induct)
+  case (1 nl dl nu du i x)
+  from "1.prems" have *: "nl div dl = nu div du" "nl \<noteq> 0" "nu \<noteq> 0" "dl > 0" "du > 0"
+    by (auto simp: cfrac_from_approx.simps Let_def split: if_splits)
+  have "\<lfloor>nl / dl\<rfloor> \<le> \<lfloor>x\<rfloor>" "\<lfloor>x\<rfloor> \<le> \<lfloor>nu / du\<rfloor>"
+    using "1.prems"(1) by (intro floor_mono; simp)+
+  hence "nl div dl \<le> \<lfloor>x\<rfloor>" "\<lfloor>x\<rfloor> \<le> nu div du"
+    by (simp_all add: floor_divide_of_int_eq)
+  with * have "\<lfloor>x\<rfloor> = nu div du"
+    by linarith
+
+  show ?case
+  proof (cases i)
+    case 0
+    with 0 and \<open>\<lfloor>x\<rfloor> = _\<close> show ?thesis using "1.prems"
+      by (auto simp: Let_def cfrac_from_approx.simps)
+  next
+    case [simp]: (Suc i')
+    from "1.prems" * have "nl mod dl \<noteq> 0"
+      by (subst (asm) cfrac_from_approx.simps) (auto split: if_splits)
+    have frac_eq: "frac x = x - nu div du"
+      using \<open>\<lfloor>x\<rfloor> = _\<close> by (simp add: frac_def)
+
+    have "frac x \<ge> nl / dl - nl div dl"
+      using * "1.prems" by (simp add: frac_eq)
+    also have "nl / dl - nl div dl = (nl - dl * (nl div dl)) / dl"
+      using * by (simp add: field_simps)
+    also have "nl - dl * (nl div dl) = nl mod dl"
+      by (subst minus_div_mult_eq_mod [symmetric]) auto
+    finally have "frac x \<ge> (nl mod dl) / dl" .
+
+    have "nl mod dl \<ge> 0"
+      using * by (intro pos_mod_sign) auto
+    with \<open>nl mod dl \<noteq> 0\<close> have "nl mod dl > 0"
+      by linarith
+    hence "0 < (nl mod dl) / dl"
+      using * by (intro divide_pos_pos) auto
+    also have "\<dots> \<le> frac x"
+      by fact
+    finally have "frac x > 0" .
+
+    have "frac x \<le> nu / du - nu div du"
+      using * "1.prems" by (simp add: frac_eq)
+    also have "\<dots> = (nu - du * (nu div du)) / du"
+      using * by (simp add: field_simps)
+    also have "nu - du * (nu div du) = nu mod du"
+      by (subst minus_div_mult_eq_mod [symmetric]) auto
+    finally have "frac x \<le> real_of_int (nu mod du) / real_of_int du" .
+
+    have "0 < frac x"
+      by fact
+    also have "\<dots> \<le> (nu mod du) / du"
+      by fact
+    finally have "nu mod du > 0"
+      using * by (auto simp: field_simps)
+
+    have "cfrac_nth (cfrac_of_real x) i = cfrac_nth (cfrac_tl (cfrac_of_real x)) i'"
+      by simp
+    also have "cfrac_tl (cfrac_of_real x) = cfrac_of_real (1 / frac x)"
+      using \<open>frac x > 0\<close> by (intro cfrac_tl_of_real) auto
+    also have "cfrac_nth (cfrac_of_real (1 / frac x)) i' =
+               cfrac_from_approx (du, nu mod du) (dl, nl mod dl) ! i'"
+    proof (rule "1.IH"[OF _ refl refl _ refl])
+      show "\<not> (nl = 0 \<or> nu = 0 \<or> dl = 0 \<or> du = 0)" "\<not> nl div dl \<noteq> nu div du"
+        using "1.prems" by (auto split: if_splits simp: Let_def cfrac_from_approx.simps)
+    next
+      show "i' < length (cfrac_from_approx (du, nu mod du) (dl, nl mod dl))" using "1.prems"
+        by (subst (asm) cfrac_from_approx.simps) (auto split: if_splits simp: Let_def)
+    next
+      have "1 / frac x \<le> dl / (nl mod dl)"
+        using \<open>frac x > 0\<close> and \<open>nl mod dl > 0\<close> and \<open>frac x \<ge> (nl mod dl) / dl\<close> and *
+        by (auto simp: field_simps)
+      moreover have "1 / frac x \<ge> du / (nu mod du)"
+        using \<open>frac x > 0\<close> and \<open>nu mod du > 0\<close> and \<open>frac x \<le> (nu mod du) / du\<close> and *
+        by (auto simp: field_simps)
+      ultimately show
+         "1 / frac x \<in> {real_of_int (fst (du, nu mod du)) / real_of_int (snd (du, nu mod du))..
+                         real_of_int (fst (dl, nl mod dl)) / real_of_int (snd (dl, nl mod dl))}"
+        by simp
+      show "snd (du, nu mod du) > 0" "snd (dl, nl mod dl) > 0" and "nl mod dl \<noteq> 0"
+        using \<open>nu mod du > 0\<close> and \<open>nl mod dl > 0\<close> by simp_all
+    qed
+    also have "cfrac_from_approx (du, nu mod du) (dl, nl mod dl) ! i' =
+               cfrac_from_approx (nl, dl) (nu, du) ! i"
+      using "1.prems" *  \<open>nl mod dl \<noteq> 0\<close> by (subst (2) cfrac_from_approx.simps) auto
+    finally show ?thesis .
+  qed
+qed
+
+definition cfrac_from_approx' :: "float \<Rightarrow> float \<Rightarrow> int list" where
+  "cfrac_from_approx' l u = cfrac_from_approx (float_to_rat l) (float_to_rat u)"
+
+lemma cfrac_from_approx'_correct:
+  assumes "x \<in> {real_of_float l..real_of_float u}"
+  assumes "i < length (cfrac_from_approx' l u)"
+  shows   "cfrac_nth (cfrac_of_real x) i = cfrac_from_approx' l u ! i"
+  using assms unfolding cfrac_from_approx'_def
+  by (intro cfrac_from_approx_correct) (auto simp: float_to_rat cfrac_from_approx'_def)
+
+definition approx_cfrac :: "nat \<Rightarrow> floatarith \<Rightarrow> int list" where
+  "approx_cfrac prec e =
+     (case approx' prec e [] of
+        None \<Rightarrow> []
+      | Some ivl \<Rightarrow> cfrac_from_approx' (lower ivl) (upper ivl))"
+
+ML_file \<open>approximation_cfrac.ML\<close>
+
+
+text \<open>Now let us do some experiments:\<close>
+
+value "let prec = 34; c = cfrac_from_approx' (lb_pi prec) (ub_pi prec) in c"
+value "let prec = 34; c = cfrac_from_approx' (lb_pi prec) (ub_pi prec)
+       in  map (\<lambda>n. (conv_num_fun ((!) c) n, conv_denom_fun ((!) c) n)) [0..<length c]"
+
+approximate_cfrac prec: 200 "pi"
+approximate_cfrac "ln 2"
+approximate_cfrac "exp 1"
+approximate_cfrac "sqrt 129"
+approximate_cfrac "(sqrt 13 + 3) / 4"
+approximate_cfrac "arctan 1"
+
+(*
+  Due to imprecision in the computation, approximate_cfrac is usually unable to determine
+  the last digit in a finite continued fraction:
+*)
+approximate_cfrac "123 / 97"
+value "cfrac_list_of_rat (123, 97)"
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/Continued_Fractions.thy b/thys/Continued_Fractions/Continued_Fractions.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Continued_Fractions.thy
@@ -0,0 +1,3871 @@
+(*
+  File:     Continued_Fractions/Continued_Fractions.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Continued Fractions\<close>
+theory Continued_Fractions
+imports
+  Complex_Main
+  "Coinductive.Lazy_LList"
+  "Coinductive.Coinductive_Nat"
+  "HOL-Number_Theory.Fib"
+  "HOL-Library.BNF_Corec"
+  "Coinductive.Coinductive_Stream"
+begin
+
+subsection \<open>Auxiliary results\<close>
+
+(* TODO: Move? *)
+coinductive linfinite :: "'a llist \<Rightarrow> bool" where
+  "linfinite xs \<Longrightarrow> linfinite (LCons x xs)"
+
+lemma llength_llist_of_stream [simp]: "llength (llist_of_stream xs) = \<infinity>"
+  by (simp add: not_lfinite_llength)
+
+lemma linfinite_conv_llength: "linfinite xs \<longleftrightarrow> llength xs = \<infinity>"
+proof
+  assume "linfinite xs"
+  thus "llength xs = \<infinity>"                          
+  proof (coinduction arbitrary: xs rule: enat_coinduct2)
+    fix xs :: "'a llist"
+    assume "llength xs \<noteq> 0" "linfinite xs"
+    thus "(\<exists>xs'::'a llist. epred (llength xs) = llength xs' \<and> epred \<infinity> = \<infinity> \<and> linfinite xs') \<or>
+             epred (llength xs) = epred \<infinity>"
+      by (intro disjI1 exI[of _ "ltl xs"]) (auto simp: linfinite.simps[of xs])
+  next
+    fix xs :: "'a llist" assume "linfinite xs"thus "(llength xs = 0) \<longleftrightarrow> (\<infinity> = (0::enat))"
+      by (subst (asm) linfinite.simps) auto
+  qed
+next
+  assume "llength xs = \<infinity>"
+  thus "linfinite xs"
+  proof (coinduction arbitrary: xs)
+    case linfinite
+    thus "\<exists>xsa x.
+             xs = LCons x xsa \<and>
+             ((\<exists>xs. xsa = xs \<and> llength xs = \<infinity>) \<or>
+              linfinite xsa)"
+      by (cases xs) (auto simp: eSuc_eq_infinity_iff)
+  qed
+qed
+
+definition lnth_default :: "'a \<Rightarrow> 'a llist \<Rightarrow> nat \<Rightarrow> 'a" where
+  "lnth_default dflt xs n = (if n < llength xs then lnth xs n else dflt)"
+
+lemma lnth_default_code [code]:
+  "lnth_default dflt xs n =
+     (if lnull xs then dflt else if n = 0 then lhd xs else lnth_default dflt (ltl xs) (n - 1))"
+proof (induction n arbitrary: xs)
+  case 0
+  thus ?case
+    by (cases xs) (auto simp: lnth_default_def simp flip: zero_enat_def)
+next
+  case (Suc n)
+  show ?case
+  proof (cases xs)
+    case LNil
+    thus ?thesis
+      by (auto simp: lnth_default_def)
+  next
+    case (LCons x xs')
+    thus ?thesis
+      by (auto simp: lnth_default_def Suc_ile_eq)
+  qed
+qed
+
+lemma enat_le_iff:
+  "enat n \<le> m \<longleftrightarrow> m = \<infinity> \<or> (\<exists>m'. m = enat m' \<and> n \<le> m')"
+  by (cases m) auto
+
+lemma enat_less_iff:
+  "enat n < m \<longleftrightarrow> m = \<infinity> \<or> (\<exists>m'. m = enat m' \<and> n < m')"
+  by (cases m) auto
+
+lemma real_of_int_divide_in_Ints_iff:
+  "real_of_int a / real_of_int b \<in> \<int> \<longleftrightarrow> b dvd a \<or> b = 0"
+proof safe
+  assume "real_of_int a / real_of_int b \<in> \<int>" "b \<noteq> 0"
+  then obtain n where "real_of_int a / real_of_int b = real_of_int n"
+    by (auto simp: Ints_def)
+  hence "real_of_int b * real_of_int n = real_of_int a"
+    using \<open>b \<noteq> 0\<close> by (auto simp: field_simps)
+  also have "real_of_int b * real_of_int n = real_of_int (b * n)"
+    by simp
+  finally have "b * n = a"
+    by linarith
+  thus "b dvd a"
+    by auto
+qed auto
+
+lemma frac_add_of_nat: "frac (of_nat y + x) = frac x"
+  unfolding frac_def by simp
+
+lemma frac_add_of_int: "frac (of_int y + x) = frac x"
+  unfolding frac_def by simp
+
+lemma frac_fraction: "frac (real_of_int a / real_of_int b) = (a mod b) / b"
+proof -
+  have "frac (a / b) = frac ((a mod b + b * (a div b)) / b)"
+    by (subst mod_mult_div_eq) auto
+  also have "(a mod b + b * (a div b)) / b = of_int (a div b) + a mod b / b"
+    unfolding of_int_add by (subst add_divide_distrib) auto
+  also have "frac \<dots> = frac (a mod b / b)"
+    by (rule frac_add_of_int)
+  also have "\<dots> = a mod b / b"
+    by (simp add: floor_divide_of_int_eq frac_def)
+  finally show ?thesis .
+qed
+
+lemma Suc_fib_ge: "Suc (fib n) \<ge> n"
+proof (induction n rule: fib.induct)
+  case (3 n)
+  show ?case
+  proof (cases "n < 2")
+    case True
+    thus ?thesis by (cases n) auto
+  next
+    case False
+    hence "Suc (Suc (Suc n)) \<le> Suc n + n" by simp
+    also have "\<dots> \<le> Suc (fib (Suc n)) + Suc (fib n)"
+      by (intro add_mono 3)
+    also have "\<dots> = Suc (Suc (fib (Suc (Suc n))))"
+      by simp
+    finally show ?thesis by (simp only: Suc_le_eq)
+  qed
+qed auto
+
+lemma fib_ge: "fib n \<ge> n - 1"
+  using Suc_fib_ge[of n] by simp
+
+lemma frac_diff_of_nat_right [simp]: "frac (x - of_nat y) = frac x"
+  using floor_diff_of_int[of x "int y"] by (simp add: frac_def)
+
+lemma funpow_cycle:
+  assumes "m > 0"
+  assumes "(f ^^ m) x = x"
+  shows   "(f ^^ k) x = (f ^^ (k mod m)) x"
+proof (induction k rule: less_induct)
+  case (less k)
+  show ?case
+  proof (cases "k < m")
+    case True
+    thus ?thesis using \<open>m > 0\<close> by simp
+  next
+    case False
+    hence "k = (k - m) + m" by simp
+    also have "(f ^^ \<dots>) x = (f ^^ (k - m)) ((f ^^ m) x)"
+      by (simp add: funpow_add)
+    also have "(f ^^ m) x = x" by fact
+    also have "(f ^^ (k - m)) x = (f ^^ (k mod m)) x"
+      using assms False by (subst less.IH) (auto simp: mod_geq)
+    finally show ?thesis .
+  qed
+qed
+
+lemma of_nat_ge_1_iff: "of_nat n \<ge> (1 :: 'a :: linordered_semidom) \<longleftrightarrow> n > 0"
+  using of_nat_le_iff[of 1 n] unfolding of_nat_1 by auto
+
+lemma not_frac_less_0: "\<not>frac x < 0"
+  by (simp add: frac_def not_less)
+
+lemma frac_le_1: "frac x \<le> 1"
+  unfolding frac_def by linarith
+
+lemma divide_in_Rats_iff1:
+  "(x::real) \<in> \<rat> \<Longrightarrow> x \<noteq> 0 \<Longrightarrow> x / y \<in> \<rat> \<longleftrightarrow> y \<in> \<rat>"
+proof safe
+  assume *: "x \<in> \<rat>" "x \<noteq> 0" "x / y \<in> \<rat>"
+  from *(1,3) have "x / (x / y) \<in> \<rat>"
+    by (rule Rats_divide)
+  also from * have "x / (x / y) = y" by simp
+  finally show "y \<in> \<rat>" .
+qed (auto intro: Rats_divide)
+
+lemma divide_in_Rats_iff2:
+  "(y::real) \<in> \<rat> \<Longrightarrow> y \<noteq> 0 \<Longrightarrow> x / y \<in> \<rat> \<longleftrightarrow> x \<in> \<rat>"
+proof safe
+  assume *: "y \<in> \<rat>" "y \<noteq> 0" "x / y \<in> \<rat>"
+  from *(3,1) have "x / y * y \<in> \<rat>"
+    by (rule Rats_mult)
+  also from * have "x / y * y = x" by simp
+  finally show "x \<in> \<rat>" .
+qed (auto intro: Rats_divide)
+
+lemma add_in_Rats_iff1: "x \<in> \<rat> \<Longrightarrow> x + y \<in> \<rat> \<longleftrightarrow> y \<in> \<rat>"
+  using Rats_diff[of "x + y" x] by auto
+
+lemma add_in_Rats_iff2: "y \<in> \<rat> \<Longrightarrow> x + y \<in> \<rat> \<longleftrightarrow> x \<in> \<rat>"
+  using Rats_diff[of "x + y" y] by auto
+
+lemma diff_in_Rats_iff1: "x \<in> \<rat> \<Longrightarrow> x - y \<in> \<rat> \<longleftrightarrow> y \<in> \<rat>"
+  using Rats_diff[of x "x - y"] by auto
+
+lemma diff_in_Rats_iff2: "y \<in> \<rat> \<Longrightarrow> x - y \<in> \<rat> \<longleftrightarrow> x \<in> \<rat>"
+  using Rats_add[of "x - y" y] by auto
+
+lemma frac_in_Rats_iff [simp]: "frac x \<in> \<rat> \<longleftrightarrow> x \<in> \<rat>"
+  by (simp add: frac_def diff_in_Rats_iff2)
+
+lemma filterlim_sequentially_shift:
+  "filterlim (\<lambda>n. f (n + m)) F sequentially \<longleftrightarrow> filterlim f F sequentially"
+proof (induction m)
+  case (Suc m)
+  have "filterlim (\<lambda>n. f (n + Suc m)) F at_top \<longleftrightarrow>
+          filterlim (\<lambda>n. f (Suc n + m)) F at_top" by simp
+  also have "\<dots> \<longleftrightarrow> filterlim (\<lambda>n. f (n + m)) F at_top"
+    by (rule filterlim_sequentially_Suc)
+  also have "\<dots> \<longleftrightarrow> filterlim f F at_top"
+    by (rule Suc.IH)
+  finally show ?case .
+qed simp_all
+
+
+subsection \<open>Bounds on alternating decreasing sums\<close>
+
+lemma alternating_decreasing_sum_bounds:
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m \<le> n" "\<And>k. k \<in> {m..n} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n} \<Longrightarrow> f (Suc k) \<le> f k"
+  defines "S \<equiv> (\<lambda>m. (\<Sum>k=m..n. (-1) ^ k * f k))"
+  shows   "if even m then S m \<in> {0..f m} else S m \<in> {-f m..0}"
+  using assms(1)
+proof (induction rule: inc_induct)
+  case (step m')
+  have [simp]: "-a \<le> b \<longleftrightarrow> a + b \<ge> (0 :: 'a)" for a b
+    by (metis le_add_same_cancel1 minus_add_cancel)
+  have [simp]: "S m' = (-1) ^ m' * f m' + S (Suc m')"
+    using step.hyps unfolding S_def
+    by (subst sum.atLeast_Suc_atMost) simp_all
+  from step.hyps have nonneg: "f m' \<ge> 0"
+    by (intro assms) auto
+  from step.hyps have mono: "f (Suc m') \<le> f m'"
+    by (intro assms) auto
+  show ?case
+  proof (cases "even m'")
+    case True
+    hence "0 \<le> f (Suc m') + S (Suc m')"
+      using step.IH by simp
+    also note mono
+    finally show ?thesis using True step.IH by auto
+  next
+    case False
+    with step.IH have "S (Suc m') \<le> f (Suc m')"
+      by simp
+    also note mono
+    finally show ?thesis using step.IH False by auto
+  qed
+qed (insert assms, auto)
+
+lemma alternating_decreasing_sum_bounds':
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m < n" "\<And>k. k \<in> {m..n-1} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n-1} \<Longrightarrow> f (Suc k) \<le> f k"
+  defines "S \<equiv> (\<lambda>m. (\<Sum>k=m..<n. (-1) ^ k * f k))"
+  shows   "if even m then S m \<in> {0..f m} else S m \<in> {-f m..0}"
+proof (cases n)
+  case 0
+  thus ?thesis using assms by auto
+next
+  case (Suc n')
+  hence "if even m then (\<Sum>k=m..n-1. (-1) ^ k * f k) \<in> {0..f m}
+           else (\<Sum>k=m..n-1. (-1) ^ k * f k) \<in> {-f m..0}"
+    using assms by (intro alternating_decreasing_sum_bounds) auto
+  also have "(\<Sum>k=m..n-1. (-1) ^ k * f k) = S m"
+    unfolding S_def by (intro sum.cong) (auto simp: Suc)
+  finally show ?thesis .
+qed
+
+lemma alternating_decreasing_sum_upper_bound:
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m \<le> n" "\<And>k. k \<in> {m..n} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "(\<Sum>k=m..n. (-1) ^ k * f k) \<le> f m"
+  using alternating_decreasing_sum_bounds[of m n f, OF assms] assms(1)
+  by (auto split: if_splits intro: order.trans[OF _ assms(2)])
+
+lemma alternating_decreasing_sum_upper_bound':
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m < n" "\<And>k. k \<in> {m..n-1} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n-1} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "(\<Sum>k=m..<n. (-1) ^ k * f k) \<le> f m"
+  using alternating_decreasing_sum_bounds'[of m n f, OF assms] assms(1)
+  by (auto split: if_splits intro: order.trans[OF _ assms(2)])
+
+lemma abs_alternating_decreasing_sum_upper_bound:
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m \<le> n" "\<And>k. k \<in> {m..n} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "\<bar>(\<Sum>k=m..n. (-1) ^ k * f k)\<bar> \<le> f m" (is "abs ?S \<le> _")
+  using alternating_decreasing_sum_bounds[of m n f, OF assms]
+  by (auto split: if_splits simp: minus_le_iff)
+
+lemma abs_alternating_decreasing_sum_upper_bound':
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m < n" "\<And>k. k \<in> {m..n-1} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n-1} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "\<bar>(\<Sum>k=m..<n. (-1) ^ k * f k)\<bar> \<le> f m"
+  using alternating_decreasing_sum_bounds'[of m n f, OF assms]
+  by (auto split: if_splits simp: minus_le_iff)
+
+lemma abs_alternating_decreasing_sum_lower_bound:
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m < n" "\<And>k. k \<in> {m..n} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "\<bar>(\<Sum>k=m..n. (-1) ^ k * f k)\<bar> \<ge> f m - f (Suc m)"
+proof -
+  have "(\<Sum>k=m..n. (-1) ^ k * f k) = (\<Sum>k\<in>insert m {m<..n}. (-1) ^ k * f k)"
+    using assms by (intro sum.cong) auto
+  also have "\<dots> = (-1) ^ m * f m + (\<Sum>k\<in>{m<..n}. (-1) ^ k * f k)"
+    by auto
+  also have "(\<Sum>k\<in>{m<..n}. (-1) ^ k * f k) = (\<Sum>k\<in>{m..<n}. (-1) ^ Suc k * f (Suc k))"
+    by (intro sum.reindex_bij_witness[of _ Suc "\<lambda>i. i - 1"]) auto
+  also have "(-1)^m * f m + \<dots> = (-1)^m * f m - (\<Sum>k\<in>{m..<n}. (-1) ^ k * f (Suc k))"
+    by (simp add: sum_negf)
+  also have "\<bar>\<dots>\<bar> \<ge> \<bar>(-1)^m * f m\<bar> - \<bar>(\<Sum>k\<in>{m..<n}. (-1) ^ k * f (Suc k))\<bar>"
+    by (rule abs_triangle_ineq2)
+  also have "\<bar>(-1)^m * f m\<bar> = f m"
+    using assms by (cases "even m") auto
+  finally have "f m - \<bar>\<Sum>k = m..<n. (- 1) ^ k * f (Suc k)\<bar>
+                  \<le> \<bar>\<Sum>k = m..n. (- 1) ^ k * f k\<bar>" .
+  moreover have "f m - \<bar>(\<Sum>k\<in>{m..<n}. (-1) ^ k * f (Suc k))\<bar> \<ge> f m - f (Suc m)"
+    using assms by (intro diff_mono abs_alternating_decreasing_sum_upper_bound') auto
+  ultimately show ?thesis by (rule order.trans[rotated])
+qed
+
+lemma abs_alternating_decreasing_sum_lower_bound':
+  fixes f :: "nat \<Rightarrow> 'a :: {linordered_ring, ring_1}"
+  assumes "m+1 < n" "\<And>k. k \<in> {m..n} \<Longrightarrow> f k \<ge> 0"
+          "\<And>k. k \<in> {m..<n} \<Longrightarrow> f (Suc k) \<le> f k"
+  shows   "\<bar>(\<Sum>k=m..<n. (-1) ^ k * f k)\<bar> \<ge> f m - f (Suc m)"
+proof (cases n)
+  case 0
+  thus ?thesis using assms by auto
+next
+  case (Suc n')
+  hence "\<bar>(\<Sum>k=m..n-1. (-1) ^ k * f k)\<bar> \<ge> f m - f (Suc m)"
+    using assms by (intro abs_alternating_decreasing_sum_lower_bound) auto
+  also have "(\<Sum>k=m..n-1. (-1) ^ k * f k) = (\<Sum>k=m..<n. (-1) ^ k * f k)"
+    by (intro sum.cong) (auto simp: Suc)
+  finally show ?thesis .
+qed
+
+lemma alternating_decreasing_suminf_bounds:
+  assumes "\<And>k. f k \<ge> (0 :: real)" "\<And>k. f (Suc k) \<le> f k"
+          "f \<longlonglongrightarrow> 0"
+  shows   "(\<Sum>k. (-1) ^ k * f k) \<in> {f 0 - f 1..f 0}"
+proof -
+  have "summable (\<lambda>k. (-1) ^ k * f k)"
+    by (intro summable_Leibniz' assms)
+  hence lim: "(\<lambda>n. \<Sum>k\<le>n. (-1) ^ k * f k) \<longlonglongrightarrow> (\<Sum>k. (-1) ^ k * f k)"
+    by (auto dest: summable_LIMSEQ')
+  have bounds: "(\<Sum>k=0..n. (- 1) ^ k * f k) \<in> {f 0 - f 1..f 0}"
+    if "n > 0" for n
+    using alternating_decreasing_sum_bounds[of 1 n f] assms that
+    by (subst sum.atLeast_Suc_atMost) auto
+  note [simp] = atLeast0AtMost
+  note [intro!] = eventually_mono[OF eventually_gt_at_top[of 0]]
+ 
+  from lim have "(\<Sum>k. (-1) ^ k * f k) \<ge> f 0 - f 1"
+    by (rule tendsto_lowerbound) (insert bounds, auto)
+  moreover from lim have "(\<Sum>k. (-1) ^ k * f k) \<le> f 0"
+    by (rule tendsto_upperbound) (use bounds in auto)
+  ultimately show ?thesis by simp
+qed
+
+lemma
+  assumes "\<And>k. k \<ge> m \<Longrightarrow> f k \<ge> (0 :: real)"
+          "\<And>k. k \<ge> m \<Longrightarrow> f (Suc k) \<le> f k" "f \<longlonglongrightarrow> 0"
+  defines "S \<equiv> (\<Sum>k. (-1) ^ (k + m) * f (k + m))"
+  shows   summable_alternating_decreasing: "summable (\<lambda>k. (-1) ^ (k + m) * f (k + m))"
+    and   alternating_decreasing_suminf_bounds':
+            "if even m then S \<in> {f m - f (Suc m) .. f m}
+               else S \<in> {-f m..f (Suc m) - f m}" (is ?th1)
+    and   abs_alternating_decreasing_suminf:
+            "abs S \<in> {f m - f (Suc m)..f m}" (is ?th2)
+proof -
+  have summable: "summable (\<lambda>k. (-1) ^ k * f (k + m))"
+    using assms by (intro summable_Leibniz') (auto simp: filterlim_sequentially_shift)
+  thus "summable (\<lambda>k. (-1) ^ (k + m) * f (k + m))"
+    by (subst add.commute) (auto simp: power_add mult.assoc intro: summable_mult)
+  have "S = (\<Sum>k. (-1) ^ m * ((-1) ^ k * f (k + m)))"
+    by (simp add: S_def power_add mult_ac)
+  also have "\<dots> = (-1) ^ m * (\<Sum>k. (-1) ^ k * f (k + m))"
+    using summable by (rule suminf_mult)
+  finally have "S = (- 1) ^ m * (\<Sum>k. (- 1) ^ k * f (k + m))" .
+  moreover have "(\<Sum>k. (-1) ^ k * f (k + m)) \<in>
+     {f (0 + m) - f (1 + m) .. f (0 + m)}"
+    using assms
+    by (intro alternating_decreasing_suminf_bounds)
+       (auto simp: filterlim_sequentially_shift)
+  ultimately show ?th1 by (auto split: if_splits)
+  thus ?th2 using assms(2)[of m] by (auto split: if_splits)
+qed
+
+lemma
+  assumes "\<And>k. k \<ge> m \<Longrightarrow> f k \<ge> (0 :: real)"
+          "\<And>k. k \<ge> m \<Longrightarrow> f (Suc k) < f k" "f \<longlonglongrightarrow> 0"
+  defines "S \<equiv> (\<Sum>k. (-1) ^ (k + m) * f (k + m))"
+  shows   alternating_decreasing_suminf_bounds_strict':
+            "if even m then S \<in> {f m - f (Suc m)<..<f m}
+               else S \<in> {-f m<..<f (Suc m) - f m}" (is ?th1)
+    and   abs_alternating_decreasing_suminf_strict:
+            "abs S \<in> {f m - f (Suc m)<..<f m}" (is ?th2)
+proof -
+  define S' where "S' = (\<Sum>k. (-1) ^ (k + Suc (Suc m)) * f (k + Suc (Suc m)))"
+  have "(\<lambda>k. (-1) ^ (k + m) * f (k + m)) sums S" using assms unfolding S_def
+    by (intro summable_sums summable_Leibniz' summable_alternating_decreasing)
+       (auto simp: less_eq_real_def)
+  from sums_split_initial_segment[OF this, of 2]
+    have S': "S' = S - (-1) ^ m * (f m - f (Suc m))"
+    by (simp_all add: sums_iff S'_def algebra_simps lessThan_nat_numeral)
+  have "if even (Suc (Suc m)) then S' \<in> {f (Suc (Suc m)) - f (Suc (Suc (Suc m)))..f (Suc (Suc m))}
+        else S' \<in> {- f (Suc (Suc m))..f (Suc (Suc (Suc m))) - f (Suc (Suc m))}" unfolding S'_def
+    using assms by (intro alternating_decreasing_suminf_bounds') (auto simp: less_eq_real_def)
+  thus ?th1 using assms(2)[of "Suc m"] assms(2)[of "Suc (Suc m)"]
+    unfolding S' by (auto simp: algebra_simps)
+  thus ?th2 using assms(2)[of m] by (auto split: if_splits)
+qed
+
+
+datatype cfrac = CFrac int "nat llist"
+
+quickcheck_generator cfrac constructors: CFrac
+
+lemma type_definition_cfrac':
+  "type_definition (\<lambda>x. case x of CFrac a b \<Rightarrow> (a, b)) (\<lambda>(x,y). CFrac x y) UNIV"
+  by (auto simp: type_definition_def split: cfrac.splits)
+
+setup_lifting type_definition_cfrac'
+
+lift_definition cfrac_of_int :: "int \<Rightarrow> cfrac" is
+  "\<lambda>n. (n, LNil)" .
+
+lemma cfrac_of_int_code [code]: "cfrac_of_int n = CFrac n LNil"
+  by (auto simp: cfrac_of_int_def)
+
+lift_definition cfrac_of_stream :: "int stream \<Rightarrow> cfrac" is
+  "\<lambda>xs. (shd xs, llist_of_stream (smap (\<lambda>x. nat (x - 1)) (stl xs)))" .
+
+instantiation cfrac :: zero
+begin
+definition zero_cfrac where "0 = cfrac_of_int 0"
+instance ..
+end
+
+instantiation cfrac :: one
+begin
+definition one_cfrac where "1 = cfrac_of_int 1"
+instance ..
+end
+
+lift_definition cfrac_tl :: "cfrac \<Rightarrow> cfrac" is
+  "\<lambda>(_, bs) \<Rightarrow> case bs of LNil \<Rightarrow> (1, LNil) | LCons b bs' \<Rightarrow> (int b + 1, bs')" .
+
+lemma cfrac_tl_code [code]:
+  "cfrac_tl (CFrac a bs) =
+     (case bs of LNil \<Rightarrow> CFrac 1 LNil | LCons b bs' \<Rightarrow> CFrac (int b + 1) bs')"
+  by (auto simp: cfrac_tl_def split: llist.splits)
+
+definition cfrac_drop :: "nat \<Rightarrow> cfrac \<Rightarrow> cfrac" where
+  "cfrac_drop n c = (cfrac_tl ^^ n) c"
+
+lemma cfrac_drop_Suc_right: "cfrac_drop (Suc n) c = cfrac_drop n (cfrac_tl c)"
+  by (simp add: cfrac_drop_def funpow_Suc_right del: funpow.simps)
+
+lemma cfrac_drop_Suc_left: "cfrac_drop (Suc n) c = cfrac_tl (cfrac_drop n c)"
+  by (simp add: cfrac_drop_def)
+
+lemma cfrac_drop_add: "cfrac_drop (m + n) c = cfrac_drop m (cfrac_drop n c)"
+  by (simp add: cfrac_drop_def funpow_add)
+
+lemma cfrac_drop_0 [simp]: "cfrac_drop 0 = (\<lambda>x. x)"
+  by (simp add: fun_eq_iff cfrac_drop_def)
+
+lemma cfrac_drop_1 [simp]: "cfrac_drop 1 = cfrac_tl"
+  by (simp add: fun_eq_iff cfrac_drop_def)
+
+lift_definition cfrac_length :: "cfrac \<Rightarrow> enat" is
+  "\<lambda>(_, bs) \<Rightarrow> llength bs" .
+
+lemma cfrac_length_code [code]: "cfrac_length (CFrac a bs) = llength bs"
+  by (simp add: cfrac_length_def)
+
+lemma cfrac_length_tl [simp]: "cfrac_length (cfrac_tl c) = cfrac_length c - 1"
+  by transfer (auto split: llist.splits)
+
+lemma enat_diff_Suc_right [simp]: "m - enat (Suc n) = m - n - 1"
+  by (auto simp: diff_enat_def enat_1_iff split: enat.splits)
+
+lemma cfrac_length_drop [simp]: "cfrac_length (cfrac_drop n c) = cfrac_length c - n"
+  by (induction n) (auto simp: cfrac_drop_def)
+
+lemma cfrac_length_of_stream [simp]: "cfrac_length (cfrac_of_stream xs) = \<infinity>"
+  by transfer auto
+
+lift_definition cfrac_nth :: "cfrac \<Rightarrow> nat \<Rightarrow> int" is
+  "\<lambda>(a :: int, bs :: nat llist). \<lambda>(n :: nat).
+      if n = 0 then a
+      else if n \<le> llength bs then int (lnth bs (n - 1)) + 1 else 1" .
+
+lemma cfrac_nth_code [code]:
+  "cfrac_nth (CFrac a bs) n = (if n = 0 then a else lnth_default 0 bs (n - 1) + 1)"
+proof -
+  have "n > 0 \<longrightarrow> enat (n - Suc 0) < llength bs \<longleftrightarrow> enat n \<le> llength bs"
+    by (metis Suc_ile_eq Suc_pred)
+  thus ?thesis by (auto simp: cfrac_nth_def lnth_default_def)
+qed
+
+lemma cfrac_nth_nonneg [simp, intro]: "n > 0 \<Longrightarrow> cfrac_nth c n \<ge> 0"
+  by transfer auto
+
+lemma cfrac_nth_nonzero [simp]: "n > 0 \<Longrightarrow> cfrac_nth c n \<noteq> 0"
+  by transfer (auto split: if_splits)
+
+lemma cfrac_nth_pos[simp, intro]: "n > 0 \<Longrightarrow> cfrac_nth c n > 0"
+  by transfer auto
+
+lemma cfrac_nth_ge_1[simp, intro]: "n > 0 \<Longrightarrow> cfrac_nth c n \<ge> 1"
+  by transfer auto
+
+lemma cfrac_nth_not_less_1[simp, intro]: "n > 0 \<Longrightarrow> \<not>cfrac_nth c n < 1"
+  by transfer (auto split: if_splits)
+
+lemma cfrac_nth_tl [simp]: "cfrac_nth (cfrac_tl c) n = cfrac_nth c (Suc n)"
+  apply transfer
+  apply (auto split: llist.splits nat.splits simp: Suc_ile_eq lnth_LCons enat_0_iff
+              simp flip: zero_enat_def)
+  done
+
+lemma cfrac_nth_drop [simp]: "cfrac_nth (cfrac_drop n c) m = cfrac_nth c (m + n)"
+  by (induction n arbitrary: m) (auto simp: cfrac_drop_def)
+
+lemma cfrac_nth_0_of_int [simp]: "cfrac_nth (cfrac_of_int n) 0 = n"
+  by transfer auto
+
+lemma cfrac_nth_gt0_of_int [simp]: "m > 0 \<Longrightarrow> cfrac_nth (cfrac_of_int n) m = 1"
+  by transfer (auto simp: enat_0_iff)
+
+lemma cfrac_nth_of_stream:
+  assumes "sset (stl xs) \<subseteq> {0<..}"
+  shows   "cfrac_nth (cfrac_of_stream xs) n = snth xs n"
+  using assms
+proof (transfer', goal_cases)
+  case (1 xs n)
+  thus ?case
+    by (cases xs; cases n) (auto simp: subset_iff)
+qed
+
+
+lift_definition cfrac :: "(nat \<Rightarrow> int) \<Rightarrow> cfrac" is
+  "\<lambda>f. (f 0, inf_llist (\<lambda>n. nat (f (Suc n) - 1)))" .
+
+definition is_cfrac :: "(nat \<Rightarrow> int) \<Rightarrow> bool" where "is_cfrac f \<longleftrightarrow> (\<forall>n>0. f n > 0)"
+
+lemma cfrac_nth_cfrac [simp]:
+  assumes "is_cfrac f"
+  shows   "cfrac_nth (cfrac f) n = f n"
+  using assms unfolding is_cfrac_def by transfer auto
+
+lemma llength_eq_infty_lnth: "llength b = \<infinity> \<Longrightarrow> inf_llist (lnth b) = b"
+  by (simp add: llength_eq_infty_conv_lfinite)
+
+lemma cfrac_cfrac_nth [simp]: "cfrac_length c = \<infinity> \<Longrightarrow> cfrac (cfrac_nth c) = c"
+  by transfer (auto simp: llength_eq_infty_lnth)
+
+lemma cfrac_length_cfrac [simp]: "cfrac_length (cfrac f) = \<infinity>"
+  by transfer auto
+
+
+lift_definition cfrac_of_list :: "int list \<Rightarrow> cfrac" is
+  "\<lambda>xs. if xs = [] then (0, LNil) else (hd xs, llist_of (map (\<lambda>n. nat n - 1) (tl xs)))" .
+
+lemma cfrac_length_of_list [simp]: "cfrac_length (cfrac_of_list xs) = length xs - 1"
+  by transfer (auto simp: zero_enat_def)
+
+lemma cfrac_of_list_Nil [simp]: "cfrac_of_list [] = 0"
+  unfolding zero_cfrac_def by transfer auto
+
+lemma cfrac_nth_of_list [simp]:
+  assumes "n < length xs" and "\<forall>i\<in>{0<..<length xs}. xs ! i > 0"
+  shows   "cfrac_nth (cfrac_of_list xs) n = xs ! n"
+  using assms
+proof (transfer, goal_cases)
+  case (1 n xs)
+  show ?case
+  proof (cases n)
+    case (Suc n')
+    with 1 have "xs ! n > 0"
+      using 1 by auto
+    hence "int (nat (tl xs ! n') - Suc 0) + 1 = xs ! Suc n'"
+      using 1(1) Suc by (auto simp: nth_tl of_nat_diff)
+    thus ?thesis
+      using Suc 1(1) by (auto simp: hd_conv_nth zero_enat_def)
+  qed (use 1 in \<open>auto simp: hd_conv_nth\<close>)
+qed
+
+
+primcorec cfrac_of_real_aux :: "real \<Rightarrow> nat llist" where
+  "cfrac_of_real_aux x =
+     (if x \<in> {0<..<1} then LCons (nat \<lfloor>1/x\<rfloor> - 1) (cfrac_of_real_aux (frac (1/x))) else LNil)"
+
+lemma cfrac_of_real_aux_code [code]:
+  "cfrac_of_real_aux x =
+     (if x > 0 \<and> x < 1 then LCons (nat \<lfloor>1/x\<rfloor> - 1) (cfrac_of_real_aux (frac (1/x))) else LNil)"
+  by (subst cfrac_of_real_aux.code) auto
+  
+
+lemma cfrac_of_real_aux_LNil [simp]: "x \<notin> {0<..<1} \<Longrightarrow> cfrac_of_real_aux x = LNil"
+  by (subst cfrac_of_real_aux.code) auto
+
+lemma cfrac_of_real_aux_0 [simp]: "cfrac_of_real_aux 0 = LNil"
+  by (subst cfrac_of_real_aux.code) auto
+
+lemma cfrac_of_real_aux_eq_LNil_iff [simp]: "cfrac_of_real_aux x = LNil \<longleftrightarrow> x \<notin> {0<..<1}"
+  by (subst cfrac_of_real_aux.code) auto
+
+lemma lnth_cfrac_of_real_aux:
+  assumes "n < llength (cfrac_of_real_aux x)"
+  shows   "lnth (cfrac_of_real_aux x) (Suc n) = lnth (cfrac_of_real_aux (frac (1/x))) n"
+  using assms
+  apply (induction n arbitrary: x)
+   apply (subst cfrac_of_real_aux.code)
+   apply auto []
+  apply (subst cfrac_of_real_aux.code)
+  apply (auto)
+  done
+
+lift_definition cfrac_of_real :: "real \<Rightarrow> cfrac" is
+  "\<lambda>x. (\<lfloor>x\<rfloor>, cfrac_of_real_aux (frac x))" .
+
+lemma cfrac_of_real_code [code]: "cfrac_of_real x = CFrac \<lfloor>x\<rfloor> (cfrac_of_real_aux (frac x))"
+  by (simp add: cfrac_of_real_def)
+
+lemma eq_epred_iff: "m = epred n \<longleftrightarrow> m = 0 \<and> n = 0 \<or> n = eSuc m"
+  by (cases m; cases n) (auto simp: enat_0_iff enat_eSuc_iff infinity_eq_eSuc_iff)
+
+lemma epred_eq_iff: "epred n = m \<longleftrightarrow> m = 0 \<and> n = 0 \<or> n = eSuc m"
+  by (cases m; cases n) (auto simp: enat_0_iff enat_eSuc_iff infinity_eq_eSuc_iff)
+
+lemma epred_less: "n > 0 \<Longrightarrow> n \<noteq> \<infinity> \<Longrightarrow> epred n < n"
+  by (cases n) (auto simp: enat_0_iff)
+
+lemma cfrac_nth_of_real_0 [simp]:
+  "cfrac_nth (cfrac_of_real x) 0 = \<lfloor>x\<rfloor>"
+  by transfer auto
+
+lemma frac_eq_0 [simp]: "x \<in> \<int> \<Longrightarrow> frac x = 0"
+  by simp
+
+lemma cfrac_tl_of_real:
+  assumes "x \<notin> \<int>"
+  shows   "cfrac_tl (cfrac_of_real x) = cfrac_of_real (1 / frac x)"
+  using assms
+proof (transfer, goal_cases)
+  case (1 x)
+  hence "int (nat \<lfloor>1 / frac x\<rfloor> - Suc 0) + 1 = \<lfloor>1 / frac x\<rfloor>"
+    by (subst of_nat_diff) (auto simp: le_nat_iff frac_le_1)
+  with \<open>x \<notin> \<int>\<close> show ?case
+  by (subst cfrac_of_real_aux.code) (auto split: llist.splits simp: frac_lt_1)
+qed
+
+lemma cfrac_nth_of_real_Suc:
+  assumes "x \<notin> \<int>"
+  shows   "cfrac_nth (cfrac_of_real x) (Suc n) = cfrac_nth (cfrac_of_real (1 / frac x)) n"
+proof -
+  have "cfrac_nth (cfrac_of_real x) (Suc n) =
+          cfrac_nth (cfrac_tl (cfrac_of_real x)) n"
+    by simp
+  also have "cfrac_tl (cfrac_of_real x) = cfrac_of_real (1 / frac x)"
+    by (simp add: cfrac_tl_of_real assms)
+  finally show ?thesis .
+qed
+
+
+fun conv :: "cfrac \<Rightarrow> nat \<Rightarrow> real" where
+  "conv c 0 = real_of_int (cfrac_nth c 0)"
+| "conv c (Suc n) = real_of_int (cfrac_nth c 0) + 1 / conv (cfrac_tl c) n"
+
+
+text \<open>
+  The numerator and denominator of a convergent:
+\<close>
+fun conv_num :: "cfrac \<Rightarrow> nat \<Rightarrow> int" where
+  "conv_num c 0 = cfrac_nth c 0"
+| "conv_num c (Suc 0) = cfrac_nth c 1 * cfrac_nth c 0 + 1"
+| "conv_num c (Suc (Suc n)) = cfrac_nth c (Suc (Suc n)) * conv_num c (Suc n) + conv_num c n"
+
+fun conv_denom :: "cfrac \<Rightarrow> nat \<Rightarrow> int" where
+  "conv_denom c 0 = 1"
+| "conv_denom c (Suc 0) = cfrac_nth c 1"
+| "conv_denom c (Suc (Suc n)) = cfrac_nth c (Suc (Suc n)) * conv_denom c (Suc n) + conv_denom c n"
+
+lemma conv_num_rec:
+  "n \<ge> 2 \<Longrightarrow> conv_num c n = cfrac_nth c n * conv_num c (n - 1) + conv_num c (n - 2)"
+  by (cases n; cases "n - 1") auto
+
+lemma conv_denom_rec:
+  "n \<ge> 2 \<Longrightarrow> conv_denom c n = cfrac_nth c n * conv_denom c (n - 1) + conv_denom c (n - 2)"
+  by (cases n; cases "n - 1") auto
+
+
+fun conv' :: "cfrac \<Rightarrow> nat \<Rightarrow> real \<Rightarrow> real" where
+  "conv' c 0 z = z"
+| "conv' c (Suc n) z = conv' c n (real_of_int (cfrac_nth c n) + 1 / z)"
+
+text \<open>
+  Occasionally, it can be useful to extend the domain of @{const conv_num} and @{const conv_denom}
+  to \<open>-1\<close> and \<open>-2\<close>.
+\<close>
+definition conv_num_int :: "cfrac \<Rightarrow> int \<Rightarrow> int" where
+  "conv_num_int c n = (if n = -1 then 1 else if n < 0 then 0 else conv_num c (nat n))"
+
+definition conv_denom_int :: "cfrac \<Rightarrow> int \<Rightarrow> int" where
+  "conv_denom_int c n = (if n = -2 then 1 else if n < 0 then 0 else conv_denom c (nat n))"
+
+lemma conv_num_int_rec:
+  assumes "n \<ge> 0"
+  shows   "conv_num_int c n = cfrac_nth c (nat n) * conv_num_int c (n - 1) + conv_num_int c (n - 2)"
+proof (cases "n \<ge> 2")
+  case True
+  define n' where "n' = nat (n - 2)"
+  have n: "n = int (Suc (Suc n'))"
+    using True by (simp add: n'_def)
+  show ?thesis
+    by (simp add: n conv_num_int_def nat_add_distrib)
+qed (use assms in \<open>auto simp: conv_num_int_def\<close>)
+
+lemma conv_denom_int_rec:
+  assumes "n \<ge> 0"
+  shows   "conv_denom_int c n = cfrac_nth c (nat n) * conv_denom_int c (n - 1) + conv_denom_int c (n - 2)"
+proof -
+  consider "n = 0" | "n = 1" | "n \<ge> 2"
+    using assms by force
+  thus ?thesis
+  proof cases
+    assume "n \<ge> 2"
+    define n' where "n' = nat (n - 2)"
+    have n: "n = int (Suc (Suc n'))"
+      using \<open>n \<ge> 2\<close> by (simp add: n'_def)
+    show ?thesis
+      by (simp add: n conv_denom_int_def nat_add_distrib)
+  qed (use assms in \<open>auto simp: conv_denom_int_def\<close>)
+qed
+
+text \<open>
+  The number \<open>[a\<^sub>0; a\<^sub>1, a\<^sub>2, \<dots>]\<close> that the infinite continued fraction converges to:
+\<close>
+definition cfrac_lim :: "cfrac \<Rightarrow> real" where
+  "cfrac_lim c =
+     (case cfrac_length c of \<infinity> \<Rightarrow> lim (conv c) | enat l \<Rightarrow> conv c l)"
+
+lemma cfrac_lim_code [code]:
+  "cfrac_lim c =
+     (case cfrac_length c of enat l \<Rightarrow> conv c l
+      | _ \<Rightarrow> Code.abort (STR ''Cannot compute infinite continued fraction'') (\<lambda>_. cfrac_lim c))"
+  by (simp add: cfrac_lim_def split: enat.splits)
+
+definition cfrac_remainder where "cfrac_remainder c n = cfrac_lim (cfrac_drop n c)"
+
+lemmas conv'_Suc_right = conv'.simps(2)
+
+lemma conv'_Suc_left:
+  assumes "z > 0"
+  shows "conv' c (Suc n) z =
+           real_of_int (cfrac_nth c 0) + 1 / conv' (cfrac_tl c) n z"
+  using assms
+proof (induction n arbitrary: z)
+  case (Suc n z)
+  have "conv' c (Suc (Suc n)) z = 
+          conv' c (Suc n) (real_of_int (cfrac_nth c (Suc n)) + 1 / z)"
+    by simp
+  also have "\<dots> = cfrac_nth c 0 + 1 / conv' (cfrac_tl c) (Suc n) z"
+    using Suc.prems by (subst Suc.IH) (auto intro!: add_nonneg_pos cfrac_nth_nonneg)
+  finally show ?case .
+qed simp_all
+
+lemmas [simp del] = conv'.simps(2)
+
+lemma conv'_left_induct:
+  assumes "\<And>c. P c 0 z" "\<And>c n. P (cfrac_tl c) n z \<Longrightarrow> P c (Suc n) z"
+  shows   "P c n z"
+  using assms by (rule conv.induct)
+
+lemma enat_less_diff_conv [simp]:
+  assumes "a = \<infinity> \<or> b < \<infinity> \<or> c < \<infinity>"
+  shows   "a < c - (b :: enat) \<longleftrightarrow> a + b < c"
+  using assms by (cases a; cases b; cases c) auto
+
+lemma conv_eq_conv': "conv c n = conv' c n (cfrac_nth c n)"
+proof (cases "n = 0")
+  case False
+  hence "cfrac_nth c n > 0" by (auto intro!: cfrac_nth_pos)
+  thus ?thesis
+    by (induction c n rule: conv.induct) (simp_all add: conv'_Suc_left)
+qed simp_all
+
+lemma conv_num_pos':
+  assumes "cfrac_nth c 0 > 0"
+  shows   "conv_num c n > 0"
+  using assms by (induction n rule: fib.induct) (auto simp: intro!: add_pos_nonneg)
+
+lemma conv_num_nonneg: "cfrac_nth c 0 \<ge> 0 \<Longrightarrow> conv_num c n \<ge> 0"
+  by (induction c n rule: conv_num.induct)
+     (auto simp: intro!: mult_nonneg_nonneg add_nonneg_nonneg
+           intro: cfrac_nth_nonneg)
+
+lemma conv_num_pos:
+  "cfrac_nth c 0 \<ge> 0 \<Longrightarrow> n > 0 \<Longrightarrow> conv_num c n > 0"
+  by (induction c n rule: conv_num.induct)
+     (auto intro!: mult_pos_pos mult_nonneg_nonneg add_pos_nonneg conv_num_nonneg cfrac_nth_pos
+           intro: cfrac_nth_nonneg simp:  enat_le_iff)
+
+lemma conv_denom_pos [simp, intro]: "conv_denom c n > 0"
+  by (induction c n rule: conv_num.induct)
+     (auto intro!: add_nonneg_pos mult_nonneg_nonneg cfrac_nth_nonneg
+           simp: enat_le_iff)
+
+lemma conv_denom_not_nonpos [simp]: "\<not>conv_denom c n \<le> 0"
+  using conv_denom_pos[of c n] by linarith
+
+lemma conv_denom_not_neg [simp]: "\<not>conv_denom c n < 0"
+  using conv_denom_pos[of c n] by linarith
+
+lemma conv_denom_nonzero [simp]: "conv_denom c n \<noteq> 0"
+  using conv_denom_pos[of c n] by linarith
+
+lemma conv_denom_nonneg [simp, intro]: "conv_denom c n \<ge> 0"
+  using conv_denom_pos[of c n] by linarith
+
+lemma conv_num_int_neg1 [simp]: "conv_num_int c (-1) = 1"
+  by (simp add: conv_num_int_def)
+
+lemma conv_num_int_neg [simp]: "n < 0 \<Longrightarrow> n \<noteq> -1 \<Longrightarrow> conv_num_int c n = 0"
+  by (simp add: conv_num_int_def)
+
+lemma conv_num_int_of_nat [simp]: "conv_num_int c (int n) = conv_num c n"
+  by (simp add: conv_num_int_def)
+
+lemma conv_num_int_nonneg [simp]: "n \<ge> 0 \<Longrightarrow> conv_num_int c n = conv_num c (nat n)"
+  by (simp add: conv_num_int_def)
+
+lemma conv_denom_int_neg2 [simp]: "conv_denom_int c (-2) = 1"
+  by (simp add: conv_denom_int_def)
+
+lemma conv_denom_int_neg [simp]: "n < 0 \<Longrightarrow> n \<noteq> -2 \<Longrightarrow> conv_denom_int c n = 0"
+  by (simp add: conv_denom_int_def)
+
+lemma conv_denom_int_of_nat [simp]: "conv_denom_int c (int n) = conv_denom c n"
+  by (simp add: conv_denom_int_def)
+
+lemma conv_denom_int_nonneg [simp]: "n \<ge> 0 \<Longrightarrow> conv_denom_int c n = conv_denom c (nat n)"
+  by (simp add: conv_denom_int_def)
+
+lemmas conv_Suc [simp del] = conv.simps(2)
+
+
+lemma conv'_gt_1:
+  assumes "cfrac_nth c 0 > 0" "x > 1"
+  shows   "conv' c n x > 1"
+  using assms
+proof (induction n arbitrary: c x)
+  case (Suc n c x)
+  from Suc.prems have pos: "cfrac_nth c n > 0" using cfrac_nth_pos[of n c]
+    by (cases "n = 0") (auto simp: enat_le_iff)
+  have "1 < 1 + 1 / x"
+    using Suc.prems by simp
+  also have "\<dots> \<le> cfrac_nth c n + 1 / x" using pos
+    by (intro add_right_mono) (auto simp: of_nat_ge_1_iff)
+  finally show ?case
+    by (subst conv'_Suc_right, intro Suc.IH)
+       (use Suc.prems in \<open>auto simp: enat_le_iff\<close>)
+qed auto
+
+lemma enat_eq_iff: "a = enat b \<longleftrightarrow> (\<exists>a'. a = enat a' \<and> a' = b)"
+  by (cases a) auto
+
+lemma eq_enat_iff: "enat a = b \<longleftrightarrow> (\<exists>b'. b = enat b' \<and> a = b')"
+  by (cases b) auto
+
+lemma enat_diff_one [simp]: "enat a - 1 = enat (a - 1)"
+  by (cases "enat (a - 1)") (auto simp flip: idiff_enat_enat)
+
+lemma conv'_eqD:
+  assumes "conv' c n x = conv' c' n x" "x > 1" "m < n"
+  shows   "cfrac_nth c m = cfrac_nth c' m"
+  using assms
+proof (induction n arbitrary: m c c')
+  case (Suc n m c c')
+  have gt: "conv' (cfrac_tl c) n x > 1" "conv' (cfrac_tl c') n x > 1"
+    by (rule conv'_gt_1;
+        use Suc.prems in \<open>force intro: cfrac_nth_pos simp: enat_le_iff\<close>)+
+  have eq: "cfrac_nth c 0 + 1 / conv' (cfrac_tl c) n x =
+            cfrac_nth c' 0 + 1 / conv' (cfrac_tl c') n x"
+    using Suc.prems by (subst (asm) (1 2) conv'_Suc_left) auto
+  hence "\<lfloor>cfrac_nth c 0 + 1 / conv' (cfrac_tl c) n x\<rfloor> =
+         \<lfloor>cfrac_nth c' 0 + 1 / conv' (cfrac_tl c') n x\<rfloor>"
+    by (simp only: )
+  also from gt have "floor (cfrac_nth c 0 + 1 / conv' (cfrac_tl c) n x) = cfrac_nth c 0"
+    by (intro floor_unique) auto
+  also from gt have "floor (cfrac_nth c' 0 + 1 / conv' (cfrac_tl c') n x) = cfrac_nth c' 0"
+    by (intro floor_unique) auto
+  finally have [simp]: "cfrac_nth c 0 = cfrac_nth c' 0" by simp
+
+  show ?case
+  proof (cases m)
+    case (Suc m')
+    from eq and gt have "conv' (cfrac_tl c) n x = conv' (cfrac_tl c') n x"
+      by simp
+    hence "cfrac_nth (cfrac_tl c) m' = cfrac_nth (cfrac_tl c') m'"
+      using Suc.prems
+      by (intro Suc.IH[of "cfrac_tl c" "cfrac_tl c'"]) (auto simp: o_def Suc enat_le_iff)
+    with Suc show ?thesis by simp
+  qed simp_all
+qed simp_all
+
+context
+  fixes c :: cfrac and h k
+  defines "h \<equiv> conv_num c" and "k \<equiv> conv_denom c"
+begin
+
+lemma conv'_num_denom_aux:
+  assumes z: "z > 0"
+  shows   "conv' c (Suc (Suc n)) z * (z * k (Suc n) + k n) = 
+             (z * h (Suc n) + h n)"
+  using z
+proof (induction n arbitrary: z)
+  case 0
+  hence "1 + z * cfrac_nth c 1 > 0"
+    by (intro add_pos_nonneg) (auto simp: cfrac_nth_nonneg)
+  with 0 show ?case
+    by (auto simp add: h_def k_def field_simps conv'_Suc_right max_def not_le)
+next
+  case (Suc n)
+  have [simp]: "h (Suc (Suc n)) = cfrac_nth c (n+2) * h (n+1) + h n"
+    by (simp add: h_def)
+  have [simp]: "k (Suc (Suc n)) = cfrac_nth c (n+2) * k (n+1) + k n"
+    by (simp add: k_def)
+  define z' where "z' = cfrac_nth c (n+2) + 1 / z"
+  from \<open>z > 0\<close> have "z' > 0"
+    by (auto simp: z'_def intro!: add_nonneg_pos cfrac_nth_nonneg)
+
+  have "z * real_of_int (h (Suc (Suc n))) + real_of_int (h (Suc n)) =
+          z * (z' * h (Suc n) + h n)"
+    using \<open>z > 0\<close> by (simp add: algebra_simps z'_def)
+  also have "\<dots> = z * (conv' c (Suc (Suc n)) z' * (z' * k (Suc n) + k n))"
+    using \<open>z' > 0\<close> by (subst Suc.IH [symmetric]) auto
+  also have "\<dots> = conv' c (Suc (Suc (Suc n))) z *
+            (z * k (Suc (Suc n)) + k (Suc n))"
+    unfolding z'_def using \<open>z > 0\<close>
+    by (subst (2) conv'_Suc_right) (simp add: algebra_simps)
+  finally show ?case ..
+qed
+
+lemma conv'_num_denom:
+  assumes "z > 0"
+  shows   "conv' c (Suc (Suc n)) z =
+             (z * h (Suc n) + h n) / (z * k (Suc n) + k n)"
+proof -
+  have "z * real_of_int (k (Suc n)) + real_of_int (k n) > 0"
+    using assms by (intro add_pos_nonneg mult_pos_pos) (auto simp: k_def)
+  with conv'_num_denom_aux[of z n] assms show ?thesis
+    by (simp add: divide_simps)
+qed
+
+lemma conv_num_denom: "conv c n = h n / k n"
+proof -
+  consider "n = 0" | "n = Suc 0" | m where "n = Suc (Suc m)"
+    using not0_implies_Suc by blast
+  thus ?thesis
+  proof cases
+    assume "n = Suc 0"
+    thus ?thesis
+      by (auto simp: h_def k_def field_simps max_def conv_Suc)
+  next
+    fix m assume [simp]: "n = Suc (Suc m)"
+    have "conv c n = conv' c (Suc (Suc m)) (cfrac_nth c (Suc (Suc m)))"
+      by (subst conv_eq_conv') simp_all
+    also have "\<dots> = h n / k n"
+      by (subst conv'_num_denom) (simp_all add: h_def k_def)
+    finally show ?thesis .
+  qed (auto simp: h_def k_def)
+qed
+
+lemma conv'_num_denom':
+  assumes "z > 0" and "n \<ge> 2"
+  shows   "conv' c n z = (z * h (n - 1) + h (n - 2)) / (z * k (n - 1) + k (n - 2))"
+  using assms conv'_num_denom[of z "n - 2"]
+  by (auto simp: eval_nat_numeral Suc_diff_Suc)
+
+lemma conv'_num_denom_int:
+  assumes "z > 0"
+  shows   "conv' c n z =
+             (z * conv_num_int c (int n - 1) + conv_num_int c (int n - 2)) /
+             (z * conv_denom_int c (int n - 1) + conv_denom_int c (int n - 2))"
+proof -
+  consider "n = 0" | "n = 1" | "n \<ge> 2" by force
+  thus ?thesis
+  proof cases
+    case 1
+    thus ?thesis using conv_num_int_neg1 by auto
+  next
+    case 2
+    thus ?thesis using assms by (auto simp: conv'_Suc_right field_simps)
+  next
+    case 3
+    thus ?thesis using conv'_num_denom'[OF assms(1), of "nat n"]
+      by (auto simp: nat_diff_distrib h_def k_def)
+  qed
+qed
+
+lemma conv_nonneg: "cfrac_nth c 0 \<ge> 0 \<Longrightarrow> conv c n \<ge> 0"
+  by (subst conv_num_denom)
+    (auto intro!: divide_nonneg_nonneg conv_num_nonneg simp: h_def k_def)
+
+lemma conv_pos:
+  assumes "cfrac_nth c 0 > 0"
+  shows   "conv c n > 0"
+proof -
+  have "conv c n = h n / k n"
+    using assms by (intro conv_num_denom)
+  also from assms have "\<dots> > 0" unfolding h_def k_def
+    by (intro divide_pos_pos) (auto intro!: conv_num_pos')
+  finally show ?thesis .
+qed
+
+lemma conv_num_denom_prod_diff:
+  "k n * h (Suc n) - k (Suc n) * h n = (-1) ^ n"
+  by (induction c n rule: conv_num.induct)
+     (auto simp: k_def h_def algebra_simps)
+
+lemma conv_num_denom_prod_diff':
+  "k (Suc n) * h n - k n * h (Suc n) = (-1) ^ Suc n"
+  by (induction c n rule: conv_num.induct)
+     (auto simp: k_def h_def algebra_simps)
+
+lemma
+  fixes n :: int
+  assumes "n \<ge> -2"
+  shows   conv_num_denom_int_prod_diff:
+            "conv_denom_int c n * conv_num_int c (n + 1) - 
+               conv_denom_int c (n + 1) * conv_num_int c n = (-1) ^ (nat (n + 2))" (is ?th1)
+  and     conv_num_denom_int_prod_diff':
+            "conv_denom_int c (n + 1) * conv_num_int c n - 
+               conv_denom_int c n * conv_num_int c (n + 1) = (-1) ^ (nat (n + 3))" (is ?th2)
+proof -
+  from assms consider "n = -2" | "n = -1" | "n \<ge> 0" by force
+  thus ?th1 using conv_num_denom_prod_diff[of "nat n"]
+    by cases (auto simp: h_def k_def nat_add_distrib)
+  moreover from assms have "nat (n + 3) = Suc (nat (n + 2))" by (simp add: nat_add_distrib)
+  ultimately show ?th2 by simp
+qed
+
+lemma coprime_conv_num_denom: "coprime (h n) (k n)"
+proof (cases n)
+  case [simp]: (Suc m)
+  {
+    fix d :: int
+    assume "d dvd h n" and "d dvd k n"
+    hence "abs d dvd abs (k n * h (Suc n) - k (Suc n) * h n)"
+      by simp
+    also have "\<dots> = 1"
+      by (subst conv_num_denom_prod_diff) auto
+    finally have "is_unit d" by simp
+  }
+  thus ?thesis by (rule coprimeI)
+qed (auto simp: h_def k_def)
+
+lemma coprime_conv_num_denom_int:
+  assumes "n \<ge> -2"
+  shows   "coprime (conv_num_int c n) (conv_denom_int c n)"
+proof -
+  from assms consider "n = -2" | "n = -1" | "n \<ge> 0" by force
+  thus ?thesis by cases (insert coprime_conv_num_denom[of "nat n"], auto simp: h_def k_def)
+qed
+
+lemma mono_conv_num:
+  assumes "cfrac_nth c 0 \<ge> 0"
+  shows   "mono h"
+proof (rule incseq_SucI)
+  show "h n \<le> h (Suc n)" for n
+  proof (cases n)
+    case 0
+    have "1 * cfrac_nth c 0 + 1 \<le> cfrac_nth c (Suc 0) * cfrac_nth c 0 + 1"
+      using assms by (intro add_mono mult_right_mono) auto
+    thus ?thesis using assms by (simp add: le_Suc_eq Suc_le_eq h_def 0)
+  next
+    case (Suc m)
+    have "1 * h (Suc m) + 0 \<le> cfrac_nth c (Suc (Suc m)) * h (Suc m) + h m"
+      using assms
+      by (intro add_mono mult_right_mono)
+         (auto simp: Suc_le_eq h_def intro!: conv_num_nonneg)
+    with Suc show ?thesis by (simp add: h_def)
+  qed
+qed
+
+lemma mono_conv_denom: "mono k"
+proof (rule incseq_SucI)
+  show "k n \<le> k (Suc n)" for n
+  proof (cases n)
+    case 0
+    thus ?thesis by (simp add: le_Suc_eq Suc_le_eq k_def)
+  next
+    case (Suc m)
+    have "1 * k (Suc m) + 0 \<le> cfrac_nth c (Suc (Suc m)) * k (Suc m) + k m"
+      by (intro add_mono mult_right_mono) (auto simp: Suc_le_eq k_def)
+    with Suc show ?thesis by (simp add: k_def)
+  qed
+qed
+
+lemma conv_num_leI: "cfrac_nth c 0 \<ge> 0 \<Longrightarrow> m \<le> n \<Longrightarrow> h m \<le> h n"
+  using mono_conv_num by (auto simp: mono_def)
+
+lemma conv_denom_leI: "m \<le> n \<Longrightarrow> k m \<le> k n"
+  using mono_conv_denom by (auto simp: mono_def)
+
+lemma conv_denom_lessI:
+  assumes "m < n" "1 < n"
+  shows   "k m < k n"
+proof (cases n)
+  case [simp]: (Suc n')
+  show ?thesis
+  proof (cases n')
+    case [simp]: (Suc n'')
+    from assms have "k m \<le> 1 * k n' + 0"
+      by (auto intro: conv_denom_leI simp: less_Suc_eq)
+    also have "\<dots> \<le> cfrac_nth c n * k n' + 0"
+      using assms by (intro add_mono mult_mono) (auto simp: Suc_le_eq k_def)
+    also have "\<dots> < cfrac_nth c n * k n' + k n''" unfolding k_def
+      by (intro add_strict_left_mono conv_denom_pos assms)
+    also have "\<dots> = k n" by (simp add: k_def)
+    finally show ?thesis .
+  qed (insert assms, auto simp: k_def)
+qed (insert assms, auto)
+
+lemma conv_num_lower_bound:
+  assumes "cfrac_nth c 0 \<ge> 0"
+  shows   "h n \<ge> fib n" unfolding h_def
+  using assms
+proof (induction c n rule: conv_denom.induct)
+  case (3 c n)
+  hence "conv_num c (Suc (Suc n)) \<ge> 1 * int (fib (Suc n)) + int (fib n)"
+    using "3.prems" unfolding conv_num.simps
+    by (intro add_mono mult_mono "3.IH") auto
+  thus ?case by simp
+qed auto
+
+lemma conv_denom_lower_bound: "k n \<ge> fib (Suc n)"
+  unfolding k_def
+proof (induction c n rule: conv_denom.induct)
+  case (3 c n)
+  hence "conv_denom c (Suc (Suc n)) \<ge> 1 * int (fib (Suc (Suc n))) + int (fib (Suc n))"
+    using "3.prems" unfolding conv_denom.simps
+    by (intro add_mono mult_mono "3.IH") auto
+  thus ?case by simp
+qed (auto simp: Suc_le_eq)
+
+lemma conv_diff_eq: "conv c (Suc n) - conv c n = (-1) ^ n / (k n * k (Suc n))"
+proof -
+  have pos: "k n > 0" "k (Suc n) > 0" unfolding k_def
+    by (intro conv_denom_pos)+
+  have "conv c (Suc n) - conv c n =
+          (k n * h (Suc n) - k (Suc n) * h n) / (k n * k (Suc n))"
+    using pos by (subst (1 2) conv_num_denom) (simp add: conv_num_denom field_simps)
+  also have "k n * h (Suc n) - k (Suc n) * h n = (-1) ^ n"
+    by (rule conv_num_denom_prod_diff)
+  finally show ?thesis by simp
+qed
+
+lemma conv_telescope:
+  assumes "m \<le> n"
+  shows   "conv c m + (\<Sum>i=m..<n. (-1) ^ i / (k i * k (Suc i))) = conv c n"
+proof -
+  have "(\<Sum>i=m..<n. (-1) ^ i / (k i * k (Suc i))) =
+          (\<Sum>i=m..<n. conv c (Suc i) - conv c i)"
+    by (simp add: conv_diff_eq assms del: conv.simps)
+  also have "conv c m + \<dots> = conv c n"
+    using assms by (induction rule: dec_induct) simp_all
+  finally show ?thesis .
+qed
+
+lemma fib_at_top: "filterlim fib at_top at_top"
+proof (rule filterlim_at_top_mono)
+  show "eventually (\<lambda>n. fib n \<ge> n - 1) at_top"
+    by (intro always_eventually fib_ge allI)
+  show "filterlim (\<lambda>n::nat. n - 1) at_top at_top"
+    by (subst filterlim_sequentially_Suc [symmetric])
+       (simp_all add: filterlim_ident)
+qed
+
+lemma conv_denom_at_top: "filterlim k at_top at_top"
+proof (rule filterlim_at_top_mono)
+  show "filterlim (\<lambda>n. int (fib (Suc n))) at_top at_top"
+    by (rule filterlim_compose[OF filterlim_int_sequentially])
+       (simp add: fib_at_top filterlim_sequentially_Suc)
+  show "eventually (\<lambda>n. fib (Suc n) \<le> k n) at_top"
+    by (intro always_eventually conv_denom_lower_bound allI)
+qed
+
+lemma
+  shows   summable_conv_telescope:
+            "summable (\<lambda>i. (-1) ^ i / (k i * k (Suc i)))" (is ?th1)
+    and   cfrac_remainder_bounds:
+            "\<bar>(\<Sum>i. (-1) ^ (i + m) / (k (i + m) * k (Suc i + m)))\<bar> \<in>
+                {1/(k m * (k m + k (Suc m))) <..< 1 / (k m * k (Suc m))}" (is ?th2)
+proof -
+  have [simp]: "k n > 0" "k n \<ge> 0" "\<not>k n = 0" for n
+    by (auto simp: k_def)
+  have k_rec: "k (Suc (Suc n)) = cfrac_nth c (Suc (Suc n)) * k (Suc n) + k n" for n
+    by (simp add: k_def)
+  have [simp]: "a + b = 0 \<longleftrightarrow> a = 0 \<and> b = 0" if "a \<ge> 0" "b \<ge> 0" for a b :: real
+    using that by linarith
+
+  define g where "g = (\<lambda>i. inverse (real_of_int (k i * k (Suc i))))"
+
+  {
+    fix m :: nat
+    have "filterlim (\<lambda>n. k n) at_top at_top" and "filterlim (\<lambda>n. k (Suc n)) at_top at_top"
+      by (force simp: filterlim_sequentially_Suc intro: conv_denom_at_top)+
+    hence lim: "g \<longlonglongrightarrow> 0"
+      unfolding g_def of_int_mult
+      by (intro tendsto_inverse_0_at_top filterlim_at_top_mult_at_top
+                filterlim_compose[OF filterlim_real_of_int_at_top])
+    from lim have A: "summable (\<lambda>n. (-1) ^ (n + m) * g (n + m))" unfolding g_def
+      by (intro summable_alternating_decreasing)
+         (auto intro!: conv_denom_leI mult_nonneg_nonneg)
+
+    have "1 / (k m * (real_of_int (k (Suc m)) + k m / 1)) \<le>
+            1 / (k m * (k (Suc m) + k m / cfrac_nth c (m+2)))"
+      by (intro divide_left_mono mult_left_mono add_left_mono mult_pos_pos add_pos_pos divide_pos_pos)
+         (auto simp: of_nat_ge_1_iff)
+    also have "\<dots> = g m - g (Suc m)"
+      by (simp add: g_def k_rec field_simps add_pos_pos)
+    finally have le: "1 / (k m * (real_of_int (k (Suc m)) + k m / 1)) \<le> g m - g (Suc m)" by simp
+    have *: "\<bar>(\<Sum>i. (-1) ^ (i + m) * g (i + m))\<bar> \<in> {g m - g (Suc m) <..< g m}"
+      using lim unfolding g_def
+      by (intro abs_alternating_decreasing_suminf_strict) (auto intro!: conv_denom_lessI)
+    also from le have "\<dots> \<subseteq> {1 / (k m * (k (Suc m) + k m)) <..< g m}"
+      by (subst greaterThanLessThan_subseteq_greaterThanLessThan) auto
+    finally have B: "\<bar>\<Sum>i. (- 1) ^ (i + m) * g (i + m)\<bar> \<in> \<dots>" .
+    note A B
+  } note AB = this
+
+  from AB(1)[of 0] show ?th1 by (simp add: field_simps g_def)
+  from AB(2)[of m] show ?th2 by (simp add: g_def divide_inverse add_ac)
+qed
+ 
+lemma convergent_conv: "convergent (conv c)"
+proof -
+  have "convergent (\<lambda>n. conv c 0 + (\<Sum>i<n. (-1) ^ i / (k i * k (Suc i))))"
+    using summable_conv_telescope
+    by (intro convergent_add convergent_const)
+       (simp_all add: summable_iff_convergent)
+  also have "\<dots> = conv c"
+    by (rule ext, subst (2) conv_telescope [of 0, symmetric]) (simp_all add: atLeast0LessThan)
+  finally show ?thesis .
+qed
+
+lemma LIMSEQ_cfrac_lim: "cfrac_length c = \<infinity> \<Longrightarrow> conv c \<longlonglongrightarrow> cfrac_lim c"
+  using convergent_conv by (auto simp: convergent_LIMSEQ_iff cfrac_lim_def)
+
+lemma cfrac_lim_nonneg:
+  assumes "cfrac_nth c 0 \<ge> 0"
+  shows   "cfrac_lim c \<ge> 0"
+proof (cases "cfrac_length c")
+  case infinity
+  have "conv c \<longlonglongrightarrow> cfrac_lim c"
+    by (rule LIMSEQ_cfrac_lim) fact
+  thus ?thesis
+    by (rule tendsto_lowerbound)
+       (auto intro!: conv_nonneg always_eventually assms)
+next
+  case (enat l)
+  thus ?thesis using assms
+    by (auto simp: cfrac_lim_def conv_nonneg)
+qed
+
+lemma sums_cfrac_lim_minus_conv:
+  assumes "cfrac_length c = \<infinity>"
+  shows "(\<lambda>i. (-1) ^ (i + m) / (k (i + m) * k (Suc i + m))) sums (cfrac_lim c - conv c m)"
+proof -
+  have "(\<lambda>n. conv c (n + m) - conv c m) \<longlonglongrightarrow> cfrac_lim c - conv c m"
+    by (auto intro!: tendsto_diff LIMSEQ_cfrac_lim simp: filterlim_sequentially_shift assms)
+  also have "(\<lambda>n. conv c (n + m) - conv c m) =
+          (\<lambda>n. (\<Sum>i=0 + m..<n + m. (-1) ^ i / (k i * k (Suc i))))"
+    by (subst conv_telescope [of m, symmetric]) simp_all
+  also have "\<dots> = (\<lambda>n. (\<Sum>i<n. (-1) ^ (i + m) / (k (i + m) * k (Suc i + m))))"
+    by (subst sum.shift_bounds_nat_ivl) (simp_all add: atLeast0LessThan)
+  finally show ?thesis unfolding sums_def .
+qed
+
+lemma cfrac_lim_minus_conv_upper_bound:
+  assumes "m \<le> cfrac_length c"
+  shows   "\<bar>cfrac_lim c - conv c m\<bar> \<le> 1 / (k m * k (Suc m))"
+proof (cases "cfrac_length c")
+  case infinity
+  have "cfrac_lim c - conv c m = (\<Sum>i. (-1) ^ (i + m) / (k (i + m) * k (Suc i + m)))"
+    using sums_cfrac_lim_minus_conv infinity by (simp add: sums_iff)
+  also note cfrac_remainder_bounds[of m]
+  finally show ?thesis by simp
+next
+  case [simp]: (enat l)
+  show ?thesis
+  proof (cases "l = m")
+    case True
+    thus ?thesis by (auto simp: cfrac_lim_def k_def)
+  next
+    case False
+    let ?S = "(\<Sum>i=m..<l. (-1) ^ i * (1 / real_of_int (k i * k (Suc i))))"
+    have [simp]: "k n \<ge> 0" "k n > 0" for n
+      by (simp_all add: k_def)
+    hence "cfrac_lim c - conv c m = conv c l - conv c m"
+      by (simp add: cfrac_lim_def)
+    also have "\<dots> = ?S"
+      using assms by (subst conv_telescope [symmetric, of m]) auto
+    finally have "cfrac_lim c - conv c m = ?S" .
+    moreover have "\<bar>?S\<bar> \<le> 1 / real_of_int (k m * k (Suc m))"
+      unfolding of_int_mult using assms False
+      by (intro abs_alternating_decreasing_sum_upper_bound' divide_nonneg_nonneg frac_le mult_mono)
+         (simp_all add: conv_denom_leI del: conv_denom.simps)
+    ultimately show ?thesis by simp
+  qed
+qed
+
+lemma cfrac_lim_minus_conv_lower_bound:
+  assumes "m < cfrac_length c"
+  shows   "\<bar>cfrac_lim c - conv c m\<bar> \<ge> 1 / (k m * (k m + k (Suc m)))"
+proof (cases "cfrac_length c")
+  case infinity
+  have "cfrac_lim c - conv c m = (\<Sum>i. (-1) ^ (i + m) / (k (i + m) * k (Suc i + m)))"
+    using sums_cfrac_lim_minus_conv infinity by (simp add: sums_iff)
+  also note cfrac_remainder_bounds[of m]
+  finally show ?thesis by simp
+next
+  case [simp]: (enat l)
+  let ?S = "(\<Sum>i=m..<l. (-1) ^ i * (1 / real_of_int (k i * k (Suc i))))"
+  have [simp]: "k n \<ge> 0" "k n > 0" for n
+    by (simp_all add: k_def)
+  hence "cfrac_lim c - conv c m = conv c l - conv c m"
+    by (simp add: cfrac_lim_def)
+  also have "\<dots> = ?S"
+    using assms by (subst conv_telescope [symmetric, of m]) (auto simp: split: enat.splits)
+  finally have "cfrac_lim c - conv c m = ?S" .
+
+  moreover have "\<bar>?S\<bar> \<ge> 1 / (k m * (k m + k (Suc m)))"
+  proof (cases "m < cfrac_length c - 1")
+    case False
+    hence [simp]: "m = l - 1" and "l > 0" using assms
+      by (auto simp: not_less)
+    have "1 / (k m * (k m + k (Suc m))) \<le> 1 / (k m * k (Suc m))"
+      unfolding of_int_mult
+      by (intro divide_left_mono mult_mono mult_pos_pos) (auto intro!: add_pos_pos)
+    also from \<open>l > 0\<close> have "{m..<l} = {m}" by auto
+    hence "1 / (k m * k (Suc m)) = \<bar>?S\<bar>"
+      by simp
+    finally show ?thesis .
+  next
+    case True
+    with assms have less: "m < l - 1"
+      by auto
+    have "k m + k (Suc m) > 0"
+      by (intro add_pos_pos) (auto simp: k_def)
+    hence "1 / (k m * (k m + k (Suc m))) \<le> 1 / (k m * k (Suc m)) - 1 / (k (Suc m) * k (Suc (Suc m)))"
+      by (simp add: divide_simps) (auto simp: k_def algebra_simps)
+    also have "\<dots> \<le> \<bar>?S\<bar>"
+      unfolding of_int_mult using less
+      by (intro abs_alternating_decreasing_sum_lower_bound' divide_nonneg_nonneg frac_le mult_mono)
+         (simp_all add: conv_denom_leI del: conv_denom.simps)
+    finally show ?thesis .
+  qed
+  ultimately show ?thesis by simp
+qed
+
+lemma cfrac_lim_minus_conv_bounds:
+  assumes "m < cfrac_length c"
+  shows   "\<bar>cfrac_lim c - conv c m\<bar> \<in> {1 / (k m * (k m + k (Suc m)))..1 / (k m * k (Suc m))}"
+  using cfrac_lim_minus_conv_lower_bound[of m] cfrac_lim_minus_conv_upper_bound[of m] assms
+  by auto
+
+end
+
+
+lemma conv_pos':
+  assumes "n > 0" "cfrac_nth c 0 \<ge> 0"
+  shows   "conv c n > 0"
+  using assms by (cases n) (auto simp: conv_Suc intro!: add_nonneg_pos conv_pos)
+
+lemma conv_in_Rats [intro]: "conv c n \<in> \<rat>"
+  by (induction c n rule: conv.induct) (auto simp: conv_Suc o_def)
+
+lemma
+  assumes "0 < z1" "z1 \<le> z2"
+  shows   conv'_even_mono: "even n \<Longrightarrow> conv' c n z1 \<le> conv' c n z2"
+    and   conv'_odd_mono:  "odd n \<Longrightarrow> conv' c n z1 \<ge> conv' c n z2"
+proof -
+  let ?P = "(\<lambda>n (f::nat\<Rightarrow>real\<Rightarrow>real). 
+               if even n then f n z1 \<le> f n z2 else f n z1 \<ge> f n z2)"
+  have "?P n (conv' c)" using assms
+  proof (induction n arbitrary: z1 z2)
+    case (Suc n)
+    note z12 = Suc.prems
+    consider "n = 0" | "even n" "n > 0" | "odd n" by force
+    thus ?case
+    proof cases
+      assume "n = 0"
+      thus ?thesis using Suc by (simp add: conv'_Suc_right field_simps)
+    next
+      assume n: "even n" "n > 0"
+      with Suc.IH have IH: "conv' c n z1 \<le> conv' c n z2"
+        if "0 < z1" "z1 \<le> z2" for z1 z2 using that by auto
+      show ?thesis using Suc.prems n z12
+        by (auto simp: conv'_Suc_right field_simps intro!: IH add_pos_nonneg mult_nonneg_nonneg)
+    next
+      assume n: "odd n"
+      hence [simp]: "n > 0" by (auto intro!: Nat.gr0I)
+      from n and Suc.IH have IH: "conv' c n z1 \<ge> conv' c n z2"
+        if "0 < z1" "z1 \<le> z2" for z1 z2 using that by auto
+      show ?thesis using Suc.prems n
+        by (auto simp: conv'_Suc_right field_simps
+                 intro!: IH add_pos_nonneg mult_nonneg_nonneg)
+    qed
+  qed auto
+  thus "even n \<Longrightarrow> conv' c n z1 \<le> conv' c n z2"
+       "odd n \<Longrightarrow> conv' c n z1 \<ge> conv' c n z2" by auto
+qed
+
+lemma
+  shows   conv_even_mono: "even n \<Longrightarrow> n \<le> m \<Longrightarrow> conv c n \<le> conv c m"
+    and   conv_odd_mono:  "odd n  \<Longrightarrow> n \<le> m \<Longrightarrow> conv c n \<ge> conv c m"
+proof -
+  assume "even n"
+  have A: "conv c n \<le> conv c (Suc (Suc n))" if "even n" for n
+  proof (cases "n = 0")
+    case False
+    with \<open>even n\<close> show ?thesis
+      by (auto simp add: conv_eq_conv' conv'_Suc_right intro: conv'_even_mono)
+  qed (auto simp:  conv_Suc)
+
+  have B: "conv c n \<le> conv c (Suc n)" if "even n" for n
+  proof (cases "n = 0")
+    case False
+    with \<open>even n\<close> show ?thesis
+      by (auto simp add: conv_eq_conv' conv'_Suc_right intro: conv'_even_mono)
+  qed (auto simp:  conv_Suc)
+
+  show "conv c n \<le> conv c m" if "n \<le> m" for m
+    using that
+  proof (induction m rule: less_induct)
+    case (less m)
+    from \<open>n \<le> m\<close> consider "m = n" | "even m" "m > n" | "odd m" "m > n"
+      by force
+    thus ?case
+    proof cases
+      assume m: "even m" "m > n"
+      with \<open>even n\<close> have m': "m - 2 \<ge> n" by presburger
+      with m have "conv c n \<le> conv c (m - 2)"
+        by (intro less.IH) auto
+      also have "\<dots> \<le> conv c (Suc (Suc (m - 2)))"
+        using m m' by (intro A) auto
+      also have "Suc (Suc (m - 2)) = m"
+        using m by presburger
+      finally show ?thesis .
+    next
+      assume m: "odd m" "m > n"
+      hence "conv c n \<le> conv c (m - 1)"
+        by (intro less.IH) auto
+      also have "\<dots> \<le> conv c (Suc (m - 1))"
+        using m by (intro B) auto
+      also have "Suc (m - 1) = m"
+        using m by simp
+      finally show ?thesis .
+    qed simp_all
+  qed
+next
+  assume "odd n"
+  have A: "conv c n \<ge> conv c (Suc (Suc n))" if "odd n" for n
+    using that
+    by (auto simp add: conv_eq_conv' conv'_Suc_right odd_pos intro!: conv'_odd_mono)
+  have B: "conv c n \<ge> conv c (Suc n)" if "odd n" for n using that
+    by (auto simp add: conv_eq_conv' conv'_Suc_right odd_pos intro!: conv'_odd_mono)
+
+  show "conv c n \<ge> conv c m" if "n \<le> m" for m
+    using that
+  proof (induction m rule: less_induct)
+    case (less m)
+    from \<open>n \<le> m\<close> consider "m = n" | "even m" "m > n" | "odd m" "m > n"
+      by force
+    thus ?case
+    proof cases
+      assume m: "odd m" "m > n"
+      with \<open>odd n\<close> have m': "m - 2 \<ge> n" "m \<ge> 2" by presburger+
+      from m and \<open>odd n\<close> have "m = Suc (Suc (m - 2))" by presburger
+      also have "conv c \<dots> \<le> conv c (m - 2)"
+        using m m' by (intro A) auto
+      also have "\<dots> \<le> conv c n"
+        using m m' by (intro less.IH) auto
+      finally show ?thesis .
+    next
+      assume m: "even m" "m > n"
+      from m have "m = Suc (m - 1)" by presburger
+      also have "conv c \<dots> \<le> conv c (m - 1)"
+        using m by (intro B) auto
+      also have "\<dots> \<le> conv c n"
+        using m by (intro less.IH) auto
+      finally show ?thesis .
+    qed simp_all
+  qed
+qed
+
+lemma
+  assumes "m \<le> cfrac_length c"
+  shows   conv_le_cfrac_lim: "even m \<Longrightarrow> conv c m \<le> cfrac_lim c"
+    and   conv_ge_cfrac_lim: "odd m \<Longrightarrow> conv c m \<ge> cfrac_lim c"
+proof -
+  have "if even m then conv c m \<le> cfrac_lim c else conv c m \<ge> cfrac_lim c"
+  proof (cases "cfrac_length c")
+    case [simp]: infinity
+    show ?thesis
+    proof (cases "even m")
+      case True
+      have "eventually (\<lambda>i. conv c m \<le> conv c i) at_top"
+        using eventually_ge_at_top[of m] by eventually_elim (rule conv_even_mono[OF True])
+      hence "conv c m \<le> cfrac_lim c"
+        by (intro tendsto_lowerbound[OF LIMSEQ_cfrac_lim]) auto
+      thus ?thesis using True by simp
+    next
+      case False
+      have "eventually (\<lambda>i. conv c m \<ge> conv c i) at_top"
+        using eventually_ge_at_top[of m] by eventually_elim (rule conv_odd_mono[OF False])
+      hence "conv c m \<ge> cfrac_lim c"
+        by (intro tendsto_upperbound[OF LIMSEQ_cfrac_lim]) auto
+      thus ?thesis using False by simp
+    qed
+  next
+    case [simp]: (enat l)
+    show ?thesis
+      using conv_even_mono[of m l c] conv_odd_mono[of m l c] assms
+      by (auto simp: cfrac_lim_def)
+  qed
+  thus "even m \<Longrightarrow> conv c m \<le> cfrac_lim c" and "odd m \<Longrightarrow> conv c m \<ge> cfrac_lim c"
+    by auto
+qed
+
+lemma cfrac_lim_ge_first: "cfrac_lim c \<ge> cfrac_nth c 0"
+  using conv_le_cfrac_lim[of 0 c] by (auto simp: less_eq_enat_def split: enat.splits)
+
+lemma cfrac_lim_pos: "cfrac_nth c 0 > 0 \<Longrightarrow> cfrac_lim c > 0"
+  by (rule less_le_trans[OF _ cfrac_lim_ge_first]) auto
+
+lemma conv'_eq_iff:
+  assumes "0 \<le> z1 \<or> 0 \<le> z2"
+  shows   "conv' c n z1 = conv' c n z2 \<longleftrightarrow> z1 = z2"
+proof
+  assume "conv' c n z1 = conv' c n z2"
+  thus "z1 = z2" using assms
+  proof (induction n arbitrary: z1 z2)
+    case (Suc n)
+    show ?case
+    proof (cases "n = 0")
+      case True
+      thus ?thesis using Suc by (auto simp: conv'_Suc_right)
+    next
+      case False
+      have "conv' c n (real_of_int (cfrac_nth c n) + 1 / z1) =
+               conv' c n (real_of_int (cfrac_nth c n) + 1 / z2)" using Suc.prems
+        by (simp add: conv'_Suc_right)
+      hence "real_of_int (cfrac_nth c n) + 1 / z1 = real_of_int (cfrac_nth c n) + 1 / z2"
+        by (rule Suc.IH)
+           (insert Suc.prems False, auto intro!: add_nonneg_pos add_nonneg_nonneg)
+      with Suc.prems show "z1 = z2" by simp
+    qed
+  qed auto
+qed auto
+
+lemma conv_even_mono_strict:
+  assumes "even n" "n < m"
+  shows   "conv c n < conv c m"
+proof (cases "m = n + 1")
+  case [simp]: True
+  show ?thesis
+  proof (cases "n = 0")
+    case True
+    thus ?thesis using assms by (auto simp: conv_Suc)
+  next
+    case False
+    hence "conv' c n (real_of_int (cfrac_nth c n)) \<noteq>
+           conv' c n (real_of_int (cfrac_nth c n) + 1 / real_of_int (cfrac_nth c (Suc n)))"
+      by (subst conv'_eq_iff) auto
+    with assms have "conv c n \<noteq> conv c m"
+      by (auto simp: conv_eq_conv' conv'_eq_iff conv'_Suc_right field_simps)
+    moreover from assms have "conv c n \<le> conv c m"
+      by (intro conv_even_mono) auto
+   
+    ultimately show ?thesis by simp
+  qed
+next
+  case False
+  show ?thesis
+  proof (cases "n = 0")
+    case True
+    thus ?thesis using assms
+      by (cases m) (auto simp: conv_Suc conv_pos)
+  next
+    case False
+    have "1 + real_of_int (cfrac_nth c (n+1)) * cfrac_nth c (n+2) > 0"
+      by (intro add_pos_nonneg) auto
+    with assms have "conv c n \<noteq> conv c (Suc (Suc n))"
+      unfolding conv_eq_conv' conv'_Suc_right using False
+      by (subst conv'_eq_iff) (auto simp: field_simps)
+    moreover from assms have "conv c n \<le> conv c (Suc (Suc n))"
+      by (intro conv_even_mono) auto
+    ultimately have "conv c n < conv c (Suc (Suc n))" by simp
+    also have "\<dots> \<le> conv c m" using assms \<open>m \<noteq> n + 1\<close>
+      by (intro conv_even_mono) auto
+    finally show ?thesis .
+  qed
+qed
+
+lemma conv_odd_mono_strict:
+  assumes "odd n" "n < m"
+  shows   "conv c n > conv c m"
+proof (cases "m = n + 1")
+  case [simp]: True
+  from assms have "n > 0" by (intro Nat.gr0I) auto
+  hence "conv' c n (real_of_int (cfrac_nth c n)) \<noteq>
+         conv' c n (real_of_int (cfrac_nth c n) + 1 / real_of_int (cfrac_nth c (Suc n)))"
+    by (subst conv'_eq_iff) auto
+  hence "conv c n \<noteq> conv c m"
+    by (simp add: conv_eq_conv' conv'_Suc_right)
+  moreover from assms have "conv c n \<ge> conv c m"
+    by (intro conv_odd_mono) auto
+  ultimately show ?thesis by simp
+next
+  case False
+  from assms have "n > 0" by (intro Nat.gr0I) auto
+  have "1 + real_of_int (cfrac_nth c (n+1)) * cfrac_nth c (n+2) > 0"
+    by (intro add_pos_nonneg) auto
+  with assms \<open>n > 0\<close> have "conv c n \<noteq> conv c (Suc (Suc n))"
+    unfolding conv_eq_conv' conv'_Suc_right
+    by (subst conv'_eq_iff) (auto simp: field_simps)
+  moreover from assms have "conv c n \<ge> conv c (Suc (Suc n))"
+    by (intro conv_odd_mono) auto
+  ultimately have "conv c n > conv c (Suc (Suc n))" by simp
+  moreover have "conv c (Suc (Suc n)) \<ge> conv c m" using assms False
+    by (intro conv_odd_mono) auto
+  ultimately show ?thesis by linarith
+qed
+
+lemma conv_less_cfrac_lim:
+  assumes "even n" "n < cfrac_length c"
+  shows   "conv c n < cfrac_lim c"
+proof (cases "cfrac_length c")
+  case (enat l)
+  with assms show ?thesis by (auto simp: cfrac_lim_def conv_even_mono_strict)
+next
+  case [simp]: infinity
+  from assms have "conv c n < conv c (n + 2)"
+    by (intro conv_even_mono_strict) auto
+  also from assms have "\<dots> \<le> cfrac_lim c"
+    by (intro conv_le_cfrac_lim) auto
+  finally show ?thesis .
+qed
+
+lemma conv_gt_cfrac_lim:
+  assumes "odd n" "n < cfrac_length c"
+  shows   "conv c n > cfrac_lim c"
+proof (cases "cfrac_length c")
+  case (enat l)
+  with assms show ?thesis by (auto simp: cfrac_lim_def conv_odd_mono_strict)
+next
+  case [simp]: infinity
+  from assms have "cfrac_lim c \<le> conv c (n + 2)"
+    by (intro conv_ge_cfrac_lim) auto
+  also from assms have "\<dots> < conv c n"
+    by (intro conv_odd_mono_strict) auto
+  finally show ?thesis .
+qed
+
+lemma conv_neq_cfrac_lim:
+  assumes "n < cfrac_length c"
+  shows   "conv c n \<noteq> cfrac_lim c"
+  using conv_gt_cfrac_lim[OF _ assms] conv_less_cfrac_lim[OF _ assms]
+  by (cases "even n") auto
+
+lemma conv_ge_first: "conv c n \<ge> cfrac_nth c 0"
+  using conv_even_mono[of 0 n c] by simp
+
+
+definition cfrac_is_zero :: "cfrac \<Rightarrow> bool" where "cfrac_is_zero c \<longleftrightarrow> c = 0"
+
+lemma cfrac_is_zero_code [code]: "cfrac_is_zero (CFrac n xs) \<longleftrightarrow> lnull xs \<and> n = 0"
+  unfolding cfrac_is_zero_def lnull_def zero_cfrac_def cfrac_of_int_def
+  by (auto simp: cfrac_length_def)
+
+
+definition cfrac_is_int where "cfrac_is_int c \<longleftrightarrow> cfrac_length c = 0"
+
+lemma cfrac_is_int_code [code]: "cfrac_is_int (CFrac n xs) \<longleftrightarrow> lnull xs"
+  unfolding cfrac_is_int_def lnull_def by (auto simp: cfrac_length_def)
+
+lemma cfrac_length_of_int [simp]: "cfrac_length (cfrac_of_int n) = 0"
+  by transfer auto
+
+lemma cfrac_is_int_of_int [simp, intro]: "cfrac_is_int (cfrac_of_int n)"
+  unfolding cfrac_is_int_def by simp
+
+lemma cfrac_is_int_iff: "cfrac_is_int c \<longleftrightarrow> (\<exists>n. c = cfrac_of_int n)"
+proof -
+  have "c = cfrac_of_int (cfrac_nth c 0)" if "cfrac_is_int c"
+    using that unfolding cfrac_is_int_def by transfer auto
+  thus ?thesis
+    by auto
+qed  
+
+lemma cfrac_lim_reduce:
+  assumes "\<not>cfrac_is_int c"
+  shows   "cfrac_lim c = cfrac_nth c 0 + 1 / cfrac_lim (cfrac_tl c)"
+proof (cases "cfrac_length c")
+  case [simp]: infinity
+  have "0 < cfrac_nth (cfrac_tl c) 0"
+    by simp
+  also have "\<dots> \<le> cfrac_lim (cfrac_tl c)"
+    by (rule cfrac_lim_ge_first)
+  finally have "(\<lambda>n. real_of_int (cfrac_nth c 0) + 1 / conv (cfrac_tl c) n) \<longlonglongrightarrow>
+           real_of_int (cfrac_nth c 0) + 1 / cfrac_lim (cfrac_tl c)"
+    by (intro tendsto_intros LIMSEQ_cfrac_lim) auto
+  also have "(\<lambda>n. real_of_int (cfrac_nth c 0) + 1 / conv (cfrac_tl c) n) = conv c \<circ> Suc"
+    by (simp add: o_def conv_Suc)
+  finally have *: "conv c \<longlonglongrightarrow> real_of_int (cfrac_nth c 0) + 1 / cfrac_lim (cfrac_tl c)"
+    by (simp add: o_def filterlim_sequentially_Suc)
+  show ?thesis
+    by (rule tendsto_unique[OF _ LIMSEQ_cfrac_lim *]) auto
+next
+  case [simp]: (enat l)
+  from assms obtain l' where [simp]: "l = Suc l'"
+    by (cases l) (auto simp: cfrac_is_int_def zero_enat_def)
+  thus ?thesis
+    by (auto simp: cfrac_lim_def conv_Suc)
+qed
+
+lemma cfrac_lim_tl:
+  assumes "\<not>cfrac_is_int c"
+  shows   "cfrac_lim (cfrac_tl c) = 1 / (cfrac_lim c - cfrac_nth c 0)"
+  using cfrac_lim_reduce[OF assms] by simp
+
+
+
+lemma cfrac_remainder_Suc':
+  assumes "n < cfrac_length c"
+  shows "cfrac_remainder c (Suc n) * (cfrac_remainder c n - cfrac_nth c n) = 1"
+proof -
+  have "0 < real_of_int (cfrac_nth c (Suc n))" by simp
+  also have "cfrac_nth c (Suc n) \<le> cfrac_remainder c (Suc n)"
+    using cfrac_lim_ge_first[of "cfrac_drop (Suc n) c"]
+    by (simp add: cfrac_remainder_def)
+  finally have "\<dots> > 0" .
+
+  have "cfrac_remainder c (Suc n) = cfrac_lim (cfrac_tl (cfrac_drop n c))"
+    by (simp add: o_def cfrac_remainder_def cfrac_drop_Suc_left)                   
+  also have "\<dots> = 1 / (cfrac_remainder c n - cfrac_nth c n)" using assms
+    by (subst cfrac_lim_tl) (auto simp: cfrac_remainder_def cfrac_is_int_def enat_less_iff enat_0_iff)
+  finally show ?thesis
+    using \<open>cfrac_remainder c (Suc n) > 0\<close>
+    by (auto simp add: cfrac_remainder_def field_simps)
+qed
+
+lemma cfrac_remainder_Suc:
+  assumes "n < cfrac_length c"
+  shows   "cfrac_remainder c (Suc n) = 1 / (cfrac_remainder c n - cfrac_nth c n)"
+proof -
+  have "cfrac_remainder c (Suc n) = cfrac_lim (cfrac_tl (cfrac_drop n c))"
+    by (simp add: o_def cfrac_remainder_def cfrac_drop_Suc_left)
+  also have "\<dots> = 1 / (cfrac_remainder c n - cfrac_nth c n)" using assms
+    by (subst cfrac_lim_tl) (auto simp: cfrac_remainder_def cfrac_is_int_def enat_less_iff enat_0_iff)
+  finally show ?thesis .
+qed
+
+lemma cfrac_remainder_0 [simp]: "cfrac_remainder c 0 = cfrac_lim c"
+  by (simp add: cfrac_remainder_def)
+
+context
+  fixes c h k x
+  defines "h \<equiv> conv_num c" and "k \<equiv> conv_denom c" and "x \<equiv> cfrac_remainder c"
+begin
+
+lemma cfrac_lim_eq_num_denom_remainder_aux:  
+  assumes "Suc (Suc n) \<le> cfrac_length c"
+  shows   "cfrac_lim c * (k (Suc n) * x (Suc (Suc n)) + k n) = h (Suc n) * x (Suc (Suc n)) + h n"
+  using assms
+proof (induction n)
+  case 0
+  have "cfrac_lim c \<noteq> cfrac_nth c 0"
+    using conv_neq_cfrac_lim[of 0 c] 0 by (auto simp: enat_le_iff)
+  moreover have "cfrac_nth c 1 * (cfrac_lim c - cfrac_nth c 0) \<noteq> 1"
+    using conv_neq_cfrac_lim[of 1 c] 0
+    by (auto simp: enat_le_iff conv_Suc field_simps)
+  ultimately show ?case using assms
+    by (auto simp: cfrac_remainder_Suc divide_simps x_def h_def k_def enat_le_iff)
+       (auto simp: field_simps)
+next
+  case (Suc n)
+  have less: "enat (Suc (Suc n)) < cfrac_length c"
+    using Suc.prems by (cases "cfrac_length c") auto
+  have *: "x (Suc (Suc n)) \<noteq> real_of_int (cfrac_nth c (Suc (Suc n)))"
+    using conv_neq_cfrac_lim[of 0 "cfrac_drop (n+2) c"] Suc.prems
+    by (cases "cfrac_length c") (auto simp: x_def cfrac_remainder_def)
+  hence "cfrac_lim c * (k (Suc (Suc n)) * x (Suc (Suc (Suc n))) + k (Suc n)) =
+           (cfrac_lim c * (k (Suc n) * x (Suc (Suc n)) + k n)) / (x (Suc (Suc n)) - cfrac_nth c (Suc (Suc n)))"
+    unfolding x_def k_def h_def using less
+    by (subst cfrac_remainder_Suc) (auto simp: field_simps)
+  also have "cfrac_lim c * (k (Suc n) * x (Suc (Suc n)) + k n) =
+               h (Suc n) * x (Suc (Suc n)) + h n" using less
+    by (intro Suc.IH) auto
+  also have "(h (Suc n) * x (Suc (Suc n)) + h n) / (x (Suc (Suc n)) - cfrac_nth c (Suc (Suc n))) = 
+               h (Suc (Suc n)) * x (Suc (Suc (Suc n))) + h (Suc n)" using *
+    unfolding x_def k_def h_def using less
+    by (subst (3) cfrac_remainder_Suc) (auto simp: field_simps)
+  finally show ?case .
+qed
+
+lemma cfrac_remainder_nonneg: "cfrac_nth c n \<ge> 0 \<Longrightarrow> cfrac_remainder c n \<ge> 0"
+  unfolding cfrac_remainder_def by (rule cfrac_lim_nonneg) auto
+
+lemma cfrac_remainder_pos: "cfrac_nth c n > 0 \<Longrightarrow> cfrac_remainder c n > 0"
+  unfolding cfrac_remainder_def by (rule cfrac_lim_pos) auto
+
+lemma cfrac_lim_eq_num_denom_remainder:
+  assumes "Suc (Suc n) < cfrac_length c"
+  shows   "cfrac_lim c = (h (Suc n) * x (Suc (Suc n)) + h n) / (k (Suc n) * x (Suc (Suc n)) + k n)"
+proof -
+  have "k (Suc n) * x (Suc (Suc n)) + k n > 0"
+    by (intro add_nonneg_pos mult_nonneg_nonneg)
+       (auto simp: k_def x_def intro!: conv_denom_pos cfrac_remainder_nonneg)
+  with cfrac_lim_eq_num_denom_remainder_aux[of n] assms show ?thesis
+    by (auto simp add: field_simps h_def k_def x_def)
+qed
+
+lemma abs_diff_successive_convs:
+  shows   "\<bar>conv c (Suc n) - conv c n\<bar> = 1 / (k n * k (Suc n))"
+proof -
+  have [simp]: "k n \<noteq> 0" for n :: nat
+    unfolding k_def using conv_denom_pos[of c n] by auto
+  have "conv c (Suc n) - conv c n = h (Suc n) / k (Suc n) - h n / k n"
+    by (simp add: conv_num_denom k_def h_def)
+  also have "\<dots> = (k n * h (Suc n) - k (Suc n) * h n) / (k n * k (Suc n))"
+    by (simp add: field_simps)
+  also have "k n * h (Suc n) - k (Suc n) * h n = (-1) ^ n"
+    unfolding h_def k_def by (intro conv_num_denom_prod_diff)
+  finally show ?thesis by (simp add: k_def)
+qed
+
+lemma conv_denom_plus2_ratio_ge: "k (Suc (Suc n)) \<ge> 2 * k n"
+proof -
+  have "1 * k n + k n \<le> cfrac_nth c (Suc (Suc n)) * k (Suc n) + k n"
+    by (intro add_mono mult_mono)
+       (auto simp: k_def Suc_le_eq intro!: conv_denom_leI)
+  thus ?thesis by (simp add: k_def)
+qed
+
+end
+
+lemma conv'_cfrac_remainder:
+  assumes "n < cfrac_length c"
+  shows   "conv' c n (cfrac_remainder c n) = cfrac_lim c"
+  using assms
+proof (induction n arbitrary: c)
+  case (Suc n c)
+  have "conv' c (Suc n) (cfrac_remainder c (Suc n)) =
+          cfrac_nth c 0 + 1 / conv' (cfrac_tl c) n (cfrac_remainder c (Suc n))"
+    using Suc.prems
+    by (subst conv'_Suc_left) (auto intro!: cfrac_remainder_pos)
+  also have "cfrac_remainder c (Suc n) = cfrac_remainder (cfrac_tl c) n"
+    by (simp add: cfrac_remainder_def cfrac_drop_Suc_right)
+  also have "conv' (cfrac_tl c) n \<dots> = cfrac_lim (cfrac_tl c)"
+    using Suc.prems by (subst Suc.IH) (auto simp: cfrac_remainder_def enat_less_iff)
+  also have "cfrac_nth c 0 + 1 / \<dots> = cfrac_lim c"
+    using Suc.prems by (intro cfrac_lim_reduce [symmetric]) (auto simp: cfrac_is_int_def)
+  finally show ?case by (simp add: cfrac_remainder_def cfrac_drop_Suc_right)
+qed auto
+
+lemma cfrac_lim_rational [intro]:
+  assumes "cfrac_length c < \<infinity>"
+  shows   "cfrac_lim c \<in> \<rat>"
+  using assms by (cases "cfrac_length c") (auto simp: cfrac_lim_def)
+
+lemma linfinite_cfrac_of_real_aux:
+  "x \<notin> \<rat> \<Longrightarrow> x \<in> {0<..<1} \<Longrightarrow> linfinite (cfrac_of_real_aux x)"
+proof (coinduction arbitrary: x)
+  case (linfinite x)
+  hence "1 / x \<notin> \<rat>" using Rats_divide[of 1 "1 / x"] by auto
+  thus ?case using linfinite Ints_subset_Rats
+    by (intro disjI1 exI[of _ "nat \<lfloor>1/x\<rfloor> - 1"] exI[of _ "cfrac_of_real_aux (frac (1/x))"] 
+              exI[of _ "frac (1/x)"] conjI)
+       (auto simp: cfrac_of_real_aux.code[of x] frac_lt_1)
+qed
+
+lemma cfrac_length_of_real_irrational:
+  assumes "x \<notin> \<rat>"
+  shows   "cfrac_length (cfrac_of_real x) = \<infinity>"
+proof (insert assms, transfer, clarify)
+  fix x :: real assume "x \<notin> \<rat>"
+  thus "llength (cfrac_of_real_aux (frac x)) = \<infinity>"
+    using linfinite_cfrac_of_real_aux[of "frac x"] Ints_subset_Rats
+    by (auto simp: linfinite_conv_llength frac_lt_1)
+qed
+
+lemma cfrac_length_of_real_reduce:
+  assumes "x \<notin> \<int>"
+  shows   "cfrac_length (cfrac_of_real x) = eSuc (cfrac_length (cfrac_of_real (1 / frac x)))"
+  using assms
+  by (transfer, subst cfrac_of_real_aux.code) (auto simp: frac_lt_1)
+
+lemma cfrac_length_of_real_int [simp]: "x \<in> \<int> \<Longrightarrow> cfrac_length (cfrac_of_real x) = 0"
+  by transfer auto
+
+lemma conv_cfrac_of_real_le_ge:
+  assumes "n \<le> cfrac_length (cfrac_of_real x)"
+  shows   "if even n then conv (cfrac_of_real x) n \<le> x else conv (cfrac_of_real x) n \<ge> x"
+  using assms
+proof (induction n arbitrary: x)
+  case (Suc n x)
+  hence [simp]: "x \<notin> \<int>"
+    using Suc by (auto simp: enat_0_iff)
+  let ?x' = "1 / frac x"
+  have "enat n \<le> cfrac_length (cfrac_of_real (1 / frac x))"
+    using Suc.prems by (auto simp: cfrac_length_of_real_reduce simp flip: eSuc_enat)
+  hence IH: "if even n then conv (cfrac_of_real ?x') n \<le> ?x' else ?x' \<le> conv (cfrac_of_real ?x') n"
+    using Suc.prems by (intro Suc.IH) auto
+  have remainder_pos: "conv (cfrac_of_real ?x') n > 0"
+    by (rule conv_pos) (auto simp: frac_le_1)
+  show ?case
+  proof (cases "even n")
+    case True
+    have "x \<le> real_of_int \<lfloor>x\<rfloor> + frac x"
+      by (simp add: frac_def)
+    also have "frac x \<le> 1 / conv (cfrac_of_real ?x') n"
+      using IH True remainder_pos frac_gt_0_iff[of x] by (simp add: field_simps)
+    finally show ?thesis using True
+      by (auto simp: conv_Suc cfrac_tl_of_real)
+  next
+    case False
+    have "real_of_int \<lfloor>x\<rfloor> + 1 / conv (cfrac_of_real ?x') n \<le> real_of_int \<lfloor>x\<rfloor> + frac x"
+      using IH False remainder_pos frac_gt_0_iff[of x] by (simp add: field_simps)
+    also have "\<dots> = x"
+      by (simp add: frac_def)
+    finally show ?thesis using False
+      by (auto simp: conv_Suc cfrac_tl_of_real)
+  qed
+qed auto
+
+lemma cfrac_lim_of_real [simp]: "cfrac_lim (cfrac_of_real x) = x"
+proof (cases "cfrac_length (cfrac_of_real x)")
+  case (enat l)
+  hence "conv (cfrac_of_real x) l = x"
+  proof (induction l arbitrary: x)
+    case 0
+    hence "x \<in> \<int>"
+      using cfrac_length_of_real_reduce zero_enat_def by fastforce
+    thus ?case by (auto elim: Ints_cases)
+  next
+    case (Suc l x)
+    hence [simp]: "x \<notin> \<int>" 
+      by (auto simp: enat_0_iff)
+    have "eSuc (cfrac_length (cfrac_of_real (1 / frac x))) = enat (Suc l)"
+      using Suc.prems by (auto simp: cfrac_length_of_real_reduce)
+    hence "conv (cfrac_of_real (1 / frac x)) l = 1 / frac x"
+      by (intro Suc.IH) (auto simp flip: eSuc_enat)
+    thus ?case
+      by (simp add: conv_Suc cfrac_tl_of_real frac_def)
+  qed
+  thus ?thesis by (simp add: enat cfrac_lim_def)
+next
+  case [simp]: infinity
+  have lim: "conv (cfrac_of_real x) \<longlonglongrightarrow> cfrac_lim (cfrac_of_real x)"
+    by (simp add: LIMSEQ_cfrac_lim)
+  have "cfrac_lim (cfrac_of_real x) \<le> x"
+  proof (rule tendsto_upperbound)
+    show "(\<lambda>n. conv (cfrac_of_real x) (n * 2)) \<longlonglongrightarrow> cfrac_lim (cfrac_of_real x)"
+      by (intro filterlim_compose[OF lim] mult_nat_right_at_top) auto
+    show "eventually (\<lambda>n. conv (cfrac_of_real x) (n * 2) \<le> x) at_top"
+      using conv_cfrac_of_real_le_ge[of "n * 2" x for n] by (intro always_eventually) auto
+  qed auto
+  moreover have "cfrac_lim (cfrac_of_real x) \<ge> x"
+  proof (rule tendsto_lowerbound)
+    show "(\<lambda>n. conv (cfrac_of_real x) (Suc (n * 2))) \<longlonglongrightarrow> cfrac_lim (cfrac_of_real x)"
+      by (intro filterlim_compose[OF lim] filterlim_compose[OF filterlim_Suc]
+                mult_nat_right_at_top) auto
+    show "eventually (\<lambda>n. conv (cfrac_of_real x) (Suc (n * 2)) \<ge> x) at_top"
+      using conv_cfrac_of_real_le_ge[of "Suc (n * 2)" x for n] by (intro always_eventually) auto
+  qed auto
+  ultimately show ?thesis by (rule antisym)
+qed
+
+lemma Ints_add_left_cancel: "x \<in> \<int> \<Longrightarrow> x + y \<in> \<int> \<longleftrightarrow> y \<in> \<int>"
+  using Ints_diff[of "x + y" x] by auto
+
+lemma Ints_add_right_cancel: "y \<in> \<int> \<Longrightarrow> x + y \<in> \<int> \<longleftrightarrow> x \<in> \<int>"
+  using Ints_diff[of "x + y" y] by auto
+
+lemma cfrac_of_real_conv':
+  fixes m n :: nat
+  assumes "x > 1" "m < n"
+  shows   "cfrac_nth (cfrac_of_real (conv' c n x)) m = cfrac_nth c m"
+  using assms
+proof (induction n arbitrary: c m)
+  case (Suc n c m)
+  from Suc.prems have gt_1: "1 < conv' (cfrac_tl c) n x"
+    by (intro conv'_gt_1) (auto simp: enat_le_iff intro: cfrac_nth_pos)
+  show ?case
+  proof (cases m)
+    case 0
+    thus ?thesis using gt_1 Suc.prems
+      by (simp add: conv'_Suc_left nat_add_distrib floor_eq_iff)
+  next
+    case (Suc m')
+    from gt_1 have "1 / conv' (cfrac_tl c) n x \<in> {0<..<1}"
+      by auto
+    have "1 / conv' (cfrac_tl c) n x \<notin> \<int>"
+    proof
+      assume "1 / conv' (cfrac_tl c) n x \<in> \<int>"
+      then obtain k :: int where k: "1 / conv' (cfrac_tl c) n x = of_int k"
+        by (elim Ints_cases)
+      have "real_of_int k \<in> {0<..<1}"
+        using gt_1 by (subst k [symmetric]) auto
+      thus False by auto
+    qed
+    hence not_int: "real_of_int (cfrac_nth c 0) + 1 / conv' (cfrac_tl c) n x \<notin> \<int>"
+      by (subst Ints_add_left_cancel) (auto simp: field_simps elim!: Ints_cases)
+    have "cfrac_nth (cfrac_of_real (conv' c (Suc n) x)) m =
+          cfrac_nth (cfrac_of_real (of_int (cfrac_nth c 0) + 1 / conv' (cfrac_tl c) n x)) (Suc m')"
+      using \<open>x > 1\<close> by (subst conv'_Suc_left) (auto simp: Suc)
+    also have "\<dots> = cfrac_nth (cfrac_of_real (1 / frac (1 / conv' (cfrac_tl c) n x))) m'" 
+      using \<open>x > 1\<close> Suc not_int by (subst cfrac_nth_of_real_Suc) (auto simp: frac_add_of_int)
+    also have "1 / conv' (cfrac_tl c) n x \<in> {0<..<1}" using gt_1
+      by (auto simp: field_simps)
+    hence "frac (1 / conv' (cfrac_tl c) n x) = 1 / conv' (cfrac_tl c) n x"
+      by (subst frac_eq) auto
+    hence "1 / frac (1 / conv' (cfrac_tl c) n x) = conv' (cfrac_tl c) n x"
+      by simp
+    also have "cfrac_nth (cfrac_of_real \<dots>) m' = cfrac_nth c m"
+      using Suc.prems by (subst Suc.IH) (auto simp: Suc enat_le_iff)
+    finally show ?thesis .
+  qed
+qed simp_all
+
+lemma cfrac_lim_irrational:
+  assumes [simp]: "cfrac_length c = \<infinity>"
+  shows   "cfrac_lim c \<notin> \<rat>"
+proof
+  assume "cfrac_lim c \<in> \<rat>"
+  then obtain a :: int and b :: nat where ab: "b > 0" "cfrac_lim c = a / b"
+    by (auto simp: Rats_eq_int_div_nat)
+  define h and k where "h = conv_num c" and "k = conv_denom c"
+
+  have "filterlim (\<lambda>m. conv_denom c (Suc m)) at_top at_top"
+    using conv_denom_at_top filterlim_Suc by (rule filterlim_compose)
+  then obtain m where m: "conv_denom c (Suc m) \<ge> b + 1"
+    by (auto simp: filterlim_at_top eventually_at_top_linorder)
+
+  have *: "(a * k m - b * h m) / (k m * b) = a / b - h m / k m"
+    using \<open>b > 0\<close> by (simp add: field_simps k_def)
+  have "\<bar>cfrac_lim c - conv c m\<bar> = \<bar>(a * k m - b * h m) / (k m * b)\<bar>"
+    by (subst *) (auto simp: ab h_def k_def conv_num_denom)
+  also have "\<dots> = \<bar>a * k m - b * h m\<bar> / (k m * b)"
+    by (simp add: k_def)
+  finally have eq: "\<bar>cfrac_lim c - conv c m\<bar> = of_int \<bar>a * k m - b * h m\<bar> / of_int (k m * b)" .
+
+  have "\<bar>cfrac_lim c - conv c m\<bar> * (k m * b) \<noteq> 0"
+    using conv_neq_cfrac_lim[of m c] \<open>b > 0\<close> by (auto simp: k_def)
+  also have "\<bar>cfrac_lim c - conv c m\<bar> * (k m * b) = of_int \<bar>a * k m - b * h m\<bar>"
+    using \<open>b > 0\<close> by (subst eq) (auto simp: k_def)
+  finally have "\<bar>a * k m - b * h m\<bar> \<ge> 1" by linarith
+  hence "real_of_int \<bar>a * k m - b * h m\<bar> \<ge> 1" by linarith
+  hence "1 / of_int (k m * b) \<le> of_int \<bar>a * k m - b * h m\<bar> / real_of_int (k m * b)"
+    using \<open>b > 0\<close> by (intro divide_right_mono) (auto simp: k_def)
+  also have "\<dots> = \<bar>cfrac_lim c - conv c m\<bar>"
+    by (rule eq [symmetric])
+  also have "\<dots> \<le> 1 / real_of_int (conv_denom c m * conv_denom c (Suc m))"
+    by (intro cfrac_lim_minus_conv_upper_bound) auto
+  also have "\<dots> = 1 / (real_of_int (k m) * real_of_int (k (Suc m)))"
+    by (simp add: k_def)
+  also have "\<dots> < 1 / (real_of_int (k m) * real b)"
+    using m \<open>b > 0\<close>
+    by (intro divide_strict_left_mono mult_strict_left_mono) (auto simp: k_def)
+  finally show False by simp
+qed
+
+lemma cfrac_infinite_iff: "cfrac_length c = \<infinity> \<longleftrightarrow> cfrac_lim c \<notin> \<rat>"
+  using cfrac_lim_irrational[of c] cfrac_lim_rational[of c] by auto
+
+lemma cfrac_lim_rational_iff: "cfrac_lim c \<in> \<rat> \<longleftrightarrow> cfrac_length c \<noteq> \<infinity>"
+  using cfrac_lim_irrational[of c] cfrac_lim_rational[of c] by auto
+
+lemma cfrac_of_real_infinite_iff [simp]: "cfrac_length (cfrac_of_real x) = \<infinity> \<longleftrightarrow> x \<notin> \<rat>"
+  by (simp add: cfrac_infinite_iff)
+
+lemma cfrac_remainder_rational_iff [simp]:
+  "cfrac_remainder c n \<in> \<rat> \<longleftrightarrow> cfrac_length c < \<infinity>"
+proof -
+  have "cfrac_remainder c n \<in> \<rat> \<longleftrightarrow> cfrac_lim (cfrac_drop n c) \<in> \<rat>"
+    by (simp add: cfrac_remainder_def)
+  also have "\<dots> \<longleftrightarrow> cfrac_length c \<noteq> \<infinity>"
+    by (cases "cfrac_length c") (auto simp add: cfrac_lim_rational_iff)
+  finally show ?thesis by simp
+qed
+
+lift_definition cfrac_cons :: "int \<Rightarrow> cfrac \<Rightarrow> cfrac" is
+  "\<lambda>a bs. case bs of (b, bs) \<Rightarrow> if b \<le> 0 then (1, LNil) else (a, LCons (nat (b - 1)) bs)" .
+
+lemma cfrac_nth_cons:
+  assumes "cfrac_nth x 0 \<ge> 1"
+  shows   "cfrac_nth (cfrac_cons a x) n = (if n = 0 then a else cfrac_nth x (n - 1))"
+  using assms
+proof (transfer, goal_cases)
+  case (1 x a n)
+  obtain b bs where [simp]: "x = (b, bs)"
+    by (cases x)
+  show ?case using 1
+    by (cases "llength bs") (auto simp: lnth_LCons eSuc_enat le_imp_diff_is_add split: nat.splits)
+qed
+
+lemma cfrac_length_cons [simp]:
+  assumes "cfrac_nth x 0 \<ge> 1"
+  shows   "cfrac_length (cfrac_cons a x) = eSuc (cfrac_length x)"
+  using assms by transfer auto
+
+lemma cfrac_tl_cons [simp]:
+  assumes "cfrac_nth x 0 \<ge> 1"
+  shows   "cfrac_tl (cfrac_cons a x) = x"
+  using assms by transfer auto
+
+lemma cfrac_cons_tl:
+  assumes "\<not>cfrac_is_int x"
+  shows   "cfrac_cons (cfrac_nth x 0) (cfrac_tl x) = x"
+  using assms unfolding cfrac_is_int_def
+  by transfer (auto split: llist.splits)
+
+
+subsection \<open>Non-canonical continued fractions\<close>
+
+text \<open>
+  As we will show later, every irrational number has a unique continued fraction
+  expansion. Every rational number \<open>x\<close>, however, has two different expansions:
+  The canonical one ends with some number \<open>n\<close> (which is not equal to 1 unless \<open>x = 1\<close>)
+  and a non-canonical one which ends with $n-1, 1$.
+
+  We now define this non-canonical expansion analogously to the canonical one before
+  and show its characteristic properties:
+
+    \<^item> The length of the non-canonical expansion is one greater than that of the
+      canonical one.
+
+    \<^item> If the expansion is infinite, the non-canonical and the canonical one coincide.
+
+    \<^item> The coefficients of the expansions are all equal except for the last two.
+      The last coefficient of the non-canonical expansion is always 1, and the
+      second to last one is the last of the canonical one minus 1.
+\<close>
+
+lift_definition cfrac_canonical :: "cfrac \<Rightarrow> bool" is
+  "\<lambda>(x, xs). \<not>lfinite xs \<or> lnull xs \<or> llast xs \<noteq> 0" .
+
+lemma cfrac_canonical [code]:
+  "cfrac_canonical (CFrac x xs) \<longleftrightarrow> lnull xs \<or> llast xs \<noteq> 0 \<or> \<not>lfinite xs"
+  by (auto simp add: cfrac_canonical_def)
+
+lemma cfrac_canonical_iff:
+  "cfrac_canonical c \<longleftrightarrow>
+     cfrac_length c \<in> {0, \<infinity>} \<or> cfrac_nth c (the_enat (cfrac_length c)) \<noteq> 1"
+proof (transfer, clarify, goal_cases)
+  case (1 x xs)
+  show ?case
+    by (cases "llength xs")
+       (auto simp: llast_def enat_0 lfinite_conv_llength_enat split: nat.splits)
+qed
+
+lemma llast_cfrac_of_real_aux_nonzero:
+  assumes "lfinite (cfrac_of_real_aux x)" "\<not>lnull (cfrac_of_real_aux x)" 
+  shows   "llast (cfrac_of_real_aux x) \<noteq> 0"
+  using assms
+proof (induction "cfrac_of_real_aux x" arbitrary: x rule: lfinite_induct)
+  case (LCons x)
+  from LCons.prems have "x \<in> {0<..<1}"
+    by (subst (asm) cfrac_of_real_aux.code) (auto split: if_splits)
+  show ?case
+  proof (cases "1 / x \<in> \<int>")
+    case False
+    thus ?thesis using LCons
+      by (auto simp: llast_LCons frac_lt_1 cfrac_of_real_aux.code[of x])
+  next
+    case True
+    then obtain n where n: "1 / x = of_int n"
+      by (elim Ints_cases)
+    have "1 / x > 1" using \<open>x \<in> _\<close> by auto
+    with n have "n > 1" by simp
+    from n have "x = 1 / of_int n"
+      using \<open>n > 1\<close> \<open>x \<in> _\<close> by (simp add: field_simps)
+    with \<open>n > 1\<close> show ?thesis
+      using LCons cfrac_of_real_aux.code[of x] by (auto simp: llast_LCons frac_lt_1)
+  qed
+qed auto
+
+lemma cfrac_canonical_of_real [intro]: "cfrac_canonical (cfrac_of_real x)"
+  by (transfer fixing: x) (use llast_cfrac_of_real_aux_nonzero[of "frac x"] in force)
+
+primcorec cfrac_of_real_alt_aux :: "real \<Rightarrow> nat llist" where
+  "cfrac_of_real_alt_aux x =
+     (if x \<in> {0<..<1} then
+        if 1 / x \<in> \<int> then
+          LCons (nat \<lfloor>1/x\<rfloor> - 2) (LCons 0 LNil)
+        else LCons (nat \<lfloor>1/x\<rfloor> - 1) (cfrac_of_real_alt_aux (frac (1/x)))
+      else LNil)"
+
+lemma cfrac_of_real_aux_alt_LNil [simp]: "x \<notin> {0<..<1} \<Longrightarrow> cfrac_of_real_alt_aux x = LNil"
+  by (subst cfrac_of_real_alt_aux.code) auto
+
+lemma cfrac_of_real_aux_alt_0 [simp]: "cfrac_of_real_alt_aux 0 = LNil"
+  by (subst cfrac_of_real_alt_aux.code) auto
+
+lemma cfrac_of_real_aux_alt_eq_LNil_iff [simp]: "cfrac_of_real_alt_aux x = LNil \<longleftrightarrow> x \<notin> {0<..<1}"
+  by (subst cfrac_of_real_alt_aux.code) auto
+
+lift_definition cfrac_of_real_alt :: "real \<Rightarrow> cfrac" is
+  "\<lambda>x. if x \<in> \<int> then (\<lfloor>x\<rfloor> - 1, LCons 0 LNil) else (\<lfloor>x\<rfloor>, cfrac_of_real_alt_aux (frac x))" .
+
+lemma cfrac_tl_of_real_alt:
+  assumes "x \<notin> \<int>"
+  shows   "cfrac_tl (cfrac_of_real_alt x) = cfrac_of_real_alt (1 / frac x)"
+  using assms
+proof (transfer, goal_cases)
+  case (1 x)
+  show ?case
+  proof (cases "1 / frac x \<in> \<int>")
+    case False
+    from 1 have "int (nat \<lfloor>1 / frac x\<rfloor> - Suc 0) + 1 = \<lfloor>1 / frac x\<rfloor>"
+      by (subst of_nat_diff) (auto simp: le_nat_iff frac_le_1)
+    with False show ?thesis
+      using \<open>x \<notin> \<int>\<close>
+      by (subst cfrac_of_real_alt_aux.code) (auto split: llist.splits simp: frac_lt_1)
+  next
+    case True
+    then obtain n where "1 / frac x = of_int n"
+      by (auto simp: Ints_def)
+    moreover have "1 / frac x > 1"
+      using 1 by (auto simp: divide_simps frac_lt_1)
+    ultimately have "1 / frac x \<ge> 2"
+      by simp
+    hence "int (nat \<lfloor>1 / frac x\<rfloor> - 2) + 2 = \<lfloor>1 / frac x\<rfloor>"
+      by (subst of_nat_diff) (auto simp: le_nat_iff frac_le_1)
+    thus ?thesis
+      using \<open>x \<notin> \<int>\<close>
+      by (subst cfrac_of_real_alt_aux.code) (auto split: llist.splits simp: frac_lt_1)
+  qed
+qed
+
+lemma cfrac_nth_of_real_alt_Suc:
+  assumes "x \<notin> \<int>"
+  shows   "cfrac_nth (cfrac_of_real_alt x) (Suc n) = cfrac_nth (cfrac_of_real_alt (1 / frac x)) n"
+proof -
+  have "cfrac_nth (cfrac_of_real_alt x) (Suc n) =
+          cfrac_nth (cfrac_tl (cfrac_of_real_alt x)) n"
+    by simp
+  also have "cfrac_tl (cfrac_of_real_alt x) = cfrac_of_real_alt (1 / frac x)"
+    by (simp add: cfrac_tl_of_real_alt assms)
+  finally show ?thesis .
+qed
+
+lemma cfrac_nth_gt0_of_real_int [simp]:
+  "m > 0 \<Longrightarrow> cfrac_nth (cfrac_of_real (of_int n)) m = 1"
+  by transfer (auto simp: lnth_LCons eSuc_def enat_0_iff split: nat.splits)
+
+lemma cfrac_nth_0_of_real_alt_int [simp]:
+  "cfrac_nth (cfrac_of_real_alt (of_int n)) 0 = n - 1"
+  by transfer auto
+
+lemma cfrac_nth_gt0_of_real_alt_int [simp]:
+  "m > 0 \<Longrightarrow> cfrac_nth (cfrac_of_real_alt (of_int n)) m = 1"
+  by transfer (auto simp: lnth_LCons eSuc_def split: nat.splits)
+
+lemma llength_cfrac_of_real_alt_aux:
+  assumes "x \<in> {0<..<1}"
+  shows   "llength (cfrac_of_real_alt_aux x) = eSuc (llength (cfrac_of_real_aux x))"
+  using assms
+proof (coinduction arbitrary: x rule: enat_coinduct)
+  case (Eq_enat x)
+  show ?case
+  proof (cases "1 / x \<in> \<int>")
+    case False
+    with Eq_enat have "frac (1 / x) \<in> {0<..<1}"
+      by (auto intro: frac_lt_1)
+    hence "\<exists>x'. llength (cfrac_of_real_alt_aux (frac (1 / x))) =
+              llength (cfrac_of_real_alt_aux x') \<and> 
+              llength (cfrac_of_real_aux (frac (1 / x))) = llength (cfrac_of_real_aux x') \<and> 
+              0 < x' \<and> x' < 1"
+      by (intro exI[of _ "frac (1 / x)"]) auto
+    thus ?thesis using False Eq_enat
+      by (auto simp: cfrac_of_real_alt_aux.code[of x] cfrac_of_real_aux.code[of x])
+  qed (use Eq_enat in \<open>auto simp: cfrac_of_real_alt_aux.code[of x] cfrac_of_real_aux.code[of x]\<close>)
+qed
+
+lemma cfrac_length_of_real_alt:
+  "cfrac_length (cfrac_of_real_alt x) = eSuc (cfrac_length (cfrac_of_real x))"
+  by transfer (auto simp: llength_cfrac_of_real_alt_aux frac_lt_1)
+
+lemma cfrac_of_real_alt_aux_eq_regular:
+  assumes "x \<in> {0<..<1}" "llength (cfrac_of_real_aux x) = \<infinity>"
+  shows   "cfrac_of_real_alt_aux x = cfrac_of_real_aux x"
+  using assms
+proof (coinduction arbitrary: x)
+  case (Eq_llist x)
+  hence "\<exists>x'. cfrac_of_real_aux (frac (1 / x)) =
+        cfrac_of_real_aux x' \<and>
+        cfrac_of_real_alt_aux (frac (1 / x)) =
+        cfrac_of_real_alt_aux x' \<and> 0 < x' \<and> x' < 1 \<and> llength (cfrac_of_real_aux x') = \<infinity>"
+    by (intro exI[of _ "frac (1 / x)"])
+       (auto simp: cfrac_of_real_aux.code[of x] cfrac_of_real_alt_aux.code[of x]
+                   eSuc_eq_infinity_iff frac_lt_1)
+  with Eq_llist show ?case
+    by (auto simp: eSuc_eq_infinity_iff)
+qed
+
+lemma cfrac_of_real_alt_irrational [simp]:
+  assumes "x \<notin> \<rat>"
+  shows   "cfrac_of_real_alt x = cfrac_of_real x"
+proof -
+  from assms have "cfrac_length (cfrac_of_real x) = \<infinity>"
+    using cfrac_length_of_real_irrational by blast
+  with assms show ?thesis
+    by transfer
+       (use Ints_subset_Rats in 
+        \<open>auto intro!: cfrac_of_real_alt_aux_eq_regular simp: frac_lt_1 llength_cfrac_of_real_alt_aux\<close>)
+qed
+
+lemma cfrac_nth_of_real_alt_0:
+  "cfrac_nth (cfrac_of_real_alt x) 0 = (if x \<in> \<int> then \<lfloor>x\<rfloor> - 1 else \<lfloor>x\<rfloor>)"
+  by transfer auto
+
+lemma cfrac_nth_of_real_alt:
+  fixes n :: nat and x :: real
+  defines "c \<equiv> cfrac_of_real x"
+  defines "c' \<equiv> cfrac_of_real_alt x"
+  defines "l \<equiv> cfrac_length c"
+  shows   "cfrac_nth c' n =
+           (if enat n = l then
+              cfrac_nth c n - 1
+            else if enat n = l + 1 then
+              1
+            else
+              cfrac_nth c n)"
+  unfolding c_def c'_def l_def
+proof (induction n arbitrary: x rule: less_induct)
+  case (less n)
+  consider "x \<notin> \<rat>" | "x \<in> \<int>" | "n = 0" "x \<in> \<rat> - \<int>" | n' where "n = Suc n'" "x \<in> \<rat> - \<int>"
+    by (cases n) auto
+  thus ?case
+  proof cases
+    assume "x \<notin> \<rat>"
+    thus ?thesis
+      by (auto simp: cfrac_length_of_real_irrational)
+  next
+    assume "x \<in> \<int>"
+    thus ?thesis
+      by (auto simp: Ints_def one_enat_def zero_enat_def)
+  next
+    assume *: "n = 0" "x \<in> \<rat> - \<int>"
+    have "enat 0 \<noteq> cfrac_length (cfrac_of_real x) + 1"
+      using zero_enat_def by auto
+    moreover have "enat 0 \<noteq> cfrac_length (cfrac_of_real x)"
+      using * cfrac_length_of_real_reduce zero_enat_def by auto
+    ultimately show ?thesis using *
+      by (auto simp: cfrac_nth_of_real_alt_0)
+  next
+    fix n' assume *: "n = Suc n'" "x \<in> \<rat> - \<int>"
+    from less.IH [of n' "1 / frac x"] and * show ?thesis
+      by (auto simp: cfrac_nth_of_real_Suc cfrac_nth_of_real_alt_Suc cfrac_length_of_real_reduce 
+                     eSuc_def one_enat_def enat_0_iff split: enat.splits)
+  qed
+qed
+
+lemma cfrac_of_real_length_eq_0_iff: "cfrac_length (cfrac_of_real x) = 0 \<longleftrightarrow> x \<in> \<int>"
+  by transfer (auto simp: frac_lt_1)
+
+lemma conv'_cong:
+  assumes "(\<And>k. k < n \<Longrightarrow> cfrac_nth c k = cfrac_nth c' k)" "n = n'" "x = y"
+  shows   "conv' c n x = conv' c' n' y"
+  using assms(1) unfolding assms(2,3) [symmetric]
+  by (induction n arbitrary: x) (auto simp: conv'_Suc_right)
+
+lemma conv_cong:
+  assumes "(\<And>k. k \<le> n \<Longrightarrow> cfrac_nth c k = cfrac_nth c' k)" "n = n'"
+  shows   "conv c n = conv c' n'"
+  using assms(1) unfolding assms(2) [symmetric]
+  by (induction n arbitrary: c c') (auto simp: conv_Suc)
+
+lemma conv'_cfrac_of_real_alt:
+  assumes "enat n \<le> cfrac_length (cfrac_of_real x)"
+  shows   "conv' (cfrac_of_real_alt x) n y = conv' (cfrac_of_real x) n y"
+proof (cases "cfrac_length (cfrac_of_real x)")
+  case infinity
+  thus ?thesis by auto
+next
+  case [simp]: (enat l')
+  with assms show ?thesis
+    by (intro conv'_cong refl; subst cfrac_nth_of_real_alt) (auto simp: one_enat_def)
+qed
+
+lemma cfrac_lim_of_real_alt [simp]: "cfrac_lim (cfrac_of_real_alt x) = x"
+proof (cases "cfrac_length (cfrac_of_real x)")
+  case infinity
+  thus ?thesis by auto
+next
+  case (enat l)
+  thus ?thesis
+  proof (induction l arbitrary: x)
+    case 0
+    hence "x \<in> \<int>"
+      using cfrac_of_real_length_eq_0_iff zero_enat_def by auto
+    thus ?case
+      by (auto simp: Ints_def cfrac_lim_def cfrac_length_of_real_alt eSuc_def conv_Suc)
+  next
+    case (Suc l x)
+    hence *: "\<not>cfrac_is_int (cfrac_of_real_alt x)" "x \<notin> \<int>"
+      by (auto simp: cfrac_is_int_def cfrac_length_of_real_alt Ints_def zero_enat_def eSuc_def)
+    hence "cfrac_lim (cfrac_of_real_alt x) =
+             of_int \<lfloor>x\<rfloor> + 1 / cfrac_lim (cfrac_tl (cfrac_of_real_alt x))"
+      by (subst cfrac_lim_reduce) (auto simp: cfrac_nth_of_real_alt_0)
+    also have "cfrac_length (cfrac_of_real (1 / frac x)) = l"
+      using Suc.prems * by (metis cfrac_length_of_real_reduce eSuc_enat eSuc_inject)
+    hence "1 / cfrac_lim (cfrac_tl (cfrac_of_real_alt x)) = frac x"
+      by (subst cfrac_tl_of_real_alt[OF *(2)], subst Suc) (use Suc.prems * in auto)
+    also have "real_of_int \<lfloor>x\<rfloor> + frac x = x"
+      by (simp add: frac_def)
+    finally show ?case .
+  qed
+qed
+
+lemma cfrac_eqI:
+  assumes "cfrac_length c = cfrac_length c'" and "\<And>n. cfrac_nth c n = cfrac_nth c' n"
+  shows   "c = c'"
+proof (use assms in transfer, safe, goal_cases)
+  case (1 a xs b ys)
+  from 1(2)[of 0] show ?case
+    by auto
+next
+  case (2 a xs b ys)
+  define f where "f = (\<lambda>xs n. if enat (Suc n) \<le> llength xs then int (lnth xs n) + 1 else 1)"
+  have "\<forall>n. f xs n = f ys n"
+    using 2(2)[of "Suc n" for n] by (auto simp: f_def cong: if_cong)
+  with 2(1) show "xs = ys"
+  proof (coinduction arbitrary: xs ys)
+    case (Eq_llist xs ys)
+    show ?case
+    proof (cases "lnull xs \<or> lnull ys")
+      case False
+      from False have *: "enat (Suc 0) \<le> llength ys"
+        using Suc_ile_eq zero_enat_def by auto
+      have "llength (ltl xs) = llength (ltl ys)"
+        using Eq_llist by (cases xs; cases ys) auto
+      moreover have "lhd xs = lhd ys"
+        using False * Eq_llist(1) spec[OF Eq_llist(2), of 0] 
+        by (auto simp: f_def lnth_0_conv_lhd)
+      moreover have "f (ltl xs) n = f (ltl ys) n" for n
+        using Eq_llist(1) * spec[OF Eq_llist(2), of "Suc n"]
+        by (cases xs; cases ys) (auto simp: f_def Suc_ile_eq split: if_splits)
+      ultimately show ?thesis
+        using False by auto
+    next
+      case True
+      thus ?thesis
+        using Eq_llist(1) by auto
+    qed
+  qed
+qed
+
+lemma cfrac_eq_0I:
+  assumes "cfrac_lim c = 0" "cfrac_nth c 0 \<ge> 0"
+  shows   "c = 0"
+proof -
+  have *: "cfrac_is_int c"
+  proof (rule ccontr)
+    assume *: "\<not>cfrac_is_int c"
+    from * have "conv c 0 < cfrac_lim c"
+      by (intro conv_less_cfrac_lim) (auto simp: cfrac_is_int_def simp flip: zero_enat_def)
+    hence "cfrac_nth c 0 < 0"
+      using assms by simp
+    thus False
+      using assms by simp
+  qed
+  from * assms have "cfrac_nth c 0 = 0"
+    by (auto simp: cfrac_lim_def cfrac_is_int_def)
+  from * and this show  "c = 0"
+    unfolding zero_cfrac_def cfrac_is_int_def by transfer auto
+qed
+
+lemma cfrac_eq_1I:
+  assumes "cfrac_lim c = 1" "cfrac_nth c 0 \<noteq> 0"
+  shows   "c = 1"
+proof -
+  have *: "cfrac_is_int c"
+  proof (rule ccontr)
+    assume *: "\<not>cfrac_is_int c"
+    from * have "conv c 0 < cfrac_lim c"
+      by (intro conv_less_cfrac_lim) (auto simp: cfrac_is_int_def simp flip: zero_enat_def)
+    hence "cfrac_nth c 0 < 0"
+      using assms by simp
+
+    have "cfrac_lim c = real_of_int (cfrac_nth c 0) + 1 / cfrac_lim (cfrac_tl c)"
+      using * by (subst cfrac_lim_reduce) auto
+    also have "real_of_int (cfrac_nth c 0) < 0"
+      using \<open>cfrac_nth c 0 < 0\<close> by simp
+    also have "1 / cfrac_lim (cfrac_tl c) \<le> 1"
+    proof -
+      have "1 \<le> cfrac_nth (cfrac_tl c) 0"
+        by auto
+      also have "\<dots> \<le> cfrac_lim (cfrac_tl c)"
+        by (rule cfrac_lim_ge_first)
+      finally show ?thesis by simp
+    qed
+    finally show False
+      using assms by simp
+  qed
+
+  from * assms have "cfrac_nth c 0 = 1"
+    by (auto simp: cfrac_lim_def cfrac_is_int_def)
+  from * and this show  "c = 1"
+    unfolding one_cfrac_def cfrac_is_int_def by transfer auto
+qed
+
+lemma cfrac_coinduct [coinduct type: cfrac]:
+  assumes "R c1 c2"
+  assumes IH: "\<And>c1 c2. R c1 c2 \<Longrightarrow>
+                cfrac_is_int c1 = cfrac_is_int c2 \<and>
+                cfrac_nth c1 0 = cfrac_nth c2 0 \<and>
+                (\<not>cfrac_is_int c1 \<longrightarrow> \<not>cfrac_is_int c2 \<longrightarrow> R (cfrac_tl c1) (cfrac_tl c2))"
+  shows   "c1 = c2"
+proof (rule cfrac_eqI)
+  show "cfrac_nth c1 n = cfrac_nth c2 n" for n
+    using assms(1)
+  proof (induction n arbitrary: c1 c2)
+    case 0
+    from IH[OF this] show ?case
+      by auto
+  next
+    case (Suc n)
+    thus ?case
+      using IH by (metis cfrac_is_int_iff cfrac_nth_0_of_int cfrac_nth_tl)
+  qed
+next
+  show "cfrac_length c1 = cfrac_length c2"
+    using assms(1)
+  proof (coinduction arbitrary: c1 c2 rule: enat_coinduct)
+    case (Eq_enat c1 c2)
+    show ?case
+    proof (cases "cfrac_is_int c1")
+      case True
+      thus ?thesis
+        using IH[OF Eq_enat(1)] by (auto simp: cfrac_is_int_def)
+    next
+      case False
+      with IH[OF Eq_enat(1)] have **: "\<not>cfrac_is_int c1" "R (cfrac_tl c1) (cfrac_tl c2)"
+        by auto
+      have *: "(cfrac_length c1 = 0) = (cfrac_length c2 = 0)"
+        using IH[OF Eq_enat(1)] by (auto simp: cfrac_is_int_def)
+      show ?thesis
+        by (intro conjI impI disjI1 *, rule exI[of _ "cfrac_tl c1"], rule exI[of _ "cfrac_tl c2"])
+           (use ** in \<open>auto simp: epred_conv_minus\<close>)
+    qed
+  qed
+qed
+
+lemma cfrac_nth_0_cases:
+  "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>  \<or>  cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor> - 1 \<and> cfrac_tl c = 1"
+proof (cases "cfrac_is_int c")
+  case True
+  hence "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+    by (auto simp: cfrac_lim_def cfrac_is_int_def)
+  thus ?thesis by blast
+next
+  case False
+  note not_int = this
+  have bounds: "1 / cfrac_lim (cfrac_tl c) \<ge> 0 \<and> 1 / cfrac_lim (cfrac_tl c) \<le> 1"
+  proof -
+    have "1 \<le> cfrac_nth (cfrac_tl c) 0"
+      by simp
+    also have "\<dots> \<le> cfrac_lim (cfrac_tl c)"
+      by (rule cfrac_lim_ge_first)
+    finally show ?thesis
+      using False by (auto simp: cfrac_lim_nonneg)
+  qed
+
+  thus ?thesis
+  proof (cases "cfrac_lim (cfrac_tl c) = 1")
+    case False
+    have "\<lfloor>cfrac_lim c\<rfloor> = cfrac_nth c 0 + \<lfloor>1 / cfrac_lim (cfrac_tl c)\<rfloor>"
+      using not_int by (subst cfrac_lim_reduce) auto
+    also have "1 / cfrac_lim (cfrac_tl c) \<ge> 0 \<and> 1 / cfrac_lim (cfrac_tl c) < 1"
+      using bounds False by (auto simp: divide_simps)
+    hence "\<lfloor>1 / cfrac_lim (cfrac_tl c)\<rfloor> = 0"
+      by linarith
+    finally show ?thesis by simp
+  next
+    case True
+    have "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor> - 1"
+      using not_int True by (subst cfrac_lim_reduce) auto
+    moreover have "cfrac_tl c = 1"
+      using True by (intro cfrac_eq_1I) auto
+    ultimately show ?thesis by blast
+  qed
+qed
+
+lemma cfrac_length_1 [simp]: "cfrac_length 1 = 0"
+  unfolding one_cfrac_def by simp
+
+lemma cfrac_nth_1 [simp]: "cfrac_nth 1 m = 1"
+  unfolding one_cfrac_def by transfer (auto simp: enat_0_iff)
+
+lemma cfrac_lim_1 [simp]: "cfrac_lim 1 = 1"
+  by (auto simp: cfrac_lim_def)
+
+
+lemma cfrac_nth_0_not_int:
+  assumes "cfrac_lim c \<notin> \<int>"
+  shows   "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+proof -
+  have "cfrac_tl c \<noteq> 1"
+  proof
+    assume eq: "cfrac_tl c = 1"
+    have "\<not>cfrac_is_int c"
+      using assms by (auto simp: cfrac_lim_def cfrac_is_int_def)
+    hence "cfrac_lim c = of_int \<lfloor>cfrac_nth c 0\<rfloor> + 1"
+      using eq by (subst cfrac_lim_reduce) auto
+    hence "cfrac_lim c \<in> \<int>"
+      by auto
+    with assms show False by auto
+  qed
+  with cfrac_nth_0_cases[of c] show ?thesis by auto
+qed
+
+lemma cfrac_of_real_cfrac_lim_irrational:
+  assumes "cfrac_lim c \<notin> \<rat>"
+  shows   "cfrac_of_real (cfrac_lim c) = c"
+proof (rule cfrac_eqI)
+  from assms show "cfrac_length (cfrac_of_real (cfrac_lim c)) = cfrac_length c"
+    using cfrac_lim_rational_iff by auto
+next
+  fix n
+  show "cfrac_nth (cfrac_of_real (cfrac_lim c)) n = cfrac_nth c n"
+    using assms
+  proof (induction n arbitrary: c)
+    case (0 c)
+    thus ?case
+      using Ints_subset_Rats by (subst cfrac_nth_0_not_int) auto
+  next
+    case (Suc n c)
+    from Suc.prems have [simp]: "cfrac_lim c \<notin> \<int>"
+      using Ints_subset_Rats by blast
+    have "cfrac_nth (cfrac_of_real (cfrac_lim c)) (Suc n) =
+          cfrac_nth (cfrac_tl (cfrac_of_real (cfrac_lim c))) n"
+      by (simp flip: cfrac_nth_tl)
+    also have "cfrac_tl (cfrac_of_real (cfrac_lim c)) = cfrac_of_real (1 / frac (cfrac_lim c))"
+      using Suc.prems Ints_subset_Rats by (subst cfrac_tl_of_real) auto
+    also have "1 / frac (cfrac_lim c) = cfrac_lim (cfrac_tl c)"
+      using Suc.prems by (subst cfrac_lim_tl) (auto simp: frac_def cfrac_is_int_def cfrac_nth_0_not_int)
+    also have "cfrac_nth (cfrac_of_real (cfrac_lim (cfrac_tl c))) n = cfrac_nth c (Suc n)"
+      using Suc.prems by (subst Suc.IH) (auto simp: cfrac_lim_rational_iff)
+    finally show ?case .
+  qed
+qed
+
+lemma cfrac_eqI_first:
+  assumes "\<not>cfrac_is_int c" "\<not>cfrac_is_int c'"
+  assumes "cfrac_nth c 0 = cfrac_nth c' 0" and "cfrac_tl c = cfrac_tl c'"
+  shows   "c = c'"
+  using assms unfolding cfrac_is_int_def
+  by transfer (auto split: llist.splits)
+
+lemma cfrac_is_int_of_real_iff: "cfrac_is_int (cfrac_of_real x) \<longleftrightarrow> x \<in> \<int>"
+  unfolding cfrac_is_int_def by transfer (use frac_lt_1 in auto)
+
+lemma cfrac_not_is_int_of_real_alt: "\<not>cfrac_is_int (cfrac_of_real_alt x)"
+  unfolding cfrac_is_int_def by transfer (auto simp: frac_lt_1)
+
+lemma cfrac_tl_of_real_alt_of_int [simp]: "cfrac_tl (cfrac_of_real_alt (of_int n)) = 1"
+  unfolding one_cfrac_def by transfer auto
+
+lemma cfrac_is_intI:
+  assumes "cfrac_nth c 0 \<ge> \<lfloor>cfrac_lim c\<rfloor>" and "cfrac_lim c \<in> \<int>"
+  shows   "cfrac_is_int c"
+proof (rule ccontr)
+  assume *: "\<not>cfrac_is_int c"
+  from * have "conv c 0 < cfrac_lim c"
+    by (intro conv_less_cfrac_lim) (auto simp: cfrac_is_int_def simp flip: zero_enat_def)
+  with assms show False
+    by (auto simp: Ints_def)
+qed
+
+lemma cfrac_eq_of_intI:
+  assumes "cfrac_nth c 0 \<ge> \<lfloor>cfrac_lim c\<rfloor>" and "cfrac_lim c \<in> \<int>"
+  shows   "c = cfrac_of_int \<lfloor>cfrac_lim c\<rfloor>"
+proof -
+  from assms have int: "cfrac_is_int c"
+    by (intro cfrac_is_intI) auto
+  have [simp]: "cfrac_lim c = cfrac_nth c 0"
+    using int by (simp add: cfrac_lim_def cfrac_is_int_def)
+  from int have "c = cfrac_of_int (cfrac_nth c 0)"
+    unfolding cfrac_is_int_def by transfer auto
+  also from assms have "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+    using int by auto
+  finally show ?thesis .
+qed
+
+lemma cfrac_lim_of_int [simp]: "cfrac_lim (cfrac_of_int n) = of_int n"
+  by (simp add: cfrac_lim_def)
+
+lemma cfrac_of_real_of_int [simp]: "cfrac_of_real (of_int n) = cfrac_of_int n"
+  by transfer auto
+
+lemma cfrac_of_real_of_nat [simp]: "cfrac_of_real (of_nat n) = cfrac_of_int (int n)"
+  by transfer auto
+
+lemma cfrac_int_cases:
+  assumes "cfrac_lim c = of_int n"
+  shows   "c = cfrac_of_int n \<or> c = cfrac_of_real_alt (of_int n)"
+proof -
+  from cfrac_nth_0_cases[of c] show ?thesis
+  proof (rule disj_forward)
+    assume eq: "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+    have "c = cfrac_of_int \<lfloor>cfrac_lim c\<rfloor>"
+      using assms eq by (intro cfrac_eq_of_intI) auto
+    with assms eq show "c = cfrac_of_int n"
+      by simp
+  next
+    assume *: "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor> - 1 \<and> cfrac_tl c = 1"
+    have "\<not>cfrac_is_int c"
+      using * by (auto simp: cfrac_is_int_def cfrac_lim_def)
+    hence "cfrac_length c = eSuc (cfrac_length (cfrac_tl c))"
+      by (subst cfrac_length_tl; cases "cfrac_length c")
+         (auto simp: cfrac_is_int_def eSuc_def enat_0_iff split: enat.splits)
+    also have "cfrac_tl c = 1"
+      using * by auto
+    finally have "cfrac_length c = 1"
+      by (simp add: eSuc_def one_enat_def)
+    show "c = cfrac_of_real_alt (of_int n)"
+      by (rule cfrac_eqI_first)
+         (use \<open>\<not>cfrac_is_int c\<close> * assms in \<open>auto simp: cfrac_not_is_int_of_real_alt\<close>)
+  qed
+qed
+
+lemma cfrac_cases:
+  "c \<in> {cfrac_of_real (cfrac_lim c), cfrac_of_real_alt (cfrac_lim c)}"
+proof (cases "cfrac_length c")
+  case infinity
+  hence "cfrac_lim c \<notin> \<rat>"
+    by (simp add: cfrac_lim_irrational)
+  thus ?thesis
+    using cfrac_of_real_cfrac_lim_irrational by simp
+next
+  case (enat l)
+  thus ?thesis
+  proof (induction l arbitrary: c)
+    case (0 c)
+    hence "c = cfrac_of_real (cfrac_nth c 0)"
+      by transfer (auto simp flip: zero_enat_def)
+    with 0 show ?case by (auto simp: cfrac_lim_def)
+  next
+    case (Suc l c)
+    show ?case
+    proof (cases "cfrac_lim c \<in> \<int>")
+      case True
+      thus ?thesis
+        using cfrac_int_cases[of c] by (force simp: Ints_def)
+    next
+      case [simp]: False
+      have "\<not>cfrac_is_int c"
+        using Suc.prems by (auto simp: cfrac_is_int_def enat_0_iff)
+      show ?thesis
+        using cfrac_nth_0_cases[of c]
+      proof (elim disjE conjE)
+        assume *: "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor> - 1" "cfrac_tl c = 1"
+        hence "cfrac_lim c \<in> \<int>"
+          using \<open>\<not>cfrac_is_int c\<close> by (subst cfrac_lim_reduce) auto
+        thus ?thesis
+          by (auto simp: cfrac_int_cases)
+      next
+        assume eq: "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+        have "cfrac_tl c = cfrac_of_real (cfrac_lim (cfrac_tl c)) \<or>
+              cfrac_tl c = cfrac_of_real_alt (cfrac_lim (cfrac_tl c))"
+          using Suc.IH[of "cfrac_tl c"] Suc.prems by auto
+        hence "c = cfrac_of_real (cfrac_lim c) \<or>
+               c = cfrac_of_real_alt (cfrac_lim c)"
+        proof (rule disj_forward)
+          assume eq': "cfrac_tl c = cfrac_of_real (cfrac_lim (cfrac_tl c))"
+          show "c = cfrac_of_real (cfrac_lim c)"
+            by (rule cfrac_eqI_first)
+               (use \<open>\<not>cfrac_is_int c\<close> eq eq' in
+                \<open>auto simp: cfrac_is_int_of_real_iff cfrac_tl_of_real cfrac_lim_tl frac_def\<close>)
+        next
+          assume eq': "cfrac_tl c = cfrac_of_real_alt (cfrac_lim (cfrac_tl c))"
+          have eq'': "cfrac_nth (cfrac_of_real_alt (cfrac_lim c)) 0 = \<lfloor>cfrac_lim c\<rfloor>"
+            using Suc.prems by (subst cfrac_nth_of_real_alt_0) auto
+          show "c = cfrac_of_real_alt (cfrac_lim c)"
+            by (rule cfrac_eqI_first)
+               (use \<open>\<not>cfrac_is_int c\<close> eq eq' eq'' in
+                \<open>auto simp: cfrac_not_is_int_of_real_alt cfrac_tl_of_real_alt cfrac_lim_tl frac_def\<close>)
+        qed
+        thus ?thesis by simp
+      qed
+    qed
+  qed
+qed
+
+lemma cfrac_lim_eq_iff:
+  assumes "cfrac_length c = \<infinity> \<or> cfrac_length c' = \<infinity>"
+  shows   "cfrac_lim c = cfrac_lim c' \<longleftrightarrow> c = c'"
+proof
+  assume *: "cfrac_lim c = cfrac_lim c'"
+  hence "cfrac_of_real (cfrac_lim c) = cfrac_of_real (cfrac_lim c')"
+    by (simp only:)
+  thus "c = c'"
+    using assms *
+    by (subst (asm) (1 2) cfrac_of_real_cfrac_lim_irrational)
+       (auto simp: cfrac_infinite_iff)
+qed auto
+
+lemma floor_cfrac_remainder:
+  assumes "cfrac_length c = \<infinity>"
+  shows   "\<lfloor>cfrac_remainder c n\<rfloor> = cfrac_nth c n"
+  by (metis add.left_neutral assms cfrac_length_drop cfrac_lim_eq_iff idiff_infinity
+            cfrac_lim_of_real cfrac_nth_drop cfrac_nth_of_real_0 cfrac_remainder_def)
+      
+
+subsection \<open>Approximation properties\<close>
+
+text \<open>
+  In this section, we will show that convergents of the continued fraction expansion of a 
+  number \<open>x\<close> are good approximations of \<open>x\<close>, and in a certain sense, the reverse holds as well.
+\<close>
+
+lemma sgn_of_int:
+  "sgn (of_int x :: 'a :: {linordered_idom}) = of_int (sgn x)"
+  by (auto simp: sgn_if)
+
+lemma conv_ge_one: "cfrac_nth c 0 > 0 \<Longrightarrow> conv c n \<ge> 1"
+  by (rule order.trans[OF _ conv_ge_first]) auto
+
+context
+  fixes c h k
+  defines "h \<equiv> conv_num c" and "k \<equiv> conv_denom c"
+begin
+
+lemma abs_diff_le_abs_add:
+  fixes x y :: real
+  assumes "x \<ge> 0 \<and> y \<ge> 0 \<or> x \<le> 0 \<and> y \<le> 0"
+  shows   "\<bar>x - y\<bar> \<le> \<bar>x + y\<bar>"
+  using assms by linarith
+
+lemma abs_diff_less_abs_add:
+  fixes x y :: real
+  assumes "x > 0 \<and> y > 0 \<or> x < 0 \<and> y < 0"
+  shows   "\<bar>x - y\<bar> < \<bar>x + y\<bar>"
+  using assms by linarith
+
+lemma abs_diff_le_imp_same_sign:
+  assumes "\<bar>x - y\<bar> \<le> d" "d < \<bar>y\<bar>"
+  shows   "sgn x = sgn (y::real)"
+  using assms by (auto simp: sgn_if)
+
+lemma conv_nonpos:
+  assumes "cfrac_nth c 0 < 0"
+  shows   "conv c n \<le> 0"
+proof (cases n)
+  case 0
+  thus ?thesis using assms by auto
+next
+  case [simp]: (Suc n')
+  have "conv c n = real_of_int (cfrac_nth c 0) + 1 / conv (cfrac_tl c) n'"
+    by (simp add: conv_Suc)
+  also have "\<dots> \<le> -1 + 1 / 1"
+    using assms by (intro add_mono divide_left_mono) (auto intro!: conv_pos conv_ge_one)
+  finally show ?thesis by simp
+qed
+
+lemma cfrac_lim_nonpos:
+  assumes "cfrac_nth c 0 < 0"
+  shows   "cfrac_lim c \<le> 0"
+proof (cases "cfrac_length c")
+  case infinity
+  show ?thesis using LIMSEQ_cfrac_lim[OF infinity]
+    by (rule tendsto_upperbound) (use assms in \<open>auto simp: conv_nonpos\<close>)
+next
+  case (enat l)
+  thus ?thesis by (auto simp: cfrac_lim_def conv_nonpos assms)
+qed
+
+lemma conv_num_nonpos:
+  assumes "cfrac_nth c 0 < 0"
+  shows   "h n \<le> 0"
+proof (induction n rule: fib.induct)
+  case 2
+  have "cfrac_nth c (Suc 0) * cfrac_nth c 0 \<le> 1 * cfrac_nth c 0"
+    using assms by (intro mult_right_mono_neg) auto
+  also have "\<dots> + 1 \<le> 0" using assms by auto
+  finally show ?case by (auto simp: h_def)
+next
+  case (3 n)
+  have "cfrac_nth c (Suc (Suc n)) * h (Suc n) \<le> 0"
+    using 3 by (simp add: mult_nonneg_nonpos)
+  also have "\<dots> + h n \<le> 0"
+    using 3 by simp
+  finally show ?case
+    by (auto simp: h_def)
+qed (use assms in \<open>auto simp: h_def\<close>)
+
+lemma conv_best_approximation_aux:
+  "cfrac_lim c \<ge> 0 \<and> h n \<ge> 0 \<or> cfrac_lim c \<le> 0 \<and> h n \<le> 0"
+proof (cases "cfrac_nth c 0 \<ge> 0")
+  case True
+  from True have "0 \<le> conv c 0"
+    by simp
+  also have "\<dots> \<le> cfrac_lim c"
+    by (rule conv_le_cfrac_lim) (auto simp: enat_0)
+  finally have "cfrac_lim c \<ge> 0" .
+  moreover from True have "h n \<ge> 0"
+    unfolding h_def by (intro conv_num_nonneg)
+  ultimately show ?thesis by (simp add: sgn_if)
+next
+  case False
+  thus ?thesis
+    using cfrac_lim_nonpos conv_num_nonpos[of n] by (auto simp: h_def)
+qed
+
+lemma conv_best_approximation_ex:
+  fixes a b :: int and x :: real
+  assumes "n \<le> cfrac_length c"
+  assumes "0 < b" and "b \<le> k n" and "coprime a b" and "n > 0"
+  assumes "(a, b) \<noteq> (h n, k n)"
+  assumes "\<not>(cfrac_length c = 1 \<and> n = 0)"
+  assumes "Suc n \<noteq> cfrac_length c \<or> cfrac_canonical c"
+  defines "x \<equiv> cfrac_lim c"
+  shows   "\<bar>k n * x - h n\<bar> < \<bar>b * x - a\<bar>"
+proof (cases "\<bar>a\<bar> = \<bar>h n\<bar> \<and> b = k n")
+  case True
+  with assms have [simp]: "a = -h n"
+    by (auto simp: abs_if split: if_splits)
+  have "k n > 0"
+    by (auto simp: k_def)
+  show ?thesis
+  proof (cases "x = 0")
+    case True
+    hence "c = cfrac_of_real 0 \<or> c = cfrac_of_real_alt 0"
+      unfolding x_def by (metis cfrac_cases empty_iff insert_iff)
+    hence False
+    proof
+      assume "c = cfrac_of_real 0"
+      thus False
+        using assms by (auto simp: enat_0_iff h_def k_def)
+    next
+      assume [simp]: "c = cfrac_of_real_alt 0"
+      hence "n = 0 \<or> n = 1"
+        using assms by (auto simp: cfrac_length_of_real_alt enat_0_iff k_def h_def eSuc_def)
+      thus False
+        using assms True
+        by (elim disjE) (auto simp: cfrac_length_of_real_alt enat_0_iff k_def h_def eSuc_def
+                                    cfrac_nth_of_real_alt one_enat_def split: if_splits)
+    qed
+    thus ?thesis ..
+  next
+    case False
+    have "h n \<noteq> 0"
+      using True assms(6) h_def by auto
+    hence "x > 0 \<and> h n > 0 \<or> x < 0 \<and> h n < 0"
+      using \<open>x \<noteq> 0\<close> conv_best_approximation_aux[of n] unfolding x_def by auto
+    hence "\<bar>real_of_int (k n) * x - real_of_int (h n)\<bar> < \<bar>real_of_int (k n) * x + real_of_int (h n)\<bar>"   
+      using \<open>k n > 0\<close>
+      by (intro abs_diff_less_abs_add) (auto simp: not_le zero_less_mult_iff mult_less_0_iff)
+    thus ?thesis using True by auto
+  qed
+next
+  case False
+  note * = this
+  show ?thesis
+  proof (cases "n = cfrac_length c")
+    case True
+    hence "x = conv c n"
+      by (auto simp: cfrac_lim_def x_def split: enat.splits)
+    also have "\<dots> = h n / k n"
+      by (auto simp: h_def k_def conv_num_denom)
+    finally have x: "x = h n / k n" .
+    hence "\<bar>k n * x - h n\<bar> = 0"
+      by (simp add: k_def)
+    also have "b * x \<noteq> a"
+    proof
+      assume "b * x = a"
+      hence "of_int (h n) * of_int b = of_int (k n) * (of_int a :: real)"
+        using assms True by (auto simp: field_simps k_def x)
+      hence "of_int (h n * b) = (of_int (k n * a) :: real)"
+        by (simp only: of_int_mult)
+      hence "h n * b = k n * a"
+        by linarith
+      hence "h n = a \<and> k n = b"
+        using assms by (subst (asm) coprime_crossproduct')
+                       (auto simp: h_def k_def coprime_conv_num_denom)
+      thus False using True False by simp
+    qed
+    hence "0 < \<bar>b * x - a\<bar>"
+      by simp
+    finally show ?thesis .
+  next
+    case False
+
+    define s where "s = (-1) ^ n * (a * k n - b * h n)"
+    define r where "r = (-1) ^ n * (b * h (Suc n) - a * k (Suc n))"
+    have "k n \<le> k (Suc n)"
+      unfolding k_def by (intro conv_denom_leI) auto
+
+    have "r * h n + s * h (Suc n) = 
+            (-1) ^ Suc n * a * (k (Suc n) * h n - k n * h (Suc n))"
+      by (simp add: s_def r_def algebra_simps h_def k_def)
+    also have "\<dots> = a" using assms unfolding h_def k_def
+      by (subst conv_num_denom_prod_diff') (auto simp: algebra_simps)
+    finally have eq1: "r * h n + s * h (Suc n) = a" .
+  
+    have "r * k n + s * k (Suc n) = 
+            (-1) ^ Suc n * b * (k (Suc n) * h n - k n * h (Suc n))"
+      by (simp add: s_def r_def algebra_simps h_def k_def)
+    also have "\<dots> = b" using assms unfolding h_def k_def
+      by (subst conv_num_denom_prod_diff') (auto simp: algebra_simps)
+    finally have eq2: "r * k n + s * k (Suc n) = b" .
+
+    have "k n < k (Suc n)"
+      using \<open>n > 0\<close> by (auto simp: k_def intro: conv_denom_lessI)
+  
+    have "r \<noteq> 0"
+    proof
+      assume "r = 0"
+      hence "a * k (Suc n) = b * h (Suc n)" by (simp add: r_def)
+      hence "abs (a * k (Suc n)) = abs (h (Suc n) * b)" by (simp only: mult_ac)
+      hence *: "abs (h (Suc n)) = abs a \<and> k (Suc n) = b"
+        unfolding abs_mult h_def k_def using coprime_conv_num_denom assms
+        by (subst (asm) coprime_crossproduct_int) auto
+      with \<open>k n < k (Suc n)\<close> and \<open>b \<le> k n\<close> show False by auto
+    qed
+
+    have "s \<noteq> 0"
+    proof
+      assume "s = 0"
+      hence "a * k n = b * h n" by (simp add: s_def)
+      hence "abs (a * k n) = abs (h n * b)" by (simp only: mult_ac)
+      hence "b = k n \<and> \<bar>a\<bar> = \<bar>h n\<bar>" unfolding abs_mult h_def k_def using coprime_conv_num_denom assms
+        by (subst (asm) coprime_crossproduct_int) auto
+      with * show False by simp
+    qed
+
+    have "r * k n + s * k (Suc n) = b" by fact
+    also have "\<dots> \<in> {0<..<k (Suc n)}" using assms \<open>k n < k (Suc n)\<close> by auto
+    finally have *: "r * k n + s * k (Suc n) \<in> \<dots>" .
+
+    have opposite_signs1: "r > 0 \<and> s < 0 \<or> r < 0 \<and> s > 0"
+    proof (cases "r \<ge> 0"; cases "s \<ge> 0")
+      assume "r \<ge> 0" "s \<ge> 0"
+      hence "0 * (k n) + 1 * (k (Suc n)) \<le> r * k n + s * k (Suc n)"
+        using \<open>s \<noteq> 0\<close> by (intro add_mono mult_mono) (auto simp: k_def)
+      with * show ?thesis by auto
+    next
+      assume "\<not>(r \<ge> 0)" "\<not>(s \<ge> 0)"
+      hence "r * k n + s * k (Suc n) \<le> 0"
+        by (intro add_nonpos_nonpos mult_nonpos_nonneg) (auto simp: k_def)
+      with * show ?thesis by auto
+    qed (insert \<open>r \<noteq> 0\<close> \<open>s \<noteq> 0\<close>, auto)
+
+    have "r \<noteq> 1"
+    proof
+      assume [simp]: "r = 1"
+      have "b = r * k n + s * k (Suc n)"
+        using \<open>r * k n + s * k (Suc n) = b\<close> ..
+      also have "s * k (Suc n) \<le> (-1) * k (Suc n)"
+        using opposite_signs1 by (intro mult_right_mono) (auto simp: k_def)
+      also have "r * k n + (-1) * k (Suc n) = k n - k (Suc n)"
+        by simp
+      also have "\<dots> \<le> 0"
+        unfolding k_def by (auto intro!: conv_denom_leI)
+      finally show False using \<open>b > 0\<close> by simp
+    qed
+
+    have "enat n \<le> cfrac_length c" "enat (Suc n) \<le> cfrac_length c"
+      using assms False by (cases "cfrac_length c"; simp)+
+    hence "conv c n \<ge> x \<and> conv c (Suc n) \<le> x \<or> conv c n \<le> x \<and> conv c (Suc n) \<ge> x"
+      using conv_ge_cfrac_lim[of n c] conv_ge_cfrac_lim[of "Suc n" c]
+            conv_le_cfrac_lim[of n c] conv_le_cfrac_lim[of "Suc n" c] assms
+      by (cases "even n") auto
+    hence opposite_signs2: "k n * x - h n \<ge> 0 \<and> k (Suc n) * x - h (Suc n) \<le> 0 \<or>
+                           k n * x - h n \<le> 0 \<and> k (Suc n) * x - h (Suc n) \<ge> 0"
+      using assms conv_denom_pos[of c n] conv_denom_pos[of c "Suc n"]
+      by (auto simp: k_def h_def conv_num_denom field_simps)
+  
+    from opposite_signs1 opposite_signs2 have same_signs:
+      "r * (k n * x - h n) \<ge> 0 \<and> s * (k (Suc n) * x - h (Suc n)) \<ge> 0 \<or>
+       r * (k n * x - h n) \<le> 0 \<and> s * (k (Suc n) * x - h (Suc n)) \<le> 0"
+      by (auto intro: mult_nonpos_nonneg mult_nonneg_nonpos mult_nonneg_nonneg mult_nonpos_nonpos)
+
+    show ?thesis
+    proof (cases "Suc n = cfrac_length c")
+      case True
+      have x: "x = h (Suc n) / k (Suc n)"
+        using True[symmetric] by (auto simp: cfrac_lim_def h_def k_def conv_num_denom x_def)
+      have "r \<noteq> -1"
+      proof
+        assume [simp]: "r = -1"
+        have "r * k n + s * k (Suc n) = b"
+          by fact
+        also have "b < k (Suc n)"
+          using \<open>b \<le> k n\<close> and \<open>k n < k (Suc n)\<close> by simp
+        finally have "(s - 1) * k (Suc n) < k n"
+          by (simp add: algebra_simps)
+        also have "k n \<le> 1 * k (Suc n)"
+          by (simp add: k_def conv_denom_leI)
+        finally have "s < 2"
+          by (subst (asm) mult_less_cancel_right) (auto simp: k_def)
+        moreover from opposite_signs1 have "s > 0" by auto
+        ultimately have [simp]: "s = 1" by simp
+
+        have "b = (cfrac_nth c (Suc n) - 1) * k n + k (n - 1)"
+          using eq2 \<open>n > 0\<close> by (cases n) (auto simp: k_def algebra_simps)
+        also have "cfrac_nth c (Suc n) > 1"
+        proof -
+          have "cfrac_canonical c"
+            using assms True by auto
+          hence "cfrac_nth c (Suc n) \<noteq> 1"
+            using True[symmetric] by (auto simp: cfrac_canonical_iff enat_0_iff)
+          moreover have "cfrac_nth c (Suc n) > 0"
+            by auto
+          ultimately show "cfrac_nth c (Suc n) > 1"
+            by linarith
+        qed
+        hence "(cfrac_nth c (Suc n) - 1) * k n + k (n - 1) \<ge> 1 * k n + k (n - 1)"
+          by (intro add_mono mult_right_mono) (auto simp: k_def)
+        finally have "b > k n"
+          using conv_denom_pos[of c "n - 1"] unfolding k_def by linarith
+        with assms show False by simp
+      qed
+      with \<open>r \<noteq> 1\<close> \<open>r \<noteq> 0\<close> have "\<bar>r\<bar> > 1"
+        by auto
+
+      from \<open>s \<noteq> 0\<close> have "k n * x \<noteq> h n"
+        using conv_num_denom_prod_diff[of c n]
+        by (auto simp: x field_simps k_def h_def simp flip: of_int_mult)
+      hence "1 * \<bar>k n * x - h n\<bar> < \<bar>r\<bar> * \<bar>k n * x - h n\<bar>"
+        using \<open>\<bar>r\<bar> > 1\<close> by (intro mult_strict_right_mono) auto
+      also have "\<dots> = \<bar>r\<bar> * \<bar>k n * x - h n\<bar> + 0" by simp
+      also have "\<dots> \<le> \<bar>r * (k n * x - h n)\<bar> + \<bar>s * (k (Suc n) * x - h (Suc n))\<bar>"
+        unfolding abs_mult of_int_abs using conv_denom_pos[of c "Suc n"] \<open>s \<noteq> 0\<close>
+        by (intro add_left_mono mult_nonneg_nonneg) (auto simp: field_simps k_def)
+      also have "\<dots> = \<bar>r * (k n * x - h n) + s * (k (Suc n) * x - h (Suc n))\<bar>"
+        using same_signs by auto
+      also have "\<dots> = \<bar>(r * k n + s * k (Suc n)) * x - (r * h n + s * h (Suc n))\<bar>"
+        by (simp add: algebra_simps)
+      also have "\<dots> = \<bar>b * x - a\<bar>"
+        unfolding eq1 eq2 by simp
+      finally show ?thesis by simp
+    next
+      case False
+      from assms have "Suc n < cfrac_length c"
+        using False \<open>Suc n \<le> cfrac_length c\<close> by force
+      have "1 * \<bar>k n * x - h n\<bar> \<le> \<bar>r\<bar> * \<bar>k n * x - h n\<bar>"
+        using \<open>r \<noteq> 0\<close> by (intro mult_right_mono) auto
+      also have "\<dots> = \<bar>r\<bar> * \<bar>k n * x - h n\<bar> + 0" by simp
+      also have "x \<noteq> h (Suc n) / k (Suc n)"
+        using conv_neq_cfrac_lim[of "Suc n" c] \<open>Suc n < cfrac_length c\<close>
+        by (auto simp: conv_num_denom h_def k_def x_def)
+      hence  "\<bar>s * (k (Suc n) * x - h (Suc n))\<bar> > 0"
+        using \<open>s \<noteq> 0\<close> by (auto simp: field_simps k_def)
+      also have "\<bar>r\<bar> * \<bar>k n * x - h n\<bar> + \<dots> \<le> 
+                 \<bar>r * (k n * x - h n)\<bar> + \<bar>s * (k (Suc n) * x - h (Suc n))\<bar>"
+        unfolding abs_mult of_int_abs by (intro add_left_mono mult_nonneg_nonneg) auto
+      also have "\<dots> = \<bar>r * (k n * x - h n) + s * (k (Suc n) * x - h (Suc n))\<bar>"
+        using same_signs by auto
+      also have "\<dots> = \<bar>(r * k n + s * k (Suc n)) * x - (r * h n + s * h (Suc n))\<bar>"
+        by (simp add: algebra_simps)
+      also have "\<dots> = \<bar>b * x - a\<bar>"
+        unfolding eq1 eq2 by simp
+      finally show ?thesis by simp
+    qed
+  qed
+qed
+
+lemma conv_best_approximation_ex_weak:
+  fixes a b :: int and x :: real
+  assumes "n \<le> cfrac_length c"
+  assumes "0 < b" and "b < k (Suc n)" and "coprime a b"
+  defines "x \<equiv> cfrac_lim c"
+  shows   "\<bar>k n * x - h n\<bar> \<le> \<bar>b * x - a\<bar>"
+proof (cases "\<bar>a\<bar> = \<bar>h n\<bar> \<and> b = k n")
+  case True
+  note * = this
+  show ?thesis
+  proof (cases "sgn a = sgn (h n)")
+    case True
+    with * have [simp]: "a = h n"
+      by (auto simp: abs_if split: if_splits)
+    thus ?thesis using * by auto
+  next
+    case False
+    with True have [simp]: "a = -h n"
+      by (auto simp: abs_if split: if_splits)
+    have "\<bar>real_of_int (k n) * x - real_of_int (h n)\<bar> \<le> \<bar>real_of_int (k n) * x + real_of_int (h n)\<bar>"
+      unfolding x_def using conv_best_approximation_aux[of n]
+      by (intro abs_diff_le_abs_add) (auto simp: k_def not_le zero_less_mult_iff)
+    thus ?thesis using True by auto
+  qed
+next
+  case False
+  note * = this
+  show ?thesis
+  proof (cases "n = cfrac_length c")
+    case True
+    hence "x = conv c n"
+      by (auto simp: cfrac_lim_def x_def split: enat.splits)
+    also have "\<dots> = h n / k n"
+      by (auto simp: h_def k_def conv_num_denom)
+    finally show ?thesis by (auto simp: k_def)
+  next
+    case False
+
+    define s where "s = (-1) ^ n * (a * k n - b * h n)"
+    define r where "r = (-1) ^ n * (b * h (Suc n) - a * k (Suc n))"
+  
+    have "r * h n + s * h (Suc n) = 
+            (-1) ^ Suc n * a * (k (Suc n) * h n - k n * h (Suc n))"
+      by (simp add: s_def r_def algebra_simps h_def k_def)
+    also have "\<dots> = a" using assms unfolding h_def k_def
+      by (subst conv_num_denom_prod_diff') (auto simp: algebra_simps)
+    finally have eq1: "r * h n + s * h (Suc n) = a" .
+  
+    have "r * k n + s * k (Suc n) = 
+            (-1) ^ Suc n * b * (k (Suc n) * h n - k n * h (Suc n))"
+      by (simp add: s_def r_def algebra_simps h_def k_def)
+    also have "\<dots> = b" using assms unfolding h_def k_def
+      by (subst conv_num_denom_prod_diff') (auto simp: algebra_simps)
+    finally have eq2: "r * k n + s * k (Suc n) = b" .
+  
+    have "r \<noteq> 0"
+    proof
+      assume "r = 0"
+      hence "a * k (Suc n) = b * h (Suc n)" by (simp add: r_def)
+      hence "abs (a * k (Suc n)) = abs (h (Suc n) * b)" by (simp only: mult_ac)
+      hence "b = k (Suc n)" unfolding abs_mult h_def k_def using coprime_conv_num_denom assms
+        by (subst (asm) coprime_crossproduct_int) auto
+      with assms show False by simp
+    qed
+  
+    have "s \<noteq> 0"
+    proof
+      assume "s = 0"
+      hence "a * k n = b * h n" by (simp add: s_def)
+      hence "abs (a * k n) = abs (h n * b)" by (simp only: mult_ac)
+      hence "b = k n \<and> \<bar>a\<bar> = \<bar>h n\<bar>" unfolding abs_mult h_def k_def using coprime_conv_num_denom assms
+        by (subst (asm) coprime_crossproduct_int) auto
+      with * show False by simp
+    qed
+
+    have "r * k n + s * k (Suc n) = b" by fact
+    also have "\<dots> \<in> {0<..<k (Suc n)}" using assms by auto
+    finally have *: "r * k n + s * k (Suc n) \<in> \<dots>" .
+    
+    have opposite_signs1: "r > 0 \<and> s < 0 \<or> r < 0 \<and> s > 0"
+    proof (cases "r \<ge> 0"; cases "s \<ge> 0")
+      assume "r \<ge> 0" "s \<ge> 0"
+      hence "0 * (k n) + 1 * (k (Suc n)) \<le> r * k n + s * k (Suc n)"
+        using \<open>s \<noteq> 0\<close> by (intro add_mono mult_mono) (auto simp: k_def)
+      with * show ?thesis by auto
+    next
+      assume "\<not>(r \<ge> 0)" "\<not>(s \<ge> 0)"
+      hence "r * k n + s * k (Suc n) \<le> 0"
+        by (intro add_nonpos_nonpos mult_nonpos_nonneg) (auto simp: k_def)
+      with * show ?thesis by auto
+    qed (insert \<open>r \<noteq> 0\<close> \<open>s \<noteq> 0\<close>, auto)
+
+    have "enat n \<le> cfrac_length c" "enat (Suc n) \<le> cfrac_length c"
+      using assms False by (cases "cfrac_length c"; simp)+
+    hence "conv c n \<ge> x \<and> conv c (Suc n) \<le> x \<or> conv c n \<le> x \<and> conv c (Suc n) \<ge> x"
+      using conv_ge_cfrac_lim[of n c] conv_ge_cfrac_lim[of "Suc n" c]
+            conv_le_cfrac_lim[of n c] conv_le_cfrac_lim[of "Suc n" c] assms
+      by (cases "even n") auto
+    hence opposite_signs2: "k n * x - h n \<ge> 0 \<and> k (Suc n) * x - h (Suc n) \<le> 0 \<or>
+                           k n * x - h n \<le> 0 \<and> k (Suc n) * x - h (Suc n) \<ge> 0"
+      using assms conv_denom_pos[of c n] conv_denom_pos[of c "Suc n"]
+      by (auto simp: k_def h_def conv_num_denom field_simps)
+  
+    from opposite_signs1 opposite_signs2 have same_signs:
+      "r * (k n * x - h n) \<ge> 0 \<and> s * (k (Suc n) * x - h (Suc n)) \<ge> 0 \<or>
+       r * (k n * x - h n) \<le> 0 \<and> s * (k (Suc n) * x - h (Suc n)) \<le> 0"
+      by (auto intro: mult_nonpos_nonneg mult_nonneg_nonpos mult_nonneg_nonneg mult_nonpos_nonpos)
+
+    have "1 * \<bar>k n * x - h n\<bar> \<le> \<bar>r\<bar> * \<bar>k n * x - h n\<bar>"
+      using \<open>r \<noteq> 0\<close> by (intro mult_right_mono) auto
+    also have "\<dots> = \<bar>r\<bar> * \<bar>k n * x - h n\<bar> + 0" by simp
+    also have "\<dots> \<le> \<bar>r * (k n * x - h n)\<bar> + \<bar>s * (k (Suc n) * x - h (Suc n))\<bar>"
+      unfolding abs_mult of_int_abs using conv_denom_pos[of c "Suc n"] \<open>s \<noteq> 0\<close>
+      by (intro add_left_mono mult_nonneg_nonneg) (auto simp: field_simps k_def)
+    also have "\<dots> = \<bar>r * (k n * x - h n) + s * (k (Suc n) * x - h (Suc n))\<bar>"
+      using same_signs by auto
+    also have "\<dots> = \<bar>(r * k n + s * k (Suc n)) * x - (r * h n + s * h (Suc n))\<bar>"
+      by (simp add: algebra_simps)
+    also have "\<dots> = \<bar>b * x - a\<bar>"
+      unfolding eq1 eq2 by simp
+    finally show ?thesis by simp
+  qed
+qed
+
+lemma cfrac_canonical_reduce:
+  "cfrac_canonical c \<longleftrightarrow>
+     cfrac_is_int c \<or> \<not>cfrac_is_int c \<and> cfrac_tl c \<noteq> 1 \<and> cfrac_canonical (cfrac_tl c)"
+  unfolding cfrac_is_int_def one_cfrac_def
+  by transfer (auto simp: cfrac_canonical_def llast_LCons split: if_splits split: llist.splits)
+             
+lemma cfrac_nth_0_conv_floor:
+  assumes "cfrac_canonical c \<or> cfrac_length c \<noteq> 1"
+  shows   "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+proof (cases "cfrac_is_int c")
+  case True
+  thus ?thesis
+    by (auto simp: cfrac_lim_def cfrac_is_int_def)
+next
+  case False
+  show ?thesis
+  proof (cases "cfrac_length c = 1")
+    case True
+    hence "cfrac_canonical c" using assms by auto
+    hence "cfrac_tl c \<noteq> 1" using False
+      by (subst (asm) cfrac_canonical_reduce) auto
+    thus ?thesis
+      using cfrac_nth_0_cases[of c] by auto
+  next
+    case False
+    hence "cfrac_length c > 1"
+      using \<open>\<not>cfrac_is_int c\<close>
+      by (cases "cfrac_length c") (auto simp: cfrac_is_int_def one_enat_def zero_enat_def)
+    have "cfrac_tl c \<noteq> 1"
+    proof
+      assume "cfrac_tl c = 1"
+      have "0 < cfrac_length c - 1"
+      proof (cases "cfrac_length c")
+        case [simp]: (enat l)
+        have "cfrac_length c - 1 = enat (l - 1)"
+          by auto
+        also have "\<dots> > enat 0"
+          using \<open>cfrac_length c > 1\<close> by (simp add: one_enat_def)
+        finally show ?thesis by (simp add: zero_enat_def)
+      qed auto
+      also have "\<dots> = cfrac_length (cfrac_tl c)"
+        by simp
+      also have "cfrac_tl c = 1"
+        by fact
+      finally show False by simp
+    qed
+    thus ?thesis using cfrac_nth_0_cases[of c] by auto
+  qed
+qed
+
+lemma conv_best_approximation_ex_nat:
+  fixes a b :: nat and x :: real
+  assumes "n \<le> cfrac_length c" "0 < b" "b < k (Suc n)" "coprime a b"
+  shows   "\<bar>k n * cfrac_lim c - h n\<bar> \<le> \<bar>b * cfrac_lim c - a\<bar>"
+  using conv_best_approximation_ex_weak[OF assms(1), of b a] assms by auto
+
+lemma abs_mult_nonneg_left:
+  assumes "x \<ge> (0 :: 'a :: {ordered_ab_group_add_abs, idom_abs_sgn})"
+  shows   "x * \<bar>y\<bar> = \<bar>x * y\<bar>"
+proof -
+  from assms have "x = \<bar>x\<bar>" by simp
+  also have "\<dots> * \<bar>y\<bar> = \<bar>x * y\<bar>" by (simp add: abs_mult)
+  finally show ?thesis .
+qed
+
+text \<open>
+  Any convergent of the continued fraction expansion of \<open>x\<close> is a best approximation of \<open>x\<close>,
+  i.e. there is no other number with a smaller denominator that approximates it better.
+\<close>
+lemma conv_best_approximation:
+  fixes a b :: int and x :: real
+  assumes "n \<le> cfrac_length c"
+  assumes "0 < b" and "b < k n" and "coprime a b"
+  defines "x \<equiv> cfrac_lim c"
+  shows   "\<bar>x - conv c n\<bar> \<le> \<bar>x - a / b\<bar>"
+proof -
+  have "b < k n" by fact
+  also have "k n \<le> k (Suc n)"
+    unfolding k_def by (intro conv_denom_leI) auto
+  finally have *: "b < k (Suc n)" by simp
+  have "\<bar>x - conv c n\<bar> = \<bar>k n * x - h n\<bar> / k n"
+    using conv_denom_pos[of c n] assms(1)
+    by (auto simp: conv_num_denom field_simps k_def h_def)
+  also have "\<dots> \<le> \<bar>b * x - a\<bar> / k n" unfolding x_def using assms *
+    by (intro divide_right_mono conv_best_approximation_ex_weak) auto
+  also from assms have "\<dots> \<le> \<bar>b * x - a\<bar> / b"
+    by (intro divide_left_mono) auto
+  also have "\<dots> = \<bar>x - a / b\<bar>" using assms by (simp add: field_simps)
+  finally show ?thesis .
+qed
+
+lemma conv_denom_partition:
+  assumes "y > 0"
+  shows   "\<exists>!n. y \<in> {k n..<k (Suc n)}"
+proof (rule ex_ex1I)
+  from conv_denom_at_top[of c] assms have *: "\<exists>n. k n \<ge> y + 1"
+    by (auto simp: k_def filterlim_at_top eventually_at_top_linorder)
+  define n where "n = (LEAST n. k n \<ge> y + 1)"
+  from LeastI_ex[OF *] have n: "k n > y" by (simp add: Suc_le_eq n_def)
+  from n and assms have "n > 0" by (intro Nat.gr0I) (auto simp: k_def)
+
+  have "k (n - 1) \<le> y"
+  proof (rule ccontr)
+    assume "\<not>k (n - 1) \<le> y"
+    hence "k (n - 1) \<ge> y + 1" by auto
+    hence "n - 1 \<ge> n" unfolding n_def by (rule Least_le)
+    with \<open>n > 0\<close> show False by simp
+  qed
+  with n and \<open>n > 0\<close> have "y \<in> {k (n - 1)..<k (Suc (n - 1))}" by auto
+  thus "\<exists>n. y \<in> {k n..<k (Suc n)}" by blast
+next
+  fix m n
+  assume "y \<in> {k m..<k (Suc m)}" "y \<in> {k n..<k (Suc n)}"
+  thus "m = n"
+  proof (induction m n rule: linorder_wlog)
+    case (le m n)
+    show "m = n"
+    proof (rule ccontr)
+      assume "m \<noteq> n"
+      with le have "k (Suc m) \<le> k n"
+        unfolding k_def by (intro conv_denom_leI assms) auto
+      with le show False by auto
+    qed
+  qed auto
+qed
+
+text \<open>
+  A fraction that approximates a real number \<open>x\<close> sufficiently well (in a certain sense)
+  is a convergent of its continued fraction expansion.
+\<close>
+lemma frac_is_convergentI:
+  fixes a b :: int and x :: real
+  defines "x \<equiv> cfrac_lim c"
+  assumes "b > 0" and "coprime a b" and "\<bar>x - a / b\<bar> < 1 / (2 * b\<^sup>2)"
+  shows   "\<exists>n. enat n \<le> cfrac_length c \<and> (a, b) = (h n, k n)"
+proof (cases "a = 0")
+  case True
+  with assms have [simp]: "a = 0" "b = 1"
+    by auto
+
+  show ?thesis
+  proof (cases x "0 :: real" rule: linorder_cases)
+    case greater
+    hence "0 < x" "x < 1/2"
+      using assms by auto
+    hence "x \<notin> \<int>"
+      by (auto simp: Ints_def)
+    hence "cfrac_nth c 0 = \<lfloor>x\<rfloor>"
+      using assms by (subst cfrac_nth_0_not_int) (auto simp: x_def)
+    also from \<open>x > 0\<close> \<open>x < 1/2\<close> have "\<dots> = 0"
+      by linarith
+    finally have "(a, b) = (h 0, k 0)"
+      by (auto simp: h_def k_def)
+    thus ?thesis by (intro exI[of _ 0]) (auto simp flip: zero_enat_def)
+  next
+    case less
+    hence "x < 0" "x > -1/2"
+      using assms by auto
+    hence "x \<notin> \<int>"
+      by (auto simp: Ints_def)
+    hence not_int: "\<not>cfrac_is_int c"
+      by (auto simp: cfrac_is_int_def x_def cfrac_lim_def)
+    have "cfrac_nth c 0 = \<lfloor>x\<rfloor>"
+      using \<open>x \<notin> \<int>\<close> assms by (subst cfrac_nth_0_not_int) (auto simp: x_def)
+    also from \<open>x < 0\<close> \<open>x > -1/2\<close> have "\<dots> = -1"
+      by linarith
+    finally have [simp]: "cfrac_nth c 0 = -1" .
+    have "cfrac_nth c (Suc 0) = cfrac_nth (cfrac_tl c) 0"
+      by simp
+    have "cfrac_lim (cfrac_tl c) = 1 / (x + 1)"
+      using not_int by (subst cfrac_lim_tl) (auto simp: x_def)
+    also from \<open>x < 0\<close> \<open>x > -1/2\<close> have "\<dots> \<in> {1<..<2}"
+      by (auto simp: divide_simps)
+    finally have *: "cfrac_lim (cfrac_tl c) \<in> {1<..<2}" .
+    have "cfrac_nth (cfrac_tl c) 0 = \<lfloor>cfrac_lim (cfrac_tl c)\<rfloor>"
+      using * by (subst cfrac_nth_0_not_int) (auto simp: Ints_def)
+    also have "\<dots> = 1"
+      using * by (simp, linarith?)
+    finally have "(a, b) = (h 1, k 1)"
+      by (auto simp: h_def k_def)
+    moreover have "cfrac_length c \<ge> 1"
+      using not_int
+      by (cases "cfrac_length c") (auto simp: cfrac_is_int_def one_enat_def zero_enat_def)
+    ultimately show ?thesis by (intro exI[of _ 1]) (auto simp: one_enat_def)   
+  next
+    case equal
+    show ?thesis
+      using cfrac_nth_0_cases[of c]
+    proof
+      assume "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor>"
+      with equal have "(a, b) = (h 0, k 0)"
+        by (simp add: x_def h_def k_def)
+      thus ?thesis by (intro exI[of _ 0]) (auto simp flip: zero_enat_def)
+    next
+      assume *: "cfrac_nth c 0 = \<lfloor>cfrac_lim c\<rfloor> - 1 \<and> cfrac_tl c = 1"
+      have [simp]: "cfrac_nth c 0 = -1"
+        using * equal by (auto simp: x_def)
+      from * have "\<not>cfrac_is_int c"
+        by (auto simp: cfrac_is_int_def cfrac_lim_def floor_minus)
+      have "cfrac_nth c 1 = cfrac_nth (cfrac_tl c) 0"
+        by auto
+      also have "cfrac_tl c = 1"
+        using * by auto
+      finally have "cfrac_nth c 1 = 1"
+        by simp
+      hence "(a, b) = (h 1, k 1)"
+        by (auto simp: h_def k_def)
+      moreover from \<open>\<not>cfrac_is_int c\<close> have "cfrac_length c \<ge> 1"
+        by (cases "cfrac_length c") (auto simp: one_enat_def zero_enat_def cfrac_is_int_def)
+      ultimately show ?thesis
+        by (intro exI[of _ 1]) (auto simp: one_enat_def)
+    qed
+  qed
+next
+  case False
+  hence a_nz: "a \<noteq> 0" by auto
+
+  have "x \<noteq> 0"
+  proof
+    assume [simp]: "x = 0"
+    hence "\<bar>a\<bar> / b < 1 / (2 * b ^ 2)"
+      using assms by simp
+    hence "\<bar>a\<bar> < 1 / (2 * b)"
+      using assms by (simp add: field_simps power2_eq_square)
+    also have "\<dots> \<le> 1 / 2"
+      using assms by (intro divide_left_mono) auto
+    finally have "a = 0" by auto
+    with \<open>a \<noteq> 0\<close> show False by simp
+  qed
+
+  show ?thesis
+  proof (rule ccontr)
+    assume no_convergent: "\<nexists>n. enat n \<le> cfrac_length c \<and> (a, b) = (h n, k n)"
+    from assms have "\<exists>!r. b \<in> {k r..<k (Suc r)}"
+      by (intro conv_denom_partition) auto
+    then obtain r where r: "b \<in> {k r..<k (Suc r)}" by auto
+    have "k r > 0"
+      using conv_denom_pos[of c r] assms by (auto simp: k_def)
+
+    show False
+    proof (cases "enat r \<le> cfrac_length c")
+      case False
+      then obtain l where l: "cfrac_length c = enat l"
+        by (cases "cfrac_length c") auto
+      have "k l \<le> k r"
+        using False l unfolding k_def by (intro conv_denom_leI) auto
+      also have "\<dots> \<le> b"
+        using r by simp
+      finally have "b \<ge> k l" .
+
+      have "x = conv c l"
+        by (auto simp: x_def cfrac_lim_def l)
+      hence x_eq: "x = h l / k l"
+        by (auto simp: conv_num_denom h_def k_def)
+      have "k l > 0"
+        by (simp add: k_def)
+
+      have "b * k l * \<bar>h l / k l - a / b\<bar> < k l / (2*b)"
+        using assms x_eq \<open>k l > 0\<close> by (auto simp: field_simps power2_eq_square)
+      also have "b * k l * \<bar>h l / k l - a / b\<bar> = \<bar>b * k l * (h l / k l - a / b)\<bar>"
+        using \<open>b > 0\<close> \<open>k l > 0\<close> by (subst abs_mult) auto
+      also have "\<dots> = of_int \<bar>b * h l - a * k l\<bar>"
+        using \<open>b > 0\<close> \<open>k l > 0\<close> by (simp add: algebra_simps)
+      also have "k l / (2 * b) < 1"
+        using \<open>b \<ge> k l\<close> \<open>b > 0\<close> by auto
+      finally have "a * k l = b * h l"
+        by linarith
+      moreover have "coprime (h l) (k l)"
+        unfolding h_def k_def by (simp add: coprime_conv_num_denom)
+      ultimately have "(a, b) = (h l, k l)"
+        using \<open>coprime a b\<close> using a_nz \<open>b > 0\<close> \<open>k l > 0\<close>
+        by (subst (asm) coprime_crossproduct') (auto simp: coprime_commute)
+      with no_convergent and l show False
+        by auto
+
+    next
+
+      case True
+      have "k r * \<bar>x - h r / k r\<bar> = \<bar>k r * x - h r\<bar>"
+        using \<open>k r > 0\<close> by (simp add: field_simps)
+      also have "\<bar>k r * x - h r\<bar> \<le> \<bar>b * x - a\<bar>"
+        using assms r True unfolding x_def by (intro conv_best_approximation_ex_weak) auto
+      also have "\<dots> = b * \<bar>x - a / b\<bar>"
+        using \<open>b > 0\<close> by (simp add: field_simps)
+      also have "\<dots> < b * (1 / (2 * b\<^sup>2))"
+        using \<open>b > 0\<close> by (intro mult_strict_left_mono assms) auto
+      finally have less: "\<bar>x - conv c r\<bar> < 1 / (2 * b * k r)"
+        using \<open>k r > 0\<close> and \<open>b > 0\<close> and assms
+        by (simp add: field_simps power2_eq_square conv_num_denom h_def k_def)
+    
+      have "\<bar>x - a / b\<bar> < 1 / (2 * b\<^sup>2)" by fact
+      also have "\<dots> = 1 / (2 * b) * (1 / b)"
+        by (simp add: power2_eq_square)
+      also have "\<dots> \<le> 1 / (2 * b) * (\<bar>a\<bar> / b)"
+        using a_nz assms by (intro mult_left_mono divide_right_mono) auto
+      also have "\<dots> < 1 / 1 * (\<bar>a\<bar> / b)"
+        using a_nz assms
+        by (intro mult_strict_right_mono divide_left_mono divide_strict_left_mono) auto
+      also have "\<dots> = \<bar>a / b\<bar>" using assms by simp
+      finally have "sgn x = sgn (a / b)"
+        by (auto simp: sgn_if split: if_splits)
+      hence "sgn x = sgn a" using assms by (auto simp: sgn_of_int)
+      hence "a \<ge> 0 \<and> x \<ge> 0 \<or> a \<le> 0 \<and> x \<le> 0"
+        by (auto simp: sgn_if split: if_splits)
+      moreover have "h r \<ge> 0 \<and> x \<ge> 0 \<or> h r \<le> 0 \<and> x \<le> 0"
+        using conv_best_approximation_aux[of r] by (auto simp: h_def x_def)
+      ultimately have signs: "h r \<ge> 0 \<and> a \<ge> 0 \<or> h r \<le> 0 \<and> a \<le> 0"
+        using \<open>x \<noteq> 0\<close> by auto
+  
+      with no_convergent assms assms True have "\<bar>h r\<bar> \<noteq> \<bar>a\<bar> \<or> b \<noteq> k r"
+        by (auto simp: h_def k_def)
+      
+      hence "\<bar>h r\<bar> * \<bar>b\<bar> \<noteq> \<bar>a\<bar> * \<bar>k r\<bar>" unfolding h_def k_def
+        using assms coprime_conv_num_denom[of c r]
+        by (subst coprime_crossproduct_int) auto
+      hence "\<bar>h r\<bar> * b \<noteq> \<bar>a\<bar> * k r" using assms by (simp add: k_def)
+      hence "k r * a - h r * b \<noteq> 0"
+        using signs by (auto simp: algebra_simps)
+      hence "\<bar>k r * a - h r * b\<bar> \<ge> 1" by presburger
+      hence "real_of_int 1 / (k r * b) \<le> \<bar>k r * a - h r * b\<bar> / (k r * b)"
+        using assms
+        by (intro divide_right_mono, subst of_int_le_iff) (auto simp: k_def)
+      also have "\<dots> = \<bar>(real_of_int (k r) * a - h r * b) / (k r * b)\<bar>"
+        using assms by (simp add: k_def)
+      also have "(real_of_int (k r) * a - h r * b) / (k r * b) = a / b - conv c r"
+        using assms \<open>k r > 0\<close> by (simp add: h_def k_def conv_num_denom field_simps)
+      also have "\<bar>a / b - conv c r\<bar> = \<bar>(x - conv c r) - (x - a / b)\<bar>"
+        by (simp add: algebra_simps)
+      also have "\<dots> \<le> \<bar>x - conv c r\<bar> + \<bar>x - a / b\<bar>"
+        by (rule abs_triangle_ineq4)
+      also have "\<dots> < 1 / (2 * b * k r) + 1 / (2 * b\<^sup>2)"
+        by (intro add_strict_mono assms less)
+      finally have "k r > b"
+        using \<open>b > 0\<close> and \<open>k r > 0\<close> by (simp add: power2_eq_square field_simps)
+      with r show False by auto
+    qed
+  qed
+qed
+
+end
+
+
+subsection \<open>Efficient code for convergents\<close>
+
+
+function conv_gen :: "(nat \<Rightarrow> int) \<Rightarrow> int \<times> int \<times> nat \<Rightarrow> nat \<Rightarrow> int" where
+  "conv_gen c (a, b, n) N =
+     (if n > N then b else conv_gen c (b, b * c n + a, Suc n) N)"
+  by auto
+termination by (relation "measure (\<lambda>(_, (_, _, n), N). Suc N - n)") auto
+
+lemmas [simp del] = conv_gen.simps
+
+lemma conv_gen_aux_simps [simp]:
+  "n > N \<Longrightarrow> conv_gen c (a, b, n) N = b"
+  "n \<le> N \<Longrightarrow> conv_gen c (a, b, n) N = conv_gen c (b, b * c n + a, Suc n) N"
+  by (subst conv_gen.simps, simp)+
+
+lemma conv_num_eq_conv_gen_aux:
+  "Suc n \<le> N \<Longrightarrow> conv_num c n = b * cfrac_nth c n + a \<Longrightarrow> 
+     conv_num c (Suc n) = conv_num c n * cfrac_nth c (Suc n) + b \<Longrightarrow>
+     conv_num c N = conv_gen (cfrac_nth c) (a, b, n) N"
+proof (induction "cfrac_nth c" "(a, b, n)" N arbitrary: c a b n rule: conv_gen.induct)
+  case (1 a b n N c)
+  show ?case
+  proof (cases "Suc (Suc n) \<le> N")
+    case True
+    thus ?thesis
+      by (subst 1) (insert "1.prems", auto)
+  next
+    case False
+    thus ?thesis using 1
+      by (auto simp: not_le less_Suc_eq)
+  qed
+qed
+
+lemma conv_denom_eq_conv_gen_aux:
+  "Suc n \<le> N \<Longrightarrow> conv_denom c n = b * cfrac_nth c n + a \<Longrightarrow> 
+     conv_denom c (Suc n) = conv_denom c n * cfrac_nth c (Suc n) + b \<Longrightarrow>
+     conv_denom c N = conv_gen (cfrac_nth c) (a, b, n) N"
+proof (induction "cfrac_nth c" "(a, b, n)" N arbitrary: c a b n rule: conv_gen.induct)
+  case (1 a b n N c)
+  show ?case
+  proof (cases "Suc (Suc n) \<le> N")
+    case True
+    thus ?thesis
+      by (subst 1) (insert "1.prems", auto)
+  next
+    case False
+    thus ?thesis using 1
+      by (auto simp: not_le less_Suc_eq)
+  qed
+qed
+
+lemma conv_num_code [code]: "conv_num c n = conv_gen (cfrac_nth c) (0, 1, 0) n"
+  using conv_num_eq_conv_gen_aux[of 0 n c 1 0] by (cases n) simp_all
+
+lemma conv_denom_code [code]: "conv_denom c n = conv_gen (cfrac_nth c) (1, 0, 0) n"
+  using conv_denom_eq_conv_gen_aux[of 0 n c 0 1] by (cases n) simp_all
+
+definition conv_num_fun where "conv_num_fun c = conv_gen c (0, 1, 0)"
+definition conv_denom_fun where "conv_denom_fun c = conv_gen c (1, 0, 0)"
+
+lemma
+  assumes "is_cfrac c"
+  shows   conv_num_fun_eq: "conv_num_fun c n = conv_num (cfrac c) n"
+    and   conv_denom_fun_eq: "conv_denom_fun c n = conv_denom (cfrac c) n"
+proof -
+  from assms have "cfrac_nth (cfrac c) = c"
+    by (intro ext) simp_all
+  thus "conv_num_fun c n = conv_num (cfrac c) n" and "conv_denom_fun c n = conv_denom (cfrac c) n"
+    by (simp_all add: conv_num_fun_def conv_num_code conv_denom_fun_def conv_denom_code)
+qed
+
+
+subsection \<open>Computing the continued fraction expansion of a rational number\<close>
+
+
+function cfrac_list_of_rat :: "int \<times> int \<Rightarrow> int list" where
+  "cfrac_list_of_rat (a, b) =
+     (if b = 0 then [0]
+      else a div b # (if a mod b = 0 then [] else cfrac_list_of_rat (b, a mod b)))"
+  by auto
+termination
+  by (relation "measure (\<lambda>(a,b). nat (abs b))") (auto simp: abs_mod_less)
+
+lemmas [simp del] = cfrac_list_of_rat.simps
+
+lemma cfrac_list_of_rat_correct:
+  "(let xs = cfrac_list_of_rat (a, b); c = cfrac_of_real (a / b)
+    in  length xs = cfrac_length c + 1 \<and> (\<forall>i<length xs. xs ! i = cfrac_nth c i))"
+proof (induction "(a, b)" arbitrary: a b rule: cfrac_list_of_rat.induct)
+  case (1 a b)
+  show ?case
+  proof (cases "b = 0")
+    case True
+    thus ?thesis
+      by (subst cfrac_list_of_rat.simps) (auto simp: one_enat_def)
+  next
+    case False
+    define c where "c = cfrac_of_real (a / b)"
+    define c' where "c' = cfrac_of_real (b / (a mod b))"
+    define xs' where "xs' = (if a mod b = 0 then [] else cfrac_list_of_rat (b, a mod b))"
+    define xs where "xs = a div b # xs'"
+
+    have [simp]: "cfrac_nth c 0 = a div b"
+      by (auto simp: c_def floor_divide_of_int_eq)
+
+    obtain l where l: "cfrac_length c = enat l"
+      by (cases "cfrac_length c") (auto simp: c_def)
+
+    have "length xs = l + 1 \<and> (\<forall>i<length xs. xs ! i = cfrac_nth c i)"
+    proof (cases "b dvd a")
+      case True
+      thus ?thesis using l
+        by (auto simp: Let_def xs_def xs'_def c_def of_int_divide_in_Ints one_enat_def enat_0_iff)
+    next
+      case False
+      have "l \<noteq> 0"
+        using l False cfrac_of_real_length_eq_0_iff[of "a / b"] \<open>b \<noteq> 0\<close>
+        by (auto simp: c_def zero_enat_def real_of_int_divide_in_Ints_iff intro!: Nat.gr0I)
+      have c': "c' = cfrac_tl c"
+        using False \<open>b \<noteq> 0\<close> unfolding c'_def c_def
+        by (subst cfrac_tl_of_real) (auto simp: real_of_int_divide_in_Ints_iff frac_fraction)
+      from 1 have "enat (length xs') = cfrac_length c' + 1"
+              and xs': "\<forall>i<length xs'. xs' ! i = cfrac_nth c' i"
+        using \<open>b \<noteq> 0\<close> \<open>\<not>b dvd a\<close> by (auto simp: Let_def xs'_def c'_def)
+
+      have "enat (length xs') = cfrac_length c' + 1"
+        by fact
+      also have "\<dots> = enat l - 1 + 1"
+        using c' l by simp
+      also have "\<dots> = enat (l - 1 + 1)"
+        by (metis enat_diff_one one_enat_def plus_enat_simps(1))
+      also have "l - 1 + 1 = l"
+        using \<open>l \<noteq> 0\<close> by simp
+      finally have [simp]: "length xs' = l"
+        by simp
+
+      from xs' show ?thesis
+        by (auto simp: xs_def nth_Cons c' split: nat.splits)
+    qed
+    thus ?thesis using l False
+      by (subst cfrac_list_of_rat.simps) (simp_all add: xs_def xs'_def c_def one_enat_def)
+  qed
+qed
+
+lemma conv_num_cong:
+  assumes "(\<And>k. k \<le> n \<Longrightarrow> cfrac_nth c k = cfrac_nth c' k)" "n = n'"
+  shows   "conv_num c n = conv_num c' n"
+proof -
+  have "conv_num c n = conv_num c' n"
+    using assms(1)
+    by (induction n arbitrary: rule: conv_num.induct) simp_all
+  thus ?thesis using assms(2)
+    by simp
+qed
+
+lemma conv_denom_cong:
+  assumes "(\<And>k. k \<le> n \<Longrightarrow> cfrac_nth c k = cfrac_nth c' k)" "n = n'"
+  shows   "conv_denom c n = conv_denom c' n'"
+proof -
+  have "conv_denom c n = conv_denom c' n"
+    using assms(1)
+    by (induction n arbitrary: rule: conv_denom.induct) simp_all
+  thus ?thesis using assms(2)
+    by simp
+qed
+
+lemma cfrac_lim_diff_le:
+  assumes "\<forall>k\<le>Suc n. cfrac_nth c1 k = cfrac_nth c2 k"
+  assumes "n \<le> cfrac_length c1" "n \<le> cfrac_length c2"
+  shows   "\<bar>cfrac_lim c1 - cfrac_lim c2\<bar> \<le> 2 / (conv_denom c1 n * conv_denom c1 (Suc n))"
+proof -
+  define d where "d = (\<lambda>k. conv_denom c1 k)"
+  have "\<bar>cfrac_lim c1 - cfrac_lim c2\<bar> \<le> \<bar>cfrac_lim c1 - conv c1 n\<bar> + \<bar>cfrac_lim c2 - conv c1 n\<bar>"
+    by linarith
+  also have "\<bar>cfrac_lim c1 - conv c1 n\<bar> \<le> 1 / (d n * d (Suc n))"
+    unfolding d_def using assms
+    by (intro cfrac_lim_minus_conv_upper_bound) auto
+  also have "conv c1 n = conv c2 n"
+    using assms by (intro conv_cong) auto
+  also have "\<bar>cfrac_lim c2 - conv c2 n\<bar> \<le> 1 / (conv_denom c2 n * conv_denom c2 (Suc n))"
+    using assms unfolding d_def by (intro cfrac_lim_minus_conv_upper_bound) auto
+  also have "conv_denom c2 n = d n"
+    unfolding d_def using assms by (intro conv_denom_cong) auto
+  also have "conv_denom c2 (Suc n) = d (Suc n)"
+    unfolding d_def using assms by (intro conv_denom_cong) auto
+  also have "1 / (d n * d (Suc n)) + 1 / (d n * d (Suc n)) = 2 / (d n * d (Suc n))"
+    by simp
+  finally show ?thesis
+    by (simp add: d_def)
+qed
+
+lemma of_int_leI: "n \<le> m \<Longrightarrow> (of_int n :: 'a :: linordered_idom) \<le> of_int m"
+  by simp
+
+lemma cfrac_lim_diff_le':
+  assumes "\<forall>k\<le>Suc n. cfrac_nth c1 k = cfrac_nth c2 k"
+  assumes "n \<le> cfrac_length c1" "n \<le> cfrac_length c2"
+  shows   "\<bar>cfrac_lim c1 - cfrac_lim c2\<bar> \<le> 2 / (fib (n+1) * fib (n+2))"
+proof -
+  have "\<bar>cfrac_lim c1 - cfrac_lim c2\<bar> \<le> 2 / (conv_denom c1 n * conv_denom c1 (Suc n))"
+    by (rule cfrac_lim_diff_le) (use assms in auto)
+  also have "\<dots> \<le> 2 / (int (fib (Suc n)) * int (fib (Suc (Suc n))))"
+    unfolding of_nat_mult of_int_mult
+    by (intro divide_left_mono mult_mono mult_pos_pos of_int_leI conv_denom_lower_bound)
+       (auto intro!: fib_neq_0_nat simp del: fib.simps)
+  also have "\<dots> = 2 / (fib (n+1) * fib (n+2))"
+    by simp
+  finally show ?thesis .
+qed
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/E_CFrac.thy b/thys/Continued_Fractions/E_CFrac.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/E_CFrac.thy
@@ -0,0 +1,369 @@
+(*
+  File:     Continued_Fractions/E_CFrac.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>The continued fraction expansion of $e$\<close>
+theory E_CFrac
+imports
+  "HOL-Analysis.Analysis"
+  "Continued_Fractions"
+  "Quadratic_Irrationals"
+begin
+
+lemma fact_real_at_top: "filterlim (fact :: nat \<Rightarrow> real) at_top at_top"
+proof (rule filterlim_at_top_mono)
+  have "real n \<le> real (fact n)" for n
+    unfolding of_nat_le_iff by (rule fact_ge_self)
+  thus "eventually (\<lambda>n. real n \<le> fact n) at_top" by simp
+qed (fact filterlim_real_sequentially)
+
+lemma filterlim_div_nat_at_top:
+  assumes "filterlim f at_top F" "m > 0"
+  shows   "filterlim (\<lambda>x. f x div m :: nat) at_top F"
+  unfolding filterlim_at_top
+proof
+  fix C :: nat
+  from assms(1) have "eventually (\<lambda>x. f x \<ge> C * m) F"
+    by (auto simp: filterlim_at_top)
+  thus "eventually (\<lambda>x. f x div m \<ge> C) F"
+  proof eventually_elim
+    case (elim x)
+    hence "(C * m) div m \<le> f x div m"
+      by (intro div_le_mono)
+    thus ?case using \<open>m > 0\<close> by simp
+  qed
+qed
+
+text \<open>
+  The continued fraction expansion of $e$ has the form
+  $[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, \ldots]$:
+\<close>
+definition e_cfrac where
+  "e_cfrac = cfrac (\<lambda>n. if n = 0 then 2 else if n mod 3 = 2 then 2 * (Suc n div 3) else 1)"
+
+lemma cfrac_nth_e:
+  "cfrac_nth e_cfrac n = (if n = 0 then 2 else if n mod 3 = 2 then 2 * (Suc n div 3) else 1)"
+  unfolding e_cfrac_def by (subst cfrac_nth_cfrac) (auto simp: is_cfrac_def)
+
+lemma cfrac_length_e [simp]: "cfrac_length e_cfrac = \<infinity>"
+  by (simp add: e_cfrac_def)
+
+
+text \<open>
+  The formalised proof follows the one from Proof Wiki~\cite{proofwiki}.
+\<close>
+
+context
+  fixes A B C :: "nat \<Rightarrow> real" and p q :: "nat \<Rightarrow> int" and a :: "nat \<Rightarrow> int"
+  defines "A \<equiv> (\<lambda>n. integral {0..1} (\<lambda>x. exp x * x ^ n * (x - 1) ^ n / fact n))"
+      and "B \<equiv> (\<lambda>n. integral {0..1} (\<lambda>x. exp x * x ^ Suc n * (x - 1) ^ n / fact n))"
+      and "C \<equiv> (\<lambda>n. integral {0..1} (\<lambda>x. exp x * x ^ n * (x - 1) ^ Suc n / fact n))"
+      and "p \<equiv> (\<lambda>n. if n \<le> 1 then 1 else conv_num e_cfrac (n - 2))"
+      and "q \<equiv> (\<lambda>n. if n = 0 then 1 else if n = 1 then 0 else conv_denom e_cfrac (n - 2))"
+      and "a \<equiv> (\<lambda>n. if n mod 3 = 2 then 2 * (Suc n div 3) else 1)"
+begin
+
+lemma
+  assumes "n \<ge> 2"
+  shows   p_rec: "p n = a (n - 2) * p (n - 1) + p (n - 2)" (is ?th1)
+    and   q_rec: "q n = a (n - 2) * q (n - 1) + q (n - 2)" (is ?th2)
+proof -
+  have n_minus_3: "n - 3 = n - Suc (Suc (Suc 0))"
+    by (simp add: numeral_3_eq_3)
+  consider "n = 2" | "n = 3" | "n \<ge> 4"
+    using assms by force
+  hence "?th1 \<and> ?th2"
+    by cases (auto simp: p_def q_def cfrac_nth_e a_def conv_num_rec conv_denom_rec n_minus_3)
+  thus ?th1 ?th2 by blast+
+qed
+
+lemma
+  assumes "n \<ge> 1"
+  shows   p_rec0: "p (3 * n) = p (3 * n - 1) + p (3 * n - 2)"
+    and   q_rec0: "q (3 * n) = q (3 * n - 1) + q (3 * n - 2)"
+proof -
+  define n' where "n' = n - 1"
+  from assms have "(3 * n' + 1) mod 3 \<noteq> 2"
+    by presburger
+  also have "(3 * n' + 1) = 3 * n - 2"
+    using assms by (simp add: n'_def)
+  finally show "p (3 * n) = p (3 * n - 1) + p (3 * n - 2)"
+               "q (3 * n) = q (3 * n - 1) + q (3 * n - 2)"
+    using assms by (subst p_rec q_rec; simp add: a_def)+
+qed
+
+lemma
+  assumes "n \<ge> 1"
+  shows   p_rec1: "p (3 * n + 1) = 2 * int n * p (3 * n) + p (3 * n - 1)"
+    and   q_rec1: "q (3 * n + 1) = 2 * int n * q (3 * n) + q (3 * n - 1)"
+proof -
+  define n' where "n' = n - 1"
+  from assms have "(3 * n' + 2) mod 3 = 2"
+    by presburger
+  also have "(3 * n' + 2) = 3 * n - 1"
+    using assms by (simp add: n'_def)
+  finally show "p (3 * n + 1) = 2 * int n * p (3 * n) + p (3 * n - 1)"
+               "q (3 * n + 1) = 2 * int n * q (3 * n) + q (3 * n - 1)"
+    using assms by (subst p_rec q_rec; simp add: a_def)+
+qed
+
+lemma p_rec2: "p (3 * n + 2) = p (3 * n + 1) + p (3 * n)"
+  and q_rec2: "q (3 * n + 2) = q (3 * n + 1) + q (3 * n)"
+  by (subst p_rec q_rec; simp add: a_def nat_mult_distrib nat_add_distrib)+
+
+lemma A_0: "A 0 = exp 1 - 1" and B_0: "B 0 = 1" and C_0: "C 0 = 2 - exp 1"
+proof -
+  have "(exp has_integral (exp 1 - exp 0)) {0..1::real}"
+    by (intro fundamental_theorem_of_calculus)
+       (auto intro!: derivative_eq_intros 
+             simp flip: has_real_derivative_iff_has_vector_derivative)
+  thus "A 0 = exp 1 - 1" by (simp add: A_def has_integral_iff)
+
+  have "((\<lambda>x. exp x * x) has_integral (exp 1 * (1 - 1) - exp 0 * (0 - 1))) {0..1::real}"
+    by (intro fundamental_theorem_of_calculus)
+       (auto intro!: derivative_eq_intros 
+             simp flip: has_real_derivative_iff_has_vector_derivative simp: algebra_simps)
+  thus "B 0 = 1" by (simp add: B_def has_integral_iff)
+
+  have "((\<lambda>x. exp x * (x - 1)) has_integral (exp 1 * (1 - 2) - exp 0 * (0 - 2))) {0..1::real}"
+    by (intro fundamental_theorem_of_calculus)
+       (auto intro!: derivative_eq_intros 
+             simp flip: has_real_derivative_iff_has_vector_derivative simp: algebra_simps)
+  thus "C 0 = 2 - exp 1" by (simp add: C_def has_integral_iff)
+qed
+
+lemma A_bound: "norm (A n) \<le> exp 1 / fact n"
+proof -
+  have "norm (exp t * t ^ n * (t - 1) ^ n / fact n) \<le> exp 1 * 1 ^ n * 1 ^ n / fact n" 
+    if "t \<in> {0..1}" for t :: real using that unfolding norm_mult norm_divide norm_power norm_fact
+    by (intro mult_mono divide_right_mono power_mono) auto
+  hence "norm (A n) \<le> exp 1 / fact n * (1 - 0)"
+    unfolding A_def by (intro integral_bound) (auto intro!: continuous_intros)
+  thus ?thesis by simp
+qed
+
+lemma B_bound: "norm (B n) \<le> exp 1 / fact n"
+proof -
+  have "norm (exp t * t ^ Suc n * (t - 1) ^ n / fact n) \<le> exp 1 * 1 ^ Suc n * 1 ^ n / fact n" 
+    if "t \<in> {0..1}" for t :: real using that unfolding norm_mult norm_divide norm_power norm_fact
+    by (intro mult_mono divide_right_mono power_mono) auto
+  hence "norm (B n) \<le> exp 1 / fact n * (1 - 0)"
+    unfolding B_def by (intro integral_bound) (auto intro!: continuous_intros)
+  thus ?thesis by simp
+qed
+
+lemma C_bound: "norm (C n) \<le> exp 1 / fact n"
+proof -
+  have "norm (exp t * t ^ n * (t - 1) ^ Suc n / fact n) \<le> exp 1 * 1 ^ n * 1 ^ Suc n / fact n" 
+    if "t \<in> {0..1}" for t :: real using that unfolding norm_mult norm_divide norm_power norm_fact
+    by (intro mult_mono divide_right_mono power_mono) auto
+  hence "norm (C n) \<le> exp 1 / fact n * (1 - 0)"
+    unfolding C_def by (intro integral_bound) (auto intro!: continuous_intros)
+  thus ?thesis by simp
+qed
+
+lemma A_Suc: "A (Suc n) = -B n - C n"
+proof -
+  let ?g = "\<lambda>x. x ^ Suc n * (x - 1) ^ Suc n * exp x / fact (Suc n)"
+  have pos: "fact n + real n * fact n > 0" by (intro add_pos_nonneg) auto
+  have "A (Suc n) + B n + C n =
+          integral {0..1} (\<lambda>x. exp x * x ^ Suc n * (x - 1) ^ Suc n / fact (Suc n) +
+             exp x * x ^ Suc n * (x - 1) ^ n / fact n + exp x * x ^ n * (x - 1) ^ Suc n / fact n)"
+    unfolding A_def B_def C_def
+    apply (subst integral_add [symmetric])
+    subgoal
+      by (auto intro!: integrable_continuous_real continuous_intros)
+    subgoal
+      by (auto intro!: integrable_continuous_real continuous_intros)
+    apply (subst integral_add [symmetric])
+      apply (auto intro!: integrable_continuous_real continuous_intros)
+    done
+  also have "\<dots> = integral {0..1} (\<lambda>x. exp x / fact (Suc n) *
+                    (x ^ Suc n * (x - 1) ^ Suc n + Suc n * x ^ Suc n * (x - 1) ^ n + 
+                     Suc n * x ^ n * (x - 1) ^ Suc n))"
+    (is "_ = integral _ ?f") 
+    apply (simp add: divide_simps)
+    apply (simp add: field_simps)?
+    done
+  also have "(?f has_integral (?g 1 - ?g 0)) {0..1}"
+    apply (intro fundamental_theorem_of_calculus)
+    subgoal
+      by simp
+    unfolding has_real_derivative_iff_has_vector_derivative [symmetric]
+    apply (rule derivative_eq_intros refl | simp)+
+    apply (simp add: algebra_simps)?
+    done
+  hence "integral {0..1} ?f = 0"
+    by (simp add: has_integral_iff)
+  finally show ?thesis by simp
+qed
+
+lemma B_Suc: "B (Suc n) = -2 * Suc n * A (Suc n) + C n"
+proof -
+  let ?g = "\<lambda>x. x ^ Suc n * (x - 1) ^ (n+2) * exp x / fact (Suc n)"
+  have pos: "fact n + real n * fact n > 0" by (intro add_pos_nonneg) auto
+  have "B (Suc n) + 2 * Suc n * A (Suc n) - C n =
+          integral {0..1} (\<lambda>x. exp x * x^(n+2) * (x - 1)^(n+1) / fact (Suc n) + 2 * Suc n *
+             exp x * x ^ Suc n * (x - 1) ^ Suc n / fact (Suc n) - exp x * x ^ n * (x - 1) ^ Suc n / fact n)"
+    unfolding A_def B_def C_def integral_mult_right [symmetric]
+    apply (subst integral_add [symmetric])
+    subgoal
+      by (auto intro!: integrable_continuous_real continuous_intros)
+    subgoal
+      by (auto intro!: integrable_continuous_real continuous_intros)
+    apply (subst integral_diff [symmetric])
+      apply (auto intro!: integrable_continuous_real continuous_intros simp: mult_ac)
+    done
+  also have "\<dots> = integral {0..1} (\<lambda>x. exp x / fact (Suc n) *
+                    (x^(n+2) * (x - 1)^(n+1) + 2 * Suc n * x ^ Suc n * (x - 1) ^ Suc n - 
+                     Suc n * x ^ n * (x - 1) ^ Suc n))"
+    (is "_ = integral _ ?f") 
+    apply (simp add: divide_simps)
+    apply (simp add: field_simps)?
+    done
+  also have "(?f has_integral (?g 1 - ?g 0)) {0..1}"
+    apply (intro fundamental_theorem_of_calculus)
+     apply (simp; fail)
+    unfolding has_real_derivative_iff_has_vector_derivative [symmetric]
+    apply (rule derivative_eq_intros refl | simp)+
+    apply (simp add: algebra_simps)?
+    done
+  hence "integral {0..1} ?f = 0"
+    by (simp add: has_integral_iff)
+  finally show ?thesis by (simp add: algebra_simps)
+qed
+
+lemma C_Suc: "C n = B n - A n"
+  unfolding A_def B_def C_def
+  by (subst integral_diff [symmetric])
+     (auto intro!: integrable_continuous_real continuous_intros simp: field_simps)
+
+lemma unfold_add_numeral: "c * n + numeral b = Suc (c * n + pred_numeral b)"
+  by simp
+
+lemma ABC:
+  "A n = q (3 * n) * exp 1 - p (3 * n) \<and>
+   B n = p (Suc (3 * n)) - q (Suc (3 * n)) * exp 1 \<and>
+   C n = p (Suc (Suc (3 * n))) - q (Suc (Suc (3 * n))) * exp 1"
+proof (induction n)
+  case 0
+  thus ?case by (simp add: A_0 B_0 C_0 a_def p_def q_def cfrac_nth_e)
+next
+  case (Suc n)
+  note [simp] =
+    conjunct1[OF Suc.IH] conjunct1[OF conjunct2[OF Suc.IH]] conjunct2[OF conjunct2[OF Suc.IH]]
+  have [simp]: "3 + m = Suc (Suc (Suc m))" for m by simp
+  
+  have A': "A (Suc n) = of_int (q (3 * Suc n)) * exp 1 - of_int (p (3 * Suc n))"
+    unfolding A_Suc
+    by (subst p_rec0 q_rec0, simp)+ (auto simp: algebra_simps)
+  have B': "B (Suc n) = of_int (p (3 * Suc n + 1)) - of_int (q (3 * Suc n + 1)) * exp 1"
+    unfolding B_Suc
+    by (subst p_rec1 q_rec1 p_rec0 q_rec0, simp)+ (auto simp: algebra_simps A_Suc)
+  have C': "C (Suc n) = of_int (p (3*Suc n+2)) - of_int (q (3*Suc n+2)) * exp 1"
+    unfolding A_Suc B_Suc C_Suc using p_rec2[of n] q_rec2[of n]
+    by ((subst p_rec2 q_rec2)+, (subst p_rec0 q_rec0 p_rec1 q_rec1, simp)+)
+       (auto simp: algebra_simps A_Suc B_Suc)
+  from A' B' C' show ?case by simp
+qed
+
+lemma q_pos: "q n > 0" if "n \<noteq> 1"
+  using that by (auto simp: q_def)
+
+lemma conv_diff_exp_bound: "norm (exp 1 - p n / q n) \<le> exp 1 / fact (n div 3)"
+proof (cases "n = 1")
+  case False
+  define n' where "n' = n div 3"
+  consider "n mod 3 = 0" | "n mod 3 = 1" | "n mod 3 = 2"
+    by force
+  hence diff [unfolded n'_def]: "q n * exp 1 - p n =
+    (if n mod 3 = 0 then A n' else if n mod 3 = 1 then -B n' else -C n')"
+  proof cases
+    assume "n mod 3 = 0"
+    hence "3 * n' = n" unfolding n'_def by presburger
+    with ABC[of n'] show ?thesis by auto
+  next
+    assume *: "n mod 3 = 1"
+    hence "Suc (3 * n') = n" unfolding n'_def by presburger
+    with * ABC[of n'] show ?thesis by auto
+  next
+    assume *: "n mod 3 = 2"
+    hence "Suc (Suc (3 * n')) = n" unfolding n'_def by presburger
+    with * ABC[of n'] show ?thesis by auto
+  qed
+
+  note [[linarith_split_limit = 0]]
+  have "norm ((q n * exp 1 - p n) / q n) \<le> exp 1 / fact (n div 3) / 1" unfolding diff norm_divide 
+    using A_bound[of "n div 3"] B_bound[of "n div 3"] C_bound[of "n div 3"] q_pos[OF \<open>n \<noteq> 1\<close>]
+    by (subst frac_le) (auto simp: of_nat_ge_1_iff)
+  also have "(q n * exp 1 - p n) / q n = exp 1 - p n / q n"
+    using q_pos[OF \<open>n \<noteq> 1\<close>] by (simp add: divide_simps)
+  finally show ?thesis by simp
+qed (auto simp: p_def q_def)
+
+theorem e_cfrac: "cfrac_lim e_cfrac = exp 1"
+proof -
+  have num: "conv_num e_cfrac n = p (n + 2)"
+   and denom: "conv_denom e_cfrac n = q (n + 2)" for n
+    by (simp_all add: p_def q_def)
+
+  have "(\<lambda>n. exp 1 - p n / q n) \<longlonglongrightarrow> 0"
+  proof (rule Lim_null_comparison)
+    show "eventually (\<lambda>n. norm (exp 1 - p n / q n) \<le> exp 1 / fact (n div 3)) at_top"
+      using conv_diff_exp_bound by (intro always_eventually) auto
+    show "(\<lambda>n. exp 1 / fact (n div 3) :: real) \<longlonglongrightarrow> 0"
+      by (rule real_tendsto_divide_at_top tendsto_const filterlim_div_nat_at_top
+               filterlim_ident filterlim_compose[OF fact_real_at_top])+ auto
+  qed
+  moreover have "eventually (\<lambda>n. exp 1 - p n / q n = exp 1 - conv e_cfrac (n - 2)) at_top"
+    using eventually_ge_at_top[of 2]
+  proof eventually_elim
+    case (elim n)
+    with num[of "n - 2"] denom[of "n - 2"] wf show ?case
+      by (simp add: eval_nat_numeral Suc_diff_Suc conv_num_denom)
+  qed
+  ultimately have "(\<lambda>n. exp 1 - conv e_cfrac (n - 2)) \<longlonglongrightarrow> 0"
+    using Lim_transform_eventually by fast
+  hence "(\<lambda>n. exp 1 - (exp 1 - conv e_cfrac (Suc (Suc n) - 2))) \<longlonglongrightarrow> exp 1 - 0"
+    by (subst filterlim_sequentially_Suc)+ (intro tendsto_diff tendsto_const)
+  hence "conv e_cfrac \<longlonglongrightarrow> exp 1" by simp
+  moreover have "conv e_cfrac \<longlonglongrightarrow> cfrac_lim e_cfrac"
+    by (intro LIMSEQ_cfrac_lim wf) auto
+  ultimately have "exp 1 = cfrac_lim e_cfrac"
+    by (rule LIMSEQ_unique)
+  thus ?thesis ..
+qed
+
+corollary e_cfrac_altdef: "e_cfrac = cfrac_of_real (exp 1)"
+  by (metis e_cfrac cfrac_infinite_iff cfrac_length_e cfrac_of_real_cfrac_lim_irrational)
+
+text \<open>
+  This also provides us with a nice proof that $e$ is not rational and not a quadratic irrational
+  either.
+\<close>
+corollary exp1_irrational: "(exp 1 :: real) \<notin> \<rat>"
+  by (metis cfrac_length_e e_cfrac cfrac_infinite_iff)
+
+corollary exp1_not_quadratic_irrational: "\<not>quadratic_irrational (exp 1 :: real)"
+proof -
+  have "range (\<lambda>n. 2 * (int n + 1)) \<subseteq> range (cfrac_nth e_cfrac)"
+  proof safe
+    fix n :: nat
+    have "cfrac_nth e_cfrac (3*n+2) \<in> range (cfrac_nth e_cfrac)"
+      by blast
+    also have "(3 * n + 2) mod 3 = 2"
+      by presburger
+    hence "cfrac_nth e_cfrac (3*n+2) = 2 * (int n + 1)"
+      by (simp add: cfrac_nth_e)
+    finally show "2 * (int n + 1) \<in> range (cfrac_nth e_cfrac)" .
+  qed
+  moreover have "infinite (range (\<lambda>n. 2 * (int n + 1)))"
+    by (subst finite_image_iff) (auto intro!: injI)
+  ultimately have "infinite (range (cfrac_nth e_cfrac))"
+    using finite_subset by blast
+  thus ?thesis using quadratic_irrational_cfrac_nth_range_finite[of e_cfrac]
+    by (auto simp: e_cfrac)
+qed
+      
+end
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/Pell_Continued_Fraction.thy b/thys/Continued_Fractions/Pell_Continued_Fraction.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Pell_Continued_Fraction.thy
@@ -0,0 +1,421 @@
+(*
+  File:     Continued_Fractions/Pell_Continued_Fraction.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>The Connection between the continued fraction expansion of square roots and Pell's equation\<close>
+theory Pell_Continued_Fraction
+imports
+  Sqrt_Nat_Cfrac
+  Pell.Pell_Algorithm
+  Polynomial_Factorization.Prime_Factorization  
+  Pell_Lifting
+begin
+
+lemma irrational_times_int_eq_intD:
+  assumes "p * real_of_int a = real_of_int b"
+  assumes "p \<notin> \<rat>"
+  shows   "a = 0 \<and> b = 0"
+proof -
+  have "a = 0"
+  proof (rule ccontr)
+    assume "a \<noteq> 0"
+    with assms(1) have "p = b / a" by (auto simp: field_simps)
+    also have "\<dots> \<in> \<rat>" by auto
+    finally show False using assms(2) by contradiction
+  qed
+  with assms show ?thesis by simp
+qed
+
+
+text \<open>
+  The solutions to Pell's equation for some non-square \<open>D\<close> are linked to the continued
+  fraction expansion of $\sqrt{D}$, which we shall show here.  
+\<close>
+
+context
+  fixes D :: nat and c h k P Q l
+  assumes nonsquare: "\<not>is_square D"
+  defines "c \<equiv> cfrac_of_real (sqrt D)"
+  defines "h \<equiv> conv_num c" and "k \<equiv> conv_denom c"
+  defines "P \<equiv> fst \<circ> sqrt_remainder_surd D" and "Q \<equiv> snd \<circ> sqrt_remainder_surd D"
+  defines "l \<equiv> sqrt_nat_period_length D"
+begin
+
+interpretation pell D
+  by unfold_locales fact+
+
+lemma cfrac_length_infinite [simp]: "cfrac_length c = \<infinity>"
+proof -
+  have "sqrt D \<notin> \<rat>"
+    using nonsquare by (simp add: irrat_sqrt_nonsquare)
+  thus ?thesis
+    by (simp add: c_def)
+qed
+
+lemma conv_num_denom_pell:
+  "h 0 ^ 2 - D * k 0 ^ 2 < 0"
+  "m > 0 \<Longrightarrow> h m ^ 2 - D * k m ^ 2 = (-1) ^ Suc m * Q m"
+proof -
+  define D' where "D' = Discrete.sqrt D"
+  have "h 0 ^ 2 - D * k 0 ^ 2 = int (D' ^ 2) - int D"
+    by (simp_all add: h_def k_def c_def Discrete_sqrt_altdef D'_def)
+  also {
+    have "int (D' ^ 2) - int D \<le> 0"
+      using Discrete.sqrt_power2_le[of D] by (simp add: D'_def)
+    moreover have "D \<noteq> D' ^ 2" using nonsquare by auto
+    ultimately have "int (D' ^ 2) - int D < 0" by linarith
+  }
+  finally show "h 0 ^ 2 - D * k 0 ^ 2 < 0" .
+next
+  assume "m > 0"
+  define n where "n = m - 1"
+  define \<alpha> where "\<alpha> = cfrac_remainder c"
+  define \<alpha>' where "\<alpha>' = sqrt_remainder_surd D"
+  have m: "m = Suc n" using \<open>m > 0\<close> by (simp add: n_def)
+  from nonsquare have "D > 1"
+    by (cases D) (auto intro!: Nat.gr0I)
+  from nonsquare have irrat: "sqrt D \<notin> \<rat>"
+    using irrat_sqrt_nonsquare by blast
+  have [simp]: "cfrac_lim c = sqrt D"
+    using irrat \<open>D > 1\<close> by (simp add: c_def)
+  have \<alpha>_pos: "\<alpha> n > 0" for n
+    unfolding \<alpha>_def using wf \<open>D > 1\<close> cfrac_remainder_pos[of c n]
+    by (cases "n = 0") auto
+  have \<alpha>': "\<alpha>' n = (P n, Q n)" for n by (simp add: \<alpha>'_def P_def Q_def)
+  have Q_pos: "Q n > 0" for n
+    using snd_sqrt_remainder_surd_pos[OF nonsquare] by (simp add: Q_def)
+  have k_pos: "k n > 0" for n
+    by (auto simp: k_def intro!: conv_denom_pos)
+  have k_nonneg: "k n \<ge> 0" for n
+    by (auto simp: k_def intro!: conv_denom_nonneg)
+
+  let ?A = "(sqrt D + P (n + 1)) * h (n + 1) + Q (n + 1) * h n"
+  let ?B = "(sqrt D + P (n + 1)) * k (n + 1) + Q (n + 1) * k n"
+  have "?B > 0" using k_pos Q_pos k_nonneg
+    by (intro add_nonneg_pos mult_nonneg_nonneg add_nonneg_nonneg) auto
+  
+  have "sqrt D = conv' c (Suc (Suc n)) (\<alpha> (Suc (Suc n)))"
+    unfolding \<alpha>_def by (subst conv'_cfrac_remainder) auto
+  also have "\<dots> = (\<alpha> (n + 2) * h (n + 1) + h n) / (\<alpha> (n + 2) * k (n + 1) + k n)"
+    using wf \<alpha>_pos by (subst conv'_num_denom) (simp_all add: h_def k_def)
+  also have "\<alpha> (n + 2) = surd_to_real D (\<alpha>' (Suc n))"
+    using surd_to_real_sqrt_remainder_surd[OF nonsquare, of "Suc n"]
+    by (simp add: \<alpha>'_def \<alpha>_def c_def)
+  also have "\<dots> = (sqrt D + P (Suc n)) / Q (Suc n)" (is "_ = ?\<alpha>")
+    by (simp add: \<alpha>' surd_to_real_def)
+  also have "?\<alpha> * h (n + 1) + h n =
+               1 / Q (n + 1) * ((sqrt D + P (n + 1)) * h (n + 1) + Q (n + 1) * h n)"
+    using Q_pos by (simp add: field_simps)
+  also have "?\<alpha> * k (n + 1) + k n =
+               1 / Q (n + 1) * ((sqrt D + P (n + 1)) * k (n + 1) + Q (n + 1) * k n)"
+    (is "_ = ?f k") using Q_pos by (simp add: field_simps)
+  also have "?f h / ?f k = ((sqrt D + P (n + 1)) * h (n + 1) + Q (n + 1) * h n) /
+                             ((sqrt D + P (n + 1)) * k (n + 1) + Q (n + 1) * k n)"
+    (is "_ = ?A / ?B") using Q_pos by (intro mult_divide_mult_cancel_left) auto
+  finally have "sqrt D * ?B = ?A"
+    using \<open>?B > 0\<close> by (simp add: divide_simps)
+  moreover have "sqrt D * sqrt D = D" by simp
+  ultimately have "sqrt D * (P (n + 1) * k (n + 1) + Q (n + 1) * k n - h (n + 1)) =
+         P (n + 1) * h (n + 1) + Q (n + 1) * h n - k (n + 1) * D"
+    unfolding of_int_add of_int_mult of_int_diff of_int_of_nat_eq of_nat_mult of_nat_add
+    by Groebner_Basis.algebra
+  from irrational_times_int_eq_intD[OF this] irrat
+    have 1: "h (Suc n) = P (Suc n) * k (Suc n) + Q (Suc n) * k n"
+     and 2: "D * k (Suc n) = P (Suc n) * h (Suc n) + Q (Suc n) * h n"
+      by (simp_all del: of_nat_add of_nat_mult)
+
+  have "h (Suc n) * h (Suc n) - D * k (Suc n) * k (Suc n) =
+          Q (Suc n) * (k n * h (Suc n) - k (Suc n) * h n)"
+    by (subst 1, subst 2) (simp add: algebra_simps)
+  also have "k n * h (Suc n) - k (Suc n) * h n = (-1) ^ n"
+    unfolding h_def k_def by (rule conv_num_denom_prod_diff)
+  finally have "h (Suc n) ^ 2 - D * k (Suc n) ^ 2 = (-1) ^ n * Q (Suc n)"
+    by (simp add: power2_eq_square algebra_simps)
+  thus "h m ^ 2 - D * k m ^ 2 = (-1) ^ Suc m * Q m"
+    by (simp add: m)
+qed
+
+text \<open>
+  Every non-trivial solution to Pell's equation is a convergent in the expansion of $\sqrt{D}$:
+\<close>
+theorem pell_solution_is_conv:
+  assumes "x\<^sup>2 = Suc (D * y\<^sup>2)" and "y > 0"
+  shows   "(int x, int y) \<in> range (\<lambda>n. (conv_num c n, conv_denom c n))"
+proof -
+  have "\<exists>n. enat n \<le> cfrac_length c \<and> (int x, int y) = (conv_num c n, conv_denom c n)"
+  proof (rule frac_is_convergentI)
+    have "gcd (x\<^sup>2) (y\<^sup>2) = 1" unfolding assms(1)
+      using gcd_add_mult[of "y\<^sup>2" D 1] by (simp add: gcd.commute)
+    thus "coprime (int x) (int y)"
+      by (simp add: coprime_iff_gcd_eq_1)
+  next
+    from assms have "D > 1"
+      using nonsquare by (cases D) (auto intro!: Nat.gr0I)
+    hence pos: "x + y * sqrt D > 0" using assms
+      by (intro add_nonneg_pos) auto
+  
+    from assms have "real (x\<^sup>2) = real (Suc (D * y\<^sup>2))"
+      by (simp only: of_nat_eq_iff)
+    hence "1 = real x ^ 2 - D * real y ^ 2"
+      unfolding of_nat_power by simp
+    also have "\<dots> = (x - y * sqrt D) * (x + y * sqrt D)"
+      by (simp add: field_simps power2_eq_square)
+    finally have *: "x - y * sqrt D = 1 / (x + y * sqrt D)"
+      using pos by (simp add: field_simps)
+  
+    from pos have "0 < 1 / (x + y * sqrt D)"
+      by (intro divide_pos_pos) auto
+    also have "\<dots> = x - y * sqrt D" by (rule * [symmetric])
+    finally have less: "y * sqrt D < x" by simp
+  
+    have "sqrt D - x / y = -((x - y * sqrt D) / y)"
+      using \<open>y > 0\<close> by (simp add: field_simps)
+    also have "\<bar>\<dots>\<bar> = (x - y * sqrt D) / y"
+      using less by simp
+    also have "(x - y * sqrt D) / y = 1 / (y * (x + y * sqrt D))"
+      using \<open>y > 0\<close> by (subst *) auto
+    also have "\<dots> \<le> 1 / (y * (y * sqrt D + y * sqrt D))"
+      using \<open>y > 0\<close> \<open>D > 1\<close> pos less
+      by (intro divide_left_mono mult_left_mono add_right_mono mult_pos_pos) auto
+    also have "\<dots> = 1 / (2 * y\<^sup>2 * sqrt D)"
+      by (simp add: power2_eq_square)
+    also have "\<dots> < 1 / (real (2 * y\<^sup>2) * 1)" using \<open>y > 0\<close> \<open>D > 1\<close>
+      by (intro divide_strict_left_mono mult_strict_left_mono mult_pos_pos) auto
+    finally show "\<bar>cfrac_lim c - int x / int y\<bar> < 1 / (2 * int y ^ 2)"
+      unfolding c_def using irrat_sqrt_nonsquare[of D] \<open>\<not>is_square D\<close> by simp
+  qed (insert assms irrat_sqrt_nonsquare[of D], auto simp: c_def)
+  thus ?thesis by auto
+qed
+
+text \<open>
+  Let \<open>l\<close> be the length of the period in the continued fraction expansion of $\sqrt{D}$ and let
+  $h_i$ and $k_i$ be the numerator and denominator of the \<open>i\<close>-th convergent.
+
+  Then the non-trivial solutions of Pell's equation are exactly the pairs of the form
+  $(h_{lm -1}, k_{lm-1})$ for any \<open>m\<close> such that $lm$ is even.
+\<close>
+lemma nontriv_solution_iff_conv_num_denom:
+  "nontriv_solution (x, y) \<longleftrightarrow>
+     (\<exists>m>0. int x = h (l * m - 1) \<and> int y = k (l * m - 1) \<and> even (l * m))"
+proof safe
+  fix m assume xy: "x = h (l * m - 1)" "y = k (l * m - 1)" 
+           and lm: "even (l * m)" and m: "m > 0"
+  have l: "l > 0" using period_nonempty[OF nonsquare] by (auto simp: l_def)
+  from lm have "l * m \<noteq> 1" by (intro notI) auto
+  with l m have lm': "l * m > 1" by (cases "l * m") auto
+
+  have "(h (l * m - 1))\<^sup>2 - D * (k (l * m - 1))\<^sup>2 =
+          (- 1) ^ Suc (l * m - 1) * int (Q (l * m - 1))"
+    using lm' by (intro conv_num_denom_pell) auto
+  also have "(- 1) ^ Suc (l * m - 1) = (1 :: int)"
+    using lm l m by (subst neg_one_even_power) auto
+  also have "Q (l * m - 1) = Q ((l * m - 1) mod l)"
+    unfolding Q_def l_def o_def by (subst sqrt_remainder_surd_periodic[OF nonsquare]) simp
+  also {
+    have "l * m - 1 = (m - 1) * l + (l - 1)"
+      using m l lm' by (cases m) (auto simp: mult_ac)
+    also have "\<dots> mod l = (l - 1) mod l"
+      by simp
+    also have "\<dots> = l - 1"
+      using l by (intro mod_less) auto
+    also have "Q \<dots> = 1"
+      using sqrt_remainder_surd_last[OF nonsquare] by (simp add: Q_def l_def)
+    finally have "Q ((l * m - 1) mod l) = 1" .
+  }
+  finally have "h (l * m - 1) ^ 2 =  D * k (l * m - 1) ^ 2 + 1"
+    unfolding of_nat_Suc by (simp add: algebra_simps)
+  hence "h (l * m - 1) ^ 2 = D * k (l * m - 1) ^ 2 + 1"
+    by (simp only: of_nat_eq_iff)
+  moreover have "k (l * m - 1) > 0"
+    unfolding k_def by (intro conv_denom_pos)
+  ultimately have "nontriv_solution (int x, int y)"
+    using xy by (simp add: nontriv_solution_def)
+  thus "nontriv_solution (x, y)"
+    by simp
+next
+  assume "nontriv_solution (x, y)"
+  hence asm: "x ^ 2 = Suc (D * y ^ 2)" "y > 0"
+    by (auto simp: nontriv_solution_def abs_square_eq_1 intro!: Nat.gr0I)
+  from asm have asm': "int x ^ 2 = int D * int y ^ 2 + 1"
+    by (metis add.commute of_nat_Suc of_nat_mult of_nat_power_eq_of_nat_cancel_iff)
+  have l: "l > 0" using period_nonempty[OF nonsquare] by (auto simp: l_def)
+  from pell_solution_is_conv[OF asm] obtain m where
+    xy: "h m = x" "k m = y" by (auto simp: c_def h_def k_def)
+
+  have m: "m > 0"
+    using asm' conv_num_denom_pell(1) xy by (intro Nat.gr0I) auto
+  have "1 = h m ^ 2 - D * k m ^ 2"
+    using asm' xy by simp
+  also have "\<dots> = (- 1) ^ Suc m * int (Q m)"
+    using conv_num_denom_pell(2)[OF m] .
+  finally have *: "(- 1) ^ Suc m * int (Q m) = 1" ..
+  from * have m': "odd m \<and> Q m = 1"
+    by (cases "even m") auto
+
+  define n where "n = Suc m div l"
+  have "l dvd Suc m"
+  proof (rule ccontr)
+    assume *: "\<not>(l dvd Suc m)"
+    have "Q m = Q (m mod l)"
+      unfolding Q_def l_def o_def by (subst sqrt_remainder_surd_periodic[OF nonsquare]) simp  
+    also {
+      have "m mod l < l" using \<open>l > 0\<close> by simp
+      moreover have "Suc (m mod l) \<noteq> l" using * l \<open>m > 0\<close>
+        using mod_Suc[of m l] by auto
+      ultimately have "m mod l < l - 1" by simp
+      hence "Q (m mod l) > 1" unfolding Q_def o_def l_def
+        by (rule snd_sqrt_remainder_surd_gt_1[OF nonsquare])
+    }
+    finally show False using m' by simp
+  qed
+  hence m_eq: "Suc m = n * l" "m = n * l - 1"
+    by (simp_all add: n_def)
+  hence "n > 0" by (auto intro!: Nat.gr0I)
+  thus "\<exists>n>0. int x = h (l * n - 1) \<and> int y = k (l * n - 1) \<and> even (l * n)"
+    using xy m_eq m' by (intro exI[of _ n]) (auto simp: mult_ac)
+qed  
+
+text \<open>
+  Consequently, the fundamental solution is $(h_n, k_n)$ where $n = l - 1$
+  if \<open>l\<close> is even and $n = 2l-1$ otherwise:
+\<close>
+lemma fund_sol_conv_num_denom:
+  defines "n \<equiv> if even l then l - 1 else 2 * l - 1"
+  shows   "fund_sol = (nat (h n), nat (k n))"
+proof (rule fund_sol_eq_sndI)
+  have [simp]: "h n \<ge> 0" "k n \<ge> 0" for n
+    by (auto simp: h_def k_def c_def intro!: conv_num_nonneg)
+  show "nontriv_solution (nat (h n), nat (k n))"
+    by (subst nontriv_solution_iff_conv_num_denom, rule exI[of _ "if even l then 1 else 2"])
+       (simp_all add: n_def mult_ac)
+next
+  fix x y :: nat assume "nontriv_solution (x, y)"
+  then obtain m where m: "m > 0" "x = h (l * m - 1)" "y = k (l * m - 1)" "even (l * m)"
+    by (subst (asm) nontriv_solution_iff_conv_num_denom) auto
+  have l: "l > 0" using period_nonempty[OF nonsquare] by (auto simp: l_def)
+  from m l have "Suc n \<le> l * m" by (auto simp: n_def)
+  hence "n \<le> l * m - 1" by simp
+  hence "k n \<le> k (l * m - 1)"
+    unfolding k_def c_def using irrat_sqrt_nonsquare[OF nonsquare]
+    by (intro conv_denom_leI) auto
+  with m show "nat (k n) \<le> y" by simp
+qed
+
+end
+
+
+text \<open>
+  The following algorithm computes the fundamental solution (or the dummy result \<open>(0, 0)\<close> if
+  \<open>D\<close> is a square) fairly quickly by computing the continued fraction expansion of $\sqrt{D}$
+  and then computing the fundamental solution as the appropriate convergent.
+\<close>
+lemma find_fund_sol_code [code]:
+  "find_fund_sol D =
+     (let info = sqrt_cfrac_info_array D;
+          l = fst info
+      in  if l = 0 then (0, 0) else
+            let
+              c = cfrac_sqrt_nth info;
+              n = if even l then l - 1 else 2 * l - 1
+          in
+            (nat (conv_num_fun c n), nat (conv_denom_fun c n)))"
+proof -
+  have *: "is_cfrac (cfrac_sqrt_nth (sqrt_cfrac_info_array D))" if "\<not>is_square D"
+    using that cfrac_sqrt_nth[of D] unfolding is_cfrac_def
+    by (metis cfrac_nth_nonzero neq0_conv of_nat_0 of_nat_0_less_iff)
+  have **: "cfrac (\<lambda>x. int (cfrac_sqrt_nth (sqrt_cfrac_info_array D) x)) = cfrac_of_real (sqrt D)"
+    if "\<not>is_square D"
+    using that cfrac_sqrt_nth[of D] * by (intro cfrac_eqI) auto
+  show ?thesis using * **
+    by (auto simp: square_test_correct find_fund_sol_correct conv_num_fun_eq conv_denom_fun_eq
+                   Let_def cfrac_sqrt_nth fund_sol_conv_num_denom conv_num_nonneg)
+qed
+
+lemma find_nth_solution_square [simp]: "is_square D \<Longrightarrow> find_nth_solution D n = (0, 0)"
+  by (simp add: find_nth_solution_def)
+
+lemma fst_find_fund_sol_eq_0_iff [simp]: "fst (find_fund_sol D) = 0 \<longleftrightarrow> is_square D"
+proof (cases "is_square D")
+  case False
+  then interpret pell D by unfold_locales
+  from False have "find_fund_sol D = fund_sol" by (simp add: find_fund_sol_correct)
+  moreover from fund_sol_is_nontriv_solution have "fst fund_sol > 0"
+    by (auto simp: nontriv_solution_def intro!: Nat.gr0I)
+  ultimately show ?thesis using False
+    by (simp add: find_fund_sol_def square_test_correct split: if_splits)
+qed (auto simp: find_fund_sol_def square_test_correct)
+
+text \<open>
+  Arbitrary solutions can now be computed as powers of the fundamental solution.
+\<close>
+lemma find_nth_solution_code [code]:
+  "find_nth_solution D n =
+     (let xy = find_fund_sol D
+      in  if fst xy = 0 then (0, 0) else efficient_pell_power D xy n)"
+proof (cases "is_square D")
+  case False
+  then interpret pell D by unfold_locales
+  from fund_sol_is_nontriv_solution have "fst fund_sol > 0"
+    by (auto simp: nontriv_solution_def intro!: Nat.gr0I)
+  thus ?thesis using False
+    by (simp add: find_nth_solution_correct Let_def nth_solution_def pell_power_def 
+                  pell_mul_commutes[of _ "fund_sol"] find_fund_sol_correct)
+qed auto
+
+lemma nth_solution_code [code]:
+  "pell.nth_solution D n = 
+     (let info = sqrt_cfrac_info_array D;
+          l = fst info
+      in  if l = 0 then
+             Code.abort (STR ''nth_solution is undefined for perfect square parameter.'')
+               (\<lambda>_. pell.nth_solution D n)
+          else
+            let
+              c = cfrac_sqrt_nth info;
+              m = if even l then l - 1 else 2 * l - 1;
+              fund_sol = (nat (conv_num_fun c m), nat (conv_denom_fun c m))
+            in
+              efficient_pell_power D fund_sol n)"
+proof (cases "is_square D")
+  case False
+  then interpret pell by unfold_locales
+  have *: "is_cfrac (cfrac_sqrt_nth (sqrt_cfrac_info_array D))"
+    using False cfrac_sqrt_nth[of D] unfolding is_cfrac_def
+    by (metis cfrac_nth_nonzero neq0_conv of_nat_0 of_nat_0_less_iff)
+  have **: "cfrac (\<lambda>x. int (cfrac_sqrt_nth (sqrt_cfrac_info_array D) x)) = cfrac_of_real (sqrt D)"
+    using False cfrac_sqrt_nth[of D] * by (intro cfrac_eqI) auto
+
+  from False * ** show ?thesis
+    by (auto simp: Let_def cfrac_sqrt_nth fund_sol_conv_num_denom nth_solution_def
+                   pell_power_def pell_mul_commutes[of _ "(_, _)"]
+                   conv_num_fun_eq conv_denom_fun_eq conv_num_nonneg)
+qed auto
+
+lemma fund_sol_code [code]:
+  "pell.fund_sol D = (let info = sqrt_cfrac_info_array D;
+          l = fst info
+      in  if l = 0 then
+             Code.abort (STR ''fund_sol is undefined for perfect square parameter.'')
+               (\<lambda>_. pell.fund_sol D)
+          else
+            let
+              c = cfrac_sqrt_nth info;
+              n = if even l then l - 1 else 2 * l - 1
+            in
+              (nat (conv_num_fun c n), nat (conv_denom_fun c n)))"
+proof (cases "is_square D")
+  case False
+  then interpret pell by unfold_locales
+  have *: "is_cfrac (cfrac_sqrt_nth (sqrt_cfrac_info_array D))"
+    using False cfrac_sqrt_nth[of D] unfolding is_cfrac_def
+    by (metis cfrac_nth_nonzero neq0_conv of_nat_0 of_nat_0_less_iff)
+  have **: "cfrac (\<lambda>x. int (cfrac_sqrt_nth (sqrt_cfrac_info_array D) x)) = cfrac_of_real (sqrt D)"
+    using False cfrac_sqrt_nth[of D] * by (intro cfrac_eqI) auto
+
+  from False * ** show ?thesis
+    by (auto simp: Let_def cfrac_sqrt_nth fund_sol_conv_num_denom nth_solution_def
+                   pell_power_def pell_mul_commutes[of _ "(_, _)"]
+                   conv_num_fun_eq conv_denom_fun_eq conv_num_nonneg)
+qed auto
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/Pell_Continued_Fraction_Tests.thy b/thys/Continued_Fractions/Pell_Continued_Fraction_Tests.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Pell_Continued_Fraction_Tests.thy
@@ -0,0 +1,98 @@
+(*
+  File:     Continued_Fractions/Pell_Continued_Fraction_Tests.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Tests for Continued Fractions of Square Roots and Pell's Equation\<close>
+theory Pell_Continued_Fraction_Tests
+imports
+  Pell.Efficient_Discrete_Sqrt
+  "HOL-Library.Code_Lazy"
+  "HOL-Library.Code_Target_Numeral"
+  Pell_Continued_Fraction
+  Pell_Lifting
+begin
+
+code_lazy_type stream
+
+(* TODO Move *)
+lemma lnth_code [code]:
+ "lnth xs 0 = (if lnull xs then undefined (0 :: nat) else lhd xs)"
+ "lnth xs (Suc n) = (if lnull xs then undefined (Suc n) else lnth (ltl xs) n)"
+  by (auto simp: lnth.simps split: llist.splits)
+
+value "let c = sqrt_cfrac 1339 in map (cfrac_nth c) [0..<30]"
+
+
+fun arg_max_list where
+  "arg_max_list _ [] = undefined"
+| "arg_max_list f (x # xs) = 
+     foldl (\<lambda>(x, y) x'. let y' = f x' in if y' > y then (x', y') else (x, y)) (x, f x) xs"
+
+
+value [code] "sqrt_cfrac_info 17"
+value [code] "sqrt_cfrac_info 1339"
+value [code] "sqrt_cfrac_info 121"
+value [code] "sqrt_nat_period_length 410286423278424"
+
+text \<open>
+  For which number $D < 100000$ does $\sqrt{D}$ have the longest period?
+\<close>
+value [code] "arg_max_list sqrt_nat_period_length [0..<100000]"
+
+
+subsection \<open>Fundamental solutions of Pell's equation\<close>
+
+value [code] "pell.fund_sol 12"
+value [code] "pell.fund_sol 13"
+value [code] "pell.fund_sol 61"
+value [code] "pell.fund_sol 661"
+value [code] "pell.fund_sol 6661"
+value [code] "pell.fund_sol 4729494"
+
+text \<open>
+  Project Euler problem \#66:
+  For which $D < 1000$ does Pell's equation have the largest fundamental solution?
+\<close>
+
+value [code] "arg_max_list (fst \<circ> find_fund_sol) [0..<1001]"
+
+
+text \<open>
+  The same for $D < 100000$:
+\<close>
+
+value [code] "arg_max_list (fst \<circ> find_fund_sol) [0..<100000]"
+
+
+text \<open>
+  The solution to the next example, which is at the core of Archimedes' cattle problem,
+  is so big that termifying the result takes extremely long.
+  Therefore, we simply compute the number of decimal digits in the result instead.
+\<close>
+
+fun log10_aux :: "nat \<Rightarrow> nat \<Rightarrow> nat" where
+  "log10_aux acc n =
+     (if n \<ge> 10000000000 then log10_aux (acc + 10) (n div 10000000000)
+      else if n = 0 then acc else log10_aux (Suc acc) (n div 10))"
+
+definition log10 where "log10 = log10_aux 0"
+
+value [code] "map_prod log10 log10 (pell.fund_sol 410286423278424)"
+
+text \<open>
+  Factoring out the square factor \<open>9314\<^sup>2\<close> does yield a significant speed-up in this case:
+\<close>
+value [code] "map_prod log10 log10 (find_fund_sol_fast 410286423278424)"
+
+
+subsection \<open>Tests for other operations\<close>
+
+value [code] "pell.nth_solution 13 100"
+value [code] "pell.nth_solution 4729494 3"
+
+value [code] "stake 10 (pell_solutions 13)"
+value [code] "stake 10 (pell_solutions 61)"
+
+value [code] "pell.nth_solution 23 8"
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/Pell_Lifting.thy b/thys/Continued_Fractions/Pell_Lifting.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Pell_Lifting.thy
@@ -0,0 +1,395 @@
+(*
+  File:     Continued_Fractions/Pell_Lifting.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Lifting solutions of Pell's Equation\<close>
+theory Pell_Lifting
+  imports Pell.Pell Pell.Pell_Algorithm
+begin
+
+subsection \<open>Auxiliary material\<close>
+
+(* TODO Move *)
+lemma (in pell) snth_pell_solutions: "snth (pell_solutions D) n = nth_solution n"
+  by (simp add: pell_solutions_def Let_def find_fund_sol_correct nonsquare_D nth_solution_def
+                pell_power_def pell_mul_commutes[of _ fund_sol])
+
+definition square_squarefree_part_nat :: "nat \<Rightarrow> nat \<times> nat" where
+  "square_squarefree_part_nat n = (square_part n, squarefree_part n)"
+
+lemma prime_factorization_squarefree_part:
+  assumes "x \<noteq> 0"
+  shows   "prime_factorization (squarefree_part x) =
+             mset_set {p \<in> prime_factors x. odd (multiplicity p x)}" (is "?lhs = ?rhs")
+proof (rule multiset_eqI)
+  fix p show "count ?lhs p = count ?rhs p"
+  proof (cases "prime p")
+    case False
+    thus ?thesis by (auto simp: count_prime_factorization)
+  next
+    case True
+    have "finite (prime_factors x)" by simp
+    hence "finite {p. p dvd x \<and> prime p}" using assms 
+      by (subst (asm) prime_factors_dvd) (auto simp: conj_commute)
+    hence "finite {p. p dvd x \<and> prime p \<and> odd (multiplicity p x)}"
+      by (rule finite_subset [rotated]) auto
+    moreover have "odd (n :: nat) \<longleftrightarrow> n mod 2 = Suc 0" for n by presburger
+    ultimately show ?thesis using assms
+      by (cases "p dvd x"; cases "even (multiplicity p x)")
+         (auto simp: count_prime_factorization prime_multiplicity_squarefree_part
+                     in_prime_factors_iff not_dvd_imp_multiplicity_0)
+  qed
+qed
+
+lemma squarefree_part_nat:
+  "squarefree_part (n :: nat) = (\<Prod>{p \<in> prime_factors n. odd (multiplicity p n)})"
+proof (cases "n = 0")
+  case False
+  hence "(\<Prod>{p \<in> prime_factors n. odd (multiplicity p n)}) = 
+          prod_mset (prime_factorization (squarefree_part n))"
+    by (subst prime_factorization_squarefree_part) (auto simp: prod_unfold_prod_mset)
+  also have "\<dots> = squarefree_part n"
+    by (intro prod_mset_prime_factorization_nat Nat.gr0I) auto
+  finally show ?thesis ..
+qed auto
+
+lemma prime_factorization_square_part:
+  assumes "x \<noteq> 0"
+  shows   "prime_factorization (square_part x) =
+             (\<Sum>p \<in> prime_factors x. replicate_mset (multiplicity p x div 2) p)" (is "?lhs = ?rhs")
+proof (rule multiset_eqI)
+  fix p show "count ?lhs p = count ?rhs p"
+  proof (cases "prime p \<and> p dvd x")
+    case False
+    thus ?thesis by (auto simp: count_prime_factorization count_sum
+                                prime_multiplicity_square_part not_dvd_imp_multiplicity_0)
+  next
+    case True
+    thus ?thesis using assms
+      by (cases "p dvd x")
+         (auto simp: count_prime_factorization prime_multiplicity_squarefree_part
+                     in_prime_factors_iff count_sum prime_multiplicity_square_part)
+  qed
+qed
+
+lemma prod_mset_sum: "prod_mset (sum f A) = (\<Prod>x\<in>A. prod_mset (f x))"
+  by (induction A rule: infinite_finite_induct) auto
+
+lemma square_part_nat:
+  assumes "n > 0"
+  shows   "square_part (n :: nat) = (\<Prod>p \<in> prime_factors n. p ^ (multiplicity p n div 2))"
+proof -
+  have "(\<Prod>p \<in> prime_factors n. p ^ (multiplicity p n div 2)) = 
+          prod_mset (prime_factorization (square_part n))" using assms
+    by (subst prime_factorization_square_part) (auto simp: prod_unfold_prod_mset prod_mset_sum)
+  also have "\<dots> = square_part n" using assms
+    by (intro prod_mset_prime_factorization_nat Nat.gr0I) auto
+  finally show ?thesis ..
+qed
+
+lemma square_squarefree_part_nat_code [code]:
+  "square_squarefree_part_nat n = (if n = 0 then (0, 1)
+     else let ps = prime_factorization n
+          in  ((\<Prod>p\<in>set_mset ps. p ^ (count ps p div 2)),
+                \<Prod>(Set.filter (\<lambda>p. odd (count ps p)) (set_mset ps))))"
+  by (cases "n = 0")
+     (auto simp: Let_def square_squarefree_part_nat_def squarefree_part_nat Set.filter_def 
+                 count_prime_factorization square_part_nat intro!: prod.cong)
+
+lemma square_part_nat_code [code_unfold]:
+  "square_part (n :: nat) = (if n = 0 then 0
+     else let ps = prime_factorization n in  (\<Prod>p\<in>set_mset ps. p ^ (count ps p div 2)))"
+  using square_squarefree_part_nat_code[of n]
+  by (simp add: square_squarefree_part_nat_def Let_def split: if_splits)
+
+lemma squarefree_part_nat_code [code_unfold]:
+  "squarefree_part (n :: nat) = (if n = 0 then 1
+     else let ps = prime_factorization n in (\<Prod>(Set.filter (\<lambda>p. odd (count ps p)) (set_mset ps))))"
+  using square_squarefree_part_nat_code[of n]
+  by (simp add: square_squarefree_part_nat_def Let_def split: if_splits)
+
+lemma is_nth_power_mult_nth_powerD:
+  assumes "is_nth_power n (a * b ^ n)" "b > 0" "n > 0"
+  shows   "is_nth_power n (a::nat)"
+proof -
+  from assms obtain k where k: "k ^ n = a * b ^ n"
+    by (auto elim: is_nth_powerE)
+  with assms(2,3) have "b dvd k"
+    by (metis dvd_triv_right pow_divides_pow_iff)
+  then obtain l where "k = b * l"
+    by auto
+  with k have "a = l ^ n" using assms(2)
+    by (simp add: power_mult_distrib)
+  thus ?thesis by auto
+qed
+
+lemma (in pell) fund_sol_eq_fstI:
+  assumes "nontriv_solution (x, y)"
+  assumes "\<And>x' y'. nontriv_solution (x', y') \<Longrightarrow> x \<le> x'"
+  shows   "fund_sol = (x, y)"
+proof -
+  have "x = fst fund_sol"
+    using fund_sol_is_nontriv_solution assms(1) fund_sol_minimal''[of "(x, y)"]
+    by (auto intro!: antisym assms(2)[of "fst fund_sol" "snd fund_sol"])
+  moreover from this have "y = snd fund_sol"
+    using assms(1) solutions_linorder_strict[of x y "fst fund_sol" "snd fund_sol"]
+          fund_sol_is_nontriv_solution
+    by (auto simp: nontriv_solution_imp_solution prod_eq_iff)
+  ultimately show ?thesis by simp
+qed
+
+lemma (in pell) fund_sol_eqI_fst':
+  assumes "nontriv_solution xy"
+  assumes "\<And>x' y'. nontriv_solution (x', y') \<Longrightarrow> fst xy \<le> x'"
+  shows   "fund_sol = xy"
+  using fund_sol_eq_fstI[of "fst xy" "snd xy"] assms by simp
+
+lemma (in pell) fund_sol_eq_sndI:
+  assumes "nontriv_solution (x, y)"
+  assumes "\<And>x' y'. nontriv_solution (x', y') \<Longrightarrow> y \<le> y'"
+  shows   "fund_sol = (x, y)"
+proof -
+  have "y = snd fund_sol"
+    using fund_sol_is_nontriv_solution assms(1) fund_sol_minimal''[of "(x, y)"]
+    by (auto intro!: antisym assms(2)[of "fst fund_sol" "snd fund_sol"])
+  moreover from this have "x = fst fund_sol"
+    using assms(1) solutions_linorder_strict[of x y "fst fund_sol" "snd fund_sol"]
+          fund_sol_is_nontriv_solution
+    by (auto simp: nontriv_solution_imp_solution prod_eq_iff)
+  ultimately show ?thesis by simp
+qed
+
+lemma (in pell) fund_sol_eqI_snd':
+  assumes "nontriv_solution xy"
+  assumes "\<And>x' y'. nontriv_solution (x', y') \<Longrightarrow> snd xy \<le> y'"
+  shows   "fund_sol = xy"
+  using fund_sol_eq_sndI[of "fst xy" "snd xy"] assms by simp
+
+
+subsection \<open>The lifting mechanism\<close>
+
+text \<open>
+  The solutions of Pell's equations for parameters \<open>D\<close> and \<open>a\<^sup>2 D\<close> stand in correspondence to
+  one another: every solution \<open>(x, y)\<close> for parameter \<open>D\<close> can be lowered to a solution \<open>(x, ay)\<close>
+  for \<open>a\<^sup>2 D\<close>, and every solution of the form \<open>(x, ay)\<close> for parameter \<open>a\<^sup>2 D\<close> can be lifted to a
+  solution \<open>(x, y)\<close> for parameter \<open>D\<close>.
+\<close>
+
+locale pell_lift = pell +
+  fixes a D' :: nat
+  assumes nz: "a > 0"
+  defines "D' \<equiv> D * a\<^sup>2"
+begin
+
+lemma nonsquare_D': "\<not>is_square D'"
+  using nonsquare_D is_nth_power_mult_nth_powerD[of 2 D a] nz by (auto simp: D'_def)
+
+definition lift_solution :: "nat \<times> nat \<Rightarrow> nat \<times> nat" where
+  "lift_solution = (\<lambda>(x, y). (x, y div a))"
+
+definition lower_solution :: "nat \<times> nat \<Rightarrow> nat \<times> nat" where
+  "lower_solution = (\<lambda>(x, y). (x, y * a))"
+
+definition liftable_solution :: "nat \<times> nat \<Rightarrow> bool" where
+  "liftable_solution = (\<lambda>(x, y). a dvd y)"
+
+sublocale lift: pell D'
+  by unfold_locales (fact nonsquare_D')
+
+lemma lift_solution_iff: "lift.solution xy \<longleftrightarrow> solution (lower_solution xy)"
+  unfolding solution_def lift.solution_def
+  by (auto simp: lower_solution_def D'_def case_prod_unfold power_mult_distrib)
+
+lemma lift_solution:
+  assumes "solution xy" "liftable_solution xy"
+  shows   "lift.solution (lift_solution xy)"
+  using assms unfolding solution_def lift.solution_def
+  by (auto simp: liftable_solution_def lift_solution_def D'_def case_prod_unfold power_mult_distrib
+           elim!: dvdE)
+
+text \<open>
+  In particular, the fundamental solution for \<open>a\<^sup>2 D\<close> is the smallest liftable solution for \<open>D\<close>:
+\<close>
+lemma lift_fund_sol:
+  assumes "\<And>n. 0 < n \<Longrightarrow> n < m \<Longrightarrow> \<not>liftable_solution (nth_solution n)"
+  assumes "liftable_solution (nth_solution m)" "m > 0"
+  shows   "lift.fund_sol = lift_solution (nth_solution m)"
+proof (rule lift.fund_sol_eqI_fst')
+  from assms have "nontriv_solution (nth_solution m)"
+    by (intro nth_solution_sound')
+  hence "lift_solution (nth_solution m) \<noteq> (1, 0)" using nz assms(2)
+    by (auto simp: lift_solution_def case_prod_unfold nontriv_solution_def liftable_solution_def)
+  with assms show "lift.nontriv_solution (lift_solution (nth_solution m))"
+    by (auto simp: lift.nontriv_solution_altdef intro: lift_solution)
+next
+  fix x' y' :: nat
+  assume *: "lift.nontriv_solution (x', y')"
+  hence nz': "x' \<noteq> 1" using nonsquare_D'
+    by (auto simp: lift.nontriv_solution_altdef lift.solution_def)
+  from * have "solution (lower_solution (x', y'))"
+    by (simp add: lift_solution_iff lift.nontriv_solution_altdef)
+  hence "lower_solution (x', y') \<in> range nth_solution" by (rule nth_solution_complete)
+  then obtain n where n: "nth_solution n = lower_solution (x', y')" by auto
+  with nz' have "n > 0" by (auto intro!: Nat.gr0I simp: nth_solution_def lower_solution_def)
+  with n have "liftable_solution (nth_solution n)"
+    by (auto simp: liftable_solution_def lower_solution_def)
+  with \<open>n > 0\<close> and assms(1)[of n] have "n \<ge> m" by (cases "n \<ge> m") auto
+  hence "fst (nth_solution m) \<le> fst (nth_solution n)"
+    using strict_mono_less_eq[OF strict_mono_nth_solution(1)] by simp
+  thus "fst (lift_solution (nth_solution m)) \<le> x'"
+    by (simp add: lift_solution_def lower_solution_def n case_prod_unfold)
+qed
+
+end
+
+
+subsection \<open>Accelerated computation of the fundamental solution for non-squarefree inputs\<close>
+
+text \<open>
+  Solving Pell's equation for some \<open>D\<close> of the form \<open>a\<^sup>2 D'\<close> can be done by solving
+  it for \<open>D'\<close> and then lifting the solution. Thus, if \<open>D\<close> is not squarefree, we can compute
+  its squarefree decomposition \<open>a\<^sup>2 D'\<close> with \<open>D'\<close> squarefree and thus speed up the computation
+  (since \<open>D'\<close> is smaller than \<open>D\<close>).
+
+  The squarefree decomposition can only be computed (according to current knowledge in mathematics)
+  through the prime decomposition. However, given how big the solutions are for even
+  moderate values of \<open>D\<close>, it is usually worth doing it if \<open>D\<close> is not squarefree.
+\<close>
+
+lemma squarefree_part_of_square [simp]:
+  assumes "is_square (x :: 'a :: {factorial_semiring, normalization_semidom_multiplicative})"
+  assumes "x \<noteq> 0"
+  shows   "squarefree_part x = unit_factor x"
+proof -
+  from assms obtain y where [simp]: "x = y ^ 2"
+    by (auto simp: is_nth_power_def)
+  have "unit_factor x * normalize x = squarefree_part x * square_part x ^ 2"
+    by (subst squarefree_decompose [symmetric]) auto
+  also have "\<dots> = squarefree_part x * normalize x"
+    by (simp add: square_part_even_power normalize_power)
+  finally show ?thesis using assms
+    by (subst (asm) mult_cancel_right) auto
+qed
+
+lemma squarefree_part_1_imp_square:
+  assumes "squarefree_part x = 1"
+  shows   "is_square x"
+proof -
+  have "is_square (square_part x ^ 2)"
+    by auto
+  also have "square_part x ^ 2 = squarefree_part x * square_part x ^ 2"
+    using assms by simp
+  also have "\<dots> = x"
+    by (rule squarefree_decompose [symmetric])
+  finally show ?thesis .
+qed  
+
+
+definition find_fund_sol_fast where
+  "find_fund_sol_fast D =
+     (let (a, D') = square_squarefree_part_nat D
+      in
+        if D' = 0 \<or> D' = 1 then (0, 0)
+        else if a = 1 then pell.fund_sol D
+        else map_prod id (\<lambda>y. y div a)
+               (shd (sdrop_while (\<lambda>(_, y). y = 0 \<or> \<not>a dvd y) (pell_solutions D'))))"
+
+lemma find_fund_sol_fast: "find_fund_sol D = find_fund_sol_fast D"
+proof (cases "is_square D \<or> square_part D = 1")
+  case True
+  thus ?thesis
+    using squarefree_part_1_imp_square[of D]
+    by (cases "D = 0")
+       (auto simp: find_fund_sol_correct find_fund_sol_fast_def
+                    square_squarefree_part_nat_def square_test_correct unit_factor_nat_def)
+next
+  case False
+  define D' a where "D' = squarefree_part D" and "a = square_part D"
+  have "D > 0"
+    using False by (intro Nat.gr0I) auto
+  have "a > 0"
+    using \<open>D > 0\<close> by (intro Nat.gr0I) (auto simp: a_def)
+  moreover have "\<not>is_square D'"
+    unfolding D'_def
+    by (metis False is_nth_power_mult is_nth_power_nth_power squarefree_decompose)
+  ultimately interpret lift: pell_lift D' a D
+    using False \<open>D > 0\<close>           
+    by unfold_locales (auto simp: D'_def a_def squarefree_decompose [symmetric])
+
+  define i where "i = (LEAST i. case lift.nth_solution i of (_, y) \<Rightarrow> y > 0 \<and> a dvd y)"
+  have ex: "\<exists>i. case lift.nth_solution i of (_, y) \<Rightarrow> y > 0 \<and> a dvd y"
+  proof -
+    define sol where "sol = lift.lift.fund_sol"
+    have is_sol: "lift.solution (lift.lower_solution sol)"
+      unfolding sol_def using lift.lift.fund_sol_is_nontriv_solution lift.lift_solution_iff by blast
+    then obtain j where j: "lift.lower_solution sol = lift.nth_solution j"
+      using lift.solution_iff_nth_solution by blast
+    have "snd (lift.lower_solution sol) > 0"
+    proof (rule Nat.gr0I)
+      assume *: "snd (lift.lower_solution sol) = 0"
+      have "lift.solution (fst (lift.lower_solution sol), snd (lift.lower_solution sol))"
+        using is_sol by simp
+      hence "fst (lift.lower_solution sol) = 1"
+        by (subst (asm) *) simp
+      with * have "lift.lower_solution sol = (1, 0)"
+        by (cases "lift.lower_solution sol") auto
+      hence "fst sol = 1"
+        unfolding lift.lower_solution_def by (auto simp: lift.lower_solution_def case_prod_unfold)
+      thus False
+        unfolding sol_def
+        using lift.lift.fund_sol_is_nontriv_solution \<open>D > 0\<close>
+        by (auto simp: lift.lift.nontriv_solution_def)
+    qed
+    moreover have "a dvd snd (lift.lower_solution sol)"
+      by (auto simp: lift.lower_solution_def case_prod_unfold)
+    ultimately show ?thesis
+      using j by (auto simp: case_prod_unfold)
+  qed
+
+  define sol where "sol = lift.nth_solution i"
+  have sol: "snd sol > 0" "a dvd snd sol"
+    using LeastI_ex[OF ex] by (simp_all add: sol_def i_def case_prod_unfold)
+  have "i > 0"
+    using sol by (intro Nat.gr0I) (auto simp: sol_def lift.nth_solution_def)
+
+  have "find_fund_sol_fast D = map_prod id (\<lambda>y. y div a)
+          (shd (sdrop_while (\<lambda>(_, y). y = 0 \<or> \<not>a dvd y) (pell_solutions D')))"
+    unfolding D'_def a_def find_fund_sol_fast_def using False squarefree_part_1_imp_square[of D]
+    by (auto simp: square_squarefree_part_nat_def)
+  also have "sdrop_while (\<lambda>(_, y). y = 0 \<or> \<not>a dvd y) (pell_solutions D') =
+             sdrop_while (Not \<circ> (\<lambda>(_, y). y > 0 \<and> a dvd y)) (pell_solutions D')"
+    by (simp add: o_def case_prod_unfold)
+  also have "\<dots> = sdrop i (pell_solutions D')"
+    using ex by (subst sdrop_while_sdrop_LEAST) (simp_all add: lift.snth_pell_solutions i_def)
+  also have "shd \<dots> = sol"
+    by (simp add: lift.snth_pell_solutions sol_def)
+  finally have eq: "find_fund_sol_fast D = map_prod id (\<lambda>y. y div a) sol" .
+
+  have "lift.lift.fund_sol = lift.lift_solution sol"
+    unfolding sol_def
+  proof (rule lift.lift_fund_sol)
+    show "i > 0" by fact
+    show "lift.liftable_solution (lift.nth_solution i)"
+      using sol by (simp add: sol_def lift.liftable_solution_def case_prod_unfold)
+  next
+    fix j :: nat assume j: "j > 0" "j < i"
+    show "\<not>lift.liftable_solution (lift.nth_solution j)"
+    proof
+      assume liftable: "lift.liftable_solution (lift.nth_solution j)"
+      have "snd (lift.nth_solution j) > 0"
+        using \<open>j > 0\<close> by (metis gr0I lift.nontriv_solution_altdef lift.nth_solution_sound' 
+                                lift.solution_0_snd_nat_iff prod.collapse)
+      hence "case lift.nth_solution j of (_, y) \<Rightarrow> y > 0 \<and> a dvd y"
+        using \<open>j > 0\<close> liftable by (auto simp: lift.liftable_solution_def)
+      hence "i \<le> j"
+        unfolding i_def by (rule Least_le)
+      thus False using \<open>j < i\<close> by simp
+    qed
+  qed
+  also have "\<dots> = find_fund_sol_fast D"
+    by (simp add: eq lift.lift_solution_def case_prod_unfold map_prod_def)
+  finally show ?thesis
+    using \<open>D > 0\<close> False by (simp add: find_fund_sol_correct)
+qed
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/Quadratic_Irrationals.thy b/thys/Continued_Fractions/Quadratic_Irrationals.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Quadratic_Irrationals.thy
@@ -0,0 +1,1018 @@
+(*
+  File:     Continued_Fractions/Quadratic Irrationals.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Quadratic Irrationals\<close>
+theory Quadratic_Irrationals
+imports
+  Continued_Fractions
+  "HOL-Computational_Algebra.Computational_Algebra"
+  "HOL-Library.Discrete"
+  "Coinductive.Coinductive_Stream"
+begin
+
+lemma snth_cycle:
+  assumes "xs \<noteq> []"
+  shows   "snth (cycle xs) n = xs ! (n mod length xs)"
+proof (induction n rule: less_induct)
+  case (less n)
+  have "snth (shift xs (cycle xs)) n = xs ! (n mod length xs)"
+  proof (cases "n < length xs")
+    case True
+    thus ?thesis
+      by (subst shift_snth_less) auto
+  next
+    case False
+    have "0 < length xs"
+      using assms by simp
+    also have "\<dots> \<le> n"
+      using False by simp
+    finally have "n > 0" .
+
+    from False have "snth (shift xs (cycle xs)) n = snth (cycle xs) (n - length xs)"
+      by (subst shift_snth_ge) auto
+    also have "\<dots> = xs ! ((n - length xs) mod length xs)"
+      using assms \<open>n > 0\<close> by (intro less) auto
+    also have "(n - length xs) mod length xs = n mod length xs"
+      using False by (simp add: mod_if)
+    finally show ?thesis .
+  qed
+  also have "shift xs (cycle xs) = cycle xs"
+    by (rule cycle_decomp [symmetric]) fact
+  finally show ?case .
+qed
+
+subsection \<open>Basic results on rationality of square roots\<close>
+
+lemma inverse_in_Rats_iff [simp]: "inverse (x :: real) \<in> \<rat> \<longleftrightarrow> x \<in> \<rat>"
+  by (auto simp: inverse_eq_divide divide_in_Rats_iff1)
+
+lemma nonneg_sqrt_nat_or_irrat:
+  assumes "x ^ 2 = real a" and "x \<ge> 0"
+  shows   "x \<in> \<nat> \<or> x \<notin> \<rat>"
+proof safe
+  assume "x \<notin> \<nat>" and "x \<in> \<rat>"
+  from Rats_abs_nat_div_natE[OF this(2)]
+    obtain p q :: nat where q_nz [simp]: "q \<noteq> 0" and "abs x = p / q" and coprime: "coprime p q" .
+  with \<open>x \<ge> 0\<close> have x: "x = p / q"
+      by simp
+  with assms have "real (q ^ 2) * real a = real (p ^ 2)"
+    by (simp add: field_simps)
+  also have "real (q ^ 2) * real a = real (q ^ 2 * a)"
+    by simp
+  finally have "p ^ 2 = q ^ 2 * a"
+    by (subst (asm) of_nat_eq_iff) auto
+  hence "q ^ 2 dvd p ^ 2"
+    by simp
+  hence "q dvd p"
+    by simp
+  with coprime have "q = 1"
+    by auto
+  with x and \<open>x \<notin> \<nat>\<close> show False
+    by simp
+qed
+
+text \<open>
+  A square root of a natural number is either an integer or irrational.
+\<close>
+corollary sqrt_nat_or_irrat:
+  assumes "x ^ 2 = real a"
+  shows   "x \<in> \<int> \<or> x \<notin> \<rat>"
+proof (cases "x \<ge> 0")
+  case True
+  with nonneg_sqrt_nat_or_irrat[OF assms this]
+    show ?thesis by (auto simp: Nats_altdef2)
+next
+  case False
+  from assms have "(-x) ^ 2 = real a"
+    by simp
+  moreover from False have "-x \<ge> 0"
+    by simp
+  ultimately have "-x \<in> \<nat> \<or> -x \<notin> \<rat>"
+    by (rule nonneg_sqrt_nat_or_irrat)
+  thus ?thesis
+    by (auto simp: Nats_altdef2 minus_in_Ints_iff)
+qed
+
+corollary sqrt_nat_or_irrat':
+  "sqrt (real a) \<in> \<nat> \<or> sqrt (real a) \<notin> \<rat>"
+  using nonneg_sqrt_nat_or_irrat[of "sqrt a" a] by auto
+
+text \<open>
+  The square root of a natural number \<open>n\<close> is again a natural number iff \<open>n is a perfect square.\<close>
+\<close>
+corollary sqrt_nat_iff_is_square:
+  "sqrt (real n) \<in> \<nat> \<longleftrightarrow> is_square n"
+proof
+  assume "sqrt (real n) \<in> \<nat>"
+  then obtain k where "sqrt (real n) = real k" by (auto elim!: Nats_cases)
+  hence "sqrt (real n) ^ 2 = real (k ^ 2)" by (simp only: of_nat_power)
+  also have "sqrt (real n) ^ 2 = real n" by simp
+  finally have "n = k ^ 2" by (simp only: of_nat_eq_iff)
+  thus "is_square n" by blast
+qed (auto elim!: is_nth_powerE)
+
+corollary irrat_sqrt_nonsquare: "\<not>is_square n \<Longrightarrow> sqrt (real n) \<notin> \<rat>"
+  using sqrt_nat_or_irrat'[of n] by (auto simp: sqrt_nat_iff_is_square)
+
+lemma sqrt_of_nat_in_Rats_iff: "sqrt (real n) \<in> \<rat> \<longleftrightarrow> is_square n"
+  using irrat_sqrt_nonsquare[of n] sqrt_nat_iff_is_square[of n] Nats_subset_Rats by blast
+
+lemma Discrete_sqrt_altdef: "Discrete.sqrt n = nat \<lfloor>sqrt n\<rfloor>"
+proof -
+  have "real (Discrete.sqrt n ^ 2) \<le> sqrt n ^ 2"
+    by simp
+  hence "Discrete.sqrt n \<le> sqrt n"
+    unfolding of_nat_power by (rule power2_le_imp_le) auto
+  moreover have "real (Suc (Discrete.sqrt n) ^ 2) > real n"
+    unfolding of_nat_less_iff by (rule Suc_sqrt_power2_gt)
+  hence "real (Discrete.sqrt n + 1) ^ 2 > sqrt n ^ 2"
+    unfolding of_nat_power by simp
+  hence "real (Discrete.sqrt n + 1) > sqrt n"
+    by (rule power2_less_imp_less) auto
+  hence "Discrete.sqrt n + 1 > sqrt n" by simp
+  ultimately show ?thesis by linarith
+qed
+
+
+subsection \<open>Definition of quadratic irrationals\<close>
+
+text \<open>
+  Irrational real numbers $x$ that satisfy a quadratic equation $a x^2 + b x + c = 0$
+  with \<open>a\<close>, \<open>b\<close>, \<open>c\<close> not all equal to 0 are called \<^emph>\<open>quadratic irrationals\<close>. These are of the form
+  $p + q \sqrt{d}$ for rational numbers \<open>p\<close>, \<open>q\<close> and a positive integer \<open>d\<close>.
+\<close>
+inductive quadratic_irrational :: "real \<Rightarrow> bool" where
+  "x \<notin> \<rat> \<Longrightarrow> real_of_int a * x ^ 2 + real_of_int b * x + real_of_int c = 0 \<Longrightarrow>
+     a \<noteq> 0 \<or> b \<noteq> 0 \<or> c \<noteq> 0 \<Longrightarrow> quadratic_irrational x"
+
+lemma quadratic_irrational_sqrt [intro]:
+  assumes "\<not>is_square n"
+  shows   "quadratic_irrational (sqrt (real n))"
+  using irrat_sqrt_nonsquare[OF assms]
+  by (intro quadratic_irrational.intros[of "sqrt n" 1 0 "-int n"]) auto
+
+lemma quadratic_irrational_uminus [intro]:
+  assumes "quadratic_irrational x"
+  shows   "quadratic_irrational (-x)"
+  using assms
+proof induction
+  case (1 x a b c)
+  thus ?case by (intro quadratic_irrational.intros[of "-x" a "-b" c]) auto
+qed
+
+lemma quadratic_irrational_uminus_iff [simp]:
+  "quadratic_irrational (-x) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_uminus[of x] quadratic_irrational_uminus[of "-x"] by auto
+
+lemma quadratic_irrational_plus_int [intro]:
+  assumes "quadratic_irrational x"
+  shows   "quadratic_irrational (x + of_int n)"
+  using assms
+proof induction
+  case (1 x a b c)
+  define x' where "x' = x + of_int n"
+  define a' b' c' where
+     "a' = a" and "b' = b - 2 * of_int n * a" and
+     "c' = a * of_int n ^ 2 - b * of_int n + c"
+  from 1 have "0 = a * (x' - of_int n) ^ 2 + b * (x' - of_int n) + c"
+    by (simp add: x'_def)
+  also have "\<dots> = a' * x' ^ 2 + b' * x' + c'"
+    by (simp add: algebra_simps a'_def b'_def c'_def power2_eq_square)
+  finally have "\<dots> = 0" ..
+  moreover have "x' \<notin> \<rat>"
+    using 1 by (auto simp: x'_def add_in_Rats_iff2)
+  moreover have "a' \<noteq> 0 \<or> b' \<noteq> 0 \<or> c' \<noteq> 0"
+    using 1 by (auto simp: a'_def b'_def c'_def)
+  ultimately show ?case
+    by (intro quadratic_irrational.intros[of "x + of_int n" a' b' c']) (auto simp: x'_def)
+qed
+
+lemma quadratic_irrational_plus_int_iff [simp]:
+  "quadratic_irrational (x + of_int n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int[of x n]
+        quadratic_irrational_plus_int[of "x + of_int n" "-n"] by auto
+
+lemma quadratic_irrational_minus_int_iff [simp]:
+  "quadratic_irrational (x - of_int n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "-n"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_plus_nat_iff [simp]:
+  "quadratic_irrational (x + of_nat n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "int n"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_minus_nat_iff [simp]:
+  "quadratic_irrational (x - of_nat n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "-int n"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_plus_1_iff [simp]:
+  "quadratic_irrational (x + 1) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x 1]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_minus_1_iff [simp]:
+  "quadratic_irrational (x - 1) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "-1"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_plus_numeral_iff [simp]:
+  "quadratic_irrational (x + numeral n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "numeral n"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_minus_numeral_iff [simp]:
+  "quadratic_irrational (x - numeral n) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_plus_int_iff[of x "-numeral n"]
+  by (simp del: quadratic_irrational_plus_int_iff)
+
+lemma quadratic_irrational_inverse:
+  assumes "quadratic_irrational x"
+  shows   "quadratic_irrational (inverse x)"
+  using assms
+proof induction
+  case (1 x a b c)
+  from 1 have "x \<noteq> 0" by auto
+  have "0 = (real_of_int a * x\<^sup>2 + real_of_int b * x + real_of_int c) / x ^ 2"
+    by (subst 1) simp
+  also have "\<dots> = real_of_int c * (inverse x) ^ 2 + real_of_int b * inverse x + real_of_int a"
+    using \<open>x \<noteq> 0\<close> by (simp add: field_simps power2_eq_square)
+  finally have "\<dots> = 0" ..
+  thus ?case using 1
+    by (intro quadratic_irrational.intros[of "inverse x" c b a]) auto
+qed
+
+lemma quadratic_irrational_inverse_iff [simp]:
+  "quadratic_irrational (inverse x) \<longleftrightarrow> quadratic_irrational x"
+  using quadratic_irrational_inverse[of x] quadratic_irrational_inverse[of "inverse x"]
+  by (cases "x = 0") auto
+
+lemma quadratic_irrational_cfrac_remainder_iff:
+  "quadratic_irrational (cfrac_remainder c n) \<longleftrightarrow> quadratic_irrational (cfrac_lim c)"
+proof (cases "cfrac_length c = \<infinity>")
+  case False
+  thus ?thesis
+    by (auto simp: quadratic_irrational.simps)
+next
+  case [simp]: True
+  show ?thesis
+  proof (induction n)
+    case (Suc n)
+    from Suc.prems have "cfrac_remainder c (Suc n) =
+                           inverse (cfrac_remainder c n - of_int (cfrac_nth c n))"
+      by (subst cfrac_remainder_Suc) (auto simp: field_simps)
+    also have "quadratic_irrational \<dots> \<longleftrightarrow> quadratic_irrational (cfrac_remainder c n)"
+      by simp
+    also have "\<dots> \<longleftrightarrow> quadratic_irrational (cfrac_lim c)"
+      by (rule Suc.IH)
+    finally show ?case .
+  qed auto
+qed
+                
+subsection \<open>Real solutions of quadratic equations\<close>
+
+text \<open>
+  For the next result, we need some basic properties of real solutions to quadratic equations.
+\<close>
+lemma quadratic_equation_reals:
+  fixes a b c :: real
+  defines "f \<equiv> (\<lambda>x. a * x ^ 2 + b * x + c)"
+  defines "discr \<equiv> (b^2 - 4 * a * c)"
+  shows   "{x. f x = 0} =
+             (if a = 0 then
+                (if b = 0 then if c = 0 then UNIV else {} else {-c/b})
+              else if discr \<ge> 0 then {(-b + sqrt discr) / (2 * a), (-b - sqrt discr) / (2 * a)}
+                                else {})" (is ?th1)                
+proof (cases "a = 0")
+  case [simp]: True
+  show ?th1
+  proof (cases "b = 0")
+    case [simp]: True
+    hence "{x. f x = 0} = (if c = 0 then UNIV else {})"
+      by (auto simp: f_def)
+    thus ?th1 by simp
+  next
+    case False
+    hence "{x. f x = 0} = {-c / b}" by (auto simp: f_def field_simps)
+    thus ?th1 using False by simp
+  qed
+next
+  case [simp]: False
+  show ?th1
+  proof (cases "discr \<ge> 0")
+    case True
+    {
+      fix x :: real
+      have "f x = a * (x - (-b + sqrt discr) / (2 * a)) * (x - (-b - sqrt discr) / (2 * a))"
+        using True by (simp add: f_def field_simps discr_def power2_eq_square)
+      also have "\<dots> = 0 \<longleftrightarrow> x \<in> {(-b + sqrt discr) / (2 * a), (-b - sqrt discr) / (2 * a)}"
+        by simp
+      finally have "f x = 0 \<longleftrightarrow> \<dots>" .
+    }
+    hence "{x. f x = 0} = {(-b + sqrt discr) / (2 * a), (-b - sqrt discr) / (2 * a)}"
+      by blast
+    thus ?th1 using True by simp
+  next
+    case False
+    {
+      fix x :: real
+      assume x: "f x = 0"
+      have "0 \<le> (x + b / (2 * a)) ^ 2" by simp
+      also have "f x = a * ((x + b / (2 * a)) ^ 2 - b ^ 2 / (4 * a ^ 2) + c / a)"
+        by (simp add: field_simps power2_eq_square f_def)
+      with x have "(x + b / (2 * a)) ^ 2 - b ^ 2 / (4 * a ^ 2) + c / a = 0"
+        by simp
+      hence "(x + b / (2 * a)) ^ 2 = b ^ 2 / (4 * a ^ 2) - c / a"
+        by (simp add: algebra_simps)
+      finally have "0 \<le> (b\<^sup>2 / (4 * a\<^sup>2) - c / a) * (4 * a\<^sup>2)"
+        by (intro mult_nonneg_nonneg) auto
+      also have "\<dots> = b\<^sup>2 - 4 * a * c" by (simp add: field_simps power2_eq_square)
+      also have "\<dots> < 0" using False by (simp add: discr_def)
+      finally have False by simp
+    }
+    hence "{x. f x = 0} = {}" by auto
+    thus ?th1 using False by simp
+  qed
+qed
+
+lemma finite_quadratic_equation_solutions_reals:
+  fixes a b c :: real
+  defines "discr \<equiv> (b^2 - 4 * a * c)"
+  shows   "finite {x. a * x ^ 2 + b * x + c = 0} \<longleftrightarrow> a \<noteq> 0 \<or> b \<noteq> 0 \<or> c \<noteq> 0"
+  by (subst quadratic_equation_reals)
+     (auto simp: discr_def card_eq_0_iff infinite_UNIV_char_0 split: if_split)
+
+lemma card_quadratic_equation_solutions_reals:
+  fixes a b c :: real
+  defines "discr \<equiv> (b^2 - 4 * a * c)"
+  shows   "card {x. a * x ^ 2 + b * x + c = 0} =
+             (if a = 0 then
+                (if b = 0 then 0 else 1)
+              else if discr \<ge> 0 then if discr = 0 then 1 else 2 else 0)" (is ?th1)                
+  by (subst quadratic_equation_reals)
+     (auto simp: discr_def card_eq_0_iff infinite_UNIV_char_0 split: if_split)
+
+lemma card_quadratic_equation_solutions_reals_le_2:
+  "card {x :: real. a * x ^ 2 + b * x + c = 0} \<le> 2"
+  by (subst card_quadratic_equation_solutions_reals) auto
+
+lemma quadratic_equation_solution_rat_iff:
+  fixes a b c :: int and x y :: real
+  defines "f \<equiv> (\<lambda>x::real. a * x ^ 2 + b * x + c)"
+  defines "discr \<equiv> nat (b ^ 2 - 4 * a * c)"
+  assumes "a \<noteq> 0" "f x = 0"
+  shows   "x \<in> \<rat> \<longleftrightarrow> is_square discr"
+proof -
+  define discr' where "discr' \<equiv> real_of_int (b ^ 2 - 4 * a * c)"
+  from assms have "x \<in> {x. f x = 0}" by simp
+  with \<open>a \<noteq> 0\<close> have "discr' \<ge> 0" unfolding discr'_def f_def of_nat_diff
+    by (subst (asm) quadratic_equation_reals) (auto simp: discr_def split: if_splits)
+  hence *: "sqrt (discr') = sqrt (real discr)" unfolding of_int_0_le_iff discr_def discr'_def
+    by (simp add: algebra_simps nat_diff_distrib)
+  from \<open>x \<in> {x. f x = 0}\<close> have "x = (-b + sqrt discr) / (2 * a) \<or> x = (-b - sqrt discr) / (2 * a)"
+    using \<open>a \<noteq> 0\<close> * unfolding discr'_def f_def
+    by (subst (asm) quadratic_equation_reals) (auto split: if_splits)
+  thus ?thesis using \<open>a \<noteq> 0\<close>
+    by (auto simp: sqrt_of_nat_in_Rats_iff divide_in_Rats_iff2 diff_in_Rats_iff2 diff_in_Rats_iff1)
+qed
+
+
+subsection \<open>Periodic continued fractions and quadratic irrationals\<close>
+
+text \<open>
+  We now show the main result: A positive irrational number has a periodic continued 
+  fraction expansion iff it is a quadratic irrational.
+
+  In principle, this statement naturally also holds for negative numbers, but the current 
+  formalisation of continued fractions only supports non-negative numbers. It also holds for
+  rational numbers in some sense, since their continued fraction expansion is finite to begin with.
+\<close>
+theorem periodic_cfrac_imp_quadratic_irrational:
+  assumes [simp]: "cfrac_length c = \<infinity>"
+      and period: "l > 0" "\<And>k. k \<ge> N \<Longrightarrow> cfrac_nth c (k + l) = cfrac_nth c k"
+  shows   "quadratic_irrational (cfrac_lim c)"
+proof -
+  define h' and k' where "h' = conv_num_int (cfrac_drop N c)" 
+                     and "k' = conv_denom_int (cfrac_drop N c)"
+  define x' where "x' = cfrac_remainder c N"
+
+  have c_pos: "cfrac_nth c n > 0" if "n \<ge> N" for n
+  proof -
+    from assms(1,2) have "cfrac_nth c (n + l) > 0" by auto
+    with assms(3)[OF that] show ?thesis by simp
+  qed
+  have k'_pos: "k' n > 0" if "n \<noteq> -1" "n \<ge> -2" for n
+    using that by (auto simp: k'_def conv_denom_int_def intro!: conv_denom_pos)
+  have k'_nonneg: "k' n \<ge> 0" if "n \<ge> -2" for n
+    using that by (auto simp: k'_def conv_denom_int_def intro!: conv_denom_pos)
+  have "cfrac_nth c (n + (N + l)) = cfrac_nth c (n + N)" for n
+    using period(2)[of "n + N"] by (simp add: add_ac)
+  have "cfrac_drop (N + l) c = cfrac_drop N c"
+    by (rule cfrac_eqI) (use period(2)[of "n + N" for n] in \<open>auto simp: algebra_simps\<close>)
+  hence x'_altdef: "x' = cfrac_remainder c (N + l)"
+    by (simp add: x'_def cfrac_remainder_def)
+  have x'_pos: "x' > 0" unfolding x'_def
+    using c_pos by (intro cfrac_remainder_pos) auto
+
+  define A where "A = (k' (int l - 1))"
+  define B where "B = k' (int l - 2) - h' (int l - 1)"
+  define C where "C = -(h' (int l - 2))"
+
+  have pos: "(k' (int l - 1) * x' + k' (int l - 2)) > 0"
+    using x'_pos \<open>l > 0\<close>
+    by (intro add_pos_nonneg mult_pos_pos) (auto intro!: k'_pos k'_nonneg)
+  have "cfrac_remainder c N = conv' (cfrac_drop N c) l (cfrac_remainder c (l + N))"
+    unfolding cfrac_remainder_def cfrac_drop_add
+    by (subst (2) cfrac_remainder_def [symmetric]) (auto simp: conv'_cfrac_remainder)
+  hence "x' = conv' (cfrac_drop N c) l x'"
+    by (subst (asm) add.commute) (simp only: x'_def [symmetric] x'_altdef [symmetric])
+  also have "\<dots> = (h' (int l - 1) * x' + h' (int l - 2)) / (k' (int l - 1) * x' + k' (int l - 2))"
+    using conv'_num_denom_int[OF x'_pos, of _ l] unfolding h'_def k'_def
+    by (simp add: mult_ac)
+  finally have "x' * (k' (int l - 1) * x' + k' (int l - 2)) = (h' (int l - 1) * x' + h' (int l - 2))"
+    using pos by (simp add: divide_simps)
+  hence quadratic: "A * x' ^ 2 + B * x' + C = 0"
+    by (simp add: algebra_simps power2_eq_square A_def B_def C_def)
+  moreover have "x' \<notin> \<rat>" unfolding x'_def
+    by auto
+  moreover have "A > 0" using \<open>l > 0\<close> by (auto simp: A_def intro!: k'_pos)
+  ultimately have "quadratic_irrational x'" using \<open>x' \<notin> \<rat>\<close>
+    by (intro quadratic_irrational.intros[of x' A B C]) simp_all
+  thus ?thesis
+    using assms by (simp add: x'_def quadratic_irrational_cfrac_remainder_iff)
+qed
+
+
+lift_definition pperiodic_cfrac :: "nat list \<Rightarrow> cfrac" is
+  "\<lambda>xs. if xs = [] then (0, LNil) else
+        (int (hd xs), llist_of_stream (cycle (map (\<lambda>n. n- 1) (tl xs @ [hd xs]))))" .
+
+definition periodic_cfrac :: "int list \<Rightarrow> int list \<Rightarrow> cfrac" where
+  "periodic_cfrac xs ys = cfrac_of_stream (Stream.shift xs (Stream.cycle ys))"
+
+lemma periodic_cfrac_Nil [simp]: "pperiodic_cfrac [] = 0"
+  unfolding zero_cfrac_def by transfer auto
+
+lemma cfrac_length_pperiodic_cfrac [simp]:
+  "xs \<noteq> [] \<Longrightarrow> cfrac_length (pperiodic_cfrac xs) = \<infinity>"
+  by transfer auto
+
+lemma cfrac_nth_pperiodic_cfrac:
+  assumes "xs \<noteq> []" and "0 \<notin> set xs"
+  shows   "cfrac_nth (pperiodic_cfrac xs) n = xs ! (n mod length xs)"
+  using assms
+proof (transfer, goal_cases)
+  case (1 xs n)
+  show ?case
+  proof (cases n)
+    case (Suc n')
+    have "int (cycle (tl (map (\<lambda>n. n - 1) xs) @ [hd (map (\<lambda>n. n - 1) xs)]) !! n') + 1 = 
+          int (stl (cycle (map (\<lambda>n. n - 1) xs)) !! n') + 1"
+      by (subst cycle.sel(2) [symmetric]) (rule refl)
+    also have "\<dots> = int (cycle (map (\<lambda>n. n - 1) xs) !! n) + 1"
+      by (simp add: Suc del: cycle.sel)
+    also have "\<dots> = int (xs ! (n mod length xs) - 1) + 1"
+      by (simp add: snth_cycle \<open>xs \<noteq> []\<close>)
+    also have "xs ! (n mod length xs) \<in> set xs"
+      using \<open>xs \<noteq> []\<close> by (auto simp: set_conv_nth)
+    with 1 have "xs ! (n mod length xs) > 0"
+      by (intro Nat.gr0I) auto
+    hence "int (xs ! (n mod length xs) - 1) + 1 = int (xs ! (n mod length xs))"
+      by simp
+    finally show ?thesis
+      using Suc 1 by (simp add: hd_conv_nth map_tl)
+  qed (use 1 in \<open>auto simp: hd_conv_nth\<close>)
+qed
+
+definition pperiodic_cfrac_info :: "nat list \<Rightarrow> int \<times> int \<times> int"where
+  "pperiodic_cfrac_info xs =
+     (let l = length xs;
+          h = conv_num_fun (\<lambda>n. xs ! n);
+          k = conv_denom_fun (\<lambda>n. xs ! n);
+          A = k (l - 1);
+          B = h (l - 1) - (if l = 1 then 0 else k (l - 2));
+          C = (if l = 1 then -1 else -h (l - 2))
+      in  (B^2-4*A*C, B, 2 * A))"
+
+lemma conv_gen_cong:
+  assumes "\<forall>k\<in>{n..N}. f k = f' k"
+  shows   "conv_gen f (a,b,n) N = conv_gen f' (a,b,n) N"
+  using assms 
+proof (induction "N - n" arbitrary: a b n N)
+  case (Suc d n N a b)
+  have "conv_gen f (b, b * f n + a, Suc n) N = conv_gen f' (b, b * f n + a, Suc n) N"
+    using Suc(2,3) by (intro Suc) auto
+  moreover have "f n = f' n"
+    using bspec[OF Suc.prems, of n] Suc(2) by auto
+  ultimately show ?case
+    by (subst (1 2) conv_gen.simps) auto
+qed (auto simp: conv_gen.simps)
+
+lemma
+  assumes "\<forall>k\<le>n. c k = cfrac_nth c' k"
+  shows   conv_num_fun_eq': "conv_num_fun c n = conv_num c' n"
+    and   conv_denom_fun_eq': "conv_denom_fun c n = conv_denom c' n"
+proof -
+  have "conv_num c' n = conv_gen (cfrac_nth c') (0, 1, 0) n"
+    unfolding conv_num_code ..
+  also have "\<dots> = conv_gen c (0, 1, 0) n"
+    unfolding conv_num_fun_def using assms by (intro conv_gen_cong) auto
+  finally show "conv_num_fun c n = conv_num c' n"
+    by (simp add: conv_num_fun_def)
+next
+  have "conv_denom c' n = conv_gen (cfrac_nth c') (1, 0, 0) n"
+    unfolding conv_denom_code ..
+  also have "\<dots> = conv_gen c (1, 0, 0) n"
+    unfolding conv_denom_fun_def using assms by (intro conv_gen_cong) auto
+  finally show "conv_denom_fun c n = conv_denom c' n"
+    by (simp add: conv_denom_fun_def)
+qed
+
+lemma gcd_minus_commute_left: "gcd (a - b :: 'a :: ring_gcd) c = gcd (b - a) c"
+  by (metis gcd.commute gcd_neg2 minus_diff_eq)
+
+lemma gcd_minus_commute_right: "gcd c (a - b :: 'a :: ring_gcd) = gcd c (b - a)"
+  by (metis gcd_neg2 minus_diff_eq)
+
+lemma periodic_cfrac_info_aux:
+  fixes D E F :: int
+  assumes "pperiodic_cfrac_info xs = (D, E, F)"
+  assumes "xs \<noteq> []" "0 \<notin> set xs"
+  shows   "cfrac_lim (pperiodic_cfrac xs) = (sqrt D + E) / F"
+    and   "D > 0" and "F > 0"
+proof -
+  define c where "c = pperiodic_cfrac xs"
+  have [simp]: "cfrac_length c = \<infinity>"
+    using assms by (simp add: c_def)
+  define h and k where "h = conv_num_int c" and "k = conv_denom_int c"
+  define x where "x = cfrac_lim c"
+  define l where "l = length xs"
+
+  define A where "A = (k (int l - 1))"
+  define B where "B = k (int l - 2) - h (int l - 1)"
+  define C where "C = -(h (int l - 2))"
+  define discr where "discr = B ^ 2 - 4 * A * C"
+
+  have "l > 0"
+    using assms by (simp add: l_def)
+  have c_pos: "cfrac_nth c n > 0" for n
+    using assms by (auto simp: c_def cfrac_nth_pperiodic_cfrac set_conv_nth)
+  have x_pos: "x > 0"
+    unfolding x_def by (intro cfrac_lim_pos c_pos)
+  have h_pos: "h n > 0" if "n > -2" for n
+    using that unfolding h_def by (auto simp: conv_num_int_def intro: conv_num_pos' c_pos)
+  have k_pos: "k n > 0" if "n > -1" for n
+    using that unfolding k_def by (auto simp: conv_denom_int_def)
+  have k_nonneg: "k n \<ge> 0" for n
+    unfolding k_def by (auto simp: conv_denom_int_def)
+
+  have pos: "(k (int l - 1) * x + k (int l - 2)) > 0"
+    using x_pos \<open>l > 0\<close>
+    by (intro add_pos_nonneg mult_pos_pos) (auto intro!: k_pos k_nonneg)
+  have "cfrac_drop l c = c"
+    using assms by (intro cfrac_eqI) (auto simp: c_def cfrac_nth_pperiodic_cfrac l_def)
+
+  have "x = conv' c l (cfrac_remainder c l)"
+    unfolding x_def by (rule conv'_cfrac_remainder[symmetric]) auto
+  also have "\<dots> = conv' c l x"
+    unfolding cfrac_remainder_def \<open>cfrac_drop l c = c\<close> x_def ..
+  finally have "x = conv' c l x" .
+  also have "\<dots> = (h (int l - 1) * x + h (int l - 2)) / (k (int l - 1) * x + k (int l - 2))"
+    using conv'_num_denom_int[OF x_pos, of _ l] unfolding h_def k_def
+    by (simp add: mult_ac)
+  finally have "x * (k (int l - 1) * x + k (int l - 2)) = (h (int l - 1) * x + h (int l - 2))"
+    using pos by (simp add: divide_simps)
+  hence quadratic: "A * x ^ 2 + B * x + C = 0"
+    by (simp add: algebra_simps power2_eq_square A_def B_def C_def)
+
+  have "A > 0" using \<open>l > 0\<close> by (auto simp: A_def intro!: k_pos)
+  have discr_altdef: "discr = (k (int l-2) - h (int l-1)) ^ 2 + 4 * k (int l-1) * h (int l-2)"
+    by (simp add: discr_def A_def B_def C_def)
+
+  have "0 < 0 + 4 * A * 1"
+    using \<open>A > 0\<close> by simp
+  also have "0 + 4 * A * 1 \<le> discr"
+    unfolding discr_altdef A_def using h_pos[of "int l - 2"] \<open>l > 0\<close>
+    by (intro add_mono mult_mono order.refl k_nonneg mult_nonneg_nonneg) auto
+  finally have "discr > 0" .
+
+  have "x \<in> {x. A * x ^ 2 + B * x + C = 0}"
+    using quadratic by simp
+  hence x_cases: "x = (-B - sqrt discr) / (2 * A) \<or> x = (-B + sqrt discr) / (2 * A)"
+    unfolding quadratic_equation_reals of_int_diff using \<open>A > 0\<close>
+    by (auto split: if_splits simp: discr_def)
+
+  have "B ^ 2 < discr"
+    unfolding discr_def by (auto intro!: mult_pos_pos k_pos h_pos \<open>l > 0\<close> simp: A_def C_def)
+  hence "\<bar>B\<bar> < sqrt discr"
+    using \<open>discr > 0\<close> by (simp add: real_less_rsqrt)
+
+  have "x = (if x \<ge> 0 then (sqrt discr - B) / (2 * A) else -(sqrt discr + B) / (2 * A))"
+    using x_cases
+  proof
+    assume x: "x = (-B - sqrt discr) / (2 * A)"
+    have "(-B - sqrt discr) / (2 * A) < 0"
+      using \<open>\<bar>B\<bar> < sqrt discr\<close> \<open>A > 0\<close> by (intro divide_neg_pos) auto
+    also note x[symmetric]
+    finally show ?thesis using x by simp
+  next
+    assume x: "x = (-B + sqrt discr) / (2 * A)"
+    have "(-B + sqrt discr) / (2 * A) > 0"
+      using \<open>\<bar>B\<bar> < sqrt discr\<close> \<open>A > 0\<close> by (intro divide_pos_pos) auto
+    also note x[symmetric]
+    finally show ?thesis using x by simp
+  qed
+  also have "x \<ge> 0 \<longleftrightarrow> floor x \<ge> 0"
+    by auto
+  also have "floor x = floor (cfrac_lim c)"
+    by (simp add: x_def)
+  also have "\<dots> = cfrac_nth c 0"
+    by (subst cfrac_nth_0_conv_floor) auto
+  also have "\<dots> = int (hd xs)"
+    using assms unfolding c_def by (subst cfrac_nth_pperiodic_cfrac) (auto simp: hd_conv_nth)
+  finally have x_eq: "x = (sqrt discr - B) / (2 * A)"
+    by simp
+
+
+  define h' where "h' = conv_num_fun (\<lambda>n. int (xs ! n))"
+  define k' where "k' = conv_denom_fun (\<lambda>n. int (xs ! n))"
+  have num_eq: "h' i = h i"
+    if "i < l" for i using that assms unfolding h'_def h_def
+    by (subst conv_num_fun_eq'[where c' = c]) (auto simp: c_def l_def cfrac_nth_pperiodic_cfrac)
+  have denom_eq: "k' i = k i"
+    if "i < l" for i using that assms unfolding k'_def k_def
+    by (subst conv_denom_fun_eq'[where c' = c]) (auto simp: c_def l_def cfrac_nth_pperiodic_cfrac)
+
+  have 1: "h (int l - 1) = h' (l - 1)"
+    by (subst num_eq) (use \<open>l > 0\<close> in \<open>auto simp: of_nat_diff\<close>)
+  have 2: "k (int l - 1) = k' (l - 1)"
+    by (subst denom_eq) (use \<open>l > 0\<close> in \<open>auto simp: of_nat_diff\<close>)
+  have 3: "h (int l - 2) = (if l = 1 then 1 else h' (l - 2))"
+    using \<open>l > 0\<close> num_eq[of "l - 2"] by (auto simp: h_def nat_diff_distrib)
+  have 4: "k (int l - 2) = (if l = 1 then 0 else k' (l - 2))"
+    using \<open>l > 0\<close> denom_eq[of "l - 2"] by (auto simp: k_def nat_diff_distrib)
+  
+  have "pperiodic_cfrac_info xs =
+          (let A = k (int l - 1);
+               B = h (int l - 1) - (if l = 1 then 0 else k (int l - 2));
+               C = (if l = 1 then -1 else - h (int l - 2))
+           in (B\<^sup>2 - 4 * A * C, B, 2 * A))"
+    unfolding pperiodic_cfrac_info_def Let_def using 1 2 3 4 \<open>l > 0\<close>
+    by (auto simp: num_eq denom_eq h'_def k'_def l_def of_nat_diff)
+  also have "\<dots> = (B\<^sup>2 - 4 * A * C, -B, 2 * A)"
+    by (simp add: Let_def A_def B_def C_def h_def k_def algebra_simps power2_commute)
+  finally have per_eq: "pperiodic_cfrac_info xs = (discr, -B, 2 * A)"
+    by (simp add: discr_def)
+
+  show "x = (sqrt (real_of_int D) + real_of_int E) / real_of_int F"
+    using per_eq assms by (simp add: x_eq)
+  show "D > 0" "F > 0"
+    using assms per_eq \<open>discr > 0\<close> \<open>A > 0\<close> by auto
+qed
+
+text \<open>
+  We can now compute surd representations for (purely) periodic continued fractions, e.g.
+  $[1, 1, 1, \ldots] = \frac{\sqrt{5} + 1}{2}$:
+\<close>
+value "pperiodic_cfrac_info [1]"
+
+text \<open>
+  We can now compute surd representations for periodic continued fractions, e.g.
+  $[\overline{1,1,1,1,6}] = \frac{\sqrt{13} + 3}{4}$:
+\<close>
+value "pperiodic_cfrac_info [1,1,1,1,6]"
+
+
+
+text \<open>
+  With a little bit of work, one could also easily derive from this a version for
+  non-purely periodic continued fraction.
+\<close>
+
+
+text \<open>
+  Next, we show that any quadratic irrational has a periodic continued fraction expansion.
+\<close>
+theorem quadratic_irrational_imp_periodic_cfrac:
+  assumes "quadratic_irrational (cfrac_lim e)"
+  obtains N l where "l > 0" and "\<And>n m. n \<ge> N \<Longrightarrow> cfrac_nth e (n + m * l) = cfrac_nth e n"
+                and "cfrac_remainder e (N + l) = cfrac_remainder e N"
+                and "cfrac_length e = \<infinity>"
+proof -
+  have [simp]: "cfrac_length e = \<infinity>"
+    using assms by (auto simp: quadratic_irrational.simps)
+  note [intro] = assms(1)
+  define x where "x = cfrac_lim e"
+  from assms obtain a b c :: int where
+    nontrivial: "a \<noteq> 0 \<or> b \<noteq> 0 \<or> c \<noteq> 0" and
+          root: "a * x^2 + b * x + c = 0" (is "?f x = 0")
+    by (auto simp: quadratic_irrational.simps x_def)
+
+  define f where "f = ?f"
+  define h and k where "h = conv_num e" and "k = conv_denom e"
+  define X where "X = cfrac_remainder e"
+  have [simp]: "k i > 0" "k i \<noteq> 0" for i
+    using conv_denom_pos[of e i] by (auto simp: k_def)
+  have k_leI: "k i \<le> k j" if "i \<le> j" for i j
+    by (auto simp: k_def intro!: conv_denom_leI that)
+  have k_nonneg: "k n \<ge> 0" for n
+    by (auto simp: k_def)
+  have k_ge_1: "k n \<ge> 1" for n
+    using k_leI[of 0 n] by (simp add: k_def)
+    
+  define R where "R = conv e"
+  define A where "A = (\<lambda>n. a * h (n - 1) ^ 2 + b * h (n - 1) * k (n - 1) + c * k (n - 1) ^ 2)"
+  define B where "B = (\<lambda>n. 2 * a * h (n - 1) * h (n - 2) + b * (h (n - 1) * k (n - 2) + h (n - 2) * k (n - 1)) + 2 * c * k (n - 1) * k (n - 2))"
+  define C where "C = (\<lambda>n. a * h (n - 2) ^ 2 + b * h (n - 2) * k (n - 2) + c * k (n - 2) ^ 2)"
+
+  define A' where "A' = nat \<lfloor>2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>a\<bar> + \<bar>b\<bar>\<rfloor>"
+  define B' where "B' = nat \<lfloor>(3 / 2) * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + 9 / 4 * \<bar>a\<bar>\<rfloor>"
+
+  have [simp]: "X n \<notin> \<rat>" for n unfolding X_def
+    by simp
+  from this[of 0] have [simp]: "x \<notin> \<rat>"
+    unfolding X_def by (simp add: x_def)
+
+  have "a \<noteq> 0"
+  proof
+    assume "a = 0"
+    with root and nontrivial have "x = 0 \<or> x = -c / b"
+      by (auto simp: divide_simps add_eq_0_iff)
+    hence "x \<in> \<rat>" by (auto simp del: \<open>x \<notin> \<rat>\<close>)
+    thus False by simp
+  qed
+
+  have bounds: "(A n, B n, C n) \<in> {-A'..A'} \<times> {-B'..B'} \<times> {-A'..A'}"
+   and X_root: "A n * X n ^ 2 + B n * X n + C n = 0" if n: "n \<ge> 2" for n
+  proof -
+    define n' where "n' = n - 2"
+    have n': "n = Suc (Suc n')" using \<open>n \<ge> 2\<close> unfolding n'_def by simp
+    have *: "of_int (k (n - Suc 0)) * X n + of_int (k (n - 2)) \<noteq> 0"
+    proof
+      assume "of_int (k (n - Suc 0)) * X n + of_int (k (n - 2)) = 0"
+      hence "X n = -k (n - 2) / k (n - 1)" by (auto simp: divide_simps mult_ac)
+      also have "\<dots> \<in> \<rat>" by auto
+      finally show False by simp
+    qed
+  
+    let ?denom = "(k (n - 1) * X n + k (n - 2))"
+    have "0 = 0 * ?denom ^ 2" by simp
+    also have "0 * ?denom ^ 2 = (a * x ^ 2 + b * x + c) * ?denom ^ 2" using root by simp
+    also have "\<dots> = a * (x * ?denom) ^ 2 + b * ?denom * (x * ?denom) + c * ?denom * ?denom"
+      by (simp add: algebra_simps power2_eq_square)
+    also have "x * ?denom = h (n - 1) * X n + h (n - 2)"
+      using cfrac_lim_eq_num_denom_remainder_aux[of "n - 2" e] \<open>n \<ge> 2\<close>
+      by (simp add: numeral_2_eq_2 Suc_diff_Suc x_def k_def h_def X_def)
+    also have "a * \<dots> ^ 2 + b * ?denom * \<dots> + c * ?denom * ?denom = A n * X n ^ 2 + B n * X n + C n"
+      by (simp add: A_def B_def C_def power2_eq_square algebra_simps)
+    finally show "A n * X n ^ 2 + B n * X n + C n = 0" ..
+  
+    have f_abs_bound: "\<bar>f (R n)\<bar> \<le> (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) * (1 / (k n * k (Suc n))) +
+                                      \<bar>a\<bar> * (1 / (k n * k (Suc n))) ^ 2" for n
+    proof -
+      have "\<bar>f (R n)\<bar> = \<bar>?f (R n) - ?f x\<bar>" by (simp add: root f_def)
+      also have "?f (R n) - ?f x = (R n - x) * (2 * a * x + b) + (R n - x) ^ 2 * a"
+        by (simp add: power2_eq_square algebra_simps)
+      also have "\<bar>\<dots>\<bar> \<le> \<bar>(R n - x) * (2 * a * x + b)\<bar> + \<bar>(R n - x) ^ 2 * a\<bar>"
+        by (rule abs_triangle_ineq)
+      also have "\<dots> = \<bar>2 * a * x + b\<bar> * \<bar>R n - x\<bar> + \<bar>a\<bar> * \<bar>R n - x\<bar> ^ 2"
+        by (simp add: abs_mult)
+      also have "\<dots> \<le> \<bar>2 * a * x + b\<bar> * (1 / (k n * k (Suc n))) + \<bar>a\<bar> * (1 / (k n * k (Suc n))) ^ 2"
+        unfolding x_def R_def using cfrac_lim_minus_conv_bounds[of n e]
+        by (intro add_mono mult_left_mono power_mono) (auto simp: k_def)
+      also have "\<bar>2 * a * x + b\<bar> \<le> 2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>"
+        by (rule order.trans[OF abs_triangle_ineq]) (auto simp: abs_mult)
+      hence "\<bar>2 * a * x + b\<bar> * (1 / (k n * k (Suc n))) + \<bar>a\<bar> * (1 / (k n * k (Suc n))) ^ 2 \<le>
+               \<dots> * (1 / (k n * k (Suc n))) + \<bar>a\<bar> * (1 / (k n * k (Suc n))) ^ 2"
+        by (intro add_mono mult_right_mono) (auto intro!: mult_nonneg_nonneg k_nonneg)
+      finally show "\<bar>f (R n)\<bar> \<le> \<dots>"
+        by (simp add: mult_right_mono add_mono divide_left_mono)
+    qed
+  
+    have h_eq_conv_k: "h i = R i * k i" for i
+      using conv_denom_pos[of e i] unfolding R_def
+      by (subst conv_num_denom) (auto simp: h_def k_def)
+  
+    have "A n = k (n - 1) ^ 2 * f (R (n - 1))" for n
+      by (simp add: algebra_simps A_def n' k_def power2_eq_square h_eq_conv_k f_def)
+    have A_bound: "\<bar>A i\<bar> \<le> A'" if "i > 0" for i
+    proof -
+      have "k i > 0"
+        by simp
+      hence "k i \<ge> 1"
+        by linarith
+      have "A i = k (i - 1) ^ 2 * f (R (i - 1))"
+        by (simp add: algebra_simps A_def k_def power2_eq_square h_eq_conv_k f_def)
+      also have "\<bar>\<dots>\<bar> = k (i - 1) ^ 2 * \<bar>f (R (i - 1))\<bar>"
+        by (simp add: abs_mult f_def)
+      also have "\<dots> \<le> k (i - 1) ^ 2 * ((2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) * (1 / (k (i - 1) * k (Suc (i - 1)))) +
+                        \<bar>a\<bar> * (1 / (k (i - 1) * k (Suc (i - 1)))) ^ 2)"
+        by (intro mult_left_mono f_abs_bound) auto
+      also have "\<dots> = k (i - 1) / k i * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + \<bar>a\<bar> / k i ^ 2" using \<open>i > 0\<close>
+        by (simp add: power2_eq_square field_simps)
+      also have "\<dots> \<le> 1 * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + \<bar>a\<bar> / 1" using \<open>i > 0\<close> \<open>k i \<ge> 1\<close>
+        by (intro add_mono divide_left_mono mult_right_mono)
+           (auto intro!: k_leI one_le_power simp: of_nat_ge_1_iff)
+      also have "\<dots> = 2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>a\<bar> + \<bar>b\<bar>" by simp
+      finally show ?thesis unfolding A'_def by linarith
+    qed
+  
+    have "C n = A (n - 1)" by (simp add: A_def C_def n')
+    hence C_bound: "\<bar>C n\<bar> \<le> A'" using A_bound[of "n - 1"] n by simp
+  
+    have "B n = k (n - 1) * k (n - 2) *
+                  (f (R (n - 1)) + f (R (n - 2)) - a * (R (n - 1) - R (n - 2)) ^ 2)"
+      by (simp add: B_def h_eq_conv_k algebra_simps power2_eq_square f_def)
+    also have "\<bar>\<dots>\<bar> = k (n - 1) * k (n - 2) * 
+                       \<bar>f (R (n - 1)) + f (R (n - 2)) - a * (R (n - 1) - R (n - 2)) ^ 2\<bar>"
+      by (simp add: abs_mult k_nonneg)
+    also have "\<dots> \<le> k (n - 1) * k (n - 2) * 
+                      (((2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) * (1 / (k (n - 1) * k (Suc (n - 1)))) +
+                          \<bar>a\<bar> * (1 / (k (n - 1) * k (Suc (n - 1)))) ^ 2) +                      
+                       ((2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) * (1 / (k (n - 2) * k (Suc (n - 2)))) +
+                          \<bar>a\<bar> * (1 / (k (n - 2) * k (Suc (n - 2)))) ^ 2) +
+                        \<bar>a\<bar> * \<bar>R (Suc (n - 2)) - R (n - 2)\<bar> ^ 2)" (is "_ \<le> _ * (?S1 + ?S2 + ?S3)")
+      by (intro mult_left_mono order.trans[OF abs_triangle_ineq4] order.trans[OF abs_triangle_ineq] 
+            add_mono f_abs_bound order.refl)
+         (insert n, auto simp: abs_mult Suc_diff_Suc numeral_2_eq_2 k_nonneg)
+    also have "\<bar>R (Suc (n - 2)) - R (n - 2)\<bar> = 1 / (k (n - 2) * k (Suc (n - 2)))"
+      unfolding R_def k_def by (rule abs_diff_successive_convs)
+    also have "of_int (k (n - 1) * k (n - 2)) * (?S1 + ?S2 + \<bar>a\<bar> * \<dots> ^ 2) = 
+                 (k (n - 2) / k n + 1) * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + 
+                 \<bar>a\<bar> * (k (n - 2) / (k (n - 1) * k n ^ 2) + 2 / (k (n - 1) * k (n - 2)))"
+      (is "_ = ?S") using n by (simp add: field_simps power2_eq_square numeral_2_eq_2 Suc_diff_Suc)
+    also {
+      have A: "2 * real_of_int (k (n - 2)) \<le> of_int (k n)"
+        using conv_denom_plus2_ratio_ge[of e "n - 2"] n
+        by (simp add: numeral_2_eq_2 Suc_diff_Suc k_def)
+      have "fib (Suc 2) \<le> k 2" unfolding k_def by (intro conv_denom_lower_bound)
+      also have "\<dots> \<le> k n" by (intro k_leI n)
+      finally have "k n \<ge> 2" by (simp add: numeral_3_eq_3)
+      hence B: "of_int (k (n - 2)) * 2 ^ 2 \<le> (of_int (k (n - 1)) * (of_int (k n))\<^sup>2 :: real)"
+        by (intro mult_mono power_mono) (auto intro: k_leI k_nonneg)
+      have C: "1 * 1 \<le> real_of_int (k (n - 1)) * of_int (k (n - 2))" using k_ge_1
+        by (intro mult_mono) (auto simp: Suc_le_eq of_nat_ge_1_iff k_nonneg)
+      note A B C
+    }
+    hence "?S \<le> (1 / 2 + 1) * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + \<bar>a\<bar> * (1 / 4 + 2)"
+      by (intro add_mono mult_right_mono mult_left_mono) (auto simp: field_simps)
+    also have "\<dots> = (3 / 2) * (2 * \<bar>a\<bar> * \<bar>x\<bar> + \<bar>b\<bar>) + 9 / 4 * \<bar>a\<bar>" by simp
+    finally have B_bound: "\<bar>B n\<bar> \<le> B'" unfolding B'_def by linarith
+    from A_bound[of n] B_bound C_bound n
+    show "(A n, B n, C n) \<in> {-A'..A'} \<times> {-B'..B'} \<times> {-A'..A'}" by auto
+  qed
+
+  have A_nz: "A n \<noteq> 0" if "n \<ge> 1" for n
+    using that
+  proof (induction n rule: dec_induct)
+    case base
+    show ?case
+    proof
+      assume "A 1 = 0"
+      hence "real_of_int (A 1) = 0" by simp
+      also have "real_of_int (A 1) =
+                   real_of_int a * of_int (cfrac_nth e 0) ^ 2 +
+                   real_of_int b * cfrac_nth e 0 + real_of_int c"
+        by (simp add: A_def h_def k_def)
+      finally have root': "\<dots> = 0" .
+
+      have "cfrac_nth e 0 \<in> \<rat>" by auto
+      also from root' and \<open>a \<noteq> 0\<close> have "?this \<longleftrightarrow> is_square (nat (b\<^sup>2 - 4 * a * c))"
+        by (intro quadratic_equation_solution_rat_iff) auto
+      also from root and \<open>a \<noteq> 0\<close> have "\<dots> \<longleftrightarrow> x \<in> \<rat>"
+        by (intro quadratic_equation_solution_rat_iff [symmetric]) auto
+      finally show False using \<open>x \<notin> \<rat>\<close> by contradiction
+    qed
+  next
+    case (step m)
+    hence nz: "C (Suc m) \<noteq> 0" by (simp add: C_def A_def)
+    show "A (Suc m) \<noteq> 0"
+    proof
+      assume [simp]: "A (Suc m) = 0"
+      have "X (Suc m) > 0" unfolding X_def
+        by (intro cfrac_remainder_pos) auto
+      with X_root[of "Suc m"] step.hyps nz have "X (Suc m) = -C (Suc m) / B (Suc m)"
+        by (auto simp: divide_simps mult_ac)
+      also have "\<dots> \<in> \<rat>" by auto
+      finally show False by simp
+    qed
+  qed 
+
+  have "finite ({-A'..A'} \<times> {-B'..B'} \<times> {-A'..A'})" by auto
+  from this and bounds have "finite ((\<lambda>n. (A n, B n, C n)) ` {2..})"
+    by (blast intro: finite_subset)
+  moreover have "infinite ({2..} :: nat set)" by (simp add: infinite_Ici)
+  ultimately have "\<exists>k1\<in>{2..}. infinite {n \<in> {2..}. (A n, B n, C n) = (A k1, B k1, C k1)}"
+    by (intro pigeonhole_infinite)
+  then obtain k0 where k0: "k0 \<ge> 2" "infinite {n \<in> {2..}. (A n, B n, C n) = (A k0, B k0, C k0)}"
+    by auto
+  from infinite_countable_subset[OF this(2)] obtain g :: "nat \<Rightarrow> _"
+    where g: "inj g" "range g \<subseteq> {n\<in>{2..}. (A n, B n, C n) = (A k0, B k0, C k0)}" by blast
+  hence g_ge_2: "g k \<ge> 2" for k by auto
+  from g have [simp]: "A (g k) = A k0" "B (g k) = B k0" "C (g k) = C k0" for k
+    by auto
+
+  from g(1) have [simp]: "g k1 = g k2 \<longleftrightarrow> k1 = k2" for k1 k2 by (auto simp: inj_def)
+  define z where "z = (A k0, B k0, C k0)"
+  let ?h = "\<lambda>k. (A (g k), B (g k), C (g k))"
+  from g have g': "distinct [g 1, g 2, g 3]" "?h 0 = z" "?h 1 = z" "?h 2 = z"
+    by (auto simp: z_def)
+  have fin: "finite {x :: real. A k0 * x ^ 2 + B k0 * x + C k0 = 0}" using A_nz[of k0] k0(1)
+    by (subst finite_quadratic_equation_solutions_reals) auto
+  from X_root[of "g 0"] X_root[of "g 1"] X_root[of "g 2"] g_ge_2 g
+    have "(X \<circ> g) ` {0, 1, 2} \<subseteq> {x. A k0 * x ^ 2 + B k0 * x + C k0 = 0}"
+    by auto
+  hence "card ((X \<circ> g) ` {0, 1, 2}) \<le> card \<dots>"
+    by (intro card_mono fin) auto
+  also have "\<dots> \<le> 2"
+    by (rule card_quadratic_equation_solutions_reals_le_2)
+  also have "\<dots> < card {0, 1, 2 :: nat}" by simp
+  finally have "\<not>inj_on (X \<circ> g) {0, 1, 2}"
+    by (rule pigeonhole)
+  then obtain m1 m2 where
+    m12: "m1 \<in> {0, 1, 2}" "m2 \<in> {0, 1, 2}" "X (g m1) = X (g m2)" "m1 \<noteq> m2"
+    unfolding inj_on_def o_def by blast
+  define n and l where "n = min (g m1) (g m2)" and "l = nat \<bar>int (g m1) - g m2\<bar>"
+  with m12 g' have l: "l > 0" "X (n + l) = X n"
+    by (auto simp: min_def nat_diff_distrib split: if_splits)
+
+  from l have "cfrac_lim (cfrac_drop (n + l) e) = cfrac_lim (cfrac_drop n e)"
+    by (simp add: X_def cfrac_remainder_def)
+  hence "cfrac_drop (n + l) e = cfrac_drop n e"
+    by (simp add: cfrac_lim_eq_iff)
+  hence "cfrac_nth (cfrac_drop (n + l) e) = cfrac_nth (cfrac_drop n e)"
+    by (simp only:)
+  hence period: "cfrac_nth e (n + l + k) = cfrac_nth e (n + k)" for k
+    by (simp add: fun_eq_iff add_ac)
+  have period: "cfrac_nth e (k + l) = cfrac_nth e k" if "k \<ge> n" for k
+    using period[of "k - n"] that by (simp add: add_ac)
+  have period: "cfrac_nth e (k + m * l) = cfrac_nth e k" if "k \<ge> n" for k m
+    using that
+  proof (induction m)
+    case (Suc m)
+    have "cfrac_nth e (k + Suc m * l) = cfrac_nth e (k + m * l + l)"
+      by (simp add: algebra_simps)
+    also have "\<dots> = cfrac_nth e (k + m * l)"
+      using Suc.prems by (intro period) auto
+    also have "\<dots> = cfrac_nth e k"
+      using Suc.prems by (intro Suc.IH) auto
+    finally show ?case .
+  qed simp_all
+
+  from this and l and that[of l n] show ?thesis by (simp add: X_def)
+qed
+
+theorem periodic_cfrac_iff_quadratic_irrational:
+  assumes "x \<notin> \<rat>" "x \<ge> 0"
+  shows   "quadratic_irrational x \<longleftrightarrow> 
+           (\<exists>N l. l > 0 \<and> (\<forall>n\<ge>N. cfrac_nth (cfrac_of_real x) (n + l) =
+                                  cfrac_nth (cfrac_of_real x) n))"
+proof safe
+  assume *: "quadratic_irrational x"
+  with assms have **: "quadratic_irrational (cfrac_lim (cfrac_of_real x))" by auto
+  obtain N l where Nl: "l > 0"
+    "\<And>n m. N \<le> n \<Longrightarrow> cfrac_nth (cfrac_of_real x) (n + m * l) = cfrac_nth (cfrac_of_real x) n"
+    "cfrac_remainder (cfrac_of_real x) (N + l) = cfrac_remainder (cfrac_of_real x) N"
+    "cfrac_length (cfrac_of_real x) = \<infinity>"
+    using quadratic_irrational_imp_periodic_cfrac [OF **] by metis
+  show "\<exists>N l. l > 0 \<and> (\<forall>n\<ge>N. cfrac_nth (cfrac_of_real x) (n + l) = cfrac_nth (cfrac_of_real x) n)"
+    by (rule exI[of _ N], rule exI[of _ l]) (insert Nl(1) Nl(2)[of _ 1], auto)
+next
+  fix N l assume "l > 0" "\<forall>n\<ge>N. cfrac_nth (cfrac_of_real x) (n + l) = cfrac_nth (cfrac_of_real x) n"
+  hence "quadratic_irrational (cfrac_lim (cfrac_of_real x))" using assms
+    by (intro periodic_cfrac_imp_quadratic_irrational[of _ l N]) auto
+  with assms show "quadratic_irrational x"
+    by simp
+qed
+
+text \<open>
+  The following result can e.g. be used to show that a number is \<^emph>\<open>not\<close> a quadratic
+  irrational.
+\<close>
+lemma quadratic_irrational_cfrac_nth_range_finite:
+  assumes "quadratic_irrational (cfrac_lim e)"
+  shows   "finite (range (cfrac_nth e))" 
+proof -
+  from quadratic_irrational_imp_periodic_cfrac[OF assms] obtain l N
+    where period: "l > 0" "\<And>m n. n \<ge> N \<Longrightarrow> cfrac_nth e (n + m * l) = cfrac_nth e n"
+    by metis
+  have "cfrac_nth e k \<in> cfrac_nth e ` {..<N+l}" for k
+  proof (cases "k < N + l")
+    case False
+    define n m where "n = N + (k - N) mod l" and "m = (k - N) div l"
+    have "cfrac_nth e n \<in> cfrac_nth e ` {..<N+l}"
+      using \<open>l > 0\<close> by (intro imageI) (auto simp: n_def)
+    also have "cfrac_nth e n = cfrac_nth e (n + m * l)"
+      by (subst period) (auto simp: n_def)
+    also have "n + m * l = k"
+      using False by (simp add: n_def m_def)
+    finally show ?thesis .
+  qed auto
+  hence "range (cfrac_nth e) \<subseteq> cfrac_nth e ` {..<N+l}"
+    by blast
+  thus ?thesis by (rule finite_subset) auto
+qed
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/ROOT b/thys/Continued_Fractions/ROOT
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/ROOT
@@ -0,0 +1,25 @@
+chapter AFP
+
+session Continued_Fractions (AFP) = "HOL-Analysis" +
+  options [timeout = 600]
+  sessions
+    "HOL-Library"
+    "HOL-Computational_Algebra"
+    "HOL-Decision_Procs"
+    "HOL-Number_Theory"
+    Polynomial_Factorization
+    Pell
+    Coinductive
+  theories
+    Continued_Fractions
+    Quadratic_Irrationals
+    E_CFrac
+    Sqrt_Nat_Cfrac
+    Pell_Continued_Fraction
+    Pell_Lifting
+    Pell_Continued_Fraction_Tests
+    Continued_Fraction_Approximation
+  document_files
+    "root.tex"
+    "root.bib"
+
diff --git a/thys/Continued_Fractions/Sqrt_Nat_Cfrac.thy b/thys/Continued_Fractions/Sqrt_Nat_Cfrac.thy
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/Sqrt_Nat_Cfrac.thy
@@ -0,0 +1,1079 @@
+(*
+  File:     Continued_Fractions/Sqrt_Nat_Cfrac.thy
+  Author:   Manuel Eberl, University of Innsbruck
+*)
+section \<open>Continued fraction expansions for square roots of naturals\<close>
+theory Sqrt_Nat_Cfrac
+imports
+  Quadratic_Irrationals
+  "HOL-Library.While_Combinator"
+  "HOL-Library.IArray"
+begin
+
+text \<open>
+  In this section, we shall explore the continued fraction expansion of $\sqrt{D}$, where $D$
+  is a natural number.
+\<close>
+
+lemma butlast_nth [simp]: "n < length xs - 1 \<Longrightarrow> butlast xs ! n = xs ! n"
+  by (induction xs arbitrary: n) (auto simp: nth_Cons split: nat.splits)
+
+text \<open>
+  The following is the length of the period in the continued fraction expansion of
+  $\sqrt{D}$ for a natural number $D$.
+\<close>
+definition sqrt_nat_period_length :: "nat \<Rightarrow> nat" where
+  "sqrt_nat_period_length D =
+     (if is_square D then 0
+      else (LEAST l. l > 0 \<and> (\<forall>n. cfrac_nth (cfrac_of_real (sqrt D)) (Suc n + l) =
+                                  cfrac_nth (cfrac_of_real (sqrt D)) (Suc n))))"
+
+text \<open>  
+  Next, we define a more workable representation for the continued fraction expansion of
+  $\sqrt{D}$ consisting of the period length, the natural number $\lfloor\sqrt{D}\rfloor$, and
+  the content of the period.
+\<close>
+definition sqrt_cfrac_info :: "nat \<Rightarrow> nat \<times> nat \<times> nat list" where
+  "sqrt_cfrac_info D =
+     (sqrt_nat_period_length D, Discrete.sqrt D, 
+      map (\<lambda>n. nat (cfrac_nth (cfrac_of_real (sqrt D)) (Suc n))) [0..<sqrt_nat_period_length D])"
+
+lemma sqrt_nat_period_length_square [simp]: "is_square D \<Longrightarrow> sqrt_nat_period_length D = 0"
+  by (auto simp: sqrt_nat_period_length_def)
+
+definition sqrt_cfrac :: "nat \<Rightarrow> cfrac"
+  where "sqrt_cfrac D = cfrac_of_real (sqrt (real D))"
+
+context
+  fixes D D' :: nat
+  defines "D' \<equiv> nat \<lfloor>sqrt D\<rfloor>"
+begin
+
+text \<open>
+  A number $\alpha = \frac{\sqrt D + p}{q}$ for \<open>p, q \<in> \<nat>\<close> is called a \<^emph>\<open>reduced quadratic surd\<close>
+  if $\alpha > 1$ and $bar\alpha \in (-1;0)$, where $\bar\alpha$ denotes the conjugate
+  $\frac{-\sqrt D + p}{q}$.
+
+  It is furthermore called \<^emph>\<open>associated\<close> to $D$ if \<open>q\<close> divides \<open>D - p\<^sup>2\<close>.
+\<close>
+definition red_assoc :: "nat \<times> nat \<Rightarrow> bool" where
+  "red_assoc = (\<lambda>(p, q).
+     q > 0 \<and> q dvd (D - p\<^sup>2) \<and> (sqrt D + p) / q > 1 \<and> (-sqrt D + p) / q \<in> {-1<..<0})"
+
+text \<open>
+  The following two functions convert between a surd represented as a pair of natural numbers
+  and the actual real number and its conjugate:
+\<close>
+definition surd_to_real :: "nat \<times> nat \<Rightarrow> real"
+  where "surd_to_real = (\<lambda>(p, q). (sqrt D + p) / q)"
+
+definition surd_to_real_cnj :: "nat \<times> nat \<Rightarrow> real"
+  where "surd_to_real_cnj = (\<lambda>(p, q). (-sqrt D + p) / q)"
+
+text \<open>
+  The next function performs a single step in the continued fraction expansion of $\sqrt{D}$.
+\<close>
+definition sqrt_remainder_step :: "nat \<times> nat \<Rightarrow> nat \<times> nat" where
+  "sqrt_remainder_step = (\<lambda>(p, q). let X = (p + D') div q; p' = X * q - p in (p', (D - p'\<^sup>2) div q))"
+
+text \<open>
+  If we iterate this step function starting from the surd
+   $\frac{1}{\sqrt{D} - \lfloor\sqrt{D}\rfloor}$, we get the entire expansion.
+\<close>
+definition sqrt_remainder_surd :: "nat \<Rightarrow> nat \<times> nat"
+  where "sqrt_remainder_surd = (\<lambda>n. (sqrt_remainder_step ^^ n) (D', D - D'\<^sup>2))"
+
+context
+  fixes sqrt_cfrac_nth :: "nat \<Rightarrow> nat" and l
+  assumes nonsquare: "\<not>is_square D"
+  defines "sqrt_cfrac_nth \<equiv> (\<lambda>n. case sqrt_remainder_surd n of (p, q) \<Rightarrow> (D' + p) div q)"
+  defines "l \<equiv> sqrt_nat_period_length D"
+begin
+
+lemma D'_pos: "D' > 0"
+  using nonsquare by (auto simp: D'_def of_nat_ge_1_iff intro: Nat.gr0I)
+
+lemma D'_sqr_less_D: "D'\<^sup>2 < D"
+proof -
+  have "D' \<le> sqrt D" by (auto simp: D'_def)
+  hence "real D' ^ 2 \<le> sqrt D ^ 2" by (intro power_mono) auto
+  also have "\<dots> = D" by simp
+  finally have "D'\<^sup>2 \<le> D" by simp
+  moreover from nonsquare have "D \<noteq> D'\<^sup>2" by auto
+  ultimately show ?thesis by simp
+qed
+
+lemma red_assoc_imp_irrat:
+  assumes "red_assoc pq"
+  shows   "surd_to_real pq \<notin> \<rat>"
+proof 
+  assume rat: "surd_to_real pq \<in> \<rat>"
+  with assms rat show False using irrat_sqrt_nonsquare[OF nonsquare]
+    by (auto simp: field_simps red_assoc_def surd_to_real_def divide_in_Rats_iff2 add_in_Rats_iff1)
+qed
+
+lemma surd_to_real_cnj_irrat:
+  assumes "red_assoc pq"
+  shows   "surd_to_real_cnj pq \<notin> \<rat>"
+proof 
+  assume rat: "surd_to_real_cnj pq \<in> \<rat>"
+  with assms rat show False using irrat_sqrt_nonsquare[OF nonsquare]
+    by (auto simp: field_simps red_assoc_def surd_to_real_cnj_def divide_in_Rats_iff2 diff_in_Rats_iff1)
+qed
+
+lemma surd_to_real_nonneg [intro]: "surd_to_real pq \<ge> 0"
+  by (auto simp: surd_to_real_def case_prod_unfold divide_simps intro!: divide_nonneg_nonneg)
+
+lemma surd_to_real_pos [intro]: "red_assoc pq \<Longrightarrow> surd_to_real pq > 0"
+  by (auto simp: surd_to_real_def case_prod_unfold divide_simps red_assoc_def
+           intro!: divide_nonneg_nonneg)
+
+lemma surd_to_real_nz [simp]: "red_assoc pq \<Longrightarrow> surd_to_real pq \<noteq> 0"
+  by (auto simp: surd_to_real_def case_prod_unfold divide_simps red_assoc_def
+           intro!: divide_nonneg_nonneg)
+
+lemma surd_to_real_cnj_nz [simp]: "red_assoc pq \<Longrightarrow> surd_to_real_cnj pq \<noteq> 0"
+  using surd_to_real_cnj_irrat[of pq] by auto
+
+lemma red_assoc_step:
+  assumes "red_assoc pq"
+  defines "X \<equiv> (D' + fst pq) div snd pq"
+  defines "pq' \<equiv> sqrt_remainder_step pq"
+  shows   "red_assoc pq'"
+          "surd_to_real pq' = 1 / frac (surd_to_real pq)"
+          "surd_to_real_cnj pq' = 1 / (surd_to_real_cnj pq - X)"
+          "X > 0" "X * snd pq \<le> 2 * D'" "X = nat \<lfloor>surd_to_real pq\<rfloor>"
+          "X = nat \<lfloor>-1 / surd_to_real_cnj pq'\<rfloor>"
+proof -
+  obtain p q where [simp]: "pq = (p, q)" by (cases pq)
+  obtain p' q' where [simp]: "pq' = (p', q')" by (cases pq')
+  define \<alpha> where "\<alpha> = (sqrt D + p) / q"
+  define \<alpha>' where "\<alpha>' = 1 / frac \<alpha>"
+  define cnj_\<alpha>' where "cnj_\<alpha>' = (-sqrt D + (X * q - int p)) / ((D - (X * q - int p)\<^sup>2) div q)"
+  from assms(1) have "\<alpha> > 0" "q > 0"
+    by (auto simp: \<alpha>_def red_assoc_def)
+  from assms(1) nonsquare have "\<alpha> \<notin> \<rat>"
+    by (auto simp: \<alpha>_def red_assoc_def divide_in_Rats_iff2 add_in_Rats_iff2 irrat_sqrt_nonsquare)
+  hence \<alpha>'_pos: "frac \<alpha> > 0" using Ints_subset_Rats by auto
+  from \<open>pq' = (p', q')\<close> have p'_def: "p' = X * q - p" and q'_def: "q' = (D - p'\<^sup>2) div q"
+    unfolding pq'_def sqrt_remainder_step_def X_def by (auto simp: Let_def add_ac)
+
+  have "D' + p = \<lfloor>sqrt D + p\<rfloor>"
+    by (auto simp: D'_def)
+  also have "\<dots> div int q = \<lfloor>(sqrt D + p) / q\<rfloor>"
+    by (subst floor_divide_real_eq_div [symmetric]) auto
+  finally have X_altdef: "X = nat \<lfloor>(sqrt D + p) / q\<rfloor>"
+    unfolding X_def zdiv_int [symmetric] by auto
+
+  have nz: "sqrt (real D) + (X * q - real p) \<noteq> 0"
+  proof
+    assume "sqrt (real D) + (X * q - real p) = 0"
+    hence "sqrt (real D) = real p - X * q" by (simp add: algebra_simps)
+    also have "\<dots> \<in> \<rat>" by auto
+    finally show False using irrat_sqrt_nonsquare nonsquare by blast
+  qed
+
+  from assms(1) have "real (p ^ 2) \<le> sqrt D ^ 2"
+    unfolding of_nat_power by (intro power_mono) (auto simp: red_assoc_def field_simps)
+  also have "sqrt D ^ 2 = D" by simp
+  finally have "p\<^sup>2 \<le> D" by (subst (asm) of_nat_le_iff)
+
+  have "frac \<alpha> = \<alpha> - X"
+    by (simp add: X_altdef frac_def \<alpha>_def)
+  also have "\<dots> = (sqrt D - (X * q - int p)) / q"
+    using \<open>q > 0\<close> by (simp add: field_simps \<alpha>_def)
+  finally have "1 / frac \<alpha> = q / (sqrt D - (X * q - int p))"
+    by simp
+  also have "\<dots> = q * (sqrt D + (X * q - int p)) /
+                    ((sqrt D - (X * q - int p)) * (sqrt D + (X * q - int p)))" (is "_ = ?A / ?B")
+    using nz by (subst mult_divide_mult_cancel_right) auto
+  also have "?B = real_of_int (D - int p ^ 2 + 2 * X * p * q - int X ^ 2 * q ^ 2)"
+    by (auto simp: algebra_simps power2_eq_square)
+  also have "q dvd (D - p ^ 2)" using assms(1) by (auto simp: red_assoc_def)
+  with \<open>p\<^sup>2 \<le> D\<close> have "int q dvd (int D - int p ^ 2)" 
+    unfolding of_nat_power [symmetric] by (subst of_nat_diff [symmetric]) auto
+  hence "D - int p ^ 2 + 2 * X * p * q - int X ^ 2 * q ^ 2 = q * ((D - (X * q - int p)\<^sup>2) div q)"
+    by (auto simp: power2_eq_square algebra_simps)
+  also have "?A / \<dots> = (sqrt D + (X * q - int p)) / ((D - (X * q - int p)\<^sup>2) div q)"
+    unfolding of_int_mult of_int_of_nat_eq
+    by (rule mult_divide_mult_cancel_left) (insert \<open>q > 0\<close>, auto)
+  finally have \<alpha>': "\<alpha>' = \<dots>" by (simp add: \<alpha>'_def)
+
+  have dvd: "q dvd (D - (X * q - int p)\<^sup>2)"
+    using assms(1) \<open>int q dvd (int D - int p ^ 2)\<close>
+    by (auto simp: power2_eq_square algebra_simps)
+
+  have "X \<le> (sqrt D + p) / q" unfolding X_altdef by simp
+  moreover have "X \<noteq> (sqrt D + p) / q"
+  proof
+    assume "X = (sqrt D + p) / q"
+    hence "sqrt D = q * X - real p" using \<open>q > 0\<close> by (auto simp: field_simps)
+    also have "\<dots> \<in> \<rat>" by auto
+    finally show False using irrat_sqrt_nonsquare[OF nonsquare] by simp
+  qed
+  ultimately have "X < (sqrt D + p) / q" by simp
+  hence *: "(X * q - int p) < sqrt D"
+    using \<open>q > 0\<close> by (simp add: field_simps)
+  moreover
+  have pos: "real_of_int (int D - (int X * int q - int p)\<^sup>2) > 0"
+  proof (cases "X * q \<ge> p")
+    case True
+    hence "real p \<le> real X * real q" unfolding of_nat_mult [symmetric] of_nat_le_iff .
+    hence "real_of_int ((X * q - int p) ^ 2) < sqrt D ^ 2" using *
+      unfolding of_int_power by (intro power_strict_mono) auto
+    also have "\<dots> = D" by simp
+    finally show ?thesis by simp
+  next
+    case False
+    hence less: "real X * real q < real p"
+      unfolding of_nat_mult [symmetric] of_nat_less_iff by auto
+    have "(real X * real q - real p)\<^sup>2 = (real p - real X * real q)\<^sup>2"
+      by (simp add: power2_eq_square algebra_simps)
+    also have "\<dots> \<le> real p ^ 2" using less by (intro power_mono) auto
+    also have "\<dots> < sqrt D ^ 2" 
+      using \<open>q > 0\<close> assms(1) unfolding of_int_power
+      by (intro power_strict_mono) (auto simp: red_assoc_def field_simps)
+    also have "\<dots> = D" by simp
+    finally show ?thesis by simp
+  qed
+  hence pos': "int D - (int X * int q - int p)\<^sup>2 > 0"
+    by (subst (asm) of_int_0_less_iff)
+  from pos have "real_of_int ((int D - (int X * int q - int p)\<^sup>2) div q) > 0"
+    using \<open>q > 0\<close> dvd by (subst real_of_int_div) (auto intro!: divide_pos_pos)
+  ultimately have cnj_neg: "cnj_\<alpha>' < 0" unfolding cnj_\<alpha>'_def using dvd
+    unfolding of_int_0_less_iff by (intro divide_neg_pos) auto
+
+  have "(p - sqrt D) / q < 0"
+    using assms(1) by (auto simp: red_assoc_def X_altdef le_nat_iff)
+  also have "X \<ge> 1"
+    using assms(1) by (auto simp: red_assoc_def X_altdef le_nat_iff)
+  hence "0 \<le> real X - 1" by simp
+  finally have "q < sqrt D + int q * X - p"
+    using \<open>q > 0\<close> by (simp add: field_simps)
+  hence "q * (sqrt D - (int q * X - p)) < (sqrt D + (int q * X - p)) * (sqrt D - (int q * X - p))"
+    using * by (intro mult_strict_right_mono) (auto simp: red_assoc_def X_altdef field_simps)
+  also have "\<dots> = D - (int q * X - p) ^ 2"
+    by (simp add: power2_eq_square algebra_simps)
+  finally have "cnj_\<alpha>' > -1"
+    using dvd pos \<open>q > 0\<close> by (simp add: real_of_int_div field_simps cnj_\<alpha>'_def)
+
+  from cnj_neg and this have "cnj_\<alpha>' \<in> {-1<..<0}" by auto
+  have "\<alpha>' > 1" using \<open>frac \<alpha> > 0\<close>
+    by (auto simp: \<alpha>'_def field_simps frac_lt_1)
+
+  have "0 = 1 + (-1 :: real)"
+    by simp
+  also have "1 + -1 < \<alpha>' + cnj_\<alpha>'"
+    using \<open>cnj_\<alpha>' > -1\<close> and \<open>\<alpha>' > 1\<close> by (intro add_strict_mono)
+  also have "\<alpha>' + cnj_\<alpha>' = 2 * (real X * q - real p) / ((int D - (int X * q - int p)\<^sup>2) div int q)"
+    by (simp add: \<alpha>' cnj_\<alpha>'_def add_divide_distrib [symmetric])
+  finally have "real X * q - real p > 0" using pos dvd \<open>q > 0\<close>
+    by (subst (asm) zero_less_divide_iff, subst (asm) (1 2 3) real_of_int_div)
+       (auto simp: field_simps)
+  hence "real (X * q) > real p" unfolding of_nat_mult by simp
+  hence p_less_Xq: "p < X * q" by (simp only: of_nat_less_iff)
+
+  from pos' and p_less_Xq have "int D > int ((X * q - p)\<^sup>2)"
+    by (subst of_nat_power) (auto simp: of_nat_diff)
+  hence pos'': "D > (X * q - p)\<^sup>2" unfolding of_nat_less_iff .
+
+  from dvd have "int q dvd int (D - (X * q - p)\<^sup>2)"
+    using p_less_Xq pos'' by (subst of_nat_diff) (auto simp: of_nat_diff)
+  with dvd have dvd': "q dvd (D - (X * q - p)\<^sup>2)"
+    by simp
+
+  have \<alpha>'_altdef: "\<alpha>' = (sqrt D + p') / q'"
+    using dvd dvd' pos'' p_less_Xq \<alpha>'
+    by (simp add: real_of_int_div p'_def q'_def real_of_nat_div mult_ac of_nat_diff)
+  have cnj_\<alpha>'_altdef: "cnj_\<alpha>' = (-sqrt D + p') / q'"
+    using dvd dvd' pos'' p_less_Xq unfolding cnj_\<alpha>'_def
+    by (simp add: real_of_int_div p'_def q'_def real_of_nat_div mult_ac of_nat_diff)
+  from dvd' have dvd'': "q' dvd (D - p'\<^sup>2)"
+    by (auto simp: mult_ac p'_def q'_def)
+  have "real ((D - p'\<^sup>2) div q) > 0" unfolding p'_def
+    by (subst real_of_nat_div[OF dvd'], rule divide_pos_pos) (insert \<open>q > 0\<close> pos'', auto)
+  hence "q' > 0" unfolding q'_def of_nat_0_less_iff .
+
+  show "red_assoc pq'" using \<open>\<alpha>' > 1\<close> and \<open>cnj_\<alpha>' \<in> _\<close> and dvd'' and \<open>q' > 0\<close>
+    by (auto simp: red_assoc_def \<alpha>'_altdef cnj_\<alpha>'_altdef)
+
+  from assms(1) have "real p < sqrt D"
+    by (auto simp add: field_simps red_assoc_def)
+  hence "p \<le> D'" unfolding D'_def by linarith
+  with * have "real (X * q) < sqrt (real D) + D'"
+    by simp
+  thus "X * snd pq \<le> 2 * D'" unfolding D'_def \<open>pq = (p, q)\<close> snd_conv by linarith
+
+  have "(sqrt D + p') / q' = \<alpha>'"
+    by (rule \<alpha>'_altdef [symmetric])
+  also have "\<alpha>' = 1 / frac ((sqrt D + p) / q)"
+    by (simp add: \<alpha>'_def \<alpha>_def)
+  finally show "surd_to_real pq' = 1 / frac (surd_to_real pq)" by (simp add: surd_to_real_def)
+  from \<open>X \<ge> 1\<close> show "X > 0" by simp
+  from X_altdef show "X = nat \<lfloor>surd_to_real pq\<rfloor>" by (simp add: surd_to_real_def)
+
+  have "sqrt (real D) < real p + 1 * real q"
+    using assms(1) by (auto simp: red_assoc_def field_simps)
+  also have "\<dots> \<le> real p + real X * real q"
+    using \<open>X > 0\<close> by (intro add_left_mono mult_right_mono) (auto simp: of_nat_ge_1_iff)
+  finally have "sqrt (real D) < \<dots>" .
+
+  have "real p < sqrt D"
+    using assms(1) by (auto simp add: field_simps red_assoc_def)
+  also have "\<dots> \<le> sqrt D + q * X"
+    by linarith
+  finally have less: "real p < sqrt D + X * q" by (simp add: algebra_simps)
+  moreover have "D + p * p' + X * q * sqrt D = q * q' + p * sqrt D + p' * sqrt D + X * p' * q"
+    using dvd' pos'' p_less_Xq \<open>q > 0\<close> unfolding p'_def q'_def of_nat_mult of_nat_add
+    by (simp add:  power2_eq_square field_simps of_nat_diff real_of_nat_div)
+  ultimately show *: "surd_to_real_cnj pq' = 1 / (surd_to_real_cnj pq - X)"
+    using \<open>q > 0\<close> \<open>q' > 0\<close> by (auto simp: surd_to_real_cnj_def field_simps)
+
+  have **: "a = nat \<lfloor>y\<rfloor>" if "x \<ge> 0" "x < 1" "real a + x = y" for a :: nat and x y :: real
+    using that by linarith
+  from assms(1) have surd_to_real_cnj: "surd_to_real_cnj (p, q) \<in> {-1<..<0}"
+    by (auto simp: surd_to_real_cnj_def red_assoc_def)
+  have "surd_to_real_cnj (p, q) < X"
+    using assms(1) less by (auto simp: surd_to_real_cnj_def field_simps red_assoc_def)
+  hence "real X = surd_to_real_cnj (p, q) - 1 / surd_to_real_cnj (p', q')" using *
+    using surd_to_real_cnj_irrat assms(1) \<open>red_assoc pq'\<close> by (auto simp: field_simps)
+  thus "X = nat \<lfloor>-1 / surd_to_real_cnj pq'\<rfloor>" using surd_to_real_cnj
+    by (intro **[of "-surd_to_real_cnj (p, q)"]) auto
+qed
+
+lemma red_assoc_denom_2D:
+  assumes "red_assoc (p, q)"
+  defines "X \<equiv> (D' + p) div q"
+  assumes "X > D'"
+  shows  "q = 1"
+proof -
+  have "X * q \<le> 2 * D'" "X > 0"
+    using red_assoc_step(4,5)[OF assms(1)] by (simp_all add: X_def)
+  note this(1)
+  also have "2 * D' < 2 * X"
+    by (intro mult_strict_left_mono assms) auto
+  finally have "q < 2" using \<open>X > 0\<close> by simp
+  moreover from assms(1) have "q > 0" by (auto simp: red_assoc_def)
+  ultimately show ?thesis by simp
+qed
+
+lemma red_assoc_denom_1:
+  assumes "red_assoc (p, 1)"
+  shows   "p = D'" 
+proof -
+  from assms have "sqrt D > p" "sqrt D < real p + 1"
+    by (auto simp: red_assoc_def)
+  thus "p = D'" unfolding D'_def
+    by linarith
+qed
+
+lemma red_assoc_begin:
+  "red_assoc (D', D - D'\<^sup>2)"
+  "surd_to_real (D', D - D'\<^sup>2) = 1 / frac (sqrt D)"
+  "surd_to_real_cnj (D', D - D'\<^sup>2) = -1 / (sqrt D + D')"
+proof -
+  have pos: "D > 0" "D' > 0"
+    using nonsquare by (auto simp: D'_def of_nat_ge_1_iff intro!: Nat.gr0I)
+
+  have "sqrt D \<noteq> D'"
+    using irrat_sqrt_nonsquare[OF nonsquare] by auto
+  moreover have "sqrt D \<ge> 0" by simp
+  hence "D' \<le> sqrt D" unfolding D'_def by linarith
+  ultimately have less: "D' < sqrt D" by simp
+
+  have "sqrt D \<noteq> D' + 1"
+    using irrat_sqrt_nonsquare[OF nonsquare] by auto
+  moreover have "sqrt D \<ge> 0" by simp
+  hence "D' \<ge> sqrt D - 1" unfolding D'_def by linarith
+  ultimately have gt: "D' > sqrt D - 1" by simp
+
+  from less have "real D' ^ 2 < sqrt D ^ 2" by (intro power_strict_mono) auto
+  also have "\<dots> = D" by simp
+  finally have less': "D'\<^sup>2 < D" unfolding of_nat_power [symmetric] of_nat_less_iff .
+
+  moreover have "real D' * (real D' - 1) < sqrt D * (sqrt D - 1)"
+    using less pos
+    by (intro mult_strict_mono diff_strict_right_mono) (auto simp: of_nat_ge_1_iff)
+  hence "D'\<^sup>2 + sqrt D < D' + D"
+    by (simp add: field_simps power2_eq_square)
+  moreover have "(sqrt D - 1) * sqrt D < real D' * (real D' + 1)"
+    using pos gt by (intro mult_strict_mono) auto
+  hence "D < sqrt D + D'\<^sup>2 + D'" by (simp add: power2_eq_square field_simps)
+  ultimately show "red_assoc (D', D - D'\<^sup>2)"
+    by (auto simp: red_assoc_def field_simps of_nat_diff less)
+
+  have frac: "frac (sqrt D) = sqrt D - D'" unfolding frac_def D'_def
+    by auto
+  show "surd_to_real (D', D - D'\<^sup>2) = 1 / frac (sqrt D)" unfolding surd_to_real_def
+    using less less' pos by (subst frac) (auto simp: of_nat_diff power2_eq_square field_simps)
+
+  have "surd_to_real_cnj (D', D - D'\<^sup>2) = -((sqrt D - D') / (D - D'\<^sup>2))"
+    using less less' pos by (auto simp: surd_to_real_cnj_def field_simps)
+  also have "real (D - D'\<^sup>2) = (sqrt D - D') * (sqrt D + D')"
+    using less' by (simp add: power2_eq_square algebra_simps of_nat_diff)
+  also have "(sqrt D - D') / \<dots> = 1 / (sqrt D + D')"
+    using less by (subst nonzero_divide_mult_cancel_left) auto
+  finally show "surd_to_real_cnj (D', D - D'\<^sup>2) = -1 / (sqrt D + D')" by simp
+qed
+
+lemma cfrac_remainder_surd_to_real:
+  assumes "red_assoc pq"
+  shows   "cfrac_remainder (cfrac_of_real (surd_to_real pq)) n =
+             surd_to_real ((sqrt_remainder_step ^^ n) pq)"
+  using assms(1)
+proof (induction n arbitrary: pq)
+  case 0
+  hence "cfrac_lim (cfrac_of_real (surd_to_real pq)) = surd_to_real pq"
+    by (intro cfrac_lim_of_real red_assoc_imp_irrat 0)
+  thus ?case using 0
+    by auto
+next
+  case (Suc n)
+  obtain p q where [simp]: "pq = (p, q)" by (cases pq)
+  have "surd_to_real ((sqrt_remainder_step ^^ Suc n) pq) = 
+          surd_to_real ((sqrt_remainder_step ^^ n) (sqrt_remainder_step (p, q)))"
+    by (subst funpow_Suc_right) auto
+  also have "\<dots> = cfrac_remainder (cfrac_of_real (surd_to_real (sqrt_remainder_step (p, q)))) n"
+    using red_assoc_step(1)[of "(p, q)"] Suc.prems
+    by (intro Suc.IH [symmetric]) (auto simp: sqrt_remainder_step_def Let_def add_ac)
+  also have "surd_to_real (sqrt_remainder_step (p, q)) = 1 / frac (surd_to_real (p, q))"
+    using red_assoc_step(2)[of "(p, q)"] Suc.prems
+    by (auto simp: sqrt_remainder_step_def Let_def add_ac surd_to_real_def)
+  also have "cfrac_of_real \<dots> = cfrac_tl (cfrac_of_real (surd_to_real (p, q)))"
+    using Suc.prems Ints_subset_Rats red_assoc_imp_irrat by (subst cfrac_tl_of_real) auto
+  also have "cfrac_remainder \<dots> n = cfrac_remainder (cfrac_of_real (surd_to_real (p, q))) (Suc n)"
+    by (simp add: cfrac_drop_Suc_right cfrac_remainder_def)
+  finally show ?case by simp
+qed
+
+lemma red_assoc_step' [intro]: "red_assoc pq \<Longrightarrow> red_assoc (sqrt_remainder_step pq)"
+  using red_assoc_step(1)[of pq]
+  by (simp add: sqrt_remainder_step_def case_prod_unfold add_ac Let_def)
+
+lemma red_assoc_steps [intro]: "red_assoc pq \<Longrightarrow> red_assoc ((sqrt_remainder_step ^^ n) pq)"
+  by (induction n) auto
+
+lemma floor_sqrt_less_sqrt: "D' < sqrt D"
+proof -
+  have "D' \<le> sqrt D" unfolding D'_def by auto
+  moreover have "sqrt D \<noteq> D'"
+    using irrat_sqrt_nonsquare[OF nonsquare] by auto
+  ultimately show ?thesis by auto
+qed
+
+lemma red_assoc_bounds: 
+  assumes "red_assoc pq"
+  shows   "pq \<in> (SIGMA p:{0<..D'}. {Suc D' - p..D' + p})"
+proof -
+  obtain p q where [simp]: "pq = (p, q)" by (cases pq)
+  from assms have *: "p < sqrt D"
+    by (auto simp: red_assoc_def field_simps)
+  hence p: "p \<le> D'" unfolding D'_def by linarith
+  from assms have "p > 0" by (auto intro!: Nat.gr0I simp: red_assoc_def)
+
+  have "q > sqrt D - p" "q < sqrt D + p" 
+    using assms by (auto simp: red_assoc_def field_simps)
+  hence "q \<ge> D' + 1 - p" "q \<le> D' + p"
+    unfolding D'_def by linarith+
+  with p \<open>p > 0\<close> show ?thesis by simp
+qed
+
+lemma surd_to_real_cnj_eq_iff: 
+  assumes "red_assoc pq" "red_assoc pq'"
+  shows   "surd_to_real_cnj pq = surd_to_real_cnj pq' \<longleftrightarrow> pq = pq'"
+proof
+  assume eq: "surd_to_real_cnj pq = surd_to_real_cnj pq'"
+  from assms have pos: "snd pq > 0" "snd pq' > 0" by (auto simp: red_assoc_def)
+  have "snd pq = snd pq'"
+  proof (rule ccontr)
+    assume "snd pq \<noteq> snd pq'"
+    with eq have "sqrt D = (real (fst pq' * snd pq) - fst pq * snd pq') / (real (snd pq) - snd pq')"
+      using pos by (auto simp: field_simps surd_to_real_cnj_def case_prod_unfold)
+    also have "\<dots> \<in> \<rat>" by auto
+    finally show False using irrat_sqrt_nonsquare[OF nonsquare] by auto
+  qed
+  moreover from this eq pos have "fst pq = fst pq'"
+    by (auto simp: surd_to_real_cnj_def case_prod_unfold)
+  ultimately show "pq = pq'" by (simp add: prod_eq_iff)
+qed auto
+
+lemma red_assoc_sqrt_remainder_surd [intro]: "red_assoc (sqrt_remainder_surd n)"
+  by (auto simp: sqrt_remainder_surd_def intro!: red_assoc_begin)
+
+lemma surd_to_real_sqrt_remainder_surd:
+  "surd_to_real (sqrt_remainder_surd n) = cfrac_remainder (cfrac_of_real (sqrt D)) (Suc n)"
+proof (induction n)
+  case 0
+  from nonsquare have "D > 0" by (auto intro!: Nat.gr0I)
+  with red_assoc_begin show ?case using nonsquare irrat_sqrt_nonsquare[OF nonsquare]
+    using Ints_subset_Rats cfrac_drop_Suc_right cfrac_remainder_def cfrac_tl_of_real
+          sqrt_remainder_surd_def by fastforce
+next
+  case (Suc n)
+  have "surd_to_real (sqrt_remainder_surd (Suc n)) =
+          surd_to_real (sqrt_remainder_step (sqrt_remainder_surd n))"
+    by (simp add: sqrt_remainder_surd_def)
+  also have "\<dots> = 1 / frac (surd_to_real (sqrt_remainder_surd n))"
+    using red_assoc_step[OF red_assoc_sqrt_remainder_surd[of n]] by simp
+  also have "surd_to_real (sqrt_remainder_surd n) =
+               cfrac_remainder (cfrac_of_real (sqrt D)) (Suc n)" (is "_ = ?X")
+    by (rule Suc.IH)
+  also have "\<lfloor>cfrac_remainder (cfrac_of_real (sqrt (real D))) (Suc n)\<rfloor> =
+               cfrac_nth (cfrac_of_real (sqrt (real D))) (Suc n)"
+    using irrat_sqrt_nonsquare[OF nonsquare] by (intro floor_cfrac_remainder) auto
+  hence "1 / frac ?X = cfrac_remainder (cfrac_of_real (sqrt D)) (Suc (Suc n))"
+    using irrat_sqrt_nonsquare[OF nonsquare]
+    by (subst cfrac_remainder_Suc[of "Suc n"])
+       (simp_all add: frac_def cfrac_length_of_real_irrational)
+  finally show ?case .
+qed
+
+lemma sqrt_cfrac: "sqrt_cfrac_nth n = cfrac_nth (cfrac_of_real (sqrt D)) (Suc n)"
+proof -
+  have "cfrac_nth (cfrac_of_real (sqrt D)) (Suc n) =
+          \<lfloor>cfrac_remainder (cfrac_of_real (sqrt D)) (Suc n)\<rfloor>"
+    using irrat_sqrt_nonsquare[OF nonsquare] by (subst floor_cfrac_remainder) auto
+  also have "cfrac_remainder (cfrac_of_real (sqrt D)) (Suc n) = surd_to_real (sqrt_remainder_surd n)"
+    by (rule surd_to_real_sqrt_remainder_surd [symmetric])
+  also have "nat \<lfloor>surd_to_real (sqrt_remainder_surd n)\<rfloor> = sqrt_cfrac_nth n"
+    unfolding sqrt_cfrac_nth_def using red_assoc_step(6)[OF red_assoc_sqrt_remainder_surd[of n]]
+    by (simp add: case_prod_unfold)
+  finally show ?thesis
+    by (simp add: nat_eq_iff)
+qed
+
+lemma sqrt_cfrac_pos: "sqrt_cfrac_nth k > 0"
+  using red_assoc_step(4)[OF red_assoc_sqrt_remainder_surd[of k]]
+  by (simp add: sqrt_cfrac_nth_def case_prod_unfold)
+
+lemma snd_sqrt_remainder_surd_pos: "snd (sqrt_remainder_surd n) > 0"
+  using red_assoc_sqrt_remainder_surd[of n] by (auto simp: red_assoc_def)
+
+
+lemma
+  shows period_nonempty:      "l > 0"
+    and period_length_le_aux: "l \<le> D' * (D' + 1)"
+    and sqrt_remainder_surd_periodic:   "\<And>n. sqrt_remainder_surd n = sqrt_remainder_surd (n mod l)"
+    and sqrt_cfrac_periodic: "\<And>n. sqrt_cfrac_nth n = sqrt_cfrac_nth (n mod l)"
+    and sqrt_remainder_surd_smallest_period:
+          "\<And>n. n \<in> {0<..<l} \<Longrightarrow> sqrt_remainder_surd n \<noteq> sqrt_remainder_surd 0"
+    and snd_sqrt_remainder_surd_gt_1:   "\<And>n. n < l - 1 \<Longrightarrow> snd (sqrt_remainder_surd n) > 1"
+    and sqrt_cfrac_le:       "\<And>n. n < l - 1 \<Longrightarrow> sqrt_cfrac_nth n \<le> D'"
+    and sqrt_remainder_surd_last:       "sqrt_remainder_surd (l - 1) = (D', 1)"
+    and sqrt_cfrac_last:     "sqrt_cfrac_nth (l - 1) = 2 * D'"
+    and sqrt_cfrac_palindrome: "\<And>n. n < l - 1 \<Longrightarrow> sqrt_cfrac_nth (l - n - 2) = sqrt_cfrac_nth n"
+    and sqrt_cfrac_smallest_period:
+          "\<And>l'. l' > 0 \<Longrightarrow> (\<And>k. sqrt_cfrac_nth (k + l') = sqrt_cfrac_nth k) \<Longrightarrow> l' \<ge> l"
+proof -
+  note [simp] = sqrt_remainder_surd_def
+  define f where "f = sqrt_remainder_surd"
+  have *[intro]: "red_assoc (f n)" for n
+    unfolding f_def by (rule red_assoc_sqrt_remainder_surd)
+
+  define S where "S = (SIGMA p:{0<..D'}. {Suc D' - p..D' + p})"
+  have [intro]: "finite S" by (simp add: S_def)
+  have "card S = (\<Sum>p=1..D'. 2 * p)" unfolding S_def
+    by (subst card_SigmaI) (auto intro!: sum.cong)
+  also have "\<dots> = D' * (D' + 1)"
+    by (induction D') (auto simp: power2_eq_square)
+  finally have [simp]: "card S = D' * (D' + 1)" .
+  
+  have "D' * (D' + 1) + 1 = card {..D' * (D' + 1)}" by simp
+  define k1 where
+    "k1 = (LEAST k1. k1 \<le> D' * (D' + 1) \<and> (\<exists>k2. k2 \<le> D' * (D' + 1) \<and> k1 \<noteq> k2 \<and> f k1 = f k2))"
+  define k2 where
+    "k2 = (LEAST k2. k2 \<le> D' * (D' + 1) \<and> k1 \<noteq> k2 \<and> f k1 = f k2)"
+  
+  have "f ` {..D' * (D' + 1)} \<subseteq> S" unfolding S_def
+    using red_assoc_bounds[OF *] by blast
+  hence "card (f ` {..D' * (D' + 1)}) \<le> card S"
+    by (intro card_mono) auto
+  also have "card S = D' * (D' + 1)" by simp
+  also have "\<dots> < card {..D' * (D' + 1)}" by simp
+  finally have "\<not>inj_on f {..D' * (D' + 1)}"
+    by (rule pigeonhole)
+  hence "\<exists>k1. k1 \<le> D' * (D' + 1) \<and> (\<exists>k2. k2 \<le> D' * (D' + 1) \<and> k1 \<noteq> k2 \<and> f k1 = f k2)"
+    by (auto simp: inj_on_def)
+  from LeastI_ex[OF this, folded k1_def]
+    have "k1 \<le> D' * (D' + 1)" "\<exists>k2\<le>D' * (D' + 1). k1 \<noteq> k2 \<and> f k1 = f k2" by auto
+  moreover from LeastI_ex[OF this(2), folded k2_def]
+    have "k2 \<le> D' * (D' + 1)" "k1 \<noteq> k2" "f k1 = f k2" by auto
+  moreover have "k1 \<le> k2"
+  proof (rule ccontr)
+    assume "\<not>(k1 \<le> k2)"
+    hence "k2 \<le> D' * (D' + 1) \<and> (\<exists>k2'. k2' \<le> D' * (D' + 1) \<and> k2 \<noteq> k2' \<and> f k2 = f k2')"
+      using \<open>k1 \<le> D' * (D' + 1)\<close> and \<open>k1 \<noteq> k2\<close> and \<open>f k1 = f k2\<close> by auto
+    hence "k1 \<le> k2" unfolding k1_def by (rule Least_le)
+    with \<open>\<not>(k1 \<le> k2)\<close> show False by simp
+  qed
+  ultimately have k12: "k1 < k2" "k2 \<le> D' * (D' + 1)" "f k1 = f k2" by auto
+
+  have [simp]: "k1 = 0"
+  proof (cases k1)
+    case (Suc k1')
+    define k2' where "k2' = k2 - 1"
+    have Suc': "k2 = Suc k2'" using k12 by (simp add: k2'_def)
+    have nz: "surd_to_real_cnj (sqrt_remainder_step (f k1')) \<noteq> 0"
+             "surd_to_real_cnj (sqrt_remainder_step (f k2')) \<noteq> 0"
+      using surd_to_real_cnj_nz[OF *[of k2]] surd_to_real_cnj_nz[OF *[of k1]] 
+      by (simp_all add: f_def Suc Suc')
+
+    define a where "a = (D' + fst (f k1)) div snd (f k1)"
+    define a' where "a' = (D' + fst (f k1')) div snd (f k1')"
+    define a'' where "a'' = (D' + fst (f k2')) div snd (f k2')"
+    have "a' = nat \<lfloor>- 1 / surd_to_real_cnj (sqrt_remainder_step (f k1'))\<rfloor>"
+      using red_assoc_step[OF *[of k1']] by (simp add: a'_def)
+    also have "sqrt_remainder_step (f k1') = f k1"
+      by (simp add: Suc f_def)
+    also have "f k1 = f k2" by fact
+    also have "f k2 = sqrt_remainder_step (f k2')" by (simp add: Suc' f_def)
+    also have "nat \<lfloor>- 1 / surd_to_real_cnj (sqrt_remainder_step (f k2'))\<rfloor> = a''"
+      using red_assoc_step[OF *[of k2']] by (simp add: a''_def)
+    finally have a'_a'': "a' = a''" .
+
+    have "surd_to_real_cnj (f k2') \<noteq> a''"
+      using surd_to_real_cnj_irrat[OF *[of k2']] by auto
+    hence "surd_to_real_cnj (f k2') = 1 / surd_to_real_cnj (sqrt_remainder_step (f k2')) + a''"
+      using red_assoc_step(3)[OF *[of k2'], folded a''_def] nz
+      by (simp add: field_simps)
+    also have "\<dots> = 1 / surd_to_real_cnj (sqrt_remainder_step (f k1')) + a'"
+      using k12 by (simp add: a'_a'' k12 Suc Suc' f_def)
+    also have nz': "surd_to_real_cnj (f k1') \<noteq> a'"
+      using surd_to_real_cnj_irrat[OF *[of k1']] by auto
+    hence "1 / surd_to_real_cnj (sqrt_remainder_step (f k1')) + a' = surd_to_real_cnj (f k1')"
+      using red_assoc_step(3)[OF *[of k1'], folded a'_def] nz nz'
+      by (simp add: field_simps)
+    finally have "f k1' = f k2'"
+      by (subst (asm) surd_to_real_cnj_eq_iff) auto
+    with k12 have "k1' \<le> D' * (D' + 1) \<and> (\<exists>k2\<le>D' * (D' + 1). k1' \<noteq> k2 \<and> f k1' = f k2)"
+      by (auto simp: Suc Suc' intro!: exI[of _ k2'])
+    hence "k1 \<le> k1'" unfolding k1_def by (rule Least_le)
+    thus "k1 = 0" by (simp add: Suc)
+  qed auto
+
+  have smallest_period: "f k \<noteq> f 0" if "k \<in> {0<..<k2}" for k
+  proof
+    assume "f k = f 0"
+    hence "k \<le> D' * (D' + 1) \<and> k1 \<noteq> k \<and> f k1 = f k"
+      using k12 that by auto
+    hence "k2 \<le> k" unfolding k2_def by (rule Least_le)
+    with that show False by auto
+  qed
+
+  have snd_f_gt_1: "snd (f k) > 1" if "k < k2 - 1" for k
+  proof -
+    have "snd (f k) \<noteq> 1"
+    proof
+      assume "snd (f k) = 1"
+      hence "f k = (D', 1)" using red_assoc_denom_1[of "fst (f k)"] *[of k]
+        by (cases "f k") auto
+      hence "sqrt_remainder_step (f k) = (D', D - D'\<^sup>2)" by (auto simp: sqrt_remainder_step_def)
+      hence "f (Suc k) = f 0" by (simp add: f_def)
+      moreover have "f (Suc k) \<noteq> f 0"
+        using that by (intro smallest_period) auto
+      ultimately show False by contradiction
+    qed
+    moreover have "snd (f k) > 0" using *[of k] by (auto simp: red_assoc_def)
+    ultimately show ?thesis by simp
+  qed
+
+  have sqrt_cfrac_le: "sqrt_cfrac_nth k \<le> D'" if "k < k2 - 1" for k
+  proof -
+    define p and q where "p = fst (f k)" and "q = snd (f k)"
+    have "q \<ge> 2" using snd_f_gt_1[of k] that by (auto simp: q_def)
+    also have "sqrt_cfrac_nth k * q \<le> D' * 2"
+      using red_assoc_step(5)[OF *[of k]]
+      by (simp add: sqrt_cfrac_nth_def p_def q_def case_prod_unfold f_def)
+    finally show ?thesis by simp
+  qed 
+
+  have last: "f (k2 - 1) = (D', 1)"
+  proof -
+    define p and q where "p = fst (f (k2 - 1))" and "q = snd (f (k2 - 1))"
+    have pq: "f (k2 - 1) = (p, q)" by (simp add: p_def q_def)
+    have "sqrt_remainder_step (f (k2 - 1)) = f (Suc (k2 - 1))"
+      by (simp add: f_def)
+    also from k12 have "Suc (k2 - 1) = k2" by simp
+    also have "f k2 = f 0"
+      using k12 by simp
+    also have "f 0 = (D', D - D'\<^sup>2)" by (simp add: f_def)
+    finally have eq: "sqrt_remainder_step (f (k2 - 1)) = (D', D - D'\<^sup>2)" .
+
+    hence "(D - D'\<^sup>2) div q = D - D'\<^sup>2" unfolding sqrt_remainder_step_def Let_def pq
+      by auto
+    moreover have "q > 0" using *[of "k2 - 1"]
+      by (auto simp: red_assoc_def q_def)
+    ultimately have "q = 1" using D'_sqr_less_D
+      by (subst (asm) div_eq_dividend_iff) auto
+    hence "p = D'"
+      using red_assoc_denom_1[of p] *[of "k2 - 1"] unfolding pq by auto
+    with \<open>q = 1\<close> show "f (k2 - 1) = (D', 1)" unfolding pq by simp
+  qed
+
+  have period: "sqrt_remainder_surd n = sqrt_remainder_surd (n mod k2)" for n
+    unfolding sqrt_remainder_surd_def using k12 by (intro funpow_cycle) (auto simp: f_def)
+  have period': "sqrt_cfrac_nth k = sqrt_cfrac_nth (k mod k2)" for k
+    using period[of k] by (simp add: sqrt_cfrac_nth_def)
+
+  have k2_le: "l \<ge> k2" if "l > 0" "\<And>k. sqrt_cfrac_nth (k + l) = sqrt_cfrac_nth k" for l
+  proof (rule ccontr)
+    assume *: "\<not>(l \<ge> k2)"
+    hence "sqrt_cfrac_nth (k2 - Suc l) = sqrt_cfrac_nth (k2 - 1)"
+      using that(2)[of "k2 - Suc l"] by simp
+    also have "\<dots> = 2 * D'"
+      using last by (simp add: sqrt_cfrac_nth_def f_def)
+    finally have "2 * D' = sqrt_cfrac_nth (k2 - Suc l)" ..
+    also have "\<dots> \<le> D'" using k12 that *
+      by (intro sqrt_cfrac_le diff_less_mono2) auto
+    finally show False using D'_pos by simp
+  qed
+
+  have "l = (LEAST l. 0 < l \<and> (\<forall>n. int (sqrt_cfrac_nth (n + l)) = int (sqrt_cfrac_nth n)))"
+    using nonsquare unfolding sqrt_cfrac_def
+    by (simp add: l_def sqrt_nat_period_length_def sqrt_cfrac)
+  hence l_altdef: "l = (LEAST l. 0 < l \<and> (\<forall>n. sqrt_cfrac_nth (n + l) = sqrt_cfrac_nth n))"
+    by simp
+
+  have [simp]: "D \<noteq> 0" using nonsquare by (auto intro!: Nat.gr0I)
+  have "\<exists>l. l > 0 \<and> (\<forall>k. sqrt_cfrac_nth (k + l) = sqrt_cfrac_nth k)"
+  proof (rule exI, safe)
+    fix k show "sqrt_cfrac_nth (k + k2) = sqrt_cfrac_nth k"
+      using period'[of k] period'[of "k + k2"] k12 by simp
+  qed (insert k12, auto)
+  from LeastI_ex[OF this, folded l_altdef]
+  have l: "l > 0" "\<And>k. sqrt_cfrac_nth (k + l) = sqrt_cfrac_nth k"
+    by (simp_all add: sqrt_cfrac)
+
+  have "l \<le> k2" unfolding l_altdef
+    by (rule Least_le) (subst (1 2) period', insert k12, auto)
+  moreover have "k2 \<le> l" using k2_le l by blast
+  ultimately have [simp]: "l = k2" by auto
+
+  define x' where "x' = (\<lambda>k. -1 / surd_to_real_cnj (f k))"
+  {
+    fix k :: nat
+    have nz: "surd_to_real_cnj (f k) \<noteq> 0" "surd_to_real_cnj (f (Suc k)) \<noteq> 0"
+      using surd_to_real_cnj_nz[OF *, of k] surd_to_real_cnj_nz[OF *, of "Suc k"]
+      by (simp_all add: f_def)
+
+    have "surd_to_real_cnj (f k) \<noteq> sqrt_cfrac_nth k"
+      using surd_to_real_cnj_irrat[OF *[of k]] by auto
+    hence "x' (Suc k) = sqrt_cfrac_nth k + 1 / x' k"
+      using red_assoc_step(3)[OF *[of k]] nz
+      by (simp add: field_simps sqrt_cfrac_nth_def case_prod_unfold f_def x'_def)
+  } note x'_Suc = this
+
+  have x'_nz: "x' k \<noteq> 0" for k
+    using surd_to_real_cnj_nz[OF *[of k]] by (auto simp: x'_def)
+  have x'_0: "x' 0 = real D' + sqrt D"
+    using red_assoc_begin by (simp add: x'_def f_def)
+
+  define c' where "c' = cfrac (\<lambda>n. sqrt_cfrac_nth (l - Suc n))"
+  define c'' where "c'' = cfrac (\<lambda>n. if n = 0 then 2 * D' else sqrt_cfrac_nth (n - 1))"
+  have nth_c' [simp]: "cfrac_nth c' n = sqrt_cfrac_nth (l - Suc n)" for n
+    unfolding c'_def by (subst cfrac_nth_cfrac) (auto simp: is_cfrac_def intro!: sqrt_cfrac_pos)
+  have nth_c'' [simp]: "cfrac_nth c'' n = (if n = 0 then 2 * D' else sqrt_cfrac_nth (n - 1))" for n
+    unfolding c''_def by (subst cfrac_nth_cfrac) (auto simp: is_cfrac_def intro!: sqrt_cfrac_pos)
+
+  have "conv' c' n (x' (l - n)) = x' l" if "n \<le> l" for n
+    using that
+  proof (induction n)
+    case (Suc n)
+    have "x' l = conv' c' n (x' (l - n))"
+      using Suc.prems by (intro Suc.IH [symmetric]) auto
+    also have "l - n = Suc (l - Suc n)"
+      using Suc.prems by simp
+    also have "x' \<dots> = cfrac_nth c' n + 1 / x' (l - Suc n)"
+      by (subst x'_Suc) simp
+    also have "conv' c' n \<dots> = conv' c' (Suc n) (x' (l - Suc n))"
+      by (simp add: conv'_Suc_right)
+    finally show ?case ..
+  qed simp_all
+  from this[of l] have conv'_x'_0: "conv' c' l (x' 0) = x' 0"
+    using k12 by (simp add: x'_def)
+
+  have "cfrac_nth (cfrac_of_real (x' 0)) n = cfrac_nth c'' n" for n
+  proof (cases n)
+    case 0
+    thus ?thesis by (simp add: x'_0 D'_def)
+  next
+    case (Suc n')
+    have "sqrt D \<notin> \<int>"
+      using red_assoc_begin(1) red_assoc_begin(2) by auto
+    hence "cfrac_nth (cfrac_of_real (real D' + sqrt (real D))) (Suc n') =
+          cfrac_nth (cfrac_of_real (sqrt (real D))) (Suc n')"
+      by (simp add: cfrac_tl_of_real frac_add_of_nat Ints_add_left_cancel flip: cfrac_nth_tl)
+    thus ?thesis using x'_nz[of 0]
+      by (simp add: x'_0 sqrt_cfrac Suc)
+  qed
+
+  show "sqrt_cfrac_nth (l - n - 2) = sqrt_cfrac_nth n" if "n < l - 1" for n
+  proof -
+    have "D > 1" using nonsquare by (cases D) (auto intro!: Nat.gr0I)
+    hence "D' + sqrt D > 0 + 1" using D'_pos by (intro add_strict_mono) auto
+    hence "x' 0 > 1" by (auto simp: x'_0)
+    hence "cfrac_nth c' (Suc n) = cfrac_nth (cfrac_of_real (conv' c' l (x' 0))) (Suc n)"
+      using \<open>n < l - 1\<close> using cfrac_of_real_conv' by auto
+    also have "\<dots> = cfrac_nth (cfrac_of_real (x' 0)) (Suc n)"
+      by (subst conv'_x'_0) auto
+    also have "\<dots> = cfrac_nth c'' (Suc n)" by fact
+    finally show "sqrt_cfrac_nth (l - n - 2) = sqrt_cfrac_nth n"
+      by simp
+  qed
+
+  show "l > 0" "l \<le> D' * (D' + 1)" using k12 by simp_all
+  show "sqrt_remainder_surd n = sqrt_remainder_surd (n mod l)"
+       "sqrt_cfrac_nth n = sqrt_cfrac_nth (n mod l)" for n
+    using period[of n] period'[of n] by simp_all
+  show "sqrt_remainder_surd n \<noteq> sqrt_remainder_surd 0" if "n \<in> {0<..<l}" for n
+    using smallest_period[of n] that by (auto simp: f_def)
+  show "snd (sqrt_remainder_surd n) > 1" if "n < l - 1" for n
+    using that snd_f_gt_1[of n] by (simp add: f_def)
+  show "f (l - 1) = (D', 1)" and "sqrt_cfrac_nth (l - 1) = 2 * D'"
+    using last by (simp_all add: sqrt_cfrac_nth_def f_def)
+  show "sqrt_cfrac_nth k \<le> D'" if "k < l - 1" for k
+    using sqrt_cfrac_le[of k] that by simp
+  show "l' \<ge> l" if "l' > 0" "\<And>k. sqrt_cfrac_nth (k + l') = sqrt_cfrac_nth k" for l'
+    using k2_le[of l'] that by auto
+qed
+
+theorem cfrac_sqrt_periodic:
+  "cfrac_nth (cfrac_of_real (sqrt D)) (Suc n) =
+   cfrac_nth (cfrac_of_real (sqrt D)) (Suc (n mod l))"
+  using sqrt_cfrac_periodic[of n] by (metis sqrt_cfrac)
+
+theorem cfrac_sqrt_le: "n \<in> {0<..<l} \<Longrightarrow> cfrac_nth (cfrac_of_real (sqrt D)) n \<le> D'"
+  using sqrt_cfrac_le[of "n - 1"]
+  by (metis Suc_less_eq Suc_pred add.right_neutral greaterThanLessThan_iff of_nat_mono
+            period_nonempty plus_1_eq_Suc sqrt_cfrac)
+
+theorem cfrac_sqrt_last: "cfrac_nth (cfrac_of_real (sqrt D)) l = 2 * D'"
+  using sqrt_cfrac_last by (metis One_nat_def Suc_pred period_nonempty sqrt_cfrac)
+
+theorem cfrac_sqrt_palindrome:
+  assumes "n \<in> {0<..<l}"
+  shows   "cfrac_nth (cfrac_of_real (sqrt D)) (l - n) = cfrac_nth (cfrac_of_real (sqrt D)) n"
+proof -
+  have "cfrac_nth (cfrac_of_real (sqrt D)) (l - n) = sqrt_cfrac_nth (l - n - 1)"
+    using assms by (subst sqrt_cfrac) (auto simp: Suc_diff_Suc)
+  also have "\<dots> = sqrt_cfrac_nth (n - 1)"
+    using assms by (subst sqrt_cfrac_palindrome [symmetric]) auto
+  also have "\<dots> = cfrac_nth (cfrac_of_real (sqrt D)) n"
+    using assms by (subst sqrt_cfrac) auto
+  finally show ?thesis .
+qed
+
+lemma sqrt_cfrac_info_palindrome:
+  assumes "sqrt_cfrac_info D = (a, b, cs)"
+  shows   "rev (butlast cs) = butlast cs"
+proof (rule List.nth_equalityI; safe?)
+  fix i assume "i < length (rev (butlast cs))"
+  with period_nonempty have "Suc i < length cs" by simp
+  thus "rev (butlast cs) ! i = butlast cs ! i"
+    using assms cfrac_sqrt_palindrome[of "Suc i"] period_nonempty unfolding l_def
+    by (auto simp: sqrt_cfrac_info_def rev_nth algebra_simps Suc_diff_Suc simp del: cfrac.simps)
+qed simp_all
+
+lemma sqrt_cfrac_info_last:
+  assumes "sqrt_cfrac_info D = (a, b, cs)"
+  shows   "last cs = 2 * Discrete.sqrt D"
+proof -
+  from assms show ?thesis using period_nonempty cfrac_sqrt_last
+    by (auto simp: sqrt_cfrac_info_def last_map l_def D'_def Discrete_sqrt_altdef)
+qed
+
+text \<open>
+  The following lemmas allow us to compute the period of the expansion of the square root:
+\<close>
+lemma while_option_sqrt_cfrac:
+  defines "step' \<equiv> (\<lambda>(as, pq). ((D' + fst pq) div snd pq # as, sqrt_remainder_step pq))"
+  defines "b \<equiv> (\<lambda>(_, pq). snd pq \<noteq> 1)"
+  defines "initial \<equiv> ([] :: nat list, (D', D - D'\<^sup>2))"
+  shows "while_option b step' initial =
+           Some (rev (map sqrt_cfrac_nth [0..<l -1]), (D', 1))"
+proof -
+  define P where 
+    "P = (\<lambda>(as, pq). let n = length as
+                     in  n < l \<and> pq = sqrt_remainder_surd n \<and> as = rev (map sqrt_cfrac_nth [0..<n]))"
+  define \<mu> :: "nat list \<times> (nat \<times> nat) \<Rightarrow> nat" where "\<mu> = (\<lambda>(as, _). l - length as)"
+  have [simp]: "P initial" using period_nonempty
+    by (auto simp: initial_def P_def sqrt_remainder_surd_def)
+  have step': "P (step' s) \<and> Suc (length (fst s)) < l" if "P s" "b s" for s
+  proof (cases s)
+    case (fields as p q)
+    define n where "n = length as"
+    from that fields sqrt_remainder_surd_last have "Suc n \<le> l"
+      by (auto simp: b_def P_def Let_def n_def [symmetric])
+    moreover from that fields sqrt_remainder_surd_last have "Suc n \<noteq> l"
+      by (auto simp: b_def P_def Let_def n_def [symmetric])
+    ultimately have "Suc n < l" by auto
+    with that fields sqrt_remainder_surd_last show "P (step' s) \<and> Suc (length (fst s)) < l"
+      by (simp add: b_def P_def Let_def n_def step'_def sqrt_cfrac_nth_def 
+                    sqrt_remainder_surd_def case_prod_unfold)
+  qed
+  have [simp]: "length (fst (step' s)) = Suc (length (fst s))" for s
+    by (simp add: step'_def case_prod_unfold)
+
+  have "\<exists>x. while_option b step' initial = Some x"
+  proof (rule measure_while_option_Some)
+    fix s assume *: "P s" "b s"
+    from step'[OF *] show "P (step' s) \<and> \<mu> (step' s) < \<mu> s"
+      by (auto simp: b_def \<mu>_def case_prod_unfold intro!: diff_less_mono2)
+  qed auto
+  then obtain x where x: "while_option b step' initial = Some x" ..
+  have "P x" by (rule while_option_rule[OF _ x]) (insert step', auto)
+  have "\<not>b x" using while_option_stop[OF x] by auto
+
+  obtain as p q where [simp]: "x = (as, (p, q))" by (cases x)
+  define n where "n = length as"
+  have [simp]: "q = 1" using \<open>\<not>b x\<close> by (auto simp: b_def)
+  have [simp]: "p = D'" using \<open>P x\<close>
+    using red_assoc_denom_1[of p] by (auto simp: P_def Let_def)
+  have "n < l" "sqrt_remainder_surd (length as) = (D', Suc 0)"
+       and as: "as = rev (map sqrt_cfrac_nth [0..<n])" using \<open>P x\<close>
+    by (auto simp: P_def Let_def n_def)
+  hence "\<not>(n < l - 1)"
+    using snd_sqrt_remainder_surd_gt_1[of n] by (intro notI) auto
+  with \<open>n < l\<close> have [simp]: "n = l - 1"  by auto
+  show ?thesis by (simp add: as x)
+qed
+
+lemma while_option_sqrt_cfrac_info:
+  defines "step' \<equiv> (\<lambda>(as, pq). ((D' + fst pq) div snd pq # as, sqrt_remainder_step pq))"
+  defines "b \<equiv> (\<lambda>(_, pq). snd pq \<noteq> 1)"
+  defines "initial \<equiv> ([], (D', D - D'\<^sup>2))"
+  shows "sqrt_cfrac_info D =
+           (case while_option b step' initial of
+             Some (as, _) \<Rightarrow> (Suc (length as), D', rev ((2 * D') # as)))"
+proof -
+  have "nat (cfrac_nth (cfrac_of_real (sqrt (real D))) (Suc k)) = sqrt_cfrac_nth k" for k
+    by (metis nat_int sqrt_cfrac)
+  thus ?thesis unfolding assms while_option_sqrt_cfrac
+    using period_nonempty sqrt_cfrac_last
+    by (cases l) (auto simp: sqrt_cfrac_info_def D'_def l_def Discrete_sqrt_altdef)
+qed
+
+end
+end
+
+lemma sqrt_nat_period_length_le: "sqrt_nat_period_length D \<le> nat \<lfloor>sqrt D\<rfloor> * (nat \<lfloor>sqrt D\<rfloor> + 1)"
+  by (cases "is_square D") (use period_length_le_aux[of D] in auto)
+
+lemma sqrt_nat_period_length_0_iff [simp]:
+  "sqrt_nat_period_length D = 0 \<longleftrightarrow> is_square D"
+  using period_nonempty[of D] by (cases "is_square D") auto
+
+lemma sqrt_nat_period_length_pos_iff [simp]:
+  "sqrt_nat_period_length D > 0 \<longleftrightarrow> \<not>is_square D"
+  using period_nonempty[of D] by (cases "is_square D") auto
+
+lemma sqrt_cfrac_info_code [code]:
+  "sqrt_cfrac_info D =
+     (let D' = Discrete.sqrt D
+      in  if D'\<^sup>2 = D then (0, D', [])
+          else
+            case while_option
+                   (\<lambda>(_, pq). snd pq \<noteq> 1)
+                   (\<lambda>(as, (p, q)). let X = (p + D') div q; p' = X * q - p
+                                   in  (X # as, p', (D - p'\<^sup>2) div q))
+                   ([], D', D - D'\<^sup>2)
+            of Some (as, _) \<Rightarrow> (Suc (length as), D', rev ((2 * D') # as)))"
+proof -
+  define D' where "D' = Discrete.sqrt D"
+  show ?thesis
+  proof (cases "is_square D")
+    case True
+    hence "D' ^ 2 = D" by (auto simp: D'_def elim!: is_nth_powerE)
+    thus ?thesis using True
+      by (simp add: D'_def Let_def sqrt_cfrac_info_def sqrt_nat_period_length_def)
+  next
+    case False
+    hence "D' ^ 2 \<noteq> D" by (subst eq_commute) auto
+    thus ?thesis using while_option_sqrt_cfrac_info[OF False]
+      by (simp add: sqrt_cfrac_info_def D'_def Let_def
+                    case_prod_unfold Discrete_sqrt_altdef add_ac sqrt_remainder_step_def)
+  qed
+qed
+
+lemma sqrt_nat_period_length_code [code]:
+  "sqrt_nat_period_length D = fst (sqrt_cfrac_info D)"
+  by (simp add: sqrt_cfrac_info_def)
+
+text \<open>
+  For efficiency reasons, it is often better to use an array instead of a list:
+\<close>
+definition sqrt_cfrac_info_array where
+  "sqrt_cfrac_info_array D = (case sqrt_cfrac_info D of (a, b, c) \<Rightarrow> (a, b, IArray c))"
+
+lemma fst_sqrt_cfrac_info_array [simp]: "fst (sqrt_cfrac_info_array D) = sqrt_nat_period_length D"
+  by (simp add: sqrt_cfrac_info_array_def sqrt_cfrac_info_def)
+
+lemma snd_sqrt_cfrac_info_array [simp]: "fst (snd (sqrt_cfrac_info_array D)) = Discrete.sqrt D"
+  by (simp add: sqrt_cfrac_info_array_def sqrt_cfrac_info_def)
+
+
+definition cfrac_sqrt_nth :: "nat \<times> nat \<times> nat iarray \<Rightarrow> nat \<Rightarrow> nat" where
+  "cfrac_sqrt_nth info n =
+     (case info of (l, a0, as) \<Rightarrow> if n = 0 then a0 else as !! ((n - 1) mod l))"
+
+lemma cfrac_sqrt_nth:
+  assumes "\<not>is_square D"
+  shows   "cfrac_nth (cfrac_of_real (sqrt D)) n =
+             int (cfrac_sqrt_nth (sqrt_cfrac_info_array D) n)" (is "?lhs = ?rhs")
+proof (cases n)
+  case (Suc n')
+  define l where "l = sqrt_nat_period_length D"
+  from period_nonempty[OF assms] have "l > 0" by (simp add: l_def)
+  have "cfrac_nth (cfrac_of_real (sqrt D)) (Suc n') =
+        cfrac_nth (cfrac_of_real (sqrt D)) (Suc (n' mod l))" unfolding l_def
+    using cfrac_sqrt_periodic[OF assms, of n'] by simp
+  also have "\<dots> = map (\<lambda>n. nat (cfrac_nth (cfrac_of_real (sqrt D)) (Suc n))) [0..<l] ! (n' mod l)"
+    using \<open>l > 0\<close> by (subst nth_map) auto
+  finally show ?thesis using Suc
+    by (simp add: sqrt_cfrac_info_array_def sqrt_cfrac_info_def l_def cfrac_sqrt_nth_def)
+qed (simp_all add: sqrt_cfrac_info_def sqrt_cfrac_info_array_def
+                   Discrete_sqrt_altdef cfrac_sqrt_nth_def)
+
+lemma sqrt_cfrac_code [code]:
+  "sqrt_cfrac D =
+     (let info = sqrt_cfrac_info_array D;
+          (l, a0, _) = info
+      in  if l = 0 then cfrac_of_int (int a0) else cfrac (cfrac_sqrt_nth info))"
+proof (cases "is_square D")
+  case True
+  hence "sqrt (real D) = of_int (Discrete.sqrt D)"
+    by (auto elim!: is_nth_powerE)
+  thus ?thesis using True
+    by (auto simp: Let_def sqrt_cfrac_info_array_def sqrt_cfrac_info_def sqrt_cfrac_def)
+next
+  case False
+  have "cfrac_sqrt_nth (sqrt_cfrac_info_array D) n > 0" if "n > 0" for n
+  proof -
+    have "int (cfrac_sqrt_nth (sqrt_cfrac_info_array D) n) > 0"
+      using False that by (subst cfrac_sqrt_nth [symmetric]) auto
+    thus ?thesis by simp
+  qed
+  moreover have "sqrt D \<notin> \<rat>"
+    using False irrat_sqrt_nonsquare by blast
+  ultimately have "sqrt_cfrac D = cfrac (cfrac_sqrt_nth (sqrt_cfrac_info_array D))"
+    using cfrac_sqrt_nth[OF False]
+    by (intro cfrac_eqI) (auto simp: sqrt_cfrac_def is_cfrac_def)
+  thus ?thesis
+    using False by (simp add: Let_def sqrt_cfrac_info_array_def sqrt_cfrac_info_def)
+qed
+
+text \<open>
+  As a test, we determine the continued fraction expansion of $\sqrt{129}$, which is
+  $[11; \overline{2, 1, 3, 1, 6, 1, 3, 1, 2, 22}]$ (a period length of 10):
+\<close>
+value "let info = sqrt_cfrac_info_array 129 in info"
+value "sqrt_nat_period_length 129"
+
+text \<open>
+  We can also compute convergents of $\sqrt{129}$ and observe that the difference between
+  the square of the convergents and 129 vanishes quickly::
+\<close>
+value "map (conv (sqrt_cfrac 129)) [0..<10]"
+value "map (\<lambda>n. \<bar>conv (sqrt_cfrac 129) n ^ 2 - 129\<bar>) [0..<20]"
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/approximation_cfrac.ML b/thys/Continued_Fractions/approximation_cfrac.ML
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/approximation_cfrac.ML
@@ -0,0 +1,80 @@
+val _ = \<comment> \<open>Trusting the oracle \<close>@{oracle_name "holds_by_evaluation"}
+signature CFRAC_APPROXIMATION_COMPUTATION = sig
+val approx_cfrac: Proof.context -> term -> term
+end
+
+structure Cfrac_Approximation_Computation : CFRAC_APPROXIMATION_COMPUTATION = struct
+
+  
+
+  val mk_int = HOLogic.mk_number \<^typ>\<open>int\<close> o @{code integer_of_int};
+
+  val term_of_int_list = map mk_int #> HOLogic.mk_list HOLogic.intT
+
+  val approx_cfrac = @{computation "int list"
+        terms: "0 :: nat" "1 :: nat" "2 :: nat" "3 :: nat" Suc
+           "(+)::nat\<Rightarrow>nat\<Rightarrow>nat" "(-)::nat\<Rightarrow>nat\<Rightarrow>nat" "(*)::nat\<Rightarrow>nat\<Rightarrow>nat"
+           "0 :: int" "1 :: int" "2 :: int" "3 :: int" "-1 :: int"
+           "(+)::int\<Rightarrow>int\<Rightarrow>int" "(-)::int\<Rightarrow>int\<Rightarrow>int" "(*)::int\<Rightarrow>int\<Rightarrow>int" "uminus::int\<Rightarrow>int"
+           approx_cfrac
+        datatypes: int integer "int list" num floatarith float}
+    (fn _ => fn x => case x of SOME lst => term_of_int_list lst
+      | NONE => error "Computation approx_cfrac failed.")
+
+end
+
+
+signature CFRAC_APPROXIMATION = sig
+  val approx_cfrac : int -> Proof.context -> term -> term
+end
+
+
+structure Cfrac_Approximation : CFRAC_APPROXIMATION = struct
+
+local
+open Approximation
+
+fun mk_approx_cfrac prec t =
+  \<^const>\<open>approx_cfrac\<close> $ (HOLogic.mk_number HOLogic.natT prec) $ t
+
+in
+
+fun approx_cfrac prec ctxt t =
+  realify t
+     |> Thm.cterm_of ctxt
+     |> (preproc_form_conv ctxt then_conv reify_form_conv ctxt)
+     |> Thm.prop_of
+     |> Logic.dest_equals |> snd
+     |> dest_interpret |> fst
+     |> mk_approx_cfrac prec
+     |> Cfrac_Approximation_Computation.approx_cfrac ctxt
+end
+
+fun approximate_cfrac_cmd prec modes raw_t state =
+  let
+    val ctxt = Toplevel.context_of state;
+    val t =
+      raw_t
+      |> Syntax.parse_term ctxt 
+      |> Type.constraint \<^typ>\<open>real\<close> 
+      |> Syntax.check_term ctxt;
+    val t' = approx_cfrac prec ctxt t;
+    val ty' = Term.type_of t';
+    val ctxt' = Proof_Context.augment t' ctxt;
+  in
+    Print_Mode.with_modes modes (fn () =>
+      Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
+        Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ()
+  end |> Pretty.writeln;
+
+val opt_modes =
+  Scan.optional (Args.$$$ "prec" |-- Args.colon |-- Parse.nat) 100 --
+  Scan.optional (\<^keyword>\<open>(\<close> |-- Parse.!!! (Scan.repeat1 Parse.name --| \<^keyword>\<open>)\<close>)) [];
+
+val _ =
+  Outer_Syntax.command \<^command_keyword>\<open>approximate_cfrac\<close>
+    "print initial fragment of continued fraction of a real number by approximation"
+    (opt_modes -- Parse.term
+      >> (fn ((prec, modes), t) => Toplevel.keep (approximate_cfrac_cmd prec modes t)));
+
+end
\ No newline at end of file
diff --git a/thys/Continued_Fractions/document/root.bib b/thys/Continued_Fractions/document/root.bib
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/document/root.bib
@@ -0,0 +1,14 @@
+@misc {proofwiki,
+  author="{Proof Wiki}",
+  url="https://proofwiki.org/wiki/Continued_Fraction_Expansion_of_Euler%27s_Number"
+}
+
+@book{khinchin,
+  title={Continued Fractions},
+  author={Khinchin, A.I.A. and Eagle, H.},
+  isbn={9780486696300},
+  lccn={97008056},
+  series={Dover books on mathematics},
+  year={1997},
+  publisher={Dover Publications}
+}
\ No newline at end of file
diff --git a/thys/Continued_Fractions/document/root.tex b/thys/Continued_Fractions/document/root.tex
new file mode 100644
--- /dev/null
+++ b/thys/Continued_Fractions/document/root.tex
@@ -0,0 +1,54 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage{isabelle,isabellesym}
+\usepackage{amsfonts, amsmath, amssymb}
+
+% this should be the last package used
+\usepackage{pdfsetup}
+
+% urls in roman style, theory text in math-similar italics
+\urlstyle{rm}
+\isabellestyle{it}
+
+
+\begin{document}
+
+\title{Continued Fractions}
+\author{Manuel Eberl}
+\maketitle
+
+\begin{abstract}
+This article provides a formalisation of continued fractions of real numbers and their basic properties.
+It also contains a proof of the classic result that the irrational numbers with periodic continued
+ fraction expansions are precisely the quadratic irrationals, i.\,e.\ real numbers that fulfil a non-trivial quadratic equation $a x^2 + b x + c = 0$ with integer coefficients.
+
+Particular attention is given to the continued fraction expansion of $\sqrt{D}$ for a non-square
+ natural number $D$. Basic results about the length and structure of its period are provided,
+ along with an executable algorithm to compute the period (and from it, the entire expansion).
+
+This is then also used to provide a fairly efficient, executable, and fully formalised algorithm to
+compute solutions to Pell's equation $x^2 - D y^2 = 1$. The performance is sufficiently good to
+find the solution to Archimedes's cattle problem in less than a second on a typical computer.
+This involves the value $D = 410286423278424$, for which the solution has over 200000 decimals.
+
+Lastly, a derivation of the continued fraction expansions of Euler's number $e$ and an executable
+function to compute continued fraction expansions using interval arithmetic is also provided.
+\end{abstract}
+
+\newpage
+\tableofcontents
+\newpage
+\parindent 0pt\parskip 0.5ex
+
+\input{session}
+
+\nocite{khinchin}
+
+\bibliographystyle{abbrv}
+\bibliography{root}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
diff --git a/thys/Go/Go_Setup.thy b/thys/Go/Go_Setup.thy
new file mode 100644
--- /dev/null
+++ b/thys/Go/Go_Setup.thy
@@ -0,0 +1,149 @@
+theory Go_Setup
+  imports "Main"
+begin
+
+ML_file \<open>code_go.ML\<close>
+
+code_identifier
+  code_module Code_Target_Nat \<rightharpoonup> (Go) Arith
+| code_module Code_Target_Int \<rightharpoonup> (Go) Arith
+| code_module Code_Numeral \<rightharpoonup> (Go) Arith
+
+code_printing
+  constant Code.abort \<rightharpoonup>
+    (Go) "panic( _ )"
+
+(* Bools *)
+code_printing
+  type_constructor bool \<rightharpoonup> (Go) "bool"
+| constant "False::bool" \<rightharpoonup> (Go) "false"
+| constant "True::bool" \<rightharpoonup> (Go) "true"
+
+code_printing
+  constant HOL.Not \<rightharpoonup> (Go) "'! _"
+| constant HOL.conj \<rightharpoonup> (Go) infixl 1 "&&"
+| constant HOL.disj \<rightharpoonup> (Go) infixl 0 "||"
+| constant HOL.implies \<rightharpoonup> (Go) "!('!((_)) || (_))"
+| constant "HOL.equal :: bool \<Rightarrow> bool \<Rightarrow> bool" \<rightharpoonup> (Go) infix 4 "=="
+
+
+(* Strings *)
+
+(* definitions to make these functions available *)
+definition "go_private_map_list" where
+  "go_private_map_list f a = map f a"
+definition "go_private_fold_list" where
+  "go_private_fold_list f a b = fold f a b"
+
+
+code_printing
+  type_constructor String.literal \<rightharpoonup> (Go) "string"
+| constant "STR ''''" \<rightharpoonup> (Go) "\"\""
+| constant "Groups.plus_class.plus :: String.literal \<Rightarrow> _ \<Rightarrow> _" \<rightharpoonup>
+    (Go) infix 6 "+"
+| constant "HOL.equal :: String.literal \<Rightarrow> String.literal \<Rightarrow> bool" \<rightharpoonup>
+    (Go) infix 4 "=="
+| constant "(\<le>) :: String.literal \<Rightarrow> String.literal \<Rightarrow> bool" \<rightharpoonup>
+    (Go) infix 4 "<="
+| constant "(<) :: String.literal \<Rightarrow> String.literal \<Rightarrow> bool" \<rightharpoonup>
+    (Go) infix 4 "<"
+
+setup \<open>
+  fold Literal.add_code ["Go"]
+\<close>
+
+
+(* Integers via big/math *)
+code_printing
+  code_module "Bigint" \<rightharpoonup> (Go) \<open>
+package Bigint
+
+import "math/big"
+
+type Int = big.Int;
+
+func MkInt(s string) Int {
+  var i Int;
+  _, e := i.SetString(s, 10);
+  if (e) {
+    return i;
+  } else {
+    panic("invalid integer literal")
+  }
+}
+
+func Uminus(a Int) Int {
+  var b Int
+  b.Neg(&a)
+  return b
+}
+
+func Minus(a, b Int) Int {
+  var c Int
+  c.Sub(&a, &b)
+  return c
+}
+
+func Plus(a, b Int) Int {
+  var c Int
+  c.Add(&a, &b)
+  return c
+}
+
+func Times (a, b Int) Int {
+  var c Int
+  c.Mul(&a, &b)
+  return c
+}
+
+func Divmod_abs(a, b Int) (Int, Int) {
+  var div, mod Int
+  div.DivMod(&a, &b, &mod)
+  div.Abs(&div)
+  return div, mod
+}
+
+func Equal(a, b Int) bool {
+  return a.Cmp(&b) == 0
+}
+
+func Less_eq(a, b Int) bool {
+  return a.Cmp(&b) != 1
+}
+
+func Less(a, b Int) bool {
+  return a.Cmp(&b) == -1
+}
+
+func Abs(a Int) Int {
+  var b Int
+  b.Abs(&a)
+  return b
+}
+\<close> for constant "uminus :: integer \<Rightarrow> _" "minus :: integer \<Rightarrow> _" "Code_Numeral.dup" "Code_Numeral.sub"
+  "(*) :: integer \<Rightarrow> _" "(+) :: integer \<Rightarrow> _" "Code_Numeral.divmod_abs" "HOL.equal :: integer \<Rightarrow> _"
+  "less_eq :: integer \<Rightarrow> _" "less :: integer \<Rightarrow> _" "abs :: integer \<Rightarrow> _"
+  "String.literal_of_asciis" "String.asciis_of_literal"
+  | type_constructor "integer" \<rightharpoonup> (Go) "Bigint.Int"
+  | constant "uminus :: integer \<Rightarrow> integer" \<rightharpoonup> (Go) "Bigint.Uminus( _ )"
+  | constant "minus :: integer \<Rightarrow> integer \<Rightarrow> integer" \<rightharpoonup> (Go) "Bigint.Minus( _, _)"
+  | constant "Code_Numeral.dup" \<rightharpoonup> (Go) "!(Bigint.MkInt(\"2\") * _)"
+  | constant "Code_Numeral.sub" \<rightharpoonup> (Go) "panic(\"sub\")"
+  | constant "(+) :: integer \<Rightarrow> _ " \<rightharpoonup> (Go) "Bigint.Plus( _, _)"
+  | constant "(*) :: integer \<Rightarrow> _ \<Rightarrow> _ " \<rightharpoonup> (Go) "Bigint.Times( _, _)"
+  | constant Code_Numeral.divmod_abs \<rightharpoonup>
+     (Go) "func () Prod[Bigint.Int, Bigint.Int] { a, b := Bigint.Divmod'_abs( _, _); return Prod[Bigint.Int, Bigint.Int]{a, b}; }()"
+  | constant "HOL.equal :: integer \<Rightarrow> _" \<rightharpoonup> (Go) "Bigint.Equal( _, _)"
+  | constant "less_eq :: integer \<Rightarrow> integer \<Rightarrow> bool " \<rightharpoonup> (Go) "Bigint.Less'_eq( _, _)"
+  | constant "less :: integer \<Rightarrow> _ " \<rightharpoonup> (Go) "Bigint.Less( _, _)"
+  | constant "abs :: integer \<Rightarrow> _" \<rightharpoonup> (Go) "Bigint.Abs( _ )"
+
+
+code_printing
+  constant "0::integer" \<rightharpoonup> (Go) "Bigint.MkInt(\"0\")"
+setup \<open>
+Numeral.add_code \<^const_name>\<open>Code_Numeral.Pos\<close> I Code_Printer.literal_numeral "Go"
+#> Numeral.add_code \<^const_name>\<open>Code_Numeral.Neg\<close> (~) Code_Printer.literal_numeral "Go"
+\<close>
+
+end
\ No newline at end of file
diff --git a/thys/Go/ROOT b/thys/Go/ROOT
new file mode 100644
--- /dev/null
+++ b/thys/Go/ROOT
@@ -0,0 +1,32 @@
+chapter AFP
+
+session Go = HOL +
+  description "A Go frontend for the code generator."
+  options [timeout = 300]
+  theories
+    Go_Setup
+  document_files
+    "root.tex"
+
+session Go_Test_Quick in "test/quick" = Go +
+  description "Quick test session with BigInts and RBTs"
+  options [timeout = 300]
+  sessions
+    "HOL-Data_Structures"
+  theories [document = false]
+    RBT_Test
+  export_files [3]
+    "*:code/export1/**"
+
+session Go_Test_Slow in "test/slow" = "HOL-Library" +
+  description "Slow test session for (almost) the entire HOL-Library"
+  options [timeout = 1200]
+  sessions
+    Go
+    "HOL-Number_Theory"
+    "HOL-Data_Structures"
+    "HOL-Examples"
+  theories [document = false]
+    Candidates
+    Generate
+    Generate_Binary_Nat
diff --git a/thys/Go/code_go.ML b/thys/Go/code_go.ML
new file mode 100644
--- /dev/null
+++ b/thys/Go/code_go.ML
@@ -0,0 +1,752 @@
+
+signature CODE_GO =
+sig
+  val target: string
+end;
+
+structure Code_Go : CODE_GO =
+struct
+
+open Basic_Code_Symbol;
+open Basic_Code_Thingol;
+open Code_Printer;
+
+infixr 5 @@;
+infixr 5 @|;
+
+val target = "Go";
+
+fun map_terms_bottom_up f (t as IConst _) = f t
+  | map_terms_bottom_up f (t as IVar _) = f t
+  | map_terms_bottom_up f (t1 `$ t2) = f
+      (map_terms_bottom_up f t1 `$ map_terms_bottom_up f t2)
+  | map_terms_bottom_up f ((v, ty) `|=> (t, rty)) = f
+      ((v, ty) `|=> (map_terms_bottom_up f t, rty))
+  | map_terms_bottom_up f (ICase { term = t, typ = ty, clauses = clauses, primitive = t0 }) = f
+      (ICase { term = map_terms_bottom_up f t, typ = ty,
+        clauses = (map o apply2) (map_terms_bottom_up f) clauses,
+        primitive = map_terms_bottom_up f t0 });
+
+fun range_of_head t =
+  case fst (Code_Thingol.unfold_app t) of
+    IConst {range, ...} => range
+
+val print_go_string =
+  let
+    fun unicode i = "\\u" ^ align_right "0" 4 (Int.fmt StringCvt.HEX i)
+    fun char "\"" = "\\\""
+      | char "\\" = "\\\\"
+      | char c =
+         let val i = ord c
+         in if i < 32 orelse i > 126
+          then unicode i
+          else if i >= 128
+          then error "non-ASCII byte in Go string literal"
+          else c
+        end;
+  in quote o translate_string char end;
+
+
+fun block_enclose (prt1, prt2) prts = (* Pretty.block_enclose (prt1, prt2) prts*)
+  Pretty.chunks [Pretty.block (Pretty.fbreaks ((Pretty.unbreakable prt1) :: prts)), Pretty.unbreakable prt2];
+
+fun print_go_numeral num = "Bigint.MkInt(\"" ^ signed_string_of_int num ^ "\")";
+
+val literals = Literals {
+  literal_string = print_go_string,
+  literal_numeral = print_go_numeral,
+  literal_list = enum "," "[" "]",
+  infix_cons = (6, "<no infix cons operator in  go>") (* TODO: this will go wrong if ever used *)
+};
+
+
+
+(* the subset of thingol we actually need for Go *)
+datatype go_stmt = Fun of typscheme * ((iterm list * iterm) * (thm option * bool)) list
+  | Datatype of vname list * ((string * vname list) * itype list) list
+  | Class of (vname * ((class * class) list * (string * itype) list))
+  | Datatypecons of string
+  | Instance of { class: string, tyco: string, vs: (vname * sort) list,
+        superinsts: (class * (itype * dict list) list) list,
+        inst_params: ((string * (const * int)) * (thm * bool)) list,
+        superinst_params: ((string * (const * int)) * (thm * bool)) list };
+
+fun print_go_stmt gen_stringer undefineds infinite_types tyco_syntax const_syntax reserved
+    args_num is_sum_type is_class_param is_constr (deresolve, deresolve_full) =
+  let
+    fun lookup_tyvar tyvars = lookup_var tyvars;
+    fun intro_tyvars vs = intro_vars (map fst vs);
+    val deresolve_const = deresolve o Constant;
+    val deresolve_class = deresolve o Type_Class;
+    val deresolve_classrel = deresolve o Class_Relation;
+    val deresolve_inst = deresolve o Class_Instance;
+    val deresolve_tyco = deresolve o Type_Constructor;
+    val oneline = Pretty.unbreakable o semicolon;
+    val block = Pretty.unbreakable o Pretty.block;
+    val spaced = Pretty.unbreakable o concat;
+
+    fun mk_dest_name name =  Long_Name.map_base_name (fn s => s^"_dest") name
+    fun applify_constraints _ head [] = head
+     | applify_constraints tyvars head vs = let
+          val anys = (block o commas o map (str o lookup_tyvar tyvars)) vs
+         in block [head, str "[", anys, Pretty.brk 1, str "any", str "]"] end
+
+    fun print_go_typ tyvars (tyco `%% tys) = (case tyco_syntax tyco of
+        NONE => apply_constraints tyvars ((str o deresolve_tyco) tyco) tys
+      | SOME (_, print) => print (K (print_go_typ tyvars)) NOBR tys)
+    | print_go_typ tyvars (ITyVar v) = (str o lookup_tyvar tyvars) v
+    and apply_constraints tyvars head vs =
+      gen_applify false "[" "]" (print_go_typ tyvars) NOBR head vs
+
+    (* uncurried types of functions in type classes are special-cased here *)
+    fun print_go_typ_uncurried_toplevel tyvars (typ as "fun" `%% _) = let
+          val (args, rtyp) = Code_Thingol.unfold_fun typ
+          val head = applify "(" ")" (print_go_typ tyvars) NOBR (str "func") args;
+        in concat [head, print_go_typ tyvars rtyp] end
+    | print_go_typ_uncurried_toplevel tyvars typ =
+        block [str "func () ", print_go_typ tyvars typ]
+
+    (* wrap a statement into an immediately called function to make it an expression *)
+    fun wrap_into_lambda tyvars typ body =
+      block_enclose
+        (concat [str "func ()", print_go_typ tyvars typ, str "{"], str "}()") body
+    fun wrap_in_return t = oneline [str "return", t]
+    fun wrap_if true = wrap_in_return
+      | wrap_if false = I
+
+    fun print_func head body = block_enclose
+      (block [str "func ", head, str " {"], str "}")
+      [body];
+    fun print_func_head tyvars vars const tvs extras params tys rty = let
+      val args = params ~~ tys
+      |> map (fn (param, ty) => let
+         val name = case param of
+           NONE => "_" | SOME n => lookup_var vars n;
+         in Pretty.block [str name, Pretty.brk 1, print_go_typ tyvars ty] end)
+      |> (curry op @ extras)
+      |> enum "," "(" ")"
+      val sym = case const of
+        SOME name => (str o deresolve) name
+      | NONE => str ""
+      val func_head = concat (applify_constraints tyvars sym tvs :: [args, rty]);
+      in func_head
+    end;
+
+    (* a definition of a datatype *)
+    fun print_go_typedef tyco vs cos reserved = let
+      val [p,m] = Name.invent (snd reserved) "p" 2
+      val ctxt = Name.declare p (Name.declare m (snd reserved))
+      val tyargs = map ITyVar vs
+      val self = tyco `%% tyargs
+      val tyvars = intro_tyvars (map (rpair []) vs) reserved;
+      val allowed_infinite = List.exists (fn n => n = tyco) infinite_types
+
+      fun print_constructor m type_name ((name,_), tys) = let
+        val named_fields = Name.invent_names ctxt "A" tys
+        val fields = named_fields
+         |> map (fn (name, arg) => oneline [str name, print_go_typ tyvars arg])
+        val head = applify_constraints tyvars (str name) vs
+        val typ = apply_constraints tyvars (str name) tyargs
+        val elim_body = if type_name = NONE
+          then let
+            val case_branch = block
+              [str "return ", (Pretty.block o commas) (map (fn (field,_) => str (p^"."^field)) named_fields)]
+          in (*Pretty.chunks
+            [oneline [str ((if null named_fields then "_ = " else m^" := ")^p^".("), typ , str ")"]
+            ,*) case_branch end
+          else Pretty.block [oneline [str "return ", (Pretty.block o commas) (map (fn (field,_) => str (p^"."^field)) named_fields)]]
+        val elim_name = mk_dest_name (case type_name of
+            NONE => name
+          | SOME name' => name')
+        val eliminator = if null tys then str "" else print_func
+          (applify "(" ")" I NOBR (Pretty.block [applify_constraints tyvars (str elim_name) vs, str ("("^p^" "), typ, str ")"])  (map (print_go_typ tyvars o snd) named_fields))
+          elim_body
+        val pretty = name ^ "(" ^ (fold (curry (op ^)) (map (K "%v") fields) "") ^ ")"
+        val constr = oneline [block_enclose (concat [str "type", head, str "struct {"], str "}")
+          fields]
+        in (constr, eliminator) end
+      in if not allowed_infinite andalso length cos = 1 then case cos of
+        [((name,_),tys)] => let
+          val name = deresolve_const name
+          val tname = deresolve_tyco tyco
+          val (constr, dest) = print_constructor m (SOME name) ((tname, []), tys)
+        in Pretty.chunks [constr, dest] end
+      else let
+          val (constrs, destrs) = cos
+            |> map (fn ((name,_),tys) => ((deresolve_const name, []),tys))
+            |> map (print_constructor m NONE)
+            |> split_list
+          val names = map (fn ((name,_),_) => (str o deresolve_const) name) cos
+          val comment = block (str "// sum type which can be " :: Pretty.commas names)
+          val any = oneline [str "type", applify_constraints tyvars ((str o deresolve_tyco) tyco) vs, str "any"]
+        in Pretty.chunks (comment :: any :: constrs @ destrs)  end
+      end;
+
+
+    fun print_classrels [] ps = Pretty.block ps
+      | print_classrels rels ps = let
+        val postfix = rels
+          |> map (fn (self, super) => (Long_Name.base_name o deresolve_classrel) (self, super))
+          |> rev
+          |> String.concatWith "."
+        in block (ps @ [str ".", str postfix]) end
+    fun print_dict tyvars (Dict (classrels, x)) =
+      print_classrels classrels (print_plain_dict tyvars x)
+    and print_plain_dict tyvars (Dict_Const (inst, args)) = let
+        val needs_mono = true (* not (length args = 0)*)
+        val (typargs, dss) = split_list args
+        val wrap = if needs_mono
+          then fn head => apply_constraints tyvars head typargs
+          else I
+      in wrap ((str o deresolve_inst) inst)
+         :: (if needs_mono then [((enum "," "(" ")") o map (print_dict tyvars) o flat) dss] else []) end
+    | print_plain_dict tyvars (Dict_Var { var, index, length, ... }) =
+      [str (if length = 1 then var ^ "_"
+         else var ^ string_of_int (index + 1) ^ "_")]
+
+    fun wrap_new_scope term =
+      block_enclose (str "{", str "};") [term]
+
+    fun type_of_primitive_pattern t =
+      let
+        val destructor = case fst (Code_Thingol.unfold_app t) of
+          IConst const => const
+        val extras = drop (args_num (#sym destructor)) (#dom destructor)
+      in extras `--> (#range destructor)
+      end
+
+    fun print_app_expr const_syntax tyvars some_thm vars
+        (app as ({ sym, dicts, dom, range, typargs, ... }, ts)) = let
+        val k = length dom
+        val l = args_num sym
+      in if length ts = k then
+        let
+          val is_constr = is_constr sym
+          val is_sum_type = is_sum_type sym
+          val is_class_param = is_class_param sym
+          val dict_args = map (print_dict tyvars) (flat dicts)
+          val typ = case snd (Code_Thingol.unfold_fun range) of
+            name `%% _ => name | ITyVar name => name
+          val allowed_infinite = List.exists (fn n => n = typ) infinite_types
+            andalso is_constr
+          val _ = if is_class_param andalso not (length dict_args = 1)
+            then warning "bug in print_app" else ()
+          val applify' = if is_constr
+            then gen_applify true "{" "}"
+            else gen_applify true "(" ")"
+          val (immediate, curried) = chop l ts
+          val symbol = if is_constr
+            then (if is_sum_type orelse allowed_infinite then sym else Type_Constructor typ)
+            else sym
+          val func_name = if is_class_param
+            then Pretty.block [hd dict_args, str ".", (str o deresolve) symbol]
+            else (str o deresolve) symbol
+          fun wrap_type_args s = if is_sum_type orelse allowed_infinite
+            then applify "(" ")" I APP (apply_constraints tyvars ((str o deresolve_tyco) typ) typargs) [s]
+            else s
+          fun wrap_type_conversion name =
+            let
+              val typargs = if is_constr
+                (* these typargs are always the same set as the outer ones, but sometimes in different order *)
+                then case range of _ `%% typargs => typargs | _ => []
+                else typargs
+            in if is_class_param then name
+              else apply_constraints tyvars name typargs
+            end
+          val immediate_args = immediate
+           |> map (print_go_expr const_syntax tyvars some_thm vars BR)
+          val invocation = (if is_class_param orelse is_constr then immediate_args else dict_args @ immediate_args)
+           |> applify' I APP (wrap_type_conversion func_name)
+           |> wrap_type_args
+          val curried_args = curried
+           |> map (enclose "(" ")" o single o print_go_expr const_syntax tyvars some_thm vars NOBR)
+          in invocation :: curried_args
+        end
+      else
+       [print_go_expr const_syntax tyvars some_thm vars BR (Code_Thingol.saturated_application k app)]
+      end
+    and print_clause _ _ _ _ [] _ =
+      raise Fail "there's a bug in the pattern-match translator"
+    | print_clause tyvars some_thm vars p ((target, pattern) :: subps) term =
+      let
+        fun print_condition vars conds (constr, typargs, range, args) p q target body = let
+          val destructor = (mk_dest_name o deresolve) constr
+          val (tyco, typargs) = case snd (Code_Thingol.unfold_fun range) of
+            a `%% typargs => (a, typargs)
+          val is_boxed = is_sum_type constr orelse List.exists (fn n => n = tyco) infinite_types
+          val names = map (fn (SOME n) => (str o lookup_var vars) n | NONE => str "_") args
+          val any_names = exists is_some args
+          val checks = conds
+            |> map (fn (var,const) => concat [
+                 str var,
+                 str "==",
+                 enclose "(" ")" [print_app false const_syntax tyvars some_thm vars NOBR (const, [])]
+               ])
+            |> separate (str "&&")
+            |> concat
+        in Pretty.chunks
+           ((if is_boxed then [oneline [(block o commas) [str (if any_names then q else "_"), str p], str ":=", 
+              applify ".(" ")" I NOBR (str target) [apply_constraints tyvars ((str o deresolve) constr) typargs]]]
+            else [oneline [str "_ =", str target]])
+          @ [(if is_boxed then block_enclose (spaced [str "if", str p, str "{"], str "}") else Pretty.chunks)
+              ((if any_names then [oneline ((Pretty.block o commas) names :: [str ":=",  applify "(" ")" str NOBR (str destructor) [if is_boxed then q else target]])]
+                else [])
+               @ [(if null conds then Pretty.chunks else (block_enclose ((spaced [str "if", checks, str "{"]), str "}")))
+                   [body]])])
+        end
+      in case pattern
+        of IConst c =>
+          let
+            val checks = concat
+              [str target, str "==", enclose "(" ")" [print_app false const_syntax tyvars some_thm vars NOBR (c, [])]]
+            val body =  (if subps = []
+              then print_go_term const_syntax tyvars some_thm vars NOBR term
+              else print_clause tyvars some_thm vars p subps term)
+          in block_enclose ((spaced [str "if", checks, str "{"]), str "}")
+               [body]
+          end
+        | _ `$ _ => (case Code_Thingol.unfold_const_app pattern of
+            NONE => raise Fail "bad application in pattern match"
+          | SOME (constr, args) => let
+            val ((arg_names, subpatterns, conds), vars') =
+              fold_rev (fn term => fn ((ts, rs, cs), vars) => case term of
+                  IConst c => let
+                  val [name] = Name.invent (snd vars) "c" 1
+                  in ((SOME name :: ts, rs,(name,c) :: cs), intro_vars [name] vars) end
+                | IVar NONE => ((NONE :: ts, rs, cs), vars)
+                | IVar (SOME v) => ((SOME v :: ts, rs, cs), intro_vars [v] vars)
+                | _ `$ _ => let
+                  val [name] = Name.invent (snd vars) "p" 1
+                  in ((SOME name :: ts, (name, term) :: rs, cs), intro_vars [name] vars) end)
+              args (([],[],[]), vars)
+            val [q] = Name.invent (snd vars) "q" 1
+            val vars = intro_vars [q] vars
+            val wrapper = print_condition vars' conds (#sym constr, #typargs constr, #range constr, arg_names) p q target
+            val subpatterns' = subpatterns @ subps
+          in wrapper (if subpatterns' = []
+            then print_go_term const_syntax tyvars some_thm vars' NOBR term
+            else print_clause tyvars some_thm vars' p subpatterns' term)
+          end)
+        | IVar v => let
+            val vars' = intro_vars (the_list v) vars
+            val name_printed = case v of
+              NONE => str "_" | SOME name => (str o lookup_var vars') name
+            val binding = oneline [name_printed, str ":=", str target]
+            val usage = case v of
+                SOME _ => oneline [str "_ =", name_printed]
+              | NONE => str ""
+            val body = if subps = []
+              then print_go_term const_syntax tyvars some_thm vars' NOBR term
+              else print_clause tyvars some_thm vars' p subps term
+          in
+            Pretty.chunks [binding, body]
+          end
+        | _ => raise Fail "bad term in pattern"
+      end
+    and print_pattern_match is_stmt tyvars some_thm vars rtyp target clauses =
+      let
+        val [target_var] = Name.invent (snd vars) "target" 1
+        val vars = intro_vars [target_var] vars
+        val [p] = Name.invent (snd vars) "m" 1
+        val vars = intro_vars [p] vars
+        val target = print_go_expr const_syntax tyvars some_thm vars NOBR target
+        val assignment = oneline [str target_var, str ":=", target]
+        val body = assignment
+           :: map (fn (pattern,term) =>
+               wrap_new_scope (print_clause tyvars some_thm vars p [(target_var, pattern)] term))
+           clauses @ [oneline [str "panic(\"match failed\")"]]
+      in if is_stmt
+        then Pretty.chunks body
+        else wrap_into_lambda tyvars rtyp body
+      end
+    and print_app is_stmt const_syntax tyvars some_thm vars fxy (app as (const, args)) =
+      if List.exists (fn name => #sym const = Constant name) undefineds then
+         args
+          (* the arguments may use otherwise-unused variables, so just print somewhere to make Go happy *)
+          |> map (print_go_expr const_syntax tyvars some_thm vars fxy)
+          |> map (fn p => oneline [ str "_ = ", p])
+          |> curry (op @) [ str ("panic(\"encountered undefined function: \" + "^print_go_string (Code_Symbol.default_base (#sym const))^")") ]
+          |> Pretty.chunks
+       else wrap_if is_stmt (gen_print_app (print_app_expr const_syntax tyvars)
+        (print_go_expr const_syntax tyvars) const_syntax some_thm vars fxy app)
+    (* go has a distinction between expressions and statements which Thingol doesn't, so we just
+       periodically have to wrap things into a lambda & return *)
+    and print_go_term const_syntax tyvars some_thm vars fxy iterm =
+        print_go_term_gen true const_syntax tyvars some_thm vars fxy iterm
+    and print_go_expr const_syntax tyvars some_thm vars fxy t =
+        print_go_term_gen false const_syntax tyvars some_thm vars fxy t
+    and print_go_term_gen is_stmt const_syntax tyvars some_thm vars fxy t = case t of
+      IConst (const as {sym,...}) => let
+        in (print_app is_stmt const_syntax tyvars some_thm vars fxy (const, [])) end
+    | t1 `$ t2 => (case Code_Thingol.unfold_const_app t of
+         SOME app =>
+          (print_app is_stmt const_syntax tyvars some_thm vars fxy app)
+       | _ => wrap_if is_stmt
+            (applify "(" ")" (print_go_expr const_syntax tyvars some_thm vars NOBR) fxy
+                    (print_go_expr const_syntax tyvars some_thm vars BR t1) [t2]))
+    | IVar NONE => raise Fail "can't return a variable with no name!"
+    | IVar (SOME v) => wrap_if is_stmt (str (lookup_var vars v))
+    | (params, tys) `|=> (t, rty) => let
+        (* horrible workaround, please fix me upstream *)
+        val rty = case t of
+           ICase c => type_of_primitive_pattern (#primitive c)
+           | _ => rty
+        val vars' = intro_vars (map_filter I [params]) vars;
+        val func_head = print_func_head tyvars vars' NONE [] [] [params] [tys] (print_go_typ tyvars rty)
+        val body = print_go_term const_syntax tyvars some_thm vars' fxy t
+      in wrap_if is_stmt (print_func func_head body) end
+    | ICase { clauses = [], ... } => let
+      val _ = warning "empty case statement; generating call to panic() ...";
+      in str "panic(\"empty case\");" end
+    (* this is a let-binding, represented as a case *)
+    | ICase (cases as { clauses = [_], ...}) =>
+      let
+        val (binds, body) = Code_Thingol.unfold_let (ICase cases);
+        val does_not_pattern_match = List.all (Code_Thingol.is_IVar o fst o fst) binds
+      in if does_not_pattern_match then
+        let
+          fun print_call t vars =
+            (print_go_expr const_syntax tyvars some_thm vars fxy t, vars);
+          fun print_bind tyvars some_thm fxy p =
+              gen_print_bind (print_go_expr const_syntax tyvars) some_thm fxy p
+          fun print_assignment ((pat, _), t) vars = vars
+            |> print_bind tyvars some_thm BR pat
+            |>> (fn p => (oneline [p, str ":=",
+                  fst (print_call t vars)]))
+          fun print_left ((IVar NONE, _), t) =
+            print_call t (* evaluate and discard the result; go does not allow declaring to blank *)
+          | print_left ((pat as IVar (SOME _), ty), t) =
+            print_assignment ((pat, ty), t)
+          val (seps_ps, vars') =
+            fold_map print_left binds vars;
+          val term = print_go_term const_syntax tyvars some_thm vars' fxy body
+        in if is_stmt then Pretty.chunks (seps_ps @ [term])
+          else wrap_into_lambda tyvars (type_of_primitive_pattern (#primitive cases)) (seps_ps @ [term])
+        end
+      else
+       print_pattern_match is_stmt tyvars some_thm vars
+         (type_of_primitive_pattern (#primitive cases)) (#term cases) (#clauses cases)
+      end
+    | ICase cases => print_pattern_match is_stmt tyvars some_thm vars
+         (type_of_primitive_pattern (#primitive cases)) (#term cases) (#clauses cases);
+
+    fun print_dict_args tyvars vs =
+      let
+        fun print_single_arg length v (index, class) =
+          let
+            val name = if length = 1 then v^"_" else v ^ string_of_int (index + 1) ^ "_"
+            val ty = apply_constraints tyvars ((str o deresolve_class) class) [ITyVar v]
+          in concat [str name, ty] end
+        fun print_single_dict (v, sort) = let
+            val args = map_index (print_single_arg (length sort) v) sort
+          in args end
+      in (flat (map print_single_dict vs))
+      end;
+
+
+    fun print_go_func const_syntax reserved const vs ty [] =
+          let
+            val (tys, ty') = Code_Thingol.unfold_fun ty;
+            val params = Name.invent (snd reserved) "a" (length tys);
+            val tyvars = intro_tyvars vs reserved;
+            val vars = intro_vars params tyvars;
+        val dict_args = print_dict_args tyvars vs
+        val head = print_func_head tyvars vars ((SOME o Constant) const) (map fst vs) dict_args (map SOME params) tys (print_go_typ tyvars ty');
+        val _ = warning ("you appear to have defined a function "^const^" with no body; generating a call to panic() ...")
+      in
+        print_func head (oneline [str ("panic("^print_go_string const^")")])
+      end
+    | print_go_func const_syntax reserved const vs ty eqs =
+      let
+        val tycos = build (fold (fn ((ts, t), _) =>
+          fold Code_Thingol.add_tyconames (t :: ts)) eqs);
+        val tyvars = reserved
+          |> intro_base_names
+               (is_none o tyco_syntax) deresolve_tyco tycos
+          |> intro_tyvars vs;
+        val simple = case eqs
+         of [((ts, _), _)] => forall Code_Thingol.is_IVar ts
+          | _ => false;
+        val vars1 = reserved
+          |> intro_tyvars vs
+          |> intro_base_names_for (is_none o const_syntax)
+               deresolve (map (snd o fst) eqs);
+        val params = if simple
+          then (map (fn IVar x => x) o fst o fst o hd) eqs
+          else map SOME (aux_params vars1 (map (fst o fst) eqs));
+        val vars2 = intro_vars (map_filter I params) vars1;
+        val (tys', ty') = Code_Thingol.unfold_fun_n (length params) ty;
+        fun print_rhs is_stmt vars' ((_, t), (some_thm, _)) =
+          print_go_term_gen is_stmt const_syntax tyvars some_thm vars' NOBR t;
+        val [p] = Name.invent (snd vars2) "m" 1
+        val vars3 = intro_vars [p] vars2
+        fun print_fun_clause ((targets, t), (some_thm, _)) =
+          let
+            val used = Code_Thingol.add_varnames t []
+            val vars' =
+              intro_vars (build (fold Code_Thingol.add_varnames targets)) vars2;
+            fun remove_unused (IVar (SOME name)) = IVar
+                (if member (op =) used name then SOME name else NONE)
+              | remove_unused t = t
+            val clauses = params ~~ targets
+              |> map (apsnd (map_terms_bottom_up remove_unused))
+              |> filter (fn (_, IVar NONE) => false | _ => true)
+              |> map_filter (fn (NONE, _) => NONE | (SOME v, t) => SOME (v,t))
+            val clause = print_clause tyvars some_thm vars' p clauses t
+          in
+            wrap_new_scope clause
+          end;
+        val dict_args = print_dict_args tyvars vs
+        val head = print_func_head tyvars vars3 ((SOME o Constant) const) (map fst vs) dict_args params tys' (print_go_typ tyvars ty');
+      in (*if null params andalso null vs then
+         print_var ((str o deresolve_const) const) (print_rhs false vars2 (hd eqs))
+       else*)
+       if simple then
+          print_func head (print_rhs true vars2 (hd eqs))
+        else
+          print_func head (Pretty.chunks
+            (map print_fun_clause eqs @ [oneline [str "panic(\"match failed\")"]]))
+      end;
+    fun print_typeclass tyvars sym ((target, (super, params))) =
+      let
+        val tyvars = intro_vars [target] tyvars
+        val super_fields = super
+          |> map (fn (self, super) => block [
+               (str o Long_Name.base_name o deresolve_classrel) (self, super),
+               Pretty.brk 1,
+               apply_constraints tyvars ((str o deresolve_class) super) [ITyVar target]
+             ])
+        val fields = params
+          |> map (fn (name,typ) => block [
+               (str o deresolve_const) name, Pretty.brk 1,
+               print_go_typ_uncurried_toplevel tyvars typ
+             ])
+          |> (curry op @) super_fields
+        val head = applify_constraints tyvars ((str o deresolve_class) sym) [target]
+      in block_enclose (concat [str "type", head, str "struct {"], str "}") fields
+      end;
+    fun print_instance tyvars (target, class) {vs, inst_params, superinsts, tyco, ...} =
+      let
+        val class_name = deresolve_class class
+        val tyvars = intro_tyvars vs tyvars
+        val tyargs = map fst vs
+        val class_head = apply_constraints tyvars (str class_name) [tyco `%% (map ITyVar tyargs)]
+        val sym = Class_Instance (target, class)
+        val instance_name = deresolve_inst (target, class)
+        val superinsts_fields = superinsts
+          |> map (fn (super, dicts) => block [
+              (str o Long_Name.base_name o deresolve_classrel) (class, super),
+              str ":", Pretty.brk 1,
+              print_dict tyvars (Dict ([], Dict_Const ((tyco, super), dicts))), str ","
+            ])
+         fun print_classparam_instance ((classparam, (const as { dom, ... }, dom_length)), (thm, _)) =
+           let
+             val aux_dom = Name.invent_names (snd reserved) "A" dom;
+             val auxs = map fst aux_dom;
+             val vars = intro_vars auxs tyvars;
+             val (aux_dom1, aux_dom2) = chop dom_length aux_dom;
+             fun abstract_using [] _ _ body = body
+               | abstract_using aux_dom should_wrap rty body = let
+                  val params = aux_dom
+                   |> map (fn (aux, ty) =>
+                       block [(str o lookup_var vars) aux, Pretty.brk 1, print_go_typ tyvars ty])
+                  val head = print_func_head tyvars vars NONE [] params [] []
+                       ((if should_wrap then print_go_typ_uncurried_toplevel else print_go_typ) tyvars rty)
+                 in print_func head (wrap_if should_wrap body) end;
+             val aux_abstract = if not (null aux_dom1) andalso not (null aux_dom2)
+               then abstract_using aux_dom1 true (map snd aux_dom2 `--> #range const) o abstract_using aux_dom2 false (#range const)
+               else abstract_using aux_dom1 false (#range const) o abstract_using aux_dom2 false (#range const)
+             val wrap_in_func = if null aux_dom1 andalso null aux_dom2
+               then print_func (print_func_head tyvars vars NONE [] [] [] [] (print_go_typ tyvars (#range const))) else I
+             val wrap_aux = case (null aux_dom1, null aux_dom2) of
+               (true, true) => print_func (print_func_head tyvars vars NONE [] [] [] [] (print_go_typ tyvars (#range const)))
+             | (false, false) => abstract_using aux_dom1 true (map snd aux_dom2 `--> #range const) o abstract_using aux_dom2 false (#range const)
+             | _ => abstract_using aux_dom1 false (#range const) o abstract_using aux_dom2 false (#range const)
+           in block [
+            (str o Long_Name.base_name o deresolve_const) classparam,
+            str ":", Pretty.brk 1,
+            (wrap_aux o wrap_in_return o print_app false const_syntax tyvars (SOME thm) vars NOBR)
+              (const, map (IVar o SOME) auxs),
+            str ","
+           ] end;
+      in let
+          val body = block_enclose (concat [str "return", class_head, str "{"],str "}")
+                      (superinsts_fields
+                        @ map print_classparam_instance inst_params)
+          val head = print_func_head tyvars reserved (SOME sym) tyargs (print_dict_args tyvars vs)
+                   [] [] class_head
+        in print_func head body end
+      end;
+    fun print_stmt (Constant const, (_, Fun ((vs, ty), raw_eqs))) =
+       print_go_func const_syntax reserved const vs ty (filter (snd o snd) raw_eqs)
+    | print_stmt (Type_Constructor tyco, (_, Datatype (vs, cos))) =
+       print_go_typedef tyco vs cos reserved
+    | print_stmt (Type_Class sym, (_, Class class)) =
+       print_typeclass reserved sym class
+    | print_stmt (Class_Instance sym, (_, Instance instance)) =
+       print_instance reserved sym instance
+    | print_stmt (_, _) = str "<unknown>" (*raise Fail "whatever this is, it's not yet supported";*)
+  in print_stmt
+  end;
+
+
+
+fun variant_capitalize s ctxt =
+  let
+    val cs = Symbol.explode s;
+    val s_lower = case cs of
+      c :: cs => Symbol.to_ascii_upper c :: cs
+  in ctxt
+    |> Name.variant (implode s_lower)
+  end;
+
+fun go_program_of_program ctxt module_name reserved identifiers exports program =
+  let
+    val variant = variant_capitalize
+    fun namify_module name_fragment ((nsp_class, nsp_object), nsp_common) =
+      let
+        val declare = Name.declare name_fragment;
+      in (name_fragment, ((declare nsp_class, declare nsp_object), declare nsp_common)) end;
+    fun namify_common base ((nsp_class, nsp_object), nsp_common) =
+      let
+        val (base', nsp_common') = variant base nsp_common
+      in
+        (base', ((Name.declare base' nsp_class, Name.declare base' nsp_object), nsp_common'))
+      end;
+    fun namify_stmt (Code_Thingol.Fun _) = namify_common
+      | namify_stmt (Code_Thingol.Datatype _) = namify_common
+      | namify_stmt (Code_Thingol.Datatypecons _) = namify_common
+      | namify_stmt (Code_Thingol.Class _) = namify_common
+      | namify_stmt (Code_Thingol.Classrel _) = namify_common
+      | namify_stmt (Code_Thingol.Classparam _) = namify_common
+      | namify_stmt (Code_Thingol.Classinst _) = namify_common;
+
+    fun modify_stmt (_, (_, Code_Thingol.Fun (_, SOME _))) = NONE
+      | modify_stmt (_, (export, Code_Thingol.Fun (x, _))) = SOME (export, Fun x)
+      | modify_stmt (_, (export, Code_Thingol.Datatype x)) = SOME (export, Datatype x)
+      | modify_stmt (_, (_, Code_Thingol.Datatypecons _)) = NONE
+      | modify_stmt (Type_Class class, (export, Code_Thingol.Class x)) =
+          SOME (export, Class x)
+      | modify_stmt (_, (_, Code_Thingol.Classrel x)) = NONE
+      | modify_stmt (_, (_, Code_Thingol.Classparam x)) = NONE
+      | modify_stmt (_, (export, Code_Thingol.Classinst inst)) =
+          SOME (export, Instance inst);
+  in
+    Code_Namespace.hierarchical_program ctxt
+      { module_name = module_name, reserved = reserved, identifiers = identifiers,
+        empty_nsp = ((reserved, reserved), reserved), namify_module = namify_module,
+        namify_stmt = namify_stmt, cyclic_modules = false,
+        class_transitive = true, class_relation_public = true, empty_data = (),
+        memorize_data = K I, modify_stmts = map modify_stmt }
+      exports program
+  end;
+
+
+
+
+fun serialize_go gen_stringer go_module undefineds infinite_types ctxt { module_name, reserved_syms,
+     identifiers, includes, class_syntax, tyco_syntax, const_syntax } program exports =
+  let
+    (* build program *)
+    val { deresolver, hierarchical_program = go_program } =
+      go_program_of_program ctxt module_name (Name.make_context reserved_syms)
+        identifiers exports program;
+
+    val go_module = if go_module = "" then "isabelle/exported" else go_module;
+
+    (* helper functions that need access to the entire program *)
+    fun lookup_constr tyco constr = case Code_Symbol.Graph.get_node program (Type_Constructor tyco)
+     of Code_Thingol.Datatype (_, constrs) =>
+           (AList.lookup (op = o apsnd fst) constrs constr)
+       | _ => NONE;
+    fun is_sum_type sym = case Code_Symbol.Graph.get_node program sym of
+     Code_Thingol.Datatypecons tyco => (case Code_Symbol.Graph.get_node program (Type_Constructor tyco)
+     of Code_Thingol.Datatype (_, []) => false
+      | Code_Thingol.Datatype (_, [_]) => false
+      | Code_Thingol.Datatype _ => true
+      | _ => false)
+     | _ => false;
+
+    fun is_class_param (sym as Constant const) = case Code_Symbol.Graph.get_node program sym
+     of Code_Thingol.Classparam _ => true
+        | _ => false
+    fun classparams_of_class class = case Code_Symbol.Graph.get_node program (Type_Class class)
+     of Code_Thingol.Class (_, (_, classparams)) => classparams;
+    fun args_num (sym as Constant const) = case Code_Symbol.Graph.get_node program sym
+     of Code_Thingol.Fun (((_, ty), []), _) =>
+          (length o fst o Code_Thingol.unfold_fun) ty
+      | Code_Thingol.Fun ((_, ((ts, _), _) :: _), _) => length ts
+      | Code_Thingol.Datatypecons tyco => length (the (lookup_constr tyco const))
+      | Code_Thingol.Classparam class =>
+          (length o fst o Code_Thingol.unfold_fun o the o AList.lookup (op =)
+            (classparams_of_class class)) const;
+    (* print the go code *)
+    fun print_stmt prefix_fragments b = ("", print_go_stmt gen_stringer undefineds infinite_types
+      tyco_syntax const_syntax (make_vars reserved_syms) args_num is_sum_type is_class_param
+      (Code_Thingol.is_constr program) (deresolver prefix_fragments, deresolver) b);
+
+    fun get_imports module_name = Module module_name
+      |> Code_Symbol.Graph.immediate_succs go_program
+      |> map (fn (Module a) => a)
+      |> (curry op @) (map fst includes)
+      |> map (fn (a) => go_module ^ "/" ^ a)
+
+    (* print modules *)
+    fun print_module _ base _ ps = (base, Pretty.chunks2
+      (str ("package " ^ base)
+      :: block_enclose (str "import (", str ")")
+          (map (str o print_go_string) (get_imports base))
+      :: (map snd ps) ))
+
+
+    (* serialization *)
+    val p = Code_Namespace.print_hierarchical {
+        print_module = print_module, print_stmt = print_stmt,
+        lift_markup = K I } go_program
+     |> curry (op @) includes
+     |> map (apfst (fn a => [a, "exported.go"]))
+
+    val is_single_module = length p = 1
+  in (
+    if is_single_module
+      then Code_Target.Singleton ("go", snd (hd p))
+      else Code_Target.Hierarchy ((["go.mod"], Pretty.chunks2 [
+        concat [str "module",(str o print_go_string) go_module],
+        str "go 1.18"
+      ]) :: p),
+    try (deresolver [])
+  ) end;
+
+
+val serializer : Code_Target.serializer =
+  Code_Target.parse_args ((Scan.optional (Args.$$$ "go_module" |-- Args.name) ""
+      -- Scan.optional (Args.$$$ "gen_stringer" >> K true) false
+      -- Scan.optional (Args.$$$ "panic_on" |-- (Scan.repeat Parse.term)) []
+      -- Scan.optional (Args.$$$ "infinite_type" |-- (Scan.repeat Parse.term)) [])
+  >> (fn (((go_module, gen_stringer), undef_terms), infinite_types) => fn lthy => let
+         val undefineds = map (fst o dest_Const o Syntax.read_term lthy) undef_terms
+         val infinite_types = map (fst o dest_Type o Syntax.parse_typ lthy) infinite_types
+       in serialize_go gen_stringer go_module undefineds infinite_types lthy end))
+
+
+val _ = Theory.setup
+  (Code_Target.add_language
+    (target, { serializer = serializer, literals = literals,
+      check = { env_var = "ISABELLE_GO",
+        make_destination = fn p => p + Path.explode "export.go",
+        make_command = fn p => "test -d export.go && cd export.go && $ISABELLE_GO build ./"^p^" || $ISABELLE_GO build ./export.go"},
+      evaluation_args = []})
+  #> Code_Target.set_printings (Type_Constructor ("fun",
+    [(target, SOME (2, fn print_go_typ => fn fxy => fn [arg, rtyp] => let
+        val head = applify "(" ")" (print_go_typ fxy) NOBR (str "func") [arg];
+      in concat [head, print_go_typ fxy rtyp] end)
+    )]))
+  #> fold (Code_Target.add_reserved target) [
+      "any", "break", "default", "func", "interface", "select", "case", "defer",
+      "go", "map", "struct", "chan", "else", "goto", "package", "switch",
+      "const", "fallthrough", "if", "range", "type", "continue", "for",
+      "import", "return", "var"
+    ]);
+
+
+end; (*struct*)
diff --git a/thys/Go/document/root.tex b/thys/Go/document/root.tex
new file mode 100644
--- /dev/null
+++ b/thys/Go/document/root.tex
@@ -0,0 +1,24 @@
+\documentclass[11pt,a4paper]{report}
+\usepackage[T1]{fontenc}
+\usepackage{isabelle,isabellesym}
+\usepackage{pdfsetup}
+\urlstyle{rm}
+\isabellestyle{it}
+
+\begin{document}
+
+\title{Go Code Generation for Isabelle}
+\author{Terru Stübinger, Lars Hupel}
+\maketitle
+
+\begin{abstract}
+  This entry contains a standalone code generation target for the Go programming language.
+  Unlike the previous targets, Go is not a functional language and encourages code in an imperative style, thus many of the features of Isabelle's language (particularly data types, pattern matching, and type classes) have to be emulated using imperative language constructs in Go.
+  To generate Go code, users can simply import this entry, which makes the Go target available.
+\end{abstract}
+
+\parindent 0pt\parskip 0.5ex
+
+\input{session}
+
+\end{document}
diff --git a/thys/Go/test/quick/RBT_Test.thy b/thys/Go/test/quick/RBT_Test.thy
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/RBT_Test.thy
@@ -0,0 +1,26 @@
+theory RBT_Test imports
+ "HOL-Data_Structures.RBT_Set"
+ "Go.Go_Setup"
+begin
+
+
+
+definition t1 :: "integer rbt" where
+  "t1 = fold insert [1,2,3,4,5] empty"
+
+fun tree_from_list :: "'a::linorder list \<Rightarrow> 'a rbt" where
+ "tree_from_list xs = fold insert xs empty"
+
+fun delete_list :: "'a::linorder list \<Rightarrow> 'a rbt \<Rightarrow> 'a rbt" where
+  "delete_list xs a = fold del xs a"
+
+fun trees_equal :: "'a::equal rbt \<Rightarrow> 'a rbt \<Rightarrow> bool" where
+  "trees_equal a b = (a = b)"
+
+export_code delete_list tree_from_list join invc trees_equal t1 in Go
+  module_name RbtTest
+
+
+export_code delete_list tree_from_list join invc trees_equal t1 checking Go?
+
+end
diff --git a/thys/Go/test/quick/export/Bigint/exported.go b/thys/Go/test/quick/export/Bigint/exported.go
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/export/Bigint/exported.go
@@ -0,0 +1,66 @@
+
+package Bigint
+
+import "math/big"
+
+type Int = big.Int;
+
+func MkInt(s string) Int {
+  var i Int;
+  _, e := i.SetString(s, 10);
+  if (e) {
+    return i;
+  } else {
+    panic("invalid integer literal")
+  }
+}
+
+func Uminus(a Int) Int {
+  var b Int
+  b.Neg(&a)
+  return b
+}
+
+func Minus(a, b Int) Int {
+  var c Int
+  c.Sub(&a, &b)
+  return c
+}
+
+func Plus(a, b Int) Int {
+  var c Int
+  c.Add(&a, &b)
+  return c
+}
+
+func Times (a, b Int) Int {
+  var c Int
+  c.Mul(&a, &b)
+  return c
+}
+
+func Divmod_abs(a, b Int) (Int, Int) {
+  var div, mod Int
+  div.DivMod(&a, &b, &mod)
+  div.Abs(&div)
+  return div, mod
+}
+
+func Equal(a, b Int) bool {
+  return a.Cmp(&b) == 0
+}
+
+func Less_eq(a, b Int) bool {
+  return a.Cmp(&b) != 1
+}
+
+func Less(a, b Int) bool {
+  return a.Cmp(&b) == -1
+}
+
+func Abs(a Int) Int {
+  var b Int
+  b.Abs(&a)
+  return b
+}
+
diff --git a/thys/Go/test/quick/export/RbtTest/exported.go b/thys/Go/test/quick/export/RbtTest/exported.go
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/export/RbtTest/exported.go
@@ -0,0 +1,1404 @@
+package RbtTest
+
+import (
+  "isabelle/exported/Bigint"
+)
+
+// sum type which can be Red, Black
+type Color any;
+type Red struct { };
+type Black struct { };
+
+
+
+func Equal_colora (x0 Color, x1 Color) bool {
+  {
+    if x0 == (Color(Red{})) {
+      if x1 == (Color(Black{})) {
+        return false;
+      }
+    }
+  };
+  {
+    if x0 == (Color(Black{})) {
+      if x1 == (Color(Red{})) {
+        return false;
+      }
+    }
+  };
+  {
+    if x0 == (Color(Black{})) {
+      if x1 == (Color(Black{})) {
+        return true;
+      }
+    }
+  };
+  {
+    if x0 == (Color(Red{})) {
+      if x1 == (Color(Red{})) {
+        return true;
+      }
+    }
+  };
+  panic("match failed");
+}
+
+type Equal[a any] struct {
+  Equala func(a, a) bool
+}
+
+func Equal_color () Equal[Color] {
+  return Equal[Color] {
+    Equala: func  (A Color, Aa Color) bool { return Equal_colora(A, Aa); },
+  }
+}
+
+type Prod[a, b any] struct { A a; Aa b; };
+func Pair_dest[a, b any](p Prod[a, b])(a, b) {
+  return  p.A, p.Aa;
+}
+
+func Eq[a any] (a_ Equal[a], aa a, b a) bool {
+  return a_.Equala(aa, b);
+}
+
+func Equal_proda[a, b any] (a_ Equal[a], b_ Equal[b], x0 Prod[a, b], x1 Prod[a, b]) bool {
+  {
+    _ = x0;
+    x1b, x2a := Pair_dest(x0);
+    _ = x1;
+    y1a, y2a := Pair_dest(x1);
+    return Eq[a](a_, x1b, y1a) && Eq[b](b_, x2a, y2a);
+  };
+  panic("match failed");
+}
+
+func Equal_prod[a, b any] (a_ Equal[a], b_ Equal[b]) Equal[Prod[a, b]] {
+  return Equal[Prod[a, b]] {
+    Equala: func  (A Prod[a, b], Aa Prod[a, b]) bool { return Equal_proda[a, b](a_, b_, A, Aa); },
+  }
+}
+
+func Equal_integer () Equal[Bigint.Int] {
+  return Equal[Bigint.Int] {
+    Equala: func  (A Bigint.Int, Aa Bigint.Int) bool { return Bigint.Equal( A, Aa); },
+  }
+}
+
+type Ord[a any] struct {
+  Less_eq func(a, a) bool
+  Less func(a, a) bool
+}
+
+func Ord_integer () Ord[Bigint.Int] {
+  return Ord[Bigint.Int] {
+    Less_eq: func  (A Bigint.Int, Aa Bigint.Int) bool { return Bigint.Less_eq( A, Aa); },
+    Less: func  (A Bigint.Int, Aa Bigint.Int) bool { return Bigint.Less( A, Aa); },
+  }
+}
+
+type Preorder[a any] struct {
+  Ord_preorder Ord[a]
+}
+
+type Order[a any] struct {
+  Preorder_order Preorder[a]
+}
+
+func Preorder_integer () Preorder[Bigint.Int] {
+  return Preorder[Bigint.Int] {
+    Ord_preorder: Ord_integer(),
+  }
+}
+
+func Order_integer () Order[Bigint.Int] {
+  return Order[Bigint.Int] {
+    Preorder_order: Preorder_integer(),
+  }
+}
+
+type Linorder[a any] struct {
+  Order_linorder Order[a]
+}
+
+func Linorder_integer () Linorder[Bigint.Int] {
+  return Linorder[Bigint.Int] {
+    Order_linorder: Order_integer(),
+  }
+}
+
+// sum type which can be One, Bit0, Bit1
+type Num any;
+type One struct { };
+type Bit0 struct { A Num; };
+type Bit1 struct { A Num; };
+
+func Bit0_dest(p Bit0)(Num) {
+  return p.A
+}
+func Bit1_dest(p Bit1)(Num) {
+  return p.A
+}
+
+// sum type which can be Nil, Cons
+type List[a any] any;
+type Nil[a any] struct { };
+type Cons[a any] struct { A a; Aa List[a]; };
+
+func Cons_dest[a any](p Cons[a])(a, List[a]) {
+  return p.A, p.Aa
+}
+
+// sum type which can be Leaf, Node
+type Tree[a any] any;
+type Leaf[a any] struct { };
+type Node[a any] struct { A Tree[a]; Aa a; Ab Tree[a]; };
+
+func Node_dest[a any](p Node[a])(Tree[a], a, Tree[a]) {
+  return p.A, p.Aa, p.Ab
+}
+
+// sum type which can be LT, EQ, GT
+type Cmp_val any;
+type LT struct { };
+type EQ struct { };
+type GT struct { };
+
+
+
+
+func Cmp[a any] (a1_ Equal[a], a2_ Linorder[a], x a, y a) Cmp_val {
+  target := a2_.Order_linorder.Preorder_order.Ord_preorder.Less(x, y);
+  {
+    if target == (true) {
+      return Cmp_val(LT{});
+    }
+  };
+  {
+    if target == (false) {
+      targeu := Eq[a](a1_, x, y);
+      {
+        if targeu == (true) {
+          return Cmp_val(EQ{});
+        }
+      };
+      {
+        if targeu == (false) {
+          return Cmp_val(GT{});
+        }
+      };
+      panic("match failed");
+    }
+  };
+  panic("match failed");
+}
+
+func Paint[a any] (c Color, x1 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    if x1 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{});
+    }
+  };
+  {
+    cb := c;
+    q, m := x1.(Node[Prod[a, Color]]);
+    if m {
+      la, p, ra := Node_dest(q);
+      _ = p;
+      ab, _ := Pair_dest(p);
+      return Tree[Prod[a, Color]](Node[Prod[a, Color]]{la, Prod[a, Color]{ab, cb}, ra});
+    }
+  };
+  panic("match failed");
+}
+
+func BaliR[a any] (t1 Tree[Prod[a, Color]], aa a, x2 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      t2a, q, p := Node_dest(q);
+      _ = q;
+      ba, d := Pair_dest(q);
+      if d == (Color(Red{})) {
+        r, m := p.(Node[Prod[a, Color]]);
+        if m {
+          t3a, r, t4a := Node_dest(r);
+          _ = r;
+          ca, e := Pair_dest(r);
+          if e == (Color(Red{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{ca, Color(Black{})}, t4a})});
+          }
+        }
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      q, p, d := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        r, m := q.(Node[Prod[a, Color]]);
+        if m {
+          t2a, r, t3a := Node_dest(r);
+          _ = r;
+          ba, e := Pair_dest(r);
+          if e == (Color(Red{})) {
+            _ = p;
+            ca, f := Pair_dest(p);
+            if f == (Color(Red{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{ca, Color(Black{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      r, q, p := Node_dest(q);
+      s, m := r.(Node[Prod[a, Color]]);
+      if m {
+        t2a, s, t3a := Node_dest(s);
+        _ = s;
+        ba, d := Pair_dest(s);
+        if d == (Color(Red{})) {
+          _ = q;
+          ca, e := Pair_dest(q);
+          if e == (Color(Red{})) {
+            t, m := p.(Node[Prod[a, Color]]);
+            if m {
+              va, t, vba := Node_dest(t);
+              _ = t;
+              vca, f := Pair_dest(t);
+              if f == (Color(Black{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{ca, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba})})});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba})});
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      d, vaa, c := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) && c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), vaa, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})})});
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      p, vaa, c := Node_dest(q);
+      if c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        q, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vba, q, vda := Node_dest(q);
+          _ = q;
+          vea, d := Pair_dest(q);
+          if d == (Color(Black{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vba, Prod[a, Color]{vea, Color(Black{})}, vda}), vaa, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})})});
+          }
+        }
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      c, vaa, p := Node_dest(q);
+      if c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        q, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vca, q, vea := Node_dest(q);
+          _ = q;
+          vfa, d := Pair_dest(q);
+          if d == (Color(Black{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), vaa, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vca, Prod[a, Color]{vfa, Color(Black{})}, vea})})});
+          }
+        }
+      }
+    }
+  };
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      q, vaa, p := Node_dest(q);
+      r, m := q.(Node[Prod[a, Color]]);
+      if m {
+        vba, r, vga := Node_dest(r);
+        _ = r;
+        vha, c := Pair_dest(r);
+        if c == (Color(Black{})) {
+          s, m := p.(Node[Prod[a, Color]]);
+          if m {
+            vca, s, vea := Node_dest(s);
+            _ = s;
+            vfa, d := Pair_dest(s);
+            if d == (Color(Black{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vba, Prod[a, Color]{vha, Color(Black{})}, vga}), vaa, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vca, Prod[a, Color]{vfa, Color(Black{})}, vea})})});
+            }
+          }
+        }
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func BaldL[a any] (x0 Tree[Prod[a, Color]], b a, t3 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      t1a, p, t2a := Node_dest(q);
+      _ = p;
+      ab, c := Pair_dest(p);
+      if c == (Color(Red{})) {
+        bb := b;
+        t3b := t3;
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{bb, Color(Red{})}, t3b});
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := b;
+      q, m := t3.(Node[Prod[a, Color]]);
+      if m {
+        t2a, p, t3b := Node_dest(q);
+        _ = p;
+        bb, c := Pair_dest(p);
+        if c == (Color(Black{})) {
+          return BaliR[a](Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), ab, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t2a, Prod[a, Color]{bb, Color(Red{})}, t3b}));
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ab := b;
+        q, m := t3.(Node[Prod[a, Color]]);
+        if m {
+          t2a, q, t3b := Node_dest(q);
+          _ = q;
+          bb, d := Pair_dest(q);
+          if d == (Color(Black{})) {
+            return BaliR[a](Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), ab, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t2a, Prod[a, Color]{bb, Color(Red{})}, t3b}));
+          }
+        }
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := b;
+      q, m := t3.(Node[Prod[a, Color]]);
+      if m {
+        q, p, t4a := Node_dest(q);
+        r, m := q.(Node[Prod[a, Color]]);
+        if m {
+          t2a, r, t3b := Node_dest(r);
+          _ = r;
+          bb, d := Pair_dest(r);
+          if d == (Color(Black{})) {
+            _ = p;
+            ca, e := Pair_dest(p);
+            if e == (Color(Red{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{bb, Color(Red{})}, BaliR[a](t3b, ca, Paint[a](Color(Red{}), t4a))});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, d := Pair_dest(p);
+      if d == (Color(Black{})) {
+        ab := b;
+        q, m := t3.(Node[Prod[a, Color]]);
+        if m {
+          r, q, t4a := Node_dest(q);
+          s, m := r.(Node[Prod[a, Color]]);
+          if m {
+            t2a, s, t3b := Node_dest(s);
+            _ = s;
+            bb, e := Pair_dest(s);
+            if e == (Color(Black{})) {
+              _ = q;
+              ca, f := Pair_dest(q);
+              if f == (Color(Red{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{bb, Color(Red{})}, BaliR[a](t3b, ca, Paint[a](Color(Red{}), t4a))});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := b;
+      if t3 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := b;
+      q, m := t3.(Node[Prod[a, Color]]);
+      if m {
+        c, p, vba := Node_dest(q);
+        if c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+          _ = p;
+          vca, d := Pair_dest(p);
+          if d == (Color(Red{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{vca, Color(Red{})}, vba})});
+          }
+        }
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := b;
+      q, m := t3.(Node[Prod[a, Color]]);
+      if m {
+        q, p, vba := Node_dest(q);
+        r, m := q.(Node[Prod[a, Color]]);
+        if m {
+          vaa, r, vea := Node_dest(r);
+          _ = r;
+          vfa, c := Pair_dest(r);
+          if c == (Color(Red{})) {
+            _ = p;
+            vca, d := Pair_dest(p);
+            if d == (Color(Red{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vaa, Prod[a, Color]{vfa, Color(Red{})}, vea}), Prod[a, Color]{vca, Color(Red{})}, vba})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ab := b;
+        if t3 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+          return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ab := b;
+        q, m := t3.(Node[Prod[a, Color]]);
+        if m {
+          d, q, vea := Node_dest(q);
+          if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+            _ = q;
+            vfa, e := Pair_dest(q);
+            if e == (Color(Red{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{vfa, Color(Red{})}, vea})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ab := b;
+        q, m := t3.(Node[Prod[a, Color]]);
+        if m {
+          r, q, vea := Node_dest(q);
+          s, m := r.(Node[Prod[a, Color]]);
+          if m {
+            vda, s, vha := Node_dest(s);
+            _ = s;
+            via, d := Pair_dest(s);
+            if d == (Color(Red{})) {
+              _ = q;
+              vfa, e := Pair_dest(q);
+              if e == (Color(Red{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vda, Prod[a, Color]{via, Color(Red{})}, vha}), Prod[a, Color]{vfa, Color(Red{})}, vea})});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func Join[a any] (x0 Tree[Prod[a, Color]], t Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      tb := t;
+      return tb;
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      vc, vaa, vba := Node_dest(q);
+      if t == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{vc, vaa, vba});
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      t1a, p, t2a := Node_dest(q);
+      _ = p;
+      ab, d := Pair_dest(p);
+      if d == (Color(Red{})) {
+        q, m := t.(Node[Prod[a, Color]]);
+        if m {
+          t3a, q, t4a := Node_dest(q);
+          _ = q;
+          ca, e := Pair_dest(q);
+          if e == (Color(Red{})) {
+            target := Join[a](t2a, t3a);
+            {
+              if target == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ca, Color(Red{})}, t4a})});
+              }
+            };
+            {
+              r, m := target.(Node[Prod[a, Color]]);
+              if m {
+                u2, r, u3 := Node_dest(r);
+                _ = r;
+                b, f := Pair_dest(r);
+                if f == (Color(Red{})) {
+                  return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Red{})}, u2}), Prod[a, Color]{b, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{u3, Prod[a, Color]{ca, Color(Red{})}, t4a})});
+                }
+              }
+            };
+            {
+              r, m := target.(Node[Prod[a, Color]]);
+              if m {
+                u2, r, u3 := Node_dest(r);
+                _ = r;
+                b, f := Pair_dest(r);
+                if f == (Color(Black{})) {
+                  return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{u2, Prod[a, Color]{b, Color(Black{})}, u3}), Prod[a, Color]{ca, Color(Red{})}, t4a})});
+                }
+              }
+            };
+            panic("match failed");
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      t1a, p, t2a := Node_dest(q);
+      _ = p;
+      ab, d := Pair_dest(p);
+      if d == (Color(Black{})) {
+        q, m := t.(Node[Prod[a, Color]]);
+        if m {
+          t3a, q, t4a := Node_dest(q);
+          _ = q;
+          ca, e := Pair_dest(q);
+          if e == (Color(Black{})) {
+            target := Join[a](t2a, t3a);
+            {
+              if target == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+                return BaldL[a](t1a, ab, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ca, Color(Black{})}, t4a}));
+              }
+            };
+            {
+              r, m := target.(Node[Prod[a, Color]]);
+              if m {
+                u2, r, u3 := Node_dest(r);
+                _ = r;
+                b, f := Pair_dest(r);
+                if f == (Color(Red{})) {
+                  return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Black{})}, u2}), Prod[a, Color]{b, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{u3, Prod[a, Color]{ca, Color(Black{})}, t4a})});
+                }
+              }
+            };
+            {
+              r, m := target.(Node[Prod[a, Color]]);
+              if m {
+                u2, r, u3 := Node_dest(r);
+                _ = r;
+                b, f := Pair_dest(r);
+                if f == (Color(Black{})) {
+                  return BaldL[a](t1a, ab, Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{u2, Prod[a, Color]{b, Color(Black{})}, u3}), Prod[a, Color]{ca, Color(Black{})}, t4a}));
+                }
+              }
+            };
+            panic("match failed");
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        q, m := t.(Node[Prod[a, Color]]);
+        if m {
+          t2a, q, t3a := Node_dest(q);
+          _ = q;
+          ab, d := Pair_dest(q);
+          if d == (Color(Red{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Join[a](Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), t2a), Prod[a, Color]{ab, Color(Red{})}, t3a});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      t1a, p, t2a := Node_dest(q);
+      _ = p;
+      ab, c := Pair_dest(p);
+      if c == (Color(Red{})) {
+        q, m := t.(Node[Prod[a, Color]]);
+        if m {
+          va, q, vba := Node_dest(q);
+          _ = q;
+          vca, d := Pair_dest(q);
+          if d == (Color(Black{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Red{})}, Join[a](t2a, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}))});
+          }
+        }
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func Fold[a, b any] (f func(a) func(b) b, x1 List[a], s b) b {
+  {
+    fb := f;
+    q, m := x1.(Cons[a]);
+    if m {
+      xa, xsa := Cons_dest(q);
+      sb := s;
+      return Fold[a, b](fb, xsa, ((fb(xa))(sb)));
+    }
+  };
+  {
+    if x1 == (List[a](Nil[a]{})) {
+      sb := s;
+      return sb;
+    }
+  };
+  panic("match failed");
+}
+
+func BaliL[a any] (x0 Tree[Prod[a, Color]], c a, t4 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      q, p, t3a := Node_dest(q);
+      r, m := q.(Node[Prod[a, Color]]);
+      if m {
+        t1a, r, t2a := Node_dest(r);
+        _ = r;
+        ab, d := Pair_dest(r);
+        if d == (Color(Red{})) {
+          _ = p;
+          ba, e := Pair_dest(p);
+          if e == (Color(Red{})) {
+            cb := c;
+            t4b := t4;
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1a, Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{cb, Color(Black{})}, t4b})});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      d, q, p := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        _ = q;
+        ab, e := Pair_dest(q);
+        if e == (Color(Red{})) {
+          r, m := p.(Node[Prod[a, Color]]);
+          if m {
+            t2a, r, t3a := Node_dest(r);
+            _ = r;
+            ba, f := Pair_dest(r);
+            if f == (Color(Red{})) {
+              cb := c;
+              t4b := t4;
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{cb, Color(Black{})}, t4b})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      r, q, p := Node_dest(q);
+      s, m := r.(Node[Prod[a, Color]]);
+      if m {
+        va, s, vba := Node_dest(s);
+        _ = s;
+        vca, d := Pair_dest(s);
+        if d == (Color(Black{})) {
+          _ = q;
+          ab, e := Pair_dest(q);
+          if e == (Color(Red{})) {
+            t, m := p.(Node[Prod[a, Color]]);
+            if m {
+              t2a, t, t3a := Node_dest(t);
+              _ = t;
+              ba, f := Pair_dest(t);
+              if f == (Color(Red{})) {
+                cb := c;
+                t4b := t4;
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Black{})}, t2a}), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{cb, Color(Black{})}, t4b})});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ab := c;
+      t2a := t4;
+      return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      d, p, vba := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        _ = p;
+        va, e := Pair_dest(p);
+        if e == (Color(Black{})) {
+          ab := c;
+          t2a := t4;
+          return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{va, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      e, vaa, d := Node_dest(q);
+      if e == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) && d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        ab := c;
+        t2a := t4;
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), vaa, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      d, vaa, p := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        q, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vb, q, vda := Node_dest(q);
+          _ = q;
+          vea, e := Pair_dest(q);
+          if e == (Color(Black{})) {
+            ab := c;
+            t2a := t4;
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), vaa, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vb, Prod[a, Color]{vea, Color(Black{})}, vda})}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      q, p, vba := Node_dest(q);
+      r, m := q.(Node[Prod[a, Color]]);
+      if m {
+        vca, r, vea := Node_dest(r);
+        _ = r;
+        vfa, d := Pair_dest(r);
+        if d == (Color(Black{})) {
+          _ = p;
+          va, e := Pair_dest(p);
+          if e == (Color(Black{})) {
+            ab := c;
+            t2a := t4;
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vca, Prod[a, Color]{vfa, Color(Black{})}, vea}), Prod[a, Color]{va, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      p, vaa, d := Node_dest(q);
+      if d == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        q, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vca, q, vea := Node_dest(q);
+          _ = q;
+          vfa, e := Pair_dest(q);
+          if e == (Color(Black{})) {
+            ab := c;
+            t2a := t4;
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vca, Prod[a, Color]{vfa, Color(Black{})}, vea}), vaa, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      q, vaa, p := Node_dest(q);
+      r, m := q.(Node[Prod[a, Color]]);
+      if m {
+        vca, r, vea := Node_dest(r);
+        _ = r;
+        vfa, d := Pair_dest(r);
+        if d == (Color(Black{})) {
+          s, m := p.(Node[Prod[a, Color]]);
+          if m {
+            vb, s, vga := Node_dest(s);
+            _ = s;
+            vha, e := Pair_dest(s);
+            if e == (Color(Black{})) {
+              ab := c;
+              t2a := t4;
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vca, Prod[a, Color]{vfa, Color(Black{})}, vea}), vaa, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vb, Prod[a, Color]{vha, Color(Black{})}, vga})}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      va, p, vba := Node_dest(q);
+      _ = p;
+      vca, d := Pair_dest(p);
+      if d == (Color(Black{})) {
+        ab := c;
+        t2a := t4;
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}), Prod[a, Color]{ab, Color(Black{})}, t2a});
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func BaldR[a any] (t1 Tree[Prod[a, Color]], aa a, x2 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    t1b := t1;
+    ac := aa;
+    q, m := x2.(Node[Prod[a, Color]]);
+    if m {
+      t2a, p, t3a := Node_dest(q);
+      _ = p;
+      ba, c := Pair_dest(p);
+      if c == (Color(Red{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t2a, Prod[a, Color]{ba, Color(Black{})}, t3a})});
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      t1b, p, t2a := Node_dest(q);
+      _ = p;
+      ac, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ba := aa;
+        if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+          return BaliL[a](Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Red{})}, t2a}), ba, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}));
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      t1b, p, t2a := Node_dest(q);
+      _ = p;
+      ac, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        ba := aa;
+        q, m := x2.(Node[Prod[a, Color]]);
+        if m {
+          va, q, vba := Node_dest(q);
+          _ = q;
+          vca, d := Pair_dest(q);
+          if d == (Color(Black{})) {
+            return BaliL[a](Tree[Prod[a, Color]](Node[Prod[a, Color]]{t1b, Prod[a, Color]{ac, Color(Red{})}, t2a}), ba, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba}));
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      t1b, q, p := Node_dest(q);
+      _ = q;
+      ac, d := Pair_dest(q);
+      if d == (Color(Red{})) {
+        r, m := p.(Node[Prod[a, Color]]);
+        if m {
+          t2a, r, t3a := Node_dest(r);
+          _ = r;
+          ba, e := Pair_dest(r);
+          if e == (Color(Black{})) {
+            ca := aa;
+            if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{BaliL[a](Paint[a](Color(Red{}), t1b), ac, t2a), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{ca, Color(Black{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      t1b, q, p := Node_dest(q);
+      _ = q;
+      ac, d := Pair_dest(q);
+      if d == (Color(Red{})) {
+        r, m := p.(Node[Prod[a, Color]]);
+        if m {
+          t2a, r, t3a := Node_dest(r);
+          _ = r;
+          ba, e := Pair_dest(r);
+          if e == (Color(Black{})) {
+            ca := aa;
+            s, m := x2.(Node[Prod[a, Color]]);
+            if m {
+              va, s, vba := Node_dest(s);
+              _ = s;
+              vca, f := Pair_dest(s);
+              if f == (Color(Black{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{BaliL[a](Paint[a](Color(Red{}), t1b), ac, t2a), Prod[a, Color]{ba, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{t3a, Prod[a, Color]{ca, Color(Black{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba})})});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    if t1 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ac := aa;
+      if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      va, p, c := Node_dest(q);
+      if c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        _ = p;
+        vca, d := Pair_dest(p);
+        if d == (Color(Red{})) {
+          ac := aa;
+          if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      vb, q, p := Node_dest(q);
+      _ = q;
+      vca, c := Pair_dest(q);
+      if c == (Color(Red{})) {
+        r, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vaa, r, vea := Node_dest(r);
+          _ = r;
+          vfa, d := Pair_dest(r);
+          if d == (Color(Red{})) {
+            ac := aa;
+            if x2 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vb, Prod[a, Color]{vca, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vaa, Prod[a, Color]{vfa, Color(Red{})}, vea})}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    if t1 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      ac := aa;
+      q, m := x2.(Node[Prod[a, Color]]);
+      if m {
+        va, p, vba := Node_dest(q);
+        _ = p;
+        vca, c := Pair_dest(p);
+        if c == (Color(Black{})) {
+          return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{va, Prod[a, Color]{vca, Color(Black{})}, vba})});
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      vaa, p, c := Node_dest(q);
+      if c == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+        _ = p;
+        vfa, d := Pair_dest(p);
+        if d == (Color(Red{})) {
+          ac := aa;
+          q, m := x2.(Node[Prod[a, Color]]);
+          if m {
+            vd, q, vba := Node_dest(q);
+            _ = q;
+            vca, e := Pair_dest(q);
+            if e == (Color(Black{})) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vaa, Prod[a, Color]{vfa, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vd, Prod[a, Color]{vca, Color(Black{})}, vba})});
+            }
+          }
+        }
+      }
+    }
+  };
+  {
+    q, m := t1.(Node[Prod[a, Color]]);
+    if m {
+      vaa, q, p := Node_dest(q);
+      _ = q;
+      vfa, c := Pair_dest(q);
+      if c == (Color(Red{})) {
+        r, m := p.(Node[Prod[a, Color]]);
+        if m {
+          vda, r, vha := Node_dest(r);
+          _ = r;
+          via, d := Pair_dest(r);
+          if d == (Color(Red{})) {
+            ac := aa;
+            s, m := x2.(Node[Prod[a, Color]]);
+            if m {
+              ve, s, vba := Node_dest(s);
+              _ = s;
+              vca, e := Pair_dest(s);
+              if e == (Color(Black{})) {
+                return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Node[Prod[a, Color]]{vaa, Prod[a, Color]{vfa, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{vda, Prod[a, Color]{via, Color(Red{})}, vha})}), Prod[a, Color]{ac, Color(Red{})}, Tree[Prod[a, Color]](Node[Prod[a, Color]]{ve, Prod[a, Color]{vca, Color(Black{})}, vba})});
+              }
+            }
+          }
+        }
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func Equal_tree[a any] (a_ Equal[a], x0 Tree[a], x1 Tree[a]) bool {
+  {
+    if x0 == (Tree[a](Leaf[a]{})) {
+      _, m := x1.(Node[a]);
+      if m {
+        return false;
+      }
+    }
+  };
+  {
+    _, m := x0.(Node[a]);
+    if m {
+      if x1 == (Tree[a](Leaf[a]{})) {
+        return false;
+      }
+    }
+  };
+  {
+    q, m := x0.(Node[a]);
+    if m {
+      x21a, x22a, x23a := Node_dest(q);
+      q, m := x1.(Node[a]);
+      if m {
+        y21a, y22a, y23a := Node_dest(q);
+        return Equal_tree[a](a_, x21a, y21a) && (Eq[a](a_, x22a, y22a) && Equal_tree[a](a_, x23a, y23a));
+      }
+    }
+  };
+  {
+    if x0 == (Tree[a](Leaf[a]{})) {
+      if x1 == (Tree[a](Leaf[a]{})) {
+        return true;
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func Colora[a any] (x0 Tree[Prod[a, Color]]) Color {
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return Color(Black{});
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      _, p, _ := Node_dest(q);
+      _ = p;
+      _, ca := Pair_dest(p);
+      return ca;
+    }
+  };
+  panic("match failed");
+}
+
+func Del[a any] (a1_ Equal[a], a2_ Linorder[a], x a, xa1 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    if xa1 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{});
+    }
+  };
+  {
+    xb := x;
+    q, m := xa1.(Node[Prod[a, Color]]);
+    if m {
+      la, p, ra := Node_dest(q);
+      _ = p;
+      ab, _ := Pair_dest(p);
+      target := Cmp[a](a1_, a2_, xb, ab);
+      {
+        if target == (Cmp_val(LT{})) {
+          targeu := ! Equal_tree[Prod[a, Color]](Equal_prod[a, Color](a1_, Equal_color()), la, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) && Equal_colora(Colora[a](la), Color(Black{}));
+          {
+            if targeu == (true) {
+              return BaldL[a](Del[a](a1_, a2_, xb, la), ab, ra);
+            }
+          };
+          {
+            if targeu == (false) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Del[a](a1_, a2_, xb, la), Prod[a, Color]{ab, Color(Red{})}, ra});
+            }
+          };
+          panic("match failed");
+        }
+      };
+      {
+        if target == (Cmp_val(EQ{})) {
+          return Join[a](la, ra);
+        }
+      };
+      {
+        if target == (Cmp_val(GT{})) {
+          targeu := ! Equal_tree[Prod[a, Color]](Equal_prod[a, Color](a1_, Equal_color()), ra, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) && Equal_colora(Colora[a](ra), Color(Black{}));
+          {
+            if targeu == (true) {
+              return BaldR[a](la, ab, Del[a](a1_, a2_, xb, ra));
+            }
+          };
+          {
+            if targeu == (false) {
+              return Tree[Prod[a, Color]](Node[Prod[a, Color]]{la, Prod[a, Color]{ab, Color(Red{})}, Del[a](a1_, a2_, xb, ra)});
+            }
+          };
+          panic("match failed");
+        }
+      };
+      panic("match failed");
+    }
+  };
+  panic("match failed");
+}
+
+func Ins[a any] (a1_ Equal[a], a2_ Linorder[a], x a, xa1 Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  {
+    xb := x;
+    if xa1 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{}), Prod[a, Color]{xb, Color(Red{})}, Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})});
+    }
+  };
+  {
+    xb := x;
+    q, m := xa1.(Node[Prod[a, Color]]);
+    if m {
+      la, p, ra := Node_dest(q);
+      _ = p;
+      ab, c := Pair_dest(p);
+      if c == (Color(Black{})) {
+        target := Cmp[a](a1_, a2_, xb, ab);
+        {
+          if target == (Cmp_val(LT{})) {
+            return BaliL[a](Ins[a](a1_, a2_, xb, la), ab, ra);
+          }
+        };
+        {
+          if target == (Cmp_val(EQ{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{la, Prod[a, Color]{ab, Color(Black{})}, ra});
+          }
+        };
+        {
+          if target == (Cmp_val(GT{})) {
+            return BaliR[a](la, ab, Ins[a](a1_, a2_, xb, ra));
+          }
+        };
+        panic("match failed");
+      }
+    }
+  };
+  {
+    xb := x;
+    q, m := xa1.(Node[Prod[a, Color]]);
+    if m {
+      la, p, ra := Node_dest(q);
+      _ = p;
+      ab, c := Pair_dest(p);
+      if c == (Color(Red{})) {
+        target := Cmp[a](a1_, a2_, xb, ab);
+        {
+          if target == (Cmp_val(LT{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{Ins[a](a1_, a2_, xb, la), Prod[a, Color]{ab, Color(Red{})}, ra});
+          }
+        };
+        {
+          if target == (Cmp_val(EQ{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{la, Prod[a, Color]{ab, Color(Red{})}, ra});
+          }
+        };
+        {
+          if target == (Cmp_val(GT{})) {
+            return Tree[Prod[a, Color]](Node[Prod[a, Color]]{la, Prod[a, Color]{ab, Color(Red{})}, Ins[a](a1_, a2_, xb, ra)});
+          }
+        };
+        panic("match failed");
+      }
+    }
+  };
+  panic("match failed");
+}
+
+func Insert[a any] (a1_ Equal[a], a2_ Linorder[a], x a, t Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  return Paint[a](Color(Black{}), Ins[a](a1_, a2_, x, t));
+}
+
+func Empty[a any] () Tree[Prod[a, Color]] {
+  return Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{});
+}
+
+func T1 () Tree[Prod[Bigint.Int, Color]] {
+  return Fold[Bigint.Int, Tree[Prod[Bigint.Int, Color]]](func  (a Bigint.Int) func(Tree[Prod[Bigint.Int, Color]]) Tree[Prod[Bigint.Int, Color]] { return func  (b Tree[Prod[Bigint.Int, Color]]) Tree[Prod[Bigint.Int, Color]] { return Insert[Bigint.Int](Equal_integer(), Linorder_integer(), a, b); }; }, List[Bigint.Int](Cons[Bigint.Int]{Bigint.MkInt("1"), List[Bigint.Int](Cons[Bigint.Int]{Bigint.MkInt("2"), List[Bigint.Int](Cons[Bigint.Int]{Bigint.MkInt("3"), List[Bigint.Int](Cons[Bigint.Int]{Bigint.MkInt("4"), List[Bigint.Int](Cons[Bigint.Int]{Bigint.MkInt("5"), List[Bigint.Int](Nil[Bigint.Int]{})})})})})}), Empty[Bigint.Int]());
+}
+
+func Invc[a any] (x0 Tree[Prod[a, Color]]) bool {
+  {
+    if x0 == (Tree[Prod[a, Color]](Leaf[Prod[a, Color]]{})) {
+      return true;
+    }
+  };
+  {
+    q, m := x0.(Node[Prod[a, Color]]);
+    if m {
+      la, p, ra := Node_dest(q);
+      _ = p;
+      _, ca := Pair_dest(p);
+      return (!(Equal_colora(ca, Color(Red{}))) || Equal_colora(Colora[a](la), Color(Black{})) && Equal_colora(Colora[a](ra), Color(Black{}))) && (Invc[a](la) && Invc[a](ra));
+    }
+  };
+  panic("match failed");
+}
+
+func Delete_list[a any] (a1_ Equal[a], a2_ Linorder[a], xs List[a], aa Tree[Prod[a, Color]]) Tree[Prod[a, Color]] {
+  return Fold[a, Tree[Prod[a, Color]]](func  (ab a) func(Tree[Prod[a, Color]]) Tree[Prod[a, Color]] { return func  (b Tree[Prod[a, Color]]) Tree[Prod[a, Color]] { return Del[a](a1_, a2_, ab, b); }; }, xs, aa);
+}
+
+func Trees_equal[a any] (a_ Equal[a], aa Tree[Prod[a, Color]], b Tree[Prod[a, Color]]) bool {
+  return Equal_tree[Prod[a, Color]](Equal_prod[a, Color](a_, Equal_color()), aa, b);
+}
+
+func Tree_from_list[a any] (a1_ Equal[a], a2_ Linorder[a], xs List[a]) Tree[Prod[a, Color]] {
+  return Fold[a, Tree[Prod[a, Color]]](func  (aa a) func(Tree[Prod[a, Color]]) Tree[Prod[a, Color]] { return func  (b Tree[Prod[a, Color]]) Tree[Prod[a, Color]] { return Insert[a](a1_, a2_, aa, b); }; }, xs, Empty[a]());
+}
diff --git a/thys/Go/test/quick/export/go.mod b/thys/Go/test/quick/export/go.mod
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/export/go.mod
@@ -0,0 +1,3 @@
+module "isabelle/exported"
+
+go 1.18
diff --git a/thys/Go/test/quick/go/Bigint b/thys/Go/test/quick/go/Bigint
new file mode 120000
--- /dev/null
+++ b/thys/Go/test/quick/go/Bigint
@@ -0,0 +1,1 @@
+../export/Bigint/
\ No newline at end of file
diff --git a/thys/Go/test/quick/go/Interface/rbt.go b/thys/Go/test/quick/go/Interface/rbt.go
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/go/Interface/rbt.go
@@ -0,0 +1,42 @@
+package rbt
+
+import "isabelle/exported/RbtTest"
+
+var T1 = RbtTest.T1()
+
+var LinorderInt = RbtTest.Linorder_integer()
+var EqualInt = RbtTest.Equal_integer()
+
+func EmptyTree[a any]() RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]] {
+	return RbtTest.Empty[a]()
+}
+
+func JoinAndCheck[a any](a_ RbtTest.Linorder[a], x, y RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]]) (RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]], bool) {
+	b := RbtTest.Join(x, y)
+	ok := RbtTest.Invc(b)
+	return b, ok
+}
+
+func DelAndCheck[a any](eq RbtTest.Equal[a], lin RbtTest.Linorder[a], list RbtTest.List[a], x RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]]) (RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]], bool) {
+	b := RbtTest.Delete_list(eq, lin, list, x)
+	ok := RbtTest.Invc(b)
+	return b, ok
+}
+
+func TreeFromList[a any](eq RbtTest.Equal[a], lin RbtTest.Linorder[a], xs RbtTest.List[a]) (RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]], bool) {
+	tree := RbtTest.Tree_from_list(eq, lin, xs)
+	ok := RbtTest.Invc(tree)
+	return tree, ok
+}
+
+func MkList[a any](vec []a) RbtTest.List[a] {
+	list := RbtTest.List[a](RbtTest.Nil[a]{})
+	for _, v := range vec {
+		list = RbtTest.List[a](RbtTest.Cons[a]{v, list})
+	}
+	return list
+}
+
+func TreesEqual[a any](eq RbtTest.Equal[a], x, y RbtTest.Tree[RbtTest.Prod[a, RbtTest.Color]]) bool {
+	return RbtTest.Trees_equal(eq, x, y)
+}
diff --git a/thys/Go/test/quick/go/Interface/rbt_test.go b/thys/Go/test/quick/go/Interface/rbt_test.go
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/go/Interface/rbt_test.go
@@ -0,0 +1,90 @@
+package rbt
+
+import (
+	"reflect"
+	"testing"
+
+	"isabelle/exported/Bigint"
+	"isabelle/exported/RbtTest"
+)
+
+type RBTBigInt = RbtTest.Prod[Bigint.Int, RbtTest.Color]
+
+func TestTreeFromList(t *testing.T) {
+	array := [5]Bigint.Int{Bigint.MkInt("1"), Bigint.MkInt("2"), Bigint.MkInt("3"), Bigint.MkInt("4"), Bigint.MkInt("5")}
+	elements := MkList(array[:])
+
+	got, ok := TreeFromList(EqualInt, LinorderInt, elements)
+	if !ok {
+		t.Fatal("new tree does not satisfy invariant")
+	}
+
+	want := RbtTest.Node[RBTBigInt]{
+		A: RbtTest.Node[RBTBigInt]{
+			A: RbtTest.Node[RBTBigInt]{
+				A: RbtTest.Leaf[RBTBigInt]{},
+				Aa: RBTBigInt{A: Bigint.MkInt("1"),
+					Aa: RbtTest.Black{},
+				},
+				Ab: RbtTest.Leaf[RBTBigInt]{},
+			},
+			Aa: RBTBigInt{
+				A:  Bigint.MkInt("2"),
+				Aa: RbtTest.Red{},
+			},
+			Ab: RbtTest.Node[RBTBigInt]{
+				A: RbtTest.Leaf[RBTBigInt]{},
+				Aa: RBTBigInt{A: Bigint.MkInt("3"),
+					Aa: RbtTest.Black{}},
+				Ab: RbtTest.Leaf[RBTBigInt]{},
+			},
+		},
+		Aa: RBTBigInt{
+			A:  Bigint.MkInt("4"),
+			Aa: RbtTest.Black{},
+		},
+		Ab: RbtTest.Node[RBTBigInt]{
+			A: RbtTest.Leaf[RBTBigInt]{},
+			Aa: RBTBigInt{
+				A:  Bigint.MkInt("5"),
+				Aa: RbtTest.Black{},
+			},
+			Ab: RbtTest.Leaf[RBTBigInt]{},
+		},
+	}
+
+	if !reflect.DeepEqual(got, want) {
+		t.Fatalf("got tree does not equal want tree")
+	}
+}
+
+func TestJoinAndCheck(t *testing.T) {
+	list := MkList([]Bigint.Int{Bigint.MkInt("1"), Bigint.MkInt("2"), Bigint.MkInt("3"), Bigint.MkInt("4"), Bigint.MkInt("5")})
+
+	tree, ok := TreeFromList(EqualInt, LinorderInt, list)
+	if !ok {
+		t.Fatal("new tree does not satisfy invariant")
+	}
+	_, ok = JoinAndCheck(LinorderInt, tree, tree)
+	if !ok {
+		t.Fatal("joining trees violated invariant")
+	}
+}
+
+func TestDelAndCheck(t *testing.T) {
+	list := MkList([]Bigint.Int{Bigint.MkInt("1"), Bigint.MkInt("2"), Bigint.MkInt("3"), Bigint.MkInt("4"), Bigint.MkInt("5")})
+
+	tree, ok := TreeFromList(EqualInt, LinorderInt, list)
+	if !ok {
+		t.Fatal("new tree does not satisfy invariant")
+	}
+	got, ok := DelAndCheck(EqualInt, LinorderInt, list, tree)
+	if !ok {
+		t.Fatal("deletion violated invariant")
+	}
+	want := EmptyTree[Bigint.Int]()
+	ok = TreesEqual(EqualInt, got, want)
+	if !ok {
+		t.Fatal("tree not empty after deletion")
+	}
+}
diff --git a/thys/Go/test/quick/go/RbtTest b/thys/Go/test/quick/go/RbtTest
new file mode 120000
--- /dev/null
+++ b/thys/Go/test/quick/go/RbtTest
@@ -0,0 +1,1 @@
+../export/RbtTest
\ No newline at end of file
diff --git a/thys/Go/test/quick/go/go.mod b/thys/Go/test/quick/go/go.mod
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/quick/go/go.mod
@@ -0,0 +1,3 @@
+module "isabelle/exported"
+
+go 1.18
diff --git a/thys/Go/test/slow/Candidates.thy b/thys/Go/test/slow/Candidates.thy
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/slow/Candidates.thy
@@ -0,0 +1,82 @@
+(* Author: Florian Haftmann, TU Muenchen *)
+
+section \<open>A huge collection of equations to generate code from\<close>
+
+theory Candidates
+imports
+  Complex_Main
+  "HOL-Library.Library"
+  "HOL-Library.Sorting_Algorithms"
+  "HOL-Library.Subseq_Order"
+  "HOL-Library.RBT"
+  "HOL-Data_Structures.Tree_Map"
+  "HOL-Data_Structures.Tree_Set"
+  "HOL-Computational_Algebra.Computational_Algebra"
+  "HOL-Computational_Algebra.Polynomial_Factorial"
+  "HOL-Number_Theory.Eratosthenes"
+  "HOL-Examples.Records"
+  "HOL-Examples.Gauss_Numbers"
+begin
+
+text \<open>Drop technical stuff from \<^theory>\<open>HOL.Quickcheck_Narrowing\<close> which is tailored towards Haskell\<close>
+
+setup \<open>
+fn thy =>
+let
+  val tycos = Sign.logical_types thy;
+  val consts = map_filter (try (curry (Axclass.param_of_inst thy)
+    \<^const_name>\<open>Quickcheck_Narrowing.partial_term_of\<close>)) tycos;
+in fold Code.declare_unimplemented_global consts thy end
+\<close>
+
+text \<open>Simple example for the predicate compiler.\<close>
+
+inductive sublist :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"
+where
+  empty: "sublist [] xs"
+| drop: "sublist ys xs \<Longrightarrow> sublist ys (x # xs)"
+| take: "sublist ys xs \<Longrightarrow> sublist (x # ys) (x # xs)"
+
+code_pred sublist .
+
+text \<open>Avoid popular infix.\<close>
+
+code_reserved SML upto
+
+text \<open>Explicit check in \<open>OCaml\<close> for correct precedence of let expressions in list expressions\<close>
+
+definition funny_list :: "bool list"
+where
+  "funny_list = [let b = True in b, False]"
+
+definition funny_list' :: "bool list"
+where
+  "funny_list' = funny_list"
+
+lemma [code]:
+  "funny_list' = [True, False]"
+  by (simp add: funny_list_def funny_list'_def)
+
+definition check_list :: unit
+where
+  "check_list = (if funny_list = funny_list' then () else undefined)"
+
+text \<open>Explicit check in \<open>Scala\<close> for correct bracketing of abstractions\<close>
+
+definition funny_funs :: "(bool \<Rightarrow> bool) list \<Rightarrow> (bool \<Rightarrow> bool) list"
+where
+  "funny_funs fs = (\<lambda>x. x \<or> True) # (\<lambda>x. x \<or> False) # fs"
+
+(*
+text \<open>Explicit checks for strings etc.\<close>
+
+definition \<open>hello = ''Hello, world!''\<close>
+
+definition \<open>hello2 = String.explode (String.implode hello)\<close>
+
+definition \<open>which_hello \<longleftrightarrow> hello \<le> hello2\<close>
+*)
+
+declare [[code abort: String.literal_of_asciis String.asciis_of_literal]]
+
+end
diff --git a/thys/Go/test/slow/Generate.thy b/thys/Go/test/slow/Generate.thy
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/slow/Generate.thy
@@ -0,0 +1,21 @@
+(* Author: Florian Haftmann, TU Muenchen *)
+
+section \<open>Pervasive test of code generator\<close>
+
+theory Generate
+imports
+  "Candidates"
+  "HOL-Library.AList_Mapping"
+  "HOL-Library.Finite_Lattice"
+  "Go.Go_Setup"
+begin
+
+text \<open>
+  If any of the checks fails, inspect the code generated
+  by a corresponding \<open>export_code\<close> command.
+\<close>
+
+
+export_code _ checking Go? (infinite_type "stream")
+
+end
diff --git a/thys/Go/test/slow/Generate_Binary_Nat.thy b/thys/Go/test/slow/Generate_Binary_Nat.thy
new file mode 100644
--- /dev/null
+++ b/thys/Go/test/slow/Generate_Binary_Nat.thy
@@ -0,0 +1,14 @@
+theory Generate_Binary_Nat
+imports
+  "Candidates"
+  "HOL-Library.AList_Mapping"
+  "HOL-Library.Finite_Lattice"
+  "HOL-Library.Code_Binary_Nat"
+  "Go.Go_Setup"
+begin
+
+
+
+export_code _ checking Go? (infinite_type "stream")
+
+end
diff --git a/thys/ROOTS b/thys/ROOTS
--- a/thys/ROOTS
+++ b/thys/ROOTS
@@ -1,804 +1,807 @@
 ABY3_Protocols
 ADS_Functor
 AI_Planning_Languages_Semantics
 AODV
 AOT
 AVL-Trees
 AWN
 Abortable_Linearizable_Modules
 Abs_Int_ITP2012
 Abstract-Hoare-Logics
 Abstract-Rewriting
 Abstract_Completeness
 Abstract_Soundness
 Ackermanns_not_PR
 Actuarial_Mathematics
 Adaptive_State_Counting
 Affine_Arithmetic
 Aggregation_Algebras
 Akra_Bazzi
 Algebraic_Numbers
 Algebraic_VCs
 Allen_Calculus
 Amicable_Numbers
 Amortized_Complexity
 AnselmGod
 Applicative_Lifting
+Approximate_Model_Counting
 Approximation_Algorithms
 Architectural_Design_Patterns
 Aristotles_Assertoric_Syllogistic
 Arith_Prog_Rel_Primes
 ArrowImpossibilityGS
 Attack_Trees
 Auto2_HOL
 Auto2_Imperative_HOL
 AutoFocus-Stream
 Automated_Stateful_Protocol_Verification
 Automatic_Refinement
 AxiomaticCategoryTheory
 BDD
 BD_Security_Compositional
 BNF_CC
 BNF_Operations
 BTree
 Balog_Szemeredi_Gowers
 Banach_Steinhaus
 Belief_Revision
 Bell_Numbers_Spivey
 BenOr_Kozen_Reif
 Berlekamp_Zassenhaus
 Bernoulli
 Bertrands_Postulate
 Bicategory
 BinarySearchTree
 Binary_Code_Imprimitive
 Binding_Syntax_Theory
 Binomial-Heaps
 Binomial-Queues
 BirdKMP
 Birkhoff_Finite_Distributive_Lattices
 Blue_Eyes
 Bondy
 Boolean_Expression_Checkers
 Boolos_Curious_Inference
 Boolos_Curious_Inference_Automated
 Bounded_Deducibility_Security
 Buchi_Complementation
 Budan_Fourier
 Buffons_Needle
 Buildings
 BytecodeLogicJmlTypes
 C2KA_DistributedSystems
 CAVA_Automata
 CAVA_LTL_Modelchecker
 CCS
 CHERI-C_Memory_Model
 CISC-Kernel
 Concentration_Inequalities
 CRDT
 CRYSTALS-Kyber
 CRYSTALS-Kyber_Security
 CSP_RefTK
 CVP_Hardness
 CYK
 CZH_Elementary_Categories
 CZH_Foundations
 CZH_Universal_Constructions
 CakeML
 CakeML_Codegen
 Call_Arity
 Card_Equiv_Relations
 Card_Multisets
 Card_Number_Partitions
 Card_Partitions
 Cardinality_Continuum
 Cartan_FP
 Case_Labeling
 Catalan_Numbers
 Category
 Category2
 Category3
 Catoids
 Cauchy
 Cayley_Hamilton
 Certification_Monads
 Ceva
 Chandy_Lamport
 Chebyshev_Polynomials
 Chord_Segments
 Circus
 Clean
 Clique_and_Monotone_Circuits
 ClockSynchInst
 Closest_Pair_Points
 CoCon
 CoSMeDis
 CoSMed
 CofGroups
 Coinductive
 Coinductive_Languages
 Collections
 Combinable_Wands
 Combinatorial_Enumeration_Algorithms
 Combinatorics_Words
 Combinatorics_Words_Graph_Lemma
 Combinatorics_Words_Lyndon
 CommCSL
 Commuting_Hermitian
 Comparison_Sort_Lower_Bound
 Compiling-Exceptions-Correctly
 Complete_Non_Orders
 Completeness
 Complex_Bounded_Operators
 Complex_Geometry
 Complx
 ComponentDependencies
 ConcurrentGC
 ConcurrentIMP
 Concurrent_Ref_Alg
 Concurrent_Revisions
 Conditional_Simplification
 Conditional_Transfer_Rule
 Consensus_Refined
 Constructive_Cryptography
 Constructive_Cryptography_CM
 Constructor_Funs
 Containers
+Continued_Fractions
 Cook_Levin
 CoreC++
 Core_DOM
 Core_SC_DOM
 Correctness_Algebras
 Cotangent_PFD_Formula
 Count_Complex_Roots
 Coupledsim_Contrasim
 CryptHOL
 CryptoBasedCompositionalProperties
 Crypto_Standards
 CubicalCategories
 Cubic_Quartic_Equations
 DCR-ExecutionEquivalence
 DFS_Framework
 DOM_Components
 DPRM_Theorem
 DPT-SAT-Solver
 DataRefinementIBP
 Datatype_Order_Generator
 Decl_Sem_Fun_PL
 Decreasing-Diagrams
 Decreasing-Diagrams-II
 Dedekind_Real
 Deep_Learning
 Delta_System_Lemma
 Density_Compiler
 Dependent_SIFUM_Refinement
 Dependent_SIFUM_Type_Systems
 Depth-First-Search
 Derangements
 Deriving
 Descartes_Sign_Rule
 Design_Theory
 Dict_Construction
 Differential_Dynamic_Logic
 Differential_Game_Logic
 DigitsInBase
 Digit_Expansions
 Dijkstra_Shortest_Path
 Diophantine_Eqns_Lin_Hom
 Directed_Sets
 Dirichlet_L
 Dirichlet_Series
 DiscretePricing
 Discrete_Summation
 Disintegration
 DiskPaxos
 Distributed_Distinct_Elements
 Dominance_CHK
 DynamicArchitectures
 Dynamic_Tables
 E_Transcendental
 Earley_Parser
 Echelon_Form
 EdmondsKarp_Maxflow
 Edwards_Elliptic_Curves_Group
 Efficient-Mergesort
 Efficient_Weighted_Path_Order
 Elimination_Of_Repeated_Factors
 Elliptic_Curves_Group_Law
 Encodability_Process_Calculi
 Epistemic_Logic
 Equivalence_Relation_Enumeration
 Ergodic_Theory
 Error_Function
 Euler_MacLaurin
 Euler_Partition
 Euler_Polyhedron_Formula
 Eudoxus_Reals
 Eval_FO
 Example-Submission
 Executable_Randomized_Algorithms
 Expander_Graphs
 Extended_Finite_State_Machine_Inference
 Extended_Finite_State_Machines
 FFT
 FLP
 FOL-Fitting
 FOL_Axiomatic
 FOL_Harrison
 FOL_Seq_Calc1
 FOL_Seq_Calc2
 FOL_Seq_Calc3
 FO_Theory_Rewriting
 FSM_Tests
 Factor_Algebraic_Polynomial
 Factored_Transition_System_Bounding
 Falling_Factorial_Sum
 Farkas
 FeatherweightJava
 Featherweight_OCL
 Fermat3_4
 FileRefinement
 FinFun
 Finger-Trees
 Finite-Map-Extras
 Finite_Automata_HF
 Finite_Fields
 Finitely_Generated_Abelian_Groups
 First_Order_Terms
 First_Welfare_Theorem
 Fishburn_Impossibility
 Fisher_Yates
 Fishers_Inequality
 Fixed_Length_Vector
 Flow_Networks
 Floyd_Warshall
 Flyspeck-Tame
 FocusStreamsCaseStudies
 Forcing
 Formal_Puiseux_Series
 Formal_SSA
 Formula_Derivatives
 Foundation_of_geometry
 Fourier
 Free-Boolean-Algebra
 Free-Groups
 Frequency_Moments
 Fresh_Identifiers
 FunWithFunctions
 FunWithTilings
 Functional-Automata
 Functional_Ordered_Resolution_Prover
 Furstenberg_Topology
 GPU_Kernel_PL
 Gabow_SCC
 GaleStewart_Games
 Gale_Shapley
 Game_Based_Crypto
 Gauss-Jordan-Elim-Fun
 Gauss_Jordan
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   <h1>
     <span class='first'>M</span>anuel <span class='first'>E</span>berl
     
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     <h2>Homepages 🌐</h2>
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       <li><a href="https://www.in.tum.de/~eberlm">https://www.in.tum.de/~eberlm</a></li>
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       <li>
         <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">
           <span class="rev">gro</span>.<span class="rev">otsivurp</span>
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         <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsibWFudWVsIiwiZWJlcmwiXX0=">
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   <h2>Entries</h2>
+    <h3 class="head">2024</h3>
+      <article class="entry">
+        <div class="item-text">
+          <h5><a class="title" href="../../entries/Continued_Fractions.html">Continued Fractions</a></h5>
+          <br>
+            by
+            <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
+
+        </div>
+        <span class="date">
+          Mar 20
+        </span>
+      </article>
     <h3 class="head">2023</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Lambert_Series.html">Lambert Series</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
         </div>
         <span class="date">
           Nov 24
         </span>
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           <h5><a class="title" href="../../entries/Polylog.html">The Polylogarithm Function</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
         </div>
         <span class="date">
           Nov 15
         </span>
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       <article class="entry">
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           <h5><a class="title" href="../../entries/Cardinality_Continuum.html">The Cardinality of the Continuum</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
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           Nov 15
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           <h5><a class="title" href="../../entries/Polynomial_Crit_Geometry.html">Two theorems about the geometry of the critical points of a complex polynomial</a></h5>
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             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
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           Nov 14
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           <h5><a class="title" href="../../entries/Chebyshev_Polynomials.html">Chebyshev Polynomials</a></h5>
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             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
         </div>
         <span class="date">
           Nov 13
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           <h5><a class="title" href="../../entries/Perfect_Fields.html">Perfect Fields</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a> and <a href="../../authors/kreuzer">Katharina Kreuzer</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJrcmV1emVyayJdfQ==">📧</a>
 
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           Nov 06
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         <div class="item-text">
           <h5><a class="title" href="../../entries/Elimination_Of_Repeated_Factors.html">Elimination of Repeated Factors Algorithm</a></h5>
           <br>
             by
             <a href="../../authors/kreuzer">Katharina Kreuzer</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJrcmV1emVyayJdfQ==">📧</a> and <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
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         <span class="date">
           Nov 06
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       <article class="entry">
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           <h5><a class="title" href="../../entries/Executable_Randomized_Algorithms.html">Executable Randomized Algorithms</a></h5>
           <br>
             by
             <a href="../../authors/karayel">Emin Karayel</a> <a class="obfuscated" data="eyJob3N0IjpbImVtaW5rYXJheWVsIiwiZGUiXSwidXNlciI6WyJtZSJdfQ==">📧</a> and <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
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         <span class="date">
           Jun 19
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     <h3 class="head">2022</h3>
       <article class="entry">
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           <h5><a class="title" href="../../entries/PAPP_Impossibility.html">The Incompatibility of Strategy-Proofness and Representation in Party-Approval Multi-Winner Elections</a></h5>
           <br>
             by
             <a href="../../authors/delemazure">Théo Delemazure</a> <a href="https://theo.delemazure.fr/">🌐</a>, <a href="../../authors/demeulemeester">Tom Demeulemeester</a> <a href="https://www.kuleuven.be/wieiswie/en/person/00131528">🌐</a>, <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>, <a href="../../authors/israel">Jonas Israel</a> <a href="https://www.algo.tu-berlin.de/menue/people/jonas_israel/">🌐</a> and <a href="../../authors/lederer">Patrick Lederer</a> <a href="https://www.cs.cit.tum.de/en/dss/members/patrick-lederer/">🌐</a>
 
         </div>
         <span class="date">
           Nov 10
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           <h5><a class="title" href="../../entries/Hales_Jewett.html">The Hales–Jewett Theorem</a></h5>
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           Apr 24
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           <h5><a class="title" href="../../entries/Zeta_3_Irrational.html">The Irrationality of ζ(3)</a></h5>
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           <h5><a class="title" href="../../entries/List_Inversions.html">The Inversions of a List</a></h5>
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           <h5><a class="title" href="../../entries/Randomised_BSTs.html">Randomised Binary Search Trees</a></h5>
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           <h5><a class="title" href="../../entries/Pi_Transcendental.html">The Transcendence of π</a></h5>
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           <h5><a class="title" href="../../entries/Symmetric_Polynomials.html">Symmetric Polynomials</a></h5>
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           <h5><a class="title" href="../../entries/Prime_Number_Theorem.html">The Prime Number Theorem</a></h5>
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           <h5><a class="title" href="../../entries/Median_Of_Medians_Selection.html">The Median-of-Medians Selection Algorithm</a></h5>
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             <a href="../../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
 
         </div>
         <span class="date">
           May 04
         </span>
       </article>
     <h3 class="head">2015</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Prime_Harmonic_Series.html">The Divergence of the Prime Harmonic Series</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Dec 28
         </span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Liouville_Numbers.html">Liouville numbers</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Dec 28
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       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Descartes_Sign_Rule.html">Descartes&#39; Rule of Signs</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Dec 28
         </span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Triangle.html">Basic Geometric Properties of Triangles</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Dec 28
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       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Akra_Bazzi.html">The Akra-Bazzi theorem and the Master theorem</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Jul 14
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       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Landau_Symbols.html">Landau Symbols</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Jul 14
         </span>
       </article>
     <h3 class="head">2014</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Density_Compiler.html">A Verified Compiler for Probability Density Functions</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>, <a href="../../authors/hoelzl">Johannes Hölzl</a> <a href="http://home.in.tum.de/~hoelzl">🌐</a> and <a href="../../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
 
         </div>
         <span class="date">
           Oct 09
         </span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Sturm_Sequences.html">Sturm&#39;s Theorem</a></h5>
           <br>
             by
             <a href="../../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
         </div>
         <span class="date">
           Jan 11
         </span>
       </article>
         
       </div>
     </div>
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           <title>The Akra-Bazzi theorem and the Master theorem</title>
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           <pubDate>Thu, 09 Oct 2014 00:00:00 +0000</pubDate>
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   <h2>Entries</h2>
+    <h3 class="head">2024</h3>
+      <article class="entry">
+        <div class="item-text">
+          <h5><a class="title" href="../../entries/Go.html">Go Code Generation for Isabelle</a></h5>
+          <br>
+            by
+            <a href="../../authors/stuebinger">Terru Stübinger</a> <a href="https://stuebinm.eu/">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
+
+        </div>
+        <span class="date">
+          Jan 22
+        </span>
+      </article>
     <h3 class="head">2023</h3>
       <article class="entry">
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           <h5><a class="title" href="../../entries/Fixed_Length_Vector.html">Fixed-length vectors</a></h5>
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             by
             <a href="../../authors/hupel">Lars Hupel</a> <a class="obfuscated" data="eyJob3N0IjpbImh1cGVsIiwiaW5mbyJdLCJ1c2VyIjpbImxhcnMiXX0=">📧</a>
 
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     <h3 class="head">2020</h3>
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             by
             <a href="../../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
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     <h3 class="head">2019</h3>
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           <h5><a class="title" href="../../entries/CakeML_Codegen.html">A Verified Code Generator from Isabelle/HOL to CakeML</a></h5>
           <br>
             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           Jul 08
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           <h5><a class="title" href="../../entries/Higher_Order_Terms.html">An Algebra for Higher-Order Terms</a></h5>
           <br>
             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           Jan 15
         </span>
       </article>
     <h3 class="head">2018</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Generic_Deriving.html">Deriving generic class instances for datatypes</a></h5>
           <br>
             by
             <a href="../../authors/raedle">Jonas Rädle</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiam9uYXMiLCJyYWVkbGUiXX0=">📧</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
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         <span class="date">
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           <h5><a class="title" href="../../entries/CakeML.html">CakeML</a></h5>
           <br>
             by
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         </div>
         <span class="date">
           Mar 12
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       </article>
     <h3 class="head">2017</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Dict_Construction.html">Dictionary Construction</a></h5>
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             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           May 24
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           <h5><a class="title" href="../../entries/Constructor_Funs.html">Constructor Functions</a></h5>
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             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           Apr 19
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       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Lazy_Case.html">Lazifying case constants</a></h5>
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             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
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     <h3 class="head">2016</h3>
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         <div class="item-text">
           <h5><a class="title" href="../../entries/Iptables_Semantics.html">Iptables Semantics</a></h5>
           <br>
             by
             <a href="../../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
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         <span class="date">
           Sep 09
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       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/IP_Addresses.html">IP Addresses</a></h5>
           <br>
             by
             <a href="../../authors/diekmann">Cornelius Diekmann</a> <a href="http://net.in.tum.de/~diekmann">🌐</a>, <a href="../../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           Jun 28
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       </article>
       <article class="entry">
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           <h5><a class="title" href="../../entries/ROBDD.html">Algorithms for Reduced Ordered Binary Decision Diagrams</a></h5>
           <br>
             by
             <a href="../../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a>, <a href="../../authors/haslbeck">Max W. Haslbeck</a> <a href="http://cl-informatik.uibk.ac.at/users/mhaslbeck/">🌐</a>, <a href="../../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
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           Apr 27
         </span>
       </article>
     <h3 class="head">2014</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Random_Graph_Subgraph_Threshold.html">Properties of Random Graphs -- Subgraph Containment</a></h5>
           <br>
             by
             <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
 
         </div>
         <span class="date">
           Feb 13
         </span>
       </article>
         
       </div>
     </div>
   </body>
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\ No newline at end of file
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+          <guid>/entries/Go.html</guid>
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           <title>Fixed-length vectors</title>
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               <li>
                 <a href="../authors/bauereiss/">Thomas Bauereiss
                 </a>
               </li>
               <li>
                 <a href="../authors/bayer/">Jonas Bayer
                 </a>
               </li>
               <li>
                 <a href="../authors/becker/">Heiko Becker
                 </a>
               </li>
               <li>
                 <a href="../authors/beeren/">Joel Beeren
                 </a>
               </li>
               <li>
                 <a href="../authors/bella/">Giampaolo Bella
                 </a>
               </li>
               <li>
                 <a href="../authors/bengtson/">Jesper Bengtson
                 </a>
               </li>
               <li>
                 <a href="../authors/bentkamp/">Alexander Bentkamp
                 </a>
               </li>
               <li>
                 <a href="../authors/benzmueller/">Christoph Benzmüller
                 </a>
               </li>
               <li>
                 <a href="../authors/beresford/">Alastair R. Beresford
                 </a>
               </li>
               <li>
                 <a href="../authors/berghofer/">Stefan Berghofer
                 </a>
               </li>
               <li>
                 <a href="../authors/bergstroem/">Axel Bergström
                 </a>
               </li>
               <li>
                 <a href="../authors/beringer/">Lennart Beringer
                 </a>
               </li>
               <li>
                 <a href="../authors/bharadwaj/">Abhijith Bharadwaj
                 </a>
               </li>
               <li>
                 <a href="../authors/bhatt/">Bhargav Bhatt
                 </a>
               </li>
               <li>
                 <a href="../authors/biendarra/">Julian Biendarra
                 </a>
               </li>
               <li>
                 <a href="../authors/bisping/">Benjamin Bisping
                 </a>
               </li>
               <li>
                 <a href="../authors/blanchette/">Jasmin Christian Blanchette
                 </a>
               </li>
               <li>
                 <a href="../authors/blasum/">Holger Blasum
                 </a>
               </li>
               <li>
                 <a href="../authors/blumson/">Ben Blumson
                 </a>
               </li>
               <li>
                 <a href="../authors/bockenek/">Joshua Bockenek
                 </a>
               </li>
               <li>
                 <a href="../authors/boehme/">Sascha Böhme
                 </a>
               </li>
               <li>
                 <a href="../authors/bohrer/">Rose Bohrer
                 </a>
               </li>
               <li>
                 <a href="../authors/bootle/">Jonathan Bootle
                 </a>
               </li>
               <li>
                 <a href="../authors/bordg/">Anthony Bordg
                 </a>
               </li>
               <li>
                 <a href="../authors/borgstroem/">Johannes Borgström
                 </a>
               </li>
               <li>
                 <a href="../authors/bortin/">Maksym Bortin
                 </a>
               </li>
               <li>
                 <a href="../authors/bottesch/">Ralph Bottesch
                 </a>
               </li>
               <li>
                 <a href="../authors/boulanger/">Frédéric Boulanger
                 </a>
               </li>
               <li>
                 <a href="../authors/bourke/">Timothy Bourke
                 </a>
               </li>
               <li>
                 <a href="../authors/boutry/">Pierre Boutry
                 </a>
               </li>
               <li>
                 <a href="../authors/boyton/">Andrew Boyton
                 </a>
               </li>
               <li>
                 <a href="../authors/bracevac/">Oliver Bračevac
                 </a>
               </li>
               <li>
                 <a href="../authors/brandt/">Felix Brandt
                 </a>
               </li>
               <li>
                 <a href="../authors/breitner/">Joachim Breitner
                 </a>
               </li>
               <li>
                 <a href="../authors/brien/">Nicolas Robinson-O&#39;Brien
                 </a>
               </li>
               <li>
                 <a href="../authors/brinkop/">Hauke Brinkop
                 </a>
               </li>
               <li>
                 <a href="../authors/brodmann/">Paul-David Brodmann
                 </a>
               </li>
               <li>
                 <a href="../authors/brucker/">Achim D. Brucker
                 </a>
               </li>
               <li>
                 <a href="../authors/bruegger/">Lukas Brügger
                 </a>
               </li>
               <li>
                 <a href="../authors/brun/">Matthias Brun
                 </a>
               </li>
               <li>
                 <a href="../authors/brunner/">Julian Brunner
                 </a>
               </li>
               <li>
                 <a href="../authors/bulwahn/">Lukas Bulwahn
                 </a>
               </li>
               <li>
                 <a href="../authors/buss/">Sebastián Buss
                 </a>
               </li>
               <li>
                 <a href="../authors/butler/">David Butler
                 </a>
               </li>
               <li>
                 <a href="../authors/buyse/">Maxime Buyse
                 </a>
               </li>
               <li>
                 <a href="../authors/caballero/">José Manuel Rodríguez Caballero
                 </a>
               </li>
               <li>
                 <a href="../authors/calk/">Cameron Calk
                 </a>
               </li>
               <li>
                 <a href="../authors/caminati/">Marco B. Caminati
                 </a>
               </li>
               <li>
                 <a href="../authors/campo/">Alejandro del Campo
                 </a>
               </li>
               <li>
                 <a href="../authors/chapman/">Peter Chapman
                 </a>
               </li>
               <li>
                 <a href="../authors/chen/">L. Chen
                 </a>
               </li>
               <li>
                 <a href="../authors/chenj/">Jamie Chen
                 </a>
               </li>
               <li>
                 <a href="../authors/chevalier/">Loïc Chevalier
                 </a>
               </li>
               <li>
                 <a href="../authors/christfort/">Axel Christfort
                 </a>
               </li>
               <li>
                 <a href="../authors/clouston/">Ranald Clouston
                 </a>
               </li>
               <li>
                 <a href="../authors/cock/">David Cock
                 </a>
               </li>
               <li>
                 <a href="../authors/coghetto/">Roland Coghetto
                 </a>
               </li>
               <li>
                 <a href="../authors/coglio/">Alessandro Coglio
                 </a>
               </li>
               <li>
                 <a href="../authors/cohen/">Ernie Cohen
                 </a>
               </li>
               <li>
                 <a href="../authors/cordwell/">Katherine Kosaian
                 </a>
               </li>
               <li>
                 <a href="../authors/cousin/">Marie Cousin
                 </a>
               </li>
               <li>
                 <a href="../authors/cremer/">Nils Cremer
                 </a>
               </li>
               <li>
                 <a href="../authors/crighton/">Aaron Crighton
                 </a>
               </li>
               <li>
                 <a href="../authors/dalvit/">Christian Dalvit
                 </a>
               </li>
               <li>
                 <a href="../authors/danilkin/">Anton Danilkin
                 </a>
               </li>
               <li>
                 <a href="../authors/dardinier/">Thibault Dardinier
                 </a>
               </li>
               <li>
                 <a href="../authors/david/">Marco David
                 </a>
               </li>
               <li>
                 <a href="../authors/debois/">Søren Debois
                 </a>
               </li>
               <li>
                 <a href="../authors/debrat/">Henri Debrat
                 </a>
               </li>
               <li>
                 <a href="../authors/decova/">Sára Decova
                 </a>
               </li>
               <li>
                 <a href="../authors/delemazure/">Théo Delemazure
                 </a>
               </li>
               <li>
                 <a href="../authors/demeulemeester/">Tom Demeulemeester
                 </a>
               </li>
               <li>
                 <a href="../authors/derrick/">John Derrick
                 </a>
               </li>
               <li>
                 <a href="../authors/desharnais/">Martin Desharnais
                 </a>
               </li>
               <li>
                 <a href="../authors/diaz/">Javier Díaz
                 </a>
               </li>
               <li>
                 <a href="../authors/diekmann/">Cornelius Diekmann
                 </a>
               </li>
               <li>
                 <a href="../authors/dirix/">Stefan Dirix
                 </a>
               </li>
               <li>
                 <a href="../authors/dittmann/">Christoph Dittmann
                 </a>
               </li>
               <li>
                 <a href="../authors/divason/">Jose Divasón
                 </a>
               </li>
               <li>
                 <a href="../authors/doczkal/">Christian Doczkal
                 </a>
               </li>
               <li>
                 <a href="../authors/dongol/">Brijesh Dongol
                 </a>
               </li>
               <li>
                 <a href="../authors/doty/">Matthew Doty
                 </a>
               </li>
               <li>
                 <a href="../authors/dubut/">Jérémy Dubut
                 </a>
               </li>
               <li>
                 <a href="../authors/dunaev/">Georgy Dunaev
                 </a>
               </li>
               <li>
                 <a href="../authors/dyckhoff/">Roy Dyckhoff
                 </a>
               </li>
               <li>
                 <a href="../authors/eberl/">Manuel Eberl
                 </a>
               </li>
               <li>
                 <a href="../authors/echenim/">Mnacho Echenim
                 </a>
               </li>
               <li>
                 <a href="../authors/edmonds/">Chelsea Edmonds
                 </a>
               </li>
               <li>
                 <a href="../authors/engelhardt/">Kai Engelhardt
                 </a>
               </li>
               <li>
                 <a href="../authors/eriksson/">Lars-Henrik Eriksson
                 </a>
               </li>
               <li>
                 <a href="../authors/esparza/">Javier Esparza
                 </a>
               </li>
               <li>
                 <a href="../authors/essmann/">Robin Eßmann
                 </a>
               </li>
               <li>
                 <a href="../authors/felgenhauer/">Bertram Felgenhauer
                 </a>
               </li>
               <li>
                 <a href="../authors/feliachi/">Abderrahmane Feliachi
                 </a>
               </li>
               <li>
                 <a href="../authors/fell/">Julian Fell
                 </a>
               </li>
               <li>
                 <a href="../authors/fernandez/">Matthew Fernandez
                 </a>
               </li>
               <li>
                 <a href="../authors/fiedler/">Ben Fiedler
                 </a>
               </li>
               <li>
                 <a href="../authors/fleuriot/">Jacques D. Fleuriot
                 </a>
               </li>
               <li>
                 <a href="../authors/fleury/">Mathias Fleury
                 </a>
               </li>
               <li>
                 <a href="../authors/foster/">Michael Foster
                 </a>
               </li>
               <li>
                 <a href="../authors/fosterj/">J. Nathan Foster
                 </a>
               </li>
               <li>
                 <a href="../authors/fosters/">Simon Foster
                 </a>
               </li>
               <li>
                 <a href="../authors/fouillard/">Valentin Fouillard
                 </a>
               </li>
               <li>
                 <a href="../authors/friedrich/">Stefan Friedrich
                 </a>
               </li>
               <li>
                 <a href="../authors/from/">Asta Halkjær From
                 </a>
               </li>
               <li>
                 <a href="../authors/fuenmayor/">David Fuenmayor
                 </a>
               </li>
               <li>
                 <a href="../authors/furusawa/">Hitoshi Furusawa
                 </a>
               </li>
               <li>
                 <a href="../authors/gammie/">Peter Gammie
                 </a>
               </li>
               <li>
                 <a href="../authors/gao/">Xin Gao
                 </a>
               </li>
               <li>
                 <a href="../authors/garvia/">Azucena Garvia
                 </a>
               </li>
               <li>
                 <a href="../authors/gaudel/">Marie-Claude Gaudel
                 </a>
               </li>
               <li>
                 <a href="../authors/gay/">Richard Gay
                 </a>
               </li>
               <li>
                 <a href="../authors/georgescu/">George Georgescu
                 </a>
               </li>
               <li>
                 <a href="../authors/gheri/">Lorenzo Gheri
                 </a>
               </li>
               <li>
                 <a href="../authors/ghourabi/">Fadoua Ghourabi
                 </a>
               </li>
               <li>
                 <a href="../authors/gioiosa/">Gianpaolo Gioiosa
                 </a>
               </li>
               <li>
                 <a href="../authors/glabbeek/">Rob van Glabbeek
                 </a>
               </li>
               <li>
                 <a href="../authors/gomes/">Victor B. F. Gomes
                 </a>
               </li>
               <li>
                 <a href="../authors/gonzalez/">Edgar Gonzàlez
                 </a>
               </li>
               <li>
                 <a href="../authors/gore/">Rajeev Gore
                 </a>
               </li>
               <li>
                 <a href="../authors/gouezel/">Sebastien Gouezel
                 </a>
               </li>
               <li>
                 <a href="../authors/grechuk/">Bogdan Grechuk
                 </a>
               </li>
               <li>
                 <a href="../authors/grewe/">Sylvia Grewe
                 </a>
               </li>
               <li>
                 <a href="../authors/griebel/">Simon Griebel
                 </a>
               </li>
               <li>
                 <a href="../authors/grov/">Gudmund Grov
                 </a>
               </li>
               <li>
                 <a href="../authors/guerraoui/">Rachid Guerraoui
                 </a>
               </li>
               <li>
                 <a href="../authors/guiol/">Hervé Guiol
                 </a>
               </li>
               <li>
                 <a href="../authors/gunther/">Emmanuel Gunther
                 </a>
               </li>
               <li>
                 <a href="../authors/gutkovas/">Ramunas Gutkovas
                 </a>
               </li>
               <li>
                 <a href="../authors/guttmann/">Walter Guttmann
                 </a>
               </li>
               <li>
                 <a href="../authors/guzman/">Laura P. Gamboa Guzman
                 </a>
               </li>
               <li>
                 <a href="../authors/haftmann/">Florian Haftmann
                 </a>
               </li>
               <li>
                 <a href="../authors/haslbeck/">Max W. Haslbeck
                 </a>
               </li>
               <li>
                 <a href="../authors/haslbeckm/">Maximilian P. L. Haslbeck
                 </a>
               </li>
               <li>
                 <a href="../authors/havle/">Oto Havle
                 </a>
               </li>
               <li>
                 <a href="../authors/hayes/">Ian J. Hayes
                 </a>
               </li>
               <li>
                 <a href="../authors/he/">Yijun He
                 </a>
               </li>
               <li>
                 <a href="../authors/heimes/">Lukas Heimes
                 </a>
               </li>
               <li>
                 <a href="../authors/helke/">Steffen Helke
                 </a>
               </li>
               <li>
                 <a href="../authors/hellauer/">Fabian Hellauer
                 </a>
               </li>
               <li>
                 <a href="../authors/heller/">Armin Heller
                 </a>
               </li>
               <li>
                 <a href="../authors/henrio/">Ludovic Henrio
                 </a>
               </li>
               <li>
                 <a href="../authors/herzberg/">Michael Herzberg
                 </a>
               </li>
               <li>
                 <a href="../authors/hess/">Andreas V. Hess
                 </a>
               </li>
               <li>
                 <a href="../authors/hetzl/">Stefan Hetzl
                 </a>
               </li>
               <li>
                 <a href="../authors/hibon/">Quentin Hibon
                 </a>
               </li>
               <li>
                 <a href="../authors/higgins/">Edward Higgins
                 </a>
               </li>
               <li>
                 <a href="../authors/hirata/">Michikazu Hirata
                 </a>
               </li>
               <li>
                 <a href="../authors/hoefner/">Peter Höfner
                 </a>
               </li>
               <li>
                 <a href="../authors/hoelzl/">Johannes Hölzl
                 </a>
               </li>
               <li>
                 <a href="../authors/hofmann/">Martin Hofmann
                 </a>
               </li>
               <li>
                 <a href="../authors/hofmeier/">Paul Hofmeier
                 </a>
               </li>
               <li>
                 <a href="../authors/holub/">Štěpán Holub
                 </a>
               </li>
               <li>
                 <a href="../authors/hosking/">Tony Hosking
                 </a>
               </li>
               <li>
                 <a href="../authors/hou/">Zhe Hou
                 </a>
               </li>
               <li>
                 <a href="../authors/hu/">Shuwei Hu
                 </a>
               </li>
               <li>
                 <a href="../authors/huffman/">Brian Huffman
                 </a>
               </li>
               <li>
                 <a href="../authors/hupel/">Lars Hupel
                 </a>
               </li>
               <li>
                 <a href="../authors/ijbema/">Mark Ijbema
                 </a>
               </li>
               <li>
                 <a href="../authors/immler/">Fabian Immler
                 </a>
               </li>
               <li>
                 <a href="../authors/israel/">Jonas Israel
                 </a>
               </li>
               <li>
                 <a href="../authors/ito/">Yosuke Ito
                 </a>
               </li>
               <li>
                 <a href="../authors/iwama/">Fumiya Iwama
                 </a>
               </li>
               <li>
                 <a href="../authors/jacobsen/">Frederik Krogsdal Jacobsen
                 </a>
               </li>
               <li>
                 <a href="../authors/jaskelioff/">Mauro Jaskelioff
                 </a>
               </li>
               <li>
                 <a href="../authors/jaskolka/">Jason Jaskolka
                 </a>
               </li>
               <li>
                 <a href="../authors/jensen/">Alexander Birch Jensen
                 </a>
               </li>
               <li>
                 <a href="../authors/jiang/">Nan Jiang
                 </a>
               </li>
               <li>
                 <a href="../authors/jiangd/">Dongchen Jiang
                 </a>
               </li>
               <li>
                 <a href="../authors/joosten/">Sebastiaan J. C. Joosten
                 </a>
               </li>
               <li>
                 <a href="../authors/jungnickel/">Tim Jungnickel
                 </a>
               </li>
               <li>
                 <a href="../authors/kadzioka/">Maya Kądziołka
                 </a>
               </li>
               <li>
                 <a href="../authors/kaliszyk/">Cezary Kaliszyk
                 </a>
               </li>
               <li>
                 <a href="../authors/kammueller/">Florian Kammüller
                 </a>
               </li>
               <li>
                 <a href="../authors/kappelmann/">Kevin Kappelmann
                 </a>
               </li>
               <li>
                 <a href="../authors/karayel/">Emin Karayel
                 </a>
               </li>
               <li>
                 <a href="../authors/kastermans/">Bart Kastermans
                 </a>
               </li>
               <li>
                 <a href="../authors/katovsky/">Alexander Katovsky
                 </a>
               </li>
               <li>
                 <a href="../authors/kaufmann/">Daniela Kaufmann
                 </a>
               </li>
               <li>
                 <a href="../authors/keefe/">Greg O&#39;Keefe
                 </a>
               </li>
               <li>
                 <a href="../authors/keinholz/">Jonas Keinholz
                 </a>
               </li>
               <li>
                 <a href="../authors/kerber/">Manfred Kerber
                 </a>
               </li>
               <li>
                 <a href="../authors/keskin/">Ata Keskin
                 </a>
               </li>
               <li>
                 <a href="../authors/ketland/">Jeffrey Ketland
                 </a>
               </li>
               <li>
                 <a href="../authors/kim/">Sunpill Kim
                 </a>
               </li>
               <li>
                 <a href="../authors/kirchner/">Daniel Kirchner
                 </a>
               </li>
               <li>
                 <a href="../authors/klein/">Gerwin Klein
                 </a>
               </li>
               <li>
                 <a href="../authors/klenze/">Tobias Klenze
                 </a>
               </li>
               <li>
                 <a href="../authors/kleppmann/">Martin Kleppmann
                 </a>
               </li>
               <li>
                 <a href="../authors/kobayashi/">Hidetsune Kobayashi
                 </a>
               </li>
               <li>
                 <a href="../authors/koerner/">Stefan Körner
                 </a>
               </li>
               <li>
                 <a href="../authors/kolanski/">Rafal Kolanski
                 </a>
               </li>
               <li>
                 <a href="../authors/koller/">Lukas Koller
                 </a>
               </li>
               <li>
                 <a href="../authors/krauss/">Alexander Krauss
                 </a>
               </li>
               <li>
                 <a href="../authors/kreuzer/">Katharina Kreuzer
                 </a>
               </li>
               <li>
                 <a href="../authors/kuncak/">Viktor Kuncak
                 </a>
               </li>
               <li>
                 <a href="../authors/kuncar/">Ondřej Kunčar
                 </a>
               </li>
               <li>
                 <a href="../authors/kurz/">Friedrich Kurz
                 </a>
               </li>
               <li>
                 <a href="../authors/lachnitt/">Hanna Lachnitt
                 </a>
               </li>
               <li>
                 <a href="../authors/lallemand/">Joseph Lallemand
                 </a>
               </li>
               <li>
                 <a href="../authors/lameris/">Cárolos Laméris
                 </a>
               </li>
               <li>
                 <a href="../authors/lammich/">Peter Lammich
                 </a>
               </li>
               <li>
                 <a href="../authors/lange/">Christoph Lange
                 </a>
               </li>
               <li>
                 <a href="../authors/langenstein/">Bruno Langenstein
                 </a>
               </li>
               <li>
                 <a href="../authors/lattuada/">Andrea Lattuada
                 </a>
               </li>
               <li>
                 <a href="../authors/lauermann/">Nils Lauermann
                 </a>
               </li>
               <li>
                 <a href="../authors/laursen/">Christian Pardillo-Laursen
                 </a>
               </li>
               <li>
                 <a href="../authors/lederer/">Patrick Lederer
                 </a>
               </li>
               <li>
                 <a href="../authors/lee/">Holden Lee
                 </a>
               </li>
               <li>
                 <a href="../authors/leek/">Kevin Lee
                 </a>
               </li>
               <li>
                 <a href="../authors/leustean/">Laurentiu Leustean
                 </a>
               </li>
               <li>
                 <a href="../authors/lewis/">Corey Lewis
                 </a>
               </li>
               <li>
                 <a href="../authors/li/">Wenda Li
                 </a>
               </li>
               <li>
                 <a href="../authors/lim/">Japheth Lim
                 </a>
               </li>
               <li>
                 <a href="../authors/lindenberg/">Christina Lindenberg
                 </a>
               </li>
               <li>
                 <a href="../authors/linker/">Sven Linker
                 </a>
               </li>
               <li>
                 <a href="../authors/liu/">Junyi Liu
                 </a>
               </li>
               <li>
                 <a href="../authors/liut/">Tao Liu
                 </a>
               </li>
               <li>
                 <a href="../authors/liuy/">Yang Liu
                 </a>
               </li>
               <li>
                 <a href="../authors/liy/">Yangjia Li
                 </a>
               </li>
               <li>
                 <a href="../authors/lochbihler/">Andreas Lochbihler
                 </a>
               </li>
               <li>
                 <a href="../authors/lochmann/">Alexander Lochmann
                 </a>
               </li>
               <li>
                 <a href="../authors/lohner/">Denis Lohner
                 </a>
               </li>
               <li>
                 <a href="../authors/loibl/">Matthias Loibl
                 </a>
               </li>
               <li>
                 <a href="../authors/londono/">Alejandro Gómez-Londoño
                 </a>
               </li>
               <li>
                 <a href="../authors/losa/">Giuliano Losa
                 </a>
               </li>
               <li>
                 <a href="../authors/lutz/">Bianca Lutz
                 </a>
               </li>
               <li>
                 <a href="../authors/lux/">Alexander Lux
                 </a>
               </li>
               <li>
                 <a href="../authors/madarasz/">Judit Madarasz
                 </a>
               </li>
               <li>
                 <a href="../authors/makarios/">T. J. M. Makarios
                 </a>
               </li>
               <li>
                 <a href="../authors/maletzky/">Alexander Maletzky
                 </a>
               </li>
               <li>
                 <a href="../authors/mansky/">Susannah Mansky
                 </a>
               </li>
               <li>
                 <a href="../authors/mantel/">Heiko Mantel
                 </a>
               </li>
               <li>
                 <a href="../authors/margetson/">James Margetson
                 </a>
               </li>
               <li>
                 <a href="../authors/maric/">Ognjen Marić
                 </a>
               </li>
               <li>
                 <a href="../authors/maricf/">Filip Marić
                 </a>
               </li>
               <li>
                 <a href="../authors/marmsoler/">Diego Marmsoler
                 </a>
               </li>
               <li>
                 <a href="../authors/massacrier/">Tanguy Massacrier
                 </a>
               </li>
               <li>
                 <a href="../authors/matache/">Cristina Matache
                 </a>
               </li>
               <li>
                 <a href="../authors/mateo/">Adrián Doña Mateo
                 </a>
               </li>
               <li>
                 <a href="../authors/matichuk/">Daniel Matichuk
                 </a>
               </li>
               <li>
                 <a href="../authors/matiyasevich/">Yuri Matiyasevich
                 </a>
               </li>
               <li>
                 <a href="../authors/maximova/">Alexandra Maximova
                 </a>
               </li>
               <li>
                 <a href="../authors/meis/">Rene Meis
                 </a>
               </li>
               <li>
                 <a href="../authors/merz/">Stephan Merz
                 </a>
               </li>
               <li>
                 <a href="../authors/messner/">Florian Messner
                 </a>
               </li>
               <li>
                 <a href="../authors/mhalla/">Mehdi Mhalla
                 </a>
               </li>
               <li>
                 <a href="../authors/michaelis/">Julius Michaelis
                 </a>
               </li>
               <li>
                 <a href="../authors/milehins/">Mihails Milehins
                 </a>
               </li>
               <li>
                 <a href="../authors/minamide/">Yasuhiko Minamide
                 </a>
               </li>
               <li>
                 <a href="../authors/mitchell/">Neil Mitchell
                 </a>
               </li>
               <li>
                 <a href="../authors/mitsch/">Stefan Mitsch
                 </a>
               </li>
               <li>
                 <a href="../authors/moedersheim/">Sebastian Mödersheim
                 </a>
               </li>
               <li>
                 <a href="../authors/moeller/">Bernhard Möller
                 </a>
               </li>
               <li>
                 <a href="../authors/montanari/">Luisa Montanari
                 </a>
               </li>
               <li>
                 <a href="../authors/mori/">Coraline Mori
                 </a>
               </li>
               <li>
                 <a href="../authors/muendler/">Niels Mündler
                 </a>
               </li>
               <li>
                 <a href="../authors/mulligan/">Dominic P. Mulligan
                 </a>
               </li>
               <li>
                 <a href="../authors/munive/">Jonathan Julian Huerta y Munive
                 </a>
               </li>
               <li>
                 <a href="../authors/murao/">H. Murao
                 </a>
               </li>
               <li>
                 <a href="../authors/murray/">Toby Murray
                 </a>
               </li>
               <li>
                 <a href="../authors/myreen/">Magnus O. Myreen
                 </a>
               </li>
               <li>
                 <a href="../authors/nagashima/">Yutaka Nagashima
                 </a>
               </li>
               <li>
                 <a href="../authors/nagele/">Julian Nagele
                 </a>
               </li>
               <li>
                 <a href="../authors/naraschewski/">Wolfgang Naraschewski
                 </a>
               </li>
               <li>
                 <a href="../authors/nedzelsky/">Michael Nedzelsky
                 </a>
               </li>
               <li>
                 <a href="../authors/nemeti/">István Németi
                 </a>
               </li>
               <li>
                 <a href="../authors/nemouchi/">Yakoub Nemouchi
                 </a>
               </li>
               <li>
                 <a href="../authors/nestmann/">Uwe Nestmann
                 </a>
               </li>
               <li>
                 <a href="../authors/neumann/">René Neumann
                 </a>
               </li>
               <li>
                 <a href="../authors/nielsen/">Finn Nielsen
                 </a>
               </li>
               <li>
                 <a href="../authors/nikiforov/">Denis Nikiforov
                 </a>
               </li>
               <li>
                 <a href="../authors/nipkow/">Tobias Nipkow
                 </a>
               </li>
               <li>
                 <a href="../authors/nishihara/">Toshiaki Nishihara
                 </a>
               </li>
               <li>
                 <a href="../authors/noce/">Pasquale Noce
                 </a>
               </li>
               <li>
                 <a href="../authors/nordhoff/">Benedikt Nordhoff
                 </a>
               </li>
               <li>
                 <a href="../authors/noschinski/">Lars Noschinski
                 </a>
               </li>
               <li>
                 <a href="../authors/obua/">Steven Obua
                 </a>
               </li>
               <li>
                 <a href="../authors/ogawa/">Mizuhito Ogawa
                 </a>
               </li>
               <li>
                 <a href="../authors/oldenburg/">Lennart Oldenburg
                 </a>
               </li>
               <li>
                 <a href="../authors/olm/">Markus Müller-Olm
                 </a>
               </li>
               <li>
                 <a href="../authors/oosterhuis/">Roelof Oosterhuis
                 </a>
               </li>
               <li>
                 <a href="../authors/oostrom/">Vincent van Oostrom
                 </a>
               </li>
               <li>
                 <a href="../authors/ortner/">Veronika Ortner
                 </a>
               </li>
               <li>
                 <a href="../authors/overbeek/">Roy Overbeek
                 </a>
               </li>
               <li>
                 <a href="../authors/pagano/">Miguel Pagano
                 </a>
               </li>
               <li>
                 <a href="../authors/pal/">Abhik Pal
                 </a>
               </li>
               <li>
                 <a href="../authors/paleo/">Bruno Woltzenlogel Paleo
                 </a>
               </li>
               <li>
                 <a href="../authors/palmer/">Jake Palmer
                 </a>
               </li>
               <li>
                 <a href="../authors/park/">Seung Hoon Park
                 </a>
               </li>
               <li>
                 <a href="../authors/parkinson/">Matthew Parkinson
                 </a>
               </li>
               <li>
                 <a href="../authors/parrow/">Joachim Parrow
                 </a>
               </li>
               <li>
                 <a href="../authors/parsert/">Julian Parsert
                 </a>
               </li>
               <li>
                 <a href="../authors/paulson/">Lawrence C. Paulson
                 </a>
               </li>
               <li>
                 <a href="../authors/peltier/">Nicolas Peltier
                 </a>
               </li>
               <li>
                 <a href="../authors/peters/">Kirstin Peters
                 </a>
               </li>
               <li>
                 <a href="../authors/petrovic/">Danijela Petrovic
                 </a>
               </li>
               <li>
                 <a href="../authors/pierzchalski/">Edward Pierzchalski
                 </a>
               </li>
               <li>
                 <a href="../authors/platzer/">André Platzer
                 </a>
               </li>
               <li>
                 <a href="../authors/pohjola/">Johannes Åman Pohjola
                 </a>
               </li>
               <li>
                 <a href="../authors/pollak/">Florian Pollak
                 </a>
               </li>
               <li>
                 <a href="../authors/popescu/">Andrei Popescu
                 </a>
               </li>
               <li>
                 <a href="../authors/porter/">Benjamin Porter
                 </a>
               </li>
               <li>
                 <a href="../authors/prathamesh/">T.V.H. Prathamesh
                 </a>
               </li>
               <li>
                 <a href="../authors/preoteasa/">Viorel Preoteasa
                 </a>
               </li>
               <li>
                 <a href="../authors/pusch/">Cornelia Pusch
                 </a>
               </li>
               <li>
                 <a href="../authors/qiu/">Qi Qiu
                 </a>
               </li>
               <li>
                 <a href="../authors/rabe/">Markus N. Rabe
                 </a>
               </li>
               <li>
                 <a href="../authors/rabing/">Mathias Schack Rabing
                 </a>
               </li>
               <li>
                 <a href="../authors/raedle/">Jonas Rädle
                 </a>
               </li>
               <li>
                 <a href="../authors/raska/">Martin Raška
                 </a>
               </li>
               <li>
                 <a href="../authors/raszyk/">Martin Raszyk
                 </a>
               </li>
               <li>
                 <a href="../authors/rau/">Martin Rau
                 </a>
               </li>
               <li>
                 <a href="../authors/rauch/">Nicole Rauch
                 </a>
               </li>
               <li>
                 <a href="../authors/raumer/">Jakob von Raumer
                 </a>
               </li>
               <li>
                 <a href="../authors/ravindran/">Binoy Ravindran
                 </a>
               </li>
               <li>
                 <a href="../authors/rawson/">Michael Rawson
                 </a>
               </li>
               <li>
                 <a href="../authors/raya/">Rodrigo Raya
                 </a>
               </li>
               <li>
                 <a href="../authors/regensburger/">Franz Regensburger
                 </a>
               </li>
               <li>
                 <a href="../authors/reiche/">Sebastian Reiche
                 </a>
               </li>
               <li>
                 <a href="../authors/reiter/">Markus Reiter
                 </a>
               </li>
               <li>
                 <a href="../authors/reynaud/">Alban Reynaud
                 </a>
               </li>
               <li>
                 <a href="../authors/ribeiro/">Pedro Ribeiro
                 </a>
               </li>
               <li>
                 <a href="../authors/richter/">Stefan Richter
                 </a>
               </li>
               <li>
                 <a href="../authors/rickmann/">Christina Rickmann
                 </a>
               </li>
               <li>
                 <a href="../authors/ridge/">Tom Ridge
                 </a>
               </li>
               <li>
                 <a href="../authors/rizaldi/">Albert Rizaldi
                 </a>
               </li>
               <li>
                 <a href="../authors/rizkallah/">Christine Rizkallah
                 </a>
               </li>
               <li>
                 <a href="../authors/robillard/">Simon Robillard
                 </a>
               </li>
               <li>
                 <a href="../authors/roessle/">Ian Roessle
                 </a>
               </li>
               <li>
                 <a href="../authors/romanos/">Ralph Romanos
                 </a>
               </li>
               <li>
                 <a href="../authors/rosskopf/">Simon Roßkopf
                 </a>
               </li>
               <li>
                 <a href="../authors/rowat/">Colin Rowat
                 </a>
               </li>
               <li>
                 <a href="../authors/sabouret/">Nicolas Sabouret
                 </a>
               </li>
               <li>
                 <a href="../authors/sachtleben/">Robert Sachtleben
                 </a>
               </li>
               <li>
                 <a href="../authors/saile/">Christian Saile
                 </a>
               </li>
               <li>
                 <a href="../authors/sanan/">David Sanan
                 </a>
               </li>
               <li>
                 <a href="../authors/sato/">Tetsuya Sato
                 </a>
               </li>
               <li>
                 <a href="../authors/sauer/">Jens Sauer
                 </a>
               </li>
               <li>
                 <a href="../authors/schaeffeler/">Maximilian Schäffeler
                 </a>
               </li>
               <li>
                 <a href="../authors/scharager/">Matias Scharager
                 </a>
               </li>
               <li>
                 <a href="../authors/schimpf/">Alexander Schimpf
                 </a>
               </li>
               <li>
                 <a href="../authors/schirmer/">Norbert Schirmer
                 </a>
               </li>
               <li>
                 <a href="../authors/schleicher/">Dierk Schleicher
                 </a>
               </li>
               <li>
                 <a href="../authors/schlichtkrull/">Anders Schlichtkrull
                 </a>
               </li>
               <li>
                 <a href="../authors/schmaltz/">Julien Schmaltz
                 </a>
               </li>
               <li>
                 <a href="../authors/schmidinger/">Lukas Schmidinger
                 </a>
               </li>
               <li>
                 <a href="../authors/schmoetten/">Richard Schmoetten
                 </a>
               </li>
               <li>
                 <a href="../authors/schneider/">Joshua Schneider
                 </a>
               </li>
               <li>
                 <a href="../authors/schoepe/">Daniel Schoepe
                 </a>
               </li>
               <li>
                 <a href="../authors/schoepf/">Jonas Schöpf
                 </a>
               </li>
               <li>
                 <a href="../authors/schou/">Morten Konggaard Schou
                 </a>
               </li>
               <li>
                 <a href="../authors/schulz/">Jakob Schulz
                 </a>
               </li>
               <li>
                 <a href="../authors/scott/">Dana Scott
                 </a>
               </li>
               <li>
                 <a href="../authors/sefidgar/">S. Reza Sefidgar
                 </a>
               </li>
               <li>
                 <a href="../authors/seidl/">Benedikt Seidl
                 </a>
               </li>
               <li>
                 <a href="../authors/seidler/">Henning Seidler
                 </a>
               </li>
               <li>
                 <a href="../authors/sewell/">Thomas Sewell
                 </a>
               </li>
               <li>
                 <a href="../authors/sickert/">Salomon Sickert
                 </a>
               </li>
               <li>
                 <a href="../authors/siek/">Jeremy Siek
                 </a>
               </li>
               <li>
                 <a href="../authors/simic/">Danijela Simić
                 </a>
               </li>
               <li>
                 <a href="../authors/sison/">Robert Sison
                 </a>
               </li>
               <li>
                 <a href="../authors/smaus/">Jan-Georg Smaus
                 </a>
               </li>
               <li>
                 <a href="../authors/smola/">Filip Smola
                 </a>
               </li>
               <li>
                 <a href="../authors/snelting/">Gregor Snelting
                 </a>
               </li>
               <li>
                 <a href="../authors/somaini/">Ivano Somaini
                 </a>
               </li>
               <li>
                 <a href="../authors/somogyi/">Dániel Somogyi
                 </a>
               </li>
               <li>
                 <a href="../authors/spasic/">Mirko Spasić
                 </a>
               </li>
               <li>
                 <a href="../authors/spichkova/">Maria Spichkova
                 </a>
               </li>
               <li>
                 <a href="../authors/spitz/">Maximilian Spitz
                 </a>
               </li>
               <li>
                 <a href="../authors/sprenger/">Christoph Sprenger
                 </a>
               </li>
               <li>
                 <a href="../authors/srba/">Jiří Srba
                 </a>
               </li>
               <li>
                 <a href="../authors/staats/">Charles Staats
                 </a>
               </li>
               <li>
                 <a href="../authors/stannett/">Mike Stannett
                 </a>
               </li>
               <li>
                 <a href="../authors/stark/">Eugene W. Stark
                 </a>
               </li>
               <li>
                 <a href="../authors/starosta/">Štěpán Starosta
                 </a>
               </li>
               <li>
                 <a href="../authors/steen/">Alexander Steen
                 </a>
               </li>
               <li>
                 <a href="../authors/steinberg/">Matías Steinberg
                 </a>
               </li>
               <li>
                 <a href="../authors/stell/">Amy Stell
                 </a>
               </li>
               <li>
                 <a href="../authors/stephan/">Werner Stephan
                 </a>
               </li>
               <li>
                 <a href="../authors/sternagel/">Christian Sternagel
                 </a>
               </li>
               <li>
                 <a href="../authors/sternagelt/">Thomas Sternagel
                 </a>
               </li>
               <li>
                 <a href="../authors/stevens/">Lukas Stevens
                 </a>
               </li>
               <li>
                 <a href="../authors/stock/">Benedikt Stock
                 </a>
               </li>
               <li>
                 <a href="../authors/stoeckl/">Bernhard Stöckl
                 </a>
               </li>
               <li>
                 <a href="../authors/stricker/">Christian Stricker
                 </a>
               </li>
               <li>
                 <a href="../authors/strnisa/">Rok Strniša
                 </a>
               </li>
               <li>
                 <a href="../authors/struth/">Georg Struth
                 </a>
               </li>
               <li>
                 <a href="../authors/stueber/">Anke Stüber
                 </a>
               </li>
               <li>
+                <a href="../authors/stuebinger/">Terru Stübinger
+                </a>
+              </li>
+              <li>
                 <a href="../authors/stuewe/">Daniel Stüwe
                 </a>
               </li>
               <li>
                 <a href="../authors/sudbrock/">Henning Sudbrock
                 </a>
               </li>
               <li>
                 <a href="../authors/sudhof/">Henry Sudhof
                 </a>
               </li>
               <li>
                 <a href="../authors/sulejmani/">Ujkan Sulejmani
                 </a>
               </li>
               <li>
                 <a href="../authors/sutcliffe/">Geoff Sutcliffe
                 </a>
               </li>
               <li>
                 <a href="../authors/sylvestre/">Jeremy Sylvestre
                 </a>
               </li>
               <li>
                 <a href="../authors/szekely/">Gergely Szekely
                 </a>
               </li>
               <li>
                 <a href="../authors/taha/">Safouan Taha
                 </a>
               </li>
               <li>
                 <a href="../authors/tan/">Yong Kiam Tan
                 </a>
               </li>
               <li>
                 <a href="../authors/tanaka/">Miki Tanaka
                 </a>
               </li>
               <li>
                 <a href="../authors/tasch/">Markus Tasch
                 </a>
               </li>
               <li>
                 <a href="../authors/taylor/">Ramsay G. Taylor
                 </a>
               </li>
               <li>
                 <a href="../authors/terraf/">Pedro Sánchez Terraf
                 </a>
               </li>
               <li>
                 <a href="../authors/thiemann/">René Thiemann
                 </a>
               </li>
               <li>
                 <a href="../authors/thommes/">Joseph Thommes
                 </a>
               </li>
               <li>
                 <a href="../authors/thomson/">Fox Thomson
                 </a>
               </li>
               <li>
                 <a href="../authors/tiu/">Alwen Tiu
                 </a>
               </li>
               <li>
                 <a href="../authors/toth/">Balazs Toth
                 </a>
               </li>
               <li>
                 <a href="../authors/tourret/">Sophie Tourret
                 </a>
               </li>
               <li>
                 <a href="../authors/trachtenherz/">David Trachtenherz
                 </a>
               </li>
               <li>
                 <a href="../authors/traut/">Christoph Traut
                 </a>
               </li>
               <li>
                 <a href="../authors/traytel/">Dmitriy Traytel
                 </a>
               </li>
               <li>
                 <a href="../authors/trelat/">Vincent Trélat
                 </a>
               </li>
               <li>
                 <a href="../authors/tuong/">Frédéric Tuong
                 </a>
               </li>
               <li>
                 <a href="../authors/tuongj/">Joseph Tuong
                 </a>
               </li>
               <li>
                 <a href="../authors/tverdyshev/">Sergey Tverdyshev
                 </a>
               </li>
               <li>
                 <a href="../authors/ullrich/">Sebastian Ullrich
                 </a>
               </li>
               <li>
                 <a href="../authors/unruh/">Dominique Unruh
                 </a>
               </li>
               <li>
                 <a href="../authors/urban/">Christian Urban
                 </a>
               </li>
               <li>
                 <a href="../authors/van/">Hai Nguyen Van
                 </a>
               </li>
               <li>
                 <a href="../authors/velykis/">Andrius Velykis
                 </a>
               </li>
               <li>
                 <a href="../authors/verbeek/">Freek Verbeek
                 </a>
               </li>
               <li>
                 <a href="../authors/villadsen/">Jørgen Villadsen
                 </a>
               </li>
               <li>
                 <a href="../authors/voisin/">Frederic Voisin
                 </a>
               </li>
               <li>
                 <a href="../authors/vytiniotis/">Dimitrios Vytiniotis
                 </a>
               </li>
               <li>
                 <a href="../authors/wagner/">Max Wagner
                 </a>
               </li>
               <li>
                 <a href="../authors/waldmann/">Uwe Waldmann
                 </a>
               </li>
               <li>
                 <a href="../authors/wand/">Daniel Wand
                 </a>
               </li>
               <li>
                 <a href="../authors/wang/">Shuling Wang
                 </a>
               </li>
               <li>
                 <a href="../authors/wassell/">Mark Wassell
                 </a>
               </li>
               <li>
                 <a href="../authors/wasserrab/">Daniel Wasserrab
                 </a>
               </li>
               <li>
                 <a href="../authors/watt/">Conrad Watt
                 </a>
               </li>
               <li>
                 <a href="../authors/weber/">Tjark Weber
                 </a>
               </li>
               <li>
                 <a href="../authors/weerwag/">Timmy Weerwag
                 </a>
               </li>
               <li>
                 <a href="../authors/weidner/">Arno Wilhelm-Weidner
                 </a>
               </li>
               <li>
                 <a href="../authors/wenninger/">Elias Wenninger
                 </a>
               </li>
               <li>
                 <a href="../authors/wenzel/">Makarius Wenzel
                 </a>
               </li>
               <li>
                 <a href="../authors/whitley/">A Whitley
                 </a>
               </li>
               <li>
                 <a href="../authors/wickerson/">John Wickerson
                 </a>
               </li>
               <li>
                 <a href="../authors/willenbrink/">Sebastian Willenbrink
                 </a>
               </li>
               <li>
                 <a href="../authors/wimmer/">Simon Wimmer
                 </a>
               </li>
               <li>
                 <a href="../authors/wirt/">Kai Wirt
                 </a>
               </li>
               <li>
                 <a href="../authors/wolff/">Burkhart Wolff
                 </a>
               </li>
               <li>
                 <a href="../authors/wu/">Chunhan Wu
                 </a>
               </li>
               <li>
                 <a href="../authors/xu/">Jian Xu
                 </a>
               </li>
               <li>
                 <a href="../authors/yamada/">Akihisa Yamada
                 </a>
               </li>
               <li>
+                <a href="../authors/yang/">Jiong Yang
+                </a>
+              </li>
+              <li>
                 <a href="../authors/ye/">Lina Ye
                 </a>
               </li>
               <li>
                 <a href="../authors/yez/">Zhengkun Ye
                 </a>
               </li>
               <li>
                 <a href="../authors/ying/">Shenggang Ying
                 </a>
               </li>
               <li>
                 <a href="../authors/yingm/">Mingsheng Ying
                 </a>
               </li>
               <li>
                 <a href="../authors/yu/">Lei Yu
                 </a>
               </li>
               <li>
                 <a href="../authors/zankl/">Harald Zankl
                 </a>
               </li>
               <li>
                 <a href="../authors/zee/">Karen Zee
                 </a>
               </li>
               <li>
                 <a href="../authors/zeller/">Peter Zeller
                 </a>
               </li>
               <li>
                 <a href="../authors/zeyda/">Frank Zeyda
                 </a>
               </li>
               <li>
                 <a href="../authors/zhan/">Bohua Zhan
                 </a>
               </li>
               <li>
                 <a href="../authors/zhang/">Yu Zhang
                 </a>
               </li>
               <li>
                 <a href="../authors/zhangx/">Xingyuan Zhang
                 </a>
               </li>
               <li>
                 <a href="../authors/zhann/">Naijun Zhan
                 </a>
               </li>
           </ul>
         </td>
       </tr>
     </tbody>
   </table>
         
       </div>
     </div>
   </body>
 </html>
\ No newline at end of file
diff --git a/web/authors/index.json b/web/authors/index.json
--- a/web/authors/index.json
+++ b/web/authors/index.json
@@ -1,2397 +1,2407 @@
 [
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   "link": "/authors/abdulaziz/",
   "name": "Mohammad Abdulaziz"
  },
  {
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   "link": "/authors/adelsberger/",
   "name": "Stephan Adelsberger"
  },
  {
   "id": 2,
   "link": "/authors/aehlig/",
   "name": "Klaus Aehlig"
  },
  {
   "id": 3,
   "link": "/authors/aissat/",
   "name": "Romain Aissat"
  },
  {
   "id": 4,
   "link": "/authors/amani/",
   "name": "Sidney Amani"
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  {
   "id": 5,
   "link": "/authors/ammer/",
   "name": "Thomas Ammer"
  },
  {
   "id": 6,
   "link": "/authors/andreka/",
   "name": "Hajnal Andreka"
  },
  {
   "id": 7,
   "link": "/authors/andronick/",
   "name": "June Andronick"
  },
  {
   "id": 8,
   "link": "/authors/aransay/",
   "name": "Jesús Aransay"
  },
  {
   "id": 9,
   "link": "/authors/argyraki/",
   "name": "Angeliki Koutsoukou-Argyraki"
  },
  {
   "id": 10,
   "link": "/authors/armstrong/",
   "name": "Alasdair Armstrong"
  },
  {
   "id": 11,
   "link": "/authors/aspinall/",
   "name": "David Aspinall"
  },
  {
   "id": 12,
   "link": "/authors/ausaf/",
   "name": "Fahad Ausaf"
  },
  {
   "id": 13,
   "link": "/authors/avigad/",
   "name": "Jeremy Avigad"
  },
  {
   "id": 14,
   "link": "/authors/back/",
   "name": "Ralph-Johan Back"
  },
  {
   "id": 15,
   "link": "/authors/baksys/",
   "name": "Mantas Bakšys"
  },
  {
   "id": 16,
   "link": "/authors/balbach/",
   "name": "Frank J. Balbach"
  },
  {
   "id": 17,
   "link": "/authors/ballarin/",
   "name": "Clemens Ballarin"
  },
  {
   "id": 18,
   "link": "/authors/ballenghien/",
   "name": "Benoît Ballenghien"
  },
  {
   "id": 19,
   "link": "/authors/barsotti/",
   "name": "Damián Barsotti"
  },
  {
   "id": 20,
   "link": "/authors/bauer/",
   "name": "Gertrud Bauer"
  },
  {
   "id": 21,
   "link": "/authors/bauereiss/",
   "name": "Thomas Bauereiss"
  },
  {
   "id": 22,
   "link": "/authors/bayer/",
   "name": "Jonas Bayer"
  },
  {
   "id": 23,
   "link": "/authors/becker/",
   "name": "Heiko Becker"
  },
  {
   "id": 24,
   "link": "/authors/beeren/",
   "name": "Joel Beeren"
  },
  {
   "id": 25,
   "link": "/authors/bella/",
   "name": "Giampaolo Bella"
  },
  {
   "id": 26,
   "link": "/authors/bengtson/",
   "name": "Jesper Bengtson"
  },
  {
   "id": 27,
   "link": "/authors/bentkamp/",
   "name": "Alexander Bentkamp"
  },
  {
   "id": 28,
   "link": "/authors/benzmueller/",
   "name": "Christoph Benzmüller"
  },
  {
   "id": 29,
   "link": "/authors/beresford/",
   "name": "Alastair R. Beresford"
  },
  {
   "id": 30,
   "link": "/authors/berghofer/",
   "name": "Stefan Berghofer"
  },
  {
   "id": 31,
   "link": "/authors/bergstroem/",
   "name": "Axel Bergström"
  },
  {
   "id": 32,
   "link": "/authors/beringer/",
   "name": "Lennart Beringer"
  },
  {
   "id": 33,
   "link": "/authors/bharadwaj/",
   "name": "Abhijith Bharadwaj"
  },
  {
   "id": 34,
   "link": "/authors/bhatt/",
   "name": "Bhargav Bhatt"
  },
  {
   "id": 35,
   "link": "/authors/biendarra/",
   "name": "Julian Biendarra"
  },
  {
   "id": 36,
   "link": "/authors/bisping/",
   "name": "Benjamin Bisping"
  },
  {
   "id": 37,
   "link": "/authors/blanchette/",
   "name": "Jasmin Christian Blanchette"
  },
  {
   "id": 38,
   "link": "/authors/blasum/",
   "name": "Holger Blasum"
  },
  {
   "id": 39,
   "link": "/authors/blumson/",
   "name": "Ben Blumson"
  },
  {
   "id": 40,
   "link": "/authors/bockenek/",
   "name": "Joshua Bockenek"
  },
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   "id": 41,
   "link": "/authors/boehme/",
   "name": "Sascha Böhme"
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   "id": 42,
   "link": "/authors/bohrer/",
   "name": "Rose Bohrer"
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   "link": "/authors/bootle/",
   "name": "Jonathan Bootle"
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   "link": "/authors/bordg/",
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   "id": 45,
   "link": "/authors/borgstroem/",
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   "id": 46,
   "link": "/authors/bortin/",
   "name": "Maksym Bortin"
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  {
   "id": 47,
   "link": "/authors/bottesch/",
   "name": "Ralph Bottesch"
  },
  {
   "id": 48,
   "link": "/authors/boulanger/",
   "name": "Frédéric Boulanger"
  },
  {
   "id": 49,
   "link": "/authors/bourke/",
   "name": "Timothy Bourke"
  },
  {
   "id": 50,
   "link": "/authors/boutry/",
   "name": "Pierre Boutry"
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   "id": 51,
   "link": "/authors/boyton/",
   "name": "Andrew Boyton"
  },
  {
   "id": 52,
   "link": "/authors/bracevac/",
   "name": "Oliver Bračevac"
  },
  {
   "id": 53,
   "link": "/authors/brandt/",
   "name": "Felix Brandt"
  },
  {
   "id": 54,
   "link": "/authors/breitner/",
   "name": "Joachim Breitner"
  },
  {
   "id": 55,
   "link": "/authors/brien/",
   "name": "Nicolas Robinson-O'Brien"
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   "id": 56,
   "link": "/authors/brinkop/",
   "name": "Hauke Brinkop"
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   "link": "/authors/brodmann/",
   "name": "Paul-David Brodmann"
  },
  {
   "id": 58,
   "link": "/authors/brucker/",
   "name": "Achim D. Brucker"
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   "link": "/authors/bruegger/",
   "name": "Lukas Brügger"
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   "link": "/authors/brun/",
   "name": "Matthias Brun"
  },
  {
   "id": 61,
   "link": "/authors/brunner/",
   "name": "Julian Brunner"
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   "link": "/authors/bulwahn/",
   "name": "Lukas Bulwahn"
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   "link": "/authors/buss/",
   "name": "Sebastián Buss"
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   "id": 64,
   "link": "/authors/butler/",
   "name": "David Butler"
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   "link": "/authors/buyse/",
   "name": "Maxime Buyse"
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   "link": "/authors/caballero/",
   "name": "José Manuel Rodríguez Caballero"
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   "id": 67,
   "link": "/authors/calk/",
   "name": "Cameron Calk"
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   "id": 68,
   "link": "/authors/caminati/",
   "name": "Marco B. Caminati"
  },
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   "id": 69,
   "link": "/authors/campo/",
   "name": "Alejandro del Campo"
  },
  {
   "id": 70,
   "link": "/authors/chapman/",
   "name": "Peter Chapman"
  },
  {
   "id": 71,
   "link": "/authors/chen/",
   "name": "L. Chen"
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  {
   "id": 72,
   "link": "/authors/chenj/",
   "name": "Jamie Chen"
  },
  {
   "id": 73,
   "link": "/authors/chevalier/",
   "name": "Loïc Chevalier"
  },
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   "id": 74,
   "link": "/authors/christfort/",
   "name": "Axel Christfort"
  },
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   "id": 75,
   "link": "/authors/clouston/",
   "name": "Ranald Clouston"
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   "id": 76,
   "link": "/authors/cock/",
   "name": "David Cock"
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   "link": "/authors/coghetto/",
   "name": "Roland Coghetto"
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   "id": 78,
   "link": "/authors/coglio/",
   "name": "Alessandro Coglio"
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   "id": 79,
   "link": "/authors/cohen/",
   "name": "Ernie Cohen"
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   "id": 80,
   "link": "/authors/cordwell/",
   "name": "Katherine Kosaian"
  },
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   "id": 81,
   "link": "/authors/cousin/",
   "name": "Marie Cousin"
  },
  {
   "id": 82,
   "link": "/authors/cremer/",
   "name": "Nils Cremer"
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  {
   "id": 83,
   "link": "/authors/crighton/",
   "name": "Aaron Crighton"
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   "link": "/authors/dalvit/",
   "name": "Christian Dalvit"
  },
  {
   "id": 85,
   "link": "/authors/danilkin/",
   "name": "Anton Danilkin"
  },
  {
   "id": 86,
   "link": "/authors/dardinier/",
   "name": "Thibault Dardinier"
  },
  {
   "id": 87,
   "link": "/authors/david/",
   "name": "Marco David"
  },
  {
   "id": 88,
   "link": "/authors/debois/",
   "name": "Søren Debois"
  },
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   "id": 89,
   "link": "/authors/debrat/",
   "name": "Henri Debrat"
  },
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   "id": 90,
   "link": "/authors/decova/",
   "name": "Sára Decova"
  },
  {
   "id": 91,
   "link": "/authors/delemazure/",
   "name": "Théo Delemazure"
  },
  {
   "id": 92,
   "link": "/authors/demeulemeester/",
   "name": "Tom Demeulemeester"
  },
  {
   "id": 93,
   "link": "/authors/derrick/",
   "name": "John Derrick"
  },
  {
   "id": 94,
   "link": "/authors/desharnais/",
   "name": "Martin Desharnais"
  },
  {
   "id": 95,
   "link": "/authors/diaz/",
   "name": "Javier Díaz"
  },
  {
   "id": 96,
   "link": "/authors/diekmann/",
   "name": "Cornelius Diekmann"
  },
  {
   "id": 97,
   "link": "/authors/dirix/",
   "name": "Stefan Dirix"
  },
  {
   "id": 98,
   "link": "/authors/dittmann/",
   "name": "Christoph Dittmann"
  },
  {
   "id": 99,
   "link": "/authors/divason/",
   "name": "Jose Divasón"
  },
  {
   "id": 100,
   "link": "/authors/doczkal/",
   "name": "Christian Doczkal"
  },
  {
   "id": 101,
   "link": "/authors/dongol/",
   "name": "Brijesh Dongol"
  },
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   "id": 102,
   "link": "/authors/doty/",
   "name": "Matthew Doty"
  },
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   "id": 103,
   "link": "/authors/dubut/",
   "name": "Jérémy Dubut"
  },
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   "id": 104,
   "link": "/authors/dunaev/",
   "name": "Georgy Dunaev"
  },
  {
   "id": 105,
   "link": "/authors/dyckhoff/",
   "name": "Roy Dyckhoff"
  },
  {
   "id": 106,
   "link": "/authors/eberl/",
   "name": "Manuel Eberl"
  },
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   "id": 107,
   "link": "/authors/echenim/",
   "name": "Mnacho Echenim"
  },
  {
   "id": 108,
   "link": "/authors/edmonds/",
   "name": "Chelsea Edmonds"
  },
  {
   "id": 109,
   "link": "/authors/engelhardt/",
   "name": "Kai Engelhardt"
  },
  {
   "id": 110,
   "link": "/authors/eriksson/",
   "name": "Lars-Henrik Eriksson"
  },
  {
   "id": 111,
   "link": "/authors/esparza/",
   "name": "Javier Esparza"
  },
  {
   "id": 112,
   "link": "/authors/essmann/",
   "name": "Robin Eßmann"
  },
  {
   "id": 113,
   "link": "/authors/felgenhauer/",
   "name": "Bertram Felgenhauer"
  },
  {
   "id": 114,
   "link": "/authors/feliachi/",
   "name": "Abderrahmane Feliachi"
  },
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   "id": 115,
   "link": "/authors/fell/",
   "name": "Julian Fell"
  },
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   "id": 116,
   "link": "/authors/fernandez/",
   "name": "Matthew Fernandez"
  },
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   "id": 117,
   "link": "/authors/fiedler/",
   "name": "Ben Fiedler"
  },
  {
   "id": 118,
   "link": "/authors/fleuriot/",
   "name": "Jacques D. Fleuriot"
  },
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   "id": 119,
   "link": "/authors/fleury/",
   "name": "Mathias Fleury"
  },
  {
   "id": 120,
   "link": "/authors/foster/",
   "name": "Michael Foster"
  },
  {
   "id": 121,
   "link": "/authors/fosterj/",
   "name": "J. Nathan Foster"
  },
  {
   "id": 122,
   "link": "/authors/fosters/",
   "name": "Simon Foster"
  },
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   "id": 123,
   "link": "/authors/fouillard/",
   "name": "Valentin Fouillard"
  },
  {
   "id": 124,
   "link": "/authors/friedrich/",
   "name": "Stefan Friedrich"
  },
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   "id": 125,
   "link": "/authors/from/",
   "name": "Asta Halkjær From"
  },
  {
   "id": 126,
   "link": "/authors/fuenmayor/",
   "name": "David Fuenmayor"
  },
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   "id": 127,
   "link": "/authors/furusawa/",
   "name": "Hitoshi Furusawa"
  },
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   "id": 128,
   "link": "/authors/gammie/",
   "name": "Peter Gammie"
  },
  {
   "id": 129,
   "link": "/authors/gao/",
   "name": "Xin Gao"
  },
  {
   "id": 130,
   "link": "/authors/garvia/",
   "name": "Azucena Garvia"
  },
  {
   "id": 131,
   "link": "/authors/gaudel/",
   "name": "Marie-Claude Gaudel"
  },
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   "id": 132,
   "link": "/authors/gay/",
   "name": "Richard Gay"
  },
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   "id": 133,
   "link": "/authors/georgescu/",
   "name": "George Georgescu"
  },
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   "id": 134,
   "link": "/authors/gheri/",
   "name": "Lorenzo Gheri"
  },
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   "id": 135,
   "link": "/authors/ghourabi/",
   "name": "Fadoua Ghourabi"
  },
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   "id": 136,
   "link": "/authors/gioiosa/",
   "name": "Gianpaolo Gioiosa"
  },
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   "id": 137,
   "link": "/authors/glabbeek/",
   "name": "Rob van Glabbeek"
  },
  {
   "id": 138,
   "link": "/authors/gomes/",
   "name": "Victor B. F. Gomes"
  },
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   "id": 139,
   "link": "/authors/gonzalez/",
   "name": "Edgar Gonzàlez"
  },
  {
   "id": 140,
   "link": "/authors/gore/",
   "name": "Rajeev Gore"
  },
  {
   "id": 141,
   "link": "/authors/gouezel/",
   "name": "Sebastien Gouezel"
  },
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   "id": 142,
   "link": "/authors/grechuk/",
   "name": "Bogdan Grechuk"
  },
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   "id": 143,
   "link": "/authors/grewe/",
   "name": "Sylvia Grewe"
  },
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   "id": 144,
   "link": "/authors/griebel/",
   "name": "Simon Griebel"
  },
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   "id": 145,
   "link": "/authors/grov/",
   "name": "Gudmund Grov"
  },
  {
   "id": 146,
   "link": "/authors/guerraoui/",
   "name": "Rachid Guerraoui"
  },
  {
   "id": 147,
   "link": "/authors/guiol/",
   "name": "Hervé Guiol"
  },
  {
   "id": 148,
   "link": "/authors/gunther/",
   "name": "Emmanuel Gunther"
  },
  {
   "id": 149,
   "link": "/authors/gutkovas/",
   "name": "Ramunas Gutkovas"
  },
  {
   "id": 150,
   "link": "/authors/guttmann/",
   "name": "Walter Guttmann"
  },
  {
   "id": 151,
   "link": "/authors/guzman/",
   "name": "Laura P. Gamboa Guzman"
  },
  {
   "id": 152,
   "link": "/authors/haftmann/",
   "name": "Florian Haftmann"
  },
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   "id": 153,
   "link": "/authors/haslbeck/",
   "name": "Max W. Haslbeck"
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   "id": 154,
   "link": "/authors/haslbeckm/",
   "name": "Maximilian P. L. Haslbeck"
  },
  {
   "id": 155,
   "link": "/authors/havle/",
   "name": "Oto Havle"
  },
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   "id": 156,
   "link": "/authors/hayes/",
   "name": "Ian J. Hayes"
  },
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   "id": 157,
   "link": "/authors/he/",
   "name": "Yijun He"
  },
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   "id": 158,
   "link": "/authors/heimes/",
   "name": "Lukas Heimes"
  },
  {
   "id": 159,
   "link": "/authors/helke/",
   "name": "Steffen Helke"
  },
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   "id": 160,
   "link": "/authors/hellauer/",
   "name": "Fabian Hellauer"
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   "id": 161,
   "link": "/authors/heller/",
   "name": "Armin Heller"
  },
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   "id": 162,
   "link": "/authors/henrio/",
   "name": "Ludovic Henrio"
  },
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   "id": 163,
   "link": "/authors/herzberg/",
   "name": "Michael Herzberg"
  },
  {
   "id": 164,
   "link": "/authors/hess/",
   "name": "Andreas V. Hess"
  },
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   "id": 165,
   "link": "/authors/hetzl/",
   "name": "Stefan Hetzl"
  },
  {
   "id": 166,
   "link": "/authors/hibon/",
   "name": "Quentin Hibon"
  },
  {
   "id": 167,
   "link": "/authors/higgins/",
   "name": "Edward Higgins"
  },
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   "id": 168,
   "link": "/authors/hirata/",
   "name": "Michikazu Hirata"
  },
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   "id": 169,
   "link": "/authors/hoefner/",
   "name": "Peter Höfner"
  },
  {
   "id": 170,
   "link": "/authors/hoelzl/",
   "name": "Johannes Hölzl"
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   "id": 171,
   "link": "/authors/hofmann/",
   "name": "Martin Hofmann"
  },
  {
   "id": 172,
   "link": "/authors/hofmeier/",
   "name": "Paul Hofmeier"
  },
  {
   "id": 173,
   "link": "/authors/holub/",
   "name": "Štěpán Holub"
  },
  {
   "id": 174,
   "link": "/authors/hosking/",
   "name": "Tony Hosking"
  },
  {
   "id": 175,
   "link": "/authors/hou/",
   "name": "Zhe Hou"
  },
  {
   "id": 176,
   "link": "/authors/hu/",
   "name": "Shuwei Hu"
  },
  {
   "id": 177,
   "link": "/authors/huffman/",
   "name": "Brian Huffman"
  },
  {
   "id": 178,
   "link": "/authors/hupel/",
   "name": "Lars Hupel"
  },
  {
   "id": 179,
   "link": "/authors/ijbema/",
   "name": "Mark Ijbema"
  },
  {
   "id": 180,
   "link": "/authors/immler/",
   "name": "Fabian Immler"
  },
  {
   "id": 181,
   "link": "/authors/israel/",
   "name": "Jonas Israel"
  },
  {
   "id": 182,
   "link": "/authors/ito/",
   "name": "Yosuke Ito"
  },
  {
   "id": 183,
   "link": "/authors/iwama/",
   "name": "Fumiya Iwama"
  },
  {
   "id": 184,
   "link": "/authors/jacobsen/",
   "name": "Frederik Krogsdal Jacobsen"
  },
  {
   "id": 185,
   "link": "/authors/jaskelioff/",
   "name": "Mauro Jaskelioff"
  },
  {
   "id": 186,
   "link": "/authors/jaskolka/",
   "name": "Jason Jaskolka"
  },
  {
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-  "link": "/authors/stuewe/",
-  "name": "Daniel Stüwe"
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+  "name": "Terru Stübinger"
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-  "link": "/authors/sudbrock/",
-  "name": "Henning Sudbrock"
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+  "name": "Daniel Stüwe"
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-  "link": "/authors/sudhof/",
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-  "link": "/authors/sulejmani/",
-  "name": "Ujkan Sulejmani"
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+  "name": "Henry Sudhof"
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-  "link": "/authors/sutcliffe/",
-  "name": "Geoff Sutcliffe"
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-  "link": "/authors/sylvestre/",
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-  "link": "/authors/tan/",
-  "name": "Yong Kiam Tan"
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-  "link": "/authors/tanaka/",
-  "name": "Miki Tanaka"
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+  "name": "Yong Kiam Tan"
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+  "name": "Miki Tanaka"
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-  "link": "/authors/taylor/",
-  "name": "Ramsay G. Taylor"
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-  "link": "/authors/terraf/",
-  "name": "Pedro Sánchez Terraf"
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-  "name": "René Thiemann"
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+  "name": "Pedro Sánchez Terraf"
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+  "name": "René Thiemann"
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+  "name": "Joseph Thommes"
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+  "name": "Fox Thomson"
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+  "name": "Alwen Tiu"
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+  "name": "Balazs Toth"
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   "id": 429,
-  "link": "/authors/trachtenherz/",
-  "name": "David Trachtenherz"
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+  "name": "Sophie Tourret"
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   "id": 430,
-  "link": "/authors/traut/",
-  "name": "Christoph Traut"
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   "id": 431,
-  "link": "/authors/traytel/",
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-  "link": "/authors/tuong/",
-  "name": "Frédéric Tuong"
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+  "name": "Vincent Trélat"
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   "id": 434,
-  "link": "/authors/tuongj/",
-  "name": "Joseph Tuong"
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-  "link": "/authors/tverdyshev/",
-  "name": "Sergey Tverdyshev"
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+  "name": "Joseph Tuong"
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   "id": 436,
-  "link": "/authors/ullrich/",
-  "name": "Sebastian Ullrich"
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+  "name": "Sergey Tverdyshev"
  },
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   "id": 437,
-  "link": "/authors/unruh/",
-  "name": "Dominique Unruh"
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+  "name": "Sebastian Ullrich"
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   "id": 438,
-  "link": "/authors/urban/",
-  "name": "Christian Urban"
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+  "name": "Dominique Unruh"
  },
  {
   "id": 439,
-  "link": "/authors/van/",
-  "name": "Hai Nguyen Van"
+  "link": "/authors/urban/",
+  "name": "Christian Urban"
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-  "link": "/authors/velykis/",
-  "name": "Andrius Velykis"
+  "link": "/authors/van/",
+  "name": "Hai Nguyen Van"
  },
  {
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-  "name": "Freek Verbeek"
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+  "name": "Andrius Velykis"
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-  "name": "Jørgen Villadsen"
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-  "name": "Frederic Voisin"
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+  "name": "Jørgen Villadsen"
  },
  {
   "id": 444,
-  "link": "/authors/vytiniotis/",
-  "name": "Dimitrios Vytiniotis"
+  "link": "/authors/voisin/",
+  "name": "Frederic Voisin"
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   "id": 445,
-  "link": "/authors/wagner/",
-  "name": "Max Wagner"
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+  "name": "Dimitrios Vytiniotis"
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   "id": 446,
-  "link": "/authors/waldmann/",
-  "name": "Uwe Waldmann"
+  "link": "/authors/wagner/",
+  "name": "Max Wagner"
  },
  {
   "id": 447,
-  "link": "/authors/wand/",
-  "name": "Daniel Wand"
+  "link": "/authors/waldmann/",
+  "name": "Uwe Waldmann"
  },
  {
   "id": 448,
-  "link": "/authors/wang/",
-  "name": "Shuling Wang"
+  "link": "/authors/wand/",
+  "name": "Daniel Wand"
  },
  {
   "id": 449,
-  "link": "/authors/wassell/",
-  "name": "Mark Wassell"
+  "link": "/authors/wang/",
+  "name": "Shuling Wang"
  },
  {
   "id": 450,
-  "link": "/authors/wasserrab/",
-  "name": "Daniel Wasserrab"
+  "link": "/authors/wassell/",
+  "name": "Mark Wassell"
  },
  {
   "id": 451,
-  "link": "/authors/watt/",
-  "name": "Conrad Watt"
+  "link": "/authors/wasserrab/",
+  "name": "Daniel Wasserrab"
  },
  {
   "id": 452,
-  "link": "/authors/weber/",
-  "name": "Tjark Weber"
+  "link": "/authors/watt/",
+  "name": "Conrad Watt"
  },
  {
   "id": 453,
-  "link": "/authors/weerwag/",
-  "name": "Timmy Weerwag"
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+  "name": "Tjark Weber"
  },
  {
   "id": 454,
-  "link": "/authors/weidner/",
-  "name": "Arno Wilhelm-Weidner"
+  "link": "/authors/weerwag/",
+  "name": "Timmy Weerwag"
  },
  {
   "id": 455,
-  "link": "/authors/wenninger/",
-  "name": "Elias Wenninger"
+  "link": "/authors/weidner/",
+  "name": "Arno Wilhelm-Weidner"
  },
  {
   "id": 456,
-  "link": "/authors/wenzel/",
-  "name": "Makarius Wenzel"
+  "link": "/authors/wenninger/",
+  "name": "Elias Wenninger"
  },
  {
   "id": 457,
-  "link": "/authors/whitley/",
-  "name": "A Whitley"
+  "link": "/authors/wenzel/",
+  "name": "Makarius Wenzel"
  },
  {
   "id": 458,
-  "link": "/authors/wickerson/",
-  "name": "John Wickerson"
+  "link": "/authors/whitley/",
+  "name": "A Whitley"
  },
  {
   "id": 459,
-  "link": "/authors/willenbrink/",
-  "name": "Sebastian Willenbrink"
+  "link": "/authors/wickerson/",
+  "name": "John Wickerson"
  },
  {
   "id": 460,
-  "link": "/authors/wimmer/",
-  "name": "Simon Wimmer"
+  "link": "/authors/willenbrink/",
+  "name": "Sebastian Willenbrink"
  },
  {
   "id": 461,
-  "link": "/authors/wirt/",
-  "name": "Kai Wirt"
+  "link": "/authors/wimmer/",
+  "name": "Simon Wimmer"
  },
  {
   "id": 462,
-  "link": "/authors/wolff/",
-  "name": "Burkhart Wolff"
+  "link": "/authors/wirt/",
+  "name": "Kai Wirt"
  },
  {
   "id": 463,
-  "link": "/authors/wu/",
-  "name": "Chunhan Wu"
+  "link": "/authors/wolff/",
+  "name": "Burkhart Wolff"
  },
  {
   "id": 464,
-  "link": "/authors/xu/",
-  "name": "Jian Xu"
+  "link": "/authors/wu/",
+  "name": "Chunhan Wu"
  },
  {
   "id": 465,
-  "link": "/authors/yamada/",
-  "name": "Akihisa Yamada"
+  "link": "/authors/xu/",
+  "name": "Jian Xu"
  },
  {
   "id": 466,
-  "link": "/authors/ye/",
-  "name": "Lina Ye"
+  "link": "/authors/yamada/",
+  "name": "Akihisa Yamada"
  },
  {
   "id": 467,
-  "link": "/authors/yez/",
-  "name": "Zhengkun Ye"
+  "link": "/authors/yang/",
+  "name": "Jiong Yang"
  },
  {
   "id": 468,
-  "link": "/authors/ying/",
-  "name": "Shenggang Ying"
+  "link": "/authors/ye/",
+  "name": "Lina Ye"
  },
  {
   "id": 469,
-  "link": "/authors/yingm/",
-  "name": "Mingsheng Ying"
+  "link": "/authors/yez/",
+  "name": "Zhengkun Ye"
  },
  {
   "id": 470,
-  "link": "/authors/yu/",
-  "name": "Lei Yu"
+  "link": "/authors/ying/",
+  "name": "Shenggang Ying"
  },
  {
   "id": 471,
-  "link": "/authors/zankl/",
-  "name": "Harald Zankl"
+  "link": "/authors/yingm/",
+  "name": "Mingsheng Ying"
  },
  {
   "id": 472,
-  "link": "/authors/zee/",
-  "name": "Karen Zee"
+  "link": "/authors/yu/",
+  "name": "Lei Yu"
  },
  {
   "id": 473,
-  "link": "/authors/zeller/",
-  "name": "Peter Zeller"
+  "link": "/authors/zankl/",
+  "name": "Harald Zankl"
  },
  {
   "id": 474,
-  "link": "/authors/zeyda/",
-  "name": "Frank Zeyda"
+  "link": "/authors/zee/",
+  "name": "Karen Zee"
  },
  {
   "id": 475,
-  "link": "/authors/zhan/",
-  "name": "Bohua Zhan"
+  "link": "/authors/zeller/",
+  "name": "Peter Zeller"
  },
  {
   "id": 476,
-  "link": "/authors/zhang/",
-  "name": "Yu Zhang"
+  "link": "/authors/zeyda/",
+  "name": "Frank Zeyda"
  },
  {
   "id": 477,
-  "link": "/authors/zhangx/",
-  "name": "Xingyuan Zhang"
+  "link": "/authors/zhan/",
+  "name": "Bohua Zhan"
  },
  {
   "id": 478,
+  "link": "/authors/zhang/",
+  "name": "Yu Zhang"
+ },
+ {
+  "id": 479,
+  "link": "/authors/zhangx/",
+  "name": "Xingyuan Zhang"
+ },
+ {
+  "id": 480,
   "link": "/authors/zhann/",
   "name": "Naijun Zhan"
  }
 ]
\ No newline at end of file
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+          <br>
+            by
+            <a href="../../authors/stuebinger">Terru Stübinger</a> <a href="https://stuebinm.eu/">🌐</a> and <a href="../../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
+
+        </div>
+        <span class="date">
+          Jan 22
+        </span>
+      </article>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/authors/stuebinger/index.xml b/web/authors/stuebinger/index.xml
new file mode 100644
--- /dev/null
+++ b/web/authors/stuebinger/index.xml
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+    <title>stuebinger on Archive of Formal Proofs
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+    <link>/authors/stuebinger/</link>
+    <description>
+        Recent content in stuebinger 
+        on Archive of Formal Proofs
+    </description>
+    <generator>Hugo -- gohugo.io</generator>
+    <language>en-gb</language>
+    
+      <lastBuildDate>Mon, 22 Jan 2024 00:00:00 +0000</lastBuildDate>
+      <atom:link href="/authors/stuebinger/index.xml" rel="self" type="application/rss+xml" />
+        <item>
+          <title>Go Code Generation for Isabelle</title>
+          <link>/entries/Go.html</link>
+          <pubDate>Mon, 22 Jan 2024 00:00:00 +0000</pubDate>
+          <guid>/entries/Go.html</guid>
+          <description></description>
+        </item>
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+</rss>
diff --git a/web/authors/tan/index.html b/web/authors/tan/index.html
--- a/web/authors/tan/index.html
+++ b/web/authors/tan/index.html
@@ -1,202 +1,215 @@
 <!DOCTYPE html>
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   <h1>
     <span class='first'>Y</span>ong <span class='first'>K</span>iam <span class='first'>T</span>an
     
   </h1>
   <div>
   </div>
 </header>
       <div>
         
     <h2>Homepages 🌐</h2>
     <ul>
       <li><a href="https://www.cs.cmu.edu/~yongkiat/">https://www.cs.cmu.edu/~yongkiat/</a></li>
     </ul>
     <h2>E-Mails 📧</h2>
     <ul>
       <li>
         <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">
           <span class="rev">ude</span>.<span class="rev">umc</span>.<span class="rev">sc</span>
 @<span class="rev">taikgnoy</span>
         </a>
       </li>
     </ul>
 
   <h2>Entries</h2>
+    <h3 class="head">2024</h3>
+      <article class="entry">
+        <div class="item-text">
+          <h5><a class="title" href="../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+          <br>
+            by
+            <a href="../../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a> and <a href="../../authors/yang">Jiong Yang</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamlvbmd5YW5nY29iZSJdfQ==">📧</a>
+
+        </div>
+        <span class="date">
+          Mar 15
+        </span>
+      </article>
     <h3 class="head">2023</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Concentration_Inequalities.html">Concentration Inequalities</a></h5>
           <br>
             by
             <a href="../../authors/karayel">Emin Karayel</a> <a class="obfuscated" data="eyJob3N0IjpbImVtaW5rYXJheWVsIiwiZGUiXSwidXNlciI6WyJtZSJdfQ==">📧</a> and <a href="../../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a>
 
         </div>
         <span class="date">
           Nov 13
         </span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Schwartz_Zippel.html">The Schwartz-Zippel Lemma</a></h5>
           <br>
             by
             <a href="../../authors/kim">Sunpill Kim</a> and <a href="../../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a>
 
         </div>
         <span class="date">
           Apr 27
         </span>
       </article>
     <h3 class="head">2022</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Quantifier_Elimination_Hybrid.html">A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL</a></h5>
           <br>
             by
             <a href="../../authors/cordwell">Katherine Kosaian</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsia2NvcmR3ZWwiXX0=">📧</a>, <a href="../../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a> and <a href="../../authors/platzer">André Platzer</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsiYXBsYXR6ZXIiXX0=">📧</a>
 
         </div>
         <span class="date">
           Dec 15
         </span>
       </article>
     <h3 class="head">2021</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/BenOr_Kozen_Reif.html">The BKR Decision Procedure for Univariate Real Arithmetic</a></h5>
           <br>
             by
             <a href="../../authors/cordwell">Katherine Kosaian</a> <a href="https://www.cs.cmu.edu/~kcordwel/">🌐</a>, <a href="../../authors/tan">Yong Kiam Tan</a> <a href="https://www.cs.cmu.edu/~yongkiat/">🌐</a> and <a href="../../authors/platzer">André Platzer</a> <a href="https://www.cs.cmu.edu/~aplatzer/">🌐</a>
 
         </div>
         <span class="date">
           Apr 24
         </span>
       </article>
     <h3 class="head">2019</h3>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Poincare_Bendixson.html">The Poincaré-Bendixson Theorem</a></h5>
           <br>
             by
             <a href="../../authors/immler">Fabian Immler</a> <a href="https://home.in.tum.de/~immler/">🌐</a> and <a href="../../authors/tan">Yong Kiam Tan</a> <a href="https://www.cs.cmu.edu/~yongkiat/">🌐</a>
 
         </div>
         <span class="date">
           Dec 18
         </span>
       </article>
         
       </div>
     </div>
   </body>
 </html>
\ No newline at end of file
diff --git a/web/authors/tan/index.xml b/web/authors/tan/index.xml
--- a/web/authors/tan/index.xml
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+      <lastBuildDate>Fri, 15 Mar 2024 00:00:00 +0000</lastBuildDate>
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         <item>
+          <title>Approximate Model Counting</title>
+          <link>/entries/Approximate_Model_Counting.html</link>
+          <pubDate>Fri, 15 Mar 2024 00:00:00 +0000</pubDate>
+          <guid>/entries/Approximate_Model_Counting.html</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Concentration Inequalities</title>
           <link>/entries/Concentration_Inequalities.html</link>
           <pubDate>Mon, 13 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Concentration_Inequalities.html</guid>
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           <title>The Schwartz-Zippel Lemma</title>
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           <pubDate>Thu, 27 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Schwartz_Zippel.html</guid>
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         <item>
           <title>A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL</title>
           <link>/entries/Quantifier_Elimination_Hybrid.html</link>
           <pubDate>Thu, 15 Dec 2022 00:00:00 +0000</pubDate>
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           <title>The BKR Decision Procedure for Univariate Real Arithmetic</title>
           <link>/entries/BenOr_Kozen_Reif.html</link>
           <pubDate>Sat, 24 Apr 2021 00:00:00 +0000</pubDate>
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           <title>The Poincaré-Bendixson Theorem</title>
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new file mode 100644
--- /dev/null
+++ b/web/authors/yang/index.html
@@ -0,0 +1,148 @@
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+<html lang="en">
+  <head>
+  <meta charset="utf-8" />
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
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+    <title>Jiong Yang - Archive of Formal Proofs</title>
+    <meta name="description" content="A collection of proof libraries, examples, and larger
+     scientific developments, mechanically checked in the theorem prover Isabelle.">
+  <link rel="alternate" type="application/rss+xml" href="../../authors/yang/index.xml" title="Archive of Formal Proofs" />
+
+  <meta property="og:title" content="yang" />
+<meta property="og:description" content="A collection of proof libraries, examples, and larger scientific developments, mechanically checked in the theorem prover Isabelle." />
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+    <form autocomplete="off" action="../../search">
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+        <input id="search-input" type="search" size="31" maxlength="255" value=""
+               aria-label="Search the AFP" list="autocomplete"><button
+               id="search-button" type="button">
+          <img src="../../images/search.svg" alt="Search"/>
+        </button>
+        <datalist id="autocomplete">
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+      </div>
+    </form>
+  <h1>
+    <span class='first'>J</span>iong <span class='first'>Y</span>ang
+    
+  </h1>
+  <div>
+  </div>
+</header>
+      <div>
+        
+    <h2>E-Mails 📧</h2>
+    <ul>
+      <li>
+        <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamlvbmd5YW5nY29iZSJdfQ==">
+          <span class="rev">moc</span>.<span class="rev">liamg</span>
+@<span class="rev">ebocgnaygnoij</span>
+        </a>
+      </li>
+    </ul>
+
+  <h2>Entries</h2>
+    <h3 class="head">2024</h3>
+      <article class="entry">
+        <div class="item-text">
+          <h5><a class="title" href="../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+          <br>
+            by
+            <a href="../../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a> and <a href="../../authors/yang">Jiong Yang</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamlvbmd5YW5nY29iZSJdfQ==">📧</a>
+
+        </div>
+        <span class="date">
+          Mar 15
+        </span>
+      </article>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/authors/yang/index.xml b/web/authors/yang/index.xml
new file mode 100644
--- /dev/null
+++ b/web/authors/yang/index.xml
@@ -0,0 +1,24 @@
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+  <channel>
+    <title>yang on Archive of Formal Proofs
+    </title>
+    <link>/authors/yang/</link>
+    <description>
+        Recent content in yang 
+        on Archive of Formal Proofs
+    </description>
+    <generator>Hugo -- gohugo.io</generator>
+    <language>en-gb</language>
+    
+      <lastBuildDate>Fri, 15 Mar 2024 00:00:00 +0000</lastBuildDate>
+      <atom:link href="/authors/yang/index.xml" rel="self" type="application/rss+xml" />
+        <item>
+          <title>Approximate Model Counting</title>
+          <link>/entries/Approximate_Model_Counting.html</link>
+          <pubDate>Fri, 15 Mar 2024 00:00:00 +0000</pubDate>
+          <guid>/entries/Approximate_Model_Counting.html</guid>
+          <description></description>
+        </item>
+  </channel>
+</rss>
diff --git a/web/data/keywords.json b/web/data/keywords.json
--- a/web/data/keywords.json
+++ b/web/data/keywords.json
@@ -1,6577 +1,6604 @@
 [{"keyword": "-automata states"},
 {"keyword": "-dimensional cube"},
+{"keyword": "-factor approximation"},
 {"keyword": "-free higher-order terms"},
 {"keyword": "0-1-2-principle"},
 {"keyword": "1 delta cdots delta"},
 {"keyword": "1 infty"},
 {"keyword": "1 infty frac"},
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 {"keyword": "ab leq int_0"},
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diff --git a/web/dependencies/coinductive/index.html b/web/dependencies/coinductive/index.html
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+++ b/web/dependencies/coinductive/index.html
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+      <h2 class="head">2024</h2>
+        <article class="entry">
+          <div class="item-text">
+            <h5><a class="title" href="../../entries/Continued_Fractions.html">Continued Fractions</a></h5>
+            <br>
+              by <a href="../../authors/eberl">Manuel Eberl</a>
+
+          </div>
+          <span class="date">Mar 20</span>
+        </article>
       <h2 class="head">2023</h2>
         <article class="entry">
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             <h5><a class="title" href="../../entries/HoareForDivergence.html">A Hoare Logic for Diverging Programs</a></h5>
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             <h5><a class="title" href="../../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</a></h5>
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           <span class="date">Nov 02</span>
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             <h5><a class="title" href="../../entries/Stream_Fusion_Code.html">Stream Fusion in HOL with Code Generation</a></h5>
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           <span class="date">Mar 11</span>
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           <span class="date">Jan 03</span>
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+          <title>Continued Fractions</title>
+          <link>/entries/Continued_Fractions.html</link>
+          <pubDate>Wed, 20 Mar 2024 00:00:00 +0000</pubDate>
+          <guid>/entries/Continued_Fractions.html</guid>
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+        <item>
           <title>A Hoare Logic for Diverging Programs</title>
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           <pubDate>Fri, 20 Jan 2023 00:00:00 +0000</pubDate>
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           <title>Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
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           <title>CryptHOL</title>
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+      <h2 class="head">2024</h2>
+        <article class="entry">
+          <div class="item-text">
+            <h5><a class="title" href="../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+            <br>
+              by <a href="../../authors/tan">Yong Kiam Tan</a> and <a href="../../authors/yang">Jiong Yang</a>
+
+          </div>
+          <span class="date">Mar 15</span>
+        </article>
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+      <h2 class="head">2024</h2>
+        <article class="entry">
+          <div class="item-text">
+            <h5><a class="title" href="../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+            <br>
+              by <a href="../../authors/tan">Yong Kiam Tan</a> and <a href="../../authors/yang">Jiong Yang</a>
+
+          </div>
+          <span class="date">Mar 15</span>
+        </article>
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diff --git a/web/dependencies/monad_normalisation/index.xml b/web/dependencies/monad_normalisation/index.xml
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+      <h2 class="head">2024</h2>
+        <article class="entry">
+          <div class="item-text">
+            <h5><a class="title" href="../../entries/Continued_Fractions.html">Continued Fractions</a></h5>
+            <br>
+              by <a href="../../authors/eberl">Manuel Eberl</a>
+
+          </div>
+          <span class="date">Mar 20</span>
+        </article>
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+            <br>
+              by <a href="../../authors/eberl">Manuel Eberl</a>
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+          </div>
+          <span class="date">Mar 20</span>
+        </article>
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             <h5><a class="title" href="../../entries/Fishers_Inequality.html">Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a></h5>
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\ No newline at end of file
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+          <pubDate>Wed, 20 Mar 2024 00:00:00 +0000</pubDate>
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           <title>Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</title>
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diff --git a/web/entries/Approximate_Model_Counting.html b/web/entries/Approximate_Model_Counting.html
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+    <meta name="description" content="Approximate model counting is the task of approximating the number of solutions to an input formula. This entry formalizes $\mathsf{ApproxMC}$, an...">
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+  <h1>
+    <span class='first'>A</span>pproximate <span class='first'>M</span>odel <span class='first'>C</span>ounting
+    
+  </h1>
+  <div>
+      <p>
+        <a href="../authors/tan">Yong Kiam Tan</a> <a class="obfuscated" data="eyJob3N0IjpbImNzIiwiY211IiwiZWR1Il0sInVzZXIiOlsieW9uZ2tpYXQiXX0=">📧</a> and <a href="../authors/yang">Jiong Yang</a> <a class="obfuscated" data="eyJob3N0IjpbImdtYWlsIiwiY29tIl0sInVzZXIiOlsiamlvbmd5YW5nY29iZSJdfQ==">📧</a>
+
+      </p>
+      <p class="date">March 15, 2024</p>
+  </div>
+</header>
+      <div>
+        
+  <main>
+    <h3>Abstract</h3>
+
+    <div class="abstract mathjax_process">Approximate model counting is the task of approximating the number of solutions
+to an input formula.  This entry formalizes $\mathsf{ApproxMC}$, an algorithm
+due to Chakraborty et al. with a
+probably approximately correct (PAC) guarantee, i.e., $\mathsf{ApproxMC}$
+returns a multiplicative $(1+\varepsilon)$-factor approximation of the model
+count with probability at least $1 - \delta$, where $\varepsilon > 0$ and $0 <
+\delta \leq 1$.  The algorithmic specification is further refined to a verified
+certificate checker that can be used to validate the results of untrusted
+$\mathsf{ApproxMC}$ implementations (assuming access to trusted randomness).</div>
+
+    <h3>License</h3>
+    <div>
+        <a href="https://isa-afp.org/LICENSE">BSD License</a>
+    </div>
+      <h3>Topics</h3>
+      <ul>
+          <li><a href="../topics/computer-science/algorithms/approximation">Computer science/Algorithms/Approximation</a></li>
+          <li><a href="../topics/computer-science/algorithms/randomized">Computer science/Algorithms/Randomized</a></li>
+      </ul>
+      <h3>Session Approximate_Model_Counting</h3>
+      <ul>
+          <li><a href="../sessions/approximate_model_counting/#ApproxMCPreliminaries">ApproxMCPreliminaries</a></li>
+          <li><a href="../sessions/approximate_model_counting/#RandomXOR">RandomXOR</a></li>
+          <li><a href="../sessions/approximate_model_counting/#RandomXORHashFamily">RandomXORHashFamily</a></li>
+          <li><a href="../sessions/approximate_model_counting/#ApproxMCCore">ApproxMCCore</a></li>
+          <li><a href="../sessions/approximate_model_counting/#ApproxMCCoreAnalysis">ApproxMCCoreAnalysis</a></li>
+          <li><a href="../sessions/approximate_model_counting/#ApproxMCAnalysis">ApproxMCAnalysis</a></li>
+          <li><a href="../sessions/approximate_model_counting/#CertCheck">CertCheck</a></li>
+          <li><a href="../sessions/approximate_model_counting/#CertCheck_CNF_XOR">CertCheck_CNF_XOR</a></li>
+      </ul>
+
+    <div class="flex-wrap">
+      <div>
+        <h3>Depends on</h3>
+        <ul class="horizontal-list">
+              <li><a href="../entries/Concentration_Inequalities.html">Concentration Inequalities</a></li>
+              <li><a href="../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></li>
+              <li><a href="../entries/Monad_Normalisation.html">Monad normalisation</a></li>
+        </ul>
+      </div>
+      </div>
+    
+  </main>
+
+  <nav class='links'>
+    <a class='popup-button' href="#cite-popup">Cite</a>
+    <a class='popup-button' href="#download-popup">Download</a>
+    <h4>PDFs</h4>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/outline.pdf">Proof outline</a>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/document.pdf">Proof document</a>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/session_graph.pdf">Dependencies</a>
+  </nav>
+
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+    <a class="cancel" href="#"></a>
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+      <h2>Cite</h2>
+      <a class="close" href="#">&times;</a>
+      <div>
+        <p style="display:none;" id="bibtex-filename">Approximate_Model_Counting-AFP</p>
+        <pre id="copy-text">@article{Approximate_Model_Counting-AFP,
+  author  = {Yong Kiam Tan and Jiong Yang},
+  title   = {Approximate Model Counting},
+  journal = {Archive of Formal Proofs},
+  month   = {March},
+  year    = {2024},
+  note    = {\url{https://isa-afp.org/entries/Approximate_Model_Counting.html},
+             Formal proof development},
+  ISSN    = {2150-914x},
+}</pre>
+        <button id="copy-bibtex">Copy</button> <a id="download-bibtex">Download</a>
+      </div>
+    </div>
+  </div>
+
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+      <a href="https://www.isa-afp.org/release/afp-Approximate_Model_Counting-current.tar.gz"
+         download>Download latest</a>
+    </div>
+  </div>
+        
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+</html>
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   <h1>
     <span class='first'>C</span>atoids, <span class='first'>C</span>ategories, <span class='first'>G</span>roupoids
     
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   <div>
       <p>
         <a href="../authors/struth">Georg Struth</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJnIiwic3RydXRoIl19">📧</a>
 
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       <p class="date">August 14, 2023</p>
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 </header>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This AFP entry formalises catoids, which are generalisations of
   single-set categories, and groupoids. More specifically, in catoids,
   the partial composition of arrows in a category is generalised to a
   multioperation, which sends pairs of elements to sets of elements,
   and the definedness condition of arrow composition -- two arrows can
   be composed if and only the target of the first matches the source
   of the second -- is relaxed. Beyond a library of basic laws for
   catoids, single-set categories and groupoids, I formalise the facts
   that every catoid can be lifted to a modal powerset quantale, that
   every groupoid can be lifted to a Dedekind quantale and to power set
   relation algebras, a special case of a famous result of Jónsson and
   Tarski. Finally, I show that single-set categories are equivalent to
   a standard axiomatisation of categories based on a set of objects
   and a set of arrows, and compare catoids with related structures
   such as multimonoid and relational monoids (monoids in the monoidal
   category Rel).</div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li>
           <li><a href="../topics/mathematics/category-theory">Mathematics/Category theory</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
         <li>Cranch, J., Doherty, S., &amp; Struth, G. (2020). <i>Convolution and Concurrency</i> (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2002.02321
         </li>
         <li>Calk, C., Fahrenberg, U., Johansen, C., Struth, G., & Ziemiański, K. (2021). $$\ell r$$-Multisemigroups, Modal Quantales and the Origin of Locality. Lecture Notes in Computer Science, 90–107. <a href="https://doi.org/10.1007/978-3-030-88701-8_6">https://doi.org/10.1007/978-3-030-88701-8_6</a>
 
         </li>
         <li>Fahrenberg, U., Johansen, C., Struth, G., & Ziemiański, K. (2023). Catoids and modal convolution algebras. Algebra Universalis, 84(2). <a href="https://doi.org/10.1007/s00012-023-00805-9">https://doi.org/10.1007/s00012-023-00805-9</a>
 
         </li>
-        <li>Calk, C., Malbos, P., Pous, D., &amp; Struth, G. (2023). <i>Higher Catoids, Higher Quantales and their Correspondences</i> (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2307.09253
+        <li>Calk, C., Malbos, P., Pous, D., &amp; Struth, G. (2023). <i>Higher Catoids, Higher Quantales and their Correspondences</i> (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2307.09253
         </li>
       </ul>
       <h3>Session Catoids</h3>
       <ul>
           <li><a href="../sessions/catoids/#Catoid">Catoid</a></li>
           <li><a href="../sessions/catoids/#Groupoid">Groupoid</a></li>
           <li><a href="../sessions/catoids/#Catoid_Lifting">Catoid_Lifting</a></li>
           <li><a href="../sessions/catoids/#Groupoid_Lifting">Groupoid_Lifting</a></li>
           <li><a href="../sessions/catoids/#Multimonoid">Multimonoid</a></li>
       </ul>
 
     <div class="flex-wrap">
       <div>
         <h3>Depends on</h3>
         <ul class="horizontal-list">
               <li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li>
               <li><a href="../entries/Quantales.html">Quantales</a></li>
               <li><a href="../entries/Quantales_Converse.html">Modal quantales, involutive quantales, Dedekind Quantales</a></li>
               <li><a href="../entries/Relation_Algebra.html">Relation Algebra</a></li>
         </ul>
       </div>
       <div>
         <h3>Used by</h3>
         <ul class="horizontal-list">
             <li>
               <a href="../entries/CubicalCategories.html">Cubical Categories</a>
             </li>
             <li>
               <a href="../entries/OmegaCatoidsQuantales.html">Higher Globular Catoids and Quantales</a>
             </li>
         </ul>
       </div>
       </div>
     
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     <h4>PDFs</h4>
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         <p style="display:none;" id="bibtex-filename">Catoids-AFP</p>
         <pre id="copy-text">@article{Catoids-AFP,
   author  = {Georg Struth},
   title   = {Catoids, Categories, Groupoids},
   journal = {Archive of Formal Proofs},
   month   = {August},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Catoids.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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             <li>
               <a href="https://www.isa-afp.org/release/afp-Catoids-2023-09-13.tar.gz">
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               : Isabelle2023
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diff --git a/web/entries/Coinductive.html b/web/entries/Coinductive.html
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   <h1>
     <span class='first'>C</span>oinductive
     
   </h1>
   <div>
       <p>
         <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
 
           with contributions from
           <a href="../authors/hoelzl">Johannes Hölzl</a> <a class="obfuscated" data="eyJob3N0IjpbImluIiwidHVtIiwiZGUiXSwidXNlciI6WyJob2VsemwiXX0=">📧</a>
 
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       <p class="date">February 12, 2010</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This article collects formalisations of general-purpose coinductive data types and sets. Currently, it contains coinductive natural numbers, coinductive lists, i.e. lazy lists or streams, infinite streams, coinductive terminated lists, coinductive resumptions, a library of operations on coinductive lists, and a version of König's lemma as an application for coinductive lists.<br>The initial theory was contributed by Paulson and Wenzel. Extensions and other coinductive formalisations of general interest are welcome.</div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>History</h3>
       <dl>
         <dt>April 3, 2014</dt>
         <dd>ccpo structure on codatatypes used to define ldrop, ldropWhile, lfilter, lconcat as least fixpoint;
 ccpo topology on coinductive lists contributed by Johannes Hölzl;
 added examples
 (revision 23cd8156bd42)<br></dd>
         <dt>September 20, 2013</dt>
         <dd>stream theory uses type and operations from HOL/BNF/Examples/Stream
 (revision 692809b2b262)<br>
 </dd>
         <dt>March 13, 2013</dt>
         <dd>construct codatatypes with the BNF package and adjust the definitions and proofs,
 setup for lifting and transfer packages
 (revision f593eda5b2c0)<br>
 </dd>
         <dt>June 27, 2012</dt>
         <dd>new codatatype stream with operations (with contributions by Peter Gammie)
 (revision dd789a56473c)<br>
 </dd>
         <dt>July 20, 2011</dt>
         <dd>new codatatype resumption
 (revision 811364c776c7)<br>
 </dd>
         <dt>February 1, 2011</dt>
         <dd>lazy implementation of coinductive (terminated) lists for the code generator
 (revision 6034973dce83)<br>
 </dd>
         <dt>August 17, 2010</dt>
         <dd>Koenig's lemma as an example application for coinductive lists
 (revision f81ce373fa96)<br>
 </dd>
         <dt>August 4, 2010</dt>
         <dd>terminated lazy lists: setup for quotient package;
 more lemmas
 (revision 6ead626f1d01)<br>
 </dd>
         <dt>June 28, 2010</dt>
         <dd>new codatatype terminated lazy lists
 (revision e12de475c558)<br>
 </dd>
         <dt>June 10, 2010</dt>
         <dd>coinductive lists: setup for quotient package
 (revision 015574f3bf3c)<br>
 </dd>
       </dl>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/computer-science/functional-programming">Computer science/Functional programming</a></li>
       </ul>
       <h3>Session Coinductive</h3>
       <ul>
           <li><a href="../sessions/coinductive/#Coinductive_Nat">Coinductive_Nat</a></li>
           <li><a href="../sessions/coinductive/#Coinductive_List">Coinductive_List</a></li>
           <li><a href="../sessions/coinductive/#Coinductive_List_Prefix">Coinductive_List_Prefix</a></li>
           <li><a href="../sessions/coinductive/#Coinductive_Stream">Coinductive_Stream</a></li>
           <li><a href="../sessions/coinductive/#TLList">TLList</a></li>
           <li><a href="../sessions/coinductive/#Quotient_Coinductive_List">Quotient_Coinductive_List</a></li>
           <li><a href="../sessions/coinductive/#Quotient_TLList">Quotient_TLList</a></li>
           <li><a href="../sessions/coinductive/#Coinductive">Coinductive</a></li>
           <li><a href="../sessions/coinductive/#Lazy_LList">Lazy_LList</a></li>
           <li><a href="../sessions/coinductive/#Lazy_TLList">Lazy_TLList</a></li>
           <li><a href="../sessions/coinductive/#CCPO_Topology">CCPO_Topology</a></li>
           <li><a href="../sessions/coinductive/#LList_CCPO_Topology">LList_CCPO_Topology</a></li>
           <li><a href="../sessions/coinductive/#TLList_CCPO">TLList_CCPO</a></li>
           <li><a href="../sessions/coinductive/#TLList_CCPO_Examples">TLList_CCPO_Examples</a></li>
           <li><a href="../sessions/coinductive/#Koenigslemma">Koenigslemma</a></li>
           <li><a href="../sessions/coinductive/#LMirror">LMirror</a></li>
           <li><a href="../sessions/coinductive/#Hamming_Stream">Hamming_Stream</a></li>
           <li><a href="../sessions/coinductive/#Resumption">Resumption</a></li>
           <li><a href="../sessions/coinductive/#Coinductive_Examples">Coinductive_Examples</a></li>
       </ul>
 
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       <div>
         <h3>Used by</h3>
         <ul class="horizontal-list">
             <li>
+              <a href="../entries/Continued_Fractions.html">Continued Fractions</a>
+            </li>
+            <li>
               <a href="../entries/HoareForDivergence.html">A Hoare Logic for Diverging Programs</a>
             </li>
             <li>
               <a href="../entries/Partial_Order_Reduction.html">Partial Order Reduction</a>
             </li>
             <li>
               <a href="../entries/CakeML.html">CakeML</a>
             </li>
             <li>
               <a href="../entries/Ordered_Resolution_Prover.html">Formalization of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a>
             </li>
             <li>
               <a href="../entries/DynamicArchitectures.html">Dynamic Architectures</a>
             </li>
             <li>
               <a href="../entries/CryptHOL.html">CryptHOL</a>
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             <li>
               <a href="../entries/Parity_Game.html">Positional Determinacy of Parity Games</a>
             </li>
             <li>
               <a href="../entries/Stream_Fusion_Code.html">Stream Fusion in HOL with Code Generation</a>
             </li>
             <li>
               <a href="../entries/Probabilistic_Noninterference.html">Probabilistic Noninterference</a>
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               <a href="../entries/Markov_Models.html">Markov Models</a>
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               <a href="../entries/JinjaThreads.html">Jinja with Threads</a>
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         <p style="display:none;" id="bibtex-filename">Coinductive-AFP</p>
         <pre id="copy-text">@article{Coinductive-AFP,
   author  = {Andreas Lochbihler},
   title   = {Coinductive},
   journal = {Archive of Formal Proofs},
   month   = {February},
   year    = {2010},
   note    = {\url{https://isa-afp.org/entries/Coinductive.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2013-03-02.tar.gz">
                 Mar 2, 2013
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               : Isabelle2013
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2013-02-16.tar.gz">
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2011-02-11.tar.gz">
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               : Isabelle2011
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2010-06-30.tar.gz">
                 Jun 30, 2010
               </a>
               : Isabelle2009-2
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2010-02-15.tar.gz">
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               <a href="https://www.isa-afp.org/release/afp-Coinductive-2010-02-14.tar.gz">
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               : Isabelle2009-1
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\ No newline at end of file
diff --git a/web/entries/Combinatorics_Words.html b/web/entries/Combinatorics_Words.html
--- a/web/entries/Combinatorics_Words.html
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   <h1>
     <span class='first'>C</span>ombinatorics on <span class='first'>W</span>ords <span class='first'>B</span>asics
     
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       <p>
         <a href="../authors/holub">Štěpán Holub</a> <a href="https://www2.karlin.mff.cuni.cz/~holub/">🌐</a>, <a href="../authors/raska">Martin Raška</a> and <a href="../authors/starosta">Štěpán Starosta</a> <a href="https://staroste.pages.fit/">🌐</a>
 
       </p>
       <p class="date">May 24, 2021</p>
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 </header>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">We formalize basics of Combinatorics on Words. This is an extension of
 existing theories on lists. We provide additional properties related
 to prefix, suffix, factor, length and rotation. The topics include
 prefix and suffix comparability, mismatch, word power, total and
 reversed morphisms, border, periods, primitivity and roots. We also
 formalize basic, mostly folklore results related to word equations:
 equidivisibility, commutation and conjugation. Slightly advanced
 properties include the Periodicity lemma (often cited as the Fine and
 Wilf theorem) and the variant of the Lyndon-Schützenberger theorem for
 words, including its full parametric solution. We support the algebraic point of view which sees words as generators of submonoids of a free monoid. This leads to the concepts of the (free) hull, the (free) basis (or code). We also provide relevant proof methods and a tool to generate reverse-symmetric claims.</div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>History</h3>
       <dl>
         <dt>August 17, 2023</dt>
         <dd>Updated to version v1.10.1.
 </dd>
         <dt>August 24, 2022</dt>
         <dd>Many updates and additions. New theories: Border_Array, Morphisms, Equations_Basic, and Binary_Code_Morphisms.
 </dd>
       </dl>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/computer-science/automata-and-formal-languages">Computer science/Automata and formal languages</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Holub, Š., &amp; Starosta, Š. (2021). <i>Formalization of Basic Combinatorics on Words</i>. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITP.2021.22
+        <li>Holub, Š., &amp; Starosta, Š. (2021). Formalization of Basic Combinatorics on Words. <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.ITP.2021.22
         </li>
         <li><a href="https://arxiv.org/abs/2104.11622">Producing symmetrical facts for lists induced by the list reversal mapping in Isabelle/HOL</a>
         </li>
         <li><a  href="https://gitlab.com/formalcow/combinatorics-on-words-formalized">Development repository</a>
         </li>
       </ul>
       <h3>Session Combinatorics_Words</h3>
       <ul>
           <li><a href="../sessions/combinatorics_words/#Arithmetical_Hints">Arithmetical_Hints</a></li>
           <li><a href="../sessions/combinatorics_words/#Reverse_Symmetry">Reverse_Symmetry</a></li>
           <li><a href="../sessions/combinatorics_words/#CoWBasic">CoWBasic</a></li>
           <li><a href="../sessions/combinatorics_words/#Border_Array">Border_Array</a></li>
           <li><a href="../sessions/combinatorics_words/#Submonoids">Submonoids</a></li>
           <li><a href="../sessions/combinatorics_words/#Morphisms">Morphisms</a></li>
           <li><a href="../sessions/combinatorics_words/#Periodicity_Lemma">Periodicity_Lemma</a></li>
           <li><a href="../sessions/combinatorics_words/#Lyndon_Schutzenberger">Lyndon_Schutzenberger</a></li>
           <li><a href="../sessions/combinatorics_words/#Binary_Code_Morphisms">Binary_Code_Morphisms</a></li>
           <li><a href="../sessions/combinatorics_words/#Equations_Basic">Equations_Basic</a></li>
       </ul>
 
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         <h3>Used by</h3>
         <ul class="horizontal-list">
             <li>
               <a href="../entries/Binary_Code_Imprimitive.html">Binary codes that do not preserve primitivity</a>
             </li>
             <li>
               <a href="../entries/Two_Generated_Word_Monoids_Intersection.html">Intersection of two monoids generated by two element codes</a>
             </li>
             <li>
               <a href="../entries/Combinatorics_Words_Graph_Lemma.html">Graph Lemma</a>
             </li>
             <li>
               <a href="../entries/Combinatorics_Words_Lyndon.html">Lyndon words</a>
             </li>
         </ul>
       </div>
       </div>
     
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         <p style="display:none;" id="bibtex-filename">Combinatorics_Words-AFP</p>
         <pre id="copy-text">@article{Combinatorics_Words-AFP,
   author  = {Štěpán Holub and Martin Raška and Štěpán Starosta},
   title   = {Combinatorics on Words Basics},
   journal = {Archive of Formal Proofs},
   month   = {May},
   year    = {2021},
   note    = {\url{https://isa-afp.org/entries/Combinatorics_Words.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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             <li>
               <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2023-09-13.tar.gz">
                 Sep 13, 2023
               </a>
               : Isabelle2023
             </li>
             <li>
               <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2022-10-27.tar.gz">
                 Oct 27, 2022
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               : Isabelle2022
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               <a href="https://www.isa-afp.org/release/afp-Combinatorics_Words-2021-12-14.tar.gz">
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\ No newline at end of file
diff --git a/web/entries/Continued_Fractions.html b/web/entries/Continued_Fractions.html
new file mode 100644
--- /dev/null
+++ b/web/entries/Continued_Fractions.html
@@ -0,0 +1,243 @@
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+    <meta name="description" content="This article provides a formalisation of continued fractions of real numbers and their basic properties. It also contains a proof of the classic result...">
+
+  <meta property="og:title" content="Continued Fractions" />
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+  <h1>
+    <span class='first'>C</span>ontinued <span class='first'>F</span>ractions
+    
+  </h1>
+  <div>
+      <p>
+        <a href="../authors/eberl">Manuel Eberl</a> <a class="obfuscated" data="eyJob3N0IjpbInBydXZpc3RvIiwib3JnIl0sInVzZXIiOlsibWFudWVsIl19">📧</a>
+
+      </p>
+      <p class="date">March 20, 2024</p>
+  </div>
+</header>
+      <div>
+        
+  <main>
+    <h3>Abstract</h3>
+
+    <div class="abstract mathjax_process"><p>This article provides a formalisation of continued fractions of real numbers and their basic properties.
+It also contains a proof of the classic result that the irrational numbers with periodic continued
+ fraction expansions are precisely the quadratic irrationals, i.e. real numbers that fulfil a non-trivial quadratic equation $a x^2 + b x + c = 0$ with integer coefficients.</p>
+<p>
+Particular attention is given to the continued fraction expansion of $\sqrt{D}$ for a non-square
+ natural number $D$. Basic results about the length and structure of its period are provided,
+ along with an executable algorithm to compute the period (and from it, the entire expansion).</p>
+<p>
+This is then also used to provide a fairly efficient, executable, and fully formalised algorithm to
+compute solutions to Pell's equation $x^2 - D y^2 = 1$. The performance is sufficiently good to
+find the solution to Archimedes's cattle problem in less than a second on a typical computer.
+This involves the value $D = 410286423278424$, for which the solution has over 200000 decimals.</p>
+<p>
+Lastly, a derivation of the continued fraction expansions of Euler's number $e$ and an executable
+function to compute continued fraction expansions using interval arithmetic is also provided.</p></div>
+
+    <h3>License</h3>
+    <div>
+        <a href="https://isa-afp.org/LICENSE">BSD License</a>
+    </div>
+      <h3>Topics</h3>
+      <ul>
+          <li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li>
+      </ul>
+      <h3>Session Continued_Fractions</h3>
+      <ul>
+          <li><a href="../sessions/continued_fractions/#Continued_Fractions">Continued_Fractions</a></li>
+          <li><a href="../sessions/continued_fractions/#Quadratic_Irrationals">Quadratic_Irrationals</a></li>
+          <li><a href="../sessions/continued_fractions/#E_CFrac">E_CFrac</a></li>
+          <li><a href="../sessions/continued_fractions/#Sqrt_Nat_Cfrac">Sqrt_Nat_Cfrac</a></li>
+          <li><a href="../sessions/continued_fractions/#Pell_Lifting">Pell_Lifting</a></li>
+          <li><a href="../sessions/continued_fractions/#Pell_Continued_Fraction">Pell_Continued_Fraction</a></li>
+          <li><a href="../sessions/continued_fractions/#Pell_Continued_Fraction_Tests">Pell_Continued_Fraction_Tests</a></li>
+          <li><a href="../sessions/continued_fractions/#Continued_Fraction_Approximation">Continued_Fraction_Approximation</a></li>
+      </ul>
+
+    <div class="flex-wrap">
+      <div>
+        <h3>Depends on</h3>
+        <ul class="horizontal-list">
+              <li><a href="../entries/Coinductive.html">Coinductive</a></li>
+              <li><a href="../entries/Pell.html">Pell&rsquo;s Equation</a></li>
+              <li><a href="../entries/Polynomial_Factorization.html">Polynomial Factorization</a></li>
+        </ul>
+      </div>
+        <div>
+          <h3>Auto-related entries</h3>
+          <ul class="horizontal-list">
+              <li><a href="../entries/Factor_Algebraic_Polynomial.html">Factorization of Polynomials with Algebraic Coefficients</a></li>
+              <li><a href="../entries/Interval_Arithmetic_Word32.html">Interval Arithmetic on 32-bit Words</a></li>
+          </ul>
+        </div>
+      </div>
+    
+  </main>
+
+  <nav class='links'>
+    <a class='popup-button' href="#cite-popup">Cite</a>
+    <a class='popup-button' href="#download-popup">Download</a>
+    <h4>PDFs</h4>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/outline.pdf">Proof outline</a>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/document.pdf">Proof document</a>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/session_graph.pdf">Dependencies</a>
+  </nav>
+
+  <div id="cite-popup" class="overlay">
+    <a class="cancel" href="#"></a>
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+      <h2>Cite</h2>
+      <a class="close" href="#">&times;</a>
+      <div>
+        <p style="display:none;" id="bibtex-filename">Continued_Fractions-AFP</p>
+        <pre id="copy-text">@article{Continued_Fractions-AFP,
+  author  = {Manuel Eberl},
+  title   = {Continued Fractions},
+  journal = {Archive of Formal Proofs},
+  month   = {March},
+  year    = {2024},
+  note    = {\url{https://isa-afp.org/entries/Continued_Fractions.html},
+             Formal proof development},
+  ISSN    = {2150-914x},
+}</pre>
+        <button id="copy-bibtex">Copy</button> <a id="download-bibtex">Download</a>
+      </div>
+    </div>
+  </div>
+
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+         download>Download latest</a>
+    </div>
+  </div>
+        
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+</html>
\ No newline at end of file
diff --git a/web/entries/Efficient_Weighted_Path_Order.html b/web/entries/Efficient_Weighted_Path_Order.html
--- a/web/entries/Efficient_Weighted_Path_Order.html
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     <title>A Verified Efficient Implementation of the Weighted Path Order - Archive of Formal Proofs</title>
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   <h1>
     <span class='first'>A</span> <span class='first'>V</span>erified <span class='first'>E</span>fficient <span class='first'>I</span>mplementation of the <span class='first'>W</span>eighted <span class='first'>P</span>ath <span class='first'>O</span>rder
     
   </h1>
   <div>
       <p>
         <a href="../authors/thiemann">René Thiemann</a> <a href="http://cl-informatik.uibk.ac.at/users/thiemann/">🌐</a> and <a href="../authors/wenninger">Elias Wenninger</a>
 
       </p>
       <p class="date">June 1, 2023</p>
   </div>
 </header>
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   <main>
     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process"><p>The Weighted Path Order (WPO) of Yamada is a powerful technique for proving
 termination. In a previous AFP entry, the WPO was defined and properties of WPO
 have been formally verified. However, the implementation of WPO was naive,
 leading to an exponential runtime in the worst case.
 </p><p>
 Therefore, in this AFP entry we provide a poly-time implementation of WPO. The
 implementation is based on memoization. Since WPO generalizes the recursive path
 order (RPO), we also easily derive an efficient implementation of RPO.
 </p></div>
 
     <h3>License</h3>
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         <a href="https://isa-afp.org/LICENSE">BSD License</a>
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       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/logic/rewriting">Logic/Rewriting</a></li>
           <li><a href="../topics/computer-science/algorithms">Computer science/Algorithms</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Thiemann, R., Schöpf, J., Sternagel, C., &amp; Yamada, A. (2020). <i>Certifying the Weighted Path Order (Invited Talk)</i>. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.FSCD.2020.4
+        <li>Thiemann, R., Schöpf, J., Sternagel, C., &amp; Yamada, A. (2020). Certifying the Weighted Path Order (Invited Talk). <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.FSCD.2020.4
         </li>
         <li>Yamada, A., Kusakari, K., & Sakabe, T. (2015). A unified ordering for termination proving. Science of Computer Programming, 111, 110–134. <a href="https://doi.org/10.1016/j.scico.2014.07.009">https://doi.org/10.1016/j.scico.2014.07.009</a>
 
         </li>
       </ul>
       <h3>Session Efficient_Weighted_Path_Order</h3>
       <ul>
           <li><a href="../sessions/efficient_weighted_path_order/#Indexed_Term">Indexed_Term</a></li>
           <li><a href="../sessions/efficient_weighted_path_order/#List_Memo_Functions">List_Memo_Functions</a></li>
           <li><a href="../sessions/efficient_weighted_path_order/#WPO_Approx">WPO_Approx</a></li>
           <li><a href="../sessions/efficient_weighted_path_order/#WPO_Mem_Impl">WPO_Mem_Impl</a></li>
           <li><a href="../sessions/efficient_weighted_path_order/#RPO_Unbounded">RPO_Unbounded</a></li>
           <li><a href="../sessions/efficient_weighted_path_order/#RPO_Mem_Impl">RPO_Mem_Impl</a></li>
       </ul>
 
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         <h3>Depends on</h3>
         <ul class="horizontal-list">
               <li><a href="../entries/Weighted_Path_Order.html">A Formalization of Weighted Path Orders and Recursive Path Orders</a></li>
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         <p style="display:none;" id="bibtex-filename">Efficient_Weighted_Path_Order-AFP</p>
         <pre id="copy-text">@article{Efficient_Weighted_Path_Order-AFP,
   author  = {René Thiemann and Elias Wenninger},
   title   = {A Verified Efficient Implementation of the Weighted Path Order},
   journal = {Archive of Formal Proofs},
   month   = {June},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Efficient_Weighted_Path_Order.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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                 Sep 13, 2023
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diff --git a/web/entries/Go.html b/web/entries/Go.html
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+    <title>Go Code Generation for Isabelle - Archive of Formal Proofs</title>
+    <meta name="description" content="This entry contains a standalone code generation target for the Go programming language.
+Unlike the previous targets, Go is not a functional language and...">
+
+  <meta property="og:title" content="Go Code Generation for Isabelle" />
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+        <datalist id="autocomplete">
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+  <h1>
+    <span class='first'>G</span>o <span class='first'>C</span>ode <span class='first'>G</span>eneration for <span class='first'>I</span>sabelle
+    
+  </h1>
+  <div>
+      <p>
+        <a href="../authors/stuebinger">Terru Stübinger</a> <a href="https://stuebinm.eu/">🌐</a> and <a href="../authors/hupel">Lars Hupel</a> <a href="https://lars.hupel.info/">🌐</a>
+
+      </p>
+      <p class="date">January 22, 2024</p>
+  </div>
+</header>
+      <div>
+        
+  <main>
+    <h3>Abstract</h3>
+
+    <div class="abstract mathjax_process">This entry contains a standalone code generation target for the Go programming language.
+Unlike the previous targets, Go is not a functional language and encourages code in an imperative style, thus many of the features of Isabelle's language (particularly data types, pattern matching, and type classes) have to be emulated using imperative language constructs in Go.
+To generate Go code, users can simply import this entry, which makes the Go target available.</div>
+
+    <h3>License</h3>
+    <div>
+        <a href="https://isa-afp.org/LICENSE">BSD License</a>
+    </div>
+      <h3>Topics</h3>
+      <ul>
+          <li><a href="../topics/tools">Tools</a></li>
+      </ul>
+      <h3>Related publications</h3>
+      <ul>
+        <li>Stübinger, T., &amp; Hupel, L. (2023). <i>Extending Isabelle/HOL's Code Generator with support for the Go programming language</i> (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2310.02704
+        </li>
+        <li>Lars Hupel, &amp; terru. (2024). <i>isabelle-prover/isabelle-go-codegen: v0.2.1</i> (Version v0.2.1) [Computer software]. Zenodo. https://doi.org/10.5281/ZENODO.8401392
+        </li>
+      </ul>
+      <h3>Session Go</h3>
+      <ul>
+          <li><a href="../sessions/go/#Go_Setup">Go_Setup</a></li>
+      </ul>
+      <h3>Session Go_Test_Quick</h3>
+      <ul>
+          <li><a href="../sessions/go_test_quick/#RBT_Test">RBT_Test</a></li>
+      </ul>
+      <h3>Session Go_Test_Slow</h3>
+      <ul>
+          <li><a href="../sessions/go_test_slow/#Candidates">Candidates</a></li>
+          <li><a href="../sessions/go_test_slow/#Generate">Generate</a></li>
+          <li><a href="../sessions/go_test_slow/#Generate_Binary_Nat">Generate_Binary_Nat</a></li>
+      </ul>
+
+    <div class="flex-wrap">
+      </div>
+    
+  </main>
+
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+    <h4>PDFs</h4>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Go/outline.pdf">Proof outline</a>
+    <a href="https://www.isa-afp.org/browser_info/current/AFP/Go/document.pdf">Proof document</a>
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+        <p style="display:none;" id="bibtex-filename">Go-AFP</p>
+        <pre id="copy-text">@article{Go-AFP,
+  author  = {Terru Stübinger and Lars Hupel},
+  title   = {Go Code Generation for Isabelle},
+  journal = {Archive of Formal Proofs},
+  month   = {January},
+  year    = {2024},
+  note    = {\url{https://isa-afp.org/entries/Go.html},
+             Formal proof development},
+  ISSN    = {2150-914x},
+}</pre>
+        <button id="copy-bibtex">Copy</button> <a id="download-bibtex">Download</a>
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+      <a href="https://www.isa-afp.org/release/afp-Go-current.tar.gz"
+         download>Download latest</a>
+    </div>
+  </div>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/entries/HoareForDivergence.html b/web/entries/HoareForDivergence.html
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   <h1>
     <span class='first'>A</span> <span class='first'>H</span>oare <span class='first'>L</span>ogic for <span class='first'>D</span>iverging <span class='first'>P</span>rograms
     
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   <div>
       <p>
         <a href="../authors/pohjola">Johannes Åman Pohjola</a> <a class="obfuscated" data="eyJob3N0IjpbInVuc3ciLCJlZHUiLCJhdSJdLCJ1c2VyIjpbImoiLCJhbWFucG9oam9sYSJdfQ==">📧</a>, <a href="../authors/myreen">Magnus O. Myreen</a> <a class="obfuscated" data="eyJob3N0IjpbImNoYWxtZXJzIiwic2UiXSwidXNlciI6WyJteXJlZW4iXX0=">📧</a> and <a href="../authors/tanaka">Miki Tanaka</a> <a class="obfuscated" data="eyJob3N0IjpbInVuc3ciLCJlZHUiLCJhdSJdLCJ1c2VyIjpbIm1pa2kiLCJ0YW5ha2EiXX0=">📧</a>
 
       </p>
       <p class="date">January 20, 2023</p>
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   <main>
     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This submission contains:
 <ol>
 <li> a formalisation of a small While language with support for output;</li>
 <li> a standard total-correctness Hoare logic that has been proved sound and complete; and</li>
 <li> a new Hoare logic for proofs about programs that diverge: this new logic has also been proved sound and complete.</li>
 </ol></div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Åman Pohjola, J., Rostedt, H., &amp; Myreen, M. O. (2019). <i>Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs</i> (Version 1.0). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITP.2019.32
+        <li>Åman Pohjola, J., Rostedt, H., &amp; Myreen, M. O. (2019). Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs. <i>Schloss Dagstuhl - Leibniz-Zentrum Fuer Informatik GmbH, Wadern/Saarbruecken, Germany</i>. https://doi.org/10.4230/LIPICS.ITP.2019.32
         </li>
       </ul>
       <h3>Session HoareForDivergence</h3>
       <ul>
           <li><a href="../sessions/hoarefordivergence/#MiscLemmas">MiscLemmas</a></li>
           <li><a href="../sessions/hoarefordivergence/#WhileLang">WhileLang</a></li>
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           <li><a href="../sessions/hoarefordivergence/#WhileLangLemmas">WhileLangLemmas</a></li>
           <li><a href="../sessions/hoarefordivergence/#StdLogicSoundness">StdLogicSoundness</a></li>
           <li><a href="../sessions/hoarefordivergence/#CoinductiveLemmas">CoinductiveLemmas</a></li>
           <li><a href="../sessions/hoarefordivergence/#DivLogic">DivLogic</a></li>
           <li><a href="../sessions/hoarefordivergence/#StdLogicCompleteness">StdLogicCompleteness</a></li>
           <li><a href="../sessions/hoarefordivergence/#DivLogicCompleteness">DivLogicCompleteness</a></li>
           <li><a href="../sessions/hoarefordivergence/#DivLogicSoundness">DivLogicSoundness</a></li>
           <li><a href="../sessions/hoarefordivergence/#Examples">Examples</a></li>
       </ul>
 
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               <li><a href="../entries/Coinductive.html">Coinductive</a></li>
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         <p style="display:none;" id="bibtex-filename">HoareForDivergence-AFP</p>
         <pre id="copy-text">@article{HoareForDivergence-AFP,
   author  = {Johannes Åman Pohjola and Magnus O. Myreen and Miki Tanaka},
   title   = {A Hoare Logic for Diverging Programs},
   journal = {Archive of Formal Proofs},
   month   = {January},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/HoareForDivergence.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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   <h1>
     <span class='first'>F</span>ormalization of <span class='first'>H</span>yper <span class='first'>H</span>oare <span class='first'>L</span>ogic: <span class='first'>A</span> <span class='first'>L</span>ogic to (<span class='first'>D</span>is-)<span class='first'>P</span>rove <span class='first'>P</span>rogram <span class='first'>H</span>yperproperties
     
   </h1>
   <div>
       <p>
         <a href="../authors/dardinier">Thibault Dardinier</a> <a class="obfuscated" data="eyJob3N0IjpbImluZiIsImV0aHoiLCJjaCJdLCJ1c2VyIjpbInRoaWJhdWx0IiwiZGFyZGluaWVyIl19">📧</a>
 
       </p>
       <p class="date">April 3, 2023</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (so-called trace properties, such as functional correctness). On the one hand, Hoare logic has been generalized to prove properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic [8]), by proving the existence of (bad combinations of) executions. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre- and post-state for functional properties or pairs of pre- and post-states for non-interference.
 
 In this entry, we formalize Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. The resulting logic is simple yet expressive: its judgments can express arbitrary trace- and hyperproperties over the terminating executions of a program. By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic. In fact, we prove that Hyper Hoare Logic subsumes the properties handled by numerous existing correctness and incorrectness logics, and can express hyperproperties that no existing Hoare logic can. We also prove that Hyper Hoare Logic is sound and complete.</div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/computer-science/programming-languages/logics">Computer science/Programming languages/Logics</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Dardinier, T., &amp; Müller, P. (2023). <i>Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)</i> (Version 3). arXiv. https://doi.org/10.48550/ARXIV.2301.10037
+        <li>Dardinier, T., &amp; Müller, P. (2023). <i>Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)</i> (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2301.10037
         </li>
       </ul>
       <h3>Session HyperHoareLogic</h3>
       <ul>
           <li><a href="../sessions/hyperhoarelogic/#Language">Language</a></li>
           <li><a href="../sessions/hyperhoarelogic/#Logic">Logic</a></li>
           <li><a href="../sessions/hyperhoarelogic/#Examples">Examples</a></li>
           <li><a href="../sessions/hyperhoarelogic/#ProgramHyperproperties">ProgramHyperproperties</a></li>
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         <pre id="copy-text">@article{HyperHoareLogic-AFP,
   author  = {Thibault Dardinier},
   title   = {Formalization of Hyper Hoare Logic: A Logic to (Dis-)Prove Program Hyperproperties},
   journal = {Archive of Formal Proofs},
   month   = {April},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/HyperHoareLogic.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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   <h1>
     <span class='first'>H</span>ypergraph <span class='first'>C</span>olouring <span class='first'>B</span>ounds
     
   </h1>
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       <p>
         <a href="../authors/edmonds">Chelsea Edmonds</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJjbGU0NyJdfQ==">📧</a> and <a href="../authors/paulson">Lawrence C. Paulson</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJscDE1Il19">📧</a>
 
       </p>
       <p class="date">September 23, 2023</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This library includes several example applications of the probabilistic method for combinatorics to establish bounds for hypergraph colourings. This focuses on Property B - the existence of a two-colouring of the vertex set of a hypergraph. A stricter bound was formalised using the Lov&aacutesz local lemma, which in turn required a surprisingly complex proof of the mutual independence principle for hypergraph edges that is often omitted on paper. The formalisation uncovered several interesting examples of circular intuition on proofs involving independence on paper. The formalisation is based on the textbook proofs from Alon and Spencer's famous textbook, <em>The Probabilistic Method</em>, further supported by notes by Zhao. The mutual independence principle proof is inspired by the less precise proof provided in Molloy and Reed's textbook on graph colourings, as it was omitted in all other sources. Additionally, this library demonstrates how locales can be used to establish a reusable probability space framework, thus minimizing the setup required for future formalisations requiring a probability space on numerous possible properties around an incidence system's vertex set.</div>
 
     <h3>License</h3>
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         <a href="https://isa-afp.org/LICENSE">BSD License</a>
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       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li>
           <li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Molloy, M., & Reed, B. (2002). Graph Colouring and the Probabilistic Method. In Algorithms and Combinatorics. Springer Berlin Heidelberg. <a href="https://doi.org/10.1007/978-3-642-04016-0">https://doi.org/10.1007/978-3-642-04016-0</a>
+        <li>Molloy, M., & Reed, B. (2002). Graph Colouring and the Probabilistic Method. Algorithms and Combinatorics. <a href="https://doi.org/10.1007/978-3-642-04016-0">https://doi.org/10.1007/978-3-642-04016-0</a>
 
         </li>
         <li>https://dl.acm.org/doi/book/10.5555/3002498
         </li>
         <li>https://yufeizhao.com/pm/probmethod_notes.pdf
         </li>
       </ul>
       <h3>Session Hypergraph_Colourings</h3>
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           <li><a href="../sessions/hypergraph_colourings/#Hypergraph_Colourings">Hypergraph_Colourings</a></li>
           <li><a href="../sessions/hypergraph_colourings/#Basic_Bounds_Application">Basic_Bounds_Application</a></li>
           <li><a href="../sessions/hypergraph_colourings/#LLL_Applications">LLL_Applications</a></li>
           <li><a href="../sessions/hypergraph_colourings/#Hypergraph_Colourings_Root">Hypergraph_Colourings_Root</a></li>
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               <li><a href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></li>
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   title   = {Hypergraph Colouring Bounds},
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diff --git a/web/entries/List_Update.html b/web/entries/List_Update.html
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   <h1>
     <span class='first'>A</span>nalysis of <span class='first'>L</span>ist <span class='first'>U</span>pdate <span class='first'>A</span>lgorithms
     
   </h1>
   <div>
       <p>
         <a href="../authors/haslbeckm">Maximilian P. L. Haslbeck</a> <a href="http://in.tum.de/~haslbema/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
 
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process"><p>
 These theories formalize the quantitative analysis of a number of classical algorithms for the list update problem: 2-competitiveness of move-to-front, the lower bound of 2 for the competitiveness of deterministic list update algorithms and 1.6-competitiveness of the randomized COMB algorithm, the best randomized list update algorithm known to date.
 The material is based on the first two chapters of <i>Online Computation
 and Competitive Analysis</i> by Borodin and El-Yaniv.
 </p>
 <p>
 For an informal description see the FSTTCS 2016 publication
 <a href="http://www21.in.tum.de/~nipkow/pubs/fsttcs16.html">Verified Analysis of List Update Algorithms</a>
 by Haslbeck and Nipkow.
 </p></div>
 
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           <li><a href="../topics/computer-science/algorithms/online">Computer science/Algorithms/Online</a></li>
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       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Haslbeck, M. P. L., &amp; Nipkow, T. (2016). <i>Verified Analysis of List Update Algorithms</i>. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.FSTTCS.2016.49
+        <li>Haslbeck, M. P. L., &amp; Nipkow, T. (2016). Verified Analysis of List Update Algorithms. <i>Schloss Dagstuhl - Leibniz-Zentrum Fuer Informatik GmbH, Wadern/Saarbruecken, Germany</i>. https://doi.org/10.4230/LIPICS.FSTTCS.2016.49
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   author  = {Maximilian P. L. Haslbeck and Tobias Nipkow},
   title   = {Analysis of List Update Algorithms},
   journal = {Archive of Formal Proofs},
   month   = {February},
   year    = {2016},
   note    = {\url{https://isa-afp.org/entries/List_Update.html},
              Formal proof development},
   ISSN    = {2150-914x},
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diff --git a/web/entries/Monad_Normalisation.html b/web/entries/Monad_Normalisation.html
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   <h1>
     <span class='first'>M</span>onad normalisation
     
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       <p>
         <a href="../authors/schneider">Joshua Schneider</a>, <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a> and <a href="../authors/lochbihler">Andreas Lochbihler</a> <a href="http://www.andreas-lochbihler.de/">🌐</a>
 
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">The usual monad laws can directly be used as rewrite rules for Isabelle’s
 simplifier to normalise monadic HOL terms and decide equivalences.
 In a commutative monad, however, the commutativity law is a
 higher-order permutative rewrite rule that makes the simplifier loop.
 This AFP entry implements a simproc that normalises monadic
 expressions in commutative monads using ordered rewriting. The
 simproc can also permute computations across control operators like if
 and case.</div>
 
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       <h3>Session Monad_Normalisation</h3>
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           <li><a href="../sessions/monad_normalisation/#Monad_Normalisation">Monad_Normalisation</a></li>
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+              <a href="../entries/Approximate_Model_Counting.html">Approximate Model Counting</a>
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         <pre id="copy-text">@article{Monad_Normalisation-AFP,
   author  = {Joshua Schneider and Manuel Eberl and Andreas Lochbihler},
   title   = {Monad normalisation},
   journal = {Archive of Formal Proofs},
   month   = {May},
   year    = {2017},
   note    = {\url{https://isa-afp.org/entries/Monad_Normalisation.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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diff --git a/web/entries/Pell.html b/web/entries/Pell.html
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@@ -1,295 +1,298 @@
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     <meta name="description" content=" This article gives the basic theory of Pell&#39;s equation x2 = 1 &#43; D&amp;thinsp;y2, where D&amp;thinsp;&amp;isin;&amp;thinsp;&amp;#8469; is a parameter and x, y are integer...">
 
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   <h1>
     <span class='first'>P</span>ell's <span class='first'>E</span>quation
     
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   <div>
       <p>
         <a href="../authors/eberl">Manuel Eberl</a> <a href="https://pruvisto.org/">🌐</a>
 
       </p>
       <p class="date">June 23, 2018</p>
   </div>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process"><p> This article gives the basic theory of Pell's equation
 <em>x</em><sup>2</sup> = 1 +
 <em>D</em>&thinsp;<em>y</em><sup>2</sup>,
 where
 <em>D</em>&thinsp;&isin;&thinsp;&#8469; is
 a parameter and <em>x</em>, <em>y</em> are
 integer variables. </p> <p> The main result that is proven
 is the following: If <em>D</em> is not a perfect square,
 then there exists a <em>fundamental solution</em>
 (<em>x</em><sub>0</sub>,
 <em>y</em><sub>0</sub>) that is not the
 trivial solution (1, 0) and which generates all other solutions
 (<em>x</em>, <em>y</em>) in the sense that
 there exists some
 <em>n</em>&thinsp;&isin;&thinsp;&#8469;
 such that |<em>x</em>| +
 |<em>y</em>|&thinsp;&radic;<span
 style="text-decoration:
 overline"><em>D</em></span> =
 (<em>x</em><sub>0</sub> +
 <em>y</em><sub>0</sub>&thinsp;&radic;<span
 style="text-decoration:
 overline"><em>D</em></span>)<sup><em>n</em></sup>.
 This also implies that the set of solutions is infinite, and it gives
 us an explicit and executable characterisation of all the solutions.
 </p> <p> Based on this, simple executable algorithms for
 computing the fundamental solution and the infinite sequence of all
 non-negative solutions are also provided. </p></div>
 
     <h3>License</h3>
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         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li>
       </ul>
       <h3>Session Pell</h3>
       <ul>
           <li><a href="../sessions/pell/#Efficient_Discrete_Sqrt">Efficient_Discrete_Sqrt</a></li>
           <li><a href="../sessions/pell/#Pell">Pell</a></li>
           <li><a href="../sessions/pell/#Pell_Algorithm">Pell_Algorithm</a></li>
           <li><a href="../sessions/pell/#Pell_Algorithm_Test">Pell_Algorithm_Test</a></li>
       </ul>
 
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       <div>
         <h3>Used by</h3>
         <ul class="horizontal-list">
             <li>
+              <a href="../entries/Continued_Fractions.html">Continued Fractions</a>
+            </li>
+            <li>
               <a href="../entries/Mersenne_Primes.html">Mersenne primes and the Lucas–Lehmer test</a>
             </li>
         </ul>
       </div>
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         <p style="display:none;" id="bibtex-filename">Pell-AFP</p>
         <pre id="copy-text">@article{Pell-AFP,
   author  = {Manuel Eberl},
   title   = {Pell&#39;s Equation},
   journal = {Archive of Formal Proofs},
   month   = {June},
   year    = {2018},
   note    = {\url{https://isa-afp.org/entries/Pell.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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diff --git a/web/entries/Polygonal_Number_Theorem.html b/web/entries/Polygonal_Number_Theorem.html
--- a/web/entries/Polygonal_Number_Theorem.html
+++ b/web/entries/Polygonal_Number_Theorem.html
@@ -1,245 +1,245 @@
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     <meta name="description" content="We formalize the proofs of Cauchy&#39;s and Legendre&#39;s Polygonal Number Theorems given in Melvyn B. Nathanson&#39;s book &#34;Additive Number Theory: The Classical...">
 
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   <h1>
     <span class='first'>P</span>olygonal <span class='first'>N</span>umber <span class='first'>T</span>heorem
     
   </h1>
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       <p>
         <a href="../authors/leek">Kevin Lee</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJrZmtsMiJdfQ==">📧</a>, <a href="../authors/yez">Zhengkun Ye</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJ6eTMwNyJdfQ==">📧</a> and <a href="../authors/argyraki">Angeliki Koutsoukou-Argyraki</a> <a class="obfuscated" data="eyJob3N0IjpbImNhbSIsImFjIiwidWsiXSwidXNlciI6WyJhazIxMTAiXX0=">📧</a>
 
       </p>
       <p class="date">August 10, 2023</p>
   </div>
 </header>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process"><p>We formalize the proofs of Cauchy's and Legendre's Polygonal Number Theorems given in Melvyn B. Nathanson's book "Additive Number Theory: The Classical Bases".</p>
 
 <p>For $m \geq 1$, the $k$-th polygonal number of order $m+2$ is defined to be $p_m(k)=\frac{mk(k-1)}{2}+k$. The theorems state that:</p>
 
 <p>1. If $m \ge 4$ and $N \geq 108m$, then $N$ can be written as the sum of $m+1$ polygonal numbers of order $m+2$, at most four of which are different from $0$ or $1$. If $N \geq 324$, then $N$ can be written as the sum of five pentagonal numbers, at least one of which is $0$ or $1$.</p>
 
 <p>2. Let $m \geq 3$ and $N \geq 28m^3$. If $m$ is odd, then $N$ is the sum of four polygonal numbers of order $m+2$. If $m$ is even, then $N$ is the sum of five polygonal numbers of order $m+2$, at least one of which is $0$ or $1$.</p>
 
 <p>We also formalize the proof of Gauss's theorem which states that every non-negative integer is the sum of three triangular numbers.</p></div>
 
     <h3>License</h3>
     <div>
         <a href="https://isa-afp.org/LICENSE">BSD License</a>
     </div>
       <h3>Topics</h3>
       <ul>
           <li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li>
           <li><a href="../topics/mathematics/combinatorics">Mathematics/Combinatorics</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Nathanson, M. B. (1996). Additive Number Theory. In Graduate Texts in Mathematics. Springer New York. <a href="https://doi.org/10.1007/978-1-4757-3845-2">https://doi.org/10.1007/978-1-4757-3845-2</a>
+        <li>Nathanson, M. B. (1996). Additive Number Theory. Graduate Texts in Mathematics. <a href="https://doi.org/10.1007/978-1-4757-3845-2">https://doi.org/10.1007/978-1-4757-3845-2</a>
 
         </li>
       </ul>
       <h3>Session Polygonal_Number_Theorem</h3>
       <ul>
           <li><a href="../sessions/polygonal_number_theorem/#Polygonal_Number_Theorem_Lemmas">Polygonal_Number_Theorem_Lemmas</a></li>
           <li><a href="../sessions/polygonal_number_theorem/#Polygonal_Number_Theorem_Gauss">Polygonal_Number_Theorem_Gauss</a></li>
           <li><a href="../sessions/polygonal_number_theorem/#Polygonal_Number_Theorem_Cauchy">Polygonal_Number_Theorem_Cauchy</a></li>
           <li><a href="../sessions/polygonal_number_theorem/#Polygonal_Number_Theorem_Legendre">Polygonal_Number_Theorem_Legendre</a></li>
       </ul>
 
     <div class="flex-wrap">
       <div>
         <h3>Depends on</h3>
         <ul class="horizontal-list">
               <li><a href="../entries/Three_Squares.html">Three Squares Theorem</a></li>
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         <pre id="copy-text">@article{Polygonal_Number_Theorem-AFP,
   author  = {Kevin Lee and Zhengkun Ye and Angeliki Koutsoukou-Argyraki},
   title   = {Polygonal Number Theorem},
   journal = {Archive of Formal Proofs},
   month   = {August},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Polygonal_Number_Theorem.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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diff --git a/web/entries/Polynomial_Factorization.html b/web/entries/Polynomial_Factorization.html
--- a/web/entries/Polynomial_Factorization.html
+++ b/web/entries/Polynomial_Factorization.html
@@ -1,352 +1,355 @@
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     <title>Polynomial Factorization - Archive of Formal Proofs</title>
     <meta name="description" content="Based on existing libraries for polynomial interpolation and matrices, we formalized several factorization algorithms for polynomials, including...">
 
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   <h1>
     <span class='first'>P</span>olynomial <span class='first'>F</span>actorization
     
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       <p>
         <a href="../authors/thiemann">René Thiemann</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsicmVuZSIsInRoaWVtYW5uIl19">📧</a> and <a href="../authors/yamada">Akihisa Yamada</a> <a class="obfuscated" data="eyJob3N0IjpbInVpYmsiLCJhYyIsImF0Il0sInVzZXIiOlsiYWtpaGlzYSIsInlhbWFkYSJdfQ==">📧</a>
 
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       <p class="date">January 29, 2016</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">Based on existing libraries for polynomial interpolation and matrices,
 we formalized several factorization algorithms for polynomials, including
 Kronecker's algorithm for integer polynomials,
 Yun's square-free factorization algorithm for field polynomials, and
 Berlekamp's algorithm for polynomials over finite fields.
 By combining the last one with Hensel's lifting,
 we derive an efficient factorization algorithm for the integer polynomials,
 which is then lifted for rational polynomials by mechanizing Gauss' lemma.
 Finally, we assembled a combined factorization algorithm for rational polynomials,
 which combines all the mentioned algorithms and additionally uses the explicit formula for roots
 of quadratic polynomials and a rational root test.
 <p>
 As side products, we developed division algorithms for polynomials over integral domains,
 as well as primality-testing and prime-factorization algorithms for integers.</div>
 
     <h3>License</h3>
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       <h3>Topics</h3>
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           <li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li>
       </ul>
       <h3>Session Polynomial_Factorization</h3>
       <ul>
           <li><a href="../sessions/polynomial_factorization/#Missing_List">Missing_List</a></li>
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               <li><a href="../entries/Show.html">Haskell&rsquo;s Show Class in Isabelle/HOL</a></li>
               <li><a href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></li>
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         <h3>Used by</h3>
         <ul class="horizontal-list">
             <li>
+              <a href="../entries/Continued_Fractions.html">Continued Fractions</a>
+            </li>
+            <li>
               <a href="../entries/Fishers_Inequality.html">Fisher&rsquo;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</a>
             </li>
             <li>
               <a href="../entries/Amicable_Numbers.html">Amicable Numbers</a>
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               <a href="../entries/Knuth_Bendix_Order.html">A Formalization of Knuth–Bendix Orders</a>
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               <a href="../entries/Gaussian_Integers.html">Gaussian Integers</a>
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               <a href="../entries/Power_Sum_Polynomials.html">Power Sum Polynomials</a>
             </li>
             <li>
               <a href="../entries/Functional_Ordered_Resolution_Prover.html">A Verified Functional Implementation of Bachmair and Ganzinger&rsquo;s Ordered Resolution Prover</a>
             </li>
             <li>
               <a href="../entries/Dirichlet_Series.html">Dirichlet Series</a>
             </li>
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               <a href="../entries/Linear_Recurrences.html">Linear Recurrences</a>
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               <a href="../entries/Subresultants.html">Subresultants</a>
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             <li>
               <a href="../entries/Berlekamp_Zassenhaus.html">The Factorization Algorithm of Berlekamp and Zassenhaus</a>
             </li>
             <li>
               <a href="../entries/Perron_Frobenius.html">Perron-Frobenius Theorem for Spectral Radius Analysis</a>
             </li>
             <li>
               <a href="../entries/Jordan_Normal_Form.html">Matrices, Jordan Normal Forms, and Spectral Radius Theory</a>
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         <p style="display:none;" id="bibtex-filename">Polynomial_Factorization-AFP</p>
         <pre id="copy-text">@article{Polynomial_Factorization-AFP,
   author  = {René Thiemann and Akihisa Yamada},
   title   = {Polynomial Factorization},
   journal = {Archive of Formal Proofs},
   month   = {January},
   year    = {2016},
   note    = {\url{https://isa-afp.org/entries/Polynomial_Factorization.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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               <a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2016-12-17.tar.gz">
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             <li>
               <a href="https://www.isa-afp.org/release/afp-Polynomial_Factorization-2016-02-22.tar.gz">
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   <h1>
     <span class='first'>P</span>urely <span class='first'>F</span>unctional, <span class='first'>S</span>imple, and <span class='first'>E</span>fficient <span class='first'>I</span>mplementation of <span class='first'>P</span>rim and <span class='first'>D</span>ijkstra
     
   </h1>
   <div>
       <p>
         <a href="../authors/lammich">Peter Lammich</a> <a href="http://www21.in.tum.de/~lammich">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
 
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       <p class="date">June 25, 2019</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">We verify purely functional, simple and efficient implementations of
 Prim's and Dijkstra's algorithms. This constitutes the first
 verification of an executable and even efficient version of
 Prim's algorithm. This entry formalizes the second part of our
 ITP-2019 proof pearl <em>Purely Functional, Simple and Efficient
 Priority Search Trees and Applications to Prim and Dijkstra</em>.</div>
 
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       <h3>Topics</h3>
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           <li><a href="../topics/computer-science/algorithms/graph">Computer science/Algorithms/Graph</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Lammich, P., &amp; Nipkow, T. (2019). <i>Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra</i> (Version 1.0). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITP.2019.23
+        <li>Lammich, P., &amp; Nipkow, T. (2019). Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra. <i>Schloss Dagstuhl - Leibniz-Zentrum Fuer Informatik GmbH, Wadern/Saarbruecken, Germany</i>. https://doi.org/10.4230/LIPICS.ITP.2019.23
         </li>
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       <h3>Session Prim_Dijkstra_Simple</h3>
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         <pre id="copy-text">@article{Prim_Dijkstra_Simple-AFP,
   author  = {Peter Lammich and Tobias Nipkow},
   title   = {Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra},
   journal = {Archive of Formal Proofs},
   month   = {June},
   year    = {2019},
   note    = {\url{https://isa-afp.org/entries/Prim_Dijkstra_Simple.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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   <h1>
     <span class='first'>P</span>ropositional <span class='first'>P</span>roof <span class='first'>S</span>ystems
     
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       <p>
         <a href="../authors/michaelis">Julius Michaelis</a> <a href="http://liftm.de/">🌐</a> and <a href="../authors/nipkow">Tobias Nipkow</a> <a href="https://www.in.tum.de/~nipkow/">🌐</a>
 
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       <p class="date">June 21, 2017</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">We formalize a range of proof systems for classical propositional
 logic (sequent calculus, natural deduction, Hilbert systems,
 resolution) and prove the most important meta-theoretic results about
 semantics and proofs: compactness, soundness, completeness,
 translations between proof systems, cut-elimination, interpolation and
 model existence.</div>
 
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-        <li>Michaelis, J., &amp; Nipkow, T. (2019). <i>Formalized Proof Systems for Propositional Logic</i> (Version 1.0). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.TYPES.2017.5
+        <li>Michaelis, J., &amp; Nipkow, T. (2018). Formalized Proof Systems for Propositional Logic. <i>Schloss Dagstuhl - Leibniz-Zentrum Fuer Informatik GmbH, Wadern/Saarbruecken, Germany</i>. https://doi.org/10.4230/LIPICS.TYPES.2017.5
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         <p style="display:none;" id="bibtex-filename">Propositional_Proof_Systems-AFP</p>
         <pre id="copy-text">@article{Propositional_Proof_Systems-AFP,
   author  = {Julius Michaelis and Tobias Nipkow},
   title   = {Propositional Proof Systems},
   journal = {Archive of Formal Proofs},
   month   = {June},
   year    = {2017},
   note    = {\url{https://isa-afp.org/entries/Propositional_Proof_Systems.html},
              Formal proof development},
   ISSN    = {2150-914x},
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   <h1>
     <span class='first'>M</span>odal quantales, involutive quantales, <span class='first'>D</span>edekind <span class='first'>Q</span>uantales
     
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       <p>
         <a href="../authors/struth">Georg Struth</a> <a class="obfuscated" data="eyJob3N0IjpbInNoZWZmaWVsZCIsImFjIiwidWsiXSwidXNlciI6WyJnIiwic3RydXRoIl19">📧</a> and <a href="../authors/calk">Cameron Calk</a>
 
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This AFP entry provides mathematical components for modal quantales,
   involutive quantales and Dedekind quantales. Modal quantales are
   simple extensions of modal Kleene algebras useful for the
   verification of recursive programs. Involutive quantales appear in
   the study of C*-algebras. Dedekind quantales are relatives of
   Tarski's relation algebras, hence relevant to program verification
   and beyond that to higher  rewriting. We also provide
   components for weaker variants such as Kleene algebras with converse
   and modal Kleene algebras with converse.</div>
 
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           <li><a href="../topics/mathematics/algebra">Mathematics/Algebra</a></li>
           <li><a href="../topics/mathematics/order">Mathematics/Order</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
         <li>Fahrenberg, U., Johansen, C., Struth, G., & Ziemiański, K. (2023). Catoids and modal convolution algebras. Algebra Universalis, 84(2). <a href="https://doi.org/10.1007/s00012-023-00805-9">https://doi.org/10.1007/s00012-023-00805-9</a>
 
         </li>
-        <li>Calk, C., Malbos, P., Pous, D., &amp; Struth, G. (2023). <i>Higher Catoids, Higher Quantales and their Correspondences</i> (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2307.09253
+        <li>Calk, C., Malbos, P., Pous, D., &amp; Struth, G. (2023). <i>Higher Catoids, Higher Quantales and their Correspondences</i> (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2307.09253
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               <li><a href="../entries/KAD.html">Kleene Algebras with Domain</a></li>
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               <li><a href="../entries/Quantales.html">Quantales</a></li>
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         <pre id="copy-text">@article{Quantales_Converse-AFP,
   author  = {Georg Struth and Cameron Calk},
   title   = {Modal quantales, involutive quantales, Dedekind Quantales},
   journal = {Archive of Formal Proofs},
   month   = {July},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Quantales_Converse.html},
              Formal proof development},
   ISSN    = {2150-914x},
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   <h1>
     <span class='first'>S</span>-<span class='first'>F</span>inite <span class='first'>M</span>easure <span class='first'>M</span>onad on <span class='first'>Q</span>uasi-<span class='first'>B</span>orel <span class='first'>S</span>paces
     
   </h1>
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       <p>
         <a href="../authors/hirata">Michikazu Hirata</a> <a class="obfuscated" data="eyJob3N0IjpbIm0iLCJ0aXRlY2giLCJhYyIsImpwIl0sInVzZXIiOlsiaGlyYXRhIiwibSIsImFjIl19">📧</a> and <a href="../authors/minamide">Yasuhiko Minamide</a> <a class="obfuscated" data="eyJob3N0IjpbImlzIiwidGl0ZWNoIiwiYWMiLCJqcCJdLCJ1c2VyIjpbIm1pbmFtaWRlIl19">📧</a>
 
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       <p class="date">August 8, 2023</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">The s-finite measure monad on quasi-Borel spaces provides a suitable denotational model for higher-order probabilistic programs with conditioning. This entry is a formalization of the s-finite measure monad and related notions, including s-finite measures, s-finite kernels, and a proof automation for quasi-Borel spaces which is an extension of our previous entry <a href="https://www.isa-afp.org/entries/Quasi_Borel_Spaces.html"><i>Quasi-Borel Spaces</i></a>. We also implement several examples of probabilistic programs in previous works and prove their property.
 This work is a part of the work by Hirata, Minamide, and Sato, <i>Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL</i> presented at the 14th Conference on Interactive Theorem Proving (ITP2023).</div>
 
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       <h3>Topics</h3>
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           <li><a href="../topics/computer-science/semantics-and-reasoning">Computer science/Semantics and reasoning</a></li>
           <li><a href="../topics/mathematics/measure-and-integration">Mathematics/Measure and integration</a></li>
           <li><a href="../topics/mathematics/probability-theory">Mathematics/Probability theory</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Hirata, M., Minamide, Y., &amp; Sato, T. (2023). <i>Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL</i>. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITP.2023.18
+        <li>Hirata, M., Minamide, Y., &amp; Sato, T. (2023). Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL. <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.ITP.2023.18
         </li>
       </ul>
       <h3>Session S_Finite_Measure_Monad</h3>
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           <li><a href="../sessions/s_finite_measure_monad/#Lemmas_S_Finite_Measure_Monad">Lemmas_S_Finite_Measure_Monad</a></li>
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               <li><a href="../entries/Standard_Borel_Spaces.html">Standard Borel Spaces</a></li>
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         <pre id="copy-text">@article{S_Finite_Measure_Monad-AFP,
   author  = {Michikazu Hirata and Yasuhiko Minamide},
   title   = {S-Finite Measure Monad on Quasi-Borel Spaces},
   journal = {Archive of Formal Proofs},
   month   = {August},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/S_Finite_Measure_Monad.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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diff --git a/web/entries/Special_Function_Bounds.html b/web/entries/Special_Function_Bounds.html
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     <meta name="description" content="This development proves upper and lower bounds for several familiar real-valued functions. For sin, cos, exp and sqrt, it defines and verifies infinite...">
 
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   <h1>
     <span class='first'>R</span>eal-<span class='first'>V</span>alued <span class='first'>S</span>pecial <span class='first'>F</span>unctions: <span class='first'>U</span>pper and <span class='first'>L</span>ower <span class='first'>B</span>ounds
     
   </h1>
   <div>
       <p>
         <a href="../authors/paulson">Lawrence C. Paulson</a> <a href="https://www.cl.cam.ac.uk/~lp15/">🌐</a>
 
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       <p class="date">August 29, 2014</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This development proves upper and lower bounds for several familiar real-valued functions. For sin, cos, exp and sqrt, it defines and verifies infinite families of upper and lower bounds, mostly based on Taylor series expansions. For arctan, ln and exp, it verifies a finite collection of upper and lower bounds, originally obtained from the functions' continued fraction expansions using the computer algebra system Maple. A common theme in these proofs is to take the difference between a function and its approximation, which should be zero at one point, and then consider the sign of the derivative. The immediate purpose of this development is to verify axioms used by MetiTarski, an automatic theorem prover for real-valued special functions. Crucial to MetiTarski's operation is the provision of upper and lower bounds for each function of interest.</div>
 
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           <li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li>
       </ul>
       <h3>Session Special_Function_Bounds</h3>
       <ul>
           <li><a href="../sessions/special_function_bounds/#Bounds_Lemmas">Bounds_Lemmas</a></li>
           <li><a href="../sessions/special_function_bounds/#Atan_CF_Bounds">Atan_CF_Bounds</a></li>
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           <li><a href="../sessions/special_function_bounds/#Log_CF_Bounds">Log_CF_Bounds</a></li>
           <li><a href="../sessions/special_function_bounds/#Sin_Cos_Bounds">Sin_Cos_Bounds</a></li>
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         <ul class="horizontal-list">
               <li><a href="../entries/Sturm_Sequences.html">Sturm&rsquo;s Theorem</a></li>
         </ul>
       </div>
+        <div>
+          <h3>Auto-related entries</h3>
+          <ul class="horizontal-list">
+              <li><a href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></li>
+          </ul>
+        </div>
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         <pre id="copy-text">@article{Special_Function_Bounds-AFP,
   author  = {Lawrence C. Paulson},
   title   = {Real-Valued Special Functions: Upper and Lower Bounds},
   journal = {Archive of Formal Proofs},
   month   = {August},
   year    = {2014},
   note    = {\url{https://isa-afp.org/entries/Special_Function_Bounds.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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     <span class='first'>S</span>tandard <span class='first'>B</span>orel <span class='first'>S</span>paces
     
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         <a href="../authors/hirata">Michikazu Hirata</a> <a class="obfuscated" data="eyJob3N0IjpbIm0iLCJ0aXRlY2giLCJhYyIsImpwIl0sInVzZXIiOlsiaGlyYXRhIiwibSIsImFjIl19">📧</a>
 
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     <div class="abstract mathjax_process">This entry includes a formalization of standard Borel spaces and (a variant of) the Borel isomorphism theorem. A separable complete metrizable topological space is called a polish space and a measurable space generated from a polish space is called a standard Borel space. We formalize the notion of standard Borel spaces by establishing set-based metric spaces, and then prove (a variant of) the Borel isomorphism theorem. The theorem states that a standard Borel spaces is either a countable discrete space or isomorphic to $\mathbb{R}$.</div>
 
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       <h3>History</h3>
       <dl>
         <dt>October 26, 2023</dt>
         <dd>adjust theories to the set-based metric space library in Isabelle2023<br>
 </dd>
       </dl>
       <h3>Topics</h3>
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           <li><a href="../topics/mathematics/analysis">Mathematics/Analysis</a></li>
           <li><a href="../topics/mathematics/topology">Mathematics/Topology</a></li>
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       <h3>Related publications</h3>
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-        <li>Hirata, M., Minamide, Y., &amp; Sato, T. (2023). <i>Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL</i>. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITP.2023.18
+        <li>Hirata, M., Minamide, Y., &amp; Sato, T. (2023). Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL. <i>Schloss Dagstuhl - Leibniz-Zentrum Für Informatik</i>. https://doi.org/10.4230/LIPICS.ITP.2023.18
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       <h3>Session Standard_Borel_Spaces</h3>
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         <pre id="copy-text">@article{Standard_Borel_Spaces-AFP,
   author  = {Michikazu Hirata},
   title   = {Standard Borel Spaces},
   journal = {Archive of Formal Proofs},
   month   = {August},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Standard_Borel_Spaces.html},
              Formal proof development},
   ISSN    = {2150-914x},
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     <span class='first'>T</span>ransport via <span class='first'>P</span>artial <span class='first'>G</span>alois <span class='first'>C</span>onnections and <span class='first'>E</span>quivalences
     
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     <div class="abstract mathjax_process">This entry contains the accompanying formalisation of the paper
 <a href="https://conf.researchr.org/details/aplas-2023/aplas-2023-research-papers/15/Transport-via-Partial-Galois-Connections-and-Equivalences">"Transport via Partial Galois Connections and Equivalences" (APLAS 2023)</a>.
 It contains a theoretical framework to transport programs via equivalences,
 subsuming the theory of <a href="https://doi.org/10.1007/978-3-319-03545-1_9">Isabelle's Lifting package</a>.
 It also contains a prototype to automate transports using this framework in Isabelle/HOL,
 but this prototype is not yet ready for production.
 Finally, it contains a library on top of Isabelle/HOL's axioms,
 including various relativised concepts on orders, functions, binary relations,
 and Galois connections and equivalences.</div>
 
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-        <li>Kappelmann, K. (2023). Transport via Partial Galois Connections and Equivalences. <i>ArXiv</i>. https://doi.org/10.48550/ARXIV.2303.05244
+        <li>Kappelmann, K. (2023). <i>Transport via Partial Galois Connections and Equivalences</i> (Version 4). arXiv. https://doi.org/10.48550/ARXIV.2303.05244
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         <p style="display:none;" id="bibtex-filename">Transport-AFP</p>
         <pre id="copy-text">@article{Transport-AFP,
   author  = {Kevin Kappelmann},
   title   = {Transport via Partial Galois Connections and Equivalences},
   journal = {Archive of Formal Proofs},
   month   = {October},
   year    = {2023},
   note    = {\url{https://isa-afp.org/entries/Transport.html},
              Formal proof development},
   ISSN    = {2150-914x},
 }</pre>
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     <span class='first'>W</span>ieferich–<span class='first'>K</span>empner <span class='first'>T</span>heorem
     
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       <p>
         <a href="../authors/chenj">Jamie Chen</a> <a href="https://gitlab.com/Jamie-Chen">🌐</a>
 
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       <p class="date">March 6, 2024</p>
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     <h3>Abstract</h3>
 
     <div class="abstract mathjax_process">This document presents a formalised proof of the Wieferich–Kempner Theorem, stating that all nonnegative integers can be expressed as the sum of nine nonnegative cubes.  The source of the proof is the book "Additive Number Theory: The Classical Bases" by Melvyn B. Nathanson.</div>
 
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         <a href="https://isa-afp.org/LICENSE.LGPL">GNU Lesser General Public License (LGPL)</a>
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       <h3>Topics</h3>
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           <li><a href="../topics/mathematics/number-theory">Mathematics/Number theory</a></li>
       </ul>
       <h3>Related publications</h3>
       <ul>
-        <li>Nathanson, M. B. (1996). Additive Number Theory. In Graduate Texts in Mathematics. Springer New York. <a href="https://doi.org/10.1007/978-1-4757-3845-2">https://doi.org/10.1007/978-1-4757-3845-2</a>
+        <li>Nathanson, M. B. (1996). Additive Number Theory. Graduate Texts in Mathematics. <a href="https://doi.org/10.1007/978-1-4757-3845-2">https://doi.org/10.1007/978-1-4757-3845-2</a>
 
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         <pre id="copy-text">@article{Wieferich_Kempner-AFP,
   author  = {Jamie Chen},
   title   = {Wieferich–Kempner Theorem},
   journal = {Archive of Formal Proofs},
   month   = {March},
   year    = {2024},
   note    = {\url{https://isa-afp.org/entries/Wieferich_Kempner.html},
              Formal proof development},
   ISSN    = {2150-914x},
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           <span class="date">Jun 28</span>
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           <span class="date">Jun 26</span>
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               by <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Feb 18</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Random_Graph_Subgraph_Threshold.html">Properties of Random Graphs -- Subgraph Containment</a></h5>
             <br>
               by <a href="../authors/hupel">Lars Hupel</a>
 
           </div>
           <span class="date">Feb 13</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Selection_Heap_Sort.html">Verification of Selection and Heap Sort Using Locales</a></h5>
             <br>
               by <a href="../authors/petrovic">Danijela Petrovic</a>
 
           </div>
           <span class="date">Feb 11</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Affine_Arithmetic.html">Affine Arithmetic</a></h5>
             <br>
               by <a href="../authors/immler">Fabian Immler</a>
 
           </div>
           <span class="date">Feb 07</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></h5>
             <br>
               by <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Feb 06</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a> and <a href="../authors/traytel">Dmitriy Traytel</a>
 
           </div>
           <span class="date">Jan 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Secondary_Sylow.html">Secondary Sylow Theorems</a></h5>
             <br>
               by <a href="../authors/raumer">Jakob von Raumer</a>
 
           </div>
           <span class="date">Jan 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Relation_Algebra.html">Relation Algebra</a></h5>
             <br>
               by <a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/fosters">Simon Foster</a>, <a href="../authors/struth">Georg Struth</a> and <a href="../authors/weber">Tjark Weber</a>
 
           </div>
           <span class="date">Jan 25</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></h5>
             <br>
               by <a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/gomes">Victor B. F. Gomes</a> and <a href="../authors/struth">Georg Struth</a>
 
           </div>
           <span class="date">Jan 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Featherweight_OCL.html">Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5</a></h5>
             <br>
               by <a href="../authors/brucker">Achim D. Brucker</a>, <a href="../authors/tuong">Frédéric Tuong</a> and <a href="../authors/wolff">Burkhart Wolff</a>
 
           </div>
           <span class="date">Jan 16</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Sturm_Sequences.html">Sturm&#39;s Theorem</a></h5>
             <br>
               by <a href="../authors/eberl">Manuel Eberl</a>
 
           </div>
           <span class="date">Jan 11</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/CryptoBasedCompositionalProperties.html">Compositional Properties of Crypto-Based Components</a></h5>
             <br>
               by <a href="../authors/spichkova">Maria Spichkova</a>
 
           </div>
           <span class="date">Jan 11</span>
         </article>
       <h2 class="head">2013</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Tail_Recursive_Functions.html">A General Method for the Proof of Theorems on Tail-recursive Functions</a></h5>
             <br>
               by <a href="../authors/noce">Pasquale Noce</a>
 
           </div>
           <span class="date">Dec 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></h5>
             <br>
               by <a href="../authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">Nov 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Incompleteness.html">Gödel&#39;s Incompleteness Theorems</a></h5>
             <br>
               by <a href="../authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">Nov 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Coinductive_Languages.html">A Codatatype of Formal Languages</a></h5>
             <br>
               by <a href="../authors/traytel">Dmitriy Traytel</a>
 
           </div>
           <span class="date">Nov 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FocusStreamsCaseStudies.html">Stream Processing Components: Isabelle/HOL Formalisation and Case Studies</a></h5>
             <br>
               by <a href="../authors/spichkova">Maria Spichkova</a>
 
           </div>
           <span class="date">Nov 14</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/GoedelGod.html">Gödel&#39;s God in Isabelle/HOL</a></h5>
             <br>
               by <a href="../authors/benzmueller">Christoph Benzmüller</a> and <a href="../authors/paleo">Bruno Woltzenlogel Paleo</a>
 
           </div>
           <span class="date">Nov 12</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Decreasing-Diagrams.html">Decreasing Diagrams</a></h5>
             <br>
               by <a href="../authors/zankl">Harald Zankl</a>
 
           </div>
           <span class="date">Nov 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Automatic_Refinement.html">Automatic Data Refinement</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Oct 02</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Native_Word.html">Native Word</a></h5>
             <br>
               by <a href="../authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">Sep 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/IEEE_Floating_Point.html">A Formal Model of IEEE Floating Point Arithmetic</a></h5>
             <br>
               by <a href="../authors/yu">Lei Yu</a>
 
           </div>
           <span class="date">Jul 27</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Pratt_Certificate.html">Pratt&#39;s Primality Certificates</a></h5>
             <br>
               by <a href="../authors/wimmer">Simon Wimmer</a> and <a href="../authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">Jul 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Lehmer.html">Lehmer&#39;s Theorem</a></h5>
             <br>
               by <a href="../authors/wimmer">Simon Wimmer</a> and <a href="../authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">Jul 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Koenigsberg_Friendship.html">The Königsberg Bridge Problem and the Friendship Theorem</a></h5>
             <br>
               by <a href="../authors/li">Wenda Li</a>
 
           </div>
           <span class="date">Jul 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Sort_Encodings.html">Sound and Complete Sort Encodings for First-Order Logic</a></h5>
             <br>
               by <a href="../authors/blanchette">Jasmin Christian Blanchette</a> and <a href="../authors/popescu">Andrei Popescu</a>
 
           </div>
           <span class="date">Jun 27</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/ShortestPath.html">An Axiomatic Characterization of the Single-Source Shortest Path Problem</a></h5>
             <br>
               by <a href="../authors/rizkallah">Christine Rizkallah</a>
 
           </div>
           <span class="date">May 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Graph_Theory.html">Graph Theory</a></h5>
             <br>
               by <a href="../authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">Apr 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Containers.html">Light-weight Containers</a></h5>
             <br>
               by <a href="../authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">Apr 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Nominal2.html">Nominal 2</a></h5>
             <br>
               by <a href="../authors/urban">Christian Urban</a>, <a href="../authors/berghofer">Stefan Berghofer</a> and <a href="../authors/kaliszyk">Cezary Kaliszyk</a>
 
           </div>
           <span class="date">Feb 21</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Launchbury.html">The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation</a></h5>
             <br>
               by <a href="../authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">Jan 31</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Ribbon_Proofs.html">Ribbon Proofs</a></h5>
             <br>
               by <a href="../authors/wickerson">John Wickerson</a>
 
           </div>
           <span class="date">Jan 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></h5>
             <br>
               by <a href="../authors/divason">Jose Divasón</a> and <a href="../authors/aransay">Jesús Aransay</a>
 
           </div>
           <span class="date">Jan 16</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Kleene_Algebra.html">Kleene Algebra</a></h5>
             <br>
               by <a href="../authors/armstrong">Alasdair Armstrong</a>, <a href="../authors/struth">Georg Struth</a> and <a href="../authors/weber">Tjark Weber</a>
 
           </div>
           <span class="date">Jan 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></h5>
             <br>
               by <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Jan 03</span>
         </article>
       <h2 class="head">2012</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a> and <a href="../authors/meis">Rene Meis</a>
 
           </div>
           <span class="date">Nov 14</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Open_Induction.html">Open Induction</a></h5>
             <br>
               by <a href="../authors/ogawa">Mizuhito Ogawa</a> and <a href="../authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">Nov 02</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Tarskis_Geometry.html">The independence of Tarski&#39;s Euclidean axiom</a></h5>
             <br>
               by <a href="../authors/makarios">T. J. M. Makarios</a>
 
           </div>
           <span class="date">Oct 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Bondy.html">Bondy&#39;s Theorem</a></h5>
             <br>
               by <a href="../authors/avigad">Jeremy Avigad</a> and <a href="../authors/hetzl">Stefan Hetzl</a>
 
           </div>
           <span class="date">Oct 27</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Possibilistic_Noninterference.html">Possibilistic Noninterference</a></h5>
             <br>
               by <a href="../authors/popescu">Andrei Popescu</a> and <a href="../authors/hoelzl">Johannes Hölzl</a>
 
           </div>
           <span class="date">Sep 10</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></h5>
             <br>
               by <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Aug 07</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Impossible_Geometry.html">Proving the Impossibility of Trisecting an Angle and Doubling the Cube</a></h5>
             <br>
               by <a href="../authors/romanos">Ralph Romanos</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">Aug 05</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Heard_Of.html">Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</a></h5>
             <br>
               by <a href="../authors/debrat">Henri Debrat</a> and <a href="../authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">Jul 27</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/PCF.html">Logical Relations for PCF</a></h5>
             <br>
               by <a href="../authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">Jul 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Tycon.html">Type Constructor Classes and Monad Transformers</a></h5>
             <br>
               by <a href="../authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">Jun 26</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Pi_Calculus.html">The pi-calculus in nominal logic</a></h5>
             <br>
               by <a href="../authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">May 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Psi_Calculi.html">Psi-calculi in Isabelle</a></h5>
             <br>
               by <a href="../authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">May 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/CCS.html">CCS in nominal logic</a></h5>
             <br>
               by <a href="../authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">May 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Circus.html">Isabelle/Circus</a></h5>
             <br>
               by <a href="../authors/feliachi">Abderrahmane Feliachi</a>, <a href="../authors/wolff">Burkhart Wolff</a> and <a href="../authors/gaudel">Marie-Claude Gaudel</a>
 
           </div>
           <span class="date">May 27</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Separation_Algebra.html">Separation Algebra</a></h5>
             <br>
               by <a href="../authors/klein">Gerwin Klein</a>, <a href="../authors/kolanski">Rafal Kolanski</a> and <a href="../authors/boyton">Andrew Boyton</a>
 
           </div>
           <span class="date">May 11</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></h5>
             <br>
               by <a href="../authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">May 07</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Inductive_Confidentiality.html">Inductive Study of Confidentiality</a></h5>
             <br>
               by <a href="../authors/bella">Giampaolo Bella</a>
 
           </div>
           <span class="date">May 02</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></h5>
             <br>
               by <a href="../authors/immler">Fabian Immler</a> and <a href="../authors/hoelzl">Johannes Hölzl</a>
 
           </div>
           <span class="date">Apr 26</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">Apr 13</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Abortable_Linearizable_Modules.html">Abortable Linearizable Modules</a></h5>
             <br>
               by <a href="../authors/guerraoui">Rachid Guerraoui</a>, <a href="../authors/kuncak">Viktor Kuncak</a> and <a href="../authors/losa">Giuliano Losa</a>
 
           </div>
           <span class="date">Mar 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Transitive-Closure-II.html">Executable Transitive Closures</a></h5>
             <br>
               by <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Feb 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></h5>
             <br>
               by <a href="../authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">Feb 06</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Refine_Monadic.html">Refinement for Monadic Programs</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Jan 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Dijkstra_Shortest_Path.html">Dijkstra&#39;s Shortest Path Algorithm</a></h5>
             <br>
               by <a href="../authors/nordhoff">Benedikt Nordhoff</a> and <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Jan 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Markov_Models.html">Markov Models</a></h5>
             <br>
               by <a href="../authors/hoelzl">Johannes Hölzl</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Jan 03</span>
         </article>
       <h2 class="head">2011</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/TLA.html">A Definitional Encoding of TLA* in Isabelle/HOL</a></h5>
             <br>
               by <a href="../authors/grov">Gudmund Grov</a> and <a href="../authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">Nov 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Efficient-Mergesort.html">Efficient Mergesort</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">Nov 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/PseudoHoops.html">Pseudo Hoops</a></h5>
             <br>
               by <a href="../authors/georgescu">George Georgescu</a>, <a href="../authors/leustean">Laurentiu Leustean</a> and <a href="../authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">Sep 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/LatticeProperties.html">Lattice Properties</a></h5>
             <br>
               by <a href="../authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">Sep 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></h5>
             <br>
               by <a href="../authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">Sep 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></h5>
             <br>
               by <a href="../authors/wu">Chunhan Wu</a>, <a href="../authors/zhangx">Xingyuan Zhang</a> and <a href="../authors/urban">Christian Urban</a>
 
           </div>
           <span class="date">Aug 26</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/Gauss-Jordan-Elim-Fun.html">Gauss-Jordan Elimination for Matrices Represented as Functions</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Aug 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Max-Card-Matching.html">Maximum Cardinality Matching</a></h5>
             <br>
               by <a href="../authors/rizkallah">Christine Rizkallah</a>
 
           </div>
           <span class="date">Jul 21</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/KBPs.html">Knowledge-based programs</a></h5>
             <br>
               by <a href="../authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">May 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/General-Triangle.html">The General Triangle Is Unique</a></h5>
             <br>
               by <a href="../authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">Apr 01</span>
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         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a> and <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Mar 14</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Nat-Interval-Logic.html">Interval Temporal Logic on Natural Numbers</a></h5>
             <br>
               by <a href="../authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">Feb 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/List-Infinite.html">Infinite Lists</a></h5>
             <br>
               by <a href="../authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">Feb 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/AutoFocus-Stream.html">AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</a></h5>
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               by <a href="../authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">Feb 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/LightweightJava.html">Lightweight Java</a></h5>
             <br>
               by <a href="../authors/strnisa">Rok Strniša</a> and <a href="../authors/parkinson">Matthew Parkinson</a>
 
           </div>
           <span class="date">Feb 07</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/RIPEMD-160-SPARK.html">RIPEMD-160</a></h5>
             <br>
               by <a href="../authors/immler">Fabian Immler</a>
 
           </div>
           <span class="date">Jan 10</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Lower_Semicontinuous.html">Lower Semicontinuous Functions</a></h5>
             <br>
               by <a href="../authors/grechuk">Bogdan Grechuk</a>
 
           </div>
           <span class="date">Jan 08</span>
         </article>
       <h2 class="head">2010</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Marriage.html">Hall&#39;s Marriage Theorem</a></h5>
             <br>
               by <a href="../authors/jiangd">Dongchen Jiang</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Dec 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Shivers-CFA.html">Shivers&#39; Control Flow Analysis</a></h5>
             <br>
               by <a href="../authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">Nov 16</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Binomial-Queues.html">Functional Binomial Queues</a></h5>
             <br>
               by <a href="../authors/neumann">René Neumann</a>
 
           </div>
           <span class="date">Oct 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Finger-Trees.html">Finger Trees</a></h5>
             <br>
               by <a href="../authors/nordhoff">Benedikt Nordhoff</a>, <a href="../authors/koerner">Stefan Körner</a> and <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Oct 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Binomial-Heaps.html">Binomial Heaps and Skew Binomial Heaps</a></h5>
             <br>
               by <a href="../authors/meis">Rene Meis</a>, <a href="../authors/nielsen">Finn Nielsen</a> and <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Oct 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Lam-ml-Normalization.html">Strong Normalization of Moggis&#39;s Computational Metalanguage</a></h5>
             <br>
               by <a href="../authors/doczkal">Christian Doczkal</a>
 
           </div>
           <span class="date">Aug 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Polynomials.html">Executable Multivariate Polynomials</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a>, <a href="../authors/thiemann">René Thiemann</a>, <a href="../authors/maletzky">Alexander Maletzky</a>, <a href="../authors/immler">Fabian Immler</a>, <a href="../authors/haftmann">Florian Haftmann</a>, <a href="../authors/lochbihler">Andreas Lochbihler</a> and <a href="../authors/bentkamp">Alexander Bentkamp</a>
 
           </div>
           <span class="date">Aug 10</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Statecharts.html">Formalizing Statecharts using Hierarchical Automata</a></h5>
             <br>
               by <a href="../authors/helke">Steffen Helke</a> and <a href="../authors/kammueller">Florian Kammüller</a>
 
           </div>
           <span class="date">Aug 08</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Free-Groups.html">Free Groups</a></h5>
             <br>
               by <a href="../authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">Jun 24</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Category2.html">Category Theory</a></h5>
             <br>
               by <a href="../authors/katovsky">Alexander Katovsky</a>
 
           </div>
           <span class="date">Jun 20</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a> and <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Jun 17</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Abstract-Rewriting.html">Abstract Rewriting</a></h5>
             <br>
               by <a href="../authors/sternagel">Christian Sternagel</a> and <a href="../authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">Jun 14</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/GraphMarkingIBP.html">Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</a></h5>
             <br>
               by <a href="../authors/preoteasa">Viorel Preoteasa</a> and <a href="../authors/back">Ralph-Johan Back</a>
 
           </div>
           <span class="date">May 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></h5>
             <br>
               by <a href="../authors/preoteasa">Viorel Preoteasa</a> and <a href="../authors/back">Ralph-Johan Back</a>
 
           </div>
           <span class="date">May 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Robbins-Conjecture.html">A Complete Proof of the Robbins Conjecture</a></h5>
             <br>
               by <a href="../authors/doty">Matthew Doty</a>
 
           </div>
           <span class="date">May 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Regular-Sets.html">Regular Sets and Expressions</a></h5>
             <br>
               by <a href="../authors/krauss">Alexander Krauss</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">May 12</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Locally-Nameless-Sigma.html">Locally Nameless Sigma Calculus</a></h5>
             <br>
               by <a href="../authors/henrio">Ludovic Henrio</a>, <a href="../authors/kammueller">Florian Kammüller</a>, <a href="../authors/lutz">Bianca Lutz</a> and <a href="../authors/sudhof">Henry Sudhof</a>
 
           </div>
           <span class="date">Apr 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Free-Boolean-Algebra.html">Free Boolean Algebra</a></h5>
             <br>
               by <a href="../authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">Mar 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/InformationFlowSlicing_Inter.html">Inter-Procedural Information Flow Noninterference via Slicing</a></h5>
             <br>
               by <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">Mar 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></h5>
             <br>
               by <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">Mar 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/List-Index.html">List Index</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Feb 20</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Coinductive.html">Coinductive</a></h5>
             <br>
               by <a href="../authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">Feb 12</span>
         </article>
       <h2 class="head">2009</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/DPT-SAT-Solver.html">A Fast SAT Solver for Isabelle in Standard ML</a></h5>
             <br>
               by <a href="../authors/heller">Armin Heller</a>
 
           </div>
           <span class="date">Dec 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Presburger-Automata.html">Formalizing the Logic-Automaton Connection</a></h5>
             <br>
               by <a href="../authors/berghofer">Stefan Berghofer</a> and <a href="../authors/reiter">Markus Reiter</a>
 
           </div>
           <span class="date">Dec 03</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Tree-Automata.html">Tree Automata</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Nov 25</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Collections.html">Collections Framework</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">Nov 25</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Perfect-Number-Thm.html">Perfect Number Theorem</a></h5>
             <br>
               by <a href="../authors/ijbema">Mark Ijbema</a>
 
           </div>
           <span class="date">Nov 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/HRB-Slicing.html">Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</a></h5>
             <br>
               by <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">Nov 13</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/WorkerWrapper.html">The Worker/Wrapper Transformation</a></h5>
             <br>
               by <a href="../authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">Oct 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Ordinals_and_Cardinals.html">Ordinals and Cardinals</a></h5>
             <br>
               by <a href="../authors/popescu">Andrei Popescu</a>
 
           </div>
           <span class="date">Sep 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/SequentInvertibility.html">Invertibility in Sequent Calculi</a></h5>
             <br>
               by <a href="../authors/chapman">Peter Chapman</a>
 
           </div>
           <span class="date">Aug 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/CofGroups.html">An Example of a Cofinitary Group in Isabelle/HOL</a></h5>
             <br>
               by <a href="../authors/kastermans">Bart Kastermans</a>
 
           </div>
           <span class="date">Aug 04</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FinFun.html">Code Generation for Functions as Data</a></h5>
             <br>
               by <a href="../authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">May 06</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Stream-Fusion.html">Stream Fusion</a></h5>
             <br>
               by <a href="../authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">Apr 29</span>
         </article>
       <h2 class="head">2008</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/BytecodeLogicJmlTypes.html">A Bytecode Logic for JML and Types</a></h5>
             <br>
               by <a href="../authors/beringer">Lennart Beringer</a> and <a href="../authors/hofmann">Martin Hofmann</a>
 
           </div>
           <span class="date">Dec 12</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/SIFPL.html">Secure information flow and program logics</a></h5>
             <br>
               by <a href="../authors/beringer">Lennart Beringer</a> and <a href="../authors/hofmann">Martin Hofmann</a>
 
           </div>
           <span class="date">Nov 10</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/SenSocialChoice.html">Some classical results in Social Choice Theory</a></h5>
             <br>
               by <a href="../authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">Nov 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FunWithTilings.html">Fun With Tilings</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a> and <a href="../authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">Nov 07</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Huffman.html">The Textbook Proof of Huffman&#39;s Algorithm</a></h5>
             <br>
               by <a href="../authors/blanchette">Jasmin Christian Blanchette</a>
 
           </div>
           <span class="date">Oct 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Slicing.html">Towards Certified Slicing</a></h5>
             <br>
               by <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">Sep 16</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/VolpanoSmith.html">A Correctness Proof for the Volpano/Smith Security Typing System</a></h5>
             <br>
               by <a href="../authors/snelting">Gregor Snelting</a> and <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">Sep 02</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/ArrowImpossibilityGS.html">Arrow and Gibbard-Satterthwaite</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Sep 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FunWithFunctions.html">Fun With Functions</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Aug 26</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/SATSolverVerification.html">Formal Verification of Modern SAT Solvers</a></h5>
             <br>
               by <a href="../authors/maricf">Filip Marić</a>
 
           </div>
           <span class="date">Jul 23</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Recursion-Theory-I.html">Recursion Theory I</a></h5>
             <br>
               by <a href="../authors/nedzelsky">Michael Nedzelsky</a>
 
           </div>
           <span class="date">Apr 05</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/BDD.html">BDD Normalisation</a></h5>
             <br>
               by <a href="../authors/ortner">Veronika Ortner</a> and <a href="../authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">Feb 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></h5>
             <br>
               by <a href="../authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">Feb 29</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/NormByEval.html">Normalization by Evaluation</a></h5>
             <br>
               by <a href="../authors/aehlig">Klaus Aehlig</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Feb 18</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/LinearQuantifierElim.html">Quantifier Elimination for Linear Arithmetic</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Jan 11</span>
         </article>
       <h2 class="head">2007</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Program-Conflict-Analysis.html">Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</a></h5>
             <br>
               by <a href="../authors/lammich">Peter Lammich</a> and <a href="../authors/olm">Markus Müller-Olm</a>
 
           </div>
           <span class="date">Dec 14</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/JinjaThreads.html">Jinja with Threads</a></h5>
             <br>
               by <a href="../authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">Dec 03</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/MuchAdoAboutTwo.html">Much Ado About Two</a></h5>
             <br>
               by <a href="../authors/boehme">Sascha Böhme</a>
 
           </div>
           <span class="date">Nov 06</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/SumSquares.html">Sums of Two and Four Squares</a></h5>
             <br>
               by <a href="../authors/oosterhuis">Roelof Oosterhuis</a>
 
           </div>
           <span class="date">Aug 12</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/Fermat3_4.html">Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples</a></h5>
             <br>
               by <a href="../authors/oosterhuis">Roelof Oosterhuis</a>
 
           </div>
           <span class="date">Aug 12</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/Valuation.html">Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma</a></h5>
             <br>
               by <a href="../authors/kobayashi">Hidetsune Kobayashi</a>
 
           </div>
           <span class="date">Aug 08</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/POPLmark-deBruijn.html">POPLmark Challenge Via de Bruijn Indices</a></h5>
             <br>
               by <a href="../authors/berghofer">Stefan Berghofer</a>
 
           </div>
           <span class="date">Aug 02</span>
         </article>
         <article class="entry">
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             <h5><a class="title" href="../entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></h5>
             <br>
               by <a href="../authors/berghofer">Stefan Berghofer</a>
 
           </div>
           <span class="date">Aug 02</span>
         </article>
       <h2 class="head">2006</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/HotelKeyCards.html">Hotel Key Card System</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Sep 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Abstract-Hoare-Logics.html">Abstract Hoare Logics</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Aug 08</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Flyspeck-Tame.html">Flyspeck I: Tame Graphs</a></h5>
             <br>
               by <a href="../authors/bauer">Gertrud Bauer</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">May 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/CoreC&#43;&#43;.html">CoreC&#43;&#43;</a></h5>
             <br>
               by <a href="../authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">May 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FeatherweightJava.html">A Theory of Featherweight Java in Isabelle/HOL</a></h5>
             <br>
               by <a href="../authors/fosterj">J. Nathan Foster</a> and <a href="../authors/vytiniotis">Dimitrios Vytiniotis</a>
 
           </div>
           <span class="date">Mar 31</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/ClockSynchInst.html">Instances of Schneider&#39;s generalized protocol of clock synchronization</a></h5>
             <br>
               by <a href="../authors/barsotti">Damián Barsotti</a>
 
           </div>
           <span class="date">Mar 15</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Cauchy.html">Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</a></h5>
             <br>
               by <a href="../authors/porter">Benjamin Porter</a>
 
           </div>
           <span class="date">Mar 14</span>
         </article>
       <h2 class="head">2005</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Ordinal.html">Countable Ordinals</a></h5>
             <br>
               by <a href="../authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">Nov 11</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FFT.html">Fast Fourier Transform</a></h5>
             <br>
               by <a href="../authors/ballarin">Clemens Ballarin</a>
 
           </div>
           <span class="date">Oct 12</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/GenClock.html">Formalization of a Generalized Protocol for Clock Synchronization</a></h5>
             <br>
               by <a href="../authors/tiu">Alwen Tiu</a>
 
           </div>
           <span class="date">Jun 24</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/DiskPaxos.html">Proving the Correctness of Disk Paxos</a></h5>
             <br>
               by <a href="../authors/jaskelioff">Mauro Jaskelioff</a> and <a href="../authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">Jun 22</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/JiveDataStoreModel.html">Jive Data and Store Model</a></h5>
             <br>
               by <a href="../authors/rauch">Nicole Rauch</a> and <a href="../authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">Jun 20</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Jinja.html">Jinja is not Java</a></h5>
             <br>
               by <a href="../authors/klein">Gerwin Klein</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Jun 01</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/RSAPSS.html">SHA1, RSA, PSS and more</a></h5>
             <br>
               by <a href="../authors/lindenberg">Christina Lindenberg</a> and <a href="../authors/wirt">Kai Wirt</a>
 
           </div>
           <span class="date">May 02</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Category.html">Category Theory to Yoneda&#39;s Lemma</a></h5>
             <br>
               by <a href="../authors/keefe">Greg O&rsquo;Keefe</a>
 
           </div>
           <span class="date">Apr 21</span>
         </article>
       <h2 class="head">2004</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/FileRefinement.html">File Refinement</a></h5>
             <br>
               by <a href="../authors/zee">Karen Zee</a> and <a href="../authors/kuncak">Viktor Kuncak</a>
 
           </div>
           <span class="date">Dec 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Integration.html">Integration theory and random variables</a></h5>
             <br>
               by <a href="../authors/richter">Stefan Richter</a>
 
           </div>
           <span class="date">Nov 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Verified-Prover.html">A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic</a></h5>
             <br>
               by <a href="../authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">Sep 28</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Ramsey-Infinite.html">Ramsey&#39;s theorem, infinitary version</a></h5>
             <br>
               by <a href="../authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">Sep 20</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Completeness.html">Completeness theorem</a></h5>
             <br>
               by <a href="../authors/margetson">James Margetson</a> and <a href="../authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">Sep 20</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Compiling-Exceptions-Correctly.html">Compiling Exceptions Correctly</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Jul 09</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Depth-First-Search.html">Depth First Search</a></h5>
             <br>
               by <a href="../authors/nishihara">Toshiaki Nishihara</a> and <a href="../authors/minamide">Yasuhiko Minamide</a>
 
           </div>
           <span class="date">Jun 24</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Group-Ring-Module.html">Groups, Rings and Modules</a></h5>
             <br>
               by <a href="../authors/kobayashi">Hidetsune Kobayashi</a>, <a href="../authors/chen">L. Chen</a> and <a href="../authors/murao">H. Murao</a>
 
           </div>
           <span class="date">May 18</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Topology.html">Topology</a></h5>
             <br>
               by <a href="../authors/friedrich">Stefan Friedrich</a>
 
           </div>
           <span class="date">Apr 26</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Lazy-Lists-II.html">Lazy Lists II</a></h5>
             <br>
               by <a href="../authors/friedrich">Stefan Friedrich</a>
 
           </div>
           <span class="date">Apr 26</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/BinarySearchTree.html">Binary Search Trees</a></h5>
             <br>
               by <a href="../authors/kuncak">Viktor Kuncak</a>
 
           </div>
           <span class="date">Apr 05</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/Functional-Automata.html">Functional Automata</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Mar 30</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/MiniML.html">Mini ML</a></h5>
             <br>
               by <a href="../authors/naraschewski">Wolfgang Naraschewski</a> and <a href="../authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">Mar 19</span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="../entries/AVL-Trees.html">AVL Trees</a></h5>
             <br>
               by <a href="../authors/nipkow">Tobias Nipkow</a> and <a href="../authors/pusch">Cornelia Pusch</a>
 
           </div>
           <span class="date">Mar 19</span>
         </article>
         
       </div>
     </div>
   </body>
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           <pubDate>Mon, 22 Jan 2024 00:00:00 +0000</pubDate>
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           <title>(Extended) Interval Analysis</title>
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           <pubDate>Sun, 21 Jan 2024 00:00:00 +0000</pubDate>
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           <title>Euler&#39;s Polyhedron Formula</title>
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           <pubDate>Mon, 14 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Catoids.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fixed-length vectors</title>
           <link>/entries/Fixed_Length_Vector.html</link>
           <pubDate>Mon, 14 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Fixed_Length_Vector.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polygonal Number Theorem</title>
           <link>/entries/Polygonal_Number_Theorem.html</link>
           <pubDate>Thu, 10 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Polygonal_Number_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>S-Finite Measure Monad on Quasi-Borel Spaces</title>
           <link>/entries/S_Finite_Measure_Monad.html</link>
           <pubDate>Tue, 08 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/S_Finite_Measure_Monad.html</guid>
           <description></description>
         </item>
         <item>
           <title>Standard Borel Spaces</title>
           <link>/entries/Standard_Borel_Spaces.html</link>
           <pubDate>Tue, 08 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Standard_Borel_Spaces.html</guid>
           <description></description>
         </item>
         <item>
           <title>Modal quantales, involutive quantales, Dedekind Quantales</title>
           <link>/entries/Quantales_Converse.html</link>
           <pubDate>Tue, 25 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Quantales_Converse.html</guid>
           <description></description>
         </item>
         <item>
           <title>Earley Parser</title>
           <link>/entries/Earley_Parser.html</link>
           <pubDate>Sun, 16 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Earley_Parser.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gray Codes for Arbitrary Numeral Systems</title>
           <link>/entries/Gray_Codes.html</link>
           <pubDate>Tue, 11 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Gray_Codes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Randomized Algorithms</title>
           <link>/entries/Executable_Randomized_Algorithms.html</link>
           <pubDate>Mon, 19 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Executable_Randomized_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>DCR Syntax and Execution Equivalent Markings</title>
           <link>/entries/DCR-ExecutionEquivalence.html</link>
           <pubDate>Fri, 16 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/DCR-ExecutionEquivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Zeckendorf’s Theorem</title>
           <link>/entries/Zeckendorf.html</link>
           <pubDate>Mon, 12 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Zeckendorf.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cryptographic Standards</title>
           <link>/entries/Crypto_Standards.html</link>
           <pubDate>Tue, 06 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Crypto_Standards.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Efficient Implementation of the Weighted Path Order</title>
           <link>/entries/Efficient_Weighted_Path_Order.html</link>
           <pubDate>Thu, 01 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Efficient_Weighted_Path_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Results on Directed Sets</title>
           <link>/entries/Directed_Sets.html</link>
           <pubDate>Wed, 24 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Directed_Sets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inner Structure, Determinism and Modal Algebra of Multirelations</title>
           <link>/entries/Multirelations_Heterogeneous.html</link>
           <pubDate>Mon, 22 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Multirelations_Heterogeneous.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Enumeration</title>
           <link>/entries/Tree_Enumeration.html</link>
           <pubDate>Tue, 09 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Tree_Enumeration.html</guid>
           <description></description>
         </item>
         <item>
           <title>MLSS Decision Procedure</title>
           <link>/entries/MLSS_Decision_Proc.html</link>
           <pubDate>Fri, 05 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/MLSS_Decision_Proc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Three Squares Theorem</title>
           <link>/entries/Three_Squares.html</link>
           <pubDate>Wed, 03 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Three_Squares.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Halting Problem is Soluble in Malament-Hogarth Spacetimes</title>
           <link>/entries/MHComputation.html</link>
           <pubDate>Sat, 29 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/MHComputation.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Schwartz-Zippel Lemma</title>
           <link>/entries/Schwartz_Zippel.html</link>
           <pubDate>Thu, 27 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Schwartz_Zippel.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of the SCL(FOL) Calculus: Simple Clause Learning for First-Order Logic</title>
           <link>/entries/Simple_Clause_Learning.html</link>
           <pubDate>Thu, 20 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Simple_Clause_Learning.html</guid>
           <description></description>
         </item>
         <item>
           <title>The CHSH inequality: Tsirelson&#39;s upper-bound and other results</title>
           <link>/entries/TsirelsonBound.html</link>
           <pubDate>Tue, 18 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/TsirelsonBound.html</guid>
           <description></description>
         </item>
         <item>
           <title>Distributed Distinct Elements</title>
           <link>/entries/Distributed_Distinct_Elements.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Distributed_Distinct_Elements.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Hyper Hoare Logic: A Logic to (Dis-)Prove Program Hyperproperties</title>
           <link>/entries/HyperHoareLogic.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HyperHoareLogic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Positional Notation for Natural Numbers in an Arbitrary Base</title>
           <link>/entries/DigitsInBase.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/DigitsInBase.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of CommCSL: A Relational Concurrent Separation Logic for Proving Information Flow Security in Concurrent Programs</title>
           <link>/entries/CommCSL.html</link>
           <pubDate>Wed, 15 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/CommCSL.html</guid>
           <description></description>
         </item>
         <item>
           <title>No Faster-Than-Light Observers (GenRel)</title>
           <link>/entries/No_FTL_observers_Gen_Rel.html</link>
           <pubDate>Sun, 05 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/No_FTL_observers_Gen_Rel.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expander Graphs</title>
           <link>/entries/Expander_Graphs.html</link>
           <pubDate>Fri, 03 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Expander_Graphs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Renaming-Enriched Sets (Rensets) and Renaming-Based Recursion</title>
           <link>/entries/Rensets.html</link>
           <pubDate>Tue, 28 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Rensets.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sound and Complete Calculus for Probability Inequalities</title>
           <link>/entries/Probability_Inequality_Completeness.html</link>
           <pubDate>Mon, 20 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Probability_Inequality_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Group Law of Edwards Elliptic Curves</title>
           <link>/entries/Edwards_Elliptic_Curves_Group.html</link>
           <pubDate>Thu, 16 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Edwards_Elliptic_Curves_Group.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hardness of Lattice Problems</title>
           <link>/entries/CVP_Hardness.html</link>
           <pubDate>Thu, 02 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/CVP_Hardness.html</guid>
           <description></description>
         </item>
         <item>
           <title>ABY3 Multiplication and Array Shuffling</title>
           <link>/entries/ABY3_Protocols.html</link>
           <pubDate>Fri, 27 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/ABY3_Protocols.html</guid>
           <description></description>
         </item>
         <item>
           <title>Given Clause Loops</title>
           <link>/entries/Given_Clause_Loops.html</link>
           <pubDate>Wed, 25 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Given_Clause_Loops.html</guid>
           <description></description>
         </item>
         <item>
           <title>Suppes&#39; Theorem For Probability Logic</title>
           <link>/entries/Suppes_Theorem.html</link>
           <pubDate>Sun, 22 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Suppes_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Hoare Logic for Diverging Programs</title>
           <link>/entries/HoareForDivergence.html</link>
           <pubDate>Fri, 20 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HoareForDivergence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strict Omega Categories</title>
           <link>/entries/StrictOmegaCategories.html</link>
           <pubDate>Sat, 14 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/StrictOmegaCategories.html</guid>
           <description></description>
         </item>
         <item>
           <title>Synthetic Completeness</title>
           <link>/entries/Synthetic_Completeness.html</link>
           <pubDate>Mon, 09 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Synthetic_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cook-Levin theorem</title>
           <link>/entries/Cook_Levin.html</link>
           <pubDate>Sun, 08 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Cook_Levin.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary codes that do not preserve primitivity</title>
           <link>/entries/Binary_Code_Imprimitive.html</link>
           <pubDate>Tue, 03 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Binary_Code_Imprimitive.html</guid>
           <description></description>
         </item>
         <item>
           <title>Intersection of two monoids generated by two element codes</title>
           <link>/entries/Two_Generated_Word_Monoids_Intersection.html</link>
           <pubDate>Tue, 03 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Two_Generated_Word_Monoids_Intersection.html</guid>
           <description></description>
         </item>
         <item>
           <title>A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL</title>
           <link>/entries/Quantifier_Elimination_Hybrid.html</link>
           <pubDate>Thu, 15 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Quantifier_Elimination_Hybrid.html</guid>
           <description></description>
         </item>
         <item>
           <title>Class-based Classical Propositional Logic</title>
           <link>/entries/Propositional_Logic_Class.html</link>
           <pubDate>Thu, 15 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Propositional_Logic_Class.html</guid>
           <description></description>
         </item>
         <item>
           <title>Birkhoff&#39;s Representation Theorem For Finite Distributive Lattices</title>
           <link>/entries/Birkhoff_Finite_Distributive_Lattices.html</link>
           <pubDate>Tue, 06 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Birkhoff_Finite_Distributive_Lattices.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automation of Boolos&#39; Curious Inference in Isabelle/HOL</title>
           <link>/entries/Boolos_Curious_Inference_Automated.html</link>
           <pubDate>Mon, 05 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Boolos_Curious_Inference_Automated.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Translation of Multitape Turing Machines into Singletape Turing Machines</title>
           <link>/entries/Multitape_To_Singletape_TM.html</link>
           <pubDate>Wed, 30 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Multitape_To_Singletape_TM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Object Theory</title>
           <link>/entries/AOT.html</link>
           <pubDate>Mon, 28 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/AOT.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal CHERI-C Memory Model</title>
           <link>/entries/CHERI-C_Memory_Model.html</link>
           <pubDate>Fri, 25 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/CHERI-C_Memory_Model.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sauer-Shelah Lemma</title>
           <link>/entries/Sauer_Shelah_Lemma.html</link>
           <pubDate>Thu, 24 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Sauer_Shelah_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kneser&#39;s Theorem and the Cauchy–Davenport Theorem</title>
           <link>/entries/Kneser_Cauchy_Davenport.html</link>
           <pubDate>Mon, 21 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Kneser_Cauchy_Davenport.html</guid>
           <description></description>
         </item>
         <item>
           <title>Turán&#39;s Graph Theorem</title>
           <link>/entries/Turans_Graph_Theorem.html</link>
           <pubDate>Mon, 14 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Turans_Graph_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial Enumeration Algorithms</title>
           <link>/entries/Combinatorial_Enumeration_Algorithms.html</link>
           <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorial_Enumeration_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Balog–Szemerédi–Gowers Theorem</title>
           <link>/entries/Balog_Szemeredi_Gowers.html</link>
           <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Balog_Szemeredi_Gowers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of Strategy-Proofness and Representation in Party-Approval Multi-Winner Elections</title>
           <link>/entries/PAPP_Impossibility.html</link>
           <pubDate>Thu, 10 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/PAPP_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of Query Optimization Algorithms</title>
           <link>/entries/Query_Optimization.html</link>
           <pubDate>Tue, 04 Oct 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Query_Optimization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum Segment Sum</title>
           <link>/entries/Maximum_Segment_Sum.html</link>
           <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Maximum_Segment_Sum.html</guid>
           <description></description>
         </item>
         <item>
           <title>Undirected Graph Theory</title>
           <link>/entries/Undirected_Graph_Theory.html</link>
           <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Undirected_Graph_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Making Arbitrary Relational Calculus Queries Safe-Range</title>
           <link>/entries/Safe_Range_RC.html</link>
           <pubDate>Wed, 28 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_Range_RC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stalnaker&#39;s Epistemic Logic</title>
           <link>/entries/Stalnaker_Logic.html</link>
           <pubDate>Fri, 23 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Stalnaker_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>p-adic Fields and p-adic Semialgebraic Sets</title>
           <link>/entries/Padic_Field.html</link>
           <pubDate>Thu, 22 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Padic_Field.html</guid>
           <description></description>
         </item>
         <item>
           <title>Risk-Free Lending</title>
           <link>/entries/Risk_Free_Lending.html</link>
           <pubDate>Sun, 18 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Risk_Free_Lending.html</guid>
           <description></description>
         </item>
         <item>
           <title>Soundness and Completeness of Implicational Logic</title>
           <link>/entries/Implicational_Logic.html</link>
           <pubDate>Tue, 13 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Implicational_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber</title>
           <link>/entries/CRYSTALS-Kyber.html</link>
           <pubDate>Thu, 08 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/CRYSTALS-Kyber.html</guid>
           <description></description>
         </item>
         <item>
           <title>Unbounded Separation Logic</title>
           <link>/entries/Separation_Logic_Unbounded.html</link>
           <pubDate>Mon, 05 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Logic_Unbounded.html</guid>
           <description></description>
         </item>
         <item>
           <title>Khovanskii&amp;#x27;s Theorem</title>
           <link>/entries/Khovanskii_Theorem.html</link>
           <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Khovanskii_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hales–Jewett Theorem</title>
           <link>/entries/Hales_Jewett.html</link>
           <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Hales_Jewett.html</guid>
           <description></description>
         </item>
         <item>
           <title>Number Theoretic Transform</title>
           <link>/entries/Number_Theoretic_Transform.html</link>
           <pubDate>Thu, 18 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Number_Theoretic_Transform.html</guid>
           <description></description>
         </item>
         <item>
           <title>Correctness of a Set-based Algorithm for Computing Strongly Connected Components of a Graph</title>
           <link>/entries/SCC_Bloemen_Sequential.html</link>
           <pubDate>Wed, 17 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/SCC_Bloemen_Sequential.html</guid>
           <description></description>
         </item>
         <item>
           <title>From THE BOOK: Two Squares via Involutions</title>
           <link>/entries/Involutions2Squares.html</link>
           <pubDate>Mon, 15 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Involutions2Squares.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Complete Test Strategies for Finite State Machines</title>
           <link>/entries/FSM_Tests.html</link>
           <pubDate>Tue, 09 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FSM_Tests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Nano JSON: Working with JSON formatted data in Isabelle/HOL and Isabelle/ML</title>
           <link>/entries/Nano_JSON.html</link>
           <pubDate>Fri, 29 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Nano_JSON.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</title>
           <link>/entries/Solidity.html</link>
           <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Solidity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simultaneous diagonalization of pairwise commuting Hermitian matrices</title>
           <link>/entries/Commuting_Hermitian.html</link>
           <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Commuting_Hermitian.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality</title>
           <link>/entries/Weighted_Arithmetic_Geometric_Mean.html</link>
           <pubDate>Mon, 11 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Weighted_Arithmetic_Geometric_Mean.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Reuse-Based Multi-Stage Compiler Verification for Language IMP</title>
           <link>/entries/IMP_Compiler_Reuse.html</link>
           <pubDate>Sun, 10 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/IMP_Compiler_Reuse.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real-Time Double-Ended Queue</title>
           <link>/entries/Real_Time_Deque.html</link>
           <pubDate>Thu, 23 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Time_Deque.html</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos&#39;s Curious Inference in Isabelle/HOL</title>
           <link>/entries/Boolos_Curious_Inference.html</link>
           <pubDate>Mon, 20 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Boolos_Curious_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Fields</title>
           <link>/entries/Finite_Fields.html</link>
           <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Finite_Fields.html</guid>
           <description></description>
         </item>
         <item>
           <title>IsaNet: Formalization of a Verification Framework for Secure Data Plane Protocols</title>
           <link>/entries/IsaNet.html</link>
           <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/IsaNet.html</guid>
           <description></description>
         </item>
         <item>
           <title>Diophantine Equations and the DPRM Theorem</title>
           <link>/entries/DPRM_Theorem.html</link>
           <pubDate>Mon, 06 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/DPRM_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Reducing Rewrite Properties to Properties on Ground Terms</title>
           <link>/entries/Rewrite_Properties_Reduction.html</link>
           <pubDate>Thu, 02 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Rewrite_Properties_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Restricted Definition of the Magic Wand to Soundly Combine Fractions of a Wand</title>
           <link>/entries/Combinable_Wands.html</link>
           <pubDate>Mon, 30 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Combinable_Wands.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Plünnecke-Ruzsa Inequality</title>
           <link>/entries/Pluennecke_Ruzsa_Inequality.html</link>
           <pubDate>Thu, 26 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Pluennecke_Ruzsa_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Framework for the Sound Automation of Magic Wands</title>
           <link>/entries/Package_logic.html</link>
           <pubDate>Wed, 18 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Package_logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Clique is not solvable by monotone circuits of polynomial size</title>
           <link>/entries/Clique_and_Monotone_Circuits.html</link>
           <pubDate>Sun, 08 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Clique_and_Monotone_Circuits.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</title>
           <link>/entries/Fishers_Inequality.html</link>
           <pubDate>Thu, 21 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Fishers_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Digit Expansions</title>
           <link>/entries/Digit_Expansions.html</link>
           <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Digit_Expansions.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Generalized Multiset Ordering is NP-Complete</title>
           <link>/entries/Multiset_Ordering_NPC.html</link>
           <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Multiset_Ordering_NPC.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sophomore&#39;s Dream</title>
           <link>/entries/Sophomores_Dream.html</link>
           <pubDate>Sun, 10 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Sophomores_Dream.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Combinator Library for Prefix-Free Codes</title>
           <link>/entries/Prefix_Free_Code_Combinators.html</link>
           <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Prefix_Free_Code_Combinators.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Randomized Approximation Algorithms for Frequency Moments</title>
           <link>/entries/Frequency_Moments.html</link>
           <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Frequency_Moments.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructing the Reals as Dedekind Cuts of Rationals</title>
           <link>/entries/Dedekind_Real.html</link>
           <pubDate>Thu, 24 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Dedekind_Real.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ackermann&#39;s Function Is Not Primitive Recursive</title>
           <link>/entries/Ackermanns_not_PR.html</link>
           <pubDate>Wed, 23 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Ackermanns_not_PR.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Naive Prover for First-Order Logic</title>
           <link>/entries/FOL_Seq_Calc3.html</link>
           <pubDate>Tue, 22 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc3.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent</title>
           <link>/entries/Cotangent_PFD_Formula.html</link>
           <pubDate>Tue, 15 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Cotangent_PFD_Formula.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Independence of the Continuum Hypothesis in Isabelle/ZF</title>
           <link>/entries/Independence_CH.html</link>
           <pubDate>Sun, 06 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Independence_CH.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive Models of Fragments of ZFC</title>
           <link>/entries/Transitive_Models.html</link>
           <pubDate>Thu, 03 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated Transition Systems</title>
           <link>/entries/ResiduatedTransitionSystem.html</link>
           <pubDate>Mon, 28 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/ResiduatedTransitionSystem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Universal Hash Families</title>
           <link>/entries/Universal_Hash_Families.html</link>
           <pubDate>Sun, 20 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Universal_Hash_Families.html</guid>
           <description></description>
         </item>
         <item>
           <title>Wetzel&#39;s Problem and the Continuum Hypothesis</title>
           <link>/entries/Wetzels_Problem.html</link>
           <pubDate>Fri, 18 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Wetzels_Problem.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Query Evaluation</title>
           <link>/entries/Eval_FO.html</link>
           <pubDate>Tue, 15 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Eval_FO.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multi-Head Monitoring of Metric Dynamic Logic</title>
           <link>/entries/VYDRA_MDL.html</link>
           <pubDate>Sun, 13 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/VYDRA_MDL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Enumeration of Equivalence Relations</title>
           <link>/entries/Equivalence_Relation_Enumeration.html</link>
           <pubDate>Fri, 04 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Equivalence_Relation_Enumeration.html</guid>
           <description></description>
         </item>
         <item>
           <title>Duality of Linear Programming</title>
           <link>/entries/LP_Duality.html</link>
           <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/LP_Duality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quasi-Borel Spaces</title>
           <link>/entries/Quasi_Borel_Spaces.html</link>
           <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Quasi_Borel_Spaces.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Theory of Rewriting</title>
           <link>/entries/FO_Theory_Rewriting.html</link>
           <pubDate>Wed, 02 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FO_Theory_Rewriting.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequent Calculus Prover for First-Order Logic with Functions</title>
           <link>/entries/FOL_Seq_Calc2.html</link>
           <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc2.html</guid>
           <description></description>
         </item>
         <item>
           <title>Young&#39;s Inequality for Increasing Functions</title>
           <link>/entries/Youngs_Inequality.html</link>
           <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Youngs_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interpolation Polynomials (in HOL-Algebra)</title>
           <link>/entries/Interpolation_Polynomials_HOL_Algebra.html</link>
           <pubDate>Sat, 29 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Interpolation_Polynomials_HOL_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Median Method</title>
           <link>/entries/Median_Method.html</link>
           <pubDate>Tue, 25 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Median_Method.html</guid>
           <description></description>
         </item>
         <item>
           <title>Actuarial Mathematics</title>
           <link>/entries/Actuarial_Mathematics.html</link>
           <pubDate>Sun, 23 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Actuarial_Mathematics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational numbers from THE BOOK</title>
           <link>/entries/Irrationals_From_THEBOOK.html</link>
           <pubDate>Sat, 08 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Irrationals_From_THEBOOK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knight&#39;s Tour Revisited Revisited</title>
           <link>/entries/Knights_Tour.html</link>
           <pubDate>Tue, 04 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Knights_Tour.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hyperdual Numbers and Forward Differentiation</title>
           <link>/entries/Hyperdual.html</link>
           <pubDate>Fri, 31 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hyperdual.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gale-Shapley Algorithm</title>
           <link>/entries/Gale_Shapley.html</link>
           <pubDate>Wed, 29 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Gale_Shapley.html</guid>
           <description></description>
         </item>
         <item>
           <title>Roth&#39;s Theorem on Arithmetic Progressions</title>
           <link>/entries/Roth_Arithmetic_Progressions.html</link>
           <pubDate>Tue, 28 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Roth_Arithmetic_Progressions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Markov Decision Processes with Rewards</title>
           <link>/entries/MDP-Rewards.html</link>
           <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MDP-Rewards.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Algorithms for Solving Markov Decision Processes</title>
           <link>/entries/MDP-Algorithms.html</link>
           <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MDP-Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Tree Relations</title>
           <link>/entries/Regular_Tree_Relations.html</link>
           <pubDate>Wed, 15 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Regular_Tree_Relations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simplicial Complexes and Boolean functions</title>
           <link>/entries/Simplicial_complexes_and_boolean_functions.html</link>
           <pubDate>Mon, 29 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Simplicial_complexes_and_boolean_functions.html</guid>
           <description></description>
         </item>
         <item>
           <title>van Emde Boas Trees</title>
           <link>/entries/Van_Emde_Boas_Trees.html</link>
           <pubDate>Tue, 23 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Van_Emde_Boas_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Foundation of geometry in planes, and some complements: Excluding the parallel axioms</title>
           <link>/entries/Foundation_of_geometry.html</link>
           <pubDate>Mon, 22 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Foundation_of_geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hahn and Jordan Decomposition Theorems</title>
           <link>/entries/Hahn_Jordan_Decomposition.html</link>
           <pubDate>Fri, 19 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hahn_Jordan_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automating Public Announcement Logic and the Wise Men Puzzle in Isabelle/HOL</title>
           <link>/entries/PAL.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/PAL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL</title>
           <link>/entries/SimplifiedOntologicalArgument.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/SimplifiedOntologicalArgument.html</guid>
           <description></description>
         </item>
         <item>
           <title>Factorization of Polynomials with Algebraic Coefficients</title>
           <link>/entries/Factor_Algebraic_Polynomial.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Factor_Algebraic_Polynomial.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real Exponents as the Limits of Sequences of Rational Exponents</title>
           <link>/entries/Real_Power.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Power.html</guid>
           <description></description>
         </item>
         <item>
           <title>Szemerédi&#39;s Regularity Lemma</title>
           <link>/entries/Szemeredi_Regularity.html</link>
           <pubDate>Fri, 05 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Szemeredi_Regularity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum and Classical Registers</title>
           <link>/entries/Registers.html</link>
           <pubDate>Thu, 28 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Registers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Belief Revision Theory</title>
           <link>/entries/Belief_Revision.html</link>
           <pubDate>Tue, 19 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Belief_Revision.html</guid>
           <description></description>
         </item>
         <item>
           <title>X86 instruction semantics and basic block symbolic execution</title>
           <link>/entries/X86_Semantics.html</link>
           <pubDate>Wed, 13 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/X86_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</title>
           <link>/entries/Correctness_Algebras.html</link>
           <pubDate>Tue, 12 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Correctness_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Quadratic Virtual Substitution for Real Arithmetic</title>
           <link>/entries/Virtual_Substitution.html</link>
           <pubDate>Sat, 02 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Virtual_Substitution.html</guid>
           <description></description>
         </item>
         <item>
           <title>Soundness and Completeness of an Axiomatic System for First-Order Logic</title>
           <link>/entries/FOL_Axiomatic.html</link>
           <pubDate>Fri, 24 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Axiomatic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complex Bounded Operators</title>
           <link>/entries/Complex_Bounded_Operators.html</link>
           <pubDate>Sat, 18 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Complex_Bounded_Operators.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Weighted Path Orders and Recursive Path Orders</title>
           <link>/entries/Weighted_Path_Order.html</link>
           <pubDate>Thu, 16 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Weighted_Path_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</title>
           <link>/entries/CZH_Foundations.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Foundations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</title>
           <link>/entries/CZH_Elementary_Categories.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Elementary_Categories.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL III: Universal Constructions</title>
           <link>/entries/CZH_Universal_Constructions.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Universal_Constructions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional Simplification</title>
           <link>/entries/Conditional_Simplification.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Conditional_Simplification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional Transfer Rule</title>
           <link>/entries/Conditional_Transfer_Rule.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Conditional_Transfer_Rule.html</guid>
           <description></description>
         </item>
         <item>
           <title>Extension of Types-To-Sets</title>
           <link>/entries/Types_To_Sets_Extension.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Types_To_Sets_Extension.html</guid>
           <description></description>
         </item>
         <item>
           <title>IDE: Introduction, Destruction, Elimination</title>
           <link>/entries/Intro_Dest_Elim.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Intro_Dest_Elim.html</guid>
           <description></description>
         </item>
         <item>
           <title>A data flow analysis algorithm for computing dominators</title>
           <link>/entries/Dominance_CHK.html</link>
           <pubDate>Sun, 05 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Dominance_CHK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Solving Cubic and Quartic Equations</title>
           <link>/entries/Cubic_Quartic_Equations.html</link>
           <pubDate>Fri, 03 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Cubic_Quartic_Equations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Logging-independent Message Anonymity in the Relational Method</title>
           <link>/entries/Logging_Independent_Anonymity.html</link>
           <pubDate>Thu, 26 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Logging_Independent_Anonymity.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Theorem of Three Circles</title>
           <link>/entries/Three_Circles.html</link>
           <pubDate>Sat, 21 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Three_Circles.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoCon: A Confidentiality-Verified Conference Management System</title>
           <link>/entries/CoCon.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoCon.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional BD Security</title>
           <link>/entries/BD_Security_Compositional.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BD_Security_Compositional.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMed: A confidentiality-verified social media platform</title>
           <link>/entries/CoSMed.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoSMed.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMeDis: A confidentiality-verified distributed social media platform</title>
           <link>/entries/CoSMeDis.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoSMeDis.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fresh identifiers</title>
           <link>/entries/Fresh_Identifiers.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Fresh_Identifiers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial Design Theory</title>
           <link>/entries/Design_Theory.html</link>
           <pubDate>Fri, 13 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Design_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Forests</title>
           <link>/entries/Relational_Forests.html</link>
           <pubDate>Tue, 03 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Forests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Schutz&#39; Independent Axioms for Minkowski Spacetime</title>
           <link>/entries/Schutz_Spacetime.html</link>
           <pubDate>Tue, 27 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Schutz_Spacetime.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finitely Generated Abelian Groups</title>
           <link>/entries/Finitely_Generated_Abelian_Groups.html</link>
           <pubDate>Wed, 07 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Finitely_Generated_Abelian_Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>SpecCheck - Specification-Based Testing for Isabelle/ML</title>
           <link>/entries/SpecCheck.html</link>
           <pubDate>Thu, 01 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/SpecCheck.html</guid>
           <description></description>
         </item>
         <item>
           <title>Van der Waerden&#39;s Theorem</title>
           <link>/entries/Van_der_Waerden.html</link>
           <pubDate>Tue, 22 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Van_der_Waerden.html</guid>
           <description></description>
         </item>
         <item>
           <title>MiniSail - A kernel language for the ISA specification language SAIL</title>
           <link>/entries/MiniSail.html</link>
           <pubDate>Fri, 18 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MiniSail.html</guid>
           <description></description>
         </item>
         <item>
           <title>Public Announcement Logic</title>
           <link>/entries/Public_Announcement_Logic.html</link>
           <pubDate>Thu, 17 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Public_Announcement_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Shorter Compiler Correctness Proof for Language IMP</title>
           <link>/entries/IMP_Compiler.html</link>
           <pubDate>Fri, 04 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IMP_Compiler.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics on Words Basics</title>
           <link>/entries/Combinatorics_Words.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Lemma</title>
           <link>/entries/Combinatorics_Words_Graph_Lemma.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words_Graph_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lyndon words</title>
           <link>/entries/Combinatorics_Words_Lyndon.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words_Lyndon.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regression Test Selection</title>
           <link>/entries/Regression_Test_Selection.html</link>
           <pubDate>Fri, 30 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Regression_Test_Selection.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle&#39;s Metalogic: Formalization and Proof Checker</title>
           <link>/entries/Metalogic_ProofChecker.html</link>
           <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Metalogic_ProofChecker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting the Exponent</title>
           <link>/entries/Lifting_the_Exponent.html</link>
           <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Lifting_the_Exponent.html</guid>
           <description></description>
         </item>
         <item>
           <title>The BKR Decision Procedure for Univariate Real Arithmetic</title>
           <link>/entries/BenOr_Kozen_Reif.html</link>
           <pubDate>Sat, 24 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BenOr_Kozen_Reif.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gale-Stewart Games</title>
           <link>/entries/GaleStewart_Games.html</link>
           <pubDate>Fri, 23 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/GaleStewart_Games.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Timely Dataflow&#39;s Progress Tracking Protocol</title>
           <link>/entries/Progress_Tracking.html</link>
           <pubDate>Tue, 13 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Progress_Tracking.html</guid>
           <description></description>
         </item>
         <item>
           <title>Information Flow Control via Dependency Tracking</title>
           <link>/entries/IFC_Tracking.html</link>
           <pubDate>Thu, 01 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IFC_Tracking.html</guid>
           <description></description>
         </item>
         <item>
           <title>Grothendieck&#39;s Schemes in Algebraic Geometry</title>
           <link>/entries/Grothendieck_Schemes.html</link>
           <pubDate>Mon, 29 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Grothendieck_Schemes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hensel&#39;s Lemma for the p-adic Integers</title>
           <link>/entries/Padic_Ints.html</link>
           <pubDate>Tue, 23 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Padic_Ints.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive Cryptography in HOL: the Communication Modeling Aspect</title>
           <link>/entries/Constructive_Cryptography_CM.html</link>
           <pubDate>Wed, 17 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Constructive_Cryptography_CM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</title>
           <link>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</link>
           <pubDate>Fri, 12 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum projective measurements and the CHSH inequality</title>
           <link>/entries/Projective_Measurements.html</link>
           <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Projective_Measurements.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hermite–Lindemann–Weierstraß Transcendence Theorem</title>
           <link>/entries/Hermite_Lindemann.html</link>
           <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hermite_Lindemann.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mereology</title>
           <link>/entries/Mereology.html</link>
           <pubDate>Mon, 01 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Mereology.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sunflower Lemma of Erdős and Rado</title>
           <link>/entries/Sunflowers.html</link>
           <pubDate>Thu, 25 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Sunflowers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Imperative Implementation of B-Trees</title>
           <link>/entries/BTree.html</link>
           <pubDate>Wed, 24 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BTree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Puiseux Series</title>
           <link>/entries/Formal_Puiseux_Series.html</link>
           <pubDate>Wed, 17 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Formal_Puiseux_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Laws of Large Numbers</title>
           <link>/entries/Laws_of_Large_Numbers.html</link>
           <pubDate>Wed, 10 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Laws_of_Large_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tarski&#39;s Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</title>
           <link>/entries/IsaGeoCoq.html</link>
           <pubDate>Sun, 31 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IsaGeoCoq.html</guid>
           <description></description>
         </item>
         <item>
           <title>Solution to the xkcd Blue Eyes puzzle</title>
           <link>/entries/Blue_Eyes.html</link>
           <pubDate>Sat, 30 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Blue_Eyes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hood-Melville Queue</title>
           <link>/entries/Hood_Melville_Queue.html</link>
           <pubDate>Mon, 18 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hood_Melville_Queue.html</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaDCI: a Java semantics with dynamic class initialization</title>
           <link>/entries/JinjaDCI.html</link>
           <pubDate>Mon, 11 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/JinjaDCI.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cofinality and the Delta System Lemma</title>
           <link>/entries/Delta_System_Lemma.html</link>
           <pubDate>Sun, 27 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Delta_System_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Topological semantics for paraconsistent and paracomplete logics</title>
           <link>/entries/Topological_Semantics.html</link>
           <pubDate>Thu, 17 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Topological_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Minimum Spanning Tree Algorithms</title>
           <link>/entries/Relational_Minimum_Spanning_Trees.html</link>
           <pubDate>Tue, 08 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Minimum_Spanning_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inline Caching and Unboxing Optimization for Interpreters</title>
           <link>/entries/Interpreter_Optimizations.html</link>
           <pubDate>Mon, 07 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Interpreter_Optimizations.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Relational Method with Message Anonymity for the Verification of Cryptographic Protocols</title>
           <link>/entries/Relational_Method.html</link>
           <pubDate>Sat, 05 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Method.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</title>
           <link>/entries/Isabelle_Marries_Dirac.html</link>
           <pubDate>Sun, 22 Nov 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_Marries_Dirac.html</guid>
           <description></description>
         </item>
         <item>
           <title>The HOL-CSP Refinement Toolkit</title>
           <link>/entries/CSP_RefTK.html</link>
           <pubDate>Thu, 19 Nov 2020 00:00:00 +0000</pubDate>
           <guid>/entries/CSP_RefTK.html</guid>
           <description></description>
         </item>
         <item>
           <title>AI Planning Languages Semantics</title>
           <link>/entries/AI_Planning_Languages_Semantics.html</link>
           <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/AI_Planning_Languages_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified SAT-Based AI Planning</title>
           <link>/entries/Verified_SAT_Based_AI_Planning.html</link>
           <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Verified_SAT_Based_AI_Planning.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sound Type System for Physical Quantities, Units, and Measurements</title>
           <link>/entries/Physical_Quantities.html</link>
           <pubDate>Tue, 20 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Physical_Quantities.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Map Extras</title>
           <link>/entries/Finite-Map-Extras.html</link>
           <pubDate>Mon, 12 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Finite-Map-Extras.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Document Object Model with Shadow Roots</title>
           <link>/entries/Shadow_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Shadow_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Safely Composable Document Object Model with Shadow Roots</title>
           <link>/entries/Shadow_SC_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Shadow_SC_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Safely Composable Web Components</title>
           <link>/entries/SC_DOM_Components.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/SC_DOM_Components.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Web Components</title>
           <link>/entries/DOM_Components.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/DOM_Components.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Safely Composable DOM</title>
           <link>/entries/Core_SC_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Core_SC_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Abstract Formalization of G&amp;ouml;del&#39;s Incompleteness Theorems</title>
           <link>/entries/Goedel_Incompleteness.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_Incompleteness.html</guid>
           <description></description>
         </item>
         <item>
           <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part I</title>
           <link>/entries/Goedel_HFSet_Semantic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_HFSet_Semantic.html</guid>
           <description></description>
         </item>
         <item>
           <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part II</title>
           <link>/entries/Goedel_HFSet_Semanticless.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_HFSet_Semanticless.html</guid>
           <description></description>
         </item>
         <item>
           <title>Robinson Arithmetic</title>
           <link>/entries/Robinson_Arithmetic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Robinson_Arithmetic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax-Independent Logic Infrastructure</title>
           <link>/entries/Syntax_Independent_Logic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Syntax_Independent_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of Extended Finite State Machines</title>
           <link>/entries/Extended_Finite_State_Machines.html</link>
           <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Extended_Finite_State_Machines.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inference of Extended Finite State Machines</title>
           <link>/entries/Extended_Finite_State_Machine_Inference.html</link>
           <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Extended_Finite_State_Machine_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Practical Algebraic Calculus Checker</title>
           <link>/entries/PAC_Checker.html</link>
           <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/PAC_Checker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Some classical results in inductive inference of recursive functions</title>
           <link>/entries/Inductive_Inference.html</link>
           <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Inductive_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Disjoint-Set Forests</title>
           <link>/entries/Relational_Disjoint_Set_Forests.html</link>
           <pubDate>Wed, 26 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Disjoint_Set_Forests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Extensions to the Comprehensive Framework for Saturation Theorem Proving</title>
           <link>/entries/Saturation_Framework_Extensions.html</link>
           <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Saturation_Framework_Extensions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Putting the `K&#39; into Bird&#39;s derivation of Knuth-Morris-Pratt string matching</title>
           <link>/entries/BirdKMP.html</link>
           <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/BirdKMP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Amicable Numbers</title>
           <link>/entries/Amicable_Numbers.html</link>
           <pubDate>Tue, 04 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Amicable_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal Partitions</title>
           <link>/entries/Ordinal_Partitions.html</link>
           <pubDate>Mon, 03 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinal_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm</title>
           <link>/entries/Chandy_Lamport.html</link>
           <pubDate>Tue, 21 Jul 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Chandy_Lamport.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Characterisations of Paths</title>
           <link>/entries/Relational_Paths.html</link>
           <pubDate>Mon, 13 Jul 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Paths.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles</title>
           <link>/entries/Safe_Distance.html</link>
           <pubDate>Mon, 01 Jun 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_Distance.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified algorithm for computing the Smith normal form of a matrix</title>
           <link>/entries/Smith_Normal_Form.html</link>
           <pubDate>Sat, 23 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Smith_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Nash-Williams Partition Theorem</title>
           <link>/entries/Nash_Williams.html</link>
           <pubDate>Sat, 16 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Nash_Williams.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Knuth–Bendix Orders</title>
           <link>/entries/Knuth_Bendix_Order.html</link>
           <pubDate>Wed, 13 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Knuth_Bendix_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationality Criteria for Series by Erdős and Straus</title>
           <link>/entries/Irrational_Series_Erdos_Straus.html</link>
           <pubDate>Tue, 12 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Irrational_Series_Erdos_Straus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion Theorem in ZF</title>
           <link>/entries/Recursion-Addition.html</link>
           <pubDate>Mon, 11 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Recursion-Addition.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation</title>
           <link>/entries/LTL_Normal_Form.html</link>
           <pubDate>Fri, 08 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Forcing in Isabelle/ZF</title>
           <link>/entries/Forcing.html</link>
           <pubDate>Wed, 06 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Forcing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Banach-Steinhaus Theorem</title>
           <link>/entries/Banach_Steinhaus.html</link>
           <pubDate>Sat, 02 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Banach_Steinhaus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Attack Trees in Isabelle for GDPR compliance of IoT healthcare systems</title>
           <link>/entries/Attack_Trees.html</link>
           <pubDate>Mon, 27 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Attack_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gaussian Integers</title>
           <link>/entries/Gaussian_Integers.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Gaussian_Integers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Power Sum Polynomials</title>
           <link>/entries/Power_Sum_Polynomials.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Power_Sum_Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Lambert W Function on the Reals</title>
           <link>/entries/Lambert_W.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Lambert_W.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices for ODEs</title>
           <link>/entries/Matrices_for_ODEs.html</link>
           <pubDate>Sun, 19 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Matrices_for_ODEs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Authenticated Data Structures As Functors</title>
           <link>/entries/ADS_Functor.html</link>
           <pubDate>Thu, 16 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/ADS_Functor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows</title>
           <link>/entries/Sliding_Window_Algorithm.html</link>
           <pubDate>Fri, 10 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Sliding_Window_Algorithm.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Comprehensive Framework for Saturation Theorem Proving</title>
           <link>/entries/Saturation_Framework.html</link>
           <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Saturation_Framework.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</title>
           <link>/entries/MFODL_Monitor_Optimized.html</link>
           <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/MFODL_Monitor_Optimized.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automated Stateful Protocol Verification</title>
           <link>/entries/Automated_Stateful_Protocol_Verification.html</link>
           <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Automated_Stateful_Protocol_Verification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stateful Protocol Composition and Typing</title>
           <link>/entries/Stateful_Protocol_Composition_and_Typing.html</link>
           <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Stateful_Protocol_Composition_and_Typing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lucas&#39;s Theorem</title>
           <link>/entries/Lucas_Theorem.html</link>
           <pubDate>Tue, 07 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Lucas_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strong Eventual Consistency of the Collaborative Editing Framework WOOT</title>
           <link>/entries/WOOT_Strong_Eventual_Consistency.html</link>
           <pubDate>Wed, 25 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/WOOT_Strong_Eventual_Consistency.html</guid>
           <description></description>
         </item>
         <item>
           <title>Furstenberg&#39;s topology and his proof of the infinitude of primes</title>
           <link>/entries/Furstenberg_Topology.html</link>
           <pubDate>Sun, 22 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Furstenberg_Topology.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Under-Approximate Relational Logic</title>
           <link>/entries/Relational-Incorrectness-Logic.html</link>
           <pubDate>Thu, 12 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational-Incorrectness-Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hello World</title>
           <link>/entries/Hello_World.html</link>
           <pubDate>Sat, 07 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Hello_World.html</guid>
           <description></description>
         </item>
         <item>
           <title>Implementing the Goodstein Function in &amp;lambda;-Calculus</title>
           <link>/entries/Goodstein_Lambda.html</link>
           <pubDate>Fri, 21 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goodstein_Lambda.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Generic Framework for Verified Compilers</title>
           <link>/entries/VeriComp.html</link>
           <pubDate>Mon, 10 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/VeriComp.html</guid>
           <description></description>
         </item>
         <item>
           <title>Arithmetic progressions and relative primes</title>
           <link>/entries/Arith_Prog_Rel_Primes.html</link>
           <pubDate>Sat, 01 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Arith_Prog_Rel_Primes.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Hierarchy of Algebras for Boolean Subsets</title>
           <link>/entries/Subset_Boolean_Algebras.html</link>
           <pubDate>Fri, 31 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Subset_Boolean_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mersenne primes and the Lucas–Lehmer test</title>
           <link>/entries/Mersenne_Primes.html</link>
           <pubDate>Fri, 17 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Mersenne_Primes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Approximation Algorithms</title>
           <link>/entries/Approximation_Algorithms.html</link>
           <pubDate>Thu, 16 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Approximation_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Closest Pair of Points Algorithms</title>
           <link>/entries/Closest_Pair_Points.html</link>
           <pubDate>Mon, 13 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Closest_Pair_Points.html</guid>
           <description></description>
         </item>
         <item>
           <title>Skip Lists</title>
           <link>/entries/Skip_Lists.html</link>
           <pubDate>Thu, 09 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Skip_Lists.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bicategories</title>
           <link>/entries/Bicategory.html</link>
           <pubDate>Mon, 06 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Bicategory.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Irrationality of ζ(3)</title>
           <link>/entries/Zeta_3_Irrational.html</link>
           <pubDate>Fri, 27 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Zeta_3_Irrational.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing a Seligman-Style Tableau System for Hybrid Logic</title>
           <link>/entries/Hybrid_Logic.html</link>
           <pubDate>Fri, 20 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Poincaré-Bendixson Theorem</title>
           <link>/entries/Poincare_Bendixson.html</link>
           <pubDate>Wed, 18 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Poincare_Bendixson.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complex Geometry</title>
           <link>/entries/Complex_Geometry.html</link>
           <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Complex_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Poincaré Disc Model</title>
           <link>/entries/Poincare_Disc.html</link>
           <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Poincare_Disc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss Sums and the Pólya–Vinogradov Inequality</title>
           <link>/entries/Gauss_Sums.html</link>
           <pubDate>Tue, 10 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss_Sums.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges</title>
           <link>/entries/Generalized_Counting_Sort.html</link>
           <pubDate>Wed, 04 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Generalized_Counting_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interval Arithmetic on 32-bit Words</title>
           <link>/entries/Interval_Arithmetic_Word32.html</link>
           <pubDate>Wed, 27 Nov 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Interval_Arithmetic_Word32.html</guid>
           <description></description>
         </item>
         <item>
           <title>Zermelo Fraenkel Set Theory in Higher-Order Logic</title>
           <link>/entries/ZFC_in_HOL.html</link>
           <pubDate>Thu, 24 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/ZFC_in_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/C</title>
           <link>/entries/Isabelle_C.html</link>
           <pubDate>Tue, 22 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_C.html</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis 2019 -- Polished Isabelle Solutions</title>
           <link>/entries/VerifyThis2019.html</link>
           <pubDate>Wed, 16 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/VerifyThis2019.html</guid>
           <description></description>
         </item>
         <item>
           <title>Aristotle&#39;s Assertoric Syllogistic</title>
           <link>/entries/Aristotles_Assertoric_Syllogistic.html</link>
           <pubDate>Tue, 08 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Aristotles_Assertoric_Syllogistic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sigma Protocols and Commitment Schemes</title>
           <link>/entries/Sigma_Commit_Crypto.html</link>
           <pubDate>Mon, 07 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Sigma_Commit_Crypto.html</guid>
           <description></description>
         </item>
         <item>
           <title>Clean - An Abstract Imperative Programming Language and its Theory</title>
           <link>/entries/Clean.html</link>
           <pubDate>Fri, 04 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Clean.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Multiway-Join Algorithms</title>
           <link>/entries/Generic_Join.html</link>
           <pubDate>Mon, 16 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Generic_Join.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification Components for Hybrid Systems</title>
           <link>/entries/Hybrid_Systems_VCs.html</link>
           <pubDate>Tue, 10 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Systems_VCs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fourier Series</title>
           <link>/entries/Fourier.html</link>
           <pubDate>Fri, 06 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Fourier.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Case Study in Basic Algebra</title>
           <link>/entries/Jacobson_Basic_Algebra.html</link>
           <pubDate>Fri, 30 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Jacobson_Basic_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation of an Adaptive State Counting Algorithm</title>
           <link>/entries/Adaptive_State_Counting.html</link>
           <pubDate>Fri, 16 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Adaptive_State_Counting.html</guid>
           <description></description>
         </item>
         <item>
           <title>Laplace Transform</title>
           <link>/entries/Laplace_Transform.html</link>
           <pubDate>Wed, 14 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Laplace_Transform.html</guid>
           <description></description>
         </item>
         <item>
           <title>Communicating Concurrent Kleene Algebra for Distributed Systems Specification</title>
           <link>/entries/C2KA_DistributedSystems.html</link>
           <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/C2KA_DistributedSystems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Programming</title>
           <link>/entries/Linear_Programming.html</link>
           <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Programming.html</guid>
           <description></description>
         </item>
         <item>
           <title>Selected Problems from the International Mathematical Olympiad 2019</title>
           <link>/entries/IMO2019.html</link>
           <pubDate>Mon, 05 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMO2019.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stellar Quorum Systems</title>
           <link>/entries/Stellar_Quorums.html</link>
           <pubDate>Thu, 01 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Stellar_Quorums.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Development of a Polychronous Polytimed Coordination Language</title>
           <link>/entries/TESL_Language.html</link>
           <pubDate>Tue, 30 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/TESL_Language.html</guid>
           <description></description>
         </item>
         <item>
           <title>Order Extension and Szpilrajn&#39;s Extension Theorem</title>
           <link>/entries/Szpilrajn.html</link>
           <pubDate>Sat, 27 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Szpilrajn.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequent Calculus for First-Order Logic</title>
           <link>/entries/FOL_Seq_Calc1.html</link>
           <pubDate>Thu, 18 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc1.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Code Generator from Isabelle/HOL to CakeML</title>
           <link>/entries/CakeML_Codegen.html</link>
           <pubDate>Mon, 08 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/CakeML_Codegen.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</title>
           <link>/entries/MFOTL_Monitor.html</link>
           <pubDate>Thu, 04 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/MFOTL_Monitor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complete Non-Orders and Fixed Points</title>
           <link>/entries/Complete_Non_Orders.html</link>
           <pubDate>Thu, 27 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Complete_Non_Orders.html</guid>
           <description></description>
         </item>
         <item>
           <title>Priority Search Trees</title>
           <link>/entries/Priority_Search_Trees.html</link>
           <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Priority_Search_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra</title>
           <link>/entries/Prim_Dijkstra_Simple.html</link>
           <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Prim_Dijkstra_Simple.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Inequalities</title>
           <link>/entries/Linear_Inequalities.html</link>
           <pubDate>Fri, 21 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Inequalities.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hilbert&#39;s Nullstellensatz</title>
           <link>/entries/Nullstellensatz.html</link>
           <pubDate>Sun, 16 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Nullstellensatz.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gröbner Bases, Macaulay Matrices and Dubé&#39;s Degree Bounds</title>
           <link>/entries/Groebner_Macaulay.html</link>
           <pubDate>Sat, 15 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Groebner_Macaulay.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary Heaps for IMP2</title>
           <link>/entries/IMP2_Binary_Heap.html</link>
           <pubDate>Thu, 13 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMP2_Binary_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>Differential Game Logic</title>
           <link>/entries/Differential_Game_Logic.html</link>
           <pubDate>Mon, 03 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Differential_Game_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multidimensional Binary Search Trees</title>
           <link>/entries/KD_Tree.html</link>
           <pubDate>Thu, 30 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/KD_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Generic Authenticated Data Structures</title>
           <link>/entries/LambdaAuth.html</link>
           <pubDate>Tue, 14 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/LambdaAuth.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multi-Party Computation</title>
           <link>/entries/Multi_Party_Computation.html</link>
           <pubDate>Thu, 09 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Multi_Party_Computation.html</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP Version 2.0</title>
           <link>/entries/HOL-CSP.html</link>
           <pubDate>Fri, 26 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/HOL-CSP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Compositional and Unified Translation of LTL into ω-Automata</title>
           <link>/entries/LTL_Master_Theorem.html</link>
           <pubDate>Tue, 16 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_Master_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>A General Theory of Syntax with Bindings</title>
           <link>/entries/Binding_Syntax_Theory.html</link>
           <pubDate>Sat, 06 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Binding_Syntax_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of Certain Infinite Series</title>
           <link>/entries/Transcendence_Series_Hancl_Rucki.html</link>
           <pubDate>Wed, 27 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Transcendence_Series_Hancl_Rucki.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum Hoare Logic</title>
           <link>/entries/QHLProver.html</link>
           <pubDate>Sun, 24 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/QHLProver.html</guid>
           <description></description>
         </item>
         <item>
           <title>Safe OCL</title>
           <link>/entries/Safe_OCL.html</link>
           <pubDate>Sat, 09 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_OCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Elementary Facts About the Distribution of Primes</title>
           <link>/entries/Prime_Distribution_Elementary.html</link>
           <pubDate>Thu, 21 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Distribution_Elementary.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kruskal&#39;s Algorithm for Minimum Spanning Forest</title>
           <link>/entries/Kruskal.html</link>
           <pubDate>Thu, 14 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Kruskal.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Primality Testing</title>
           <link>/entries/Probabilistic_Prime_Tests.html</link>
           <pubDate>Mon, 11 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Prime_Tests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Universal Turing Machine</title>
           <link>/entries/Universal_Turing_Machine.html</link>
           <pubDate>Fri, 08 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Universal_Turing_Machine.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming</title>
           <link>/entries/UTP.html</link>
           <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/UTP.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Inversions of a List</title>
           <link>/entries/List_Inversions.html</link>
           <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/List_Inversions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Farkas&#39; Lemma and Motzkin&#39;s Transposition Theorem</title>
           <link>/entries/Farkas.html</link>
           <pubDate>Thu, 17 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Farkas.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Algebra for Higher-Order Terms</title>
           <link>/entries/Higher_Order_Terms.html</link>
           <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Higher_Order_Terms.html</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2 – Simple Program Verification in Isabelle/HOL</title>
           <link>/entries/IMP2.html</link>
           <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMP2.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Reduction Theorem for Store Buffers</title>
           <link>/entries/Store_Buffer_Reduction.html</link>
           <pubDate>Mon, 07 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Store_Buffer_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Document Object Model</title>
           <link>/entries/Core_DOM.html</link>
           <pubDate>Wed, 26 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Core_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Concurrent Revisions</title>
           <link>/entries/Concurrent_Revisions.html</link>
           <pubDate>Tue, 25 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Concurrent_Revisions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verifying Imperative Programs using Auto2</title>
           <link>/entries/Auto2_Imperative_HOL.html</link>
           <pubDate>Fri, 21 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Auto2_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive Cryptography in HOL</title>
           <link>/entries/Constructive_Cryptography.html</link>
           <pubDate>Mon, 17 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Constructive_Cryptography.html</guid>
           <description></description>
         </item>
         <item>
           <title>Properties of Orderings and Lattices</title>
           <link>/entries/Order_Lattice_Props.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Order_Lattice_Props.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales</title>
           <link>/entries/Quantales.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Quantales.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transformer Semantics</title>
           <link>/entries/Transformer_Semantics.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Transformer_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
           <link>/entries/Functional_Ordered_Resolution_Prover.html</link>
           <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Functional_Ordered_Resolution_Prover.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Saturation</title>
           <link>/entries/Graph_Saturation.html</link>
           <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Graph_Saturation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Auto2 Prover</title>
           <link>/entries/Auto2_HOL.html</link>
           <pubDate>Tue, 20 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Auto2_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matroids</title>
           <link>/entries/Matroids.html</link>
           <pubDate>Fri, 16 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Matroids.html</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving generic class instances for datatypes</title>
           <link>/entries/Generic_Deriving.html</link>
           <pubDate>Tue, 06 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Generic_Deriving.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation and Evaluation of Alan Gewirth&#39;s Proof for the Principle of Generic Consistency in Isabelle/HOL</title>
           <link>/entries/GewirthPGCProof.html</link>
           <pubDate>Tue, 30 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/GewirthPGCProof.html</guid>
           <description></description>
         </item>
         <item>
           <title>Epistemic Logic: Completeness of Modal Logics</title>
           <link>/entries/Epistemic_Logic.html</link>
           <pubDate>Mon, 29 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Epistemic_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Smooth Manifolds</title>
           <link>/entries/Smooth_Manifolds.html</link>
           <pubDate>Mon, 22 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Smooth_Manifolds.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_EPO.html</link>
           <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_EPO.html</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised Binary Search Trees</title>
           <link>/entries/Randomised_BSTs.html</link>
           <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Randomised_BSTs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Upper Bounding Diameters of State Spaces of Factored Transition Systems</title>
           <link>/entries/Factored_Transition_System_Bounding.html</link>
           <pubDate>Fri, 12 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Factored_Transition_System_Bounding.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of π</title>
           <link>/entries/Pi_Transcendental.html</link>
           <pubDate>Fri, 28 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Pi_Transcendental.html</guid>
           <description></description>
         </item>
         <item>
           <title>Symmetric Polynomials</title>
           <link>/entries/Symmetric_Polynomials.html</link>
           <pubDate>Tue, 25 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Symmetric_Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>Signature-Based Gröbner Basis Algorithms</title>
           <link>/entries/Signature_Groebner.html</link>
           <pubDate>Thu, 20 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Signature_Groebner.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Prime Number Theorem</title>
           <link>/entries/Prime_Number_Theorem.html</link>
           <pubDate>Wed, 19 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Number_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Aggregation Algebras</title>
           <link>/entries/Aggregation_Algebras.html</link>
           <pubDate>Sat, 15 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Aggregation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Octonions</title>
           <link>/entries/Octonions.html</link>
           <pubDate>Fri, 14 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Octonions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quaternions</title>
           <link>/entries/Quaternions.html</link>
           <pubDate>Wed, 05 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Quaternions.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Budan–Fourier Theorem and Counting Real Roots with Multiplicity</title>
           <link>/entries/Budan_Fourier.html</link>
           <pubDate>Sun, 02 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Budan_Fourier.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Incremental Simplex Algorithm with Unsatisfiable Core Generation</title>
           <link>/entries/Simplex.html</link>
           <pubDate>Fri, 24 Aug 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Simplex.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minsky Machines</title>
           <link>/entries/Minsky_Machines.html</link>
           <pubDate>Tue, 14 Aug 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Minsky_Machines.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pricing in discrete financial models</title>
           <link>/entries/DiscretePricing.html</link>
           <pubDate>Mon, 16 Jul 2018 00:00:00 +0000</pubDate>
           <guid>/entries/DiscretePricing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Von-Neumann-Morgenstern Utility Theorem</title>
           <link>/entries/Neumann_Morgenstern_Utility.html</link>
           <pubDate>Wed, 04 Jul 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Neumann_Morgenstern_Utility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pell&#39;s Equation</title>
           <link>/entries/Pell.html</link>
           <pubDate>Sat, 23 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Pell.html</guid>
           <description></description>
         </item>
         <item>
           <title>Projective Geometry</title>
           <link>/entries/Projective_Geometry.html</link>
           <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Projective_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Localization of a Commutative Ring</title>
           <link>/entries/Localization_Ring.html</link>
           <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Localization_Ring.html</guid>
           <description></description>
         </item>
         <item>
           <title>Partial Order Reduction</title>
           <link>/entries/Partial_Order_Reduction.html</link>
           <pubDate>Tue, 05 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Partial_Order_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>Optimal Binary Search Trees</title>
           <link>/entries/Optimal_BST.html</link>
           <pubDate>Sun, 27 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Optimal_BST.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hidden Markov Models</title>
           <link>/entries/Hidden_Markov_Models.html</link>
           <pubDate>Fri, 25 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Hidden_Markov_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Timed Automata</title>
           <link>/entries/Probabilistic_Timed_Automata.html</link>
           <pubDate>Thu, 24 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Timed_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Axiom Systems for Category Theory in Free Logic</title>
           <link>/entries/AxiomaticCategoryTheory.html</link>
           <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/AxiomaticCategoryTheory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational Rapidly Convergent Series</title>
           <link>/entries/Irrationality_J_Hancl.html</link>
           <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Irrationality_J_Hancl.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monadification, Memoization and Dynamic Programming</title>
           <link>/entries/Monad_Memo_DP.html</link>
           <pubDate>Tue, 22 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Monad_Memo_DP.html</guid>
           <description></description>
         </item>
         <item>
           <title>OpSets: Sequential Specifications for Replicated Datatypes</title>
           <link>/entries/OpSets.html</link>
           <pubDate>Thu, 10 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/OpSets.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties</title>
           <link>/entries/Modular_Assembly_Kit_Security.html</link>
           <pubDate>Mon, 07 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Modular_Assembly_Kit_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>WebAssembly</title>
           <link>/entries/WebAssembly.html</link>
           <pubDate>Sun, 29 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/WebAssembly.html</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis 2018 - Polished Isabelle Solutions</title>
           <link>/entries/VerifyThis2018.html</link>
           <pubDate>Fri, 27 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/VerifyThis2018.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded Natural Functors with Covariance and Contravariance</title>
           <link>/entries/BNF_CC.html</link>
           <pubDate>Tue, 24 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/BNF_CC.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency</title>
           <link>/entries/Fishburn_Impossibility.html</link>
           <pubDate>Thu, 22 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Fishburn_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Weight-Balanced Trees</title>
           <link>/entries/Weight_Balanced_Trees.html</link>
           <pubDate>Tue, 13 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Weight_Balanced_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML</title>
           <link>/entries/CakeML.html</link>
           <pubDate>Mon, 12 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/CakeML.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Theory of Architectural Design Patterns</title>
           <link>/entries/Architectural_Design_Patterns.html</link>
           <pubDate>Thu, 01 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Architectural_Design_Patterns.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hoare Logics for Time Bounds</title>
           <link>/entries/Hoare_Time.html</link>
           <pubDate>Mon, 26 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Hoare_Time.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified factorization algorithm for integer polynomials with polynomial complexity</title>
           <link>/entries/LLL_Factorization.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/LLL_Factorization.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Terms</title>
           <link>/entries/First_Order_Terms.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/First_Order_Terms.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Error Function</title>
           <link>/entries/Error_Function.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Error_Function.html</guid>
           <description></description>
         </item>
         <item>
           <title>Treaps</title>
           <link>/entries/Treaps.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Treaps.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified LLL algorithm</title>
           <link>/entries/LLL_Basis_Reduction.html</link>
           <pubDate>Fri, 02 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/LLL_Basis_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
           <link>/entries/Ordered_Resolution_Prover.html</link>
           <pubDate>Thu, 18 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Ordered_Resolution_Prover.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gromov Hyperbolicity</title>
           <link>/entries/Gromov_Hyperbolicity.html</link>
           <pubDate>Tue, 16 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Gromov_Hyperbolicity.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Isabelle/HOL formalisation of Green&#39;s Theorem</title>
           <link>/entries/Green.html</link>
           <pubDate>Thu, 11 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Green.html</guid>
           <description></description>
         </item>
         <item>
           <title>Taylor Models</title>
           <link>/entries/Taylor_Models.html</link>
           <pubDate>Mon, 08 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Taylor_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Falling Factorial of a Sum</title>
           <link>/entries/Falling_Factorial_Sum.html</link>
           <pubDate>Fri, 22 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Falling_Factorial_Sum.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet L-Functions and Dirichlet&#39;s Theorem</title>
           <link>/entries/Dirichlet_L.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dirichlet_L.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Mason–Stothers Theorem</title>
           <link>/entries/Mason_Stothers.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Mason_Stothers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Median-of-Medians Selection Algorithm</title>
           <link>/entries/Median_Of_Medians_Selection.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Median_Of_Medians_Selection.html</guid>
           <description></description>
         </item>
         <item>
           <title>Operations on Bounded Natural Functors</title>
           <link>/entries/BNF_Operations.html</link>
           <pubDate>Tue, 19 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/BNF_Operations.html</guid>
           <description></description>
         </item>
         <item>
           <title>The string search algorithm by Knuth, Morris and Pratt</title>
           <link>/entries/Knuth_Morris_Pratt.html</link>
           <pubDate>Mon, 18 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Knuth_Morris_Pratt.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stochastic Matrices and the Perron-Frobenius Theorem</title>
           <link>/entries/Stochastic_Matrices.html</link>
           <pubDate>Wed, 22 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stochastic_Matrices.html</guid>
           <description></description>
         </item>
         <item>
           <title>The IMAP CmRDT</title>
           <link>/entries/IMAP-CRDT.html</link>
           <pubDate>Thu, 09 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/IMAP-CRDT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid Multi-Lane Spatial Logic</title>
           <link>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</link>
           <pubDate>Mon, 06 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Kuratowski Closure-Complement Theorem</title>
           <link>/entries/Kuratowski_Closure_Complement.html</link>
           <pubDate>Thu, 26 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Kuratowski_Closure_Complement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Büchi Complementation</title>
           <link>/entries/Buchi_Complementation.html</link>
           <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Buchi_Complementation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transition Systems and Automata</title>
           <link>/entries/Transition_Systems_and_Automata.html</link>
           <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Transition_Systems_and_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Count the Number of Complex Roots</title>
           <link>/entries/Count_Complex_Roots.html</link>
           <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Count_Complex_Roots.html</guid>
           <description></description>
         </item>
         <item>
           <title>Evaluate Winding Numbers through Cauchy Indices</title>
           <link>/entries/Winding_Number_Eval.html</link>
           <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Winding_Number_Eval.html</guid>
           <description></description>
         </item>
         <item>
           <title>Homogeneous Linear Diophantine Equations</title>
           <link>/entries/Diophantine_Eqns_Lin_Hom.html</link>
           <pubDate>Sat, 14 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Diophantine_Eqns_Lin_Hom.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet Series</title>
           <link>/entries/Dirichlet_Series.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dirichlet_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Recurrences</title>
           <link>/entries/Linear_Recurrences.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Recurrences.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hurwitz and Riemann ζ Functions</title>
           <link>/entries/Zeta_Function.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Zeta_Function.html</guid>
           <description></description>
         </item>
         <item>
           <title>Computer-assisted Reconstruction and Assessment of E. J. Lowe&#39;s Modal Ontological Argument</title>
           <link>/entries/Lowe_Ontological_Argument.html</link>
           <pubDate>Thu, 21 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Lowe_Ontological_Argument.html</guid>
           <description></description>
         </item>
         <item>
           <title>Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL</title>
           <link>/entries/PLM.html</link>
           <pubDate>Sun, 17 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/PLM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Anselm&#39;s God in Isabelle/HOL</title>
           <link>/entries/AnselmGod.html</link>
           <pubDate>Wed, 06 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/AnselmGod.html</guid>
           <description></description>
         </item>
         <item>
           <title>Microeconomics and the First Welfare Theorem</title>
           <link>/entries/First_Welfare_Theorem.html</link>
           <pubDate>Fri, 01 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/First_Welfare_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Orbit-Stabiliser Theorem with Application to Rotational Symmetries</title>
           <link>/entries/Orbit_Stabiliser.html</link>
           <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Orbit_Stabiliser.html</guid>
           <description></description>
         </item>
         <item>
           <title>Root-Balanced Tree</title>
           <link>/entries/Root_Balanced_Tree.html</link>
           <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Root_Balanced_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>The LambdaMu-calculus</title>
           <link>/entries/LambdaMu.html</link>
           <pubDate>Wed, 16 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/LambdaMu.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stewart&#39;s Theorem and Apollonius&#39; Theorem</title>
           <link>/entries/Stewart_Apollonius.html</link>
           <pubDate>Mon, 31 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stewart_Apollonius.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dynamic Architectures</title>
           <link>/entries/DynamicArchitectures.html</link>
           <pubDate>Fri, 28 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/DynamicArchitectures.html</guid>
           <description></description>
         </item>
         <item>
           <title>Declarative Semantics for Functional Languages</title>
           <link>/entries/Decl_Sem_Fun_PL.html</link>
           <pubDate>Fri, 21 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Decl_Sem_Fun_PL.html</guid>
           <description></description>
         </item>
         <item>
           <title>HOLCF-Prelude</title>
           <link>/entries/HOLCF-Prelude.html</link>
           <pubDate>Sat, 15 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/HOLCF-Prelude.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minkowski&#39;s Theorem</title>
           <link>/entries/Minkowskis_Theorem.html</link>
           <pubDate>Thu, 13 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Minkowskis_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus</title>
           <link>/entries/Name_Carrying_Type_Inference.html</link>
           <pubDate>Sun, 09 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Name_Carrying_Type_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes</title>
           <link>/entries/CRDT.html</link>
           <pubDate>Fri, 07 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/CRDT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone-Kleene Relation Algebras</title>
           <link>/entries/Stone_Kleene_Relation_Algebras.html</link>
           <pubDate>Thu, 06 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Kleene_Relation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional Proof Systems</title>
           <link>/entries/Propositional_Proof_Systems.html</link>
           <pubDate>Wed, 21 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Propositional_Proof_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Partial Semigroups and Convolution Algebras</title>
           <link>/entries/PSemigroupsConvolution.html</link>
           <pubDate>Tue, 13 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/PSemigroupsConvolution.html</guid>
           <description></description>
         </item>
         <item>
           <title>Buffon&#39;s Needle Problem</title>
           <link>/entries/Buffons_Needle.html</link>
           <pubDate>Tue, 06 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Buffons_Needle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Flow Networks and the Min-Cut-Max-Flow Theorem</title>
           <link>/entries/Flow_Networks.html</link>
           <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Flow_Networks.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Push-Relabel Algorithms</title>
           <link>/entries/Prpu_Maxflow.html</link>
           <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Prpu_Maxflow.html</guid>
           <description></description>
         </item>
         <item>
           <title>Optics</title>
           <link>/entries/Optics.html</link>
           <pubDate>Thu, 25 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Optics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Developing Security Protocols by Refinement</title>
           <link>/entries/Security_Protocol_Refinement.html</link>
           <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Security_Protocol_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dictionary Construction</title>
           <link>/entries/Dict_Construction.html</link>
           <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dict_Construction.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Floyd-Warshall Algorithm for Shortest Paths</title>
           <link>/entries/Floyd_Warshall.html</link>
           <pubDate>Mon, 08 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Floyd_Warshall.html</guid>
           <description></description>
         </item>
         <item>
           <title>CryptHOL</title>
           <link>/entries/CryptHOL.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/CryptHOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Effect polymorphism in higher-order logic</title>
           <link>/entries/Monomorphic_Monad.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Monomorphic_Monad.html</guid>
           <description></description>
         </item>
         <item>
           <title>Game-based cryptography in HOL</title>
           <link>/entries/Game_Based_Crypto.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Game_Based_Crypto.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monad normalisation</title>
           <link>/entries/Monad_Normalisation.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Monad_Normalisation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic while loop</title>
           <link>/entries/Probabilistic_While.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_While.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monoidal Categories</title>
           <link>/entries/MonoidalCategory.html</link>
           <pubDate>Thu, 04 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/MonoidalCategory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Types, Tableaus and Gödel’s God in Isabelle/HOL</title>
           <link>/entries/Types_Tableaus_and_Goedels_God.html</link>
           <pubDate>Mon, 01 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Types_Tableaus_and_Goedels_God.html</guid>
           <description></description>
         </item>
         <item>
           <title>Local Lexing</title>
           <link>/entries/LocalLexing.html</link>
           <pubDate>Fri, 28 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/LocalLexing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructor Functions</title>
           <link>/entries/Constructor_Funs.html</link>
           <pubDate>Wed, 19 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Constructor_Funs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lazifying case constants</title>
           <link>/entries/Lazy_Case.html</link>
           <pubDate>Tue, 18 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Lazy_Case.html</guid>
           <description></description>
         </item>
         <item>
           <title>Subresultants</title>
           <link>/entries/Subresultants.html</link>
           <pubDate>Thu, 06 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Subresultants.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expected Shape of Random Binary Search Trees</title>
           <link>/entries/Random_BSTs.html</link>
           <pubDate>Tue, 04 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Random_BSTs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lower bound on comparison-based sorting algorithms</title>
           <link>/entries/Comparison_Sort_Lower_Bound.html</link>
           <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Comparison_Sort_Lower_Bound.html</guid>
           <description></description>
         </item>
         <item>
           <title>The number of comparisons in QuickSort</title>
           <link>/entries/Quick_Sort_Cost.html</link>
           <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Quick_Sort_Cost.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Euler–MacLaurin Formula</title>
           <link>/entries/Euler_MacLaurin.html</link>
           <pubDate>Fri, 10 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Euler_MacLaurin.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Group Law for Elliptic Curves</title>
           <link>/entries/Elliptic_Curves_Group_Law.html</link>
           <pubDate>Tue, 28 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Elliptic_Curves_Group_Law.html</guid>
           <description></description>
         </item>
         <item>
           <title>Menger&#39;s Theorem</title>
           <link>/entries/Menger.html</link>
           <pubDate>Sun, 26 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Menger.html</guid>
           <description></description>
         </item>
         <item>
           <title>Differential Dynamic Logic</title>
           <link>/entries/Differential_Dynamic_Logic.html</link>
           <pubDate>Mon, 13 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Differential_Dynamic_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Soundness</title>
           <link>/entries/Abstract_Soundness.html</link>
           <pubDate>Fri, 10 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract_Soundness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone Relation Algebras</title>
           <link>/entries/Stone_Relation_Algebras.html</link>
           <pubDate>Tue, 07 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Relation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Refining Authenticated Key Agreement with Strong Adversaries</title>
           <link>/entries/Key_Agreement_Strong_Adversaries.html</link>
           <pubDate>Tue, 31 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Key_Agreement_Strong_Adversaries.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bernoulli Numbers</title>
           <link>/entries/Bernoulli.html</link>
           <pubDate>Tue, 24 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Bernoulli.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bertrand&#39;s postulate</title>
           <link>/entries/Bertrands_Postulate.html</link>
           <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Bertrands_Postulate.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minimal Static Single Assignment Form</title>
           <link>/entries/Minimal_SSA.html</link>
           <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Minimal_SSA.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of e</title>
           <link>/entries/E_Transcendental.html</link>
           <pubDate>Thu, 12 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/E_Transcendental.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Network Models and Their Application to Firewall Policies</title>
           <link>/entries/UPF_Firewall.html</link>
           <pubDate>Sun, 08 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/UPF_Firewall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of a Diffie-Hellman Password-based Authentication Protocol by Extending the Inductive Method</title>
           <link>/entries/Password_Authentication_Protocol.html</link>
           <pubDate>Tue, 03 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Password_Authentication_Protocol.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Logic According to Harrison</title>
           <link>/entries/FOL_Harrison.html</link>
           <pubDate>Sun, 01 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Harrison.html</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent Refinement Algebra and Rely Quotients</title>
           <link>/entries/Concurrent_Ref_Alg.html</link>
           <pubDate>Fri, 30 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Concurrent_Ref_Alg.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Twelvefold Way</title>
           <link>/entries/Twelvefold_Way.html</link>
           <pubDate>Thu, 29 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Twelvefold_Way.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proof Strategy Language</title>
           <link>/entries/Proof_Strategy_Language.html</link>
           <pubDate>Tue, 20 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Proof_Strategy_Language.html</guid>
           <description></description>
         </item>
         <item>
           <title>Paraconsistency</title>
           <link>/entries/Paraconsistency.html</link>
           <pubDate>Wed, 07 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Paraconsistency.html</guid>
           <description></description>
         </item>
         <item>
           <title>COMPLX: A Verification Framework for Concurrent Imperative Programs</title>
           <link>/entries/Complx.html</link>
           <pubDate>Tue, 29 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Complx.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Interpretation of Annotated Commands</title>
           <link>/entries/Abs_Int_ITP2012.html</link>
           <pubDate>Wed, 23 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Abs_Int_ITP2012.html</guid>
           <description></description>
         </item>
         <item>
           <title>Separata: Isabelle tactics for Separation Algebra</title>
           <link>/entries/Separata.html</link>
           <pubDate>Wed, 16 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Separata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_KBOs.html</link>
           <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_KBOs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</title>
           <link>/entries/Nested_Multisets_Ordinals.html</link>
           <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Nested_Multisets_Ordinals.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expressiveness of Deep Learning</title>
           <link>/entries/Deep_Learning.html</link>
           <pubDate>Thu, 10 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Deep_Learning.html</guid>
           <description></description>
         </item>
         <item>
           <title>Modal Logics for Nominal Transition Systems</title>
           <link>/entries/Modal_Logics_for_NTS.html</link>
           <pubDate>Tue, 25 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Modal_Logics_for_NTS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stable Matching</title>
           <link>/entries/Stable_Matching.html</link>
           <pubDate>Mon, 24 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stable_Matching.html</guid>
           <description></description>
         </item>
         <item>
           <title>LOFT — Verified Migration of Linux Firewalls to SDN</title>
           <link>/entries/LOFT.html</link>
           <pubDate>Fri, 21 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/LOFT.html</guid>
           <description></description>
         </item>
         <item>
           <title>A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor</title>
           <link>/entries/SPARCv8.html</link>
           <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SPARCv8.html</guid>
           <description></description>
         </item>
         <item>
           <title>Source Coding Theorem</title>
           <link>/entries/Source_Coding_Theorem.html</link>
           <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Source_Coding_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Factorization Algorithm of Berlekamp and Zassenhaus</title>
           <link>/entries/Berlekamp_Zassenhaus.html</link>
           <pubDate>Fri, 14 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Berlekamp_Zassenhaus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Intersecting Chords Theorem</title>
           <link>/entries/Chord_Segments.html</link>
           <pubDate>Tue, 11 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Chord_Segments.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lp spaces</title>
           <link>/entries/Lp.html</link>
           <pubDate>Wed, 05 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lp.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher–Yates shuffle</title>
           <link>/entries/Fisher_Yates.html</link>
           <pubDate>Fri, 30 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Fisher_Yates.html</guid>
           <description></description>
         </item>
         <item>
           <title>Allen&#39;s Interval Calculus</title>
           <link>/entries/Allen_Calculus.html</link>
           <pubDate>Thu, 29 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Allen_Calculus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_RPOs.html</link>
           <pubDate>Fri, 23 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_RPOs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables Semantics</title>
           <link>/entries/Iptables_Semantics.html</link>
           <pubDate>Fri, 09 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Iptables_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Variant of the Superposition Calculus</title>
           <link>/entries/SuperCalc.html</link>
           <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SuperCalc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone Algebras</title>
           <link>/entries/Stone_Algebras.html</link>
           <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stirling&#39;s formula</title>
           <link>/entries/Stirling_Formula.html</link>
           <pubDate>Thu, 01 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stirling_Formula.html</guid>
           <description></description>
         </item>
         <item>
           <title>Routing</title>
           <link>/entries/Routing.html</link>
           <pubDate>Wed, 31 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Routing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simple Firewall</title>
           <link>/entries/Simple_Firewall.html</link>
           <pubDate>Wed, 24 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Simple_Firewall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths</title>
           <link>/entries/InfPathElimination.html</link>
           <pubDate>Thu, 18 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/InfPathElimination.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing the Edmonds-Karp Algorithm</title>
           <link>/entries/EdmondsKarp_Maxflow.html</link>
           <pubDate>Fri, 12 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/EdmondsKarp_Maxflow.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Imperative Refinement Framework</title>
           <link>/entries/Refine_Imperative_HOL.html</link>
           <pubDate>Mon, 08 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Refine_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ptolemy&#39;s Theorem</title>
           <link>/entries/Ptolemys_Theorem.html</link>
           <pubDate>Sun, 07 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Ptolemys_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Surprise Paradox</title>
           <link>/entries/Surprise_Paradox.html</link>
           <pubDate>Sun, 17 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Surprise_Paradox.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pairing Heap</title>
           <link>/entries/Pairing_Heap.html</link>
           <pubDate>Thu, 14 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Pairing_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Framework for Verifying Depth-First Search Algorithms</title>
           <link>/entries/DFS_Framework.html</link>
           <pubDate>Tue, 05 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/DFS_Framework.html</guid>
           <description></description>
         </item>
         <item>
           <title>Chamber Complexes, Coxeter Systems, and Buildings</title>
           <link>/entries/Buildings.html</link>
           <pubDate>Fri, 01 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Buildings.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Resolution Calculus for First-Order Logic</title>
           <link>/entries/Resolution_FOL.html</link>
           <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Resolution_FOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Z Property</title>
           <link>/entries/Rewriting_Z.html</link>
           <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Rewriting_Z.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional Security-Preserving Refinement for Concurrent Imperative Programs</title>
           <link>/entries/Dependent_SIFUM_Refinement.html</link>
           <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Dependent_SIFUM_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>IP Addresses</title>
           <link>/entries/IP_Addresses.html</link>
           <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/IP_Addresses.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Multisets</title>
           <link>/entries/Card_Multisets.html</link>
           <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Multisets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory with Adjunctions and Limits</title>
           <link>/entries/Category3.html</link>
           <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Category3.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Dependent Security Type System for Concurrent Imperative Programs</title>
           <link>/entries/Dependent_SIFUM_Type_Systems.html</link>
           <pubDate>Sat, 25 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Dependent_SIFUM_Type_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Catalan Numbers</title>
           <link>/entries/Catalan_Numbers.html</link>
           <pubDate>Tue, 21 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Catalan_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Program Construction and Verification Components Based on Kleene Algebra</title>
           <link>/entries/Algebraic_VCs.html</link>
           <pubDate>Sat, 18 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Algebraic_VCs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conservation of CSP Noninterference Security under Concurrent Composition</title>
           <link>/entries/Noninterference_Concurrent_Composition.html</link>
           <pubDate>Mon, 13 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Concurrent_Composition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Machine Word Library</title>
           <link>/entries/Word_Lib.html</link>
           <pubDate>Thu, 09 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Word_Lib.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Decomposition</title>
           <link>/entries/Tree_Decomposition.html</link>
           <pubDate>Tue, 31 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Tree_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Equivalence Relations</title>
           <link>/entries/Card_Equiv_Relations.html</link>
           <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Equiv_Relations.html</guid>
           <description></description>
         </item>
         <item>
           <title>POSIX Lexing with Derivatives of Regular Expressions</title>
           <link>/entries/Posix-Lexing.html</link>
           <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Posix-Lexing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Perron-Frobenius Theorem for Spectral Radius Analysis</title>
           <link>/entries/Perron_Frobenius.html</link>
           <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Perron_Frobenius.html</guid>
           <description></description>
         </item>
         <item>
           <title>The meta theory of the Incredible Proof Machine</title>
           <link>/entries/Incredible_Proof_Machine.html</link>
           <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Incredible_Proof_Machine.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Constructive Proof for FLP</title>
           <link>/entries/FLP.html</link>
           <pubDate>Wed, 18 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/FLP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</title>
           <link>/entries/MFMC_Countable.html</link>
           <pubDate>Mon, 09 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/MFMC_Countable.html</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised Social Choice Theory</title>
           <link>/entries/Randomised_Social_Choice.html</link>
           <pubDate>Thu, 05 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Randomised_Social_Choice.html</guid>
           <description></description>
         </item>
         <item>
           <title>Spivey&#39;s Generalized Recurrence for Bell Numbers</title>
           <link>/entries/Bell_Numbers_Spivey.html</link>
           <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Bell_Numbers_Spivey.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of SD-Efficiency and SD-Strategy-Proofness</title>
           <link>/entries/SDS_Impossibility.html</link>
           <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SDS_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gröbner Bases Theory</title>
           <link>/entries/Groebner_Bases.html</link>
           <pubDate>Mon, 02 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Groebner_Bases.html</guid>
           <description></description>
         </item>
         <item>
           <title>No Faster-Than-Light Observers</title>
           <link>/entries/No_FTL_observers.html</link>
           <pubDate>Thu, 28 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/No_FTL_observers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A formalisation of the Cocke-Younger-Kasami algorithm</title>
           <link>/entries/CYK.html</link>
           <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/CYK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algorithms for Reduced Ordered Binary Decision Diagrams</title>
           <link>/entries/ROBDD.html</link>
           <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/ROBDD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conservation of CSP Noninterference Security under Sequential Composition</title>
           <link>/entries/Noninterference_Sequential_Composition.html</link>
           <pubDate>Tue, 26 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Sequential_Composition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebras with Domain</title>
           <link>/entries/KAD.html</link>
           <pubDate>Tue, 12 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/KAD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional Resolution and Prime Implicates Generation</title>
           <link>/entries/PropResPI.html</link>
           <pubDate>Fri, 11 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/PropResPI.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cartan Fixed Point Theorems</title>
           <link>/entries/Cartan_FP.html</link>
           <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Cartan_FP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Timed Automata</title>
           <link>/entries/Timed_Automata.html</link>
           <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Timed_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Temporal Logic</title>
           <link>/entries/LTL.html</link>
           <pubDate>Tue, 01 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/LTL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Analysis of List Update Algorithms</title>
           <link>/entries/List_Update.html</link>
           <pubDate>Wed, 17 Feb 2016 00:00:00 +0000</pubDate>
           <guid>/entries/List_Update.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Construction of Static Single Assignment Form</title>
           <link>/entries/Formal_SSA.html</link>
           <pubDate>Fri, 05 Feb 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Formal_SSA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial Factorization</title>
           <link>/entries/Polynomial_Factorization.html</link>
           <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomial_Factorization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial Interpolation</title>
           <link>/entries/Polynomial_Interpolation.html</link>
           <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomial_Interpolation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knot Theory</title>
           <link>/entries/Knot_Theory.html</link>
           <pubDate>Wed, 20 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Knot_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tensor Product of Matrices</title>
           <link>/entries/Matrix_Tensor.html</link>
           <pubDate>Mon, 18 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Matrix_Tensor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Number Partitions</title>
           <link>/entries/Card_Number_Partitions.html</link>
           <pubDate>Thu, 14 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Number_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Basic Geometric Properties of Triangles</title>
           <link>/entries/Triangle.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Triangle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Descartes&#39; Rule of Signs</title>
           <link>/entries/Descartes_Sign_Rule.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Descartes_Sign_Rule.html</guid>
           <description></description>
         </item>
         <item>
           <title>Liouville numbers</title>
           <link>/entries/Liouville_Numbers.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Liouville_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Divergence of the Prime Harmonic Series</title>
           <link>/entries/Prime_Harmonic_Series.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Harmonic_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebraic Numbers in Isabelle/HOL</title>
           <link>/entries/Algebraic_Numbers.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Algebraic_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Applicative Lifting</title>
           <link>/entries/Applicative_Lifting.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Applicative_Lifting.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Stern-Brocot Tree</title>
           <link>/entries/Stern_Brocot.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Stern_Brocot.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Set Partitions</title>
           <link>/entries/Card_Partitions.html</link>
           <pubDate>Sat, 12 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Latin Square</title>
           <link>/entries/Latin_Square.html</link>
           <pubDate>Wed, 02 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Latin_Square.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ergodic Theory</title>
           <link>/entries/Ergodic_Theory.html</link>
           <pubDate>Tue, 01 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Ergodic_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Euler&#39;s Partition Theorem</title>
           <link>/entries/Euler_Partition.html</link>
           <pubDate>Thu, 19 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Euler_Partition.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Tortoise and Hare Algorithm</title>
           <link>/entries/TortoiseHare.html</link>
           <pubDate>Wed, 18 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/TortoiseHare.html</guid>
           <description></description>
         </item>
         <item>
           <title>Planarity Certificates</title>
           <link>/entries/Planarity_Certificates.html</link>
           <pubDate>Wed, 11 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Planarity_Certificates.html</guid>
           <description></description>
         </item>
         <item>
           <title>Positional Determinacy of Parity Games</title>
           <link>/entries/Parity_Game.html</link>
           <pubDate>Mon, 02 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Parity_Game.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Meta-Model for the Isabelle API</title>
           <link>/entries/Isabelle_Meta_Model.html</link>
           <pubDate>Wed, 16 Sep 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_Meta_Model.html</guid>
           <description></description>
         </item>
         <item>
           <title>Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</title>
           <link>/entries/LTL_to_DRA.html</link>
           <pubDate>Fri, 04 Sep 2015 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_to_DRA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices, Jordan Normal Forms, and Spectral Radius Theory</title>
           <link>/entries/Jordan_Normal_Form.html</link>
           <pubDate>Fri, 21 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Jordan_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing Diagrams II</title>
           <link>/entries/Decreasing-Diagrams-II.html</link>
           <pubDate>Thu, 20 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Decreasing-Diagrams-II.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Inductive Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Inductive_Unwinding.html</link>
           <pubDate>Tue, 18 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Inductive_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>Representations of Finite Groups</title>
           <link>/entries/Rep_Fin_Groups.html</link>
           <pubDate>Wed, 12 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Rep_Fin_Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Analysing and Comparing Encodability Criteria for Process Calculi</title>
           <link>/entries/Encodability_Process_Calculi.html</link>
           <pubDate>Mon, 10 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Encodability_Process_Calculi.html</guid>
           <description></description>
         </item>
         <item>
           <title>Generating Cases from Labeled Subgoals</title>
           <link>/entries/Case_Labeling.html</link>
           <pubDate>Tue, 21 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Case_Labeling.html</guid>
           <description></description>
         </item>
         <item>
           <title>Landau Symbols</title>
           <link>/entries/Landau_Symbols.html</link>
           <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Landau_Symbols.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Akra-Bazzi theorem and the Master theorem</title>
           <link>/entries/Akra_Bazzi.html</link>
           <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Akra_Bazzi.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite Normal Form</title>
           <link>/entries/Hermite.html</link>
           <pubDate>Tue, 07 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Hermite.html</guid>
           <description></description>
         </item>
         <item>
           <title>Derangements Formula</title>
           <link>/entries/Derangements.html</link>
           <pubDate>Sat, 27 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Derangements.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary Multirelations</title>
           <link>/entries/Multirelations.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Multirelations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Reasoning about Lists via List Interleaving</title>
           <link>/entries/List_Interleaving.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/List_Interleaving.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Generic Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Generic_Unwinding.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Generic_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Ipurge Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Ipurge_Unwinding.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Ipurge_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>Parameterized Dynamic Tables</title>
           <link>/entries/Dynamic_Tables.html</link>
           <pubDate>Sun, 07 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Dynamic_Tables.html</guid>
           <description></description>
         </item>
         <item>
           <title>Derivatives of Logical Formulas</title>
           <link>/entries/Formula_Derivatives.html</link>
           <pubDate>Thu, 28 May 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Formula_Derivatives.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Zoo of Probabilistic Systems</title>
           <link>/entries/Probabilistic_System_Zoo.html</link>
           <pubDate>Wed, 27 May 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_System_Zoo.html</guid>
           <description></description>
         </item>
         <item>
           <title>VCG - Combinatorial Vickrey-Clarke-Groves Auctions</title>
           <link>/entries/Vickrey_Clarke_Groves.html</link>
           <pubDate>Thu, 30 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Vickrey_Clarke_Groves.html</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated Lattices</title>
           <link>/entries/Residuated_Lattices.html</link>
           <pubDate>Wed, 15 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Residuated_Lattices.html</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent IMP</title>
           <link>/entries/ConcurrentIMP.html</link>
           <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/ConcurrentIMP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO</title>
           <link>/entries/ConcurrentGC.html</link>
           <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/ConcurrentGC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Trie</title>
           <link>/entries/Trie.html</link>
           <pubDate>Mon, 30 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Trie.html</guid>
           <description></description>
         </item>
         <item>
           <title>Consensus Refined</title>
           <link>/entries/Consensus_Refined.html</link>
           <pubDate>Wed, 18 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Consensus_Refined.html</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving class instances for datatypes</title>
           <link>/entries/Deriving.html</link>
           <pubDate>Wed, 11 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Deriving.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Safety of Call Arity</title>
           <link>/entries/Call_Arity.html</link>
           <pubDate>Fri, 20 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Call_Arity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Echelon Form</title>
           <link>/entries/Echelon_Form.html</link>
           <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Echelon_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>QR Decomposition</title>
           <link>/entries/QR_Decomposition.html</link>
           <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/QR_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Automata in Hereditarily Finite Set Theory</title>
           <link>/entries/Finite_Automata_HF.html</link>
           <pubDate>Thu, 05 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Finite_Automata_HF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of the UpDown Scheme</title>
           <link>/entries/UpDown_Scheme.html</link>
           <pubDate>Wed, 28 Jan 2015 00:00:00 +0000</pubDate>
           <guid>/entries/UpDown_Scheme.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Unified Policy Framework (UPF)</title>
           <link>/entries/UPF.html</link>
           <pubDate>Fri, 28 Nov 2014 00:00:00 +0000</pubDate>
           <guid>/entries/UPF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Loop freedom of the (untimed) AODV routing protocol</title>
           <link>/entries/AODV.html</link>
           <pubDate>Thu, 23 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/AODV.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting Definition Option</title>
           <link>/entries/Lifting_Definition_Option.html</link>
           <pubDate>Mon, 13 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Lifting_Definition_Option.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Fusion in HOL with Code Generation</title>
           <link>/entries/Stream_Fusion_Code.html</link>
           <pubDate>Fri, 10 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Stream_Fusion_Code.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Compiler for Probability Density Functions</title>
           <link>/entries/Density_Compiler.html</link>
           <pubDate>Thu, 09 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Density_Compiler.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Refinement Calculus for Reactive Systems</title>
           <link>/entries/RefinementReactive.html</link>
           <pubDate>Wed, 08 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/RefinementReactive.html</guid>
           <description></description>
         </item>
         <item>
           <title>Certification Monads</title>
           <link>/entries/Certification_Monads.html</link>
           <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Certification_Monads.html</guid>
           <description></description>
         </item>
         <item>
           <title>XML</title>
           <link>/entries/XML.html</link>
           <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/XML.html</guid>
           <description></description>
         </item>
         <item>
           <title>Imperative Insertion Sort</title>
           <link>/entries/Imperative_Insertion_Sort.html</link>
           <pubDate>Thu, 25 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Imperative_Insertion_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sturm–Tarski Theorem</title>
           <link>/entries/Sturm_Tarski.html</link>
           <pubDate>Fri, 19 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Sturm_Tarski.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cayley-Hamilton Theorem</title>
           <link>/entries/Cayley_Hamilton.html</link>
           <pubDate>Mon, 15 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Cayley_Hamilton.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Jordan-Hölder Theorem</title>
           <link>/entries/Jordan_Hoelder.html</link>
           <pubDate>Tue, 09 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Jordan_Hoelder.html</guid>
           <description></description>
         </item>
         <item>
           <title>Priority Queues Based on Braun Trees</title>
           <link>/entries/Priority_Queue_Braun.html</link>
           <pubDate>Thu, 04 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Priority_Queue_Braun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan Algorithm and Its Applications</title>
           <link>/entries/Gauss_Jordan.html</link>
           <pubDate>Wed, 03 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss_Jordan.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real-Valued Special Functions: Upper and Lower Bounds</title>
           <link>/entries/Special_Function_Bounds.html</link>
           <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Special_Function_Bounds.html</guid>
           <description></description>
         </item>
         <item>
           <title>Vector Spaces</title>
           <link>/entries/VectorSpace.html</link>
           <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/VectorSpace.html</guid>
           <description></description>
         </item>
         <item>
           <title>Skew Heap</title>
           <link>/entries/Skew_Heap.html</link>
           <pubDate>Wed, 13 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Skew_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>Splay Tree</title>
           <link>/entries/Splay_Tree.html</link>
           <pubDate>Tue, 12 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Splay_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Haskell&#39;s Show Class in Isabelle/HOL</title>
           <link>/entries/Show.html</link>
           <pubDate>Tue, 29 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Show.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Specification of a Generic Separation Kernel</title>
           <link>/entries/CISC-Kernel.html</link>
           <pubDate>Fri, 18 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CISC-Kernel.html</guid>
           <description></description>
         </item>
         <item>
           <title>pGCL for Isabelle</title>
           <link>/entries/pGCL.html</link>
           <pubDate>Sun, 13 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/pGCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Amortized Complexity Verified</title>
           <link>/entries/Amortized_Complexity.html</link>
           <pubDate>Mon, 07 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Amortized_Complexity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Network Security Policy Verification</title>
           <link>/entries/Network_Security_Policy_Verification.html</link>
           <pubDate>Fri, 04 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Network_Security_Policy_Verification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pop-Refinement</title>
           <link>/entries/Pop_Refinement.html</link>
           <pubDate>Thu, 03 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Pop_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</title>
           <link>/entries/MSO_Regex_Equivalence.html</link>
           <pubDate>Thu, 12 Jun 2014 00:00:00 +0000</pubDate>
           <guid>/entries/MSO_Regex_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Boolean Expression Checkers</title>
           <link>/entries/Boolean_Expression_Checkers.html</link>
           <pubDate>Sun, 08 Jun 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Boolean_Expression_Checkers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Fully Verified Executable LTL Model Checker</title>
           <link>/entries/CAVA_LTL_Modelchecker.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CAVA_LTL_Modelchecker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Converting Linear-Time Temporal Logic to Generalized Büchi Automata</title>
           <link>/entries/LTL_to_GBA.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_to_GBA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Promela Formalization</title>
           <link>/entries/Promela.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Promela.html</guid>
           <description></description>
         </item>
         <item>
           <title>The CAVA Automata Library</title>
           <link>/entries/CAVA_Automata.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CAVA_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Efficient Implementation of Gabow&#39;s Strongly Connected Components Algorithm</title>
           <link>/entries/Gabow_SCC.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Gabow_SCC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference Security in Communicating Sequential Processes</title>
           <link>/entries/Noninterference_CSP.html</link>
           <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_CSP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive closure according to Roy-Floyd-Warshall</title>
           <link>/entries/Roy_Floyd_Warshall.html</link>
           <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Roy_Floyd_Warshall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Algebras</title>
           <link>/entries/Regular_Algebras.html</link>
           <pubDate>Wed, 21 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Regular_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation and Analysis of Component Dependencies</title>
           <link>/entries/ComponentDependencies.html</link>
           <pubDate>Mon, 28 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/ComponentDependencies.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Assumptions and Guarantees for Compositional Noninterference</title>
           <link>/entries/SIFUM_Type_Systems.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/SIFUM_Type_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Declassification with WHAT-and-WHERE-Security</title>
           <link>/entries/WHATandWHERE_Security.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/WHATandWHERE_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Strong Security</title>
           <link>/entries/Strong_Security.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Strong_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded-Deducibility Security</title>
           <link>/entries/Bounded_Deducibility_Security.html</link>
           <pubDate>Tue, 22 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Bounded_Deducibility_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>A shallow embedding of HyperCTL*</title>
           <link>/entries/HyperCTL.html</link>
           <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/HyperCTL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Completeness</title>
           <link>/entries/Abstract_Completeness.html</link>
           <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Discrete Summation</title>
           <link>/entries/Discrete_Summation.html</link>
           <pubDate>Sun, 13 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Discrete_Summation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax and semantics of a GPU kernel programming language</title>
           <link>/entries/GPU_Kernel_PL.html</link>
           <pubDate>Thu, 03 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/GPU_Kernel_PL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Noninterference</title>
           <link>/entries/Probabilistic_Noninterference.html</link>
           <pubDate>Tue, 11 Mar 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Noninterference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mechanization of the Algebra for Wireless Networks (AWN)</title>
           <link>/entries/AWN.html</link>
           <pubDate>Sat, 08 Mar 2014 00:00:00 +0000</pubDate>
           <guid>/entries/AWN.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mutually Recursive Partial Functions</title>
           <link>/entries/Partial_Function_MR.html</link>
           <pubDate>Tue, 18 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Partial_Function_MR.html</guid>
           <description></description>
         </item>
         <item>
           <title>Properties of Random Graphs -- Subgraph Containment</title>
           <link>/entries/Random_Graph_Subgraph_Threshold.html</link>
           <pubDate>Thu, 13 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Random_Graph_Subgraph_Threshold.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of Selection and Heap Sort Using Locales</title>
           <link>/entries/Selection_Heap_Sort.html</link>
           <pubDate>Tue, 11 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Selection_Heap_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Affine Arithmetic</title>
           <link>/entries/Affine_Arithmetic.html</link>
           <pubDate>Fri, 07 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Affine_Arithmetic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Implementing field extensions of the form Q[sqrt(b)]</title>
           <link>/entries/Real_Impl.html</link>
           <pubDate>Thu, 06 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Impl.html</guid>
           <description></description>
         </item>
         <item>
           <title>Unified Decision Procedures for Regular Expression Equivalence</title>
           <link>/entries/Regex_Equivalence.html</link>
           <pubDate>Thu, 30 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Regex_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Secondary Sylow Theorems</title>
           <link>/entries/Secondary_Sylow.html</link>
           <pubDate>Tue, 28 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Secondary_Sylow.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relation Algebra</title>
           <link>/entries/Relation_Algebra.html</link>
           <pubDate>Sat, 25 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Relation_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebra with Tests and Demonic Refinement Algebras</title>
           <link>/entries/KAT_and_DRA.html</link>
           <pubDate>Thu, 23 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/KAT_and_DRA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5</title>
           <link>/entries/Featherweight_OCL.html</link>
           <pubDate>Thu, 16 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Featherweight_OCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional Properties of Crypto-Based Components</title>
           <link>/entries/CryptoBasedCompositionalProperties.html</link>
           <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CryptoBasedCompositionalProperties.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm&#39;s Theorem</title>
           <link>/entries/Sturm_Sequences.html</link>
           <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Sturm_Sequences.html</guid>
           <description></description>
         </item>
         <item>
           <title>A General Method for the Proof of Theorems on Tail-recursive Functions</title>
           <link>/entries/Tail_Recursive_Functions.html</link>
           <pubDate>Sun, 01 Dec 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Tail_Recursive_Functions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gödel&#39;s Incompleteness Theorems</title>
           <link>/entries/Incompleteness.html</link>
           <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Incompleteness.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hereditarily Finite Sets</title>
           <link>/entries/HereditarilyFinite.html</link>
           <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/HereditarilyFinite.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Codatatype of Formal Languages</title>
           <link>/entries/Coinductive_Languages.html</link>
           <pubDate>Fri, 15 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Coinductive_Languages.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Processing Components: Isabelle/HOL Formalisation and Case Studies</title>
           <link>/entries/FocusStreamsCaseStudies.html</link>
           <pubDate>Thu, 14 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/FocusStreamsCaseStudies.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gödel&#39;s God in Isabelle/HOL</title>
           <link>/entries/GoedelGod.html</link>
           <pubDate>Tue, 12 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/GoedelGod.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing Diagrams</title>
           <link>/entries/Decreasing-Diagrams.html</link>
           <pubDate>Fri, 01 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Decreasing-Diagrams.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automatic Data Refinement</title>
           <link>/entries/Automatic_Refinement.html</link>
           <pubDate>Wed, 02 Oct 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Automatic_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Native Word</title>
           <link>/entries/Native_Word.html</link>
           <pubDate>Tue, 17 Sep 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Native_Word.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of IEEE Floating Point Arithmetic</title>
           <link>/entries/IEEE_Floating_Point.html</link>
           <pubDate>Sat, 27 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/IEEE_Floating_Point.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lehmer&#39;s Theorem</title>
           <link>/entries/Lehmer.html</link>
           <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Lehmer.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pratt&#39;s Primality Certificates</title>
           <link>/entries/Pratt_Certificate.html</link>
           <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Pratt_Certificate.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Königsberg Bridge Problem and the Friendship Theorem</title>
           <link>/entries/Koenigsberg_Friendship.html</link>
           <pubDate>Fri, 19 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Koenigsberg_Friendship.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sound and Complete Sort Encodings for First-Order Logic</title>
           <link>/entries/Sort_Encodings.html</link>
           <pubDate>Thu, 27 Jun 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Sort_Encodings.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Axiomatic Characterization of the Single-Source Shortest Path Problem</title>
           <link>/entries/ShortestPath.html</link>
           <pubDate>Wed, 22 May 2013 00:00:00 +0000</pubDate>
           <guid>/entries/ShortestPath.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Theory</title>
           <link>/entries/Graph_Theory.html</link>
           <pubDate>Sun, 28 Apr 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Graph_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Light-weight Containers</title>
           <link>/entries/Containers.html</link>
           <pubDate>Mon, 15 Apr 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Containers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal 2</title>
           <link>/entries/Nominal2.html</link>
           <pubDate>Thu, 21 Feb 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Nominal2.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation</title>
           <link>/entries/Launchbury.html</link>
           <pubDate>Thu, 31 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Launchbury.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ribbon Proofs</title>
           <link>/entries/Ribbon_Proofs.html</link>
           <pubDate>Sat, 19 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Ribbon_Proofs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Rank-Nullity Theorem in Linear Algebra</title>
           <link>/entries/Rank_Nullity_Theorem.html</link>
           <pubDate>Wed, 16 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Rank_Nullity_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebra</title>
           <link>/entries/Kleene_Algebra.html</link>
           <pubDate>Tue, 15 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Kleene_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Computing N-th Roots using the Babylonian Method</title>
           <link>/entries/Sqrt_Babylonian.html</link>
           <pubDate>Thu, 03 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Sqrt_Babylonian.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Separation Logic Framework for Imperative HOL</title>
           <link>/entries/Separation_Logic_Imperative_HOL.html</link>
           <pubDate>Wed, 14 Nov 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Logic_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Open Induction</title>
           <link>/entries/Open_Induction.html</link>
           <pubDate>Fri, 02 Nov 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Open_Induction.html</guid>
           <description></description>
         </item>
         <item>
           <title>The independence of Tarski&#39;s Euclidean axiom</title>
           <link>/entries/Tarskis_Geometry.html</link>
           <pubDate>Tue, 30 Oct 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Tarskis_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bondy&#39;s Theorem</title>
           <link>/entries/Bondy.html</link>
           <pubDate>Sat, 27 Oct 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Bondy.html</guid>
           <description></description>
         </item>
         <item>
           <title>Possibilistic Noninterference</title>
           <link>/entries/Possibilistic_Noninterference.html</link>
           <pubDate>Mon, 10 Sep 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Possibilistic_Noninterference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Generating linear orders for datatypes</title>
           <link>/entries/Datatype_Order_Generator.html</link>
           <pubDate>Tue, 07 Aug 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Datatype_Order_Generator.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proving the Impossibility of Trisecting an Angle and Doubling the Cube</title>
           <link>/entries/Impossible_Geometry.html</link>
           <pubDate>Sun, 05 Aug 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Impossible_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</title>
           <link>/entries/Heard_Of.html</link>
           <pubDate>Fri, 27 Jul 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Heard_Of.html</guid>
           <description></description>
         </item>
         <item>
           <title>Logical Relations for PCF</title>
           <link>/entries/PCF.html</link>
           <pubDate>Sun, 01 Jul 2012 00:00:00 +0000</pubDate>
           <guid>/entries/PCF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Type Constructor Classes and Monad Transformers</title>
           <link>/entries/Tycon.html</link>
           <pubDate>Tue, 26 Jun 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Tycon.html</guid>
           <description></description>
         </item>
         <item>
           <title>CCS in nominal logic</title>
           <link>/entries/CCS.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/CCS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Psi-calculi in Isabelle</title>
           <link>/entries/Psi_Calculi.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Psi_Calculi.html</guid>
           <description></description>
         </item>
         <item>
           <title>The pi-calculus in nominal logic</title>
           <link>/entries/Pi_Calculus.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Pi_Calculus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/Circus</title>
           <link>/entries/Circus.html</link>
           <pubDate>Sun, 27 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Circus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Separation Algebra</title>
           <link>/entries/Separation_Algebra.html</link>
           <pubDate>Fri, 11 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stuttering Equivalence</title>
           <link>/entries/Stuttering_Equivalence.html</link>
           <pubDate>Mon, 07 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Stuttering_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive Study of Confidentiality</title>
           <link>/entries/Inductive_Confidentiality.html</link>
           <pubDate>Wed, 02 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Inductive_Confidentiality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinary Differential Equations</title>
           <link>/entries/Ordinary_Differential_Equations.html</link>
           <pubDate>Thu, 26 Apr 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinary_Differential_Equations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Well-Quasi-Orders</title>
           <link>/entries/Well_Quasi_Orders.html</link>
           <pubDate>Fri, 13 Apr 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Well_Quasi_Orders.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abortable Linearizable Modules</title>
           <link>/entries/Abortable_Linearizable_Modules.html</link>
           <pubDate>Thu, 01 Mar 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Abortable_Linearizable_Modules.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Transitive Closures</title>
           <link>/entries/Transitive-Closure-II.html</link>
           <pubDate>Wed, 29 Feb 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive-Closure-II.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Probabilistic Proof of the Girth-Chromatic Number Theorem</title>
           <link>/entries/Girth_Chromatic.html</link>
           <pubDate>Mon, 06 Feb 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Girth_Chromatic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dijkstra&#39;s Shortest Path Algorithm</title>
           <link>/entries/Dijkstra_Shortest_Path.html</link>
           <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Dijkstra_Shortest_Path.html</guid>
           <description></description>
         </item>
         <item>
           <title>Refinement for Monadic Programs</title>
           <link>/entries/Refine_Monadic.html</link>
           <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Refine_Monadic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Markov Models</title>
           <link>/entries/Markov_Models.html</link>
           <pubDate>Tue, 03 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Markov_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Definitional Encoding of TLA* in Isabelle/HOL</title>
           <link>/entries/TLA.html</link>
           <pubDate>Sat, 19 Nov 2011 00:00:00 +0000</pubDate>
           <guid>/entries/TLA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient Mergesort</title>
           <link>/entries/Efficient-Mergesort.html</link>
           <pubDate>Wed, 09 Nov 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Efficient-Mergesort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebra of Monotonic Boolean Transformers</title>
           <link>/entries/MonoBoolTranAlgebra.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/MonoBoolTranAlgebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lattice Properties</title>
           <link>/entries/LatticeProperties.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/LatticeProperties.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pseudo Hoops</title>
           <link>/entries/PseudoHoops.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/PseudoHoops.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Myhill-Nerode Theorem Based on Regular Expressions</title>
           <link>/entries/Myhill-Nerode.html</link>
           <pubDate>Fri, 26 Aug 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Myhill-Nerode.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan Elimination for Matrices Represented as Functions</title>
           <link>/entries/Gauss-Jordan-Elim-Fun.html</link>
           <pubDate>Fri, 19 Aug 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss-Jordan-Elim-Fun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum Cardinality Matching</title>
           <link>/entries/Max-Card-Matching.html</link>
           <pubDate>Thu, 21 Jul 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Max-Card-Matching.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knowledge-based programs</title>
           <link>/entries/KBPs.html</link>
           <pubDate>Tue, 17 May 2011 00:00:00 +0000</pubDate>
           <guid>/entries/KBPs.html</guid>
           <description></description>
         </item>
         <item>
           <title>The General Triangle Is Unique</title>
           <link>/entries/General-Triangle.html</link>
           <pubDate>Fri, 01 Apr 2011 00:00:00 +0000</pubDate>
           <guid>/entries/General-Triangle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Transitive Closures of Finite Relations</title>
           <link>/entries/Transitive-Closure.html</link>
           <pubDate>Mon, 14 Mar 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive-Closure.html</guid>
           <description></description>
         </item>
         <item>
           <title>AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</title>
           <link>/entries/AutoFocus-Stream.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/AutoFocus-Stream.html</guid>
           <description></description>
         </item>
         <item>
           <title>Infinite Lists</title>
           <link>/entries/List-Infinite.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/List-Infinite.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interval Temporal Logic on Natural Numbers</title>
           <link>/entries/Nat-Interval-Logic.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Nat-Interval-Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lightweight Java</title>
           <link>/entries/LightweightJava.html</link>
           <pubDate>Mon, 07 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/LightweightJava.html</guid>
           <description></description>
         </item>
         <item>
           <title>RIPEMD-160</title>
           <link>/entries/RIPEMD-160-SPARK.html</link>
           <pubDate>Mon, 10 Jan 2011 00:00:00 +0000</pubDate>
           <guid>/entries/RIPEMD-160-SPARK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lower Semicontinuous Functions</title>
           <link>/entries/Lower_Semicontinuous.html</link>
           <pubDate>Sat, 08 Jan 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Lower_Semicontinuous.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hall&#39;s Marriage Theorem</title>
           <link>/entries/Marriage.html</link>
           <pubDate>Fri, 17 Dec 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Marriage.html</guid>
           <description></description>
         </item>
         <item>
           <title>Shivers&#39; Control Flow Analysis</title>
           <link>/entries/Shivers-CFA.html</link>
           <pubDate>Tue, 16 Nov 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Shivers-CFA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial Heaps and Skew Binomial Heaps</title>
           <link>/entries/Binomial-Heaps.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Binomial-Heaps.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finger Trees</title>
           <link>/entries/Finger-Trees.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Finger-Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Functional Binomial Queues</title>
           <link>/entries/Binomial-Queues.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Binomial-Queues.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strong Normalization of Moggis&#39;s Computational Metalanguage</title>
           <link>/entries/Lam-ml-Normalization.html</link>
           <pubDate>Sun, 29 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Lam-ml-Normalization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Multivariate Polynomials</title>
           <link>/entries/Polynomials.html</link>
           <pubDate>Tue, 10 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Statecharts using Hierarchical Automata</title>
           <link>/entries/Statecharts.html</link>
           <pubDate>Sun, 08 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Statecharts.html</guid>
           <description></description>
         </item>
         <item>
           <title>Free Groups</title>
           <link>/entries/Free-Groups.html</link>
           <pubDate>Thu, 24 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Free-Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory</title>
           <link>/entries/Category2.html</link>
           <pubDate>Sun, 20 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Category2.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Matrix Operations on Matrices of Arbitrary Dimensions</title>
           <link>/entries/Matrix.html</link>
           <pubDate>Thu, 17 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Matrix.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Rewriting</title>
           <link>/entries/Abstract-Rewriting.html</link>
           <pubDate>Mon, 14 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract-Rewriting.html</guid>
           <description></description>
         </item>
         <item>
           <title>Semantics and Data Refinement of Invariant Based Programs</title>
           <link>/entries/DataRefinementIBP.html</link>
           <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/DataRefinementIBP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</title>
           <link>/entries/GraphMarkingIBP.html</link>
           <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/GraphMarkingIBP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Complete Proof of the Robbins Conjecture</title>
           <link>/entries/Robbins-Conjecture.html</link>
           <pubDate>Sat, 22 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Robbins-Conjecture.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Sets and Expressions</title>
           <link>/entries/Regular-Sets.html</link>
           <pubDate>Wed, 12 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Regular-Sets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Locally Nameless Sigma Calculus</title>
           <link>/entries/Locally-Nameless-Sigma.html</link>
           <pubDate>Fri, 30 Apr 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Locally-Nameless-Sigma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Free Boolean Algebra</title>
           <link>/entries/Free-Boolean-Algebra.html</link>
           <pubDate>Mon, 29 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Free-Boolean-Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Information Flow Noninterference via Slicing</title>
           <link>/entries/InformationFlowSlicing.html</link>
           <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/InformationFlowSlicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inter-Procedural Information Flow Noninterference via Slicing</title>
           <link>/entries/InformationFlowSlicing_Inter.html</link>
           <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/InformationFlowSlicing_Inter.html</guid>
           <description></description>
         </item>
         <item>
           <title>List Index</title>
           <link>/entries/List-Index.html</link>
           <pubDate>Sat, 20 Feb 2010 00:00:00 +0000</pubDate>
           <guid>/entries/List-Index.html</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive</title>
           <link>/entries/Coinductive.html</link>
           <pubDate>Fri, 12 Feb 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Coinductive.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Fast SAT Solver for Isabelle in Standard ML</title>
           <link>/entries/DPT-SAT-Solver.html</link>
           <pubDate>Wed, 09 Dec 2009 00:00:00 +0000</pubDate>
           <guid>/entries/DPT-SAT-Solver.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing the Logic-Automaton Connection</title>
           <link>/entries/Presburger-Automata.html</link>
           <pubDate>Thu, 03 Dec 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Presburger-Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Collections Framework</title>
           <link>/entries/Collections.html</link>
           <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Collections.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Automata</title>
           <link>/entries/Tree-Automata.html</link>
           <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Tree-Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect Number Theorem</title>
           <link>/entries/Perfect-Number-Thm.html</link>
           <pubDate>Sun, 22 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Perfect-Number-Thm.html</guid>
           <description></description>
         </item>
         <item>
           <title>Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</title>
           <link>/entries/HRB-Slicing.html</link>
           <pubDate>Fri, 13 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/HRB-Slicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Worker/Wrapper Transformation</title>
           <link>/entries/WorkerWrapper.html</link>
           <pubDate>Fri, 30 Oct 2009 00:00:00 +0000</pubDate>
           <guid>/entries/WorkerWrapper.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinals and Cardinals</title>
           <link>/entries/Ordinals_and_Cardinals.html</link>
           <pubDate>Tue, 01 Sep 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinals_and_Cardinals.html</guid>
           <description></description>
         </item>
         <item>
           <title>Invertibility in Sequent Calculi</title>
           <link>/entries/SequentInvertibility.html</link>
           <pubDate>Fri, 28 Aug 2009 00:00:00 +0000</pubDate>
           <guid>/entries/SequentInvertibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Example of a Cofinitary Group in Isabelle/HOL</title>
           <link>/entries/CofGroups.html</link>
           <pubDate>Tue, 04 Aug 2009 00:00:00 +0000</pubDate>
           <guid>/entries/CofGroups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Code Generation for Functions as Data</title>
           <link>/entries/FinFun.html</link>
           <pubDate>Wed, 06 May 2009 00:00:00 +0000</pubDate>
           <guid>/entries/FinFun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Fusion</title>
           <link>/entries/Stream-Fusion.html</link>
           <pubDate>Wed, 29 Apr 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Stream-Fusion.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Bytecode Logic for JML and Types</title>
           <link>/entries/BytecodeLogicJmlTypes.html</link>
           <pubDate>Fri, 12 Dec 2008 00:00:00 +0000</pubDate>
           <guid>/entries/BytecodeLogicJmlTypes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Secure information flow and program logics</title>
           <link>/entries/SIFPL.html</link>
           <pubDate>Mon, 10 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SIFPL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Some classical results in Social Choice Theory</title>
           <link>/entries/SenSocialChoice.html</link>
           <pubDate>Sun, 09 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SenSocialChoice.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fun With Tilings</title>
           <link>/entries/FunWithTilings.html</link>
           <pubDate>Fri, 07 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/FunWithTilings.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Textbook Proof of Huffman&#39;s Algorithm</title>
           <link>/entries/Huffman.html</link>
           <pubDate>Wed, 15 Oct 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Huffman.html</guid>
           <description></description>
         </item>
         <item>
           <title>Towards Certified Slicing</title>
           <link>/entries/Slicing.html</link>
           <pubDate>Tue, 16 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Slicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Correctness Proof for the Volpano/Smith Security Typing System</title>
           <link>/entries/VolpanoSmith.html</link>
           <pubDate>Tue, 02 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/VolpanoSmith.html</guid>
           <description></description>
         </item>
         <item>
           <title>Arrow and Gibbard-Satterthwaite</title>
           <link>/entries/ArrowImpossibilityGS.html</link>
           <pubDate>Mon, 01 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/ArrowImpossibilityGS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fun With Functions</title>
           <link>/entries/FunWithFunctions.html</link>
           <pubDate>Tue, 26 Aug 2008 00:00:00 +0000</pubDate>
           <guid>/entries/FunWithFunctions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Verification of Modern SAT Solvers</title>
           <link>/entries/SATSolverVerification.html</link>
           <pubDate>Wed, 23 Jul 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SATSolverVerification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion Theory I</title>
           <link>/entries/Recursion-Theory-I.html</link>
           <pubDate>Sat, 05 Apr 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Recursion-Theory-I.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</title>
           <link>/entries/Simpl.html</link>
           <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Simpl.html</guid>
           <description></description>
         </item>
         <item>
           <title>BDD Normalisation</title>
           <link>/entries/BDD.html</link>
           <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/BDD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Normalization by Evaluation</title>
           <link>/entries/NormByEval.html</link>
           <pubDate>Mon, 18 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/NormByEval.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantifier Elimination for Linear Arithmetic</title>
           <link>/entries/LinearQuantifierElim.html</link>
           <pubDate>Fri, 11 Jan 2008 00:00:00 +0000</pubDate>
           <guid>/entries/LinearQuantifierElim.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</title>
           <link>/entries/Program-Conflict-Analysis.html</link>
           <pubDate>Fri, 14 Dec 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Program-Conflict-Analysis.html</guid>
           <description></description>
         </item>
         <item>
           <title>Jinja with Threads</title>
           <link>/entries/JinjaThreads.html</link>
           <pubDate>Mon, 03 Dec 2007 00:00:00 +0000</pubDate>
           <guid>/entries/JinjaThreads.html</guid>
           <description></description>
         </item>
         <item>
           <title>Much Ado About Two</title>
           <link>/entries/MuchAdoAboutTwo.html</link>
           <pubDate>Tue, 06 Nov 2007 00:00:00 +0000</pubDate>
           <guid>/entries/MuchAdoAboutTwo.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples</title>
           <link>/entries/Fermat3_4.html</link>
           <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Fermat3_4.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sums of Two and Four Squares</title>
           <link>/entries/SumSquares.html</link>
           <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/SumSquares.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma</title>
           <link>/entries/Valuation.html</link>
           <pubDate>Wed, 08 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Valuation.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Logic According to Fitting</title>
           <link>/entries/FOL-Fitting.html</link>
           <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/FOL-Fitting.html</guid>
           <description></description>
         </item>
         <item>
           <title>POPLmark Challenge Via de Bruijn Indices</title>
           <link>/entries/POPLmark-deBruijn.html</link>
           <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/POPLmark-deBruijn.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hotel Key Card System</title>
           <link>/entries/HotelKeyCards.html</link>
           <pubDate>Sat, 09 Sep 2006 00:00:00 +0000</pubDate>
           <guid>/entries/HotelKeyCards.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Hoare Logics</title>
           <link>/entries/Abstract-Hoare-Logics.html</link>
           <pubDate>Tue, 08 Aug 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract-Hoare-Logics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck I: Tame Graphs</title>
           <link>/entries/Flyspeck-Tame.html</link>
           <pubDate>Mon, 22 May 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Flyspeck-Tame.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoreC&#43;&#43;</title>
           <link>/entries/CoreC&#43;&#43;.html</link>
           <pubDate>Mon, 15 May 2006 00:00:00 +0000</pubDate>
           <guid>/entries/CoreC&#43;&#43;.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Theory of Featherweight Java in Isabelle/HOL</title>
           <link>/entries/FeatherweightJava.html</link>
           <pubDate>Fri, 31 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/FeatherweightJava.html</guid>
           <description></description>
         </item>
         <item>
           <title>Instances of Schneider&#39;s generalized protocol of clock synchronization</title>
           <link>/entries/ClockSynchInst.html</link>
           <pubDate>Wed, 15 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/ClockSynchInst.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</title>
           <link>/entries/Cauchy.html</link>
           <pubDate>Tue, 14 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Cauchy.html</guid>
           <description></description>
         </item>
         <item>
           <title>Countable Ordinals</title>
           <link>/entries/Ordinal.html</link>
           <pubDate>Fri, 11 Nov 2005 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinal.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fast Fourier Transform</title>
           <link>/entries/FFT.html</link>
           <pubDate>Wed, 12 Oct 2005 00:00:00 +0000</pubDate>
           <guid>/entries/FFT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Generalized Protocol for Clock Synchronization</title>
           <link>/entries/GenClock.html</link>
           <pubDate>Fri, 24 Jun 2005 00:00:00 +0000</pubDate>
           <guid>/entries/GenClock.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proving the Correctness of Disk Paxos</title>
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     The Archive of Formal Proofs is a collection of proof libraries, examples, and larger scientific developments,
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       <h2 class="year">2024</h2>
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+            <h5><a class="title" href="./entries/Continued_Fractions.html">Continued Fractions</a></h5>
+            <br>
+            by <a href="./authors/eberl">Manuel Eberl</a>
+
+          </div>
+          <span class="date">
+            Mar 20
+          </span>
+        </article>
+        <article class="entry">
+          <div class="item-text">
+            <h5><a class="title" href="./entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+            <br>
+            by <a href="./authors/tan">Yong Kiam Tan</a> and <a href="./authors/yang">Jiong Yang</a>
+
+          </div>
+          <span class="date">
+            Mar 15
+          </span>
+        </article>
+        <article class="entry">
+          <div class="item-text">
             <h5><a class="title" href="./entries/Wieferich_Kempner.html">Wieferich–Kempner Theorem</a></h5>
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             <h5><a class="title" href="./entries/QBF_Solver_Verification.html">Verified QBF Solving</a></h5>
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             <h5><a class="title" href="./entries/Karatsuba.html">Karatsuba Multiplication on Integers</a></h5>
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             by <a href="./authors/schulz">Jakob Schulz</a> and <a href="./authors/karayel">Emin Karayel</a>
 
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             <h5><a class="title" href="./entries/IMP_Noninterference.html">Information Flow Control via Stateful Intransitive Noninterference in Language IMP</a></h5>
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             <h5><a class="title" href="./entries/Sumcheck_Protocol.html">The Sumcheck Protocol</a></h5>
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             Jan 24
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+            <h5><a class="title" href="./entries/Go.html">Go Code Generation for Isabelle</a></h5>
+            <br>
+            by <a href="./authors/stuebinger">Terru Stübinger</a> and <a href="./authors/hupel">Lars Hupel</a>
+
+          </div>
+          <span class="date">
+            Jan 22
+          </span>
+        </article>
+        <article class="entry">
+          <div class="item-text">
             <h5><a class="title" href="./entries/Isabelle_hoops.html">Decomposition of totally ordered hoops</a></h5>
             <br>
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             <h5><a class="title" href="./entries/HOL-CSP_OpSem.html">Operational Semantics formally proven in HOL-CSP</a></h5>
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             <h5><a class="title" href="./entries/CRYSTALS-Kyber_Security.html">CRYSTALS-Kyber_Security</a></h5>
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             Dec 18
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             <h5><a class="title" href="./entries/HOL-CSPM.html">HOL-CSPM - Architectural operators for HOL-CSP</a></h5>
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             <h5><a class="title" href="./entries/Cardinality_Continuum.html">The Cardinality of the Continuum</a></h5>
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             Nov 15
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             <h5><a class="title" href="./entries/Polynomial_Crit_Geometry.html">Two theorems about the geometry of the critical points of a complex polynomial</a></h5>
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             Nov 14
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             <h5><a class="title" href="./entries/Concentration_Inequalities.html">Concentration Inequalities</a></h5>
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           <span class="date">
             Nov 13
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             <h5><a class="title" href="./entries/Chebyshev_Polynomials.html">Chebyshev Polynomials</a></h5>
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             by <a href="./authors/eberl">Manuel Eberl</a>
 
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           <span class="date">
             Nov 13
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             <h5><a class="title" href="./entries/Nominal_Myhill_Nerode.html">Myhill-Nerode Theorem for Nominal G-Automata</a></h5>
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           <span class="date">
             Nov 10
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             <h5><a class="title" href="./entries/Perfect_Fields.html">Perfect Fields</a></h5>
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             Nov 06
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           <span class="date">
             Nov 06
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             <h5><a class="title" href="./entries/Q0_Metatheory.html">Metatheory of Q0</a></h5>
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             Nov 04
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           <span class="date">
             Nov 02
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             <h5><a class="title" href="./entries/Pushdown_Systems.html">Pushdown Systems</a></h5>
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             by <a href="./authors/schlichtkrull">Anders Schlichtkrull</a>, <a href="./authors/schou">Morten Konggaard Schou</a>, <a href="./authors/srba">Jiří Srba</a> and <a href="./authors/traytel">Dmitriy Traytel</a>
 
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           <span class="date">
             Oct 31
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             <h5><a class="title" href="./entries/Labeled_Transition_Systems.html">Labeled Transition Systems</a></h5>
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             by <a href="./authors/schlichtkrull">Anders Schlichtkrull</a>, <a href="./authors/schou">Morten Konggaard Schou</a>, <a href="./authors/srba">Jiří Srba</a> and <a href="./authors/traytel">Dmitriy Traytel</a>
 
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           <span class="date">
             Oct 31
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             <h5><a class="title" href="./entries/Eudoxus_Reals.html">Eudoxus Reals</a></h5>
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             Oct 29
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             <h5><a class="title" href="./entries/Transport.html">Transport via Partial Galois Connections and Equivalences</a></h5>
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             by <a href="./authors/kappelmann">Kevin Kappelmann</a>
 
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           <span class="date">
             Oct 11
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             <h5><a class="title" href="./entries/Hypergraph_Colourings.html">Hypergraph Colouring Bounds</a></h5>
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             by <a href="./authors/edmonds">Chelsea Edmonds</a> and <a href="./authors/paulson">Lawrence C. Paulson</a>
 
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             Sep 23
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             <h5><a class="title" href="./entries/Relational_Cardinality.html">Cardinality and Representation of Stone Relation Algebras</a></h5>
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           <span class="date">
             Sep 22
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             Sep 01
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             Jul 15
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             Jun 01
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             May 25
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             May 24
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           <span class="date">
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           </div>
           <span class="date">
             May 05
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           <span class="date">
             May 05
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           <span class="date">
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           <span class="date">
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             May 01
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             Apr 19
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             Apr 18
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           </div>
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             Apr 06
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             Mar 15
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             Feb 13
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             Feb 10
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             Feb 07
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           </div>
           <span class="date">
             Jan 31
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             Jan 17
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           </div>
           <span class="date">
             Jan 12
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           </div>
           <span class="date">
             Jan 08
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           </div>
           <span class="date">
             Jan 03
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           </div>
           <span class="date">
             Jan 01
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         </article>
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     <div>
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           </div>
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             Dec 30
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             Dec 29
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           </div>
           <span class="date">
             Dec 20
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           </div>
           <span class="date">
             Dec 07
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             Nov 29
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             Nov 23
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           </div>
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             Nov 16
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             Nov 12
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           </div>
           <span class="date">
             Nov 12
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             Nov 10
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           </div>
           <span class="date">
             Oct 25
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             Oct 24
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             Oct 21
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             Oct 19
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           </div>
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             Oct 19
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             Oct 14
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             Oct 11
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             Sep 30
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             Sep 29
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             Sep 23
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             Jun 25
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             Jun 09
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             May 24
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             Jan 29
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             Jan 29
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           <span class="date">
             Jan 20
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     </div>
     <div>
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         <article class="entry">
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           <span class="date">
             Nov 11
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           </div>
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             Nov 02
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           </div>
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           </div>
           <span class="date">
             Sep 04
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           </div>
           <span class="date">
             Aug 21
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           </div>
           <span class="date">
             Aug 20
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           </div>
           <span class="date">
             Aug 18
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           <span class="date">
             Aug 12
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           </div>
           <span class="date">
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           </div>
           <span class="date">
             Jul 21
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           </div>
           <span class="date">
             Jul 14
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             Jul 14
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           <span class="date">
             Jul 07
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           <span class="date">
             Jun 27
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           <span class="date">
             Jun 11
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           </div>
           <span class="date">
             Jun 11
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             Jun 11
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             Jun 07
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             May 28
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             May 27
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           <span class="date">
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           <span class="date">
             Apr 13
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             Apr 13
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           <span class="date">
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           <span class="date">
             Feb 12
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           <span class="date">
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           <span class="date">
             Jan 28
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             Oct 10
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             Oct 09
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             Jul 18
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             <h5><a class="title" href="./entries/CAVA_Automata.html">The CAVA Automata Library</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             May 28
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Promela.html">Promela Formalization</a></h5>
             <br>
             by <a href="./authors/neumann">René Neumann</a>
 
           </div>
           <span class="date">
             May 28
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/LTL_to_GBA.html">Converting Linear-Time Temporal Logic to Generalized Büchi Automata</a></h5>
             <br>
             by <a href="./authors/schimpf">Alexander Schimpf</a> and <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             May 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/CAVA_LTL_Modelchecker.html">A Fully Verified Executable LTL Model Checker</a></h5>
             <br>
             by <a href="./authors/esparza">Javier Esparza</a>, <a href="./authors/lammich">Peter Lammich</a>, <a href="./authors/neumann">René Neumann</a>, <a href="./authors/nipkow">Tobias Nipkow</a>, <a href="./authors/schimpf">Alexander Schimpf</a> and <a href="./authors/smaus">Jan-Georg Smaus</a>
 
           </div>
           <span class="date">
             May 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Roy_Floyd_Warshall.html">Transitive closure according to Roy-Floyd-Warshall</a></h5>
             <br>
             by <a href="./authors/wenzel">Makarius Wenzel</a>
 
           </div>
           <span class="date">
             May 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Noninterference_CSP.html">Noninterference Security in Communicating Sequential Processes</a></h5>
             <br>
             by <a href="./authors/noce">Pasquale Noce</a>
 
           </div>
           <span class="date">
             May 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Regular_Algebras.html">Regular Algebras</a></h5>
             <br>
             by <a href="./authors/fosters">Simon Foster</a> and <a href="./authors/struth">Georg Struth</a>
 
           </div>
           <span class="date">
             May 21
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/ComponentDependencies.html">Formalisation and Analysis of Component Dependencies</a></h5>
             <br>
             by <a href="./authors/spichkova">Maria Spichkova</a>
 
           </div>
           <span class="date">
             Apr 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Strong_Security.html">A Formalization of Strong Security</a></h5>
             <br>
             by <a href="./authors/grewe">Sylvia Grewe</a>, <a href="./authors/lux">Alexander Lux</a>, <a href="./authors/mantel">Heiko Mantel</a> and <a href="./authors/sauer">Jens Sauer</a>
 
           </div>
           <span class="date">
             Apr 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/WHATandWHERE_Security.html">A Formalization of Declassification with WHAT-and-WHERE-Security</a></h5>
             <br>
             by <a href="./authors/grewe">Sylvia Grewe</a>, <a href="./authors/lux">Alexander Lux</a>, <a href="./authors/mantel">Heiko Mantel</a> and <a href="./authors/sauer">Jens Sauer</a>
 
           </div>
           <span class="date">
             Apr 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SIFUM_Type_Systems.html">A Formalization of Assumptions and Guarantees for Compositional Noninterference</a></h5>
             <br>
             by <a href="./authors/grewe">Sylvia Grewe</a>, <a href="./authors/mantel">Heiko Mantel</a> and <a href="./authors/schoepe">Daniel Schoepe</a>
 
           </div>
           <span class="date">
             Apr 23
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Bounded_Deducibility_Security.html">Bounded-Deducibility Security</a></h5>
             <br>
             by <a href="./authors/popescu">Andrei Popescu</a>, <a href="./authors/lammich">Peter Lammich</a> and <a href="./authors/bauereiss">Thomas Bauereiss</a>
 
           </div>
           <span class="date">
             Apr 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Abstract_Completeness.html">Abstract Completeness</a></h5>
             <br>
             by <a href="./authors/blanchette">Jasmin Christian Blanchette</a>, <a href="./authors/popescu">Andrei Popescu</a> and <a href="./authors/traytel">Dmitriy Traytel</a>
 
           </div>
           <span class="date">
             Apr 16
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/HyperCTL.html">A shallow embedding of HyperCTL*</a></h5>
             <br>
             by <a href="./authors/rabe">Markus N. Rabe</a>, <a href="./authors/lammich">Peter Lammich</a> and <a href="./authors/popescu">Andrei Popescu</a>
 
           </div>
           <span class="date">
             Apr 16
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Discrete_Summation.html">Discrete Summation</a></h5>
             <br>
             by <a href="./authors/haftmann">Florian Haftmann</a>
 
           </div>
           <span class="date">
             Apr 13
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/GPU_Kernel_PL.html">Syntax and semantics of a GPU kernel programming language</a></h5>
             <br>
             by <a href="./authors/wickerson">John Wickerson</a>
 
           </div>
           <span class="date">
             Apr 03
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Probabilistic_Noninterference.html">Probabilistic Noninterference</a></h5>
             <br>
             by <a href="./authors/popescu">Andrei Popescu</a> and <a href="./authors/hoelzl">Johannes Hölzl</a>
 
           </div>
           <span class="date">
             Mar 11
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/AWN.html">Mechanization of the Algebra for Wireless Networks (AWN)</a></h5>
             <br>
             by <a href="./authors/bourke">Timothy Bourke</a>
 
           </div>
           <span class="date">
             Mar 08
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Partial_Function_MR.html">Mutually Recursive Partial Functions</a></h5>
             <br>
             by <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Feb 18
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Random_Graph_Subgraph_Threshold.html">Properties of Random Graphs -- Subgraph Containment</a></h5>
             <br>
             by <a href="./authors/hupel">Lars Hupel</a>
 
           </div>
           <span class="date">
             Feb 13
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Selection_Heap_Sort.html">Verification of Selection and Heap Sort Using Locales</a></h5>
             <br>
             by <a href="./authors/petrovic">Danijela Petrovic</a>
 
           </div>
           <span class="date">
             Feb 11
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Affine_Arithmetic.html">Affine Arithmetic</a></h5>
             <br>
             by <a href="./authors/immler">Fabian Immler</a>
 
           </div>
           <span class="date">
             Feb 07
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></h5>
             <br>
             by <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Feb 06
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Regex_Equivalence.html">Unified Decision Procedures for Regular Expression Equivalence</a></h5>
             <br>
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           </div>
           <span class="date">
             Jan 30
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Secondary_Sylow.html">Secondary Sylow Theorems</a></h5>
             <br>
             by <a href="./authors/raumer">Jakob von Raumer</a>
 
           </div>
           <span class="date">
             Jan 28
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Relation_Algebra.html">Relation Algebra</a></h5>
             <br>
             by <a href="./authors/armstrong">Alasdair Armstrong</a>, <a href="./authors/fosters">Simon Foster</a>, <a href="./authors/struth">Georg Struth</a> and <a href="./authors/weber">Tjark Weber</a>
 
           </div>
           <span class="date">
             Jan 25
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         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/KAT_and_DRA.html">Kleene Algebra with Tests and Demonic Refinement Algebras</a></h5>
             <br>
             by <a href="./authors/armstrong">Alasdair Armstrong</a>, <a href="./authors/gomes">Victor B. F. Gomes</a> and <a href="./authors/struth">Georg Struth</a>
 
           </div>
           <span class="date">
             Jan 23
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         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Featherweight_OCL.html">Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5</a></h5>
             <br>
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           </div>
           <span class="date">
             Jan 16
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Sturm_Sequences.html">Sturm&#39;s Theorem</a></h5>
             <br>
             by <a href="./authors/eberl">Manuel Eberl</a>
 
           </div>
           <span class="date">
             Jan 11
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/CryptoBasedCompositionalProperties.html">Compositional Properties of Crypto-Based Components</a></h5>
             <br>
             by <a href="./authors/spichkova">Maria Spichkova</a>
 
           </div>
           <span class="date">
             Jan 11
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2013</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Tail_Recursive_Functions.html">A General Method for the Proof of Theorems on Tail-recursive Functions</a></h5>
             <br>
             by <a href="./authors/noce">Pasquale Noce</a>
 
           </div>
           <span class="date">
             Dec 01
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/HereditarilyFinite.html">The Hereditarily Finite Sets</a></h5>
             <br>
             by <a href="./authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">
             Nov 17
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Incompleteness.html">Gödel&#39;s Incompleteness Theorems</a></h5>
             <br>
             by <a href="./authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">
             Nov 17
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Coinductive_Languages.html">A Codatatype of Formal Languages</a></h5>
             <br>
             by <a href="./authors/traytel">Dmitriy Traytel</a>
 
           </div>
           <span class="date">
             Nov 15
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         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FocusStreamsCaseStudies.html">Stream Processing Components: Isabelle/HOL Formalisation and Case Studies</a></h5>
             <br>
             by <a href="./authors/spichkova">Maria Spichkova</a>
 
           </div>
           <span class="date">
             Nov 14
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           <div class="item-text">
             <h5><a class="title" href="./entries/GoedelGod.html">Gödel&#39;s God in Isabelle/HOL</a></h5>
             <br>
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           </div>
           <span class="date">
             Nov 12
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Decreasing-Diagrams.html">Decreasing Diagrams</a></h5>
             <br>
             by <a href="./authors/zankl">Harald Zankl</a>
 
           </div>
           <span class="date">
             Nov 01
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Automatic_Refinement.html">Automatic Data Refinement</a></h5>
             <br>
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           </div>
           <span class="date">
             Oct 02
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Native_Word.html">Native Word</a></h5>
             <br>
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           </div>
           <span class="date">
             Sep 17
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/IEEE_Floating_Point.html">A Formal Model of IEEE Floating Point Arithmetic</a></h5>
             <br>
             by <a href="./authors/yu">Lei Yu</a>
 
           </div>
           <span class="date">
             Jul 27
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         </article>
         <article class="entry">
           <div class="item-text">
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             <br>
             by <a href="./authors/wimmer">Simon Wimmer</a> and <a href="./authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">
             Jul 22
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Lehmer.html">Lehmer&#39;s Theorem</a></h5>
             <br>
             by <a href="./authors/wimmer">Simon Wimmer</a> and <a href="./authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">
             Jul 22
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Koenigsberg_Friendship.html">The Königsberg Bridge Problem and the Friendship Theorem</a></h5>
             <br>
             by <a href="./authors/li">Wenda Li</a>
 
           </div>
           <span class="date">
             Jul 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Sort_Encodings.html">Sound and Complete Sort Encodings for First-Order Logic</a></h5>
             <br>
             by <a href="./authors/blanchette">Jasmin Christian Blanchette</a> and <a href="./authors/popescu">Andrei Popescu</a>
 
           </div>
           <span class="date">
             Jun 27
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/ShortestPath.html">An Axiomatic Characterization of the Single-Source Shortest Path Problem</a></h5>
             <br>
             by <a href="./authors/rizkallah">Christine Rizkallah</a>
 
           </div>
           <span class="date">
             May 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Graph_Theory.html">Graph Theory</a></h5>
             <br>
             by <a href="./authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">
             Apr 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Containers.html">Light-weight Containers</a></h5>
             <br>
             by <a href="./authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">
             Apr 15
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Nominal2.html">Nominal 2</a></h5>
             <br>
             by <a href="./authors/urban">Christian Urban</a>, <a href="./authors/berghofer">Stefan Berghofer</a> and <a href="./authors/kaliszyk">Cezary Kaliszyk</a>
 
           </div>
           <span class="date">
             Feb 21
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Launchbury.html">The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation</a></h5>
             <br>
             by <a href="./authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">
             Jan 31
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Ribbon_Proofs.html">Ribbon Proofs</a></h5>
             <br>
             by <a href="./authors/wickerson">John Wickerson</a>
 
           </div>
           <span class="date">
             Jan 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Rank_Nullity_Theorem.html">Rank-Nullity Theorem in Linear Algebra</a></h5>
             <br>
             by <a href="./authors/divason">Jose Divasón</a> and <a href="./authors/aransay">Jesús Aransay</a>
 
           </div>
           <span class="date">
             Jan 16
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Kleene_Algebra.html">Kleene Algebra</a></h5>
             <br>
             by <a href="./authors/armstrong">Alasdair Armstrong</a>, <a href="./authors/struth">Georg Struth</a> and <a href="./authors/weber">Tjark Weber</a>
 
           </div>
           <span class="date">
             Jan 15
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></h5>
             <br>
             by <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Jan 03
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2012</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Separation_Logic_Imperative_HOL.html">A Separation Logic Framework for Imperative HOL</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a> and <a href="./authors/meis">Rene Meis</a>
 
           </div>
           <span class="date">
             Nov 14
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Open_Induction.html">Open Induction</a></h5>
             <br>
             by <a href="./authors/ogawa">Mizuhito Ogawa</a> and <a href="./authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">
             Nov 02
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Tarskis_Geometry.html">The independence of Tarski&#39;s Euclidean axiom</a></h5>
             <br>
             by <a href="./authors/makarios">T. J. M. Makarios</a>
 
           </div>
           <span class="date">
             Oct 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Bondy.html">Bondy&#39;s Theorem</a></h5>
             <br>
             by <a href="./authors/avigad">Jeremy Avigad</a> and <a href="./authors/hetzl">Stefan Hetzl</a>
 
           </div>
           <span class="date">
             Oct 27
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Possibilistic_Noninterference.html">Possibilistic Noninterference</a></h5>
             <br>
             by <a href="./authors/popescu">Andrei Popescu</a> and <a href="./authors/hoelzl">Johannes Hölzl</a>
 
           </div>
           <span class="date">
             Sep 10
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Datatype_Order_Generator.html">Generating linear orders for datatypes</a></h5>
             <br>
             by <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Aug 07
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Impossible_Geometry.html">Proving the Impossibility of Trisecting an Angle and Doubling the Cube</a></h5>
             <br>
             by <a href="./authors/romanos">Ralph Romanos</a> and <a href="./authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">
             Aug 05
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         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Heard_Of.html">Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</a></h5>
             <br>
             by <a href="./authors/debrat">Henri Debrat</a> and <a href="./authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">
             Jul 27
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/PCF.html">Logical Relations for PCF</a></h5>
             <br>
             by <a href="./authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">
             Jul 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Tycon.html">Type Constructor Classes and Monad Transformers</a></h5>
             <br>
             by <a href="./authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">
             Jun 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Pi_Calculus.html">The pi-calculus in nominal logic</a></h5>
             <br>
             by <a href="./authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">
             May 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Psi_Calculi.html">Psi-calculi in Isabelle</a></h5>
             <br>
             by <a href="./authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">
             May 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/CCS.html">CCS in nominal logic</a></h5>
             <br>
             by <a href="./authors/bengtson">Jesper Bengtson</a>
 
           </div>
           <span class="date">
             May 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Circus.html">Isabelle/Circus</a></h5>
             <br>
             by <a href="./authors/feliachi">Abderrahmane Feliachi</a>, <a href="./authors/wolff">Burkhart Wolff</a> and <a href="./authors/gaudel">Marie-Claude Gaudel</a>
 
           </div>
           <span class="date">
             May 27
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Separation_Algebra.html">Separation Algebra</a></h5>
             <br>
             by <a href="./authors/klein">Gerwin Klein</a>, <a href="./authors/kolanski">Rafal Kolanski</a> and <a href="./authors/boyton">Andrew Boyton</a>
 
           </div>
           <span class="date">
             May 11
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Stuttering_Equivalence.html">Stuttering Equivalence</a></h5>
             <br>
             by <a href="./authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">
             May 07
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Inductive_Confidentiality.html">Inductive Study of Confidentiality</a></h5>
             <br>
             by <a href="./authors/bella">Giampaolo Bella</a>
 
           </div>
           <span class="date">
             May 02
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></h5>
             <br>
             by <a href="./authors/immler">Fabian Immler</a> and <a href="./authors/hoelzl">Johannes Hölzl</a>
 
           </div>
           <span class="date">
             Apr 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Well_Quasi_Orders.html">Well-Quasi-Orders</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">
             Apr 13
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Abortable_Linearizable_Modules.html">Abortable Linearizable Modules</a></h5>
             <br>
             by <a href="./authors/guerraoui">Rachid Guerraoui</a>, <a href="./authors/kuncak">Viktor Kuncak</a> and <a href="./authors/losa">Giuliano Losa</a>
 
           </div>
           <span class="date">
             Mar 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Transitive-Closure-II.html">Executable Transitive Closures</a></h5>
             <br>
             by <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Feb 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Girth_Chromatic.html">A Probabilistic Proof of the Girth-Chromatic Number Theorem</a></h5>
             <br>
             by <a href="./authors/noschinski">Lars Noschinski</a>
 
           </div>
           <span class="date">
             Feb 06
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Refine_Monadic.html">Refinement for Monadic Programs</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Jan 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Dijkstra_Shortest_Path.html">Dijkstra&#39;s Shortest Path Algorithm</a></h5>
             <br>
             by <a href="./authors/nordhoff">Benedikt Nordhoff</a> and <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Jan 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Markov_Models.html">Markov Models</a></h5>
             <br>
             by <a href="./authors/hoelzl">Johannes Hölzl</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Jan 03
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2011</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/TLA.html">A Definitional Encoding of TLA* in Isabelle/HOL</a></h5>
             <br>
             by <a href="./authors/grov">Gudmund Grov</a> and <a href="./authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">
             Nov 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Efficient-Mergesort.html">Efficient Mergesort</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a>
 
           </div>
           <span class="date">
             Nov 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/PseudoHoops.html">Pseudo Hoops</a></h5>
             <br>
             by <a href="./authors/georgescu">George Georgescu</a>, <a href="./authors/leustean">Laurentiu Leustean</a> and <a href="./authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">
             Sep 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/LatticeProperties.html">Lattice Properties</a></h5>
             <br>
             by <a href="./authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">
             Sep 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/MonoBoolTranAlgebra.html">Algebra of Monotonic Boolean Transformers</a></h5>
             <br>
             by <a href="./authors/preoteasa">Viorel Preoteasa</a>
 
           </div>
           <span class="date">
             Sep 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Myhill-Nerode.html">The Myhill-Nerode Theorem Based on Regular Expressions</a></h5>
             <br>
             by <a href="./authors/wu">Chunhan Wu</a>, <a href="./authors/zhangx">Xingyuan Zhang</a> and <a href="./authors/urban">Christian Urban</a>
 
           </div>
           <span class="date">
             Aug 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Gauss-Jordan-Elim-Fun.html">Gauss-Jordan Elimination for Matrices Represented as Functions</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Aug 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Max-Card-Matching.html">Maximum Cardinality Matching</a></h5>
             <br>
             by <a href="./authors/rizkallah">Christine Rizkallah</a>
 
           </div>
           <span class="date">
             Jul 21
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/KBPs.html">Knowledge-based programs</a></h5>
             <br>
             by <a href="./authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">
             May 17
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/General-Triangle.html">The General Triangle Is Unique</a></h5>
             <br>
             by <a href="./authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">
             Apr 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Transitive-Closure.html">Executable Transitive Closures of Finite Relations</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a> and <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Mar 14
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Nat-Interval-Logic.html">Interval Temporal Logic on Natural Numbers</a></h5>
             <br>
             by <a href="./authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">
             Feb 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/List-Infinite.html">Infinite Lists</a></h5>
             <br>
             by <a href="./authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">
             Feb 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/AutoFocus-Stream.html">AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</a></h5>
             <br>
             by <a href="./authors/trachtenherz">David Trachtenherz</a>
 
           </div>
           <span class="date">
             Feb 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/LightweightJava.html">Lightweight Java</a></h5>
             <br>
             by <a href="./authors/strnisa">Rok Strniša</a> and <a href="./authors/parkinson">Matthew Parkinson</a>
 
           </div>
           <span class="date">
             Feb 07
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/RIPEMD-160-SPARK.html">RIPEMD-160</a></h5>
             <br>
             by <a href="./authors/immler">Fabian Immler</a>
 
           </div>
           <span class="date">
             Jan 10
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Lower_Semicontinuous.html">Lower Semicontinuous Functions</a></h5>
             <br>
             by <a href="./authors/grechuk">Bogdan Grechuk</a>
 
           </div>
           <span class="date">
             Jan 08
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2010</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Marriage.html">Hall&#39;s Marriage Theorem</a></h5>
             <br>
             by <a href="./authors/jiangd">Dongchen Jiang</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Dec 17
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Shivers-CFA.html">Shivers&#39; Control Flow Analysis</a></h5>
             <br>
             by <a href="./authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">
             Nov 16
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Binomial-Queues.html">Functional Binomial Queues</a></h5>
             <br>
             by <a href="./authors/neumann">René Neumann</a>
 
           </div>
           <span class="date">
             Oct 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Finger-Trees.html">Finger Trees</a></h5>
             <br>
             by <a href="./authors/nordhoff">Benedikt Nordhoff</a>, <a href="./authors/koerner">Stefan Körner</a> and <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Oct 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Binomial-Heaps.html">Binomial Heaps and Skew Binomial Heaps</a></h5>
             <br>
             by <a href="./authors/meis">Rene Meis</a>, <a href="./authors/nielsen">Finn Nielsen</a> and <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Oct 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Lam-ml-Normalization.html">Strong Normalization of Moggis&#39;s Computational Metalanguage</a></h5>
             <br>
             by <a href="./authors/doczkal">Christian Doczkal</a>
 
           </div>
           <span class="date">
             Aug 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Polynomials.html">Executable Multivariate Polynomials</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a>, <a href="./authors/thiemann">René Thiemann</a>, <a href="./authors/maletzky">Alexander Maletzky</a>, <a href="./authors/immler">Fabian Immler</a>, <a href="./authors/haftmann">Florian Haftmann</a>, <a href="./authors/lochbihler">Andreas Lochbihler</a> and <a href="./authors/bentkamp">Alexander Bentkamp</a>
 
           </div>
           <span class="date">
             Aug 10
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Statecharts.html">Formalizing Statecharts using Hierarchical Automata</a></h5>
             <br>
             by <a href="./authors/helke">Steffen Helke</a> and <a href="./authors/kammueller">Florian Kammüller</a>
 
           </div>
           <span class="date">
             Aug 08
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Free-Groups.html">Free Groups</a></h5>
             <br>
             by <a href="./authors/breitner">Joachim Breitner</a>
 
           </div>
           <span class="date">
             Jun 24
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Category2.html">Category Theory</a></h5>
             <br>
             by <a href="./authors/katovsky">Alexander Katovsky</a>
 
           </div>
           <span class="date">
             Jun 20
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Matrix.html">Executable Matrix Operations on Matrices of Arbitrary Dimensions</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a> and <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Jun 17
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Abstract-Rewriting.html">Abstract Rewriting</a></h5>
             <br>
             by <a href="./authors/sternagel">Christian Sternagel</a> and <a href="./authors/thiemann">René Thiemann</a>
 
           </div>
           <span class="date">
             Jun 14
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/GraphMarkingIBP.html">Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</a></h5>
             <br>
             by <a href="./authors/preoteasa">Viorel Preoteasa</a> and <a href="./authors/back">Ralph-Johan Back</a>
 
           </div>
           <span class="date">
             May 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/DataRefinementIBP.html">Semantics and Data Refinement of Invariant Based Programs</a></h5>
             <br>
             by <a href="./authors/preoteasa">Viorel Preoteasa</a> and <a href="./authors/back">Ralph-Johan Back</a>
 
           </div>
           <span class="date">
             May 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Robbins-Conjecture.html">A Complete Proof of the Robbins Conjecture</a></h5>
             <br>
             by <a href="./authors/doty">Matthew Doty</a>
 
           </div>
           <span class="date">
             May 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Regular-Sets.html">Regular Sets and Expressions</a></h5>
             <br>
             by <a href="./authors/krauss">Alexander Krauss</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             May 12
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Locally-Nameless-Sigma.html">Locally Nameless Sigma Calculus</a></h5>
             <br>
             by <a href="./authors/henrio">Ludovic Henrio</a>, <a href="./authors/kammueller">Florian Kammüller</a>, <a href="./authors/lutz">Bianca Lutz</a> and <a href="./authors/sudhof">Henry Sudhof</a>
 
           </div>
           <span class="date">
             Apr 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Free-Boolean-Algebra.html">Free Boolean Algebra</a></h5>
             <br>
             by <a href="./authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">
             Mar 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/InformationFlowSlicing_Inter.html">Inter-Procedural Information Flow Noninterference via Slicing</a></h5>
             <br>
             by <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             Mar 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/InformationFlowSlicing.html">Information Flow Noninterference via Slicing</a></h5>
             <br>
             by <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             Mar 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/List-Index.html">List Index</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Feb 20
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Coinductive.html">Coinductive</a></h5>
             <br>
             by <a href="./authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">
             Feb 12
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2009</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/DPT-SAT-Solver.html">A Fast SAT Solver for Isabelle in Standard ML</a></h5>
             <br>
             by <a href="./authors/heller">Armin Heller</a>
 
           </div>
           <span class="date">
             Dec 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Presburger-Automata.html">Formalizing the Logic-Automaton Connection</a></h5>
             <br>
             by <a href="./authors/berghofer">Stefan Berghofer</a> and <a href="./authors/reiter">Markus Reiter</a>
 
           </div>
           <span class="date">
             Dec 03
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Tree-Automata.html">Tree Automata</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Nov 25
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Collections.html">Collections Framework</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a>
 
           </div>
           <span class="date">
             Nov 25
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Perfect-Number-Thm.html">Perfect Number Theorem</a></h5>
             <br>
             by <a href="./authors/ijbema">Mark Ijbema</a>
 
           </div>
           <span class="date">
             Nov 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/HRB-Slicing.html">Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</a></h5>
             <br>
             by <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             Nov 13
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/WorkerWrapper.html">The Worker/Wrapper Transformation</a></h5>
             <br>
             by <a href="./authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">
             Oct 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Ordinals_and_Cardinals.html">Ordinals and Cardinals</a></h5>
             <br>
             by <a href="./authors/popescu">Andrei Popescu</a>
 
           </div>
           <span class="date">
             Sep 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SequentInvertibility.html">Invertibility in Sequent Calculi</a></h5>
             <br>
             by <a href="./authors/chapman">Peter Chapman</a>
 
           </div>
           <span class="date">
             Aug 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/CofGroups.html">An Example of a Cofinitary Group in Isabelle/HOL</a></h5>
             <br>
             by <a href="./authors/kastermans">Bart Kastermans</a>
 
           </div>
           <span class="date">
             Aug 04
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FinFun.html">Code Generation for Functions as Data</a></h5>
             <br>
             by <a href="./authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">
             May 06
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Stream-Fusion.html">Stream Fusion</a></h5>
             <br>
             by <a href="./authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">
             Apr 29
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2008</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/BytecodeLogicJmlTypes.html">A Bytecode Logic for JML and Types</a></h5>
             <br>
             by <a href="./authors/beringer">Lennart Beringer</a> and <a href="./authors/hofmann">Martin Hofmann</a>
 
           </div>
           <span class="date">
             Dec 12
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SIFPL.html">Secure information flow and program logics</a></h5>
             <br>
             by <a href="./authors/beringer">Lennart Beringer</a> and <a href="./authors/hofmann">Martin Hofmann</a>
 
           </div>
           <span class="date">
             Nov 10
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SenSocialChoice.html">Some classical results in Social Choice Theory</a></h5>
             <br>
             by <a href="./authors/gammie">Peter Gammie</a>
 
           </div>
           <span class="date">
             Nov 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FunWithTilings.html">Fun With Tilings</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a> and <a href="./authors/paulson">Lawrence C. Paulson</a>
 
           </div>
           <span class="date">
             Nov 07
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Huffman.html">The Textbook Proof of Huffman&#39;s Algorithm</a></h5>
             <br>
             by <a href="./authors/blanchette">Jasmin Christian Blanchette</a>
 
           </div>
           <span class="date">
             Oct 15
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Slicing.html">Towards Certified Slicing</a></h5>
             <br>
             by <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             Sep 16
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/VolpanoSmith.html">A Correctness Proof for the Volpano/Smith Security Typing System</a></h5>
             <br>
             by <a href="./authors/snelting">Gregor Snelting</a> and <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             Sep 02
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/ArrowImpossibilityGS.html">Arrow and Gibbard-Satterthwaite</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Sep 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FunWithFunctions.html">Fun With Functions</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Aug 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SATSolverVerification.html">Formal Verification of Modern SAT Solvers</a></h5>
             <br>
             by <a href="./authors/maricf">Filip Marić</a>
 
           </div>
           <span class="date">
             Jul 23
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Recursion-Theory-I.html">Recursion Theory I</a></h5>
             <br>
             by <a href="./authors/nedzelsky">Michael Nedzelsky</a>
 
           </div>
           <span class="date">
             Apr 05
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/BDD.html">BDD Normalisation</a></h5>
             <br>
             by <a href="./authors/ortner">Veronika Ortner</a> and <a href="./authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">
             Feb 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Simpl.html">A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</a></h5>
             <br>
             by <a href="./authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">
             Feb 29
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/NormByEval.html">Normalization by Evaluation</a></h5>
             <br>
             by <a href="./authors/aehlig">Klaus Aehlig</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Feb 18
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/LinearQuantifierElim.html">Quantifier Elimination for Linear Arithmetic</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Jan 11
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2007</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Program-Conflict-Analysis.html">Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</a></h5>
             <br>
             by <a href="./authors/lammich">Peter Lammich</a> and <a href="./authors/olm">Markus Müller-Olm</a>
 
           </div>
           <span class="date">
             Dec 14
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/JinjaThreads.html">Jinja with Threads</a></h5>
             <br>
             by <a href="./authors/lochbihler">Andreas Lochbihler</a>
 
           </div>
           <span class="date">
             Dec 03
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/MuchAdoAboutTwo.html">Much Ado About Two</a></h5>
             <br>
             by <a href="./authors/boehme">Sascha Böhme</a>
 
           </div>
           <span class="date">
             Nov 06
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/SumSquares.html">Sums of Two and Four Squares</a></h5>
             <br>
             by <a href="./authors/oosterhuis">Roelof Oosterhuis</a>
 
           </div>
           <span class="date">
             Aug 12
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Fermat3_4.html">Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples</a></h5>
             <br>
             by <a href="./authors/oosterhuis">Roelof Oosterhuis</a>
 
           </div>
           <span class="date">
             Aug 12
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Valuation.html">Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma</a></h5>
             <br>
             by <a href="./authors/kobayashi">Hidetsune Kobayashi</a>
 
           </div>
           <span class="date">
             Aug 08
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/POPLmark-deBruijn.html">POPLmark Challenge Via de Bruijn Indices</a></h5>
             <br>
             by <a href="./authors/berghofer">Stefan Berghofer</a>
 
           </div>
           <span class="date">
             Aug 02
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FOL-Fitting.html">First-Order Logic According to Fitting</a></h5>
             <br>
             by <a href="./authors/berghofer">Stefan Berghofer</a>
 
           </div>
           <span class="date">
             Aug 02
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2006</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/HotelKeyCards.html">Hotel Key Card System</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Sep 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Abstract-Hoare-Logics.html">Abstract Hoare Logics</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Aug 08
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Flyspeck-Tame.html">Flyspeck I: Tame Graphs</a></h5>
             <br>
             by <a href="./authors/bauer">Gertrud Bauer</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             May 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/CoreC&#43;&#43;.html">CoreC&#43;&#43;</a></h5>
             <br>
             by <a href="./authors/wasserrab">Daniel Wasserrab</a>
 
           </div>
           <span class="date">
             May 15
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FeatherweightJava.html">A Theory of Featherweight Java in Isabelle/HOL</a></h5>
             <br>
             by <a href="./authors/fosterj">J. Nathan Foster</a> and <a href="./authors/vytiniotis">Dimitrios Vytiniotis</a>
 
           </div>
           <span class="date">
             Mar 31
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/ClockSynchInst.html">Instances of Schneider&#39;s generalized protocol of clock synchronization</a></h5>
             <br>
             by <a href="./authors/barsotti">Damián Barsotti</a>
 
           </div>
           <span class="date">
             Mar 15
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Cauchy.html">Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</a></h5>
             <br>
             by <a href="./authors/porter">Benjamin Porter</a>
 
           </div>
           <span class="date">
             Mar 14
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2005</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Ordinal.html">Countable Ordinals</a></h5>
             <br>
             by <a href="./authors/huffman">Brian Huffman</a>
 
           </div>
           <span class="date">
             Nov 11
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FFT.html">Fast Fourier Transform</a></h5>
             <br>
             by <a href="./authors/ballarin">Clemens Ballarin</a>
 
           </div>
           <span class="date">
             Oct 12
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/GenClock.html">Formalization of a Generalized Protocol for Clock Synchronization</a></h5>
             <br>
             by <a href="./authors/tiu">Alwen Tiu</a>
 
           </div>
           <span class="date">
             Jun 24
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/DiskPaxos.html">Proving the Correctness of Disk Paxos</a></h5>
             <br>
             by <a href="./authors/jaskelioff">Mauro Jaskelioff</a> and <a href="./authors/merz">Stephan Merz</a>
 
           </div>
           <span class="date">
             Jun 22
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/JiveDataStoreModel.html">Jive Data and Store Model</a></h5>
             <br>
             by <a href="./authors/rauch">Nicole Rauch</a> and <a href="./authors/schirmer">Norbert Schirmer</a>
 
           </div>
           <span class="date">
             Jun 20
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Jinja.html">Jinja is not Java</a></h5>
             <br>
             by <a href="./authors/klein">Gerwin Klein</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Jun 01
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/RSAPSS.html">SHA1, RSA, PSS and more</a></h5>
             <br>
             by <a href="./authors/lindenberg">Christina Lindenberg</a> and <a href="./authors/wirt">Kai Wirt</a>
 
           </div>
           <span class="date">
             May 02
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Category.html">Category Theory to Yoneda&#39;s Lemma</a></h5>
             <br>
             by <a href="./authors/keefe">Greg O&rsquo;Keefe</a>
 
           </div>
           <span class="date">
             Apr 21
           </span>
         </article>
     </div>
     <div>
       <h2 class="year">2004</h2>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/FileRefinement.html">File Refinement</a></h5>
             <br>
             by <a href="./authors/zee">Karen Zee</a> and <a href="./authors/kuncak">Viktor Kuncak</a>
 
           </div>
           <span class="date">
             Dec 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Integration.html">Integration theory and random variables</a></h5>
             <br>
             by <a href="./authors/richter">Stefan Richter</a>
 
           </div>
           <span class="date">
             Nov 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Verified-Prover.html">A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic</a></h5>
             <br>
             by <a href="./authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">
             Sep 28
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Ramsey-Infinite.html">Ramsey&#39;s theorem, infinitary version</a></h5>
             <br>
             by <a href="./authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">
             Sep 20
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Completeness.html">Completeness theorem</a></h5>
             <br>
             by <a href="./authors/margetson">James Margetson</a> and <a href="./authors/ridge">Tom Ridge</a>
 
           </div>
           <span class="date">
             Sep 20
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Compiling-Exceptions-Correctly.html">Compiling Exceptions Correctly</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Jul 09
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Depth-First-Search.html">Depth First Search</a></h5>
             <br>
             by <a href="./authors/nishihara">Toshiaki Nishihara</a> and <a href="./authors/minamide">Yasuhiko Minamide</a>
 
           </div>
           <span class="date">
             Jun 24
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Group-Ring-Module.html">Groups, Rings and Modules</a></h5>
             <br>
             by <a href="./authors/kobayashi">Hidetsune Kobayashi</a>, <a href="./authors/chen">L. Chen</a> and <a href="./authors/murao">H. Murao</a>
 
           </div>
           <span class="date">
             May 18
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Topology.html">Topology</a></h5>
             <br>
             by <a href="./authors/friedrich">Stefan Friedrich</a>
 
           </div>
           <span class="date">
             Apr 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Lazy-Lists-II.html">Lazy Lists II</a></h5>
             <br>
             by <a href="./authors/friedrich">Stefan Friedrich</a>
 
           </div>
           <span class="date">
             Apr 26
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/BinarySearchTree.html">Binary Search Trees</a></h5>
             <br>
             by <a href="./authors/kuncak">Viktor Kuncak</a>
 
           </div>
           <span class="date">
             Apr 05
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/Functional-Automata.html">Functional Automata</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Mar 30
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/MiniML.html">Mini ML</a></h5>
             <br>
             by <a href="./authors/naraschewski">Wolfgang Naraschewski</a> and <a href="./authors/nipkow">Tobias Nipkow</a>
 
           </div>
           <span class="date">
             Mar 19
           </span>
         </article>
         <article class="entry">
           <div class="item-text">
             <h5><a class="title" href="./entries/AVL-Trees.html">AVL Trees</a></h5>
             <br>
             by <a href="./authors/nipkow">Tobias Nipkow</a> and <a href="./authors/pusch">Cornelia Pusch</a>
 
           </div>
           <span class="date">
             Mar 19
           </span>
         </article>
     </div>
         
       </div>
     </div>
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           <link>/entries/QBF_Solver_Verification.html</link>
           <pubDate>Wed, 06 Mar 2024 00:00:00 +0000</pubDate>
           <guid>/entries/QBF_Solver_Verification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Wieferich–Kempner Theorem</title>
           <link>/entries/Wieferich_Kempner.html</link>
           <pubDate>Wed, 06 Mar 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Wieferich_Kempner.html</guid>
           <description></description>
         </item>
         <item>
           <title>Karatsuba Multiplication on Integers</title>
           <link>/entries/Karatsuba.html</link>
           <pubDate>Mon, 19 Feb 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Karatsuba.html</guid>
           <description></description>
         </item>
         <item>
           <title>Information Flow Control via Stateful Intransitive Noninterference in Language IMP</title>
           <link>/entries/IMP_Noninterference.html</link>
           <pubDate>Mon, 12 Feb 2024 00:00:00 +0000</pubDate>
           <guid>/entries/IMP_Noninterference.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sumcheck Protocol</title>
           <link>/entries/Sumcheck_Protocol.html</link>
           <pubDate>Fri, 02 Feb 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Sumcheck_Protocol.html</guid>
           <description></description>
         </item>
         <item>
           <title>Region Quadtrees</title>
           <link>/entries/Region_Quadtrees.html</link>
           <pubDate>Fri, 26 Jan 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Region_Quadtrees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cubical Categories</title>
           <link>/entries/CubicalCategories.html</link>
           <pubDate>Wed, 24 Jan 2024 00:00:00 +0000</pubDate>
           <guid>/entries/CubicalCategories.html</guid>
           <description></description>
         </item>
         <item>
           <title>Higher Globular Catoids and Quantales</title>
           <link>/entries/OmegaCatoidsQuantales.html</link>
           <pubDate>Wed, 24 Jan 2024 00:00:00 +0000</pubDate>
           <guid>/entries/OmegaCatoidsQuantales.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decomposition of totally ordered hoops</title>
           <link>/entries/Isabelle_hoops.html</link>
           <pubDate>Mon, 22 Jan 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_hoops.html</guid>
           <description></description>
         </item>
         <item>
+          <title>Go Code Generation for Isabelle</title>
+          <link>/entries/Go.html</link>
+          <pubDate>Mon, 22 Jan 2024 00:00:00 +0000</pubDate>
+          <guid>/entries/Go.html</guid>
+          <description></description>
+        </item>
+        <item>
           <title>(Extended) Interval Analysis</title>
           <link>/entries/Interval_Analysis.html</link>
           <pubDate>Sun, 21 Jan 2024 00:00:00 +0000</pubDate>
           <guid>/entries/Interval_Analysis.html</guid>
           <description></description>
         </item>
         <item>
           <title>Operational Semantics formally proven in HOL-CSP</title>
           <link>/entries/HOL-CSP_OpSem.html</link>
           <pubDate>Sun, 24 Dec 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HOL-CSP_OpSem.html</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber_Security</title>
           <link>/entries/CRYSTALS-Kyber_Security.html</link>
           <pubDate>Mon, 18 Dec 2023 00:00:00 +0000</pubDate>
           <guid>/entries/CRYSTALS-Kyber_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSPM - Architectural operators for HOL-CSP</title>
           <link>/entries/HOL-CSPM.html</link>
           <pubDate>Tue, 05 Dec 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HOL-CSPM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knuth–Morris–Pratt String Search</title>
           <link>/entries/KnuthMorrisPratt.html</link>
           <pubDate>Mon, 27 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/KnuthMorrisPratt.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lambert Series</title>
           <link>/entries/Lambert_Series.html</link>
           <pubDate>Fri, 24 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Lambert_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>Martingales</title>
           <link>/entries/Martingales.html</link>
           <pubDate>Tue, 21 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Martingales.html</guid>
           <description></description>
         </item>
         <item>
           <title>Soundness of the Q0 proof system for higher-order logic</title>
           <link>/entries/Q0_Soundness.html</link>
           <pubDate>Mon, 20 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Q0_Soundness.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cardinality of the Continuum</title>
           <link>/entries/Cardinality_Continuum.html</link>
           <pubDate>Wed, 15 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Cardinality_Continuum.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Polylogarithm Function</title>
           <link>/entries/Polylog.html</link>
           <pubDate>Wed, 15 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Polylog.html</guid>
           <description></description>
         </item>
         <item>
           <title>Two theorems about the geometry of the critical points of a complex polynomial</title>
           <link>/entries/Polynomial_Crit_Geometry.html</link>
           <pubDate>Tue, 14 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomial_Crit_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Chebyshev Polynomials</title>
           <link>/entries/Chebyshev_Polynomials.html</link>
           <pubDate>Mon, 13 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Chebyshev_Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>Concentration Inequalities</title>
           <link>/entries/Concentration_Inequalities.html</link>
           <pubDate>Mon, 13 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Concentration_Inequalities.html</guid>
           <description></description>
         </item>
         <item>
           <title>Myhill-Nerode Theorem for Nominal G-Automata</title>
           <link>/entries/Nominal_Myhill_Nerode.html</link>
           <pubDate>Fri, 10 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Nominal_Myhill_Nerode.html</guid>
           <description></description>
         </item>
         <item>
           <title>Elimination of Repeated Factors Algorithm</title>
           <link>/entries/Elimination_Of_Repeated_Factors.html</link>
           <pubDate>Mon, 06 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Elimination_Of_Repeated_Factors.html</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect Fields</title>
           <link>/entries/Perfect_Fields.html</link>
           <pubDate>Mon, 06 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Perfect_Fields.html</guid>
           <description></description>
         </item>
         <item>
           <title>Metatheory of Q0</title>
           <link>/entries/Q0_Metatheory.html</link>
           <pubDate>Sat, 04 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Q0_Metatheory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Disintegration Theorem</title>
           <link>/entries/Disintegration.html</link>
           <pubDate>Thu, 02 Nov 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Disintegration.html</guid>
           <description></description>
         </item>
         <item>
           <title>Labeled Transition Systems</title>
           <link>/entries/Labeled_Transition_Systems.html</link>
           <pubDate>Tue, 31 Oct 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Labeled_Transition_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pushdown Systems</title>
           <link>/entries/Pushdown_Systems.html</link>
           <pubDate>Tue, 31 Oct 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Pushdown_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Eudoxus Reals</title>
           <link>/entries/Eudoxus_Reals.html</link>
           <pubDate>Sun, 29 Oct 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Eudoxus_Reals.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transport via Partial Galois Connections and Equivalences</title>
           <link>/entries/Transport.html</link>
           <pubDate>Wed, 11 Oct 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Transport.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraph Colouring Bounds</title>
           <link>/entries/Hypergraph_Colourings.html</link>
           <pubDate>Sat, 23 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Hypergraph_Colourings.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality and Representation of Stone Relation Algebras</title>
           <link>/entries/Relational_Cardinality.html</link>
           <pubDate>Fri, 22 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Cardinality.html</guid>
           <description></description>
         </item>
         <item>
           <title>General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma</title>
           <link>/entries/Lovasz_Local.html</link>
           <pubDate>Wed, 20 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Lovasz_Local.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraphs</title>
           <link>/entries/Hypergraph_Basics.html</link>
           <pubDate>Wed, 20 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Hypergraph_Basics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Unification Utilities for Isabelle/ML</title>
           <link>/entries/ML_Unification.html</link>
           <pubDate>Tue, 19 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/ML_Unification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Euler&#39;s Polyhedron Formula</title>
           <link>/entries/Euler_Polyhedron_Formula.html</link>
           <pubDate>Sat, 16 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Euler_Polyhedron_Formula.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conformance Relations between Input/Output Languages</title>
           <link>/entries/IO_Language_Conformance.html</link>
           <pubDate>Fri, 01 Sep 2023 00:00:00 +0000</pubDate>
           <guid>/entries/IO_Language_Conformance.html</guid>
           <description></description>
         </item>
         <item>
           <title>Coupled Similarity and Contrasimilarity, and How to Compute Them</title>
           <link>/entries/Coupledsim_Contrasim.html</link>
           <pubDate>Fri, 18 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Coupledsim_Contrasim.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ceva&#39;s Theorem</title>
           <link>/entries/Ceva.html</link>
           <pubDate>Wed, 16 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Ceva.html</guid>
           <description></description>
         </item>
         <item>
           <title>Catoids, Categories, Groupoids</title>
           <link>/entries/Catoids.html</link>
           <pubDate>Mon, 14 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Catoids.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fixed-length vectors</title>
           <link>/entries/Fixed_Length_Vector.html</link>
           <pubDate>Mon, 14 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Fixed_Length_Vector.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polygonal Number Theorem</title>
           <link>/entries/Polygonal_Number_Theorem.html</link>
           <pubDate>Thu, 10 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Polygonal_Number_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>S-Finite Measure Monad on Quasi-Borel Spaces</title>
           <link>/entries/S_Finite_Measure_Monad.html</link>
           <pubDate>Tue, 08 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/S_Finite_Measure_Monad.html</guid>
           <description></description>
         </item>
         <item>
           <title>Standard Borel Spaces</title>
           <link>/entries/Standard_Borel_Spaces.html</link>
           <pubDate>Tue, 08 Aug 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Standard_Borel_Spaces.html</guid>
           <description></description>
         </item>
         <item>
           <title>Modal quantales, involutive quantales, Dedekind Quantales</title>
           <link>/entries/Quantales_Converse.html</link>
           <pubDate>Tue, 25 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Quantales_Converse.html</guid>
           <description></description>
         </item>
         <item>
           <title>Earley Parser</title>
           <link>/entries/Earley_Parser.html</link>
           <pubDate>Sun, 16 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Earley_Parser.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gray Codes for Arbitrary Numeral Systems</title>
           <link>/entries/Gray_Codes.html</link>
           <pubDate>Tue, 11 Jul 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Gray_Codes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Randomized Algorithms</title>
           <link>/entries/Executable_Randomized_Algorithms.html</link>
           <pubDate>Mon, 19 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Executable_Randomized_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>DCR Syntax and Execution Equivalent Markings</title>
           <link>/entries/DCR-ExecutionEquivalence.html</link>
           <pubDate>Fri, 16 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/DCR-ExecutionEquivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Zeckendorf’s Theorem</title>
           <link>/entries/Zeckendorf.html</link>
           <pubDate>Mon, 12 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Zeckendorf.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cryptographic Standards</title>
           <link>/entries/Crypto_Standards.html</link>
           <pubDate>Tue, 06 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Crypto_Standards.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Efficient Implementation of the Weighted Path Order</title>
           <link>/entries/Efficient_Weighted_Path_Order.html</link>
           <pubDate>Thu, 01 Jun 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Efficient_Weighted_Path_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Results on Directed Sets</title>
           <link>/entries/Directed_Sets.html</link>
           <pubDate>Wed, 24 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Directed_Sets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inner Structure, Determinism and Modal Algebra of Multirelations</title>
           <link>/entries/Multirelations_Heterogeneous.html</link>
           <pubDate>Mon, 22 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Multirelations_Heterogeneous.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Enumeration</title>
           <link>/entries/Tree_Enumeration.html</link>
           <pubDate>Tue, 09 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Tree_Enumeration.html</guid>
           <description></description>
         </item>
         <item>
           <title>MLSS Decision Procedure</title>
           <link>/entries/MLSS_Decision_Proc.html</link>
           <pubDate>Fri, 05 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/MLSS_Decision_Proc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Three Squares Theorem</title>
           <link>/entries/Three_Squares.html</link>
           <pubDate>Wed, 03 May 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Three_Squares.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Halting Problem is Soluble in Malament-Hogarth Spacetimes</title>
           <link>/entries/MHComputation.html</link>
           <pubDate>Sat, 29 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/MHComputation.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Schwartz-Zippel Lemma</title>
           <link>/entries/Schwartz_Zippel.html</link>
           <pubDate>Thu, 27 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Schwartz_Zippel.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of the SCL(FOL) Calculus: Simple Clause Learning for First-Order Logic</title>
           <link>/entries/Simple_Clause_Learning.html</link>
           <pubDate>Thu, 20 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Simple_Clause_Learning.html</guid>
           <description></description>
         </item>
         <item>
           <title>The CHSH inequality: Tsirelson&#39;s upper-bound and other results</title>
           <link>/entries/TsirelsonBound.html</link>
           <pubDate>Tue, 18 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/TsirelsonBound.html</guid>
           <description></description>
         </item>
         <item>
           <title>Distributed Distinct Elements</title>
           <link>/entries/Distributed_Distinct_Elements.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Distributed_Distinct_Elements.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Hyper Hoare Logic: A Logic to (Dis-)Prove Program Hyperproperties</title>
           <link>/entries/HyperHoareLogic.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HyperHoareLogic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Positional Notation for Natural Numbers in an Arbitrary Base</title>
           <link>/entries/DigitsInBase.html</link>
           <pubDate>Mon, 03 Apr 2023 00:00:00 +0000</pubDate>
           <guid>/entries/DigitsInBase.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of CommCSL: A Relational Concurrent Separation Logic for Proving Information Flow Security in Concurrent Programs</title>
           <link>/entries/CommCSL.html</link>
           <pubDate>Wed, 15 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/CommCSL.html</guid>
           <description></description>
         </item>
         <item>
           <title>No Faster-Than-Light Observers (GenRel)</title>
           <link>/entries/No_FTL_observers_Gen_Rel.html</link>
           <pubDate>Sun, 05 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/No_FTL_observers_Gen_Rel.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expander Graphs</title>
           <link>/entries/Expander_Graphs.html</link>
           <pubDate>Fri, 03 Mar 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Expander_Graphs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Renaming-Enriched Sets (Rensets) and Renaming-Based Recursion</title>
           <link>/entries/Rensets.html</link>
           <pubDate>Tue, 28 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Rensets.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sound and Complete Calculus for Probability Inequalities</title>
           <link>/entries/Probability_Inequality_Completeness.html</link>
           <pubDate>Mon, 20 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Probability_Inequality_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Group Law of Edwards Elliptic Curves</title>
           <link>/entries/Edwards_Elliptic_Curves_Group.html</link>
           <pubDate>Thu, 16 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Edwards_Elliptic_Curves_Group.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hardness of Lattice Problems</title>
           <link>/entries/CVP_Hardness.html</link>
           <pubDate>Thu, 02 Feb 2023 00:00:00 +0000</pubDate>
           <guid>/entries/CVP_Hardness.html</guid>
           <description></description>
         </item>
         <item>
           <title>ABY3 Multiplication and Array Shuffling</title>
           <link>/entries/ABY3_Protocols.html</link>
           <pubDate>Fri, 27 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/ABY3_Protocols.html</guid>
           <description></description>
         </item>
         <item>
           <title>Given Clause Loops</title>
           <link>/entries/Given_Clause_Loops.html</link>
           <pubDate>Wed, 25 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Given_Clause_Loops.html</guid>
           <description></description>
         </item>
         <item>
           <title>Suppes&#39; Theorem For Probability Logic</title>
           <link>/entries/Suppes_Theorem.html</link>
           <pubDate>Sun, 22 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Suppes_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Hoare Logic for Diverging Programs</title>
           <link>/entries/HoareForDivergence.html</link>
           <pubDate>Fri, 20 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/HoareForDivergence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strict Omega Categories</title>
           <link>/entries/StrictOmegaCategories.html</link>
           <pubDate>Sat, 14 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/StrictOmegaCategories.html</guid>
           <description></description>
         </item>
         <item>
           <title>Synthetic Completeness</title>
           <link>/entries/Synthetic_Completeness.html</link>
           <pubDate>Mon, 09 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Synthetic_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cook-Levin theorem</title>
           <link>/entries/Cook_Levin.html</link>
           <pubDate>Sun, 08 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Cook_Levin.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary codes that do not preserve primitivity</title>
           <link>/entries/Binary_Code_Imprimitive.html</link>
           <pubDate>Tue, 03 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Binary_Code_Imprimitive.html</guid>
           <description></description>
         </item>
         <item>
           <title>Intersection of two monoids generated by two element codes</title>
           <link>/entries/Two_Generated_Word_Monoids_Intersection.html</link>
           <pubDate>Tue, 03 Jan 2023 00:00:00 +0000</pubDate>
           <guid>/entries/Two_Generated_Word_Monoids_Intersection.html</guid>
           <description></description>
         </item>
         <item>
           <title>A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL</title>
           <link>/entries/Quantifier_Elimination_Hybrid.html</link>
           <pubDate>Thu, 15 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Quantifier_Elimination_Hybrid.html</guid>
           <description></description>
         </item>
         <item>
           <title>Class-based Classical Propositional Logic</title>
           <link>/entries/Propositional_Logic_Class.html</link>
           <pubDate>Thu, 15 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Propositional_Logic_Class.html</guid>
           <description></description>
         </item>
         <item>
           <title>Birkhoff&#39;s Representation Theorem For Finite Distributive Lattices</title>
           <link>/entries/Birkhoff_Finite_Distributive_Lattices.html</link>
           <pubDate>Tue, 06 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Birkhoff_Finite_Distributive_Lattices.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automation of Boolos&#39; Curious Inference in Isabelle/HOL</title>
           <link>/entries/Boolos_Curious_Inference_Automated.html</link>
           <pubDate>Mon, 05 Dec 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Boolos_Curious_Inference_Automated.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Translation of Multitape Turing Machines into Singletape Turing Machines</title>
           <link>/entries/Multitape_To_Singletape_TM.html</link>
           <pubDate>Wed, 30 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Multitape_To_Singletape_TM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Object Theory</title>
           <link>/entries/AOT.html</link>
           <pubDate>Mon, 28 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/AOT.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal CHERI-C Memory Model</title>
           <link>/entries/CHERI-C_Memory_Model.html</link>
           <pubDate>Fri, 25 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/CHERI-C_Memory_Model.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sauer-Shelah Lemma</title>
           <link>/entries/Sauer_Shelah_Lemma.html</link>
           <pubDate>Thu, 24 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Sauer_Shelah_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kneser&#39;s Theorem and the Cauchy–Davenport Theorem</title>
           <link>/entries/Kneser_Cauchy_Davenport.html</link>
           <pubDate>Mon, 21 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Kneser_Cauchy_Davenport.html</guid>
           <description></description>
         </item>
         <item>
           <title>Turán&#39;s Graph Theorem</title>
           <link>/entries/Turans_Graph_Theorem.html</link>
           <pubDate>Mon, 14 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Turans_Graph_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial Enumeration Algorithms</title>
           <link>/entries/Combinatorial_Enumeration_Algorithms.html</link>
           <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorial_Enumeration_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Balog–Szemerédi–Gowers Theorem</title>
           <link>/entries/Balog_Szemeredi_Gowers.html</link>
           <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Balog_Szemeredi_Gowers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of Strategy-Proofness and Representation in Party-Approval Multi-Winner Elections</title>
           <link>/entries/PAPP_Impossibility.html</link>
           <pubDate>Thu, 10 Nov 2022 00:00:00 +0000</pubDate>
           <guid>/entries/PAPP_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of Query Optimization Algorithms</title>
           <link>/entries/Query_Optimization.html</link>
           <pubDate>Tue, 04 Oct 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Query_Optimization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum Segment Sum</title>
           <link>/entries/Maximum_Segment_Sum.html</link>
           <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Maximum_Segment_Sum.html</guid>
           <description></description>
         </item>
         <item>
           <title>Undirected Graph Theory</title>
           <link>/entries/Undirected_Graph_Theory.html</link>
           <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Undirected_Graph_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Making Arbitrary Relational Calculus Queries Safe-Range</title>
           <link>/entries/Safe_Range_RC.html</link>
           <pubDate>Wed, 28 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_Range_RC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stalnaker&#39;s Epistemic Logic</title>
           <link>/entries/Stalnaker_Logic.html</link>
           <pubDate>Fri, 23 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Stalnaker_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>p-adic Fields and p-adic Semialgebraic Sets</title>
           <link>/entries/Padic_Field.html</link>
           <pubDate>Thu, 22 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Padic_Field.html</guid>
           <description></description>
         </item>
         <item>
           <title>Risk-Free Lending</title>
           <link>/entries/Risk_Free_Lending.html</link>
           <pubDate>Sun, 18 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Risk_Free_Lending.html</guid>
           <description></description>
         </item>
         <item>
           <title>Soundness and Completeness of Implicational Logic</title>
           <link>/entries/Implicational_Logic.html</link>
           <pubDate>Tue, 13 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Implicational_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber</title>
           <link>/entries/CRYSTALS-Kyber.html</link>
           <pubDate>Thu, 08 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/CRYSTALS-Kyber.html</guid>
           <description></description>
         </item>
         <item>
           <title>Unbounded Separation Logic</title>
           <link>/entries/Separation_Logic_Unbounded.html</link>
           <pubDate>Mon, 05 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Logic_Unbounded.html</guid>
           <description></description>
         </item>
         <item>
           <title>Khovanskii&amp;#x27;s Theorem</title>
           <link>/entries/Khovanskii_Theorem.html</link>
           <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Khovanskii_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hales–Jewett Theorem</title>
           <link>/entries/Hales_Jewett.html</link>
           <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Hales_Jewett.html</guid>
           <description></description>
         </item>
         <item>
           <title>Number Theoretic Transform</title>
           <link>/entries/Number_Theoretic_Transform.html</link>
           <pubDate>Thu, 18 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Number_Theoretic_Transform.html</guid>
           <description></description>
         </item>
         <item>
           <title>Correctness of a Set-based Algorithm for Computing Strongly Connected Components of a Graph</title>
           <link>/entries/SCC_Bloemen_Sequential.html</link>
           <pubDate>Wed, 17 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/SCC_Bloemen_Sequential.html</guid>
           <description></description>
         </item>
         <item>
           <title>From THE BOOK: Two Squares via Involutions</title>
           <link>/entries/Involutions2Squares.html</link>
           <pubDate>Mon, 15 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Involutions2Squares.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Complete Test Strategies for Finite State Machines</title>
           <link>/entries/FSM_Tests.html</link>
           <pubDate>Tue, 09 Aug 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FSM_Tests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Nano JSON: Working with JSON formatted data in Isabelle/HOL and Isabelle/ML</title>
           <link>/entries/Nano_JSON.html</link>
           <pubDate>Fri, 29 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Nano_JSON.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</title>
           <link>/entries/Solidity.html</link>
           <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Solidity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simultaneous diagonalization of pairwise commuting Hermitian matrices</title>
           <link>/entries/Commuting_Hermitian.html</link>
           <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Commuting_Hermitian.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality</title>
           <link>/entries/Weighted_Arithmetic_Geometric_Mean.html</link>
           <pubDate>Mon, 11 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Weighted_Arithmetic_Geometric_Mean.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Reuse-Based Multi-Stage Compiler Verification for Language IMP</title>
           <link>/entries/IMP_Compiler_Reuse.html</link>
           <pubDate>Sun, 10 Jul 2022 00:00:00 +0000</pubDate>
           <guid>/entries/IMP_Compiler_Reuse.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real-Time Double-Ended Queue</title>
           <link>/entries/Real_Time_Deque.html</link>
           <pubDate>Thu, 23 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Time_Deque.html</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos&#39;s Curious Inference in Isabelle/HOL</title>
           <link>/entries/Boolos_Curious_Inference.html</link>
           <pubDate>Mon, 20 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Boolos_Curious_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Fields</title>
           <link>/entries/Finite_Fields.html</link>
           <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Finite_Fields.html</guid>
           <description></description>
         </item>
         <item>
           <title>IsaNet: Formalization of a Verification Framework for Secure Data Plane Protocols</title>
           <link>/entries/IsaNet.html</link>
           <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/IsaNet.html</guid>
           <description></description>
         </item>
         <item>
           <title>Diophantine Equations and the DPRM Theorem</title>
           <link>/entries/DPRM_Theorem.html</link>
           <pubDate>Mon, 06 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/DPRM_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Reducing Rewrite Properties to Properties on Ground Terms</title>
           <link>/entries/Rewrite_Properties_Reduction.html</link>
           <pubDate>Thu, 02 Jun 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Rewrite_Properties_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Restricted Definition of the Magic Wand to Soundly Combine Fractions of a Wand</title>
           <link>/entries/Combinable_Wands.html</link>
           <pubDate>Mon, 30 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Combinable_Wands.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Plünnecke-Ruzsa Inequality</title>
           <link>/entries/Pluennecke_Ruzsa_Inequality.html</link>
           <pubDate>Thu, 26 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Pluennecke_Ruzsa_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Framework for the Sound Automation of Magic Wands</title>
           <link>/entries/Package_logic.html</link>
           <pubDate>Wed, 18 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Package_logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Clique is not solvable by monotone circuits of polynomial size</title>
           <link>/entries/Clique_and_Monotone_Circuits.html</link>
           <pubDate>Sun, 08 May 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Clique_and_Monotone_Circuits.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</title>
           <link>/entries/Fishers_Inequality.html</link>
           <pubDate>Thu, 21 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Fishers_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Digit Expansions</title>
           <link>/entries/Digit_Expansions.html</link>
           <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Digit_Expansions.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Generalized Multiset Ordering is NP-Complete</title>
           <link>/entries/Multiset_Ordering_NPC.html</link>
           <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Multiset_Ordering_NPC.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sophomore&#39;s Dream</title>
           <link>/entries/Sophomores_Dream.html</link>
           <pubDate>Sun, 10 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Sophomores_Dream.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Combinator Library for Prefix-Free Codes</title>
           <link>/entries/Prefix_Free_Code_Combinators.html</link>
           <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Prefix_Free_Code_Combinators.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Randomized Approximation Algorithms for Frequency Moments</title>
           <link>/entries/Frequency_Moments.html</link>
           <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Frequency_Moments.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructing the Reals as Dedekind Cuts of Rationals</title>
           <link>/entries/Dedekind_Real.html</link>
           <pubDate>Thu, 24 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Dedekind_Real.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ackermann&#39;s Function Is Not Primitive Recursive</title>
           <link>/entries/Ackermanns_not_PR.html</link>
           <pubDate>Wed, 23 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Ackermanns_not_PR.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Naive Prover for First-Order Logic</title>
           <link>/entries/FOL_Seq_Calc3.html</link>
           <pubDate>Tue, 22 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc3.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent</title>
           <link>/entries/Cotangent_PFD_Formula.html</link>
           <pubDate>Tue, 15 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Cotangent_PFD_Formula.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Independence of the Continuum Hypothesis in Isabelle/ZF</title>
           <link>/entries/Independence_CH.html</link>
           <pubDate>Sun, 06 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Independence_CH.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive Models of Fragments of ZFC</title>
           <link>/entries/Transitive_Models.html</link>
           <pubDate>Thu, 03 Mar 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated Transition Systems</title>
           <link>/entries/ResiduatedTransitionSystem.html</link>
           <pubDate>Mon, 28 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/ResiduatedTransitionSystem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Universal Hash Families</title>
           <link>/entries/Universal_Hash_Families.html</link>
           <pubDate>Sun, 20 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Universal_Hash_Families.html</guid>
           <description></description>
         </item>
         <item>
           <title>Wetzel&#39;s Problem and the Continuum Hypothesis</title>
           <link>/entries/Wetzels_Problem.html</link>
           <pubDate>Fri, 18 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Wetzels_Problem.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Query Evaluation</title>
           <link>/entries/Eval_FO.html</link>
           <pubDate>Tue, 15 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Eval_FO.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multi-Head Monitoring of Metric Dynamic Logic</title>
           <link>/entries/VYDRA_MDL.html</link>
           <pubDate>Sun, 13 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/VYDRA_MDL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Enumeration of Equivalence Relations</title>
           <link>/entries/Equivalence_Relation_Enumeration.html</link>
           <pubDate>Fri, 04 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Equivalence_Relation_Enumeration.html</guid>
           <description></description>
         </item>
         <item>
           <title>Duality of Linear Programming</title>
           <link>/entries/LP_Duality.html</link>
           <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/LP_Duality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quasi-Borel Spaces</title>
           <link>/entries/Quasi_Borel_Spaces.html</link>
           <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Quasi_Borel_Spaces.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Theory of Rewriting</title>
           <link>/entries/FO_Theory_Rewriting.html</link>
           <pubDate>Wed, 02 Feb 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FO_Theory_Rewriting.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequent Calculus Prover for First-Order Logic with Functions</title>
           <link>/entries/FOL_Seq_Calc2.html</link>
           <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc2.html</guid>
           <description></description>
         </item>
         <item>
           <title>Young&#39;s Inequality for Increasing Functions</title>
           <link>/entries/Youngs_Inequality.html</link>
           <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Youngs_Inequality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interpolation Polynomials (in HOL-Algebra)</title>
           <link>/entries/Interpolation_Polynomials_HOL_Algebra.html</link>
           <pubDate>Sat, 29 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Interpolation_Polynomials_HOL_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Median Method</title>
           <link>/entries/Median_Method.html</link>
           <pubDate>Tue, 25 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Median_Method.html</guid>
           <description></description>
         </item>
         <item>
           <title>Actuarial Mathematics</title>
           <link>/entries/Actuarial_Mathematics.html</link>
           <pubDate>Sun, 23 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Actuarial_Mathematics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational numbers from THE BOOK</title>
           <link>/entries/Irrationals_From_THEBOOK.html</link>
           <pubDate>Sat, 08 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Irrationals_From_THEBOOK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knight&#39;s Tour Revisited Revisited</title>
           <link>/entries/Knights_Tour.html</link>
           <pubDate>Tue, 04 Jan 2022 00:00:00 +0000</pubDate>
           <guid>/entries/Knights_Tour.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hyperdual Numbers and Forward Differentiation</title>
           <link>/entries/Hyperdual.html</link>
           <pubDate>Fri, 31 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hyperdual.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gale-Shapley Algorithm</title>
           <link>/entries/Gale_Shapley.html</link>
           <pubDate>Wed, 29 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Gale_Shapley.html</guid>
           <description></description>
         </item>
         <item>
           <title>Roth&#39;s Theorem on Arithmetic Progressions</title>
           <link>/entries/Roth_Arithmetic_Progressions.html</link>
           <pubDate>Tue, 28 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Roth_Arithmetic_Progressions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Markov Decision Processes with Rewards</title>
           <link>/entries/MDP-Rewards.html</link>
           <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MDP-Rewards.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Algorithms for Solving Markov Decision Processes</title>
           <link>/entries/MDP-Algorithms.html</link>
           <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MDP-Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Tree Relations</title>
           <link>/entries/Regular_Tree_Relations.html</link>
           <pubDate>Wed, 15 Dec 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Regular_Tree_Relations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simplicial Complexes and Boolean functions</title>
           <link>/entries/Simplicial_complexes_and_boolean_functions.html</link>
           <pubDate>Mon, 29 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Simplicial_complexes_and_boolean_functions.html</guid>
           <description></description>
         </item>
         <item>
           <title>van Emde Boas Trees</title>
           <link>/entries/Van_Emde_Boas_Trees.html</link>
           <pubDate>Tue, 23 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Van_Emde_Boas_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Foundation of geometry in planes, and some complements: Excluding the parallel axioms</title>
           <link>/entries/Foundation_of_geometry.html</link>
           <pubDate>Mon, 22 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Foundation_of_geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hahn and Jordan Decomposition Theorems</title>
           <link>/entries/Hahn_Jordan_Decomposition.html</link>
           <pubDate>Fri, 19 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hahn_Jordan_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automating Public Announcement Logic and the Wise Men Puzzle in Isabelle/HOL</title>
           <link>/entries/PAL.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/PAL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL</title>
           <link>/entries/SimplifiedOntologicalArgument.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/SimplifiedOntologicalArgument.html</guid>
           <description></description>
         </item>
         <item>
           <title>Factorization of Polynomials with Algebraic Coefficients</title>
           <link>/entries/Factor_Algebraic_Polynomial.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Factor_Algebraic_Polynomial.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real Exponents as the Limits of Sequences of Rational Exponents</title>
           <link>/entries/Real_Power.html</link>
           <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Power.html</guid>
           <description></description>
         </item>
         <item>
           <title>Szemerédi&#39;s Regularity Lemma</title>
           <link>/entries/Szemeredi_Regularity.html</link>
           <pubDate>Fri, 05 Nov 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Szemeredi_Regularity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum and Classical Registers</title>
           <link>/entries/Registers.html</link>
           <pubDate>Thu, 28 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Registers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Belief Revision Theory</title>
           <link>/entries/Belief_Revision.html</link>
           <pubDate>Tue, 19 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Belief_Revision.html</guid>
           <description></description>
         </item>
         <item>
           <title>X86 instruction semantics and basic block symbolic execution</title>
           <link>/entries/X86_Semantics.html</link>
           <pubDate>Wed, 13 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/X86_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</title>
           <link>/entries/Correctness_Algebras.html</link>
           <pubDate>Tue, 12 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Correctness_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Quadratic Virtual Substitution for Real Arithmetic</title>
           <link>/entries/Virtual_Substitution.html</link>
           <pubDate>Sat, 02 Oct 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Virtual_Substitution.html</guid>
           <description></description>
         </item>
         <item>
           <title>Soundness and Completeness of an Axiomatic System for First-Order Logic</title>
           <link>/entries/FOL_Axiomatic.html</link>
           <pubDate>Fri, 24 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Axiomatic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complex Bounded Operators</title>
           <link>/entries/Complex_Bounded_Operators.html</link>
           <pubDate>Sat, 18 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Complex_Bounded_Operators.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Weighted Path Orders and Recursive Path Orders</title>
           <link>/entries/Weighted_Path_Order.html</link>
           <pubDate>Thu, 16 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Weighted_Path_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</title>
           <link>/entries/CZH_Foundations.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Foundations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</title>
           <link>/entries/CZH_Elementary_Categories.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Elementary_Categories.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory for ZFC in HOL III: Universal Constructions</title>
           <link>/entries/CZH_Universal_Constructions.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CZH_Universal_Constructions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional Simplification</title>
           <link>/entries/Conditional_Simplification.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Conditional_Simplification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional Transfer Rule</title>
           <link>/entries/Conditional_Transfer_Rule.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Conditional_Transfer_Rule.html</guid>
           <description></description>
         </item>
         <item>
           <title>Extension of Types-To-Sets</title>
           <link>/entries/Types_To_Sets_Extension.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Types_To_Sets_Extension.html</guid>
           <description></description>
         </item>
         <item>
           <title>IDE: Introduction, Destruction, Elimination</title>
           <link>/entries/Intro_Dest_Elim.html</link>
           <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Intro_Dest_Elim.html</guid>
           <description></description>
         </item>
         <item>
           <title>A data flow analysis algorithm for computing dominators</title>
           <link>/entries/Dominance_CHK.html</link>
           <pubDate>Sun, 05 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Dominance_CHK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Solving Cubic and Quartic Equations</title>
           <link>/entries/Cubic_Quartic_Equations.html</link>
           <pubDate>Fri, 03 Sep 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Cubic_Quartic_Equations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Logging-independent Message Anonymity in the Relational Method</title>
           <link>/entries/Logging_Independent_Anonymity.html</link>
           <pubDate>Thu, 26 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Logging_Independent_Anonymity.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Theorem of Three Circles</title>
           <link>/entries/Three_Circles.html</link>
           <pubDate>Sat, 21 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Three_Circles.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoCon: A Confidentiality-Verified Conference Management System</title>
           <link>/entries/CoCon.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoCon.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional BD Security</title>
           <link>/entries/BD_Security_Compositional.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BD_Security_Compositional.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMed: A confidentiality-verified social media platform</title>
           <link>/entries/CoSMed.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoSMed.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMeDis: A confidentiality-verified distributed social media platform</title>
           <link>/entries/CoSMeDis.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/CoSMeDis.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fresh identifiers</title>
           <link>/entries/Fresh_Identifiers.html</link>
           <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Fresh_Identifiers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial Design Theory</title>
           <link>/entries/Design_Theory.html</link>
           <pubDate>Fri, 13 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Design_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Forests</title>
           <link>/entries/Relational_Forests.html</link>
           <pubDate>Tue, 03 Aug 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Forests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Schutz&#39; Independent Axioms for Minkowski Spacetime</title>
           <link>/entries/Schutz_Spacetime.html</link>
           <pubDate>Tue, 27 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Schutz_Spacetime.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finitely Generated Abelian Groups</title>
           <link>/entries/Finitely_Generated_Abelian_Groups.html</link>
           <pubDate>Wed, 07 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Finitely_Generated_Abelian_Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>SpecCheck - Specification-Based Testing for Isabelle/ML</title>
           <link>/entries/SpecCheck.html</link>
           <pubDate>Thu, 01 Jul 2021 00:00:00 +0000</pubDate>
           <guid>/entries/SpecCheck.html</guid>
           <description></description>
         </item>
         <item>
           <title>Van der Waerden&#39;s Theorem</title>
           <link>/entries/Van_der_Waerden.html</link>
           <pubDate>Tue, 22 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Van_der_Waerden.html</guid>
           <description></description>
         </item>
         <item>
           <title>MiniSail - A kernel language for the ISA specification language SAIL</title>
           <link>/entries/MiniSail.html</link>
           <pubDate>Fri, 18 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/MiniSail.html</guid>
           <description></description>
         </item>
         <item>
           <title>Public Announcement Logic</title>
           <link>/entries/Public_Announcement_Logic.html</link>
           <pubDate>Thu, 17 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Public_Announcement_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Shorter Compiler Correctness Proof for Language IMP</title>
           <link>/entries/IMP_Compiler.html</link>
           <pubDate>Fri, 04 Jun 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IMP_Compiler.html</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics on Words Basics</title>
           <link>/entries/Combinatorics_Words.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Lemma</title>
           <link>/entries/Combinatorics_Words_Graph_Lemma.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words_Graph_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lyndon words</title>
           <link>/entries/Combinatorics_Words_Lyndon.html</link>
           <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Combinatorics_Words_Lyndon.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regression Test Selection</title>
           <link>/entries/Regression_Test_Selection.html</link>
           <pubDate>Fri, 30 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Regression_Test_Selection.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle&#39;s Metalogic: Formalization and Proof Checker</title>
           <link>/entries/Metalogic_ProofChecker.html</link>
           <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Metalogic_ProofChecker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting the Exponent</title>
           <link>/entries/Lifting_the_Exponent.html</link>
           <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Lifting_the_Exponent.html</guid>
           <description></description>
         </item>
         <item>
           <title>The BKR Decision Procedure for Univariate Real Arithmetic</title>
           <link>/entries/BenOr_Kozen_Reif.html</link>
           <pubDate>Sat, 24 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BenOr_Kozen_Reif.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gale-Stewart Games</title>
           <link>/entries/GaleStewart_Games.html</link>
           <pubDate>Fri, 23 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/GaleStewart_Games.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Timely Dataflow&#39;s Progress Tracking Protocol</title>
           <link>/entries/Progress_Tracking.html</link>
           <pubDate>Tue, 13 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Progress_Tracking.html</guid>
           <description></description>
         </item>
         <item>
           <title>Information Flow Control via Dependency Tracking</title>
           <link>/entries/IFC_Tracking.html</link>
           <pubDate>Thu, 01 Apr 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IFC_Tracking.html</guid>
           <description></description>
         </item>
         <item>
           <title>Grothendieck&#39;s Schemes in Algebraic Geometry</title>
           <link>/entries/Grothendieck_Schemes.html</link>
           <pubDate>Mon, 29 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Grothendieck_Schemes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hensel&#39;s Lemma for the p-adic Integers</title>
           <link>/entries/Padic_Ints.html</link>
           <pubDate>Tue, 23 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Padic_Ints.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive Cryptography in HOL: the Communication Modeling Aspect</title>
           <link>/entries/Constructive_Cryptography_CM.html</link>
           <pubDate>Wed, 17 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Constructive_Cryptography_CM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</title>
           <link>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</link>
           <pubDate>Fri, 12 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum projective measurements and the CHSH inequality</title>
           <link>/entries/Projective_Measurements.html</link>
           <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Projective_Measurements.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hermite–Lindemann–Weierstraß Transcendence Theorem</title>
           <link>/entries/Hermite_Lindemann.html</link>
           <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hermite_Lindemann.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mereology</title>
           <link>/entries/Mereology.html</link>
           <pubDate>Mon, 01 Mar 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Mereology.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sunflower Lemma of Erdős and Rado</title>
           <link>/entries/Sunflowers.html</link>
           <pubDate>Thu, 25 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Sunflowers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Imperative Implementation of B-Trees</title>
           <link>/entries/BTree.html</link>
           <pubDate>Wed, 24 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/BTree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Puiseux Series</title>
           <link>/entries/Formal_Puiseux_Series.html</link>
           <pubDate>Wed, 17 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Formal_Puiseux_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Laws of Large Numbers</title>
           <link>/entries/Laws_of_Large_Numbers.html</link>
           <pubDate>Wed, 10 Feb 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Laws_of_Large_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tarski&#39;s Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</title>
           <link>/entries/IsaGeoCoq.html</link>
           <pubDate>Sun, 31 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/IsaGeoCoq.html</guid>
           <description></description>
         </item>
         <item>
           <title>Solution to the xkcd Blue Eyes puzzle</title>
           <link>/entries/Blue_Eyes.html</link>
           <pubDate>Sat, 30 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Blue_Eyes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hood-Melville Queue</title>
           <link>/entries/Hood_Melville_Queue.html</link>
           <pubDate>Mon, 18 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/Hood_Melville_Queue.html</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaDCI: a Java semantics with dynamic class initialization</title>
           <link>/entries/JinjaDCI.html</link>
           <pubDate>Mon, 11 Jan 2021 00:00:00 +0000</pubDate>
           <guid>/entries/JinjaDCI.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cofinality and the Delta System Lemma</title>
           <link>/entries/Delta_System_Lemma.html</link>
           <pubDate>Sun, 27 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Delta_System_Lemma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Topological semantics for paraconsistent and paracomplete logics</title>
           <link>/entries/Topological_Semantics.html</link>
           <pubDate>Thu, 17 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Topological_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Minimum Spanning Tree Algorithms</title>
           <link>/entries/Relational_Minimum_Spanning_Trees.html</link>
           <pubDate>Tue, 08 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Minimum_Spanning_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inline Caching and Unboxing Optimization for Interpreters</title>
           <link>/entries/Interpreter_Optimizations.html</link>
           <pubDate>Mon, 07 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Interpreter_Optimizations.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Relational Method with Message Anonymity for the Verification of Cryptographic Protocols</title>
           <link>/entries/Relational_Method.html</link>
           <pubDate>Sat, 05 Dec 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Method.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</title>
           <link>/entries/Isabelle_Marries_Dirac.html</link>
           <pubDate>Sun, 22 Nov 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_Marries_Dirac.html</guid>
           <description></description>
         </item>
         <item>
           <title>The HOL-CSP Refinement Toolkit</title>
           <link>/entries/CSP_RefTK.html</link>
           <pubDate>Thu, 19 Nov 2020 00:00:00 +0000</pubDate>
           <guid>/entries/CSP_RefTK.html</guid>
           <description></description>
         </item>
         <item>
           <title>AI Planning Languages Semantics</title>
           <link>/entries/AI_Planning_Languages_Semantics.html</link>
           <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/AI_Planning_Languages_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified SAT-Based AI Planning</title>
           <link>/entries/Verified_SAT_Based_AI_Planning.html</link>
           <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Verified_SAT_Based_AI_Planning.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sound Type System for Physical Quantities, Units, and Measurements</title>
           <link>/entries/Physical_Quantities.html</link>
           <pubDate>Tue, 20 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Physical_Quantities.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Map Extras</title>
           <link>/entries/Finite-Map-Extras.html</link>
           <pubDate>Mon, 12 Oct 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Finite-Map-Extras.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Document Object Model with Shadow Roots</title>
           <link>/entries/Shadow_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Shadow_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Safely Composable Document Object Model with Shadow Roots</title>
           <link>/entries/Shadow_SC_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Shadow_SC_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Safely Composable Web Components</title>
           <link>/entries/SC_DOM_Components.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/SC_DOM_Components.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Web Components</title>
           <link>/entries/DOM_Components.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/DOM_Components.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Safely Composable DOM</title>
           <link>/entries/Core_SC_DOM.html</link>
           <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Core_SC_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Abstract Formalization of G&amp;ouml;del&#39;s Incompleteness Theorems</title>
           <link>/entries/Goedel_Incompleteness.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_Incompleteness.html</guid>
           <description></description>
         </item>
         <item>
           <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part I</title>
           <link>/entries/Goedel_HFSet_Semantic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_HFSet_Semantic.html</guid>
           <description></description>
         </item>
         <item>
           <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part II</title>
           <link>/entries/Goedel_HFSet_Semanticless.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goedel_HFSet_Semanticless.html</guid>
           <description></description>
         </item>
         <item>
           <title>Robinson Arithmetic</title>
           <link>/entries/Robinson_Arithmetic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Robinson_Arithmetic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax-Independent Logic Infrastructure</title>
           <link>/entries/Syntax_Independent_Logic.html</link>
           <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Syntax_Independent_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of Extended Finite State Machines</title>
           <link>/entries/Extended_Finite_State_Machines.html</link>
           <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Extended_Finite_State_Machines.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inference of Extended Finite State Machines</title>
           <link>/entries/Extended_Finite_State_Machine_Inference.html</link>
           <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Extended_Finite_State_Machine_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Practical Algebraic Calculus Checker</title>
           <link>/entries/PAC_Checker.html</link>
           <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/PAC_Checker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Some classical results in inductive inference of recursive functions</title>
           <link>/entries/Inductive_Inference.html</link>
           <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Inductive_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Disjoint-Set Forests</title>
           <link>/entries/Relational_Disjoint_Set_Forests.html</link>
           <pubDate>Wed, 26 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Disjoint_Set_Forests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Extensions to the Comprehensive Framework for Saturation Theorem Proving</title>
           <link>/entries/Saturation_Framework_Extensions.html</link>
           <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Saturation_Framework_Extensions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Putting the `K&#39; into Bird&#39;s derivation of Knuth-Morris-Pratt string matching</title>
           <link>/entries/BirdKMP.html</link>
           <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/BirdKMP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Amicable Numbers</title>
           <link>/entries/Amicable_Numbers.html</link>
           <pubDate>Tue, 04 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Amicable_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal Partitions</title>
           <link>/entries/Ordinal_Partitions.html</link>
           <pubDate>Mon, 03 Aug 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinal_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm</title>
           <link>/entries/Chandy_Lamport.html</link>
           <pubDate>Tue, 21 Jul 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Chandy_Lamport.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relational Characterisations of Paths</title>
           <link>/entries/Relational_Paths.html</link>
           <pubDate>Mon, 13 Jul 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational_Paths.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles</title>
           <link>/entries/Safe_Distance.html</link>
           <pubDate>Mon, 01 Jun 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_Distance.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified algorithm for computing the Smith normal form of a matrix</title>
           <link>/entries/Smith_Normal_Form.html</link>
           <pubDate>Sat, 23 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Smith_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Nash-Williams Partition Theorem</title>
           <link>/entries/Nash_Williams.html</link>
           <pubDate>Sat, 16 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Nash_Williams.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Knuth–Bendix Orders</title>
           <link>/entries/Knuth_Bendix_Order.html</link>
           <pubDate>Wed, 13 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Knuth_Bendix_Order.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationality Criteria for Series by Erdős and Straus</title>
           <link>/entries/Irrational_Series_Erdos_Straus.html</link>
           <pubDate>Tue, 12 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Irrational_Series_Erdos_Straus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion Theorem in ZF</title>
           <link>/entries/Recursion-Addition.html</link>
           <pubDate>Mon, 11 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Recursion-Addition.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation</title>
           <link>/entries/LTL_Normal_Form.html</link>
           <pubDate>Fri, 08 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Forcing in Isabelle/ZF</title>
           <link>/entries/Forcing.html</link>
           <pubDate>Wed, 06 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Forcing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Banach-Steinhaus Theorem</title>
           <link>/entries/Banach_Steinhaus.html</link>
           <pubDate>Sat, 02 May 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Banach_Steinhaus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Attack Trees in Isabelle for GDPR compliance of IoT healthcare systems</title>
           <link>/entries/Attack_Trees.html</link>
           <pubDate>Mon, 27 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Attack_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gaussian Integers</title>
           <link>/entries/Gaussian_Integers.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Gaussian_Integers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Power Sum Polynomials</title>
           <link>/entries/Power_Sum_Polynomials.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Power_Sum_Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Lambert W Function on the Reals</title>
           <link>/entries/Lambert_W.html</link>
           <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Lambert_W.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices for ODEs</title>
           <link>/entries/Matrices_for_ODEs.html</link>
           <pubDate>Sun, 19 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Matrices_for_ODEs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Authenticated Data Structures As Functors</title>
           <link>/entries/ADS_Functor.html</link>
           <pubDate>Thu, 16 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/ADS_Functor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows</title>
           <link>/entries/Sliding_Window_Algorithm.html</link>
           <pubDate>Fri, 10 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Sliding_Window_Algorithm.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Comprehensive Framework for Saturation Theorem Proving</title>
           <link>/entries/Saturation_Framework.html</link>
           <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Saturation_Framework.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</title>
           <link>/entries/MFODL_Monitor_Optimized.html</link>
           <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/MFODL_Monitor_Optimized.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automated Stateful Protocol Verification</title>
           <link>/entries/Automated_Stateful_Protocol_Verification.html</link>
           <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Automated_Stateful_Protocol_Verification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stateful Protocol Composition and Typing</title>
           <link>/entries/Stateful_Protocol_Composition_and_Typing.html</link>
           <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Stateful_Protocol_Composition_and_Typing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lucas&#39;s Theorem</title>
           <link>/entries/Lucas_Theorem.html</link>
           <pubDate>Tue, 07 Apr 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Lucas_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strong Eventual Consistency of the Collaborative Editing Framework WOOT</title>
           <link>/entries/WOOT_Strong_Eventual_Consistency.html</link>
           <pubDate>Wed, 25 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/WOOT_Strong_Eventual_Consistency.html</guid>
           <description></description>
         </item>
         <item>
           <title>Furstenberg&#39;s topology and his proof of the infinitude of primes</title>
           <link>/entries/Furstenberg_Topology.html</link>
           <pubDate>Sun, 22 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Furstenberg_Topology.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Under-Approximate Relational Logic</title>
           <link>/entries/Relational-Incorrectness-Logic.html</link>
           <pubDate>Thu, 12 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Relational-Incorrectness-Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hello World</title>
           <link>/entries/Hello_World.html</link>
           <pubDate>Sat, 07 Mar 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Hello_World.html</guid>
           <description></description>
         </item>
         <item>
           <title>Implementing the Goodstein Function in &amp;lambda;-Calculus</title>
           <link>/entries/Goodstein_Lambda.html</link>
           <pubDate>Fri, 21 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Goodstein_Lambda.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Generic Framework for Verified Compilers</title>
           <link>/entries/VeriComp.html</link>
           <pubDate>Mon, 10 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/VeriComp.html</guid>
           <description></description>
         </item>
         <item>
           <title>Arithmetic progressions and relative primes</title>
           <link>/entries/Arith_Prog_Rel_Primes.html</link>
           <pubDate>Sat, 01 Feb 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Arith_Prog_Rel_Primes.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Hierarchy of Algebras for Boolean Subsets</title>
           <link>/entries/Subset_Boolean_Algebras.html</link>
           <pubDate>Fri, 31 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Subset_Boolean_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mersenne primes and the Lucas–Lehmer test</title>
           <link>/entries/Mersenne_Primes.html</link>
           <pubDate>Fri, 17 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Mersenne_Primes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Approximation Algorithms</title>
           <link>/entries/Approximation_Algorithms.html</link>
           <pubDate>Thu, 16 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Approximation_Algorithms.html</guid>
           <description></description>
         </item>
         <item>
           <title>Closest Pair of Points Algorithms</title>
           <link>/entries/Closest_Pair_Points.html</link>
           <pubDate>Mon, 13 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Closest_Pair_Points.html</guid>
           <description></description>
         </item>
         <item>
           <title>Skip Lists</title>
           <link>/entries/Skip_Lists.html</link>
           <pubDate>Thu, 09 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Skip_Lists.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bicategories</title>
           <link>/entries/Bicategory.html</link>
           <pubDate>Mon, 06 Jan 2020 00:00:00 +0000</pubDate>
           <guid>/entries/Bicategory.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Irrationality of ζ(3)</title>
           <link>/entries/Zeta_3_Irrational.html</link>
           <pubDate>Fri, 27 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Zeta_3_Irrational.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing a Seligman-Style Tableau System for Hybrid Logic</title>
           <link>/entries/Hybrid_Logic.html</link>
           <pubDate>Fri, 20 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Poincaré-Bendixson Theorem</title>
           <link>/entries/Poincare_Bendixson.html</link>
           <pubDate>Wed, 18 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Poincare_Bendixson.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complex Geometry</title>
           <link>/entries/Complex_Geometry.html</link>
           <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Complex_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Poincaré Disc Model</title>
           <link>/entries/Poincare_Disc.html</link>
           <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Poincare_Disc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss Sums and the Pólya–Vinogradov Inequality</title>
           <link>/entries/Gauss_Sums.html</link>
           <pubDate>Tue, 10 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss_Sums.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges</title>
           <link>/entries/Generalized_Counting_Sort.html</link>
           <pubDate>Wed, 04 Dec 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Generalized_Counting_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interval Arithmetic on 32-bit Words</title>
           <link>/entries/Interval_Arithmetic_Word32.html</link>
           <pubDate>Wed, 27 Nov 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Interval_Arithmetic_Word32.html</guid>
           <description></description>
         </item>
         <item>
           <title>Zermelo Fraenkel Set Theory in Higher-Order Logic</title>
           <link>/entries/ZFC_in_HOL.html</link>
           <pubDate>Thu, 24 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/ZFC_in_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/C</title>
           <link>/entries/Isabelle_C.html</link>
           <pubDate>Tue, 22 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_C.html</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis 2019 -- Polished Isabelle Solutions</title>
           <link>/entries/VerifyThis2019.html</link>
           <pubDate>Wed, 16 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/VerifyThis2019.html</guid>
           <description></description>
         </item>
         <item>
           <title>Aristotle&#39;s Assertoric Syllogistic</title>
           <link>/entries/Aristotles_Assertoric_Syllogistic.html</link>
           <pubDate>Tue, 08 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Aristotles_Assertoric_Syllogistic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sigma Protocols and Commitment Schemes</title>
           <link>/entries/Sigma_Commit_Crypto.html</link>
           <pubDate>Mon, 07 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Sigma_Commit_Crypto.html</guid>
           <description></description>
         </item>
         <item>
           <title>Clean - An Abstract Imperative Programming Language and its Theory</title>
           <link>/entries/Clean.html</link>
           <pubDate>Fri, 04 Oct 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Clean.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Multiway-Join Algorithms</title>
           <link>/entries/Generic_Join.html</link>
           <pubDate>Mon, 16 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Generic_Join.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification Components for Hybrid Systems</title>
           <link>/entries/Hybrid_Systems_VCs.html</link>
           <pubDate>Tue, 10 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Systems_VCs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fourier Series</title>
           <link>/entries/Fourier.html</link>
           <pubDate>Fri, 06 Sep 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Fourier.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Case Study in Basic Algebra</title>
           <link>/entries/Jacobson_Basic_Algebra.html</link>
           <pubDate>Fri, 30 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Jacobson_Basic_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation of an Adaptive State Counting Algorithm</title>
           <link>/entries/Adaptive_State_Counting.html</link>
           <pubDate>Fri, 16 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Adaptive_State_Counting.html</guid>
           <description></description>
         </item>
         <item>
           <title>Laplace Transform</title>
           <link>/entries/Laplace_Transform.html</link>
           <pubDate>Wed, 14 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Laplace_Transform.html</guid>
           <description></description>
         </item>
         <item>
           <title>Communicating Concurrent Kleene Algebra for Distributed Systems Specification</title>
           <link>/entries/C2KA_DistributedSystems.html</link>
           <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/C2KA_DistributedSystems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Programming</title>
           <link>/entries/Linear_Programming.html</link>
           <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Programming.html</guid>
           <description></description>
         </item>
         <item>
           <title>Selected Problems from the International Mathematical Olympiad 2019</title>
           <link>/entries/IMO2019.html</link>
           <pubDate>Mon, 05 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMO2019.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stellar Quorum Systems</title>
           <link>/entries/Stellar_Quorums.html</link>
           <pubDate>Thu, 01 Aug 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Stellar_Quorums.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Development of a Polychronous Polytimed Coordination Language</title>
           <link>/entries/TESL_Language.html</link>
           <pubDate>Tue, 30 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/TESL_Language.html</guid>
           <description></description>
         </item>
         <item>
           <title>Order Extension and Szpilrajn&#39;s Extension Theorem</title>
           <link>/entries/Szpilrajn.html</link>
           <pubDate>Sat, 27 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Szpilrajn.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequent Calculus for First-Order Logic</title>
           <link>/entries/FOL_Seq_Calc1.html</link>
           <pubDate>Thu, 18 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Seq_Calc1.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Code Generator from Isabelle/HOL to CakeML</title>
           <link>/entries/CakeML_Codegen.html</link>
           <pubDate>Mon, 08 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/CakeML_Codegen.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</title>
           <link>/entries/MFOTL_Monitor.html</link>
           <pubDate>Thu, 04 Jul 2019 00:00:00 +0000</pubDate>
           <guid>/entries/MFOTL_Monitor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Complete Non-Orders and Fixed Points</title>
           <link>/entries/Complete_Non_Orders.html</link>
           <pubDate>Thu, 27 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Complete_Non_Orders.html</guid>
           <description></description>
         </item>
         <item>
           <title>Priority Search Trees</title>
           <link>/entries/Priority_Search_Trees.html</link>
           <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Priority_Search_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra</title>
           <link>/entries/Prim_Dijkstra_Simple.html</link>
           <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Prim_Dijkstra_Simple.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Inequalities</title>
           <link>/entries/Linear_Inequalities.html</link>
           <pubDate>Fri, 21 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Inequalities.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hilbert&#39;s Nullstellensatz</title>
           <link>/entries/Nullstellensatz.html</link>
           <pubDate>Sun, 16 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Nullstellensatz.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gröbner Bases, Macaulay Matrices and Dubé&#39;s Degree Bounds</title>
           <link>/entries/Groebner_Macaulay.html</link>
           <pubDate>Sat, 15 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Groebner_Macaulay.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary Heaps for IMP2</title>
           <link>/entries/IMP2_Binary_Heap.html</link>
           <pubDate>Thu, 13 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMP2_Binary_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>Differential Game Logic</title>
           <link>/entries/Differential_Game_Logic.html</link>
           <pubDate>Mon, 03 Jun 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Differential_Game_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multidimensional Binary Search Trees</title>
           <link>/entries/KD_Tree.html</link>
           <pubDate>Thu, 30 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/KD_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Generic Authenticated Data Structures</title>
           <link>/entries/LambdaAuth.html</link>
           <pubDate>Tue, 14 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/LambdaAuth.html</guid>
           <description></description>
         </item>
         <item>
           <title>Multi-Party Computation</title>
           <link>/entries/Multi_Party_Computation.html</link>
           <pubDate>Thu, 09 May 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Multi_Party_Computation.html</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP Version 2.0</title>
           <link>/entries/HOL-CSP.html</link>
           <pubDate>Fri, 26 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/HOL-CSP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Compositional and Unified Translation of LTL into ω-Automata</title>
           <link>/entries/LTL_Master_Theorem.html</link>
           <pubDate>Tue, 16 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_Master_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>A General Theory of Syntax with Bindings</title>
           <link>/entries/Binding_Syntax_Theory.html</link>
           <pubDate>Sat, 06 Apr 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Binding_Syntax_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of Certain Infinite Series</title>
           <link>/entries/Transcendence_Series_Hancl_Rucki.html</link>
           <pubDate>Wed, 27 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Transcendence_Series_Hancl_Rucki.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantum Hoare Logic</title>
           <link>/entries/QHLProver.html</link>
           <pubDate>Sun, 24 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/QHLProver.html</guid>
           <description></description>
         </item>
         <item>
           <title>Safe OCL</title>
           <link>/entries/Safe_OCL.html</link>
           <pubDate>Sat, 09 Mar 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Safe_OCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Elementary Facts About the Distribution of Primes</title>
           <link>/entries/Prime_Distribution_Elementary.html</link>
           <pubDate>Thu, 21 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Distribution_Elementary.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kruskal&#39;s Algorithm for Minimum Spanning Forest</title>
           <link>/entries/Kruskal.html</link>
           <pubDate>Thu, 14 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Kruskal.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Primality Testing</title>
           <link>/entries/Probabilistic_Prime_Tests.html</link>
           <pubDate>Mon, 11 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Prime_Tests.html</guid>
           <description></description>
         </item>
         <item>
           <title>Universal Turing Machine</title>
           <link>/entries/Universal_Turing_Machine.html</link>
           <pubDate>Fri, 08 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Universal_Turing_Machine.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming</title>
           <link>/entries/UTP.html</link>
           <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/UTP.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Inversions of a List</title>
           <link>/entries/List_Inversions.html</link>
           <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
           <guid>/entries/List_Inversions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Farkas&#39; Lemma and Motzkin&#39;s Transposition Theorem</title>
           <link>/entries/Farkas.html</link>
           <pubDate>Thu, 17 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Farkas.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Algebra for Higher-Order Terms</title>
           <link>/entries/Higher_Order_Terms.html</link>
           <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Higher_Order_Terms.html</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2 – Simple Program Verification in Isabelle/HOL</title>
           <link>/entries/IMP2.html</link>
           <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/IMP2.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Reduction Theorem for Store Buffers</title>
           <link>/entries/Store_Buffer_Reduction.html</link>
           <pubDate>Mon, 07 Jan 2019 00:00:00 +0000</pubDate>
           <guid>/entries/Store_Buffer_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of the Document Object Model</title>
           <link>/entries/Core_DOM.html</link>
           <pubDate>Wed, 26 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Core_DOM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Concurrent Revisions</title>
           <link>/entries/Concurrent_Revisions.html</link>
           <pubDate>Tue, 25 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Concurrent_Revisions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verifying Imperative Programs using Auto2</title>
           <link>/entries/Auto2_Imperative_HOL.html</link>
           <pubDate>Fri, 21 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Auto2_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive Cryptography in HOL</title>
           <link>/entries/Constructive_Cryptography.html</link>
           <pubDate>Mon, 17 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Constructive_Cryptography.html</guid>
           <description></description>
         </item>
         <item>
           <title>Properties of Orderings and Lattices</title>
           <link>/entries/Order_Lattice_Props.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Order_Lattice_Props.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales</title>
           <link>/entries/Quantales.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Quantales.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transformer Semantics</title>
           <link>/entries/Transformer_Semantics.html</link>
           <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Transformer_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
           <link>/entries/Functional_Ordered_Resolution_Prover.html</link>
           <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Functional_Ordered_Resolution_Prover.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Saturation</title>
           <link>/entries/Graph_Saturation.html</link>
           <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Graph_Saturation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Auto2 Prover</title>
           <link>/entries/Auto2_HOL.html</link>
           <pubDate>Tue, 20 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Auto2_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matroids</title>
           <link>/entries/Matroids.html</link>
           <pubDate>Fri, 16 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Matroids.html</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving generic class instances for datatypes</title>
           <link>/entries/Generic_Deriving.html</link>
           <pubDate>Tue, 06 Nov 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Generic_Deriving.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation and Evaluation of Alan Gewirth&#39;s Proof for the Principle of Generic Consistency in Isabelle/HOL</title>
           <link>/entries/GewirthPGCProof.html</link>
           <pubDate>Tue, 30 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/GewirthPGCProof.html</guid>
           <description></description>
         </item>
         <item>
           <title>Epistemic Logic: Completeness of Modal Logics</title>
           <link>/entries/Epistemic_Logic.html</link>
           <pubDate>Mon, 29 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Epistemic_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Smooth Manifolds</title>
           <link>/entries/Smooth_Manifolds.html</link>
           <pubDate>Mon, 22 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Smooth_Manifolds.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_EPO.html</link>
           <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_EPO.html</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised Binary Search Trees</title>
           <link>/entries/Randomised_BSTs.html</link>
           <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Randomised_BSTs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Upper Bounding Diameters of State Spaces of Factored Transition Systems</title>
           <link>/entries/Factored_Transition_System_Bounding.html</link>
           <pubDate>Fri, 12 Oct 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Factored_Transition_System_Bounding.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of π</title>
           <link>/entries/Pi_Transcendental.html</link>
           <pubDate>Fri, 28 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Pi_Transcendental.html</guid>
           <description></description>
         </item>
         <item>
           <title>Symmetric Polynomials</title>
           <link>/entries/Symmetric_Polynomials.html</link>
           <pubDate>Tue, 25 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Symmetric_Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>Signature-Based Gröbner Basis Algorithms</title>
           <link>/entries/Signature_Groebner.html</link>
           <pubDate>Thu, 20 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Signature_Groebner.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Prime Number Theorem</title>
           <link>/entries/Prime_Number_Theorem.html</link>
           <pubDate>Wed, 19 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Number_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Aggregation Algebras</title>
           <link>/entries/Aggregation_Algebras.html</link>
           <pubDate>Sat, 15 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Aggregation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Octonions</title>
           <link>/entries/Octonions.html</link>
           <pubDate>Fri, 14 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Octonions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quaternions</title>
           <link>/entries/Quaternions.html</link>
           <pubDate>Wed, 05 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Quaternions.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Budan–Fourier Theorem and Counting Real Roots with Multiplicity</title>
           <link>/entries/Budan_Fourier.html</link>
           <pubDate>Sun, 02 Sep 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Budan_Fourier.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Incremental Simplex Algorithm with Unsatisfiable Core Generation</title>
           <link>/entries/Simplex.html</link>
           <pubDate>Fri, 24 Aug 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Simplex.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minsky Machines</title>
           <link>/entries/Minsky_Machines.html</link>
           <pubDate>Tue, 14 Aug 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Minsky_Machines.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pricing in discrete financial models</title>
           <link>/entries/DiscretePricing.html</link>
           <pubDate>Mon, 16 Jul 2018 00:00:00 +0000</pubDate>
           <guid>/entries/DiscretePricing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Von-Neumann-Morgenstern Utility Theorem</title>
           <link>/entries/Neumann_Morgenstern_Utility.html</link>
           <pubDate>Wed, 04 Jul 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Neumann_Morgenstern_Utility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pell&#39;s Equation</title>
           <link>/entries/Pell.html</link>
           <pubDate>Sat, 23 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Pell.html</guid>
           <description></description>
         </item>
         <item>
           <title>Projective Geometry</title>
           <link>/entries/Projective_Geometry.html</link>
           <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Projective_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Localization of a Commutative Ring</title>
           <link>/entries/Localization_Ring.html</link>
           <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Localization_Ring.html</guid>
           <description></description>
         </item>
         <item>
           <title>Partial Order Reduction</title>
           <link>/entries/Partial_Order_Reduction.html</link>
           <pubDate>Tue, 05 Jun 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Partial_Order_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>Optimal Binary Search Trees</title>
           <link>/entries/Optimal_BST.html</link>
           <pubDate>Sun, 27 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Optimal_BST.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hidden Markov Models</title>
           <link>/entries/Hidden_Markov_Models.html</link>
           <pubDate>Fri, 25 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Hidden_Markov_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Timed Automata</title>
           <link>/entries/Probabilistic_Timed_Automata.html</link>
           <pubDate>Thu, 24 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Timed_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Axiom Systems for Category Theory in Free Logic</title>
           <link>/entries/AxiomaticCategoryTheory.html</link>
           <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/AxiomaticCategoryTheory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational Rapidly Convergent Series</title>
           <link>/entries/Irrationality_J_Hancl.html</link>
           <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Irrationality_J_Hancl.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monadification, Memoization and Dynamic Programming</title>
           <link>/entries/Monad_Memo_DP.html</link>
           <pubDate>Tue, 22 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Monad_Memo_DP.html</guid>
           <description></description>
         </item>
         <item>
           <title>OpSets: Sequential Specifications for Replicated Datatypes</title>
           <link>/entries/OpSets.html</link>
           <pubDate>Thu, 10 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/OpSets.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties</title>
           <link>/entries/Modular_Assembly_Kit_Security.html</link>
           <pubDate>Mon, 07 May 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Modular_Assembly_Kit_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>WebAssembly</title>
           <link>/entries/WebAssembly.html</link>
           <pubDate>Sun, 29 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/WebAssembly.html</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis 2018 - Polished Isabelle Solutions</title>
           <link>/entries/VerifyThis2018.html</link>
           <pubDate>Fri, 27 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/VerifyThis2018.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded Natural Functors with Covariance and Contravariance</title>
           <link>/entries/BNF_CC.html</link>
           <pubDate>Tue, 24 Apr 2018 00:00:00 +0000</pubDate>
           <guid>/entries/BNF_CC.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency</title>
           <link>/entries/Fishburn_Impossibility.html</link>
           <pubDate>Thu, 22 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Fishburn_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Weight-Balanced Trees</title>
           <link>/entries/Weight_Balanced_Trees.html</link>
           <pubDate>Tue, 13 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Weight_Balanced_Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML</title>
           <link>/entries/CakeML.html</link>
           <pubDate>Mon, 12 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/CakeML.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Theory of Architectural Design Patterns</title>
           <link>/entries/Architectural_Design_Patterns.html</link>
           <pubDate>Thu, 01 Mar 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Architectural_Design_Patterns.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hoare Logics for Time Bounds</title>
           <link>/entries/Hoare_Time.html</link>
           <pubDate>Mon, 26 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Hoare_Time.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified factorization algorithm for integer polynomials with polynomial complexity</title>
           <link>/entries/LLL_Factorization.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/LLL_Factorization.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Terms</title>
           <link>/entries/First_Order_Terms.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/First_Order_Terms.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Error Function</title>
           <link>/entries/Error_Function.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Error_Function.html</guid>
           <description></description>
         </item>
         <item>
           <title>Treaps</title>
           <link>/entries/Treaps.html</link>
           <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Treaps.html</guid>
           <description></description>
         </item>
         <item>
           <title>A verified LLL algorithm</title>
           <link>/entries/LLL_Basis_Reduction.html</link>
           <pubDate>Fri, 02 Feb 2018 00:00:00 +0000</pubDate>
           <guid>/entries/LLL_Basis_Reduction.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
           <link>/entries/Ordered_Resolution_Prover.html</link>
           <pubDate>Thu, 18 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Ordered_Resolution_Prover.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gromov Hyperbolicity</title>
           <link>/entries/Gromov_Hyperbolicity.html</link>
           <pubDate>Tue, 16 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Gromov_Hyperbolicity.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Isabelle/HOL formalisation of Green&#39;s Theorem</title>
           <link>/entries/Green.html</link>
           <pubDate>Thu, 11 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Green.html</guid>
           <description></description>
         </item>
         <item>
           <title>Taylor Models</title>
           <link>/entries/Taylor_Models.html</link>
           <pubDate>Mon, 08 Jan 2018 00:00:00 +0000</pubDate>
           <guid>/entries/Taylor_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Falling Factorial of a Sum</title>
           <link>/entries/Falling_Factorial_Sum.html</link>
           <pubDate>Fri, 22 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Falling_Factorial_Sum.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet L-Functions and Dirichlet&#39;s Theorem</title>
           <link>/entries/Dirichlet_L.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dirichlet_L.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Mason–Stothers Theorem</title>
           <link>/entries/Mason_Stothers.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Mason_Stothers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Median-of-Medians Selection Algorithm</title>
           <link>/entries/Median_Of_Medians_Selection.html</link>
           <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Median_Of_Medians_Selection.html</guid>
           <description></description>
         </item>
         <item>
           <title>Operations on Bounded Natural Functors</title>
           <link>/entries/BNF_Operations.html</link>
           <pubDate>Tue, 19 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/BNF_Operations.html</guid>
           <description></description>
         </item>
         <item>
           <title>The string search algorithm by Knuth, Morris and Pratt</title>
           <link>/entries/Knuth_Morris_Pratt.html</link>
           <pubDate>Mon, 18 Dec 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Knuth_Morris_Pratt.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stochastic Matrices and the Perron-Frobenius Theorem</title>
           <link>/entries/Stochastic_Matrices.html</link>
           <pubDate>Wed, 22 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stochastic_Matrices.html</guid>
           <description></description>
         </item>
         <item>
           <title>The IMAP CmRDT</title>
           <link>/entries/IMAP-CRDT.html</link>
           <pubDate>Thu, 09 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/IMAP-CRDT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid Multi-Lane Spatial Logic</title>
           <link>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</link>
           <pubDate>Mon, 06 Nov 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Kuratowski Closure-Complement Theorem</title>
           <link>/entries/Kuratowski_Closure_Complement.html</link>
           <pubDate>Thu, 26 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Kuratowski_Closure_Complement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Büchi Complementation</title>
           <link>/entries/Buchi_Complementation.html</link>
           <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Buchi_Complementation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transition Systems and Automata</title>
           <link>/entries/Transition_Systems_and_Automata.html</link>
           <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Transition_Systems_and_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Count the Number of Complex Roots</title>
           <link>/entries/Count_Complex_Roots.html</link>
           <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Count_Complex_Roots.html</guid>
           <description></description>
         </item>
         <item>
           <title>Evaluate Winding Numbers through Cauchy Indices</title>
           <link>/entries/Winding_Number_Eval.html</link>
           <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Winding_Number_Eval.html</guid>
           <description></description>
         </item>
         <item>
           <title>Homogeneous Linear Diophantine Equations</title>
           <link>/entries/Diophantine_Eqns_Lin_Hom.html</link>
           <pubDate>Sat, 14 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Diophantine_Eqns_Lin_Hom.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet Series</title>
           <link>/entries/Dirichlet_Series.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dirichlet_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Recurrences</title>
           <link>/entries/Linear_Recurrences.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Linear_Recurrences.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hurwitz and Riemann ζ Functions</title>
           <link>/entries/Zeta_Function.html</link>
           <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Zeta_Function.html</guid>
           <description></description>
         </item>
         <item>
           <title>Computer-assisted Reconstruction and Assessment of E. J. Lowe&#39;s Modal Ontological Argument</title>
           <link>/entries/Lowe_Ontological_Argument.html</link>
           <pubDate>Thu, 21 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Lowe_Ontological_Argument.html</guid>
           <description></description>
         </item>
         <item>
           <title>Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL</title>
           <link>/entries/PLM.html</link>
           <pubDate>Sun, 17 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/PLM.html</guid>
           <description></description>
         </item>
         <item>
           <title>Anselm&#39;s God in Isabelle/HOL</title>
           <link>/entries/AnselmGod.html</link>
           <pubDate>Wed, 06 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/AnselmGod.html</guid>
           <description></description>
         </item>
         <item>
           <title>Microeconomics and the First Welfare Theorem</title>
           <link>/entries/First_Welfare_Theorem.html</link>
           <pubDate>Fri, 01 Sep 2017 00:00:00 +0000</pubDate>
           <guid>/entries/First_Welfare_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Orbit-Stabiliser Theorem with Application to Rotational Symmetries</title>
           <link>/entries/Orbit_Stabiliser.html</link>
           <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Orbit_Stabiliser.html</guid>
           <description></description>
         </item>
         <item>
           <title>Root-Balanced Tree</title>
           <link>/entries/Root_Balanced_Tree.html</link>
           <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Root_Balanced_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>The LambdaMu-calculus</title>
           <link>/entries/LambdaMu.html</link>
           <pubDate>Wed, 16 Aug 2017 00:00:00 +0000</pubDate>
           <guid>/entries/LambdaMu.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stewart&#39;s Theorem and Apollonius&#39; Theorem</title>
           <link>/entries/Stewart_Apollonius.html</link>
           <pubDate>Mon, 31 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stewart_Apollonius.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dynamic Architectures</title>
           <link>/entries/DynamicArchitectures.html</link>
           <pubDate>Fri, 28 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/DynamicArchitectures.html</guid>
           <description></description>
         </item>
         <item>
           <title>Declarative Semantics for Functional Languages</title>
           <link>/entries/Decl_Sem_Fun_PL.html</link>
           <pubDate>Fri, 21 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Decl_Sem_Fun_PL.html</guid>
           <description></description>
         </item>
         <item>
           <title>HOLCF-Prelude</title>
           <link>/entries/HOLCF-Prelude.html</link>
           <pubDate>Sat, 15 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/HOLCF-Prelude.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minkowski&#39;s Theorem</title>
           <link>/entries/Minkowskis_Theorem.html</link>
           <pubDate>Thu, 13 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Minkowskis_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus</title>
           <link>/entries/Name_Carrying_Type_Inference.html</link>
           <pubDate>Sun, 09 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Name_Carrying_Type_Inference.html</guid>
           <description></description>
         </item>
         <item>
           <title>A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes</title>
           <link>/entries/CRDT.html</link>
           <pubDate>Fri, 07 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/CRDT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone-Kleene Relation Algebras</title>
           <link>/entries/Stone_Kleene_Relation_Algebras.html</link>
           <pubDate>Thu, 06 Jul 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Kleene_Relation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional Proof Systems</title>
           <link>/entries/Propositional_Proof_Systems.html</link>
           <pubDate>Wed, 21 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Propositional_Proof_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Partial Semigroups and Convolution Algebras</title>
           <link>/entries/PSemigroupsConvolution.html</link>
           <pubDate>Tue, 13 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/PSemigroupsConvolution.html</guid>
           <description></description>
         </item>
         <item>
           <title>Buffon&#39;s Needle Problem</title>
           <link>/entries/Buffons_Needle.html</link>
           <pubDate>Tue, 06 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Buffons_Needle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Flow Networks and the Min-Cut-Max-Flow Theorem</title>
           <link>/entries/Flow_Networks.html</link>
           <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Flow_Networks.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Push-Relabel Algorithms</title>
           <link>/entries/Prpu_Maxflow.html</link>
           <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Prpu_Maxflow.html</guid>
           <description></description>
         </item>
         <item>
           <title>Optics</title>
           <link>/entries/Optics.html</link>
           <pubDate>Thu, 25 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Optics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Developing Security Protocols by Refinement</title>
           <link>/entries/Security_Protocol_Refinement.html</link>
           <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Security_Protocol_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dictionary Construction</title>
           <link>/entries/Dict_Construction.html</link>
           <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Dict_Construction.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Floyd-Warshall Algorithm for Shortest Paths</title>
           <link>/entries/Floyd_Warshall.html</link>
           <pubDate>Mon, 08 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Floyd_Warshall.html</guid>
           <description></description>
         </item>
         <item>
           <title>CryptHOL</title>
           <link>/entries/CryptHOL.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/CryptHOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Effect polymorphism in higher-order logic</title>
           <link>/entries/Monomorphic_Monad.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Monomorphic_Monad.html</guid>
           <description></description>
         </item>
         <item>
           <title>Game-based cryptography in HOL</title>
           <link>/entries/Game_Based_Crypto.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Game_Based_Crypto.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monad normalisation</title>
           <link>/entries/Monad_Normalisation.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Monad_Normalisation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic while loop</title>
           <link>/entries/Probabilistic_While.html</link>
           <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_While.html</guid>
           <description></description>
         </item>
         <item>
           <title>Monoidal Categories</title>
           <link>/entries/MonoidalCategory.html</link>
           <pubDate>Thu, 04 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/MonoidalCategory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Types, Tableaus and Gödel’s God in Isabelle/HOL</title>
           <link>/entries/Types_Tableaus_and_Goedels_God.html</link>
           <pubDate>Mon, 01 May 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Types_Tableaus_and_Goedels_God.html</guid>
           <description></description>
         </item>
         <item>
           <title>Local Lexing</title>
           <link>/entries/LocalLexing.html</link>
           <pubDate>Fri, 28 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/LocalLexing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Constructor Functions</title>
           <link>/entries/Constructor_Funs.html</link>
           <pubDate>Wed, 19 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Constructor_Funs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lazifying case constants</title>
           <link>/entries/Lazy_Case.html</link>
           <pubDate>Tue, 18 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Lazy_Case.html</guid>
           <description></description>
         </item>
         <item>
           <title>Subresultants</title>
           <link>/entries/Subresultants.html</link>
           <pubDate>Thu, 06 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Subresultants.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expected Shape of Random Binary Search Trees</title>
           <link>/entries/Random_BSTs.html</link>
           <pubDate>Tue, 04 Apr 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Random_BSTs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lower bound on comparison-based sorting algorithms</title>
           <link>/entries/Comparison_Sort_Lower_Bound.html</link>
           <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Comparison_Sort_Lower_Bound.html</guid>
           <description></description>
         </item>
         <item>
           <title>The number of comparisons in QuickSort</title>
           <link>/entries/Quick_Sort_Cost.html</link>
           <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Quick_Sort_Cost.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Euler–MacLaurin Formula</title>
           <link>/entries/Euler_MacLaurin.html</link>
           <pubDate>Fri, 10 Mar 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Euler_MacLaurin.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Group Law for Elliptic Curves</title>
           <link>/entries/Elliptic_Curves_Group_Law.html</link>
           <pubDate>Tue, 28 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Elliptic_Curves_Group_Law.html</guid>
           <description></description>
         </item>
         <item>
           <title>Menger&#39;s Theorem</title>
           <link>/entries/Menger.html</link>
           <pubDate>Sun, 26 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Menger.html</guid>
           <description></description>
         </item>
         <item>
           <title>Differential Dynamic Logic</title>
           <link>/entries/Differential_Dynamic_Logic.html</link>
           <pubDate>Mon, 13 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Differential_Dynamic_Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Soundness</title>
           <link>/entries/Abstract_Soundness.html</link>
           <pubDate>Fri, 10 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract_Soundness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone Relation Algebras</title>
           <link>/entries/Stone_Relation_Algebras.html</link>
           <pubDate>Tue, 07 Feb 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Relation_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Refining Authenticated Key Agreement with Strong Adversaries</title>
           <link>/entries/Key_Agreement_Strong_Adversaries.html</link>
           <pubDate>Tue, 31 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Key_Agreement_Strong_Adversaries.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bernoulli Numbers</title>
           <link>/entries/Bernoulli.html</link>
           <pubDate>Tue, 24 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Bernoulli.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bertrand&#39;s postulate</title>
           <link>/entries/Bertrands_Postulate.html</link>
           <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Bertrands_Postulate.html</guid>
           <description></description>
         </item>
         <item>
           <title>Minimal Static Single Assignment Form</title>
           <link>/entries/Minimal_SSA.html</link>
           <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Minimal_SSA.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Transcendence of e</title>
           <link>/entries/E_Transcendental.html</link>
           <pubDate>Thu, 12 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/E_Transcendental.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Network Models and Their Application to Firewall Policies</title>
           <link>/entries/UPF_Firewall.html</link>
           <pubDate>Sun, 08 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/UPF_Firewall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of a Diffie-Hellman Password-based Authentication Protocol by Extending the Inductive Method</title>
           <link>/entries/Password_Authentication_Protocol.html</link>
           <pubDate>Tue, 03 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/Password_Authentication_Protocol.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Logic According to Harrison</title>
           <link>/entries/FOL_Harrison.html</link>
           <pubDate>Sun, 01 Jan 2017 00:00:00 +0000</pubDate>
           <guid>/entries/FOL_Harrison.html</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent Refinement Algebra and Rely Quotients</title>
           <link>/entries/Concurrent_Ref_Alg.html</link>
           <pubDate>Fri, 30 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Concurrent_Ref_Alg.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Twelvefold Way</title>
           <link>/entries/Twelvefold_Way.html</link>
           <pubDate>Thu, 29 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Twelvefold_Way.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proof Strategy Language</title>
           <link>/entries/Proof_Strategy_Language.html</link>
           <pubDate>Tue, 20 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Proof_Strategy_Language.html</guid>
           <description></description>
         </item>
         <item>
           <title>Paraconsistency</title>
           <link>/entries/Paraconsistency.html</link>
           <pubDate>Wed, 07 Dec 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Paraconsistency.html</guid>
           <description></description>
         </item>
         <item>
           <title>COMPLX: A Verification Framework for Concurrent Imperative Programs</title>
           <link>/entries/Complx.html</link>
           <pubDate>Tue, 29 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Complx.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Interpretation of Annotated Commands</title>
           <link>/entries/Abs_Int_ITP2012.html</link>
           <pubDate>Wed, 23 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Abs_Int_ITP2012.html</guid>
           <description></description>
         </item>
         <item>
           <title>Separata: Isabelle tactics for Separation Algebra</title>
           <link>/entries/Separata.html</link>
           <pubDate>Wed, 16 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Separata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_KBOs.html</link>
           <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_KBOs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</title>
           <link>/entries/Nested_Multisets_Ordinals.html</link>
           <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Nested_Multisets_Ordinals.html</guid>
           <description></description>
         </item>
         <item>
           <title>Expressiveness of Deep Learning</title>
           <link>/entries/Deep_Learning.html</link>
           <pubDate>Thu, 10 Nov 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Deep_Learning.html</guid>
           <description></description>
         </item>
         <item>
           <title>Modal Logics for Nominal Transition Systems</title>
           <link>/entries/Modal_Logics_for_NTS.html</link>
           <pubDate>Tue, 25 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Modal_Logics_for_NTS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stable Matching</title>
           <link>/entries/Stable_Matching.html</link>
           <pubDate>Mon, 24 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stable_Matching.html</guid>
           <description></description>
         </item>
         <item>
           <title>LOFT — Verified Migration of Linux Firewalls to SDN</title>
           <link>/entries/LOFT.html</link>
           <pubDate>Fri, 21 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/LOFT.html</guid>
           <description></description>
         </item>
         <item>
           <title>A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor</title>
           <link>/entries/SPARCv8.html</link>
           <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SPARCv8.html</guid>
           <description></description>
         </item>
         <item>
           <title>Source Coding Theorem</title>
           <link>/entries/Source_Coding_Theorem.html</link>
           <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Source_Coding_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Factorization Algorithm of Berlekamp and Zassenhaus</title>
           <link>/entries/Berlekamp_Zassenhaus.html</link>
           <pubDate>Fri, 14 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Berlekamp_Zassenhaus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Intersecting Chords Theorem</title>
           <link>/entries/Chord_Segments.html</link>
           <pubDate>Tue, 11 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Chord_Segments.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lp spaces</title>
           <link>/entries/Lp.html</link>
           <pubDate>Wed, 05 Oct 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lp.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher–Yates shuffle</title>
           <link>/entries/Fisher_Yates.html</link>
           <pubDate>Fri, 30 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Fisher_Yates.html</guid>
           <description></description>
         </item>
         <item>
           <title>Allen&#39;s Interval Calculus</title>
           <link>/entries/Allen_Calculus.html</link>
           <pubDate>Thu, 29 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Allen_Calculus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</title>
           <link>/entries/Lambda_Free_RPOs.html</link>
           <pubDate>Fri, 23 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Lambda_Free_RPOs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables Semantics</title>
           <link>/entries/Iptables_Semantics.html</link>
           <pubDate>Fri, 09 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Iptables_Semantics.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Variant of the Superposition Calculus</title>
           <link>/entries/SuperCalc.html</link>
           <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SuperCalc.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stone Algebras</title>
           <link>/entries/Stone_Algebras.html</link>
           <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stone_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stirling&#39;s formula</title>
           <link>/entries/Stirling_Formula.html</link>
           <pubDate>Thu, 01 Sep 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Stirling_Formula.html</guid>
           <description></description>
         </item>
         <item>
           <title>Routing</title>
           <link>/entries/Routing.html</link>
           <pubDate>Wed, 31 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Routing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Simple Firewall</title>
           <link>/entries/Simple_Firewall.html</link>
           <pubDate>Wed, 24 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Simple_Firewall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths</title>
           <link>/entries/InfPathElimination.html</link>
           <pubDate>Thu, 18 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/InfPathElimination.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing the Edmonds-Karp Algorithm</title>
           <link>/entries/EdmondsKarp_Maxflow.html</link>
           <pubDate>Fri, 12 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/EdmondsKarp_Maxflow.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Imperative Refinement Framework</title>
           <link>/entries/Refine_Imperative_HOL.html</link>
           <pubDate>Mon, 08 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Refine_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ptolemy&#39;s Theorem</title>
           <link>/entries/Ptolemys_Theorem.html</link>
           <pubDate>Sun, 07 Aug 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Ptolemys_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Surprise Paradox</title>
           <link>/entries/Surprise_Paradox.html</link>
           <pubDate>Sun, 17 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Surprise_Paradox.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pairing Heap</title>
           <link>/entries/Pairing_Heap.html</link>
           <pubDate>Thu, 14 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Pairing_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Framework for Verifying Depth-First Search Algorithms</title>
           <link>/entries/DFS_Framework.html</link>
           <pubDate>Tue, 05 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/DFS_Framework.html</guid>
           <description></description>
         </item>
         <item>
           <title>Chamber Complexes, Coxeter Systems, and Buildings</title>
           <link>/entries/Buildings.html</link>
           <pubDate>Fri, 01 Jul 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Buildings.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Resolution Calculus for First-Order Logic</title>
           <link>/entries/Resolution_FOL.html</link>
           <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Resolution_FOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Z Property</title>
           <link>/entries/Rewriting_Z.html</link>
           <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Rewriting_Z.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional Security-Preserving Refinement for Concurrent Imperative Programs</title>
           <link>/entries/Dependent_SIFUM_Refinement.html</link>
           <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Dependent_SIFUM_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>IP Addresses</title>
           <link>/entries/IP_Addresses.html</link>
           <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/IP_Addresses.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Multisets</title>
           <link>/entries/Card_Multisets.html</link>
           <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Multisets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory with Adjunctions and Limits</title>
           <link>/entries/Category3.html</link>
           <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Category3.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Dependent Security Type System for Concurrent Imperative Programs</title>
           <link>/entries/Dependent_SIFUM_Type_Systems.html</link>
           <pubDate>Sat, 25 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Dependent_SIFUM_Type_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>Catalan Numbers</title>
           <link>/entries/Catalan_Numbers.html</link>
           <pubDate>Tue, 21 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Catalan_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Program Construction and Verification Components Based on Kleene Algebra</title>
           <link>/entries/Algebraic_VCs.html</link>
           <pubDate>Sat, 18 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Algebraic_VCs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conservation of CSP Noninterference Security under Concurrent Composition</title>
           <link>/entries/Noninterference_Concurrent_Composition.html</link>
           <pubDate>Mon, 13 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Concurrent_Composition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Machine Word Library</title>
           <link>/entries/Word_Lib.html</link>
           <pubDate>Thu, 09 Jun 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Word_Lib.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Decomposition</title>
           <link>/entries/Tree_Decomposition.html</link>
           <pubDate>Tue, 31 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Tree_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Equivalence Relations</title>
           <link>/entries/Card_Equiv_Relations.html</link>
           <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Equiv_Relations.html</guid>
           <description></description>
         </item>
         <item>
           <title>POSIX Lexing with Derivatives of Regular Expressions</title>
           <link>/entries/Posix-Lexing.html</link>
           <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Posix-Lexing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Perron-Frobenius Theorem for Spectral Radius Analysis</title>
           <link>/entries/Perron_Frobenius.html</link>
           <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Perron_Frobenius.html</guid>
           <description></description>
         </item>
         <item>
           <title>The meta theory of the Incredible Proof Machine</title>
           <link>/entries/Incredible_Proof_Machine.html</link>
           <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Incredible_Proof_Machine.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Constructive Proof for FLP</title>
           <link>/entries/FLP.html</link>
           <pubDate>Wed, 18 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/FLP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</title>
           <link>/entries/MFMC_Countable.html</link>
           <pubDate>Mon, 09 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/MFMC_Countable.html</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised Social Choice Theory</title>
           <link>/entries/Randomised_Social_Choice.html</link>
           <pubDate>Thu, 05 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Randomised_Social_Choice.html</guid>
           <description></description>
         </item>
         <item>
           <title>Spivey&#39;s Generalized Recurrence for Bell Numbers</title>
           <link>/entries/Bell_Numbers_Spivey.html</link>
           <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Bell_Numbers_Spivey.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Incompatibility of SD-Efficiency and SD-Strategy-Proofness</title>
           <link>/entries/SDS_Impossibility.html</link>
           <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/SDS_Impossibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gröbner Bases Theory</title>
           <link>/entries/Groebner_Bases.html</link>
           <pubDate>Mon, 02 May 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Groebner_Bases.html</guid>
           <description></description>
         </item>
         <item>
           <title>No Faster-Than-Light Observers</title>
           <link>/entries/No_FTL_observers.html</link>
           <pubDate>Thu, 28 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/No_FTL_observers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A formalisation of the Cocke-Younger-Kasami algorithm</title>
           <link>/entries/CYK.html</link>
           <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/CYK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algorithms for Reduced Ordered Binary Decision Diagrams</title>
           <link>/entries/ROBDD.html</link>
           <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/ROBDD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Conservation of CSP Noninterference Security under Sequential Composition</title>
           <link>/entries/Noninterference_Sequential_Composition.html</link>
           <pubDate>Tue, 26 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Sequential_Composition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebras with Domain</title>
           <link>/entries/KAD.html</link>
           <pubDate>Tue, 12 Apr 2016 00:00:00 +0000</pubDate>
           <guid>/entries/KAD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional Resolution and Prime Implicates Generation</title>
           <link>/entries/PropResPI.html</link>
           <pubDate>Fri, 11 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/PropResPI.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cartan Fixed Point Theorems</title>
           <link>/entries/Cartan_FP.html</link>
           <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Cartan_FP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Timed Automata</title>
           <link>/entries/Timed_Automata.html</link>
           <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Timed_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Linear Temporal Logic</title>
           <link>/entries/LTL.html</link>
           <pubDate>Tue, 01 Mar 2016 00:00:00 +0000</pubDate>
           <guid>/entries/LTL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Analysis of List Update Algorithms</title>
           <link>/entries/List_Update.html</link>
           <pubDate>Wed, 17 Feb 2016 00:00:00 +0000</pubDate>
           <guid>/entries/List_Update.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Construction of Static Single Assignment Form</title>
           <link>/entries/Formal_SSA.html</link>
           <pubDate>Fri, 05 Feb 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Formal_SSA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial Factorization</title>
           <link>/entries/Polynomial_Factorization.html</link>
           <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomial_Factorization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial Interpolation</title>
           <link>/entries/Polynomial_Interpolation.html</link>
           <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomial_Interpolation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knot Theory</title>
           <link>/entries/Knot_Theory.html</link>
           <pubDate>Wed, 20 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Knot_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tensor Product of Matrices</title>
           <link>/entries/Matrix_Tensor.html</link>
           <pubDate>Mon, 18 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Matrix_Tensor.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Number Partitions</title>
           <link>/entries/Card_Number_Partitions.html</link>
           <pubDate>Thu, 14 Jan 2016 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Number_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Basic Geometric Properties of Triangles</title>
           <link>/entries/Triangle.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Triangle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Descartes&#39; Rule of Signs</title>
           <link>/entries/Descartes_Sign_Rule.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Descartes_Sign_Rule.html</guid>
           <description></description>
         </item>
         <item>
           <title>Liouville numbers</title>
           <link>/entries/Liouville_Numbers.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Liouville_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Divergence of the Prime Harmonic Series</title>
           <link>/entries/Prime_Harmonic_Series.html</link>
           <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Prime_Harmonic_Series.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebraic Numbers in Isabelle/HOL</title>
           <link>/entries/Algebraic_Numbers.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Algebraic_Numbers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Applicative Lifting</title>
           <link>/entries/Applicative_Lifting.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Applicative_Lifting.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Stern-Brocot Tree</title>
           <link>/entries/Stern_Brocot.html</link>
           <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Stern_Brocot.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality of Set Partitions</title>
           <link>/entries/Card_Partitions.html</link>
           <pubDate>Sat, 12 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Card_Partitions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Latin Square</title>
           <link>/entries/Latin_Square.html</link>
           <pubDate>Wed, 02 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Latin_Square.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ergodic Theory</title>
           <link>/entries/Ergodic_Theory.html</link>
           <pubDate>Tue, 01 Dec 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Ergodic_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Euler&#39;s Partition Theorem</title>
           <link>/entries/Euler_Partition.html</link>
           <pubDate>Thu, 19 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Euler_Partition.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Tortoise and Hare Algorithm</title>
           <link>/entries/TortoiseHare.html</link>
           <pubDate>Wed, 18 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/TortoiseHare.html</guid>
           <description></description>
         </item>
         <item>
           <title>Planarity Certificates</title>
           <link>/entries/Planarity_Certificates.html</link>
           <pubDate>Wed, 11 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Planarity_Certificates.html</guid>
           <description></description>
         </item>
         <item>
           <title>Positional Determinacy of Parity Games</title>
           <link>/entries/Parity_Game.html</link>
           <pubDate>Mon, 02 Nov 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Parity_Game.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Meta-Model for the Isabelle API</title>
           <link>/entries/Isabelle_Meta_Model.html</link>
           <pubDate>Wed, 16 Sep 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Isabelle_Meta_Model.html</guid>
           <description></description>
         </item>
         <item>
           <title>Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</title>
           <link>/entries/LTL_to_DRA.html</link>
           <pubDate>Fri, 04 Sep 2015 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_to_DRA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices, Jordan Normal Forms, and Spectral Radius Theory</title>
           <link>/entries/Jordan_Normal_Form.html</link>
           <pubDate>Fri, 21 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Jordan_Normal_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing Diagrams II</title>
           <link>/entries/Decreasing-Diagrams-II.html</link>
           <pubDate>Thu, 20 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Decreasing-Diagrams-II.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Inductive Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Inductive_Unwinding.html</link>
           <pubDate>Tue, 18 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Inductive_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>Representations of Finite Groups</title>
           <link>/entries/Rep_Fin_Groups.html</link>
           <pubDate>Wed, 12 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Rep_Fin_Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Analysing and Comparing Encodability Criteria for Process Calculi</title>
           <link>/entries/Encodability_Process_Calculi.html</link>
           <pubDate>Mon, 10 Aug 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Encodability_Process_Calculi.html</guid>
           <description></description>
         </item>
         <item>
           <title>Generating Cases from Labeled Subgoals</title>
           <link>/entries/Case_Labeling.html</link>
           <pubDate>Tue, 21 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Case_Labeling.html</guid>
           <description></description>
         </item>
         <item>
           <title>Landau Symbols</title>
           <link>/entries/Landau_Symbols.html</link>
           <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Landau_Symbols.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Akra-Bazzi theorem and the Master theorem</title>
           <link>/entries/Akra_Bazzi.html</link>
           <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Akra_Bazzi.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite Normal Form</title>
           <link>/entries/Hermite.html</link>
           <pubDate>Tue, 07 Jul 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Hermite.html</guid>
           <description></description>
         </item>
         <item>
           <title>Derangements Formula</title>
           <link>/entries/Derangements.html</link>
           <pubDate>Sat, 27 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Derangements.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary Multirelations</title>
           <link>/entries/Multirelations.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Multirelations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Reasoning about Lists via List Interleaving</title>
           <link>/entries/List_Interleaving.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/List_Interleaving.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Generic Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Generic_Unwinding.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Generic_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Ipurge Unwinding Theorem for CSP Noninterference Security</title>
           <link>/entries/Noninterference_Ipurge_Unwinding.html</link>
           <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_Ipurge_Unwinding.html</guid>
           <description></description>
         </item>
         <item>
           <title>Parameterized Dynamic Tables</title>
           <link>/entries/Dynamic_Tables.html</link>
           <pubDate>Sun, 07 Jun 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Dynamic_Tables.html</guid>
           <description></description>
         </item>
         <item>
           <title>Derivatives of Logical Formulas</title>
           <link>/entries/Formula_Derivatives.html</link>
           <pubDate>Thu, 28 May 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Formula_Derivatives.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Zoo of Probabilistic Systems</title>
           <link>/entries/Probabilistic_System_Zoo.html</link>
           <pubDate>Wed, 27 May 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_System_Zoo.html</guid>
           <description></description>
         </item>
         <item>
           <title>VCG - Combinatorial Vickrey-Clarke-Groves Auctions</title>
           <link>/entries/Vickrey_Clarke_Groves.html</link>
           <pubDate>Thu, 30 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Vickrey_Clarke_Groves.html</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated Lattices</title>
           <link>/entries/Residuated_Lattices.html</link>
           <pubDate>Wed, 15 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Residuated_Lattices.html</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent IMP</title>
           <link>/entries/ConcurrentIMP.html</link>
           <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/ConcurrentIMP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO</title>
           <link>/entries/ConcurrentGC.html</link>
           <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
           <guid>/entries/ConcurrentGC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Trie</title>
           <link>/entries/Trie.html</link>
           <pubDate>Mon, 30 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Trie.html</guid>
           <description></description>
         </item>
         <item>
           <title>Consensus Refined</title>
           <link>/entries/Consensus_Refined.html</link>
           <pubDate>Wed, 18 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Consensus_Refined.html</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving class instances for datatypes</title>
           <link>/entries/Deriving.html</link>
           <pubDate>Wed, 11 Mar 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Deriving.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Safety of Call Arity</title>
           <link>/entries/Call_Arity.html</link>
           <pubDate>Fri, 20 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Call_Arity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Echelon Form</title>
           <link>/entries/Echelon_Form.html</link>
           <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Echelon_Form.html</guid>
           <description></description>
         </item>
         <item>
           <title>QR Decomposition</title>
           <link>/entries/QR_Decomposition.html</link>
           <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/QR_Decomposition.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finite Automata in Hereditarily Finite Set Theory</title>
           <link>/entries/Finite_Automata_HF.html</link>
           <pubDate>Thu, 05 Feb 2015 00:00:00 +0000</pubDate>
           <guid>/entries/Finite_Automata_HF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of the UpDown Scheme</title>
           <link>/entries/UpDown_Scheme.html</link>
           <pubDate>Wed, 28 Jan 2015 00:00:00 +0000</pubDate>
           <guid>/entries/UpDown_Scheme.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Unified Policy Framework (UPF)</title>
           <link>/entries/UPF.html</link>
           <pubDate>Fri, 28 Nov 2014 00:00:00 +0000</pubDate>
           <guid>/entries/UPF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Loop freedom of the (untimed) AODV routing protocol</title>
           <link>/entries/AODV.html</link>
           <pubDate>Thu, 23 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/AODV.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting Definition Option</title>
           <link>/entries/Lifting_Definition_Option.html</link>
           <pubDate>Mon, 13 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Lifting_Definition_Option.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Fusion in HOL with Code Generation</title>
           <link>/entries/Stream_Fusion_Code.html</link>
           <pubDate>Fri, 10 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Stream_Fusion_Code.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Verified Compiler for Probability Density Functions</title>
           <link>/entries/Density_Compiler.html</link>
           <pubDate>Thu, 09 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Density_Compiler.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Refinement Calculus for Reactive Systems</title>
           <link>/entries/RefinementReactive.html</link>
           <pubDate>Wed, 08 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/RefinementReactive.html</guid>
           <description></description>
         </item>
         <item>
           <title>Certification Monads</title>
           <link>/entries/Certification_Monads.html</link>
           <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Certification_Monads.html</guid>
           <description></description>
         </item>
         <item>
           <title>XML</title>
           <link>/entries/XML.html</link>
           <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
           <guid>/entries/XML.html</guid>
           <description></description>
         </item>
         <item>
           <title>Imperative Insertion Sort</title>
           <link>/entries/Imperative_Insertion_Sort.html</link>
           <pubDate>Thu, 25 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Imperative_Insertion_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Sturm–Tarski Theorem</title>
           <link>/entries/Sturm_Tarski.html</link>
           <pubDate>Fri, 19 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Sturm_Tarski.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Cayley-Hamilton Theorem</title>
           <link>/entries/Cayley_Hamilton.html</link>
           <pubDate>Mon, 15 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Cayley_Hamilton.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Jordan-Hölder Theorem</title>
           <link>/entries/Jordan_Hoelder.html</link>
           <pubDate>Tue, 09 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Jordan_Hoelder.html</guid>
           <description></description>
         </item>
         <item>
           <title>Priority Queues Based on Braun Trees</title>
           <link>/entries/Priority_Queue_Braun.html</link>
           <pubDate>Thu, 04 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Priority_Queue_Braun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan Algorithm and Its Applications</title>
           <link>/entries/Gauss_Jordan.html</link>
           <pubDate>Wed, 03 Sep 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss_Jordan.html</guid>
           <description></description>
         </item>
         <item>
           <title>Real-Valued Special Functions: Upper and Lower Bounds</title>
           <link>/entries/Special_Function_Bounds.html</link>
           <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Special_Function_Bounds.html</guid>
           <description></description>
         </item>
         <item>
           <title>Vector Spaces</title>
           <link>/entries/VectorSpace.html</link>
           <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/VectorSpace.html</guid>
           <description></description>
         </item>
         <item>
           <title>Skew Heap</title>
           <link>/entries/Skew_Heap.html</link>
           <pubDate>Wed, 13 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Skew_Heap.html</guid>
           <description></description>
         </item>
         <item>
           <title>Splay Tree</title>
           <link>/entries/Splay_Tree.html</link>
           <pubDate>Tue, 12 Aug 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Splay_Tree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Haskell&#39;s Show Class in Isabelle/HOL</title>
           <link>/entries/Show.html</link>
           <pubDate>Tue, 29 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Show.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Specification of a Generic Separation Kernel</title>
           <link>/entries/CISC-Kernel.html</link>
           <pubDate>Fri, 18 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CISC-Kernel.html</guid>
           <description></description>
         </item>
         <item>
           <title>pGCL for Isabelle</title>
           <link>/entries/pGCL.html</link>
           <pubDate>Sun, 13 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/pGCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Amortized Complexity Verified</title>
           <link>/entries/Amortized_Complexity.html</link>
           <pubDate>Mon, 07 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Amortized_Complexity.html</guid>
           <description></description>
         </item>
         <item>
           <title>Network Security Policy Verification</title>
           <link>/entries/Network_Security_Policy_Verification.html</link>
           <pubDate>Fri, 04 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Network_Security_Policy_Verification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pop-Refinement</title>
           <link>/entries/Pop_Refinement.html</link>
           <pubDate>Thu, 03 Jul 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Pop_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</title>
           <link>/entries/MSO_Regex_Equivalence.html</link>
           <pubDate>Thu, 12 Jun 2014 00:00:00 +0000</pubDate>
           <guid>/entries/MSO_Regex_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Boolean Expression Checkers</title>
           <link>/entries/Boolean_Expression_Checkers.html</link>
           <pubDate>Sun, 08 Jun 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Boolean_Expression_Checkers.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Fully Verified Executable LTL Model Checker</title>
           <link>/entries/CAVA_LTL_Modelchecker.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CAVA_LTL_Modelchecker.html</guid>
           <description></description>
         </item>
         <item>
           <title>Converting Linear-Time Temporal Logic to Generalized Büchi Automata</title>
           <link>/entries/LTL_to_GBA.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/LTL_to_GBA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Promela Formalization</title>
           <link>/entries/Promela.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Promela.html</guid>
           <description></description>
         </item>
         <item>
           <title>The CAVA Automata Library</title>
           <link>/entries/CAVA_Automata.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CAVA_Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verified Efficient Implementation of Gabow&#39;s Strongly Connected Components Algorithm</title>
           <link>/entries/Gabow_SCC.html</link>
           <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Gabow_SCC.html</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference Security in Communicating Sequential Processes</title>
           <link>/entries/Noninterference_CSP.html</link>
           <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Noninterference_CSP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive closure according to Roy-Floyd-Warshall</title>
           <link>/entries/Roy_Floyd_Warshall.html</link>
           <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Roy_Floyd_Warshall.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Algebras</title>
           <link>/entries/Regular_Algebras.html</link>
           <pubDate>Wed, 21 May 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Regular_Algebras.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalisation and Analysis of Component Dependencies</title>
           <link>/entries/ComponentDependencies.html</link>
           <pubDate>Mon, 28 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/ComponentDependencies.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Assumptions and Guarantees for Compositional Noninterference</title>
           <link>/entries/SIFUM_Type_Systems.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/SIFUM_Type_Systems.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Declassification with WHAT-and-WHERE-Security</title>
           <link>/entries/WHATandWHERE_Security.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/WHATandWHERE_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formalization of Strong Security</title>
           <link>/entries/Strong_Security.html</link>
           <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Strong_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded-Deducibility Security</title>
           <link>/entries/Bounded_Deducibility_Security.html</link>
           <pubDate>Tue, 22 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Bounded_Deducibility_Security.html</guid>
           <description></description>
         </item>
         <item>
           <title>A shallow embedding of HyperCTL*</title>
           <link>/entries/HyperCTL.html</link>
           <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/HyperCTL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Completeness</title>
           <link>/entries/Abstract_Completeness.html</link>
           <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract_Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Discrete Summation</title>
           <link>/entries/Discrete_Summation.html</link>
           <pubDate>Sun, 13 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Discrete_Summation.html</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax and semantics of a GPU kernel programming language</title>
           <link>/entries/GPU_Kernel_PL.html</link>
           <pubDate>Thu, 03 Apr 2014 00:00:00 +0000</pubDate>
           <guid>/entries/GPU_Kernel_PL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic Noninterference</title>
           <link>/entries/Probabilistic_Noninterference.html</link>
           <pubDate>Tue, 11 Mar 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Probabilistic_Noninterference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mechanization of the Algebra for Wireless Networks (AWN)</title>
           <link>/entries/AWN.html</link>
           <pubDate>Sat, 08 Mar 2014 00:00:00 +0000</pubDate>
           <guid>/entries/AWN.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mutually Recursive Partial Functions</title>
           <link>/entries/Partial_Function_MR.html</link>
           <pubDate>Tue, 18 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Partial_Function_MR.html</guid>
           <description></description>
         </item>
         <item>
           <title>Properties of Random Graphs -- Subgraph Containment</title>
           <link>/entries/Random_Graph_Subgraph_Threshold.html</link>
           <pubDate>Thu, 13 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Random_Graph_Subgraph_Threshold.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of Selection and Heap Sort Using Locales</title>
           <link>/entries/Selection_Heap_Sort.html</link>
           <pubDate>Tue, 11 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Selection_Heap_Sort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Affine Arithmetic</title>
           <link>/entries/Affine_Arithmetic.html</link>
           <pubDate>Fri, 07 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Affine_Arithmetic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Implementing field extensions of the form Q[sqrt(b)]</title>
           <link>/entries/Real_Impl.html</link>
           <pubDate>Thu, 06 Feb 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Real_Impl.html</guid>
           <description></description>
         </item>
         <item>
           <title>Unified Decision Procedures for Regular Expression Equivalence</title>
           <link>/entries/Regex_Equivalence.html</link>
           <pubDate>Thu, 30 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Regex_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Secondary Sylow Theorems</title>
           <link>/entries/Secondary_Sylow.html</link>
           <pubDate>Tue, 28 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Secondary_Sylow.html</guid>
           <description></description>
         </item>
         <item>
           <title>Relation Algebra</title>
           <link>/entries/Relation_Algebra.html</link>
           <pubDate>Sat, 25 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Relation_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebra with Tests and Demonic Refinement Algebras</title>
           <link>/entries/KAT_and_DRA.html</link>
           <pubDate>Thu, 23 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/KAT_and_DRA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5</title>
           <link>/entries/Featherweight_OCL.html</link>
           <pubDate>Thu, 16 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Featherweight_OCL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compositional Properties of Crypto-Based Components</title>
           <link>/entries/CryptoBasedCompositionalProperties.html</link>
           <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/CryptoBasedCompositionalProperties.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm&#39;s Theorem</title>
           <link>/entries/Sturm_Sequences.html</link>
           <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
           <guid>/entries/Sturm_Sequences.html</guid>
           <description></description>
         </item>
         <item>
           <title>A General Method for the Proof of Theorems on Tail-recursive Functions</title>
           <link>/entries/Tail_Recursive_Functions.html</link>
           <pubDate>Sun, 01 Dec 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Tail_Recursive_Functions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gödel&#39;s Incompleteness Theorems</title>
           <link>/entries/Incompleteness.html</link>
           <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Incompleteness.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Hereditarily Finite Sets</title>
           <link>/entries/HereditarilyFinite.html</link>
           <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/HereditarilyFinite.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Codatatype of Formal Languages</title>
           <link>/entries/Coinductive_Languages.html</link>
           <pubDate>Fri, 15 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Coinductive_Languages.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Processing Components: Isabelle/HOL Formalisation and Case Studies</title>
           <link>/entries/FocusStreamsCaseStudies.html</link>
           <pubDate>Thu, 14 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/FocusStreamsCaseStudies.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gödel&#39;s God in Isabelle/HOL</title>
           <link>/entries/GoedelGod.html</link>
           <pubDate>Tue, 12 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/GoedelGod.html</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing Diagrams</title>
           <link>/entries/Decreasing-Diagrams.html</link>
           <pubDate>Fri, 01 Nov 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Decreasing-Diagrams.html</guid>
           <description></description>
         </item>
         <item>
           <title>Automatic Data Refinement</title>
           <link>/entries/Automatic_Refinement.html</link>
           <pubDate>Wed, 02 Oct 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Automatic_Refinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Native Word</title>
           <link>/entries/Native_Word.html</link>
           <pubDate>Tue, 17 Sep 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Native_Word.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Formal Model of IEEE Floating Point Arithmetic</title>
           <link>/entries/IEEE_Floating_Point.html</link>
           <pubDate>Sat, 27 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/IEEE_Floating_Point.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lehmer&#39;s Theorem</title>
           <link>/entries/Lehmer.html</link>
           <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Lehmer.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pratt&#39;s Primality Certificates</title>
           <link>/entries/Pratt_Certificate.html</link>
           <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Pratt_Certificate.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Königsberg Bridge Problem and the Friendship Theorem</title>
           <link>/entries/Koenigsberg_Friendship.html</link>
           <pubDate>Fri, 19 Jul 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Koenigsberg_Friendship.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sound and Complete Sort Encodings for First-Order Logic</title>
           <link>/entries/Sort_Encodings.html</link>
           <pubDate>Thu, 27 Jun 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Sort_Encodings.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Axiomatic Characterization of the Single-Source Shortest Path Problem</title>
           <link>/entries/ShortestPath.html</link>
           <pubDate>Wed, 22 May 2013 00:00:00 +0000</pubDate>
           <guid>/entries/ShortestPath.html</guid>
           <description></description>
         </item>
         <item>
           <title>Graph Theory</title>
           <link>/entries/Graph_Theory.html</link>
           <pubDate>Sun, 28 Apr 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Graph_Theory.html</guid>
           <description></description>
         </item>
         <item>
           <title>Light-weight Containers</title>
           <link>/entries/Containers.html</link>
           <pubDate>Mon, 15 Apr 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Containers.html</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal 2</title>
           <link>/entries/Nominal2.html</link>
           <pubDate>Thu, 21 Feb 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Nominal2.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation</title>
           <link>/entries/Launchbury.html</link>
           <pubDate>Thu, 31 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Launchbury.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ribbon Proofs</title>
           <link>/entries/Ribbon_Proofs.html</link>
           <pubDate>Sat, 19 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Ribbon_Proofs.html</guid>
           <description></description>
         </item>
         <item>
           <title>Rank-Nullity Theorem in Linear Algebra</title>
           <link>/entries/Rank_Nullity_Theorem.html</link>
           <pubDate>Wed, 16 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Rank_Nullity_Theorem.html</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene Algebra</title>
           <link>/entries/Kleene_Algebra.html</link>
           <pubDate>Tue, 15 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Kleene_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Computing N-th Roots using the Babylonian Method</title>
           <link>/entries/Sqrt_Babylonian.html</link>
           <pubDate>Thu, 03 Jan 2013 00:00:00 +0000</pubDate>
           <guid>/entries/Sqrt_Babylonian.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Separation Logic Framework for Imperative HOL</title>
           <link>/entries/Separation_Logic_Imperative_HOL.html</link>
           <pubDate>Wed, 14 Nov 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Logic_Imperative_HOL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Open Induction</title>
           <link>/entries/Open_Induction.html</link>
           <pubDate>Fri, 02 Nov 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Open_Induction.html</guid>
           <description></description>
         </item>
         <item>
           <title>The independence of Tarski&#39;s Euclidean axiom</title>
           <link>/entries/Tarskis_Geometry.html</link>
           <pubDate>Tue, 30 Oct 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Tarskis_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Bondy&#39;s Theorem</title>
           <link>/entries/Bondy.html</link>
           <pubDate>Sat, 27 Oct 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Bondy.html</guid>
           <description></description>
         </item>
         <item>
           <title>Possibilistic Noninterference</title>
           <link>/entries/Possibilistic_Noninterference.html</link>
           <pubDate>Mon, 10 Sep 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Possibilistic_Noninterference.html</guid>
           <description></description>
         </item>
         <item>
           <title>Generating linear orders for datatypes</title>
           <link>/entries/Datatype_Order_Generator.html</link>
           <pubDate>Tue, 07 Aug 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Datatype_Order_Generator.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proving the Impossibility of Trisecting an Angle and Doubling the Cube</title>
           <link>/entries/Impossible_Geometry.html</link>
           <pubDate>Sun, 05 Aug 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Impossible_Geometry.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</title>
           <link>/entries/Heard_Of.html</link>
           <pubDate>Fri, 27 Jul 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Heard_Of.html</guid>
           <description></description>
         </item>
         <item>
           <title>Logical Relations for PCF</title>
           <link>/entries/PCF.html</link>
           <pubDate>Sun, 01 Jul 2012 00:00:00 +0000</pubDate>
           <guid>/entries/PCF.html</guid>
           <description></description>
         </item>
         <item>
           <title>Type Constructor Classes and Monad Transformers</title>
           <link>/entries/Tycon.html</link>
           <pubDate>Tue, 26 Jun 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Tycon.html</guid>
           <description></description>
         </item>
         <item>
           <title>CCS in nominal logic</title>
           <link>/entries/CCS.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/CCS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Psi-calculi in Isabelle</title>
           <link>/entries/Psi_Calculi.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Psi_Calculi.html</guid>
           <description></description>
         </item>
         <item>
           <title>The pi-calculus in nominal logic</title>
           <link>/entries/Pi_Calculus.html</link>
           <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Pi_Calculus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle/Circus</title>
           <link>/entries/Circus.html</link>
           <pubDate>Sun, 27 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Circus.html</guid>
           <description></description>
         </item>
         <item>
           <title>Separation Algebra</title>
           <link>/entries/Separation_Algebra.html</link>
           <pubDate>Fri, 11 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Separation_Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stuttering Equivalence</title>
           <link>/entries/Stuttering_Equivalence.html</link>
           <pubDate>Mon, 07 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Stuttering_Equivalence.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive Study of Confidentiality</title>
           <link>/entries/Inductive_Confidentiality.html</link>
           <pubDate>Wed, 02 May 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Inductive_Confidentiality.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinary Differential Equations</title>
           <link>/entries/Ordinary_Differential_Equations.html</link>
           <pubDate>Thu, 26 Apr 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinary_Differential_Equations.html</guid>
           <description></description>
         </item>
         <item>
           <title>Well-Quasi-Orders</title>
           <link>/entries/Well_Quasi_Orders.html</link>
           <pubDate>Fri, 13 Apr 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Well_Quasi_Orders.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abortable Linearizable Modules</title>
           <link>/entries/Abortable_Linearizable_Modules.html</link>
           <pubDate>Thu, 01 Mar 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Abortable_Linearizable_Modules.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Transitive Closures</title>
           <link>/entries/Transitive-Closure-II.html</link>
           <pubDate>Wed, 29 Feb 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive-Closure-II.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Probabilistic Proof of the Girth-Chromatic Number Theorem</title>
           <link>/entries/Girth_Chromatic.html</link>
           <pubDate>Mon, 06 Feb 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Girth_Chromatic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Dijkstra&#39;s Shortest Path Algorithm</title>
           <link>/entries/Dijkstra_Shortest_Path.html</link>
           <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Dijkstra_Shortest_Path.html</guid>
           <description></description>
         </item>
         <item>
           <title>Refinement for Monadic Programs</title>
           <link>/entries/Refine_Monadic.html</link>
           <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Refine_Monadic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Markov Models</title>
           <link>/entries/Markov_Models.html</link>
           <pubDate>Tue, 03 Jan 2012 00:00:00 +0000</pubDate>
           <guid>/entries/Markov_Models.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Definitional Encoding of TLA* in Isabelle/HOL</title>
           <link>/entries/TLA.html</link>
           <pubDate>Sat, 19 Nov 2011 00:00:00 +0000</pubDate>
           <guid>/entries/TLA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient Mergesort</title>
           <link>/entries/Efficient-Mergesort.html</link>
           <pubDate>Wed, 09 Nov 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Efficient-Mergesort.html</guid>
           <description></description>
         </item>
         <item>
           <title>Algebra of Monotonic Boolean Transformers</title>
           <link>/entries/MonoBoolTranAlgebra.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/MonoBoolTranAlgebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lattice Properties</title>
           <link>/entries/LatticeProperties.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/LatticeProperties.html</guid>
           <description></description>
         </item>
         <item>
           <title>Pseudo Hoops</title>
           <link>/entries/PseudoHoops.html</link>
           <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
           <guid>/entries/PseudoHoops.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Myhill-Nerode Theorem Based on Regular Expressions</title>
           <link>/entries/Myhill-Nerode.html</link>
           <pubDate>Fri, 26 Aug 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Myhill-Nerode.html</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan Elimination for Matrices Represented as Functions</title>
           <link>/entries/Gauss-Jordan-Elim-Fun.html</link>
           <pubDate>Fri, 19 Aug 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Gauss-Jordan-Elim-Fun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum Cardinality Matching</title>
           <link>/entries/Max-Card-Matching.html</link>
           <pubDate>Thu, 21 Jul 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Max-Card-Matching.html</guid>
           <description></description>
         </item>
         <item>
           <title>Knowledge-based programs</title>
           <link>/entries/KBPs.html</link>
           <pubDate>Tue, 17 May 2011 00:00:00 +0000</pubDate>
           <guid>/entries/KBPs.html</guid>
           <description></description>
         </item>
         <item>
           <title>The General Triangle Is Unique</title>
           <link>/entries/General-Triangle.html</link>
           <pubDate>Fri, 01 Apr 2011 00:00:00 +0000</pubDate>
           <guid>/entries/General-Triangle.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Transitive Closures of Finite Relations</title>
           <link>/entries/Transitive-Closure.html</link>
           <pubDate>Mon, 14 Mar 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Transitive-Closure.html</guid>
           <description></description>
         </item>
         <item>
           <title>AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</title>
           <link>/entries/AutoFocus-Stream.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/AutoFocus-Stream.html</guid>
           <description></description>
         </item>
         <item>
           <title>Infinite Lists</title>
           <link>/entries/List-Infinite.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/List-Infinite.html</guid>
           <description></description>
         </item>
         <item>
           <title>Interval Temporal Logic on Natural Numbers</title>
           <link>/entries/Nat-Interval-Logic.html</link>
           <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Nat-Interval-Logic.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lightweight Java</title>
           <link>/entries/LightweightJava.html</link>
           <pubDate>Mon, 07 Feb 2011 00:00:00 +0000</pubDate>
           <guid>/entries/LightweightJava.html</guid>
           <description></description>
         </item>
         <item>
           <title>RIPEMD-160</title>
           <link>/entries/RIPEMD-160-SPARK.html</link>
           <pubDate>Mon, 10 Jan 2011 00:00:00 +0000</pubDate>
           <guid>/entries/RIPEMD-160-SPARK.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lower Semicontinuous Functions</title>
           <link>/entries/Lower_Semicontinuous.html</link>
           <pubDate>Sat, 08 Jan 2011 00:00:00 +0000</pubDate>
           <guid>/entries/Lower_Semicontinuous.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hall&#39;s Marriage Theorem</title>
           <link>/entries/Marriage.html</link>
           <pubDate>Fri, 17 Dec 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Marriage.html</guid>
           <description></description>
         </item>
         <item>
           <title>Shivers&#39; Control Flow Analysis</title>
           <link>/entries/Shivers-CFA.html</link>
           <pubDate>Tue, 16 Nov 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Shivers-CFA.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial Heaps and Skew Binomial Heaps</title>
           <link>/entries/Binomial-Heaps.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Binomial-Heaps.html</guid>
           <description></description>
         </item>
         <item>
           <title>Finger Trees</title>
           <link>/entries/Finger-Trees.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Finger-Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Functional Binomial Queues</title>
           <link>/entries/Binomial-Queues.html</link>
           <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Binomial-Queues.html</guid>
           <description></description>
         </item>
         <item>
           <title>Strong Normalization of Moggis&#39;s Computational Metalanguage</title>
           <link>/entries/Lam-ml-Normalization.html</link>
           <pubDate>Sun, 29 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Lam-ml-Normalization.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Multivariate Polynomials</title>
           <link>/entries/Polynomials.html</link>
           <pubDate>Tue, 10 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Polynomials.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing Statecharts using Hierarchical Automata</title>
           <link>/entries/Statecharts.html</link>
           <pubDate>Sun, 08 Aug 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Statecharts.html</guid>
           <description></description>
         </item>
         <item>
           <title>Free Groups</title>
           <link>/entries/Free-Groups.html</link>
           <pubDate>Thu, 24 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Free-Groups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory</title>
           <link>/entries/Category2.html</link>
           <pubDate>Sun, 20 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Category2.html</guid>
           <description></description>
         </item>
         <item>
           <title>Executable Matrix Operations on Matrices of Arbitrary Dimensions</title>
           <link>/entries/Matrix.html</link>
           <pubDate>Thu, 17 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Matrix.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Rewriting</title>
           <link>/entries/Abstract-Rewriting.html</link>
           <pubDate>Mon, 14 Jun 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract-Rewriting.html</guid>
           <description></description>
         </item>
         <item>
           <title>Semantics and Data Refinement of Invariant Based Programs</title>
           <link>/entries/DataRefinementIBP.html</link>
           <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/DataRefinementIBP.html</guid>
           <description></description>
         </item>
         <item>
           <title>Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</title>
           <link>/entries/GraphMarkingIBP.html</link>
           <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/GraphMarkingIBP.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Complete Proof of the Robbins Conjecture</title>
           <link>/entries/Robbins-Conjecture.html</link>
           <pubDate>Sat, 22 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Robbins-Conjecture.html</guid>
           <description></description>
         </item>
         <item>
           <title>Regular Sets and Expressions</title>
           <link>/entries/Regular-Sets.html</link>
           <pubDate>Wed, 12 May 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Regular-Sets.html</guid>
           <description></description>
         </item>
         <item>
           <title>Locally Nameless Sigma Calculus</title>
           <link>/entries/Locally-Nameless-Sigma.html</link>
           <pubDate>Fri, 30 Apr 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Locally-Nameless-Sigma.html</guid>
           <description></description>
         </item>
         <item>
           <title>Free Boolean Algebra</title>
           <link>/entries/Free-Boolean-Algebra.html</link>
           <pubDate>Mon, 29 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Free-Boolean-Algebra.html</guid>
           <description></description>
         </item>
         <item>
           <title>Information Flow Noninterference via Slicing</title>
           <link>/entries/InformationFlowSlicing.html</link>
           <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/InformationFlowSlicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>Inter-Procedural Information Flow Noninterference via Slicing</title>
           <link>/entries/InformationFlowSlicing_Inter.html</link>
           <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
           <guid>/entries/InformationFlowSlicing_Inter.html</guid>
           <description></description>
         </item>
         <item>
           <title>List Index</title>
           <link>/entries/List-Index.html</link>
           <pubDate>Sat, 20 Feb 2010 00:00:00 +0000</pubDate>
           <guid>/entries/List-Index.html</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive</title>
           <link>/entries/Coinductive.html</link>
           <pubDate>Fri, 12 Feb 2010 00:00:00 +0000</pubDate>
           <guid>/entries/Coinductive.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Fast SAT Solver for Isabelle in Standard ML</title>
           <link>/entries/DPT-SAT-Solver.html</link>
           <pubDate>Wed, 09 Dec 2009 00:00:00 +0000</pubDate>
           <guid>/entries/DPT-SAT-Solver.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalizing the Logic-Automaton Connection</title>
           <link>/entries/Presburger-Automata.html</link>
           <pubDate>Thu, 03 Dec 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Presburger-Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Collections Framework</title>
           <link>/entries/Collections.html</link>
           <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Collections.html</guid>
           <description></description>
         </item>
         <item>
           <title>Tree Automata</title>
           <link>/entries/Tree-Automata.html</link>
           <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Tree-Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect Number Theorem</title>
           <link>/entries/Perfect-Number-Thm.html</link>
           <pubDate>Sun, 22 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Perfect-Number-Thm.html</guid>
           <description></description>
         </item>
         <item>
           <title>Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</title>
           <link>/entries/HRB-Slicing.html</link>
           <pubDate>Fri, 13 Nov 2009 00:00:00 +0000</pubDate>
           <guid>/entries/HRB-Slicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Worker/Wrapper Transformation</title>
           <link>/entries/WorkerWrapper.html</link>
           <pubDate>Fri, 30 Oct 2009 00:00:00 +0000</pubDate>
           <guid>/entries/WorkerWrapper.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinals and Cardinals</title>
           <link>/entries/Ordinals_and_Cardinals.html</link>
           <pubDate>Tue, 01 Sep 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinals_and_Cardinals.html</guid>
           <description></description>
         </item>
         <item>
           <title>Invertibility in Sequent Calculi</title>
           <link>/entries/SequentInvertibility.html</link>
           <pubDate>Fri, 28 Aug 2009 00:00:00 +0000</pubDate>
           <guid>/entries/SequentInvertibility.html</guid>
           <description></description>
         </item>
         <item>
           <title>An Example of a Cofinitary Group in Isabelle/HOL</title>
           <link>/entries/CofGroups.html</link>
           <pubDate>Tue, 04 Aug 2009 00:00:00 +0000</pubDate>
           <guid>/entries/CofGroups.html</guid>
           <description></description>
         </item>
         <item>
           <title>Code Generation for Functions as Data</title>
           <link>/entries/FinFun.html</link>
           <pubDate>Wed, 06 May 2009 00:00:00 +0000</pubDate>
           <guid>/entries/FinFun.html</guid>
           <description></description>
         </item>
         <item>
           <title>Stream Fusion</title>
           <link>/entries/Stream-Fusion.html</link>
           <pubDate>Wed, 29 Apr 2009 00:00:00 +0000</pubDate>
           <guid>/entries/Stream-Fusion.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Bytecode Logic for JML and Types</title>
           <link>/entries/BytecodeLogicJmlTypes.html</link>
           <pubDate>Fri, 12 Dec 2008 00:00:00 +0000</pubDate>
           <guid>/entries/BytecodeLogicJmlTypes.html</guid>
           <description></description>
         </item>
         <item>
           <title>Secure information flow and program logics</title>
           <link>/entries/SIFPL.html</link>
           <pubDate>Mon, 10 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SIFPL.html</guid>
           <description></description>
         </item>
         <item>
           <title>Some classical results in Social Choice Theory</title>
           <link>/entries/SenSocialChoice.html</link>
           <pubDate>Sun, 09 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SenSocialChoice.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fun With Tilings</title>
           <link>/entries/FunWithTilings.html</link>
           <pubDate>Fri, 07 Nov 2008 00:00:00 +0000</pubDate>
           <guid>/entries/FunWithTilings.html</guid>
           <description></description>
         </item>
         <item>
           <title>The Textbook Proof of Huffman&#39;s Algorithm</title>
           <link>/entries/Huffman.html</link>
           <pubDate>Wed, 15 Oct 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Huffman.html</guid>
           <description></description>
         </item>
         <item>
           <title>Towards Certified Slicing</title>
           <link>/entries/Slicing.html</link>
           <pubDate>Tue, 16 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Slicing.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Correctness Proof for the Volpano/Smith Security Typing System</title>
           <link>/entries/VolpanoSmith.html</link>
           <pubDate>Tue, 02 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/VolpanoSmith.html</guid>
           <description></description>
         </item>
         <item>
           <title>Arrow and Gibbard-Satterthwaite</title>
           <link>/entries/ArrowImpossibilityGS.html</link>
           <pubDate>Mon, 01 Sep 2008 00:00:00 +0000</pubDate>
           <guid>/entries/ArrowImpossibilityGS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fun With Functions</title>
           <link>/entries/FunWithFunctions.html</link>
           <pubDate>Tue, 26 Aug 2008 00:00:00 +0000</pubDate>
           <guid>/entries/FunWithFunctions.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formal Verification of Modern SAT Solvers</title>
           <link>/entries/SATSolverVerification.html</link>
           <pubDate>Wed, 23 Jul 2008 00:00:00 +0000</pubDate>
           <guid>/entries/SATSolverVerification.html</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion Theory I</title>
           <link>/entries/Recursion-Theory-I.html</link>
           <pubDate>Sat, 05 Apr 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Recursion-Theory-I.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</title>
           <link>/entries/Simpl.html</link>
           <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/Simpl.html</guid>
           <description></description>
         </item>
         <item>
           <title>BDD Normalisation</title>
           <link>/entries/BDD.html</link>
           <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/BDD.html</guid>
           <description></description>
         </item>
         <item>
           <title>Normalization by Evaluation</title>
           <link>/entries/NormByEval.html</link>
           <pubDate>Mon, 18 Feb 2008 00:00:00 +0000</pubDate>
           <guid>/entries/NormByEval.html</guid>
           <description></description>
         </item>
         <item>
           <title>Quantifier Elimination for Linear Arithmetic</title>
           <link>/entries/LinearQuantifierElim.html</link>
           <pubDate>Fri, 11 Jan 2008 00:00:00 +0000</pubDate>
           <guid>/entries/LinearQuantifierElim.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</title>
           <link>/entries/Program-Conflict-Analysis.html</link>
           <pubDate>Fri, 14 Dec 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Program-Conflict-Analysis.html</guid>
           <description></description>
         </item>
         <item>
           <title>Jinja with Threads</title>
           <link>/entries/JinjaThreads.html</link>
           <pubDate>Mon, 03 Dec 2007 00:00:00 +0000</pubDate>
           <guid>/entries/JinjaThreads.html</guid>
           <description></description>
         </item>
         <item>
           <title>Much Ado About Two</title>
           <link>/entries/MuchAdoAboutTwo.html</link>
           <pubDate>Tue, 06 Nov 2007 00:00:00 +0000</pubDate>
           <guid>/entries/MuchAdoAboutTwo.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples</title>
           <link>/entries/Fermat3_4.html</link>
           <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Fermat3_4.html</guid>
           <description></description>
         </item>
         <item>
           <title>Sums of Two and Four Squares</title>
           <link>/entries/SumSquares.html</link>
           <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/SumSquares.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma</title>
           <link>/entries/Valuation.html</link>
           <pubDate>Wed, 08 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/Valuation.html</guid>
           <description></description>
         </item>
         <item>
           <title>First-Order Logic According to Fitting</title>
           <link>/entries/FOL-Fitting.html</link>
           <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/FOL-Fitting.html</guid>
           <description></description>
         </item>
         <item>
           <title>POPLmark Challenge Via de Bruijn Indices</title>
           <link>/entries/POPLmark-deBruijn.html</link>
           <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
           <guid>/entries/POPLmark-deBruijn.html</guid>
           <description></description>
         </item>
         <item>
           <title>Hotel Key Card System</title>
           <link>/entries/HotelKeyCards.html</link>
           <pubDate>Sat, 09 Sep 2006 00:00:00 +0000</pubDate>
           <guid>/entries/HotelKeyCards.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract Hoare Logics</title>
           <link>/entries/Abstract-Hoare-Logics.html</link>
           <pubDate>Tue, 08 Aug 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Abstract-Hoare-Logics.html</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck I: Tame Graphs</title>
           <link>/entries/Flyspeck-Tame.html</link>
           <pubDate>Mon, 22 May 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Flyspeck-Tame.html</guid>
           <description></description>
         </item>
         <item>
           <title>CoreC&#43;&#43;</title>
           <link>/entries/CoreC&#43;&#43;.html</link>
           <pubDate>Mon, 15 May 2006 00:00:00 +0000</pubDate>
           <guid>/entries/CoreC&#43;&#43;.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Theory of Featherweight Java in Isabelle/HOL</title>
           <link>/entries/FeatherweightJava.html</link>
           <pubDate>Fri, 31 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/FeatherweightJava.html</guid>
           <description></description>
         </item>
         <item>
           <title>Instances of Schneider&#39;s generalized protocol of clock synchronization</title>
           <link>/entries/ClockSynchInst.html</link>
           <pubDate>Wed, 15 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/ClockSynchInst.html</guid>
           <description></description>
         </item>
         <item>
           <title>Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</title>
           <link>/entries/Cauchy.html</link>
           <pubDate>Tue, 14 Mar 2006 00:00:00 +0000</pubDate>
           <guid>/entries/Cauchy.html</guid>
           <description></description>
         </item>
         <item>
           <title>Countable Ordinals</title>
           <link>/entries/Ordinal.html</link>
           <pubDate>Fri, 11 Nov 2005 00:00:00 +0000</pubDate>
           <guid>/entries/Ordinal.html</guid>
           <description></description>
         </item>
         <item>
           <title>Fast Fourier Transform</title>
           <link>/entries/FFT.html</link>
           <pubDate>Wed, 12 Oct 2005 00:00:00 +0000</pubDate>
           <guid>/entries/FFT.html</guid>
           <description></description>
         </item>
         <item>
           <title>Formalization of a Generalized Protocol for Clock Synchronization</title>
           <link>/entries/GenClock.html</link>
           <pubDate>Fri, 24 Jun 2005 00:00:00 +0000</pubDate>
           <guid>/entries/GenClock.html</guid>
           <description></description>
         </item>
         <item>
           <title>Proving the Correctness of Disk Paxos</title>
           <link>/entries/DiskPaxos.html</link>
           <pubDate>Wed, 22 Jun 2005 00:00:00 +0000</pubDate>
           <guid>/entries/DiskPaxos.html</guid>
           <description></description>
         </item>
         <item>
           <title>Jive Data and Store Model</title>
           <link>/entries/JiveDataStoreModel.html</link>
           <pubDate>Mon, 20 Jun 2005 00:00:00 +0000</pubDate>
           <guid>/entries/JiveDataStoreModel.html</guid>
           <description></description>
         </item>
         <item>
           <title>Jinja is not Java</title>
           <link>/entries/Jinja.html</link>
           <pubDate>Wed, 01 Jun 2005 00:00:00 +0000</pubDate>
           <guid>/entries/Jinja.html</guid>
           <description></description>
         </item>
         <item>
           <title>SHA1, RSA, PSS and more</title>
           <link>/entries/RSAPSS.html</link>
           <pubDate>Mon, 02 May 2005 00:00:00 +0000</pubDate>
           <guid>/entries/RSAPSS.html</guid>
           <description></description>
         </item>
         <item>
           <title>Category Theory to Yoneda&#39;s Lemma</title>
           <link>/entries/Category.html</link>
           <pubDate>Thu, 21 Apr 2005 00:00:00 +0000</pubDate>
           <guid>/entries/Category.html</guid>
           <description></description>
         </item>
         <item>
           <title>File Refinement</title>
           <link>/entries/FileRefinement.html</link>
           <pubDate>Thu, 09 Dec 2004 00:00:00 +0000</pubDate>
           <guid>/entries/FileRefinement.html</guid>
           <description></description>
         </item>
         <item>
           <title>Integration theory and random variables</title>
           <link>/entries/Integration.html</link>
           <pubDate>Fri, 19 Nov 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Integration.html</guid>
           <description></description>
         </item>
         <item>
           <title>A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic</title>
           <link>/entries/Verified-Prover.html</link>
           <pubDate>Tue, 28 Sep 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Verified-Prover.html</guid>
           <description></description>
         </item>
         <item>
           <title>Completeness theorem</title>
           <link>/entries/Completeness.html</link>
           <pubDate>Mon, 20 Sep 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Completeness.html</guid>
           <description></description>
         </item>
         <item>
           <title>Ramsey&#39;s theorem, infinitary version</title>
           <link>/entries/Ramsey-Infinite.html</link>
           <pubDate>Mon, 20 Sep 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Ramsey-Infinite.html</guid>
           <description></description>
         </item>
         <item>
           <title>Compiling Exceptions Correctly</title>
           <link>/entries/Compiling-Exceptions-Correctly.html</link>
           <pubDate>Fri, 09 Jul 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Compiling-Exceptions-Correctly.html</guid>
           <description></description>
         </item>
         <item>
           <title>Depth First Search</title>
           <link>/entries/Depth-First-Search.html</link>
           <pubDate>Thu, 24 Jun 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Depth-First-Search.html</guid>
           <description></description>
         </item>
         <item>
           <title>Groups, Rings and Modules</title>
           <link>/entries/Group-Ring-Module.html</link>
           <pubDate>Tue, 18 May 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Group-Ring-Module.html</guid>
           <description></description>
         </item>
         <item>
           <title>Lazy Lists II</title>
           <link>/entries/Lazy-Lists-II.html</link>
           <pubDate>Mon, 26 Apr 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Lazy-Lists-II.html</guid>
           <description></description>
         </item>
         <item>
           <title>Topology</title>
           <link>/entries/Topology.html</link>
           <pubDate>Mon, 26 Apr 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Topology.html</guid>
           <description></description>
         </item>
         <item>
           <title>Binary Search Trees</title>
           <link>/entries/BinarySearchTree.html</link>
           <pubDate>Mon, 05 Apr 2004 00:00:00 +0000</pubDate>
           <guid>/entries/BinarySearchTree.html</guid>
           <description></description>
         </item>
         <item>
           <title>Functional Automata</title>
           <link>/entries/Functional-Automata.html</link>
           <pubDate>Tue, 30 Mar 2004 00:00:00 +0000</pubDate>
           <guid>/entries/Functional-Automata.html</guid>
           <description></description>
         </item>
         <item>
           <title>AVL Trees</title>
           <link>/entries/AVL-Trees.html</link>
           <pubDate>Fri, 19 Mar 2004 00:00:00 +0000</pubDate>
           <guid>/entries/AVL-Trees.html</guid>
           <description></description>
         </item>
         <item>
           <title>Mini ML</title>
           <link>/entries/MiniML.html</link>
           <pubDate>Fri, 19 Mar 2004 00:00:00 +0000</pubDate>
           <guid>/entries/MiniML.html</guid>
           <description></description>
         </item>
         <item>
           <title>Abortable_Linearizable_Modules</title>
           <link>/sessions/abortable_linearizable_modules/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abortable_linearizable_modules/</guid>
           <description></description>
         </item>
         <item>
           <title>Abs_Int_ITP2012</title>
           <link>/sessions/abs_int_itp2012/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abs_int_itp2012/</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract_Completeness</title>
           <link>/sessions/abstract_completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abstract_completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract_Soundness</title>
           <link>/sessions/abstract_soundness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abstract_soundness/</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract-Hoare-Logics</title>
           <link>/sessions/abstract-hoare-logics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abstract-hoare-logics/</guid>
           <description></description>
         </item>
         <item>
           <title>Abstract-Rewriting</title>
           <link>/sessions/abstract-rewriting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/abstract-rewriting/</guid>
           <description></description>
         </item>
         <item>
           <title>ABY3_Protocols</title>
           <link>/sessions/aby3_protocols/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/aby3_protocols/</guid>
           <description></description>
         </item>
         <item>
           <title>Ackermanns_not_PR</title>
           <link>/sessions/ackermanns_not_pr/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ackermanns_not_pr/</guid>
           <description></description>
         </item>
         <item>
           <title>Actuarial_Mathematics</title>
           <link>/sessions/actuarial_mathematics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/actuarial_mathematics/</guid>
           <description></description>
         </item>
         <item>
           <title>Adaptive_State_Counting</title>
           <link>/sessions/adaptive_state_counting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/adaptive_state_counting/</guid>
           <description></description>
         </item>
         <item>
           <title>ADS_Functor</title>
           <link>/sessions/ads_functor/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ads_functor/</guid>
           <description></description>
         </item>
         <item>
           <title>Affine_Arithmetic</title>
           <link>/sessions/affine_arithmetic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/affine_arithmetic/</guid>
           <description></description>
         </item>
         <item>
           <title>Aggregation_Algebras</title>
           <link>/sessions/aggregation_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/aggregation_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>AI_Planning_Languages_Semantics</title>
           <link>/sessions/ai_planning_languages_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ai_planning_languages_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Akra_Bazzi</title>
           <link>/sessions/akra_bazzi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/akra_bazzi/</guid>
           <description></description>
         </item>
         <item>
           <title>Algebraic_Numbers</title>
           <link>/sessions/algebraic_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/algebraic_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Algebraic_VCs</title>
           <link>/sessions/algebraic_vcs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/algebraic_vcs/</guid>
           <description></description>
         </item>
         <item>
           <title>Allen_Calculus</title>
           <link>/sessions/allen_calculus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/allen_calculus/</guid>
           <description></description>
         </item>
         <item>
           <title>Amicable_Numbers</title>
           <link>/sessions/amicable_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/amicable_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Amortized_Complexity</title>
           <link>/sessions/amortized_complexity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/amortized_complexity/</guid>
           <description></description>
         </item>
         <item>
           <title>AnselmGod</title>
           <link>/sessions/anselmgod/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/anselmgod/</guid>
           <description></description>
         </item>
         <item>
           <title>AODV</title>
           <link>/sessions/aodv/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/aodv/</guid>
           <description></description>
         </item>
         <item>
           <title>AOT</title>
           <link>/sessions/aot/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/aot/</guid>
           <description></description>
         </item>
         <item>
           <title>Applicative_Lifting</title>
           <link>/sessions/applicative_lifting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/applicative_lifting/</guid>
           <description></description>
         </item>
         <item>
+          <title>Approximate_Model_Counting</title>
+          <link>/sessions/approximate_model_counting/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/approximate_model_counting/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Approximation_Algorithms</title>
           <link>/sessions/approximation_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/approximation_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Architectural_Design_Patterns</title>
           <link>/sessions/architectural_design_patterns/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/architectural_design_patterns/</guid>
           <description></description>
         </item>
         <item>
           <title>Aristotles_Assertoric_Syllogistic</title>
           <link>/sessions/aristotles_assertoric_syllogistic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/aristotles_assertoric_syllogistic/</guid>
           <description></description>
         </item>
         <item>
           <title>Arith_Prog_Rel_Primes</title>
           <link>/sessions/arith_prog_rel_primes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/arith_prog_rel_primes/</guid>
           <description></description>
         </item>
         <item>
           <title>ArrowImpossibilityGS</title>
           <link>/sessions/arrowimpossibilitygs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/arrowimpossibilitygs/</guid>
           <description></description>
         </item>
         <item>
           <title>Attack_Trees</title>
           <link>/sessions/attack_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/attack_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Auto2_HOL</title>
           <link>/sessions/auto2_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/auto2_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>Auto2_Imperative_HOL</title>
           <link>/sessions/auto2_imperative_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/auto2_imperative_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>AutoFocus-Stream</title>
           <link>/sessions/autofocus-stream/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/autofocus-stream/</guid>
           <description></description>
         </item>
         <item>
           <title>Automated_Stateful_Protocol_Verification</title>
           <link>/sessions/automated_stateful_protocol_verification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/automated_stateful_protocol_verification/</guid>
           <description></description>
         </item>
         <item>
           <title>Automatic_Refinement</title>
           <link>/sessions/automatic_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/automatic_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>AVL-Trees</title>
           <link>/sessions/avl-trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/avl-trees/</guid>
           <description></description>
         </item>
         <item>
           <title>AWN</title>
           <link>/sessions/awn/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/awn/</guid>
           <description></description>
         </item>
         <item>
           <title>AxiomaticCategoryTheory</title>
           <link>/sessions/axiomaticcategorytheory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/axiomaticcategorytheory/</guid>
           <description></description>
         </item>
         <item>
           <title>Balog_Szemeredi_Gowers</title>
           <link>/sessions/balog_szemeredi_gowers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/balog_szemeredi_gowers/</guid>
           <description></description>
         </item>
         <item>
           <title>Banach_Steinhaus</title>
           <link>/sessions/banach_steinhaus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/banach_steinhaus/</guid>
           <description></description>
         </item>
         <item>
           <title>BD_Security_Compositional</title>
           <link>/sessions/bd_security_compositional/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bd_security_compositional/</guid>
           <description></description>
         </item>
         <item>
           <title>BDD</title>
           <link>/sessions/bdd/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bdd/</guid>
           <description></description>
         </item>
         <item>
           <title>Belief_Revision</title>
           <link>/sessions/belief_revision/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/belief_revision/</guid>
           <description></description>
         </item>
         <item>
           <title>Bell_Numbers_Spivey</title>
           <link>/sessions/bell_numbers_spivey/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bell_numbers_spivey/</guid>
           <description></description>
         </item>
         <item>
           <title>BenOr_Kozen_Reif</title>
           <link>/sessions/benor_kozen_reif/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/benor_kozen_reif/</guid>
           <description></description>
         </item>
         <item>
           <title>Berlekamp_Zassenhaus</title>
           <link>/sessions/berlekamp_zassenhaus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/berlekamp_zassenhaus/</guid>
           <description></description>
         </item>
         <item>
           <title>Bernoulli</title>
           <link>/sessions/bernoulli/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bernoulli/</guid>
           <description></description>
         </item>
         <item>
           <title>Bertrands_Postulate</title>
           <link>/sessions/bertrands_postulate/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bertrands_postulate/</guid>
           <description></description>
         </item>
         <item>
           <title>Bicategory</title>
           <link>/sessions/bicategory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bicategory/</guid>
           <description></description>
         </item>
         <item>
           <title>Binary_Code_Imprimitive</title>
           <link>/sessions/binary_code_imprimitive/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binary_code_imprimitive/</guid>
           <description></description>
         </item>
         <item>
           <title>BinarySearchTree</title>
           <link>/sessions/binarysearchtree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binarysearchtree/</guid>
           <description></description>
         </item>
         <item>
           <title>Binding_Syntax_Theory</title>
           <link>/sessions/binding_syntax_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binding_syntax_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial-Heaps</title>
           <link>/sessions/binomial-heaps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binomial-heaps/</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial-Queues</title>
           <link>/sessions/binomial-queues/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binomial-queues/</guid>
           <description></description>
         </item>
         <item>
           <title>BirdKMP</title>
           <link>/sessions/birdkmp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/birdkmp/</guid>
           <description></description>
         </item>
         <item>
           <title>Birkhoff_Finite_Distributive_Lattices</title>
           <link>/sessions/birkhoff_finite_distributive_lattices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/birkhoff_finite_distributive_lattices/</guid>
           <description></description>
         </item>
         <item>
           <title>Blue_Eyes</title>
           <link>/sessions/blue_eyes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/blue_eyes/</guid>
           <description></description>
         </item>
         <item>
           <title>BNF_CC</title>
           <link>/sessions/bnf_cc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bnf_cc/</guid>
           <description></description>
         </item>
         <item>
           <title>BNF_Operations</title>
           <link>/sessions/bnf_operations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bnf_operations/</guid>
           <description></description>
         </item>
         <item>
           <title>Bondy</title>
           <link>/sessions/bondy/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bondy/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolean_Expression_Checkers</title>
           <link>/sessions/boolean_expression_checkers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolean_expression_checkers/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos_Curious_Inference</title>
           <link>/sessions/boolos_curious_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolos_curious_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos_Curious_Inference_Automated</title>
           <link>/sessions/boolos_curious_inference_automated/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolos_curious_inference_automated/</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded_Deducibility_Security</title>
           <link>/sessions/bounded_deducibility_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bounded_deducibility_security/</guid>
           <description></description>
         </item>
         <item>
           <title>BTree</title>
           <link>/sessions/btree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/btree/</guid>
           <description></description>
         </item>
         <item>
           <title>Buchi_Complementation</title>
           <link>/sessions/buchi_complementation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buchi_complementation/</guid>
           <description></description>
         </item>
         <item>
           <title>Budan_Fourier</title>
           <link>/sessions/budan_fourier/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/budan_fourier/</guid>
           <description></description>
         </item>
         <item>
           <title>Buffons_Needle</title>
           <link>/sessions/buffons_needle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buffons_needle/</guid>
           <description></description>
         </item>
         <item>
           <title>Buildings</title>
           <link>/sessions/buildings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buildings/</guid>
           <description></description>
         </item>
         <item>
           <title>BytecodeLogicJmlTypes</title>
           <link>/sessions/bytecodelogicjmltypes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bytecodelogicjmltypes/</guid>
           <description></description>
         </item>
         <item>
           <title>C2KA_DistributedSystems</title>
           <link>/sessions/c2ka_distributedsystems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/c2ka_distributedsystems/</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML</title>
           <link>/sessions/cakeml/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cakeml/</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML_Codegen</title>
           <link>/sessions/cakeml_codegen/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cakeml_codegen/</guid>
           <description></description>
         </item>
         <item>
           <title>Call_Arity</title>
           <link>/sessions/call_arity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/call_arity/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Equiv_Relations</title>
           <link>/sessions/card_equiv_relations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_equiv_relations/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Multisets</title>
           <link>/sessions/card_multisets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_multisets/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Number_Partitions</title>
           <link>/sessions/card_number_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_number_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Partitions</title>
           <link>/sessions/card_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality_Continuum</title>
           <link>/sessions/cardinality_continuum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cardinality_continuum/</guid>
           <description></description>
         </item>
         <item>
           <title>Cartan_FP</title>
           <link>/sessions/cartan_fp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cartan_fp/</guid>
           <description></description>
         </item>
         <item>
           <title>Case_Labeling</title>
           <link>/sessions/case_labeling/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/case_labeling/</guid>
           <description></description>
         </item>
         <item>
           <title>Catalan_Numbers</title>
           <link>/sessions/catalan_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/catalan_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Category</title>
           <link>/sessions/category/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category/</guid>
           <description></description>
         </item>
         <item>
           <title>Category2</title>
           <link>/sessions/category2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category2/</guid>
           <description></description>
         </item>
         <item>
           <title>Category3</title>
           <link>/sessions/category3/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category3/</guid>
           <description></description>
         </item>
         <item>
           <title>Catoids</title>
           <link>/sessions/catoids/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/catoids/</guid>
           <description></description>
         </item>
         <item>
           <title>Cauchy</title>
           <link>/sessions/cauchy/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cauchy/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Automata</title>
           <link>/sessions/cava_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Base</title>
           <link>/sessions/cava_base/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_base/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_LTL_Modelchecker</title>
           <link>/sessions/cava_ltl_modelchecker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_ltl_modelchecker/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Setup</title>
           <link>/sessions/cava_setup/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_setup/</guid>
           <description></description>
         </item>
         <item>
           <title>Cayley_Hamilton</title>
           <link>/sessions/cayley_hamilton/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cayley_hamilton/</guid>
           <description></description>
         </item>
         <item>
           <title>CCS</title>
           <link>/sessions/ccs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ccs/</guid>
           <description></description>
         </item>
         <item>
           <title>Certification_Monads</title>
           <link>/sessions/certification_monads/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/certification_monads/</guid>
           <description></description>
         </item>
         <item>
           <title>Ceva</title>
           <link>/sessions/ceva/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ceva/</guid>
           <description></description>
         </item>
         <item>
           <title>Chandy_Lamport</title>
           <link>/sessions/chandy_lamport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chandy_lamport/</guid>
           <description></description>
         </item>
         <item>
           <title>Chebyshev_Polynomials</title>
           <link>/sessions/chebyshev_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chebyshev_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>CHERI-C_Memory_Model</title>
           <link>/sessions/cheri-c_memory_model/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cheri-c_memory_model/</guid>
           <description></description>
         </item>
         <item>
           <title>Chord_Segments</title>
           <link>/sessions/chord_segments/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chord_segments/</guid>
           <description></description>
         </item>
         <item>
           <title>Circus</title>
           <link>/sessions/circus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/circus/</guid>
           <description></description>
         </item>
         <item>
           <title>CISC-Kernel</title>
           <link>/sessions/cisc-kernel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cisc-kernel/</guid>
           <description></description>
         </item>
         <item>
           <title>Clean</title>
           <link>/sessions/clean/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clean/</guid>
           <description></description>
         </item>
         <item>
           <title>Clique_and_Monotone_Circuits</title>
           <link>/sessions/clique_and_monotone_circuits/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clique_and_monotone_circuits/</guid>
           <description></description>
         </item>
         <item>
           <title>ClockSynchInst</title>
           <link>/sessions/clocksynchinst/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clocksynchinst/</guid>
           <description></description>
         </item>
         <item>
           <title>Closest_Pair_Points</title>
           <link>/sessions/closest_pair_points/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/closest_pair_points/</guid>
           <description></description>
         </item>
         <item>
           <title>CoCon</title>
           <link>/sessions/cocon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cocon/</guid>
           <description></description>
         </item>
         <item>
           <title>CofGroups</title>
           <link>/sessions/cofgroups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cofgroups/</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive</title>
           <link>/sessions/coinductive/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coinductive/</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive_Languages</title>
           <link>/sessions/coinductive_languages/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coinductive_languages/</guid>
           <description></description>
         </item>
         <item>
           <title>Collections</title>
           <link>/sessions/collections/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/collections/</guid>
           <description></description>
         </item>
         <item>
           <title>Collections_Examples</title>
           <link>/sessions/collections_examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/collections_examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinable_Wands</title>
           <link>/sessions/combinable_wands/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinable_wands/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial_Enumeration_Algorithms</title>
           <link>/sessions/combinatorial_enumeration_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorial_enumeration_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words</title>
           <link>/sessions/combinatorics_words/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words_Graph_Lemma</title>
           <link>/sessions/combinatorics_words_graph_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words_graph_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words_Lyndon</title>
           <link>/sessions/combinatorics_words_lyndon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words_lyndon/</guid>
           <description></description>
         </item>
         <item>
           <title>CommCSL</title>
           <link>/sessions/commcsl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/commcsl/</guid>
           <description></description>
         </item>
         <item>
           <title>Commuting_Hermitian</title>
           <link>/sessions/commuting_hermitian/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/commuting_hermitian/</guid>
           <description></description>
         </item>
         <item>
           <title>Comparison_Sort_Lower_Bound</title>
           <link>/sessions/comparison_sort_lower_bound/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/comparison_sort_lower_bound/</guid>
           <description></description>
         </item>
         <item>
           <title>Compiling-Exceptions-Correctly</title>
           <link>/sessions/compiling-exceptions-correctly/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/compiling-exceptions-correctly/</guid>
           <description></description>
         </item>
         <item>
           <title>Complete_Non_Orders</title>
           <link>/sessions/complete_non_orders/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complete_non_orders/</guid>
           <description></description>
         </item>
         <item>
           <title>Completeness</title>
           <link>/sessions/completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Bounded_Operators</title>
           <link>/sessions/complex_bounded_operators/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_bounded_operators/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Bounded_Operators_Dependencies</title>
           <link>/sessions/complex_bounded_operators_dependencies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_bounded_operators_dependencies/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Geometry</title>
           <link>/sessions/complex_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Complx</title>
           <link>/sessions/complx/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complx/</guid>
           <description></description>
         </item>
         <item>
           <title>ComponentDependencies</title>
           <link>/sessions/componentdependencies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/componentdependencies/</guid>
           <description></description>
         </item>
         <item>
           <title>Concentration_Inequalities</title>
           <link>/sessions/concentration_inequalities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concentration_inequalities/</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent_Ref_Alg</title>
           <link>/sessions/concurrent_ref_alg/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrent_ref_alg/</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent_Revisions</title>
           <link>/sessions/concurrent_revisions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrent_revisions/</guid>
           <description></description>
         </item>
         <item>
           <title>ConcurrentGC</title>
           <link>/sessions/concurrentgc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrentgc/</guid>
           <description></description>
         </item>
         <item>
           <title>ConcurrentIMP</title>
           <link>/sessions/concurrentimp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrentimp/</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional_Simplification</title>
           <link>/sessions/conditional_simplification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/conditional_simplification/</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional_Transfer_Rule</title>
           <link>/sessions/conditional_transfer_rule/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/conditional_transfer_rule/</guid>
           <description></description>
         </item>
         <item>
           <title>Consensus_Refined</title>
           <link>/sessions/consensus_refined/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/consensus_refined/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive_Cryptography</title>
           <link>/sessions/constructive_cryptography/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructive_cryptography/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive_Cryptography_CM</title>
           <link>/sessions/constructive_cryptography_cm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructive_cryptography_cm/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructor_Funs</title>
           <link>/sessions/constructor_funs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructor_funs/</guid>
           <description></description>
         </item>
         <item>
           <title>Containers</title>
           <link>/sessions/containers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/containers/</guid>
           <description></description>
         </item>
         <item>
           <title>Containers-Benchmarks</title>
           <link>/sessions/containers-benchmarks/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/containers-benchmarks/</guid>
           <description></description>
         </item>
         <item>
+          <title>Continued_Fractions</title>
+          <link>/sessions/continued_fractions/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/continued_fractions/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Cook_Levin</title>
           <link>/sessions/cook_levin/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cook_levin/</guid>
           <description></description>
         </item>
         <item>
           <title>Core_DOM</title>
           <link>/sessions/core_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/core_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Core_SC_DOM</title>
           <link>/sessions/core_sc_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/core_sc_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>CoreC&#43;&#43;</title>
           <link>/sessions/corec&#43;&#43;/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/corec&#43;&#43;/</guid>
           <description></description>
         </item>
         <item>
           <title>Correctness_Algebras</title>
           <link>/sessions/correctness_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/correctness_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMed</title>
           <link>/sessions/cosmed/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cosmed/</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMeDis</title>
           <link>/sessions/cosmedis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cosmedis/</guid>
           <description></description>
         </item>
         <item>
           <title>Cotangent_PFD_Formula</title>
           <link>/sessions/cotangent_pfd_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cotangent_pfd_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Count_Complex_Roots</title>
           <link>/sessions/count_complex_roots/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/count_complex_roots/</guid>
           <description></description>
         </item>
         <item>
           <title>Coupledsim_Contrasim</title>
           <link>/sessions/coupledsim_contrasim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coupledsim_contrasim/</guid>
           <description></description>
         </item>
         <item>
           <title>CRDT</title>
           <link>/sessions/crdt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crdt/</guid>
           <description></description>
         </item>
         <item>
           <title>CryptHOL</title>
           <link>/sessions/crypthol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crypthol/</guid>
           <description></description>
         </item>
         <item>
           <title>Crypto_Standards</title>
           <link>/sessions/crypto_standards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crypto_standards/</guid>
           <description></description>
         </item>
         <item>
           <title>CryptoBasedCompositionalProperties</title>
           <link>/sessions/cryptobasedcompositionalproperties/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cryptobasedcompositionalproperties/</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber</title>
           <link>/sessions/crystals-kyber/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crystals-kyber/</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber_Security</title>
           <link>/sessions/crystals-kyber_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crystals-kyber_security/</guid>
           <description></description>
         </item>
         <item>
           <title>CSP_RefTK</title>
           <link>/sessions/csp_reftk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/csp_reftk/</guid>
           <description></description>
         </item>
         <item>
           <title>Cubic_Quartic_Equations</title>
           <link>/sessions/cubic_quartic_equations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cubic_quartic_equations/</guid>
           <description></description>
         </item>
         <item>
           <title>CubicalCategories</title>
           <link>/sessions/cubicalcategories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cubicalcategories/</guid>
           <description></description>
         </item>
         <item>
           <title>CVP_Hardness</title>
           <link>/sessions/cvp_hardness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cvp_hardness/</guid>
           <description></description>
         </item>
         <item>
           <title>CYK</title>
           <link>/sessions/cyk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cyk/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Elementary_Categories</title>
           <link>/sessions/czh_elementary_categories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_elementary_categories/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Foundations</title>
           <link>/sessions/czh_foundations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_foundations/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Universal_Constructions</title>
           <link>/sessions/czh_universal_constructions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_universal_constructions/</guid>
           <description></description>
         </item>
         <item>
           <title>DataRefinementIBP</title>
           <link>/sessions/datarefinementibp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/datarefinementibp/</guid>
           <description></description>
         </item>
         <item>
           <title>Datatype_Order_Generator</title>
           <link>/sessions/datatype_order_generator/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/datatype_order_generator/</guid>
           <description></description>
         </item>
         <item>
           <title>DCR-ExecutionEquivalence</title>
           <link>/sessions/dcr-executionequivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dcr-executionequivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Decl_Sem_Fun_PL</title>
           <link>/sessions/decl_sem_fun_pl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decl_sem_fun_pl/</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing-Diagrams</title>
           <link>/sessions/decreasing-diagrams/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decreasing-diagrams/</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing-Diagrams-II</title>
           <link>/sessions/decreasing-diagrams-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decreasing-diagrams-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Dedekind_Real</title>
           <link>/sessions/dedekind_real/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dedekind_real/</guid>
           <description></description>
         </item>
         <item>
           <title>Deep_Learning</title>
           <link>/sessions/deep_learning/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/deep_learning/</guid>
           <description></description>
         </item>
         <item>
           <title>Delta_System_Lemma</title>
           <link>/sessions/delta_system_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/delta_system_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>Density_Compiler</title>
           <link>/sessions/density_compiler/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/density_compiler/</guid>
           <description></description>
         </item>
         <item>
           <title>Dependent_SIFUM_Refinement</title>
           <link>/sessions/dependent_sifum_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dependent_sifum_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>Dependent_SIFUM_Type_Systems</title>
           <link>/sessions/dependent_sifum_type_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dependent_sifum_type_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Depth-First-Search</title>
           <link>/sessions/depth-first-search/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/depth-first-search/</guid>
           <description></description>
         </item>
         <item>
           <title>Derangements</title>
           <link>/sessions/derangements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/derangements/</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving</title>
           <link>/sessions/deriving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/deriving/</guid>
           <description></description>
         </item>
         <item>
           <title>Descartes_Sign_Rule</title>
           <link>/sessions/descartes_sign_rule/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/descartes_sign_rule/</guid>
           <description></description>
         </item>
         <item>
           <title>Design_Theory</title>
           <link>/sessions/design_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/design_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>DFS_Framework</title>
           <link>/sessions/dfs_framework/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dfs_framework/</guid>
           <description></description>
         </item>
         <item>
           <title>Dict_Construction</title>
           <link>/sessions/dict_construction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dict_construction/</guid>
           <description></description>
         </item>
         <item>
           <title>Differential_Dynamic_Logic</title>
           <link>/sessions/differential_dynamic_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/differential_dynamic_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Differential_Game_Logic</title>
           <link>/sessions/differential_game_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/differential_game_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Digit_Expansions</title>
           <link>/sessions/digit_expansions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/digit_expansions/</guid>
           <description></description>
         </item>
         <item>
           <title>DigitsInBase</title>
           <link>/sessions/digitsinbase/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/digitsinbase/</guid>
           <description></description>
         </item>
         <item>
           <title>Dijkstra_Shortest_Path</title>
           <link>/sessions/dijkstra_shortest_path/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dijkstra_shortest_path/</guid>
           <description></description>
         </item>
         <item>
           <title>Diophantine_Eqns_Lin_Hom</title>
           <link>/sessions/diophantine_eqns_lin_hom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/diophantine_eqns_lin_hom/</guid>
           <description></description>
         </item>
         <item>
           <title>Directed_Sets</title>
           <link>/sessions/directed_sets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/directed_sets/</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet_L</title>
           <link>/sessions/dirichlet_l/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dirichlet_l/</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet_Series</title>
           <link>/sessions/dirichlet_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dirichlet_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Discrete_Summation</title>
           <link>/sessions/discrete_summation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/discrete_summation/</guid>
           <description></description>
         </item>
         <item>
           <title>DiscretePricing</title>
           <link>/sessions/discretepricing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/discretepricing/</guid>
           <description></description>
         </item>
         <item>
           <title>Disintegration</title>
           <link>/sessions/disintegration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/disintegration/</guid>
           <description></description>
         </item>
         <item>
           <title>DiskPaxos</title>
           <link>/sessions/diskpaxos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/diskpaxos/</guid>
           <description></description>
         </item>
         <item>
           <title>Distributed_Distinct_Elements</title>
           <link>/sessions/distributed_distinct_elements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/distributed_distinct_elements/</guid>
           <description></description>
         </item>
         <item>
           <title>DOM_Components</title>
           <link>/sessions/dom_components/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dom_components/</guid>
           <description></description>
         </item>
         <item>
           <title>Dominance_CHK</title>
           <link>/sessions/dominance_chk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dominance_chk/</guid>
           <description></description>
         </item>
         <item>
           <title>DPRM_Theorem</title>
           <link>/sessions/dprm_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dprm_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>DPT-SAT-Solver</title>
           <link>/sessions/dpt-sat-solver/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dpt-sat-solver/</guid>
           <description></description>
         </item>
         <item>
           <title>Dynamic_Tables</title>
           <link>/sessions/dynamic_tables/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dynamic_tables/</guid>
           <description></description>
         </item>
         <item>
           <title>DynamicArchitectures</title>
           <link>/sessions/dynamicarchitectures/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dynamicarchitectures/</guid>
           <description></description>
         </item>
         <item>
           <title>E_Transcendental</title>
           <link>/sessions/e_transcendental/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/e_transcendental/</guid>
           <description></description>
         </item>
         <item>
           <title>Earley_Parser</title>
           <link>/sessions/earley_parser/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/earley_parser/</guid>
           <description></description>
         </item>
         <item>
           <title>Echelon_Form</title>
           <link>/sessions/echelon_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/echelon_form/</guid>
           <description></description>
         </item>
         <item>
           <title>EdmondsKarp_Maxflow</title>
           <link>/sessions/edmondskarp_maxflow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/edmondskarp_maxflow/</guid>
           <description></description>
         </item>
         <item>
           <title>Edwards_Elliptic_Curves_Group</title>
           <link>/sessions/edwards_elliptic_curves_group/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/edwards_elliptic_curves_group/</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient_Weighted_Path_Order</title>
           <link>/sessions/efficient_weighted_path_order/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/efficient_weighted_path_order/</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient-Mergesort</title>
           <link>/sessions/efficient-mergesort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/efficient-mergesort/</guid>
           <description></description>
         </item>
         <item>
           <title>Elimination_Of_Repeated_Factors</title>
           <link>/sessions/elimination_of_repeated_factors/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/elimination_of_repeated_factors/</guid>
           <description></description>
         </item>
         <item>
           <title>Elliptic_Curves_Group_Law</title>
           <link>/sessions/elliptic_curves_group_law/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/elliptic_curves_group_law/</guid>
           <description></description>
         </item>
         <item>
           <title>Encodability_Process_Calculi</title>
           <link>/sessions/encodability_process_calculi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/encodability_process_calculi/</guid>
           <description></description>
         </item>
         <item>
           <title>Epistemic_Logic</title>
           <link>/sessions/epistemic_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/epistemic_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Equivalence_Relation_Enumeration</title>
           <link>/sessions/equivalence_relation_enumeration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/equivalence_relation_enumeration/</guid>
           <description></description>
         </item>
         <item>
           <title>Ergodic_Theory</title>
           <link>/sessions/ergodic_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ergodic_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Error_Function</title>
           <link>/sessions/error_function/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/error_function/</guid>
           <description></description>
         </item>
         <item>
           <title>Eudoxus_Reals</title>
           <link>/sessions/eudoxus_reals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/eudoxus_reals/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_MacLaurin</title>
           <link>/sessions/euler_maclaurin/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_maclaurin/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_Partition</title>
           <link>/sessions/euler_partition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_partition/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_Polyhedron_Formula</title>
           <link>/sessions/euler_polyhedron_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_polyhedron_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Eval_FO</title>
           <link>/sessions/eval_fo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/eval_fo/</guid>
           <description></description>
         </item>
         <item>
           <title>Example-Submission</title>
           <link>/sessions/example-submission/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/example-submission/</guid>
           <description></description>
         </item>
         <item>
           <title>Executable_Randomized_Algorithms</title>
           <link>/sessions/executable_randomized_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/executable_randomized_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Expander_Graphs</title>
           <link>/sessions/expander_graphs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/expander_graphs/</guid>
           <description></description>
         </item>
         <item>
           <title>Extended_Finite_State_Machine_Inference</title>
           <link>/sessions/extended_finite_state_machine_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/extended_finite_state_machine_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Extended_Finite_State_Machines</title>
           <link>/sessions/extended_finite_state_machines/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/extended_finite_state_machines/</guid>
           <description></description>
         </item>
         <item>
           <title>Factor_Algebraic_Polynomial</title>
           <link>/sessions/factor_algebraic_polynomial/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/factor_algebraic_polynomial/</guid>
           <description></description>
         </item>
         <item>
           <title>Factored_Transition_System_Bounding</title>
           <link>/sessions/factored_transition_system_bounding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/factored_transition_system_bounding/</guid>
           <description></description>
         </item>
         <item>
           <title>Falling_Factorial_Sum</title>
           <link>/sessions/falling_factorial_sum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/falling_factorial_sum/</guid>
           <description></description>
         </item>
         <item>
           <title>Farkas</title>
           <link>/sessions/farkas/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/farkas/</guid>
           <description></description>
         </item>
         <item>
           <title>Featherweight_OCL</title>
           <link>/sessions/featherweight_ocl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/featherweight_ocl/</guid>
           <description></description>
         </item>
         <item>
           <title>FeatherweightJava</title>
           <link>/sessions/featherweightjava/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/featherweightjava/</guid>
           <description></description>
         </item>
         <item>
           <title>Fermat3_4</title>
           <link>/sessions/fermat3_4/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fermat3_4/</guid>
           <description></description>
         </item>
         <item>
           <title>FFT</title>
           <link>/sessions/fft/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fft/</guid>
           <description></description>
         </item>
         <item>
           <title>FileRefinement</title>
           <link>/sessions/filerefinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/filerefinement/</guid>
           <description></description>
         </item>
         <item>
           <title>FinFun</title>
           <link>/sessions/finfun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finfun/</guid>
           <description></description>
         </item>
         <item>
           <title>Finger-Trees</title>
           <link>/sessions/finger-trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finger-trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite_Automata_HF</title>
           <link>/sessions/finite_automata_hf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite_automata_hf/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite_Fields</title>
           <link>/sessions/finite_fields/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite_fields/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite-Map-Extras</title>
           <link>/sessions/finite-map-extras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite-map-extras/</guid>
           <description></description>
         </item>
         <item>
           <title>Finitely_Generated_Abelian_Groups</title>
           <link>/sessions/finitely_generated_abelian_groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finitely_generated_abelian_groups/</guid>
           <description></description>
         </item>
         <item>
           <title>First_Order_Terms</title>
           <link>/sessions/first_order_terms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/first_order_terms/</guid>
           <description></description>
         </item>
         <item>
           <title>First_Welfare_Theorem</title>
           <link>/sessions/first_welfare_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/first_welfare_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Fishburn_Impossibility</title>
           <link>/sessions/fishburn_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fishburn_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher_Yates</title>
           <link>/sessions/fisher_yates/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fisher_yates/</guid>
           <description></description>
         </item>
         <item>
           <title>Fishers_Inequality</title>
           <link>/sessions/fishers_inequality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fishers_inequality/</guid>
           <description></description>
         </item>
         <item>
           <title>Fixed_Length_Vector</title>
           <link>/sessions/fixed_length_vector/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fixed_length_vector/</guid>
           <description></description>
         </item>
         <item>
           <title>Flow_Networks</title>
           <link>/sessions/flow_networks/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flow_networks/</guid>
           <description></description>
         </item>
         <item>
           <title>Floyd_Warshall</title>
           <link>/sessions/floyd_warshall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/floyd_warshall/</guid>
           <description></description>
         </item>
         <item>
           <title>FLP</title>
           <link>/sessions/flp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flp/</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck-Tame</title>
           <link>/sessions/flyspeck-tame/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flyspeck-tame/</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck-Tame-Computation</title>
           <link>/sessions/flyspeck-tame-computation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flyspeck-tame-computation/</guid>
           <description></description>
         </item>
         <item>
           <title>FO_Theory_Rewriting</title>
           <link>/sessions/fo_theory_rewriting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fo_theory_rewriting/</guid>
           <description></description>
         </item>
         <item>
           <title>FocusStreamsCaseStudies</title>
           <link>/sessions/focusstreamscasestudies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/focusstreamscasestudies/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Axiomatic</title>
           <link>/sessions/fol_axiomatic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_axiomatic/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Harrison</title>
           <link>/sessions/fol_harrison/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_harrison/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc1</title>
           <link>/sessions/fol_seq_calc1/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc1/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc2</title>
           <link>/sessions/fol_seq_calc2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc2/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc3</title>
           <link>/sessions/fol_seq_calc3/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc3/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL-Fitting</title>
           <link>/sessions/fol-fitting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol-fitting/</guid>
           <description></description>
         </item>
         <item>
           <title>Forcing</title>
           <link>/sessions/forcing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/forcing/</guid>
           <description></description>
         </item>
         <item>
           <title>Formal_Puiseux_Series</title>
           <link>/sessions/formal_puiseux_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formal_puiseux_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Formal_SSA</title>
           <link>/sessions/formal_ssa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formal_ssa/</guid>
           <description></description>
         </item>
         <item>
           <title>Formula_Derivatives</title>
           <link>/sessions/formula_derivatives/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formula_derivatives/</guid>
           <description></description>
         </item>
         <item>
           <title>Formula_Derivatives-Examples</title>
           <link>/sessions/formula_derivatives-examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formula_derivatives-examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Foundation_of_geometry</title>
           <link>/sessions/foundation_of_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/foundation_of_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Fourier</title>
           <link>/sessions/fourier/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fourier/</guid>
           <description></description>
         </item>
         <item>
           <title>Free-Boolean-Algebra</title>
           <link>/sessions/free-boolean-algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/free-boolean-algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Free-Groups</title>
           <link>/sessions/free-groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/free-groups/</guid>
           <description></description>
         </item>
         <item>
           <title>Frequency_Moments</title>
           <link>/sessions/frequency_moments/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/frequency_moments/</guid>
           <description></description>
         </item>
         <item>
           <title>Fresh_Identifiers</title>
           <link>/sessions/fresh_identifiers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fresh_identifiers/</guid>
           <description></description>
         </item>
         <item>
           <title>FSM_Tests</title>
           <link>/sessions/fsm_tests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fsm_tests/</guid>
           <description></description>
         </item>
         <item>
           <title>Functional_Ordered_Resolution_Prover</title>
           <link>/sessions/functional_ordered_resolution_prover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/functional_ordered_resolution_prover/</guid>
           <description></description>
         </item>
         <item>
           <title>Functional-Automata</title>
           <link>/sessions/functional-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/functional-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>FunWithFunctions</title>
           <link>/sessions/funwithfunctions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/funwithfunctions/</guid>
           <description></description>
         </item>
         <item>
           <title>FunWithTilings</title>
           <link>/sessions/funwithtilings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/funwithtilings/</guid>
           <description></description>
         </item>
         <item>
           <title>Furstenberg_Topology</title>
           <link>/sessions/furstenberg_topology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/furstenberg_topology/</guid>
           <description></description>
         </item>
         <item>
           <title>Gabow_SCC</title>
           <link>/sessions/gabow_scc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gabow_scc/</guid>
           <description></description>
         </item>
         <item>
           <title>Gale_Shapley</title>
           <link>/sessions/gale_shapley/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gale_shapley/</guid>
           <description></description>
         </item>
         <item>
           <title>GaleStewart_Games</title>
           <link>/sessions/galestewart_games/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/galestewart_games/</guid>
           <description></description>
         </item>
         <item>
           <title>Game_Based_Crypto</title>
           <link>/sessions/game_based_crypto/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/game_based_crypto/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss_Jordan</title>
           <link>/sessions/gauss_jordan/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss_jordan/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss_Sums</title>
           <link>/sessions/gauss_sums/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss_sums/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan-Elim-Fun</title>
           <link>/sessions/gauss-jordan-elim-fun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss-jordan-elim-fun/</guid>
           <description></description>
         </item>
         <item>
           <title>Gaussian_Integers</title>
           <link>/sessions/gaussian_integers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gaussian_integers/</guid>
           <description></description>
         </item>
         <item>
           <title>GenClock</title>
           <link>/sessions/genclock/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/genclock/</guid>
           <description></description>
         </item>
         <item>
           <title>General-Triangle</title>
           <link>/sessions/general-triangle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/general-triangle/</guid>
           <description></description>
         </item>
         <item>
           <title>Generalized_Counting_Sort</title>
           <link>/sessions/generalized_counting_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generalized_counting_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>Generic_Deriving</title>
           <link>/sessions/generic_deriving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generic_deriving/</guid>
           <description></description>
         </item>
         <item>
           <title>Generic_Join</title>
           <link>/sessions/generic_join/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generic_join/</guid>
           <description></description>
         </item>
         <item>
           <title>GewirthPGCProof</title>
           <link>/sessions/gewirthpgcproof/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gewirthpgcproof/</guid>
           <description></description>
         </item>
         <item>
           <title>Girth_Chromatic</title>
           <link>/sessions/girth_chromatic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/girth_chromatic/</guid>
           <description></description>
         </item>
         <item>
           <title>Given_Clause_Loops</title>
           <link>/sessions/given_clause_loops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/given_clause_loops/</guid>
           <description></description>
         </item>
         <item>
+          <title>Go</title>
+          <link>/sessions/go/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go/</guid>
+          <description></description>
+        </item>
+        <item>
+          <title>Go_Test_Quick</title>
+          <link>/sessions/go_test_quick/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go_test_quick/</guid>
+          <description></description>
+        </item>
+        <item>
+          <title>Go_Test_Slow</title>
+          <link>/sessions/go_test_slow/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go_test_slow/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Goedel_HFSet_Semantic</title>
           <link>/sessions/goedel_hfset_semantic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_hfset_semantic/</guid>
           <description></description>
         </item>
         <item>
           <title>Goedel_HFSet_Semanticless</title>
           <link>/sessions/goedel_hfset_semanticless/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_hfset_semanticless/</guid>
           <description></description>
         </item>
         <item>
           <title>Goedel_Incompleteness</title>
           <link>/sessions/goedel_incompleteness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_incompleteness/</guid>
           <description></description>
         </item>
         <item>
           <title>GoedelGod</title>
           <link>/sessions/goedelgod/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedelgod/</guid>
           <description></description>
         </item>
         <item>
           <title>Goodstein_Lambda</title>
           <link>/sessions/goodstein_lambda/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goodstein_lambda/</guid>
           <description></description>
         </item>
         <item>
           <title>GPU_Kernel_PL</title>
           <link>/sessions/gpu_kernel_pl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gpu_kernel_pl/</guid>
           <description></description>
         </item>
         <item>
           <title>Graph_Saturation</title>
           <link>/sessions/graph_saturation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graph_saturation/</guid>
           <description></description>
         </item>
         <item>
           <title>Graph_Theory</title>
           <link>/sessions/graph_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graph_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>GraphMarkingIBP</title>
           <link>/sessions/graphmarkingibp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graphmarkingibp/</guid>
           <description></description>
         </item>
         <item>
           <title>Gray_Codes</title>
           <link>/sessions/gray_codes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gray_codes/</guid>
           <description></description>
         </item>
         <item>
           <title>Green</title>
           <link>/sessions/green/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/green/</guid>
           <description></description>
         </item>
         <item>
           <title>Groebner_Bases</title>
           <link>/sessions/groebner_bases/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/groebner_bases/</guid>
           <description></description>
         </item>
         <item>
           <title>Groebner_Macaulay</title>
           <link>/sessions/groebner_macaulay/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/groebner_macaulay/</guid>
           <description></description>
         </item>
         <item>
           <title>Gromov_Hyperbolicity</title>
           <link>/sessions/gromov_hyperbolicity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gromov_hyperbolicity/</guid>
           <description></description>
         </item>
         <item>
           <title>Grothendieck_Schemes</title>
           <link>/sessions/grothendieck_schemes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/grothendieck_schemes/</guid>
           <description></description>
         </item>
         <item>
           <title>Group-Ring-Module</title>
           <link>/sessions/group-ring-module/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/group-ring-module/</guid>
           <description></description>
         </item>
         <item>
           <title>Hahn_Jordan_Decomposition</title>
           <link>/sessions/hahn_jordan_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hahn_jordan_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Hales_Jewett</title>
           <link>/sessions/hales_jewett/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hales_jewett/</guid>
           <description></description>
         </item>
         <item>
           <title>Heard_Of</title>
           <link>/sessions/heard_of/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/heard_of/</guid>
           <description></description>
         </item>
         <item>
           <title>Hello_World</title>
           <link>/sessions/hello_world/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hello_world/</guid>
           <description></description>
         </item>
         <item>
           <title>HereditarilyFinite</title>
           <link>/sessions/hereditarilyfinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hereditarilyfinite/</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite</title>
           <link>/sessions/hermite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hermite/</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite_Lindemann</title>
           <link>/sessions/hermite_lindemann/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hermite_lindemann/</guid>
           <description></description>
         </item>
         <item>
           <title>Hidden_Markov_Models</title>
           <link>/sessions/hidden_markov_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hidden_markov_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Higher_Order_Terms</title>
           <link>/sessions/higher_order_terms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/higher_order_terms/</guid>
           <description></description>
         </item>
         <item>
           <title>Hoare_Time</title>
           <link>/sessions/hoare_time/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hoare_time/</guid>
           <description></description>
         </item>
         <item>
           <title>HoareForDivergence</title>
           <link>/sessions/hoarefordivergence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hoarefordivergence/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP</title>
           <link>/sessions/hol-csp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-csp/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP_OpSem</title>
           <link>/sessions/hol-csp_opsem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-csp_opsem/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSPM</title>
           <link>/sessions/hol-cspm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-cspm/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-ARCH-COMP</title>
           <link>/sessions/hol-ode-arch-comp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-arch-comp/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-Examples</title>
           <link>/sessions/hol-ode-examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-examples/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-Numerics</title>
           <link>/sessions/hol-ode-numerics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-numerics/</guid>
           <description></description>
         </item>
         <item>
           <title>HOLCF-Prelude</title>
           <link>/sessions/holcf-prelude/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/holcf-prelude/</guid>
           <description></description>
         </item>
         <item>
           <title>Hood_Melville_Queue</title>
           <link>/sessions/hood_melville_queue/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hood_melville_queue/</guid>
           <description></description>
         </item>
         <item>
           <title>HotelKeyCards</title>
           <link>/sessions/hotelkeycards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hotelkeycards/</guid>
           <description></description>
         </item>
         <item>
           <title>HRB-Slicing</title>
           <link>/sessions/hrb-slicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hrb-slicing/</guid>
           <description></description>
         </item>
         <item>
           <title>Huffman</title>
           <link>/sessions/huffman/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/huffman/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Logic</title>
           <link>/sessions/hybrid_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Multi_Lane_Spatial_Logic</title>
           <link>/sessions/hybrid_multi_lane_spatial_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_multi_lane_spatial_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Systems_VCs</title>
           <link>/sessions/hybrid_systems_vcs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_systems_vcs/</guid>
           <description></description>
         </item>
         <item>
           <title>HyperCTL</title>
           <link>/sessions/hyperctl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperctl/</guid>
           <description></description>
         </item>
         <item>
           <title>Hyperdual</title>
           <link>/sessions/hyperdual/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperdual/</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraph_Basics</title>
           <link>/sessions/hypergraph_basics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hypergraph_basics/</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraph_Colourings</title>
           <link>/sessions/hypergraph_colourings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hypergraph_colourings/</guid>
           <description></description>
         </item>
         <item>
           <title>HyperHoareLogic</title>
           <link>/sessions/hyperhoarelogic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperhoarelogic/</guid>
           <description></description>
         </item>
         <item>
           <title>IEEE_Floating_Point</title>
           <link>/sessions/ieee_floating_point/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ieee_floating_point/</guid>
           <description></description>
         </item>
         <item>
           <title>IFC_Tracking</title>
           <link>/sessions/ifc_tracking/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ifc_tracking/</guid>
           <description></description>
         </item>
         <item>
           <title>IMAP-CRDT</title>
           <link>/sessions/imap-crdt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imap-crdt/</guid>
           <description></description>
         </item>
         <item>
           <title>IMO2019</title>
           <link>/sessions/imo2019/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imo2019/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Compiler</title>
           <link>/sessions/imp_compiler/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_compiler/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Compiler_Reuse</title>
           <link>/sessions/imp_compiler_reuse/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_compiler_reuse/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Noninterference</title>
           <link>/sessions/imp_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2</title>
           <link>/sessions/imp2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp2/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2_Binary_Heap</title>
           <link>/sessions/imp2_binary_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp2_binary_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>Imperative_Insertion_Sort</title>
           <link>/sessions/imperative_insertion_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imperative_insertion_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>Implicational_Logic</title>
           <link>/sessions/implicational_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/implicational_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Impossible_Geometry</title>
           <link>/sessions/impossible_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/impossible_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Incompleteness</title>
           <link>/sessions/incompleteness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/incompleteness/</guid>
           <description></description>
         </item>
         <item>
           <title>Incredible_Proof_Machine</title>
           <link>/sessions/incredible_proof_machine/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/incredible_proof_machine/</guid>
           <description></description>
         </item>
         <item>
           <title>Independence_CH</title>
           <link>/sessions/independence_ch/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/independence_ch/</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive_Confidentiality</title>
           <link>/sessions/inductive_confidentiality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/inductive_confidentiality/</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive_Inference</title>
           <link>/sessions/inductive_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/inductive_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>InformationFlowSlicing</title>
           <link>/sessions/informationflowslicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/informationflowslicing/</guid>
           <description></description>
         </item>
         <item>
           <title>InformationFlowSlicing_Inter</title>
           <link>/sessions/informationflowslicing_inter/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/informationflowslicing_inter/</guid>
           <description></description>
         </item>
         <item>
           <title>InfPathElimination</title>
           <link>/sessions/infpathelimination/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/infpathelimination/</guid>
           <description></description>
         </item>
         <item>
           <title>Integration</title>
           <link>/sessions/integration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/integration/</guid>
           <description></description>
         </item>
         <item>
           <title>Interpolation_Polynomials_HOL_Algebra</title>
           <link>/sessions/interpolation_polynomials_hol_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interpolation_polynomials_hol_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Interpreter_Optimizations</title>
           <link>/sessions/interpreter_optimizations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interpreter_optimizations/</guid>
           <description></description>
         </item>
         <item>
           <title>Interval_Analysis</title>
           <link>/sessions/interval_analysis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interval_analysis/</guid>
           <description></description>
         </item>
         <item>
           <title>Interval_Arithmetic_Word32</title>
           <link>/sessions/interval_arithmetic_word32/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interval_arithmetic_word32/</guid>
           <description></description>
         </item>
         <item>
           <title>Intro_Dest_Elim</title>
           <link>/sessions/intro_dest_elim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/intro_dest_elim/</guid>
           <description></description>
         </item>
         <item>
           <title>Involutions2Squares</title>
           <link>/sessions/involutions2squares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/involutions2squares/</guid>
           <description></description>
         </item>
         <item>
           <title>IO_Language_Conformance</title>
           <link>/sessions/io_language_conformance/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/io_language_conformance/</guid>
           <description></description>
         </item>
         <item>
           <title>IP_Addresses</title>
           <link>/sessions/ip_addresses/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ip_addresses/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics</title>
           <link>/sessions/iptables_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics_Examples</title>
           <link>/sessions/iptables_semantics_examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics_examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics_Examples_Big</title>
           <link>/sessions/iptables_semantics_examples_big/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics_examples_big/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational_Series_Erdos_Straus</title>
           <link>/sessions/irrational_series_erdos_straus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrational_series_erdos_straus/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationality_J_Hancl</title>
           <link>/sessions/irrationality_j_hancl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrationality_j_hancl/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationals_From_THEBOOK</title>
           <link>/sessions/irrationals_from_thebook/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrationals_from_thebook/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_C</title>
           <link>/sessions/isabelle_c/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_c/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_hoops</title>
           <link>/sessions/isabelle_hoops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_hoops/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_Marries_Dirac</title>
           <link>/sessions/isabelle_marries_dirac/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_marries_dirac/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_Meta_Model</title>
           <link>/sessions/isabelle_meta_model/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_meta_model/</guid>
           <description></description>
         </item>
         <item>
           <title>IsaGeoCoq</title>
           <link>/sessions/isageocoq/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isageocoq/</guid>
           <description></description>
         </item>
         <item>
           <title>IsaNet</title>
           <link>/sessions/isanet/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isanet/</guid>
           <description></description>
         </item>
         <item>
           <title>Jacobson_Basic_Algebra</title>
           <link>/sessions/jacobson_basic_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jacobson_basic_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Jinja</title>
           <link>/sessions/jinja/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinja/</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaDCI</title>
           <link>/sessions/jinjadci/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinjadci/</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaThreads</title>
           <link>/sessions/jinjathreads/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinjathreads/</guid>
           <description></description>
         </item>
         <item>
           <title>JiveDataStoreModel</title>
           <link>/sessions/jivedatastoremodel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jivedatastoremodel/</guid>
           <description></description>
         </item>
         <item>
           <title>Jordan_Hoelder</title>
           <link>/sessions/jordan_hoelder/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jordan_hoelder/</guid>
           <description></description>
         </item>
         <item>
           <title>Jordan_Normal_Form</title>
           <link>/sessions/jordan_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jordan_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>KAD</title>
           <link>/sessions/kad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kad/</guid>
           <description></description>
         </item>
         <item>
           <title>Karatsuba</title>
           <link>/sessions/karatsuba/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/karatsuba/</guid>
           <description></description>
         </item>
         <item>
           <title>KAT_and_DRA</title>
           <link>/sessions/kat_and_dra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kat_and_dra/</guid>
           <description></description>
         </item>
         <item>
           <title>KBPs</title>
           <link>/sessions/kbps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kbps/</guid>
           <description></description>
         </item>
         <item>
           <title>KD_Tree</title>
           <link>/sessions/kd_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kd_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Key_Agreement_Strong_Adversaries</title>
           <link>/sessions/key_agreement_strong_adversaries/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/key_agreement_strong_adversaries/</guid>
           <description></description>
         </item>
         <item>
           <title>Khovanskii_Theorem</title>
           <link>/sessions/khovanskii_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/khovanskii_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene_Algebra</title>
           <link>/sessions/kleene_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kleene_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Kneser_Cauchy_Davenport</title>
           <link>/sessions/kneser_cauchy_davenport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kneser_cauchy_davenport/</guid>
           <description></description>
         </item>
         <item>
           <title>Knights_Tour</title>
           <link>/sessions/knights_tour/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knights_tour/</guid>
           <description></description>
         </item>
         <item>
           <title>Knot_Theory</title>
           <link>/sessions/knot_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knot_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Knuth_Bendix_Order</title>
           <link>/sessions/knuth_bendix_order/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuth_bendix_order/</guid>
           <description></description>
         </item>
         <item>
           <title>Knuth_Morris_Pratt</title>
           <link>/sessions/knuth_morris_pratt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuth_morris_pratt/</guid>
           <description></description>
         </item>
         <item>
           <title>KnuthMorrisPratt</title>
           <link>/sessions/knuthmorrispratt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuthmorrispratt/</guid>
           <description></description>
         </item>
         <item>
           <title>Koenigsberg_Friendship</title>
           <link>/sessions/koenigsberg_friendship/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/koenigsberg_friendship/</guid>
           <description></description>
         </item>
         <item>
           <title>Kruskal</title>
           <link>/sessions/kruskal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kruskal/</guid>
           <description></description>
         </item>
         <item>
           <title>Kuratowski_Closure_Complement</title>
           <link>/sessions/kuratowski_closure_complement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kuratowski_closure_complement/</guid>
           <description></description>
         </item>
         <item>
           <title>Labeled_Transition_Systems</title>
           <link>/sessions/labeled_transition_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/labeled_transition_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Lam-ml-Normalization</title>
           <link>/sessions/lam-ml-normalization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lam-ml-normalization/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_EPO</title>
           <link>/sessions/lambda_free_epo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_epo/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_KBOs</title>
           <link>/sessions/lambda_free_kbos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_kbos/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_RPOs</title>
           <link>/sessions/lambda_free_rpos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_rpos/</guid>
           <description></description>
         </item>
         <item>
           <title>LambdaAuth</title>
           <link>/sessions/lambdaauth/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambdaauth/</guid>
           <description></description>
         </item>
         <item>
           <title>LambdaMu</title>
           <link>/sessions/lambdamu/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambdamu/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambert_Series</title>
           <link>/sessions/lambert_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambert_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambert_W</title>
           <link>/sessions/lambert_w/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambert_w/</guid>
           <description></description>
         </item>
         <item>
           <title>Landau_Symbols</title>
           <link>/sessions/landau_symbols/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/landau_symbols/</guid>
           <description></description>
         </item>
         <item>
           <title>Laplace_Transform</title>
           <link>/sessions/laplace_transform/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/laplace_transform/</guid>
           <description></description>
         </item>
         <item>
           <title>Latin_Square</title>
           <link>/sessions/latin_square/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/latin_square/</guid>
           <description></description>
         </item>
         <item>
           <title>LatticeProperties</title>
           <link>/sessions/latticeproperties/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/latticeproperties/</guid>
           <description></description>
         </item>
         <item>
           <title>Launchbury</title>
           <link>/sessions/launchbury/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/launchbury/</guid>
           <description></description>
         </item>
         <item>
           <title>Laws_of_Large_Numbers</title>
           <link>/sessions/laws_of_large_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/laws_of_large_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Lazy_Case</title>
           <link>/sessions/lazy_case/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lazy_case/</guid>
           <description></description>
         </item>
         <item>
           <title>Lazy-Lists-II</title>
           <link>/sessions/lazy-lists-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lazy-lists-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Lehmer</title>
           <link>/sessions/lehmer/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lehmer/</guid>
           <description></description>
         </item>
         <item>
           <title>LEM</title>
           <link>/sessions/lem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lem/</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting_Definition_Option</title>
           <link>/sessions/lifting_definition_option/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lifting_definition_option/</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting_the_Exponent</title>
           <link>/sessions/lifting_the_exponent/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lifting_the_exponent/</guid>
           <description></description>
         </item>
         <item>
           <title>LightweightJava</title>
           <link>/sessions/lightweightjava/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lightweightjava/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Inequalities</title>
           <link>/sessions/linear_inequalities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_inequalities/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Programming</title>
           <link>/sessions/linear_programming/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_programming/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Recurrences</title>
           <link>/sessions/linear_recurrences/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_recurrences/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Recurrences_Solver</title>
           <link>/sessions/linear_recurrences_solver/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_recurrences_solver/</guid>
           <description></description>
         </item>
         <item>
           <title>LinearQuantifierElim</title>
           <link>/sessions/linearquantifierelim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linearquantifierelim/</guid>
           <description></description>
         </item>
         <item>
           <title>Liouville_Numbers</title>
           <link>/sessions/liouville_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/liouville_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Interleaving</title>
           <link>/sessions/list_interleaving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_interleaving/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Inversions</title>
           <link>/sessions/list_inversions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_inversions/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Update</title>
           <link>/sessions/list_update/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_update/</guid>
           <description></description>
         </item>
         <item>
           <title>List-Index</title>
           <link>/sessions/list-index/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list-index/</guid>
           <description></description>
         </item>
         <item>
           <title>List-Infinite</title>
           <link>/sessions/list-infinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list-infinite/</guid>
           <description></description>
         </item>
         <item>
           <title>LLL_Basis_Reduction</title>
           <link>/sessions/lll_basis_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lll_basis_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>LLL_Factorization</title>
           <link>/sessions/lll_factorization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lll_factorization/</guid>
           <description></description>
         </item>
         <item>
           <title>Localization_Ring</title>
           <link>/sessions/localization_ring/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/localization_ring/</guid>
           <description></description>
         </item>
         <item>
           <title>LocalLexing</title>
           <link>/sessions/locallexing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/locallexing/</guid>
           <description></description>
         </item>
         <item>
           <title>Locally-Nameless-Sigma</title>
           <link>/sessions/locally-nameless-sigma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/locally-nameless-sigma/</guid>
           <description></description>
         </item>
         <item>
           <title>LOFT</title>
           <link>/sessions/loft/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/loft/</guid>
           <description></description>
         </item>
         <item>
           <title>Logging_Independent_Anonymity</title>
           <link>/sessions/logging_independent_anonymity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/logging_independent_anonymity/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_Approximation</title>
           <link>/sessions/lorenz_approximation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_approximation/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_C0</title>
           <link>/sessions/lorenz_c0/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_c0/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_C1</title>
           <link>/sessions/lorenz_c1/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_c1/</guid>
           <description></description>
         </item>
         <item>
           <title>Lovasz_Local</title>
           <link>/sessions/lovasz_local/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lovasz_local/</guid>
           <description></description>
         </item>
         <item>
           <title>Lowe_Ontological_Argument</title>
           <link>/sessions/lowe_ontological_argument/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lowe_ontological_argument/</guid>
           <description></description>
         </item>
         <item>
           <title>Lower_Semicontinuous</title>
           <link>/sessions/lower_semicontinuous/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lower_semicontinuous/</guid>
           <description></description>
         </item>
         <item>
           <title>Lp</title>
           <link>/sessions/lp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lp/</guid>
           <description></description>
         </item>
         <item>
           <title>LP_Duality</title>
           <link>/sessions/lp_duality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lp_duality/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL</title>
           <link>/sessions/ltl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_Master_Theorem</title>
           <link>/sessions/ltl_master_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_master_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_Normal_Form</title>
           <link>/sessions/ltl_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_to_DRA</title>
           <link>/sessions/ltl_to_dra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_to_dra/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_to_GBA</title>
           <link>/sessions/ltl_to_gba/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_to_gba/</guid>
           <description></description>
         </item>
         <item>
           <title>Lucas_Theorem</title>
           <link>/sessions/lucas_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lucas_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Markov_Models</title>
           <link>/sessions/markov_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/markov_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Marriage</title>
           <link>/sessions/marriage/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/marriage/</guid>
           <description></description>
         </item>
         <item>
           <title>Martingales</title>
           <link>/sessions/martingales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/martingales/</guid>
           <description></description>
         </item>
         <item>
           <title>Mason_Stothers</title>
           <link>/sessions/mason_stothers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mason_stothers/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices_for_ODEs</title>
           <link>/sessions/matrices_for_odes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrices_for_odes/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrix</title>
           <link>/sessions/matrix/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrix/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrix_Tensor</title>
           <link>/sessions/matrix_tensor/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrix_tensor/</guid>
           <description></description>
         </item>
         <item>
           <title>Matroids</title>
           <link>/sessions/matroids/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matroids/</guid>
           <description></description>
         </item>
         <item>
           <title>Max-Card-Matching</title>
           <link>/sessions/max-card-matching/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/max-card-matching/</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum_Segment_Sum</title>
           <link>/sessions/maximum_segment_sum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/maximum_segment_sum/</guid>
           <description></description>
         </item>
         <item>
           <title>MDP-Algorithms</title>
           <link>/sessions/mdp-algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mdp-algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>MDP-Rewards</title>
           <link>/sessions/mdp-rewards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mdp-rewards/</guid>
           <description></description>
         </item>
         <item>
           <title>Median_Method</title>
           <link>/sessions/median_method/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/median_method/</guid>
           <description></description>
         </item>
         <item>
           <title>Median_Of_Medians_Selection</title>
           <link>/sessions/median_of_medians_selection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/median_of_medians_selection/</guid>
           <description></description>
         </item>
         <item>
           <title>Menger</title>
           <link>/sessions/menger/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/menger/</guid>
           <description></description>
         </item>
         <item>
           <title>Mereology</title>
           <link>/sessions/mereology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mereology/</guid>
           <description></description>
         </item>
         <item>
           <title>Mersenne_Primes</title>
           <link>/sessions/mersenne_primes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mersenne_primes/</guid>
           <description></description>
         </item>
         <item>
           <title>Metalogic_ProofChecker</title>
           <link>/sessions/metalogic_proofchecker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/metalogic_proofchecker/</guid>
           <description></description>
         </item>
         <item>
           <title>MFMC_Countable</title>
           <link>/sessions/mfmc_countable/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfmc_countable/</guid>
           <description></description>
         </item>
         <item>
           <title>MFODL_Monitor_Optimized</title>
           <link>/sessions/mfodl_monitor_optimized/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfodl_monitor_optimized/</guid>
           <description></description>
         </item>
         <item>
           <title>MFOTL_Monitor</title>
           <link>/sessions/mfotl_monitor/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfotl_monitor/</guid>
           <description></description>
         </item>
         <item>
           <title>MHComputation</title>
           <link>/sessions/mhcomputation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mhcomputation/</guid>
           <description></description>
         </item>
         <item>
           <title>Minimal_SSA</title>
           <link>/sessions/minimal_ssa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minimal_ssa/</guid>
           <description></description>
         </item>
         <item>
           <title>MiniML</title>
           <link>/sessions/miniml/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/miniml/</guid>
           <description></description>
         </item>
         <item>
           <title>MiniSail</title>
           <link>/sessions/minisail/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minisail/</guid>
           <description></description>
         </item>
         <item>
           <title>Minkowskis_Theorem</title>
           <link>/sessions/minkowskis_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minkowskis_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Minsky_Machines</title>
           <link>/sessions/minsky_machines/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minsky_machines/</guid>
           <description></description>
         </item>
         <item>
           <title>ML_Unification</title>
           <link>/sessions/ml_unification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ml_unification/</guid>
           <description></description>
         </item>
         <item>
           <title>MLSS_Decision_Proc</title>
           <link>/sessions/mlss_decision_proc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mlss_decision_proc/</guid>
           <description></description>
         </item>
         <item>
           <title>Modal_Logics_for_NTS</title>
           <link>/sessions/modal_logics_for_nts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modal_logics_for_nts/</guid>
           <description></description>
         </item>
         <item>
           <title>Modular_arithmetic_LLL_and_HNF_algorithms</title>
           <link>/sessions/modular_arithmetic_lll_and_hnf_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modular_arithmetic_lll_and_hnf_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Modular_Assembly_Kit_Security</title>
           <link>/sessions/modular_assembly_kit_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modular_assembly_kit_security/</guid>
           <description></description>
         </item>
         <item>
           <title>Monad_Memo_DP</title>
           <link>/sessions/monad_memo_dp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monad_memo_dp/</guid>
           <description></description>
         </item>
         <item>
           <title>Monad_Normalisation</title>
           <link>/sessions/monad_normalisation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monad_normalisation/</guid>
           <description></description>
         </item>
         <item>
           <title>MonoBoolTranAlgebra</title>
           <link>/sessions/monobooltranalgebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monobooltranalgebra/</guid>
           <description></description>
         </item>
         <item>
           <title>MonoidalCategory</title>
           <link>/sessions/monoidalcategory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monoidalcategory/</guid>
           <description></description>
         </item>
         <item>
           <title>Monomorphic_Monad</title>
           <link>/sessions/monomorphic_monad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monomorphic_monad/</guid>
           <description></description>
         </item>
         <item>
           <title>MSO_Regex_Equivalence</title>
           <link>/sessions/mso_regex_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mso_regex_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>MuchAdoAboutTwo</title>
           <link>/sessions/muchadoabouttwo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/muchadoabouttwo/</guid>
           <description></description>
         </item>
         <item>
           <title>Multi_Party_Computation</title>
           <link>/sessions/multi_party_computation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multi_party_computation/</guid>
           <description></description>
         </item>
         <item>
           <title>Multirelations</title>
           <link>/sessions/multirelations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multirelations/</guid>
           <description></description>
         </item>
         <item>
           <title>Multirelations_Heterogeneous</title>
           <link>/sessions/multirelations_heterogeneous/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multirelations_heterogeneous/</guid>
           <description></description>
         </item>
         <item>
           <title>Multiset_Ordering_NPC</title>
           <link>/sessions/multiset_ordering_npc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multiset_ordering_npc/</guid>
           <description></description>
         </item>
         <item>
           <title>Multitape_To_Singletape_TM</title>
           <link>/sessions/multitape_to_singletape_tm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multitape_to_singletape_tm/</guid>
           <description></description>
         </item>
         <item>
           <title>Myhill-Nerode</title>
           <link>/sessions/myhill-nerode/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/myhill-nerode/</guid>
           <description></description>
         </item>
         <item>
           <title>Name_Carrying_Type_Inference</title>
           <link>/sessions/name_carrying_type_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/name_carrying_type_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Nano_JSON</title>
           <link>/sessions/nano_json/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nano_json/</guid>
           <description></description>
         </item>
         <item>
           <title>Nash_Williams</title>
           <link>/sessions/nash_williams/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nash_williams/</guid>
           <description></description>
         </item>
         <item>
           <title>Nat-Interval-Logic</title>
           <link>/sessions/nat-interval-logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nat-interval-logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Native_Word</title>
           <link>/sessions/native_word/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/native_word/</guid>
           <description></description>
         </item>
         <item>
           <title>Nested_Multisets_Ordinals</title>
           <link>/sessions/nested_multisets_ordinals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nested_multisets_ordinals/</guid>
           <description></description>
         </item>
         <item>
           <title>Network_Security_Policy_Verification</title>
           <link>/sessions/network_security_policy_verification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/network_security_policy_verification/</guid>
           <description></description>
         </item>
         <item>
           <title>Neumann_Morgenstern_Utility</title>
           <link>/sessions/neumann_morgenstern_utility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/neumann_morgenstern_utility/</guid>
           <description></description>
         </item>
         <item>
           <title>No_FTL_observers</title>
           <link>/sessions/no_ftl_observers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/no_ftl_observers/</guid>
           <description></description>
         </item>
         <item>
           <title>No_FTL_observers_Gen_Rel</title>
           <link>/sessions/no_ftl_observers_gen_rel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/no_ftl_observers_gen_rel/</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal_Myhill_Nerode</title>
           <link>/sessions/nominal_myhill_nerode/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nominal_myhill_nerode/</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal2</title>
           <link>/sessions/nominal2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nominal2/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Concurrent_Composition</title>
           <link>/sessions/noninterference_concurrent_composition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_concurrent_composition/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_CSP</title>
           <link>/sessions/noninterference_csp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_csp/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Generic_Unwinding</title>
           <link>/sessions/noninterference_generic_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_generic_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Inductive_Unwinding</title>
           <link>/sessions/noninterference_inductive_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_inductive_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Ipurge_Unwinding</title>
           <link>/sessions/noninterference_ipurge_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_ipurge_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Sequential_Composition</title>
           <link>/sessions/noninterference_sequential_composition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_sequential_composition/</guid>
           <description></description>
         </item>
         <item>
           <title>NormByEval</title>
           <link>/sessions/normbyeval/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/normbyeval/</guid>
           <description></description>
         </item>
         <item>
           <title>Nullstellensatz</title>
           <link>/sessions/nullstellensatz/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nullstellensatz/</guid>
           <description></description>
         </item>
         <item>
           <title>Number_Theoretic_Transform</title>
           <link>/sessions/number_theoretic_transform/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/number_theoretic_transform/</guid>
           <description></description>
         </item>
         <item>
           <title>Octonions</title>
           <link>/sessions/octonions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/octonions/</guid>
           <description></description>
         </item>
         <item>
           <title>Old_Datatype_Show</title>
           <link>/sessions/old_datatype_show/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/old_datatype_show/</guid>
           <description></description>
         </item>
         <item>
           <title>OmegaCatoidsQuantales</title>
           <link>/sessions/omegacatoidsquantales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/omegacatoidsquantales/</guid>
           <description></description>
         </item>
         <item>
           <title>Open_Induction</title>
           <link>/sessions/open_induction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/open_induction/</guid>
           <description></description>
         </item>
         <item>
           <title>OpSets</title>
           <link>/sessions/opsets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/opsets/</guid>
           <description></description>
         </item>
         <item>
           <title>Optics</title>
           <link>/sessions/optics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/optics/</guid>
           <description></description>
         </item>
         <item>
           <title>Optimal_BST</title>
           <link>/sessions/optimal_bst/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/optimal_bst/</guid>
           <description></description>
         </item>
         <item>
           <title>Orbit_Stabiliser</title>
           <link>/sessions/orbit_stabiliser/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/orbit_stabiliser/</guid>
           <description></description>
         </item>
         <item>
           <title>Order_Lattice_Props</title>
           <link>/sessions/order_lattice_props/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/order_lattice_props/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordered_Resolution_Prover</title>
           <link>/sessions/ordered_resolution_prover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordered_resolution_prover/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal</title>
           <link>/sessions/ordinal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinal/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal_Partitions</title>
           <link>/sessions/ordinal_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinal_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinals_and_Cardinals</title>
           <link>/sessions/ordinals_and_cardinals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinals_and_cardinals/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinary_Differential_Equations</title>
           <link>/sessions/ordinary_differential_equations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinary_differential_equations/</guid>
           <description></description>
         </item>
         <item>
           <title>PAC_Checker</title>
           <link>/sessions/pac_checker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pac_checker/</guid>
           <description></description>
         </item>
         <item>
           <title>Package_logic</title>
           <link>/sessions/package_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/package_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Padic_Field</title>
           <link>/sessions/padic_field/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/padic_field/</guid>
           <description></description>
         </item>
         <item>
           <title>Padic_Ints</title>
           <link>/sessions/padic_ints/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/padic_ints/</guid>
           <description></description>
         </item>
         <item>
           <title>Pairing_Heap</title>
           <link>/sessions/pairing_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pairing_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>PAL</title>
           <link>/sessions/pal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pal/</guid>
           <description></description>
         </item>
         <item>
           <title>PAPP_Impossibility</title>
           <link>/sessions/papp_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/papp_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Paraconsistency</title>
           <link>/sessions/paraconsistency/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/paraconsistency/</guid>
           <description></description>
         </item>
         <item>
           <title>Parity_Game</title>
           <link>/sessions/parity_game/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/parity_game/</guid>
           <description></description>
         </item>
         <item>
           <title>Partial_Function_MR</title>
           <link>/sessions/partial_function_mr/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/partial_function_mr/</guid>
           <description></description>
         </item>
         <item>
           <title>Partial_Order_Reduction</title>
           <link>/sessions/partial_order_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/partial_order_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Password_Authentication_Protocol</title>
           <link>/sessions/password_authentication_protocol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/password_authentication_protocol/</guid>
           <description></description>
         </item>
         <item>
           <title>PCF</title>
           <link>/sessions/pcf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pcf/</guid>
           <description></description>
         </item>
         <item>
           <title>Pell</title>
           <link>/sessions/pell/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pell/</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect_Fields</title>
           <link>/sessions/perfect_fields/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perfect_fields/</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect-Number-Thm</title>
           <link>/sessions/perfect-number-thm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perfect-number-thm/</guid>
           <description></description>
         </item>
         <item>
           <title>Perron_Frobenius</title>
           <link>/sessions/perron_frobenius/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perron_frobenius/</guid>
           <description></description>
         </item>
         <item>
           <title>pGCL</title>
           <link>/sessions/pgcl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pgcl/</guid>
           <description></description>
         </item>
         <item>
           <title>Physical_Quantities</title>
           <link>/sessions/physical_quantities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/physical_quantities/</guid>
           <description></description>
         </item>
         <item>
           <title>Pi_Calculus</title>
           <link>/sessions/pi_calculus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pi_calculus/</guid>
           <description></description>
         </item>
         <item>
           <title>Pi_Transcendental</title>
           <link>/sessions/pi_transcendental/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pi_transcendental/</guid>
           <description></description>
         </item>
         <item>
           <title>Planarity_Certificates</title>
           <link>/sessions/planarity_certificates/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/planarity_certificates/</guid>
           <description></description>
         </item>
         <item>
           <title>PLM</title>
           <link>/sessions/plm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/plm/</guid>
           <description></description>
         </item>
         <item>
           <title>Pluennecke_Ruzsa_Inequality</title>
           <link>/sessions/pluennecke_ruzsa_inequality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pluennecke_ruzsa_inequality/</guid>
           <description></description>
         </item>
         <item>
           <title>Poincare_Bendixson</title>
           <link>/sessions/poincare_bendixson/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poincare_bendixson/</guid>
           <description></description>
         </item>
         <item>
           <title>Poincare_Disc</title>
           <link>/sessions/poincare_disc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poincare_disc/</guid>
           <description></description>
         </item>
         <item>
           <title>Polygonal_Number_Theorem</title>
           <link>/sessions/polygonal_number_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polygonal_number_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Polylog</title>
           <link>/sessions/polylog/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polylog/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Crit_Geometry</title>
           <link>/sessions/polynomial_crit_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_crit_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Factorization</title>
           <link>/sessions/polynomial_factorization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_factorization/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Interpolation</title>
           <link>/sessions/polynomial_interpolation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_interpolation/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomials</title>
           <link>/sessions/polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Pop_Refinement</title>
           <link>/sessions/pop_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pop_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>POPLmark-deBruijn</title>
           <link>/sessions/poplmark-debruijn/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poplmark-debruijn/</guid>
           <description></description>
         </item>
         <item>
           <title>Posix-Lexing</title>
           <link>/sessions/posix-lexing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/posix-lexing/</guid>
           <description></description>
         </item>
         <item>
           <title>Possibilistic_Noninterference</title>
           <link>/sessions/possibilistic_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/possibilistic_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>Power_Sum_Polynomials</title>
           <link>/sessions/power_sum_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/power_sum_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Pratt_Certificate</title>
           <link>/sessions/pratt_certificate/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pratt_certificate/</guid>
           <description></description>
         </item>
         <item>
           <title>Prefix_Free_Code_Combinators</title>
           <link>/sessions/prefix_free_code_combinators/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prefix_free_code_combinators/</guid>
           <description></description>
         </item>
         <item>
           <title>Presburger-Automata</title>
           <link>/sessions/presburger-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/presburger-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Prim_Dijkstra_Simple</title>
           <link>/sessions/prim_dijkstra_simple/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prim_dijkstra_simple/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Distribution_Elementary</title>
           <link>/sessions/prime_distribution_elementary/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_distribution_elementary/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Harmonic_Series</title>
           <link>/sessions/prime_harmonic_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_harmonic_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Number_Theorem</title>
           <link>/sessions/prime_number_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_number_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Priority_Queue_Braun</title>
           <link>/sessions/priority_queue_braun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/priority_queue_braun/</guid>
           <description></description>
         </item>
         <item>
           <title>Priority_Search_Trees</title>
           <link>/sessions/priority_search_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/priority_search_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Noninterference</title>
           <link>/sessions/probabilistic_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Prime_Tests</title>
           <link>/sessions/probabilistic_prime_tests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_prime_tests/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_System_Zoo</title>
           <link>/sessions/probabilistic_system_zoo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_system_zoo/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Timed_Automata</title>
           <link>/sessions/probabilistic_timed_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_timed_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_While</title>
           <link>/sessions/probabilistic_while/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_while/</guid>
           <description></description>
         </item>
         <item>
           <title>Probability_Inequality_Completeness</title>
           <link>/sessions/probability_inequality_completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probability_inequality_completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Program-Conflict-Analysis</title>
           <link>/sessions/program-conflict-analysis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/program-conflict-analysis/</guid>
           <description></description>
         </item>
         <item>
           <title>Progress_Tracking</title>
           <link>/sessions/progress_tracking/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/progress_tracking/</guid>
           <description></description>
         </item>
         <item>
           <title>Projective_Geometry</title>
           <link>/sessions/projective_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/projective_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Projective_Measurements</title>
           <link>/sessions/projective_measurements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/projective_measurements/</guid>
           <description></description>
         </item>
         <item>
           <title>Promela</title>
           <link>/sessions/promela/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/promela/</guid>
           <description></description>
         </item>
         <item>
           <title>Proof_Strategy_Language</title>
           <link>/sessions/proof_strategy_language/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/proof_strategy_language/</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional_Logic_Class</title>
           <link>/sessions/propositional_logic_class/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/propositional_logic_class/</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional_Proof_Systems</title>
           <link>/sessions/propositional_proof_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/propositional_proof_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>PropResPI</title>
           <link>/sessions/proprespi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/proprespi/</guid>
           <description></description>
         </item>
         <item>
           <title>Prpu_Maxflow</title>
           <link>/sessions/prpu_maxflow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prpu_maxflow/</guid>
           <description></description>
         </item>
         <item>
           <title>PSemigroupsConvolution</title>
           <link>/sessions/psemigroupsconvolution/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/psemigroupsconvolution/</guid>
           <description></description>
         </item>
         <item>
           <title>PseudoHoops</title>
           <link>/sessions/pseudohoops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pseudohoops/</guid>
           <description></description>
         </item>
         <item>
           <title>Psi_Calculi</title>
           <link>/sessions/psi_calculi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/psi_calculi/</guid>
           <description></description>
         </item>
         <item>
           <title>Ptolemys_Theorem</title>
           <link>/sessions/ptolemys_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ptolemys_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Public_Announcement_Logic</title>
           <link>/sessions/public_announcement_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/public_announcement_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Pushdown_Systems</title>
           <link>/sessions/pushdown_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pushdown_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Q0_Metatheory</title>
           <link>/sessions/q0_metatheory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/q0_metatheory/</guid>
           <description></description>
         </item>
         <item>
           <title>Q0_Soundness</title>
           <link>/sessions/q0_soundness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/q0_soundness/</guid>
           <description></description>
         </item>
         <item>
           <title>QBF_Solver_Verification</title>
           <link>/sessions/qbf_solver_verification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qbf_solver_verification/</guid>
           <description></description>
         </item>
         <item>
           <title>QHLProver</title>
           <link>/sessions/qhlprover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qhlprover/</guid>
           <description></description>
         </item>
         <item>
           <title>QR_Decomposition</title>
           <link>/sessions/qr_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qr_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales</title>
           <link>/sessions/quantales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantales/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales_Converse</title>
           <link>/sessions/quantales_converse/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantales_converse/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantifier_Elimination_Hybrid</title>
           <link>/sessions/quantifier_elimination_hybrid/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantifier_elimination_hybrid/</guid>
           <description></description>
         </item>
         <item>
           <title>Quasi_Borel_Spaces</title>
           <link>/sessions/quasi_borel_spaces/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quasi_borel_spaces/</guid>
           <description></description>
         </item>
         <item>
           <title>Quaternions</title>
           <link>/sessions/quaternions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quaternions/</guid>
           <description></description>
         </item>
         <item>
           <title>Query_Optimization</title>
           <link>/sessions/query_optimization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/query_optimization/</guid>
           <description></description>
         </item>
         <item>
           <title>Quick_Sort_Cost</title>
           <link>/sessions/quick_sort_cost/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quick_sort_cost/</guid>
           <description></description>
         </item>
         <item>
           <title>Ramsey-Infinite</title>
           <link>/sessions/ramsey-infinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ramsey-infinite/</guid>
           <description></description>
         </item>
         <item>
           <title>Random_BSTs</title>
           <link>/sessions/random_bsts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/random_bsts/</guid>
           <description></description>
         </item>
         <item>
           <title>Random_Graph_Subgraph_Threshold</title>
           <link>/sessions/random_graph_subgraph_threshold/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/random_graph_subgraph_threshold/</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised_BSTs</title>
           <link>/sessions/randomised_bsts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/randomised_bsts/</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised_Social_Choice</title>
           <link>/sessions/randomised_social_choice/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/randomised_social_choice/</guid>
           <description></description>
         </item>
         <item>
           <title>Rank_Nullity_Theorem</title>
           <link>/sessions/rank_nullity_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rank_nullity_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Impl</title>
           <link>/sessions/real_impl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_impl/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Power</title>
           <link>/sessions/real_power/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_power/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Time_Deque</title>
           <link>/sessions/real_time_deque/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_time_deque/</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion-Addition</title>
           <link>/sessions/recursion-addition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/recursion-addition/</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion-Theory-I</title>
           <link>/sessions/recursion-theory-i/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/recursion-theory-i/</guid>
           <description></description>
         </item>
         <item>
           <title>Refine_Imperative_HOL</title>
           <link>/sessions/refine_imperative_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refine_imperative_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>Refine_Monadic</title>
           <link>/sessions/refine_monadic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refine_monadic/</guid>
           <description></description>
         </item>
         <item>
           <title>RefinementReactive</title>
           <link>/sessions/refinementreactive/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refinementreactive/</guid>
           <description></description>
         </item>
         <item>
           <title>Regex_Equivalence</title>
           <link>/sessions/regex_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regex_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Region_Quadtrees</title>
           <link>/sessions/region_quadtrees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/region_quadtrees/</guid>
           <description></description>
         </item>
         <item>
           <title>Registers</title>
           <link>/sessions/registers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/registers/</guid>
           <description></description>
         </item>
         <item>
           <title>Regression_Test_Selection</title>
           <link>/sessions/regression_test_selection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regression_test_selection/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular_Algebras</title>
           <link>/sessions/regular_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular_Tree_Relations</title>
           <link>/sessions/regular_tree_relations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular_tree_relations/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular-Sets</title>
           <link>/sessions/regular-sets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular-sets/</guid>
           <description></description>
         </item>
         <item>
           <title>Relation_Algebra</title>
           <link>/sessions/relation_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relation_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Cardinality</title>
           <link>/sessions/relational_cardinality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_cardinality/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Disjoint_Set_Forests</title>
           <link>/sessions/relational_disjoint_set_forests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_disjoint_set_forests/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Forests</title>
           <link>/sessions/relational_forests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_forests/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Method</title>
           <link>/sessions/relational_method/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_method/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Minimum_Spanning_Trees</title>
           <link>/sessions/relational_minimum_spanning_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_minimum_spanning_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Paths</title>
           <link>/sessions/relational_paths/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_paths/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational-Incorrectness-Logic</title>
           <link>/sessions/relational-incorrectness-logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational-incorrectness-logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Rensets</title>
           <link>/sessions/rensets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rensets/</guid>
           <description></description>
         </item>
         <item>
           <title>Rep_Fin_Groups</title>
           <link>/sessions/rep_fin_groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rep_fin_groups/</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated_Lattices</title>
           <link>/sessions/residuated_lattices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/residuated_lattices/</guid>
           <description></description>
         </item>
         <item>
           <title>ResiduatedTransitionSystem</title>
           <link>/sessions/residuatedtransitionsystem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/residuatedtransitionsystem/</guid>
           <description></description>
         </item>
         <item>
           <title>Resolution_FOL</title>
           <link>/sessions/resolution_fol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/resolution_fol/</guid>
           <description></description>
         </item>
         <item>
           <title>Rewrite_Properties_Reduction</title>
           <link>/sessions/rewrite_properties_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rewrite_properties_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Rewriting_Z</title>
           <link>/sessions/rewriting_z/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rewriting_z/</guid>
           <description></description>
         </item>
         <item>
           <title>Ribbon_Proofs</title>
           <link>/sessions/ribbon_proofs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ribbon_proofs/</guid>
           <description></description>
         </item>
         <item>
           <title>RIPEMD-160-SPARK</title>
           <link>/sessions/ripemd-160-spark/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ripemd-160-spark/</guid>
           <description></description>
         </item>
         <item>
           <title>Risk_Free_Lending</title>
           <link>/sessions/risk_free_lending/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/risk_free_lending/</guid>
           <description></description>
         </item>
         <item>
           <title>Robbins-Conjecture</title>
           <link>/sessions/robbins-conjecture/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robbins-conjecture/</guid>
           <description></description>
         </item>
         <item>
           <title>ROBDD</title>
           <link>/sessions/robdd/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robdd/</guid>
           <description></description>
         </item>
         <item>
           <title>Robinson_Arithmetic</title>
           <link>/sessions/robinson_arithmetic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robinson_arithmetic/</guid>
           <description></description>
         </item>
         <item>
           <title>Root_Balanced_Tree</title>
           <link>/sessions/root_balanced_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/root_balanced_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Roth_Arithmetic_Progressions</title>
           <link>/sessions/roth_arithmetic_progressions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/roth_arithmetic_progressions/</guid>
           <description></description>
         </item>
         <item>
           <title>Routing</title>
           <link>/sessions/routing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/routing/</guid>
           <description></description>
         </item>
         <item>
           <title>Roy_Floyd_Warshall</title>
           <link>/sessions/roy_floyd_warshall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/roy_floyd_warshall/</guid>
           <description></description>
         </item>
         <item>
           <title>RSAPSS</title>
           <link>/sessions/rsapss/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rsapss/</guid>
           <description></description>
         </item>
         <item>
           <title>S_Finite_Measure_Monad</title>
           <link>/sessions/s_finite_measure_monad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/s_finite_measure_monad/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_Distance</title>
           <link>/sessions/safe_distance/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_distance/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_OCL</title>
           <link>/sessions/safe_ocl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_ocl/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_Range_RC</title>
           <link>/sessions/safe_range_rc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_range_rc/</guid>
           <description></description>
         </item>
         <item>
           <title>SATSolverVerification</title>
           <link>/sessions/satsolververification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/satsolververification/</guid>
           <description></description>
         </item>
         <item>
           <title>Saturation_Framework</title>
           <link>/sessions/saturation_framework/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/saturation_framework/</guid>
           <description></description>
         </item>
         <item>
           <title>Saturation_Framework_Extensions</title>
           <link>/sessions/saturation_framework_extensions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/saturation_framework_extensions/</guid>
           <description></description>
         </item>
         <item>
           <title>Sauer_Shelah_Lemma</title>
           <link>/sessions/sauer_shelah_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sauer_shelah_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>SC_DOM_Components</title>
           <link>/sessions/sc_dom_components/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sc_dom_components/</guid>
           <description></description>
         </item>
         <item>
           <title>SCC_Bloemen_Sequential</title>
           <link>/sessions/scc_bloemen_sequential/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/scc_bloemen_sequential/</guid>
           <description></description>
         </item>
         <item>
           <title>Schutz_Spacetime</title>
           <link>/sessions/schutz_spacetime/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/schutz_spacetime/</guid>
           <description></description>
         </item>
         <item>
           <title>Schwartz_Zippel</title>
           <link>/sessions/schwartz_zippel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/schwartz_zippel/</guid>
           <description></description>
         </item>
         <item>
           <title>SDS_Impossibility</title>
           <link>/sessions/sds_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sds_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Secondary_Sylow</title>
           <link>/sessions/secondary_sylow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/secondary_sylow/</guid>
           <description></description>
         </item>
         <item>
           <title>Security_Protocol_Refinement</title>
           <link>/sessions/security_protocol_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/security_protocol_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>Selection_Heap_Sort</title>
           <link>/sessions/selection_heap_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/selection_heap_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>SenSocialChoice</title>
           <link>/sessions/sensocialchoice/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sensocialchoice/</guid>
           <description></description>
         </item>
         <item>
           <title>Separata</title>
           <link>/sessions/separata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separata/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Algebra</title>
           <link>/sessions/separation_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Logic_Imperative_HOL</title>
           <link>/sessions/separation_logic_imperative_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_logic_imperative_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Logic_Unbounded</title>
           <link>/sessions/separation_logic_unbounded/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_logic_unbounded/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_Basic</title>
           <link>/sessions/sepref_basic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_basic/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_IICF</title>
           <link>/sessions/sepref_iicf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_iicf/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_Prereq</title>
           <link>/sessions/sepref_prereq/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_prereq/</guid>
           <description></description>
         </item>
         <item>
           <title>SequentInvertibility</title>
           <link>/sessions/sequentinvertibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sequentinvertibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Shadow_DOM</title>
           <link>/sessions/shadow_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shadow_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Shadow_SC_DOM</title>
           <link>/sessions/shadow_sc_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shadow_sc_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Shivers-CFA</title>
           <link>/sessions/shivers-cfa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shivers-cfa/</guid>
           <description></description>
         </item>
         <item>
           <title>ShortestPath</title>
           <link>/sessions/shortestpath/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shortestpath/</guid>
           <description></description>
         </item>
         <item>
           <title>Show</title>
           <link>/sessions/show/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/show/</guid>
           <description></description>
         </item>
         <item>
           <title>SIFPL</title>
           <link>/sessions/sifpl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sifpl/</guid>
           <description></description>
         </item>
         <item>
           <title>SIFUM_Type_Systems</title>
           <link>/sessions/sifum_type_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sifum_type_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Sigma_Commit_Crypto</title>
           <link>/sessions/sigma_commit_crypto/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sigma_commit_crypto/</guid>
           <description></description>
         </item>
         <item>
           <title>Signature_Groebner</title>
           <link>/sessions/signature_groebner/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/signature_groebner/</guid>
           <description></description>
         </item>
         <item>
           <title>Simpl</title>
           <link>/sessions/simpl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simpl/</guid>
           <description></description>
         </item>
         <item>
           <title>Simple_Clause_Learning</title>
           <link>/sessions/simple_clause_learning/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simple_clause_learning/</guid>
           <description></description>
         </item>
         <item>
           <title>Simple_Firewall</title>
           <link>/sessions/simple_firewall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simple_firewall/</guid>
           <description></description>
         </item>
         <item>
           <title>Simplex</title>
           <link>/sessions/simplex/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplex/</guid>
           <description></description>
         </item>
         <item>
           <title>Simplicial_complexes_and_boolean_functions</title>
           <link>/sessions/simplicial_complexes_and_boolean_functions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplicial_complexes_and_boolean_functions/</guid>
           <description></description>
         </item>
         <item>
           <title>SimplifiedOntologicalArgument</title>
           <link>/sessions/simplifiedontologicalargument/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplifiedontologicalargument/</guid>
           <description></description>
         </item>
         <item>
           <title>Skew_Heap</title>
           <link>/sessions/skew_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/skew_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>Skip_Lists</title>
           <link>/sessions/skip_lists/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/skip_lists/</guid>
           <description></description>
         </item>
         <item>
           <title>Slicing</title>
           <link>/sessions/slicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/slicing/</guid>
           <description></description>
         </item>
         <item>
           <title>Sliding_Window_Algorithm</title>
           <link>/sessions/sliding_window_algorithm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sliding_window_algorithm/</guid>
           <description></description>
         </item>
         <item>
           <title>SM</title>
           <link>/sessions/sm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sm/</guid>
           <description></description>
         </item>
         <item>
           <title>SM_Base</title>
           <link>/sessions/sm_base/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sm_base/</guid>
           <description></description>
         </item>
         <item>
           <title>Smith_Normal_Form</title>
           <link>/sessions/smith_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/smith_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>Smooth_Manifolds</title>
           <link>/sessions/smooth_manifolds/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/smooth_manifolds/</guid>
           <description></description>
         </item>
         <item>
           <title>Solidity</title>
           <link>/sessions/solidity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/solidity/</guid>
           <description></description>
         </item>
         <item>
           <title>Sophomores_Dream</title>
           <link>/sessions/sophomores_dream/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sophomores_dream/</guid>
           <description></description>
         </item>
         <item>
           <title>Sort_Encodings</title>
           <link>/sessions/sort_encodings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sort_encodings/</guid>
           <description></description>
         </item>
         <item>
           <title>Source_Coding_Theorem</title>
           <link>/sessions/source_coding_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/source_coding_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>SPARCv8</title>
           <link>/sessions/sparcv8/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sparcv8/</guid>
           <description></description>
         </item>
         <item>
           <title>SpecCheck</title>
           <link>/sessions/speccheck/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/speccheck/</guid>
           <description></description>
         </item>
         <item>
           <title>Special_Function_Bounds</title>
           <link>/sessions/special_function_bounds/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/special_function_bounds/</guid>
           <description></description>
         </item>
         <item>
           <title>Splay_Tree</title>
           <link>/sessions/splay_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/splay_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Sqrt_Babylonian</title>
           <link>/sessions/sqrt_babylonian/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sqrt_babylonian/</guid>
           <description></description>
         </item>
         <item>
           <title>Stable_Matching</title>
           <link>/sessions/stable_matching/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stable_matching/</guid>
           <description></description>
         </item>
         <item>
           <title>Stalnaker_Logic</title>
           <link>/sessions/stalnaker_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stalnaker_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Standard_Borel_Spaces</title>
           <link>/sessions/standard_borel_spaces/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/standard_borel_spaces/</guid>
           <description></description>
         </item>
         <item>
           <title>Statecharts</title>
           <link>/sessions/statecharts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/statecharts/</guid>
           <description></description>
         </item>
         <item>
           <title>Stateful_Protocol_Composition_and_Typing</title>
           <link>/sessions/stateful_protocol_composition_and_typing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stateful_protocol_composition_and_typing/</guid>
           <description></description>
         </item>
         <item>
           <title>Stellar_Quorums</title>
           <link>/sessions/stellar_quorums/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stellar_quorums/</guid>
           <description></description>
         </item>
         <item>
           <title>Stern_Brocot</title>
           <link>/sessions/stern_brocot/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stern_brocot/</guid>
           <description></description>
         </item>
         <item>
           <title>Stewart_Apollonius</title>
           <link>/sessions/stewart_apollonius/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stewart_apollonius/</guid>
           <description></description>
         </item>
         <item>
           <title>Stirling_Formula</title>
           <link>/sessions/stirling_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stirling_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Stochastic_Matrices</title>
           <link>/sessions/stochastic_matrices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stochastic_matrices/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Algebras</title>
           <link>/sessions/stone_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Kleene_Relation_Algebras</title>
           <link>/sessions/stone_kleene_relation_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_kleene_relation_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Relation_Algebras</title>
           <link>/sessions/stone_relation_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_relation_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Store_Buffer_Reduction</title>
           <link>/sessions/store_buffer_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/store_buffer_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Stream_Fusion_Code</title>
           <link>/sessions/stream_fusion_code/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stream_fusion_code/</guid>
           <description></description>
         </item>
         <item>
           <title>Stream-Fusion</title>
           <link>/sessions/stream-fusion/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stream-fusion/</guid>
           <description></description>
         </item>
         <item>
           <title>StrictOmegaCategories</title>
           <link>/sessions/strictomegacategories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/strictomegacategories/</guid>
           <description></description>
         </item>
         <item>
           <title>Strong_Security</title>
           <link>/sessions/strong_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/strong_security/</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm_Sequences</title>
           <link>/sessions/sturm_sequences/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sturm_sequences/</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm_Tarski</title>
           <link>/sessions/sturm_tarski/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sturm_tarski/</guid>
           <description></description>
         </item>
         <item>
           <title>Stuttering_Equivalence</title>
           <link>/sessions/stuttering_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stuttering_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Subresultants</title>
           <link>/sessions/subresultants/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/subresultants/</guid>
           <description></description>
         </item>
         <item>
           <title>Subset_Boolean_Algebras</title>
           <link>/sessions/subset_boolean_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/subset_boolean_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Sumcheck_Protocol</title>
           <link>/sessions/sumcheck_protocol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sumcheck_protocol/</guid>
           <description></description>
         </item>
         <item>
           <title>SumSquares</title>
           <link>/sessions/sumsquares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sumsquares/</guid>
           <description></description>
         </item>
         <item>
           <title>Sunflowers</title>
           <link>/sessions/sunflowers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sunflowers/</guid>
           <description></description>
         </item>
         <item>
           <title>SuperCalc</title>
           <link>/sessions/supercalc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/supercalc/</guid>
           <description></description>
         </item>
         <item>
           <title>Suppes_Theorem</title>
           <link>/sessions/suppes_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/suppes_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Surprise_Paradox</title>
           <link>/sessions/surprise_paradox/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/surprise_paradox/</guid>
           <description></description>
         </item>
         <item>
           <title>Symmetric_Polynomials</title>
           <link>/sessions/symmetric_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/symmetric_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax_Independent_Logic</title>
           <link>/sessions/syntax_independent_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/syntax_independent_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Synthetic_Completeness</title>
           <link>/sessions/synthetic_completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/synthetic_completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Szemeredi_Regularity</title>
           <link>/sessions/szemeredi_regularity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/szemeredi_regularity/</guid>
           <description></description>
         </item>
         <item>
           <title>Szpilrajn</title>
           <link>/sessions/szpilrajn/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/szpilrajn/</guid>
           <description></description>
         </item>
         <item>
           <title>Tail_Recursive_Functions</title>
           <link>/sessions/tail_recursive_functions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tail_recursive_functions/</guid>
           <description></description>
         </item>
         <item>
           <title>Tarskis_Geometry</title>
           <link>/sessions/tarskis_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tarskis_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Taylor_Models</title>
           <link>/sessions/taylor_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/taylor_models/</guid>
           <description></description>
         </item>
         <item>
           <title>TESL_Language</title>
           <link>/sessions/tesl_language/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tesl_language/</guid>
           <description></description>
         </item>
         <item>
           <title>Three_Circles</title>
           <link>/sessions/three_circles/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/three_circles/</guid>
           <description></description>
         </item>
         <item>
           <title>Three_Squares</title>
           <link>/sessions/three_squares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/three_squares/</guid>
           <description></description>
         </item>
         <item>
           <title>Timed_Automata</title>
           <link>/sessions/timed_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/timed_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>TLA</title>
           <link>/sessions/tla/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tla/</guid>
           <description></description>
         </item>
         <item>
           <title>Topological_Semantics</title>
           <link>/sessions/topological_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/topological_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Topology</title>
           <link>/sessions/topology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/topology/</guid>
           <description></description>
         </item>
         <item>
           <title>TortoiseHare</title>
           <link>/sessions/tortoisehare/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tortoisehare/</guid>
           <description></description>
         </item>
         <item>
           <title>Transcendence_Series_Hancl_Rucki</title>
           <link>/sessions/transcendence_series_hancl_rucki/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transcendence_series_hancl_rucki/</guid>
           <description></description>
         </item>
         <item>
           <title>Transformer_Semantics</title>
           <link>/sessions/transformer_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transformer_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Transition_Systems_and_Automata</title>
           <link>/sessions/transition_systems_and_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transition_systems_and_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive_Models</title>
           <link>/sessions/transitive_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive-Closure</title>
           <link>/sessions/transitive-closure/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive-closure/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive-Closure-II</title>
           <link>/sessions/transitive-closure-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive-closure-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Transport</title>
           <link>/sessions/transport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transport/</guid>
           <description></description>
         </item>
         <item>
           <title>Treaps</title>
           <link>/sessions/treaps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/treaps/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree_Decomposition</title>
           <link>/sessions/tree_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree_Enumeration</title>
           <link>/sessions/tree_enumeration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree_enumeration/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree-Automata</title>
           <link>/sessions/tree-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Triangle</title>
           <link>/sessions/triangle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/triangle/</guid>
           <description></description>
         </item>
         <item>
           <title>Trie</title>
           <link>/sessions/trie/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/trie/</guid>
           <description></description>
         </item>
         <item>
           <title>TsirelsonBound</title>
           <link>/sessions/tsirelsonbound/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tsirelsonbound/</guid>
           <description></description>
         </item>
         <item>
           <title>Turans_Graph_Theorem</title>
           <link>/sessions/turans_graph_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/turans_graph_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Twelvefold_Way</title>
           <link>/sessions/twelvefold_way/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/twelvefold_way/</guid>
           <description></description>
         </item>
         <item>
           <title>Two_Generated_Word_Monoids_Intersection</title>
           <link>/sessions/two_generated_word_monoids_intersection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/two_generated_word_monoids_intersection/</guid>
           <description></description>
         </item>
         <item>
           <title>Tycon</title>
           <link>/sessions/tycon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tycon/</guid>
           <description></description>
         </item>
         <item>
           <title>Types_Tableaus_and_Goedels_God</title>
           <link>/sessions/types_tableaus_and_goedels_god/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/types_tableaus_and_goedels_god/</guid>
           <description></description>
         </item>
         <item>
           <title>Types_To_Sets_Extension</title>
           <link>/sessions/types_to_sets_extension/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/types_to_sets_extension/</guid>
           <description></description>
         </item>
         <item>
           <title>Undirected_Graph_Theory</title>
           <link>/sessions/undirected_graph_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/undirected_graph_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Universal_Hash_Families</title>
           <link>/sessions/universal_hash_families/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/universal_hash_families/</guid>
           <description></description>
         </item>
         <item>
           <title>Universal_Turing_Machine</title>
           <link>/sessions/universal_turing_machine/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/universal_turing_machine/</guid>
           <description></description>
         </item>
         <item>
           <title>UpDown_Scheme</title>
           <link>/sessions/updown_scheme/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/updown_scheme/</guid>
           <description></description>
         </item>
         <item>
           <title>UPF</title>
           <link>/sessions/upf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/upf/</guid>
           <description></description>
         </item>
         <item>
           <title>UPF_Firewall</title>
           <link>/sessions/upf_firewall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
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diff --git a/web/sessions/approximate_model_counting/index.html b/web/sessions/approximate_model_counting/index.html
new file mode 100644
--- /dev/null
+++ b/web/sessions/approximate_model_counting/index.html
@@ -0,0 +1,105 @@
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+    </form>
+  <h1>
+    <span class='first'>A</span>pproximate_<span class='first'>M</span>odel_<span class='first'>C</span>ounting
+    
+  </h1>
+  <div>
+  </div>
+</header>
+      <div>
+        
+  <main id="theories">
+      <a id="ApproxMCPreliminaries" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/ApproxMCPreliminaries.html"><h2>ApproxMCPreliminaries</h2></a>
+      <a id="RandomXOR" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/RandomXOR.html"><h2>RandomXOR</h2></a>
+      <a id="RandomXORHashFamily" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/RandomXORHashFamily.html"><h2>RandomXORHashFamily</h2></a>
+      <a id="ApproxMCCore" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/ApproxMCCore.html"><h2>ApproxMCCore</h2></a>
+      <a id="ApproxMCCoreAnalysis" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/ApproxMCCoreAnalysis.html"><h2>ApproxMCCoreAnalysis</h2></a>
+      <a id="ApproxMCAnalysis" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/ApproxMCAnalysis.html"><h2>ApproxMCAnalysis</h2></a>
+      <a id="CertCheck" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/CertCheck.html"><h2>CertCheck</h2></a>
+      <a id="CertCheck_CNF_XOR" href="https://www.isa-afp.org/browser_info/current/AFP/Approximate_Model_Counting/CertCheck_CNF_XOR.html"><h2>CertCheck_CNF_XOR</h2></a>
+  </main>
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\ No newline at end of file
diff --git a/web/sessions/continued_fractions/index.html b/web/sessions/continued_fractions/index.html
new file mode 100644
--- /dev/null
+++ b/web/sessions/continued_fractions/index.html
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+    </form>
+  <h1>
+    <span class='first'>C</span>ontinued_<span class='first'>F</span>ractions
+    
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+  <div>
+  </div>
+</header>
+      <div>
+        
+  <main id="theories">
+      <a id="Continued_Fractions" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Continued_Fractions.html"><h2>Continued_Fractions</h2></a>
+      <a id="Quadratic_Irrationals" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Quadratic_Irrationals.html"><h2>Quadratic_Irrationals</h2></a>
+      <a id="E_CFrac" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/E_CFrac.html"><h2>E_CFrac</h2></a>
+      <a id="Sqrt_Nat_Cfrac" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Sqrt_Nat_Cfrac.html"><h2>Sqrt_Nat_Cfrac</h2></a>
+      <a id="Pell_Lifting" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Pell_Lifting.html"><h2>Pell_Lifting</h2></a>
+      <a id="Pell_Continued_Fraction" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Pell_Continued_Fraction.html"><h2>Pell_Continued_Fraction</h2></a>
+      <a id="Pell_Continued_Fraction_Tests" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Pell_Continued_Fraction_Tests.html"><h2>Pell_Continued_Fraction_Tests</h2></a>
+      <a id="Continued_Fraction_Approximation" href="https://www.isa-afp.org/browser_info/current/AFP/Continued_Fractions/Continued_Fraction_Approximation.html"><h2>Continued_Fraction_Approximation</h2></a>
+  </main>
+        
+      </div>
+    </div>
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+</html>
\ No newline at end of file
diff --git a/web/sessions/go/index.html b/web/sessions/go/index.html
new file mode 100644
--- /dev/null
+++ b/web/sessions/go/index.html
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+  </h1>
+  <div>
+  </div>
+</header>
+      <div>
+        
+  <main id="theories">
+      <a id="Go_Setup" href="https://www.isa-afp.org/browser_info/current/AFP/Go/Go_Setup.html"><h2>Go_Setup</h2></a>
+  </main>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/sessions/go_test_quick/index.html b/web/sessions/go_test_quick/index.html
new file mode 100644
--- /dev/null
+++ b/web/sessions/go_test_quick/index.html
@@ -0,0 +1,98 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+  <meta charset="utf-8" />
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+    <title>Go_Test_Quick - Archive of Formal Proofs</title>
+    <meta name="description" content="A collection of proof libraries, examples, and larger
+     scientific developments, mechanically checked in the theorem prover Isabelle.">
+
+  <meta property="og:title" content="Go_Test_Quick" />
+<meta property="og:description" content="" />
+<meta property="og:type" content="article" />
+<meta property="og:url" content="/sessions/go_test_quick/" /><meta property="og:image" content="/images/afp.png"/><meta property="article:section" content="sessions" />
+
+<meta property="og:site_name" content="Archive of Formal Proofs" />
+
+
+  <meta name="twitter:card" content="summary_large_image"/>
+<meta name="twitter:image" content="/images/afp.png"/>
+
+<meta name="twitter:title" content="Go_Test_Quick"/>
+<meta name="twitter:description" content=""/>
+
+  <link rel="stylesheet" type="text/css" href="../../css/front.min.css">
+    <link rel="stylesheet" type="text/css" href="../../css/isabelle.css">
+
+  <link rel="icon" href="../../images/favicon.ico" type="image/icon">
+
+  <script src="../../js/obfuscate.js"></script>
+  <script src="../../js/flexsearch.bundle.js"></script>
+  <script src="../../js/scroll-spy.js"></script>
+  <script src="../../js/theory.js"></script>
+  <script src="../../js/util.js"></script>
+    <script src="../../js/header-search.js"></script>
+  <script src="../../js/search-autocomplete.js"></script>
+</head>
+
+  <body class='mathjax_ignore theories'>
+    <aside>
+        
+<div id="menu-toggle">
+  <input id="toggle" type="checkbox" />
+  <label for="toggle">
+    <span>menu</span>
+    <img src="../../images/menu.svg" alt="Menu" />
+  </label>
+
+  <a href="../../" class='logo-link'>
+    <img src="../../images/afp.png" alt='Logo of the Archive of Formal Proofs'
+         class="logo">
+  </a>
+
+  <nav id="menu">
+  <div>
+    <a href="../../" class='logo-link'>
+      <img src="../../images/afp.png" alt='Logo of the Archive of Formal Proofs'
+           class="logo">
+    </a>
+      <ul id="return">
+        <li><a href="../../entries/Go.html">Return to entry</a></li>
+      </ul>
+    <hr>
+    <ul id="theory-navbar" class="list-group"></ul>
+  </div>
+  </nav>
+</div>
+    </aside>
+    <div class='content'>
+      <header>
+    <form autocomplete="off" action="../../search">
+      <div class='form-container'>
+        <input id="search-input" type="search" size="31" maxlength="255" value=""
+               aria-label="Search the AFP" list="autocomplete"><button
+               id="search-button" type="button">
+          <img src="../../images/search.svg" alt="Search"/>
+        </button>
+        <datalist id="autocomplete">
+        </datalist>
+      </div>
+    </form>
+  <h1>
+    <span class='first'>G</span>o_<span class='first'>T</span>est_<span class='first'>Q</span>uick
+    
+  </h1>
+  <div>
+  </div>
+</header>
+      <div>
+        
+  <main id="theories">
+      <a id="RBT_Test" href="https://www.isa-afp.org/browser_info/current/AFP/Go_Test_Quick/RBT_Test.html"><h2>RBT_Test</h2></a>
+  </main>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/sessions/go_test_slow/index.html b/web/sessions/go_test_slow/index.html
new file mode 100644
--- /dev/null
+++ b/web/sessions/go_test_slow/index.html
@@ -0,0 +1,100 @@
+<!DOCTYPE html>
+<html lang="en">
+  <head>
+  <meta charset="utf-8" />
+  <meta http-equiv="X-UA-Compatible" content="IE=edge">
+  <meta name="viewport" content="width=device-width, initial-scale=1">
+    <title>Go_Test_Slow - Archive of Formal Proofs</title>
+    <meta name="description" content="A collection of proof libraries, examples, and larger
+     scientific developments, mechanically checked in the theorem prover Isabelle.">
+
+  <meta property="og:title" content="Go_Test_Slow" />
+<meta property="og:description" content="" />
+<meta property="og:type" content="article" />
+<meta property="og:url" content="/sessions/go_test_slow/" /><meta property="og:image" content="/images/afp.png"/><meta property="article:section" content="sessions" />
+
+<meta property="og:site_name" content="Archive of Formal Proofs" />
+
+
+  <meta name="twitter:card" content="summary_large_image"/>
+<meta name="twitter:image" content="/images/afp.png"/>
+
+<meta name="twitter:title" content="Go_Test_Slow"/>
+<meta name="twitter:description" content=""/>
+
+  <link rel="stylesheet" type="text/css" href="../../css/front.min.css">
+    <link rel="stylesheet" type="text/css" href="../../css/isabelle.css">
+
+  <link rel="icon" href="../../images/favicon.ico" type="image/icon">
+
+  <script src="../../js/obfuscate.js"></script>
+  <script src="../../js/flexsearch.bundle.js"></script>
+  <script src="../../js/scroll-spy.js"></script>
+  <script src="../../js/theory.js"></script>
+  <script src="../../js/util.js"></script>
+    <script src="../../js/header-search.js"></script>
+  <script src="../../js/search-autocomplete.js"></script>
+</head>
+
+  <body class='mathjax_ignore theories'>
+    <aside>
+        
+<div id="menu-toggle">
+  <input id="toggle" type="checkbox" />
+  <label for="toggle">
+    <span>menu</span>
+    <img src="../../images/menu.svg" alt="Menu" />
+  </label>
+
+  <a href="../../" class='logo-link'>
+    <img src="../../images/afp.png" alt='Logo of the Archive of Formal Proofs'
+         class="logo">
+  </a>
+
+  <nav id="menu">
+  <div>
+    <a href="../../" class='logo-link'>
+      <img src="../../images/afp.png" alt='Logo of the Archive of Formal Proofs'
+           class="logo">
+    </a>
+      <ul id="return">
+        <li><a href="../../entries/Go.html">Return to entry</a></li>
+      </ul>
+    <hr>
+    <ul id="theory-navbar" class="list-group"></ul>
+  </div>
+  </nav>
+</div>
+    </aside>
+    <div class='content'>
+      <header>
+    <form autocomplete="off" action="../../search">
+      <div class='form-container'>
+        <input id="search-input" type="search" size="31" maxlength="255" value=""
+               aria-label="Search the AFP" list="autocomplete"><button
+               id="search-button" type="button">
+          <img src="../../images/search.svg" alt="Search"/>
+        </button>
+        <datalist id="autocomplete">
+        </datalist>
+      </div>
+    </form>
+  <h1>
+    <span class='first'>G</span>o_<span class='first'>T</span>est_<span class='first'>S</span>low
+    
+  </h1>
+  <div>
+  </div>
+</header>
+      <div>
+        
+  <main id="theories">
+      <a id="Candidates" href="https://www.isa-afp.org/browser_info/current/AFP/Go_Test_Slow/Candidates.html"><h2>Candidates</h2></a>
+      <a id="Generate" href="https://www.isa-afp.org/browser_info/current/AFP/Go_Test_Slow/Generate.html"><h2>Generate</h2></a>
+      <a id="Generate_Binary_Nat" href="https://www.isa-afp.org/browser_info/current/AFP/Go_Test_Slow/Generate_Binary_Nat.html"><h2>Generate_Binary_Nat</h2></a>
+  </main>
+        
+      </div>
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/web/sessions/index.xml b/web/sessions/index.xml
--- a/web/sessions/index.xml
+++ b/web/sessions/index.xml
@@ -1,5812 +1,5847 @@
 <?xml version="1.0" encoding="utf-8" standalone="yes"?>
 <rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom">
   <channel>
     <title>Sessions on Archive of Formal Proofs
     </title>
     <link>/sessions/</link>
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         Recent content in Sessions 
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     <generator>Hugo -- gohugo.io</generator>
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           <description></description>
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           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/applicative_lifting/</guid>
           <description></description>
         </item>
         <item>
+          <title>Approximate_Model_Counting</title>
+          <link>/sessions/approximate_model_counting/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/approximate_model_counting/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Approximation_Algorithms</title>
           <link>/sessions/approximation_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/approximation_algorithms/</guid>
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         <item>
           <title>BinarySearchTree</title>
           <link>/sessions/binarysearchtree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binarysearchtree/</guid>
           <description></description>
         </item>
         <item>
           <title>Binding_Syntax_Theory</title>
           <link>/sessions/binding_syntax_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binding_syntax_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial-Heaps</title>
           <link>/sessions/binomial-heaps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binomial-heaps/</guid>
           <description></description>
         </item>
         <item>
           <title>Binomial-Queues</title>
           <link>/sessions/binomial-queues/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/binomial-queues/</guid>
           <description></description>
         </item>
         <item>
           <title>BirdKMP</title>
           <link>/sessions/birdkmp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/birdkmp/</guid>
           <description></description>
         </item>
         <item>
           <title>Birkhoff_Finite_Distributive_Lattices</title>
           <link>/sessions/birkhoff_finite_distributive_lattices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/birkhoff_finite_distributive_lattices/</guid>
           <description></description>
         </item>
         <item>
           <title>Blue_Eyes</title>
           <link>/sessions/blue_eyes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/blue_eyes/</guid>
           <description></description>
         </item>
         <item>
           <title>BNF_CC</title>
           <link>/sessions/bnf_cc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bnf_cc/</guid>
           <description></description>
         </item>
         <item>
           <title>BNF_Operations</title>
           <link>/sessions/bnf_operations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bnf_operations/</guid>
           <description></description>
         </item>
         <item>
           <title>Bondy</title>
           <link>/sessions/bondy/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bondy/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolean_Expression_Checkers</title>
           <link>/sessions/boolean_expression_checkers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolean_expression_checkers/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos_Curious_Inference</title>
           <link>/sessions/boolos_curious_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolos_curious_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Boolos_Curious_Inference_Automated</title>
           <link>/sessions/boolos_curious_inference_automated/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/boolos_curious_inference_automated/</guid>
           <description></description>
         </item>
         <item>
           <title>Bounded_Deducibility_Security</title>
           <link>/sessions/bounded_deducibility_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bounded_deducibility_security/</guid>
           <description></description>
         </item>
         <item>
           <title>BTree</title>
           <link>/sessions/btree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/btree/</guid>
           <description></description>
         </item>
         <item>
           <title>Buchi_Complementation</title>
           <link>/sessions/buchi_complementation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buchi_complementation/</guid>
           <description></description>
         </item>
         <item>
           <title>Budan_Fourier</title>
           <link>/sessions/budan_fourier/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/budan_fourier/</guid>
           <description></description>
         </item>
         <item>
           <title>Buffons_Needle</title>
           <link>/sessions/buffons_needle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buffons_needle/</guid>
           <description></description>
         </item>
         <item>
           <title>Buildings</title>
           <link>/sessions/buildings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/buildings/</guid>
           <description></description>
         </item>
         <item>
           <title>BytecodeLogicJmlTypes</title>
           <link>/sessions/bytecodelogicjmltypes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/bytecodelogicjmltypes/</guid>
           <description></description>
         </item>
         <item>
           <title>C2KA_DistributedSystems</title>
           <link>/sessions/c2ka_distributedsystems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/c2ka_distributedsystems/</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML</title>
           <link>/sessions/cakeml/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cakeml/</guid>
           <description></description>
         </item>
         <item>
           <title>CakeML_Codegen</title>
           <link>/sessions/cakeml_codegen/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cakeml_codegen/</guid>
           <description></description>
         </item>
         <item>
           <title>Call_Arity</title>
           <link>/sessions/call_arity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/call_arity/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Equiv_Relations</title>
           <link>/sessions/card_equiv_relations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_equiv_relations/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Multisets</title>
           <link>/sessions/card_multisets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_multisets/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Number_Partitions</title>
           <link>/sessions/card_number_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_number_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Card_Partitions</title>
           <link>/sessions/card_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/card_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Cardinality_Continuum</title>
           <link>/sessions/cardinality_continuum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cardinality_continuum/</guid>
           <description></description>
         </item>
         <item>
           <title>Cartan_FP</title>
           <link>/sessions/cartan_fp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cartan_fp/</guid>
           <description></description>
         </item>
         <item>
           <title>Case_Labeling</title>
           <link>/sessions/case_labeling/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/case_labeling/</guid>
           <description></description>
         </item>
         <item>
           <title>Catalan_Numbers</title>
           <link>/sessions/catalan_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/catalan_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Category</title>
           <link>/sessions/category/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category/</guid>
           <description></description>
         </item>
         <item>
           <title>Category2</title>
           <link>/sessions/category2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category2/</guid>
           <description></description>
         </item>
         <item>
           <title>Category3</title>
           <link>/sessions/category3/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/category3/</guid>
           <description></description>
         </item>
         <item>
           <title>Catoids</title>
           <link>/sessions/catoids/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/catoids/</guid>
           <description></description>
         </item>
         <item>
           <title>Cauchy</title>
           <link>/sessions/cauchy/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cauchy/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Automata</title>
           <link>/sessions/cava_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Base</title>
           <link>/sessions/cava_base/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_base/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_LTL_Modelchecker</title>
           <link>/sessions/cava_ltl_modelchecker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_ltl_modelchecker/</guid>
           <description></description>
         </item>
         <item>
           <title>CAVA_Setup</title>
           <link>/sessions/cava_setup/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cava_setup/</guid>
           <description></description>
         </item>
         <item>
           <title>Cayley_Hamilton</title>
           <link>/sessions/cayley_hamilton/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cayley_hamilton/</guid>
           <description></description>
         </item>
         <item>
           <title>CCS</title>
           <link>/sessions/ccs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ccs/</guid>
           <description></description>
         </item>
         <item>
           <title>Certification_Monads</title>
           <link>/sessions/certification_monads/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/certification_monads/</guid>
           <description></description>
         </item>
         <item>
           <title>Ceva</title>
           <link>/sessions/ceva/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ceva/</guid>
           <description></description>
         </item>
         <item>
           <title>Chandy_Lamport</title>
           <link>/sessions/chandy_lamport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chandy_lamport/</guid>
           <description></description>
         </item>
         <item>
           <title>Chebyshev_Polynomials</title>
           <link>/sessions/chebyshev_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chebyshev_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>CHERI-C_Memory_Model</title>
           <link>/sessions/cheri-c_memory_model/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cheri-c_memory_model/</guid>
           <description></description>
         </item>
         <item>
           <title>Chord_Segments</title>
           <link>/sessions/chord_segments/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/chord_segments/</guid>
           <description></description>
         </item>
         <item>
           <title>Circus</title>
           <link>/sessions/circus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/circus/</guid>
           <description></description>
         </item>
         <item>
           <title>CISC-Kernel</title>
           <link>/sessions/cisc-kernel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cisc-kernel/</guid>
           <description></description>
         </item>
         <item>
           <title>Clean</title>
           <link>/sessions/clean/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clean/</guid>
           <description></description>
         </item>
         <item>
           <title>Clique_and_Monotone_Circuits</title>
           <link>/sessions/clique_and_monotone_circuits/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clique_and_monotone_circuits/</guid>
           <description></description>
         </item>
         <item>
           <title>ClockSynchInst</title>
           <link>/sessions/clocksynchinst/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/clocksynchinst/</guid>
           <description></description>
         </item>
         <item>
           <title>Closest_Pair_Points</title>
           <link>/sessions/closest_pair_points/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/closest_pair_points/</guid>
           <description></description>
         </item>
         <item>
           <title>CoCon</title>
           <link>/sessions/cocon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cocon/</guid>
           <description></description>
         </item>
         <item>
           <title>CofGroups</title>
           <link>/sessions/cofgroups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cofgroups/</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive</title>
           <link>/sessions/coinductive/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coinductive/</guid>
           <description></description>
         </item>
         <item>
           <title>Coinductive_Languages</title>
           <link>/sessions/coinductive_languages/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coinductive_languages/</guid>
           <description></description>
         </item>
         <item>
           <title>Collections</title>
           <link>/sessions/collections/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/collections/</guid>
           <description></description>
         </item>
         <item>
           <title>Collections_Examples</title>
           <link>/sessions/collections_examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/collections_examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinable_Wands</title>
           <link>/sessions/combinable_wands/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinable_wands/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorial_Enumeration_Algorithms</title>
           <link>/sessions/combinatorial_enumeration_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorial_enumeration_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words</title>
           <link>/sessions/combinatorics_words/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words_Graph_Lemma</title>
           <link>/sessions/combinatorics_words_graph_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words_graph_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>Combinatorics_Words_Lyndon</title>
           <link>/sessions/combinatorics_words_lyndon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/combinatorics_words_lyndon/</guid>
           <description></description>
         </item>
         <item>
           <title>CommCSL</title>
           <link>/sessions/commcsl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/commcsl/</guid>
           <description></description>
         </item>
         <item>
           <title>Commuting_Hermitian</title>
           <link>/sessions/commuting_hermitian/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/commuting_hermitian/</guid>
           <description></description>
         </item>
         <item>
           <title>Comparison_Sort_Lower_Bound</title>
           <link>/sessions/comparison_sort_lower_bound/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/comparison_sort_lower_bound/</guid>
           <description></description>
         </item>
         <item>
           <title>Compiling-Exceptions-Correctly</title>
           <link>/sessions/compiling-exceptions-correctly/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/compiling-exceptions-correctly/</guid>
           <description></description>
         </item>
         <item>
           <title>Complete_Non_Orders</title>
           <link>/sessions/complete_non_orders/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complete_non_orders/</guid>
           <description></description>
         </item>
         <item>
           <title>Completeness</title>
           <link>/sessions/completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Bounded_Operators</title>
           <link>/sessions/complex_bounded_operators/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_bounded_operators/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Bounded_Operators_Dependencies</title>
           <link>/sessions/complex_bounded_operators_dependencies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_bounded_operators_dependencies/</guid>
           <description></description>
         </item>
         <item>
           <title>Complex_Geometry</title>
           <link>/sessions/complex_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complex_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Complx</title>
           <link>/sessions/complx/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/complx/</guid>
           <description></description>
         </item>
         <item>
           <title>ComponentDependencies</title>
           <link>/sessions/componentdependencies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/componentdependencies/</guid>
           <description></description>
         </item>
         <item>
           <title>Concentration_Inequalities</title>
           <link>/sessions/concentration_inequalities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concentration_inequalities/</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent_Ref_Alg</title>
           <link>/sessions/concurrent_ref_alg/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrent_ref_alg/</guid>
           <description></description>
         </item>
         <item>
           <title>Concurrent_Revisions</title>
           <link>/sessions/concurrent_revisions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrent_revisions/</guid>
           <description></description>
         </item>
         <item>
           <title>ConcurrentGC</title>
           <link>/sessions/concurrentgc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrentgc/</guid>
           <description></description>
         </item>
         <item>
           <title>ConcurrentIMP</title>
           <link>/sessions/concurrentimp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/concurrentimp/</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional_Simplification</title>
           <link>/sessions/conditional_simplification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/conditional_simplification/</guid>
           <description></description>
         </item>
         <item>
           <title>Conditional_Transfer_Rule</title>
           <link>/sessions/conditional_transfer_rule/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/conditional_transfer_rule/</guid>
           <description></description>
         </item>
         <item>
           <title>Consensus_Refined</title>
           <link>/sessions/consensus_refined/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/consensus_refined/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive_Cryptography</title>
           <link>/sessions/constructive_cryptography/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructive_cryptography/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructive_Cryptography_CM</title>
           <link>/sessions/constructive_cryptography_cm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructive_cryptography_cm/</guid>
           <description></description>
         </item>
         <item>
           <title>Constructor_Funs</title>
           <link>/sessions/constructor_funs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/constructor_funs/</guid>
           <description></description>
         </item>
         <item>
           <title>Containers</title>
           <link>/sessions/containers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/containers/</guid>
           <description></description>
         </item>
         <item>
           <title>Containers-Benchmarks</title>
           <link>/sessions/containers-benchmarks/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/containers-benchmarks/</guid>
           <description></description>
         </item>
         <item>
+          <title>Continued_Fractions</title>
+          <link>/sessions/continued_fractions/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/continued_fractions/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Cook_Levin</title>
           <link>/sessions/cook_levin/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cook_levin/</guid>
           <description></description>
         </item>
         <item>
           <title>Core_DOM</title>
           <link>/sessions/core_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/core_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Core_SC_DOM</title>
           <link>/sessions/core_sc_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/core_sc_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>CoreC&#43;&#43;</title>
           <link>/sessions/corec&#43;&#43;/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/corec&#43;&#43;/</guid>
           <description></description>
         </item>
         <item>
           <title>Correctness_Algebras</title>
           <link>/sessions/correctness_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/correctness_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMed</title>
           <link>/sessions/cosmed/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cosmed/</guid>
           <description></description>
         </item>
         <item>
           <title>CoSMeDis</title>
           <link>/sessions/cosmedis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cosmedis/</guid>
           <description></description>
         </item>
         <item>
           <title>Cotangent_PFD_Formula</title>
           <link>/sessions/cotangent_pfd_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cotangent_pfd_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Count_Complex_Roots</title>
           <link>/sessions/count_complex_roots/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/count_complex_roots/</guid>
           <description></description>
         </item>
         <item>
           <title>Coupledsim_Contrasim</title>
           <link>/sessions/coupledsim_contrasim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/coupledsim_contrasim/</guid>
           <description></description>
         </item>
         <item>
           <title>CRDT</title>
           <link>/sessions/crdt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crdt/</guid>
           <description></description>
         </item>
         <item>
           <title>CryptHOL</title>
           <link>/sessions/crypthol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crypthol/</guid>
           <description></description>
         </item>
         <item>
           <title>Crypto_Standards</title>
           <link>/sessions/crypto_standards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crypto_standards/</guid>
           <description></description>
         </item>
         <item>
           <title>CryptoBasedCompositionalProperties</title>
           <link>/sessions/cryptobasedcompositionalproperties/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cryptobasedcompositionalproperties/</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber</title>
           <link>/sessions/crystals-kyber/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crystals-kyber/</guid>
           <description></description>
         </item>
         <item>
           <title>CRYSTALS-Kyber_Security</title>
           <link>/sessions/crystals-kyber_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/crystals-kyber_security/</guid>
           <description></description>
         </item>
         <item>
           <title>CSP_RefTK</title>
           <link>/sessions/csp_reftk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/csp_reftk/</guid>
           <description></description>
         </item>
         <item>
           <title>Cubic_Quartic_Equations</title>
           <link>/sessions/cubic_quartic_equations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cubic_quartic_equations/</guid>
           <description></description>
         </item>
         <item>
           <title>CubicalCategories</title>
           <link>/sessions/cubicalcategories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cubicalcategories/</guid>
           <description></description>
         </item>
         <item>
           <title>CVP_Hardness</title>
           <link>/sessions/cvp_hardness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cvp_hardness/</guid>
           <description></description>
         </item>
         <item>
           <title>CYK</title>
           <link>/sessions/cyk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/cyk/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Elementary_Categories</title>
           <link>/sessions/czh_elementary_categories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_elementary_categories/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Foundations</title>
           <link>/sessions/czh_foundations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_foundations/</guid>
           <description></description>
         </item>
         <item>
           <title>CZH_Universal_Constructions</title>
           <link>/sessions/czh_universal_constructions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/czh_universal_constructions/</guid>
           <description></description>
         </item>
         <item>
           <title>DataRefinementIBP</title>
           <link>/sessions/datarefinementibp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/datarefinementibp/</guid>
           <description></description>
         </item>
         <item>
           <title>Datatype_Order_Generator</title>
           <link>/sessions/datatype_order_generator/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/datatype_order_generator/</guid>
           <description></description>
         </item>
         <item>
           <title>DCR-ExecutionEquivalence</title>
           <link>/sessions/dcr-executionequivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dcr-executionequivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Decl_Sem_Fun_PL</title>
           <link>/sessions/decl_sem_fun_pl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decl_sem_fun_pl/</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing-Diagrams</title>
           <link>/sessions/decreasing-diagrams/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decreasing-diagrams/</guid>
           <description></description>
         </item>
         <item>
           <title>Decreasing-Diagrams-II</title>
           <link>/sessions/decreasing-diagrams-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/decreasing-diagrams-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Dedekind_Real</title>
           <link>/sessions/dedekind_real/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dedekind_real/</guid>
           <description></description>
         </item>
         <item>
           <title>Deep_Learning</title>
           <link>/sessions/deep_learning/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/deep_learning/</guid>
           <description></description>
         </item>
         <item>
           <title>Delta_System_Lemma</title>
           <link>/sessions/delta_system_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/delta_system_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>Density_Compiler</title>
           <link>/sessions/density_compiler/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/density_compiler/</guid>
           <description></description>
         </item>
         <item>
           <title>Dependent_SIFUM_Refinement</title>
           <link>/sessions/dependent_sifum_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dependent_sifum_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>Dependent_SIFUM_Type_Systems</title>
           <link>/sessions/dependent_sifum_type_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dependent_sifum_type_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Depth-First-Search</title>
           <link>/sessions/depth-first-search/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/depth-first-search/</guid>
           <description></description>
         </item>
         <item>
           <title>Derangements</title>
           <link>/sessions/derangements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/derangements/</guid>
           <description></description>
         </item>
         <item>
           <title>Deriving</title>
           <link>/sessions/deriving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/deriving/</guid>
           <description></description>
         </item>
         <item>
           <title>Descartes_Sign_Rule</title>
           <link>/sessions/descartes_sign_rule/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/descartes_sign_rule/</guid>
           <description></description>
         </item>
         <item>
           <title>Design_Theory</title>
           <link>/sessions/design_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/design_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>DFS_Framework</title>
           <link>/sessions/dfs_framework/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dfs_framework/</guid>
           <description></description>
         </item>
         <item>
           <title>Dict_Construction</title>
           <link>/sessions/dict_construction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dict_construction/</guid>
           <description></description>
         </item>
         <item>
           <title>Differential_Dynamic_Logic</title>
           <link>/sessions/differential_dynamic_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/differential_dynamic_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Differential_Game_Logic</title>
           <link>/sessions/differential_game_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/differential_game_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Digit_Expansions</title>
           <link>/sessions/digit_expansions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/digit_expansions/</guid>
           <description></description>
         </item>
         <item>
           <title>DigitsInBase</title>
           <link>/sessions/digitsinbase/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/digitsinbase/</guid>
           <description></description>
         </item>
         <item>
           <title>Dijkstra_Shortest_Path</title>
           <link>/sessions/dijkstra_shortest_path/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dijkstra_shortest_path/</guid>
           <description></description>
         </item>
         <item>
           <title>Diophantine_Eqns_Lin_Hom</title>
           <link>/sessions/diophantine_eqns_lin_hom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/diophantine_eqns_lin_hom/</guid>
           <description></description>
         </item>
         <item>
           <title>Directed_Sets</title>
           <link>/sessions/directed_sets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/directed_sets/</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet_L</title>
           <link>/sessions/dirichlet_l/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dirichlet_l/</guid>
           <description></description>
         </item>
         <item>
           <title>Dirichlet_Series</title>
           <link>/sessions/dirichlet_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dirichlet_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Discrete_Summation</title>
           <link>/sessions/discrete_summation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/discrete_summation/</guid>
           <description></description>
         </item>
         <item>
           <title>DiscretePricing</title>
           <link>/sessions/discretepricing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/discretepricing/</guid>
           <description></description>
         </item>
         <item>
           <title>Disintegration</title>
           <link>/sessions/disintegration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/disintegration/</guid>
           <description></description>
         </item>
         <item>
           <title>DiskPaxos</title>
           <link>/sessions/diskpaxos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/diskpaxos/</guid>
           <description></description>
         </item>
         <item>
           <title>Distributed_Distinct_Elements</title>
           <link>/sessions/distributed_distinct_elements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/distributed_distinct_elements/</guid>
           <description></description>
         </item>
         <item>
           <title>DOM_Components</title>
           <link>/sessions/dom_components/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dom_components/</guid>
           <description></description>
         </item>
         <item>
           <title>Dominance_CHK</title>
           <link>/sessions/dominance_chk/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dominance_chk/</guid>
           <description></description>
         </item>
         <item>
           <title>DPRM_Theorem</title>
           <link>/sessions/dprm_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dprm_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>DPT-SAT-Solver</title>
           <link>/sessions/dpt-sat-solver/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dpt-sat-solver/</guid>
           <description></description>
         </item>
         <item>
           <title>Dynamic_Tables</title>
           <link>/sessions/dynamic_tables/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dynamic_tables/</guid>
           <description></description>
         </item>
         <item>
           <title>DynamicArchitectures</title>
           <link>/sessions/dynamicarchitectures/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/dynamicarchitectures/</guid>
           <description></description>
         </item>
         <item>
           <title>E_Transcendental</title>
           <link>/sessions/e_transcendental/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/e_transcendental/</guid>
           <description></description>
         </item>
         <item>
           <title>Earley_Parser</title>
           <link>/sessions/earley_parser/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/earley_parser/</guid>
           <description></description>
         </item>
         <item>
           <title>Echelon_Form</title>
           <link>/sessions/echelon_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/echelon_form/</guid>
           <description></description>
         </item>
         <item>
           <title>EdmondsKarp_Maxflow</title>
           <link>/sessions/edmondskarp_maxflow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/edmondskarp_maxflow/</guid>
           <description></description>
         </item>
         <item>
           <title>Edwards_Elliptic_Curves_Group</title>
           <link>/sessions/edwards_elliptic_curves_group/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/edwards_elliptic_curves_group/</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient_Weighted_Path_Order</title>
           <link>/sessions/efficient_weighted_path_order/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/efficient_weighted_path_order/</guid>
           <description></description>
         </item>
         <item>
           <title>Efficient-Mergesort</title>
           <link>/sessions/efficient-mergesort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/efficient-mergesort/</guid>
           <description></description>
         </item>
         <item>
           <title>Elimination_Of_Repeated_Factors</title>
           <link>/sessions/elimination_of_repeated_factors/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/elimination_of_repeated_factors/</guid>
           <description></description>
         </item>
         <item>
           <title>Elliptic_Curves_Group_Law</title>
           <link>/sessions/elliptic_curves_group_law/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/elliptic_curves_group_law/</guid>
           <description></description>
         </item>
         <item>
           <title>Encodability_Process_Calculi</title>
           <link>/sessions/encodability_process_calculi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/encodability_process_calculi/</guid>
           <description></description>
         </item>
         <item>
           <title>Epistemic_Logic</title>
           <link>/sessions/epistemic_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/epistemic_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Equivalence_Relation_Enumeration</title>
           <link>/sessions/equivalence_relation_enumeration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/equivalence_relation_enumeration/</guid>
           <description></description>
         </item>
         <item>
           <title>Ergodic_Theory</title>
           <link>/sessions/ergodic_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ergodic_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Error_Function</title>
           <link>/sessions/error_function/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/error_function/</guid>
           <description></description>
         </item>
         <item>
           <title>Eudoxus_Reals</title>
           <link>/sessions/eudoxus_reals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/eudoxus_reals/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_MacLaurin</title>
           <link>/sessions/euler_maclaurin/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_maclaurin/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_Partition</title>
           <link>/sessions/euler_partition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_partition/</guid>
           <description></description>
         </item>
         <item>
           <title>Euler_Polyhedron_Formula</title>
           <link>/sessions/euler_polyhedron_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/euler_polyhedron_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Eval_FO</title>
           <link>/sessions/eval_fo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/eval_fo/</guid>
           <description></description>
         </item>
         <item>
           <title>Example-Submission</title>
           <link>/sessions/example-submission/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/example-submission/</guid>
           <description></description>
         </item>
         <item>
           <title>Executable_Randomized_Algorithms</title>
           <link>/sessions/executable_randomized_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/executable_randomized_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Expander_Graphs</title>
           <link>/sessions/expander_graphs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/expander_graphs/</guid>
           <description></description>
         </item>
         <item>
           <title>Extended_Finite_State_Machine_Inference</title>
           <link>/sessions/extended_finite_state_machine_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/extended_finite_state_machine_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Extended_Finite_State_Machines</title>
           <link>/sessions/extended_finite_state_machines/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/extended_finite_state_machines/</guid>
           <description></description>
         </item>
         <item>
           <title>Factor_Algebraic_Polynomial</title>
           <link>/sessions/factor_algebraic_polynomial/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/factor_algebraic_polynomial/</guid>
           <description></description>
         </item>
         <item>
           <title>Factored_Transition_System_Bounding</title>
           <link>/sessions/factored_transition_system_bounding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/factored_transition_system_bounding/</guid>
           <description></description>
         </item>
         <item>
           <title>Falling_Factorial_Sum</title>
           <link>/sessions/falling_factorial_sum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/falling_factorial_sum/</guid>
           <description></description>
         </item>
         <item>
           <title>Farkas</title>
           <link>/sessions/farkas/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/farkas/</guid>
           <description></description>
         </item>
         <item>
           <title>Featherweight_OCL</title>
           <link>/sessions/featherweight_ocl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/featherweight_ocl/</guid>
           <description></description>
         </item>
         <item>
           <title>FeatherweightJava</title>
           <link>/sessions/featherweightjava/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/featherweightjava/</guid>
           <description></description>
         </item>
         <item>
           <title>Fermat3_4</title>
           <link>/sessions/fermat3_4/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fermat3_4/</guid>
           <description></description>
         </item>
         <item>
           <title>FFT</title>
           <link>/sessions/fft/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fft/</guid>
           <description></description>
         </item>
         <item>
           <title>FileRefinement</title>
           <link>/sessions/filerefinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/filerefinement/</guid>
           <description></description>
         </item>
         <item>
           <title>FinFun</title>
           <link>/sessions/finfun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finfun/</guid>
           <description></description>
         </item>
         <item>
           <title>Finger-Trees</title>
           <link>/sessions/finger-trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finger-trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite_Automata_HF</title>
           <link>/sessions/finite_automata_hf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite_automata_hf/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite_Fields</title>
           <link>/sessions/finite_fields/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite_fields/</guid>
           <description></description>
         </item>
         <item>
           <title>Finite-Map-Extras</title>
           <link>/sessions/finite-map-extras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finite-map-extras/</guid>
           <description></description>
         </item>
         <item>
           <title>Finitely_Generated_Abelian_Groups</title>
           <link>/sessions/finitely_generated_abelian_groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/finitely_generated_abelian_groups/</guid>
           <description></description>
         </item>
         <item>
           <title>First_Order_Terms</title>
           <link>/sessions/first_order_terms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/first_order_terms/</guid>
           <description></description>
         </item>
         <item>
           <title>First_Welfare_Theorem</title>
           <link>/sessions/first_welfare_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/first_welfare_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Fishburn_Impossibility</title>
           <link>/sessions/fishburn_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fishburn_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Fisher_Yates</title>
           <link>/sessions/fisher_yates/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fisher_yates/</guid>
           <description></description>
         </item>
         <item>
           <title>Fishers_Inequality</title>
           <link>/sessions/fishers_inequality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fishers_inequality/</guid>
           <description></description>
         </item>
         <item>
           <title>Fixed_Length_Vector</title>
           <link>/sessions/fixed_length_vector/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fixed_length_vector/</guid>
           <description></description>
         </item>
         <item>
           <title>Flow_Networks</title>
           <link>/sessions/flow_networks/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flow_networks/</guid>
           <description></description>
         </item>
         <item>
           <title>Floyd_Warshall</title>
           <link>/sessions/floyd_warshall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/floyd_warshall/</guid>
           <description></description>
         </item>
         <item>
           <title>FLP</title>
           <link>/sessions/flp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flp/</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck-Tame</title>
           <link>/sessions/flyspeck-tame/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flyspeck-tame/</guid>
           <description></description>
         </item>
         <item>
           <title>Flyspeck-Tame-Computation</title>
           <link>/sessions/flyspeck-tame-computation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/flyspeck-tame-computation/</guid>
           <description></description>
         </item>
         <item>
           <title>FO_Theory_Rewriting</title>
           <link>/sessions/fo_theory_rewriting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fo_theory_rewriting/</guid>
           <description></description>
         </item>
         <item>
           <title>FocusStreamsCaseStudies</title>
           <link>/sessions/focusstreamscasestudies/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/focusstreamscasestudies/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Axiomatic</title>
           <link>/sessions/fol_axiomatic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_axiomatic/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Harrison</title>
           <link>/sessions/fol_harrison/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_harrison/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc1</title>
           <link>/sessions/fol_seq_calc1/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc1/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc2</title>
           <link>/sessions/fol_seq_calc2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc2/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL_Seq_Calc3</title>
           <link>/sessions/fol_seq_calc3/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol_seq_calc3/</guid>
           <description></description>
         </item>
         <item>
           <title>FOL-Fitting</title>
           <link>/sessions/fol-fitting/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fol-fitting/</guid>
           <description></description>
         </item>
         <item>
           <title>Forcing</title>
           <link>/sessions/forcing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/forcing/</guid>
           <description></description>
         </item>
         <item>
           <title>Formal_Puiseux_Series</title>
           <link>/sessions/formal_puiseux_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formal_puiseux_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Formal_SSA</title>
           <link>/sessions/formal_ssa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formal_ssa/</guid>
           <description></description>
         </item>
         <item>
           <title>Formula_Derivatives</title>
           <link>/sessions/formula_derivatives/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formula_derivatives/</guid>
           <description></description>
         </item>
         <item>
           <title>Formula_Derivatives-Examples</title>
           <link>/sessions/formula_derivatives-examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/formula_derivatives-examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Foundation_of_geometry</title>
           <link>/sessions/foundation_of_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/foundation_of_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Fourier</title>
           <link>/sessions/fourier/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fourier/</guid>
           <description></description>
         </item>
         <item>
           <title>Free-Boolean-Algebra</title>
           <link>/sessions/free-boolean-algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/free-boolean-algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Free-Groups</title>
           <link>/sessions/free-groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/free-groups/</guid>
           <description></description>
         </item>
         <item>
           <title>Frequency_Moments</title>
           <link>/sessions/frequency_moments/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/frequency_moments/</guid>
           <description></description>
         </item>
         <item>
           <title>Fresh_Identifiers</title>
           <link>/sessions/fresh_identifiers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fresh_identifiers/</guid>
           <description></description>
         </item>
         <item>
           <title>FSM_Tests</title>
           <link>/sessions/fsm_tests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/fsm_tests/</guid>
           <description></description>
         </item>
         <item>
           <title>Functional_Ordered_Resolution_Prover</title>
           <link>/sessions/functional_ordered_resolution_prover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/functional_ordered_resolution_prover/</guid>
           <description></description>
         </item>
         <item>
           <title>Functional-Automata</title>
           <link>/sessions/functional-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/functional-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>FunWithFunctions</title>
           <link>/sessions/funwithfunctions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/funwithfunctions/</guid>
           <description></description>
         </item>
         <item>
           <title>FunWithTilings</title>
           <link>/sessions/funwithtilings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/funwithtilings/</guid>
           <description></description>
         </item>
         <item>
           <title>Furstenberg_Topology</title>
           <link>/sessions/furstenberg_topology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/furstenberg_topology/</guid>
           <description></description>
         </item>
         <item>
           <title>Gabow_SCC</title>
           <link>/sessions/gabow_scc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gabow_scc/</guid>
           <description></description>
         </item>
         <item>
           <title>Gale_Shapley</title>
           <link>/sessions/gale_shapley/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gale_shapley/</guid>
           <description></description>
         </item>
         <item>
           <title>GaleStewart_Games</title>
           <link>/sessions/galestewart_games/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/galestewart_games/</guid>
           <description></description>
         </item>
         <item>
           <title>Game_Based_Crypto</title>
           <link>/sessions/game_based_crypto/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/game_based_crypto/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss_Jordan</title>
           <link>/sessions/gauss_jordan/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss_jordan/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss_Sums</title>
           <link>/sessions/gauss_sums/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss_sums/</guid>
           <description></description>
         </item>
         <item>
           <title>Gauss-Jordan-Elim-Fun</title>
           <link>/sessions/gauss-jordan-elim-fun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gauss-jordan-elim-fun/</guid>
           <description></description>
         </item>
         <item>
           <title>Gaussian_Integers</title>
           <link>/sessions/gaussian_integers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gaussian_integers/</guid>
           <description></description>
         </item>
         <item>
           <title>GenClock</title>
           <link>/sessions/genclock/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/genclock/</guid>
           <description></description>
         </item>
         <item>
           <title>General-Triangle</title>
           <link>/sessions/general-triangle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/general-triangle/</guid>
           <description></description>
         </item>
         <item>
           <title>Generalized_Counting_Sort</title>
           <link>/sessions/generalized_counting_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generalized_counting_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>Generic_Deriving</title>
           <link>/sessions/generic_deriving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generic_deriving/</guid>
           <description></description>
         </item>
         <item>
           <title>Generic_Join</title>
           <link>/sessions/generic_join/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/generic_join/</guid>
           <description></description>
         </item>
         <item>
           <title>GewirthPGCProof</title>
           <link>/sessions/gewirthpgcproof/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gewirthpgcproof/</guid>
           <description></description>
         </item>
         <item>
           <title>Girth_Chromatic</title>
           <link>/sessions/girth_chromatic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/girth_chromatic/</guid>
           <description></description>
         </item>
         <item>
           <title>Given_Clause_Loops</title>
           <link>/sessions/given_clause_loops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/given_clause_loops/</guid>
           <description></description>
         </item>
         <item>
+          <title>Go</title>
+          <link>/sessions/go/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go/</guid>
+          <description></description>
+        </item>
+        <item>
+          <title>Go_Test_Quick</title>
+          <link>/sessions/go_test_quick/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go_test_quick/</guid>
+          <description></description>
+        </item>
+        <item>
+          <title>Go_Test_Slow</title>
+          <link>/sessions/go_test_slow/</link>
+          <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
+          <guid>/sessions/go_test_slow/</guid>
+          <description></description>
+        </item>
+        <item>
           <title>Goedel_HFSet_Semantic</title>
           <link>/sessions/goedel_hfset_semantic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_hfset_semantic/</guid>
           <description></description>
         </item>
         <item>
           <title>Goedel_HFSet_Semanticless</title>
           <link>/sessions/goedel_hfset_semanticless/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_hfset_semanticless/</guid>
           <description></description>
         </item>
         <item>
           <title>Goedel_Incompleteness</title>
           <link>/sessions/goedel_incompleteness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedel_incompleteness/</guid>
           <description></description>
         </item>
         <item>
           <title>GoedelGod</title>
           <link>/sessions/goedelgod/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goedelgod/</guid>
           <description></description>
         </item>
         <item>
           <title>Goodstein_Lambda</title>
           <link>/sessions/goodstein_lambda/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/goodstein_lambda/</guid>
           <description></description>
         </item>
         <item>
           <title>GPU_Kernel_PL</title>
           <link>/sessions/gpu_kernel_pl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gpu_kernel_pl/</guid>
           <description></description>
         </item>
         <item>
           <title>Graph_Saturation</title>
           <link>/sessions/graph_saturation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graph_saturation/</guid>
           <description></description>
         </item>
         <item>
           <title>Graph_Theory</title>
           <link>/sessions/graph_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graph_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>GraphMarkingIBP</title>
           <link>/sessions/graphmarkingibp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/graphmarkingibp/</guid>
           <description></description>
         </item>
         <item>
           <title>Gray_Codes</title>
           <link>/sessions/gray_codes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gray_codes/</guid>
           <description></description>
         </item>
         <item>
           <title>Green</title>
           <link>/sessions/green/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/green/</guid>
           <description></description>
         </item>
         <item>
           <title>Groebner_Bases</title>
           <link>/sessions/groebner_bases/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/groebner_bases/</guid>
           <description></description>
         </item>
         <item>
           <title>Groebner_Macaulay</title>
           <link>/sessions/groebner_macaulay/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/groebner_macaulay/</guid>
           <description></description>
         </item>
         <item>
           <title>Gromov_Hyperbolicity</title>
           <link>/sessions/gromov_hyperbolicity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/gromov_hyperbolicity/</guid>
           <description></description>
         </item>
         <item>
           <title>Grothendieck_Schemes</title>
           <link>/sessions/grothendieck_schemes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/grothendieck_schemes/</guid>
           <description></description>
         </item>
         <item>
           <title>Group-Ring-Module</title>
           <link>/sessions/group-ring-module/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/group-ring-module/</guid>
           <description></description>
         </item>
         <item>
           <title>Hahn_Jordan_Decomposition</title>
           <link>/sessions/hahn_jordan_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hahn_jordan_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Hales_Jewett</title>
           <link>/sessions/hales_jewett/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hales_jewett/</guid>
           <description></description>
         </item>
         <item>
           <title>Heard_Of</title>
           <link>/sessions/heard_of/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/heard_of/</guid>
           <description></description>
         </item>
         <item>
           <title>Hello_World</title>
           <link>/sessions/hello_world/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hello_world/</guid>
           <description></description>
         </item>
         <item>
           <title>HereditarilyFinite</title>
           <link>/sessions/hereditarilyfinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hereditarilyfinite/</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite</title>
           <link>/sessions/hermite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hermite/</guid>
           <description></description>
         </item>
         <item>
           <title>Hermite_Lindemann</title>
           <link>/sessions/hermite_lindemann/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hermite_lindemann/</guid>
           <description></description>
         </item>
         <item>
           <title>Hidden_Markov_Models</title>
           <link>/sessions/hidden_markov_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hidden_markov_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Higher_Order_Terms</title>
           <link>/sessions/higher_order_terms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/higher_order_terms/</guid>
           <description></description>
         </item>
         <item>
           <title>Hoare_Time</title>
           <link>/sessions/hoare_time/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hoare_time/</guid>
           <description></description>
         </item>
         <item>
           <title>HoareForDivergence</title>
           <link>/sessions/hoarefordivergence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hoarefordivergence/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP</title>
           <link>/sessions/hol-csp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-csp/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSP_OpSem</title>
           <link>/sessions/hol-csp_opsem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-csp_opsem/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-CSPM</title>
           <link>/sessions/hol-cspm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-cspm/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-ARCH-COMP</title>
           <link>/sessions/hol-ode-arch-comp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-arch-comp/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-Examples</title>
           <link>/sessions/hol-ode-examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-examples/</guid>
           <description></description>
         </item>
         <item>
           <title>HOL-ODE-Numerics</title>
           <link>/sessions/hol-ode-numerics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hol-ode-numerics/</guid>
           <description></description>
         </item>
         <item>
           <title>HOLCF-Prelude</title>
           <link>/sessions/holcf-prelude/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/holcf-prelude/</guid>
           <description></description>
         </item>
         <item>
           <title>Hood_Melville_Queue</title>
           <link>/sessions/hood_melville_queue/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hood_melville_queue/</guid>
           <description></description>
         </item>
         <item>
           <title>HotelKeyCards</title>
           <link>/sessions/hotelkeycards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hotelkeycards/</guid>
           <description></description>
         </item>
         <item>
           <title>HRB-Slicing</title>
           <link>/sessions/hrb-slicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hrb-slicing/</guid>
           <description></description>
         </item>
         <item>
           <title>Huffman</title>
           <link>/sessions/huffman/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/huffman/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Logic</title>
           <link>/sessions/hybrid_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Multi_Lane_Spatial_Logic</title>
           <link>/sessions/hybrid_multi_lane_spatial_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_multi_lane_spatial_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Hybrid_Systems_VCs</title>
           <link>/sessions/hybrid_systems_vcs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hybrid_systems_vcs/</guid>
           <description></description>
         </item>
         <item>
           <title>HyperCTL</title>
           <link>/sessions/hyperctl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperctl/</guid>
           <description></description>
         </item>
         <item>
           <title>Hyperdual</title>
           <link>/sessions/hyperdual/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperdual/</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraph_Basics</title>
           <link>/sessions/hypergraph_basics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hypergraph_basics/</guid>
           <description></description>
         </item>
         <item>
           <title>Hypergraph_Colourings</title>
           <link>/sessions/hypergraph_colourings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hypergraph_colourings/</guid>
           <description></description>
         </item>
         <item>
           <title>HyperHoareLogic</title>
           <link>/sessions/hyperhoarelogic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/hyperhoarelogic/</guid>
           <description></description>
         </item>
         <item>
           <title>IEEE_Floating_Point</title>
           <link>/sessions/ieee_floating_point/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ieee_floating_point/</guid>
           <description></description>
         </item>
         <item>
           <title>IFC_Tracking</title>
           <link>/sessions/ifc_tracking/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ifc_tracking/</guid>
           <description></description>
         </item>
         <item>
           <title>IMAP-CRDT</title>
           <link>/sessions/imap-crdt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imap-crdt/</guid>
           <description></description>
         </item>
         <item>
           <title>IMO2019</title>
           <link>/sessions/imo2019/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imo2019/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Compiler</title>
           <link>/sessions/imp_compiler/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_compiler/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Compiler_Reuse</title>
           <link>/sessions/imp_compiler_reuse/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_compiler_reuse/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP_Noninterference</title>
           <link>/sessions/imp_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2</title>
           <link>/sessions/imp2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp2/</guid>
           <description></description>
         </item>
         <item>
           <title>IMP2_Binary_Heap</title>
           <link>/sessions/imp2_binary_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imp2_binary_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>Imperative_Insertion_Sort</title>
           <link>/sessions/imperative_insertion_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/imperative_insertion_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>Implicational_Logic</title>
           <link>/sessions/implicational_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/implicational_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Impossible_Geometry</title>
           <link>/sessions/impossible_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/impossible_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Incompleteness</title>
           <link>/sessions/incompleteness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/incompleteness/</guid>
           <description></description>
         </item>
         <item>
           <title>Incredible_Proof_Machine</title>
           <link>/sessions/incredible_proof_machine/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/incredible_proof_machine/</guid>
           <description></description>
         </item>
         <item>
           <title>Independence_CH</title>
           <link>/sessions/independence_ch/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/independence_ch/</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive_Confidentiality</title>
           <link>/sessions/inductive_confidentiality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/inductive_confidentiality/</guid>
           <description></description>
         </item>
         <item>
           <title>Inductive_Inference</title>
           <link>/sessions/inductive_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/inductive_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>InformationFlowSlicing</title>
           <link>/sessions/informationflowslicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/informationflowslicing/</guid>
           <description></description>
         </item>
         <item>
           <title>InformationFlowSlicing_Inter</title>
           <link>/sessions/informationflowslicing_inter/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/informationflowslicing_inter/</guid>
           <description></description>
         </item>
         <item>
           <title>InfPathElimination</title>
           <link>/sessions/infpathelimination/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/infpathelimination/</guid>
           <description></description>
         </item>
         <item>
           <title>Integration</title>
           <link>/sessions/integration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/integration/</guid>
           <description></description>
         </item>
         <item>
           <title>Interpolation_Polynomials_HOL_Algebra</title>
           <link>/sessions/interpolation_polynomials_hol_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interpolation_polynomials_hol_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Interpreter_Optimizations</title>
           <link>/sessions/interpreter_optimizations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interpreter_optimizations/</guid>
           <description></description>
         </item>
         <item>
           <title>Interval_Analysis</title>
           <link>/sessions/interval_analysis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interval_analysis/</guid>
           <description></description>
         </item>
         <item>
           <title>Interval_Arithmetic_Word32</title>
           <link>/sessions/interval_arithmetic_word32/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/interval_arithmetic_word32/</guid>
           <description></description>
         </item>
         <item>
           <title>Intro_Dest_Elim</title>
           <link>/sessions/intro_dest_elim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/intro_dest_elim/</guid>
           <description></description>
         </item>
         <item>
           <title>Involutions2Squares</title>
           <link>/sessions/involutions2squares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/involutions2squares/</guid>
           <description></description>
         </item>
         <item>
           <title>IO_Language_Conformance</title>
           <link>/sessions/io_language_conformance/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/io_language_conformance/</guid>
           <description></description>
         </item>
         <item>
           <title>IP_Addresses</title>
           <link>/sessions/ip_addresses/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ip_addresses/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics</title>
           <link>/sessions/iptables_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics_Examples</title>
           <link>/sessions/iptables_semantics_examples/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics_examples/</guid>
           <description></description>
         </item>
         <item>
           <title>Iptables_Semantics_Examples_Big</title>
           <link>/sessions/iptables_semantics_examples_big/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/iptables_semantics_examples_big/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrational_Series_Erdos_Straus</title>
           <link>/sessions/irrational_series_erdos_straus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrational_series_erdos_straus/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationality_J_Hancl</title>
           <link>/sessions/irrationality_j_hancl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrationality_j_hancl/</guid>
           <description></description>
         </item>
         <item>
           <title>Irrationals_From_THEBOOK</title>
           <link>/sessions/irrationals_from_thebook/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/irrationals_from_thebook/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_C</title>
           <link>/sessions/isabelle_c/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_c/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_hoops</title>
           <link>/sessions/isabelle_hoops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_hoops/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_Marries_Dirac</title>
           <link>/sessions/isabelle_marries_dirac/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_marries_dirac/</guid>
           <description></description>
         </item>
         <item>
           <title>Isabelle_Meta_Model</title>
           <link>/sessions/isabelle_meta_model/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isabelle_meta_model/</guid>
           <description></description>
         </item>
         <item>
           <title>IsaGeoCoq</title>
           <link>/sessions/isageocoq/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isageocoq/</guid>
           <description></description>
         </item>
         <item>
           <title>IsaNet</title>
           <link>/sessions/isanet/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/isanet/</guid>
           <description></description>
         </item>
         <item>
           <title>Jacobson_Basic_Algebra</title>
           <link>/sessions/jacobson_basic_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jacobson_basic_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Jinja</title>
           <link>/sessions/jinja/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinja/</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaDCI</title>
           <link>/sessions/jinjadci/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinjadci/</guid>
           <description></description>
         </item>
         <item>
           <title>JinjaThreads</title>
           <link>/sessions/jinjathreads/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jinjathreads/</guid>
           <description></description>
         </item>
         <item>
           <title>JiveDataStoreModel</title>
           <link>/sessions/jivedatastoremodel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jivedatastoremodel/</guid>
           <description></description>
         </item>
         <item>
           <title>Jordan_Hoelder</title>
           <link>/sessions/jordan_hoelder/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jordan_hoelder/</guid>
           <description></description>
         </item>
         <item>
           <title>Jordan_Normal_Form</title>
           <link>/sessions/jordan_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/jordan_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>KAD</title>
           <link>/sessions/kad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kad/</guid>
           <description></description>
         </item>
         <item>
           <title>Karatsuba</title>
           <link>/sessions/karatsuba/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/karatsuba/</guid>
           <description></description>
         </item>
         <item>
           <title>KAT_and_DRA</title>
           <link>/sessions/kat_and_dra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kat_and_dra/</guid>
           <description></description>
         </item>
         <item>
           <title>KBPs</title>
           <link>/sessions/kbps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kbps/</guid>
           <description></description>
         </item>
         <item>
           <title>KD_Tree</title>
           <link>/sessions/kd_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kd_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Key_Agreement_Strong_Adversaries</title>
           <link>/sessions/key_agreement_strong_adversaries/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/key_agreement_strong_adversaries/</guid>
           <description></description>
         </item>
         <item>
           <title>Khovanskii_Theorem</title>
           <link>/sessions/khovanskii_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/khovanskii_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Kleene_Algebra</title>
           <link>/sessions/kleene_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kleene_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Kneser_Cauchy_Davenport</title>
           <link>/sessions/kneser_cauchy_davenport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kneser_cauchy_davenport/</guid>
           <description></description>
         </item>
         <item>
           <title>Knights_Tour</title>
           <link>/sessions/knights_tour/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knights_tour/</guid>
           <description></description>
         </item>
         <item>
           <title>Knot_Theory</title>
           <link>/sessions/knot_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knot_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Knuth_Bendix_Order</title>
           <link>/sessions/knuth_bendix_order/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuth_bendix_order/</guid>
           <description></description>
         </item>
         <item>
           <title>Knuth_Morris_Pratt</title>
           <link>/sessions/knuth_morris_pratt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuth_morris_pratt/</guid>
           <description></description>
         </item>
         <item>
           <title>KnuthMorrisPratt</title>
           <link>/sessions/knuthmorrispratt/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/knuthmorrispratt/</guid>
           <description></description>
         </item>
         <item>
           <title>Koenigsberg_Friendship</title>
           <link>/sessions/koenigsberg_friendship/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/koenigsberg_friendship/</guid>
           <description></description>
         </item>
         <item>
           <title>Kruskal</title>
           <link>/sessions/kruskal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kruskal/</guid>
           <description></description>
         </item>
         <item>
           <title>Kuratowski_Closure_Complement</title>
           <link>/sessions/kuratowski_closure_complement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/kuratowski_closure_complement/</guid>
           <description></description>
         </item>
         <item>
           <title>Labeled_Transition_Systems</title>
           <link>/sessions/labeled_transition_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/labeled_transition_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Lam-ml-Normalization</title>
           <link>/sessions/lam-ml-normalization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lam-ml-normalization/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_EPO</title>
           <link>/sessions/lambda_free_epo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_epo/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_KBOs</title>
           <link>/sessions/lambda_free_kbos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_kbos/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambda_Free_RPOs</title>
           <link>/sessions/lambda_free_rpos/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambda_free_rpos/</guid>
           <description></description>
         </item>
         <item>
           <title>LambdaAuth</title>
           <link>/sessions/lambdaauth/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambdaauth/</guid>
           <description></description>
         </item>
         <item>
           <title>LambdaMu</title>
           <link>/sessions/lambdamu/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambdamu/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambert_Series</title>
           <link>/sessions/lambert_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambert_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Lambert_W</title>
           <link>/sessions/lambert_w/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lambert_w/</guid>
           <description></description>
         </item>
         <item>
           <title>Landau_Symbols</title>
           <link>/sessions/landau_symbols/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/landau_symbols/</guid>
           <description></description>
         </item>
         <item>
           <title>Laplace_Transform</title>
           <link>/sessions/laplace_transform/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/laplace_transform/</guid>
           <description></description>
         </item>
         <item>
           <title>Latin_Square</title>
           <link>/sessions/latin_square/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/latin_square/</guid>
           <description></description>
         </item>
         <item>
           <title>LatticeProperties</title>
           <link>/sessions/latticeproperties/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/latticeproperties/</guid>
           <description></description>
         </item>
         <item>
           <title>Launchbury</title>
           <link>/sessions/launchbury/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/launchbury/</guid>
           <description></description>
         </item>
         <item>
           <title>Laws_of_Large_Numbers</title>
           <link>/sessions/laws_of_large_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/laws_of_large_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>Lazy_Case</title>
           <link>/sessions/lazy_case/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lazy_case/</guid>
           <description></description>
         </item>
         <item>
           <title>Lazy-Lists-II</title>
           <link>/sessions/lazy-lists-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lazy-lists-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Lehmer</title>
           <link>/sessions/lehmer/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lehmer/</guid>
           <description></description>
         </item>
         <item>
           <title>LEM</title>
           <link>/sessions/lem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lem/</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting_Definition_Option</title>
           <link>/sessions/lifting_definition_option/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lifting_definition_option/</guid>
           <description></description>
         </item>
         <item>
           <title>Lifting_the_Exponent</title>
           <link>/sessions/lifting_the_exponent/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lifting_the_exponent/</guid>
           <description></description>
         </item>
         <item>
           <title>LightweightJava</title>
           <link>/sessions/lightweightjava/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lightweightjava/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Inequalities</title>
           <link>/sessions/linear_inequalities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_inequalities/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Programming</title>
           <link>/sessions/linear_programming/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_programming/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Recurrences</title>
           <link>/sessions/linear_recurrences/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_recurrences/</guid>
           <description></description>
         </item>
         <item>
           <title>Linear_Recurrences_Solver</title>
           <link>/sessions/linear_recurrences_solver/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linear_recurrences_solver/</guid>
           <description></description>
         </item>
         <item>
           <title>LinearQuantifierElim</title>
           <link>/sessions/linearquantifierelim/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/linearquantifierelim/</guid>
           <description></description>
         </item>
         <item>
           <title>Liouville_Numbers</title>
           <link>/sessions/liouville_numbers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/liouville_numbers/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Interleaving</title>
           <link>/sessions/list_interleaving/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_interleaving/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Inversions</title>
           <link>/sessions/list_inversions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_inversions/</guid>
           <description></description>
         </item>
         <item>
           <title>List_Update</title>
           <link>/sessions/list_update/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list_update/</guid>
           <description></description>
         </item>
         <item>
           <title>List-Index</title>
           <link>/sessions/list-index/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list-index/</guid>
           <description></description>
         </item>
         <item>
           <title>List-Infinite</title>
           <link>/sessions/list-infinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/list-infinite/</guid>
           <description></description>
         </item>
         <item>
           <title>LLL_Basis_Reduction</title>
           <link>/sessions/lll_basis_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lll_basis_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>LLL_Factorization</title>
           <link>/sessions/lll_factorization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lll_factorization/</guid>
           <description></description>
         </item>
         <item>
           <title>Localization_Ring</title>
           <link>/sessions/localization_ring/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/localization_ring/</guid>
           <description></description>
         </item>
         <item>
           <title>LocalLexing</title>
           <link>/sessions/locallexing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/locallexing/</guid>
           <description></description>
         </item>
         <item>
           <title>Locally-Nameless-Sigma</title>
           <link>/sessions/locally-nameless-sigma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/locally-nameless-sigma/</guid>
           <description></description>
         </item>
         <item>
           <title>LOFT</title>
           <link>/sessions/loft/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/loft/</guid>
           <description></description>
         </item>
         <item>
           <title>Logging_Independent_Anonymity</title>
           <link>/sessions/logging_independent_anonymity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/logging_independent_anonymity/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_Approximation</title>
           <link>/sessions/lorenz_approximation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_approximation/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_C0</title>
           <link>/sessions/lorenz_c0/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_c0/</guid>
           <description></description>
         </item>
         <item>
           <title>Lorenz_C1</title>
           <link>/sessions/lorenz_c1/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lorenz_c1/</guid>
           <description></description>
         </item>
         <item>
           <title>Lovasz_Local</title>
           <link>/sessions/lovasz_local/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lovasz_local/</guid>
           <description></description>
         </item>
         <item>
           <title>Lowe_Ontological_Argument</title>
           <link>/sessions/lowe_ontological_argument/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lowe_ontological_argument/</guid>
           <description></description>
         </item>
         <item>
           <title>Lower_Semicontinuous</title>
           <link>/sessions/lower_semicontinuous/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lower_semicontinuous/</guid>
           <description></description>
         </item>
         <item>
           <title>Lp</title>
           <link>/sessions/lp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lp/</guid>
           <description></description>
         </item>
         <item>
           <title>LP_Duality</title>
           <link>/sessions/lp_duality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lp_duality/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL</title>
           <link>/sessions/ltl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_Master_Theorem</title>
           <link>/sessions/ltl_master_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_master_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_Normal_Form</title>
           <link>/sessions/ltl_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_to_DRA</title>
           <link>/sessions/ltl_to_dra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_to_dra/</guid>
           <description></description>
         </item>
         <item>
           <title>LTL_to_GBA</title>
           <link>/sessions/ltl_to_gba/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ltl_to_gba/</guid>
           <description></description>
         </item>
         <item>
           <title>Lucas_Theorem</title>
           <link>/sessions/lucas_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/lucas_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Markov_Models</title>
           <link>/sessions/markov_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/markov_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Marriage</title>
           <link>/sessions/marriage/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/marriage/</guid>
           <description></description>
         </item>
         <item>
           <title>Martingales</title>
           <link>/sessions/martingales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/martingales/</guid>
           <description></description>
         </item>
         <item>
           <title>Mason_Stothers</title>
           <link>/sessions/mason_stothers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mason_stothers/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrices_for_ODEs</title>
           <link>/sessions/matrices_for_odes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrices_for_odes/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrix</title>
           <link>/sessions/matrix/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrix/</guid>
           <description></description>
         </item>
         <item>
           <title>Matrix_Tensor</title>
           <link>/sessions/matrix_tensor/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matrix_tensor/</guid>
           <description></description>
         </item>
         <item>
           <title>Matroids</title>
           <link>/sessions/matroids/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/matroids/</guid>
           <description></description>
         </item>
         <item>
           <title>Max-Card-Matching</title>
           <link>/sessions/max-card-matching/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/max-card-matching/</guid>
           <description></description>
         </item>
         <item>
           <title>Maximum_Segment_Sum</title>
           <link>/sessions/maximum_segment_sum/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/maximum_segment_sum/</guid>
           <description></description>
         </item>
         <item>
           <title>MDP-Algorithms</title>
           <link>/sessions/mdp-algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mdp-algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>MDP-Rewards</title>
           <link>/sessions/mdp-rewards/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mdp-rewards/</guid>
           <description></description>
         </item>
         <item>
           <title>Median_Method</title>
           <link>/sessions/median_method/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/median_method/</guid>
           <description></description>
         </item>
         <item>
           <title>Median_Of_Medians_Selection</title>
           <link>/sessions/median_of_medians_selection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/median_of_medians_selection/</guid>
           <description></description>
         </item>
         <item>
           <title>Menger</title>
           <link>/sessions/menger/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/menger/</guid>
           <description></description>
         </item>
         <item>
           <title>Mereology</title>
           <link>/sessions/mereology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mereology/</guid>
           <description></description>
         </item>
         <item>
           <title>Mersenne_Primes</title>
           <link>/sessions/mersenne_primes/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mersenne_primes/</guid>
           <description></description>
         </item>
         <item>
           <title>Metalogic_ProofChecker</title>
           <link>/sessions/metalogic_proofchecker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/metalogic_proofchecker/</guid>
           <description></description>
         </item>
         <item>
           <title>MFMC_Countable</title>
           <link>/sessions/mfmc_countable/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfmc_countable/</guid>
           <description></description>
         </item>
         <item>
           <title>MFODL_Monitor_Optimized</title>
           <link>/sessions/mfodl_monitor_optimized/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfodl_monitor_optimized/</guid>
           <description></description>
         </item>
         <item>
           <title>MFOTL_Monitor</title>
           <link>/sessions/mfotl_monitor/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mfotl_monitor/</guid>
           <description></description>
         </item>
         <item>
           <title>MHComputation</title>
           <link>/sessions/mhcomputation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mhcomputation/</guid>
           <description></description>
         </item>
         <item>
           <title>Minimal_SSA</title>
           <link>/sessions/minimal_ssa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minimal_ssa/</guid>
           <description></description>
         </item>
         <item>
           <title>MiniML</title>
           <link>/sessions/miniml/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/miniml/</guid>
           <description></description>
         </item>
         <item>
           <title>MiniSail</title>
           <link>/sessions/minisail/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minisail/</guid>
           <description></description>
         </item>
         <item>
           <title>Minkowskis_Theorem</title>
           <link>/sessions/minkowskis_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minkowskis_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Minsky_Machines</title>
           <link>/sessions/minsky_machines/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/minsky_machines/</guid>
           <description></description>
         </item>
         <item>
           <title>ML_Unification</title>
           <link>/sessions/ml_unification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ml_unification/</guid>
           <description></description>
         </item>
         <item>
           <title>MLSS_Decision_Proc</title>
           <link>/sessions/mlss_decision_proc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mlss_decision_proc/</guid>
           <description></description>
         </item>
         <item>
           <title>Modal_Logics_for_NTS</title>
           <link>/sessions/modal_logics_for_nts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modal_logics_for_nts/</guid>
           <description></description>
         </item>
         <item>
           <title>Modular_arithmetic_LLL_and_HNF_algorithms</title>
           <link>/sessions/modular_arithmetic_lll_and_hnf_algorithms/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modular_arithmetic_lll_and_hnf_algorithms/</guid>
           <description></description>
         </item>
         <item>
           <title>Modular_Assembly_Kit_Security</title>
           <link>/sessions/modular_assembly_kit_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/modular_assembly_kit_security/</guid>
           <description></description>
         </item>
         <item>
           <title>Monad_Memo_DP</title>
           <link>/sessions/monad_memo_dp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monad_memo_dp/</guid>
           <description></description>
         </item>
         <item>
           <title>Monad_Normalisation</title>
           <link>/sessions/monad_normalisation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monad_normalisation/</guid>
           <description></description>
         </item>
         <item>
           <title>MonoBoolTranAlgebra</title>
           <link>/sessions/monobooltranalgebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monobooltranalgebra/</guid>
           <description></description>
         </item>
         <item>
           <title>MonoidalCategory</title>
           <link>/sessions/monoidalcategory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monoidalcategory/</guid>
           <description></description>
         </item>
         <item>
           <title>Monomorphic_Monad</title>
           <link>/sessions/monomorphic_monad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/monomorphic_monad/</guid>
           <description></description>
         </item>
         <item>
           <title>MSO_Regex_Equivalence</title>
           <link>/sessions/mso_regex_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/mso_regex_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>MuchAdoAboutTwo</title>
           <link>/sessions/muchadoabouttwo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/muchadoabouttwo/</guid>
           <description></description>
         </item>
         <item>
           <title>Multi_Party_Computation</title>
           <link>/sessions/multi_party_computation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multi_party_computation/</guid>
           <description></description>
         </item>
         <item>
           <title>Multirelations</title>
           <link>/sessions/multirelations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multirelations/</guid>
           <description></description>
         </item>
         <item>
           <title>Multirelations_Heterogeneous</title>
           <link>/sessions/multirelations_heterogeneous/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multirelations_heterogeneous/</guid>
           <description></description>
         </item>
         <item>
           <title>Multiset_Ordering_NPC</title>
           <link>/sessions/multiset_ordering_npc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multiset_ordering_npc/</guid>
           <description></description>
         </item>
         <item>
           <title>Multitape_To_Singletape_TM</title>
           <link>/sessions/multitape_to_singletape_tm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/multitape_to_singletape_tm/</guid>
           <description></description>
         </item>
         <item>
           <title>Myhill-Nerode</title>
           <link>/sessions/myhill-nerode/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/myhill-nerode/</guid>
           <description></description>
         </item>
         <item>
           <title>Name_Carrying_Type_Inference</title>
           <link>/sessions/name_carrying_type_inference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/name_carrying_type_inference/</guid>
           <description></description>
         </item>
         <item>
           <title>Nano_JSON</title>
           <link>/sessions/nano_json/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nano_json/</guid>
           <description></description>
         </item>
         <item>
           <title>Nash_Williams</title>
           <link>/sessions/nash_williams/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nash_williams/</guid>
           <description></description>
         </item>
         <item>
           <title>Nat-Interval-Logic</title>
           <link>/sessions/nat-interval-logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nat-interval-logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Native_Word</title>
           <link>/sessions/native_word/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/native_word/</guid>
           <description></description>
         </item>
         <item>
           <title>Nested_Multisets_Ordinals</title>
           <link>/sessions/nested_multisets_ordinals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nested_multisets_ordinals/</guid>
           <description></description>
         </item>
         <item>
           <title>Network_Security_Policy_Verification</title>
           <link>/sessions/network_security_policy_verification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/network_security_policy_verification/</guid>
           <description></description>
         </item>
         <item>
           <title>Neumann_Morgenstern_Utility</title>
           <link>/sessions/neumann_morgenstern_utility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/neumann_morgenstern_utility/</guid>
           <description></description>
         </item>
         <item>
           <title>No_FTL_observers</title>
           <link>/sessions/no_ftl_observers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/no_ftl_observers/</guid>
           <description></description>
         </item>
         <item>
           <title>No_FTL_observers_Gen_Rel</title>
           <link>/sessions/no_ftl_observers_gen_rel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/no_ftl_observers_gen_rel/</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal_Myhill_Nerode</title>
           <link>/sessions/nominal_myhill_nerode/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nominal_myhill_nerode/</guid>
           <description></description>
         </item>
         <item>
           <title>Nominal2</title>
           <link>/sessions/nominal2/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nominal2/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Concurrent_Composition</title>
           <link>/sessions/noninterference_concurrent_composition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_concurrent_composition/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_CSP</title>
           <link>/sessions/noninterference_csp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_csp/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Generic_Unwinding</title>
           <link>/sessions/noninterference_generic_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_generic_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Inductive_Unwinding</title>
           <link>/sessions/noninterference_inductive_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_inductive_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Ipurge_Unwinding</title>
           <link>/sessions/noninterference_ipurge_unwinding/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_ipurge_unwinding/</guid>
           <description></description>
         </item>
         <item>
           <title>Noninterference_Sequential_Composition</title>
           <link>/sessions/noninterference_sequential_composition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/noninterference_sequential_composition/</guid>
           <description></description>
         </item>
         <item>
           <title>NormByEval</title>
           <link>/sessions/normbyeval/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/normbyeval/</guid>
           <description></description>
         </item>
         <item>
           <title>Nullstellensatz</title>
           <link>/sessions/nullstellensatz/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/nullstellensatz/</guid>
           <description></description>
         </item>
         <item>
           <title>Number_Theoretic_Transform</title>
           <link>/sessions/number_theoretic_transform/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/number_theoretic_transform/</guid>
           <description></description>
         </item>
         <item>
           <title>Octonions</title>
           <link>/sessions/octonions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/octonions/</guid>
           <description></description>
         </item>
         <item>
           <title>Old_Datatype_Show</title>
           <link>/sessions/old_datatype_show/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/old_datatype_show/</guid>
           <description></description>
         </item>
         <item>
           <title>OmegaCatoidsQuantales</title>
           <link>/sessions/omegacatoidsquantales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/omegacatoidsquantales/</guid>
           <description></description>
         </item>
         <item>
           <title>Open_Induction</title>
           <link>/sessions/open_induction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/open_induction/</guid>
           <description></description>
         </item>
         <item>
           <title>OpSets</title>
           <link>/sessions/opsets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/opsets/</guid>
           <description></description>
         </item>
         <item>
           <title>Optics</title>
           <link>/sessions/optics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/optics/</guid>
           <description></description>
         </item>
         <item>
           <title>Optimal_BST</title>
           <link>/sessions/optimal_bst/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/optimal_bst/</guid>
           <description></description>
         </item>
         <item>
           <title>Orbit_Stabiliser</title>
           <link>/sessions/orbit_stabiliser/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/orbit_stabiliser/</guid>
           <description></description>
         </item>
         <item>
           <title>Order_Lattice_Props</title>
           <link>/sessions/order_lattice_props/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/order_lattice_props/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordered_Resolution_Prover</title>
           <link>/sessions/ordered_resolution_prover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordered_resolution_prover/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal</title>
           <link>/sessions/ordinal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinal/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinal_Partitions</title>
           <link>/sessions/ordinal_partitions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinal_partitions/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinals_and_Cardinals</title>
           <link>/sessions/ordinals_and_cardinals/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinals_and_cardinals/</guid>
           <description></description>
         </item>
         <item>
           <title>Ordinary_Differential_Equations</title>
           <link>/sessions/ordinary_differential_equations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ordinary_differential_equations/</guid>
           <description></description>
         </item>
         <item>
           <title>PAC_Checker</title>
           <link>/sessions/pac_checker/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pac_checker/</guid>
           <description></description>
         </item>
         <item>
           <title>Package_logic</title>
           <link>/sessions/package_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/package_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Padic_Field</title>
           <link>/sessions/padic_field/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/padic_field/</guid>
           <description></description>
         </item>
         <item>
           <title>Padic_Ints</title>
           <link>/sessions/padic_ints/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/padic_ints/</guid>
           <description></description>
         </item>
         <item>
           <title>Pairing_Heap</title>
           <link>/sessions/pairing_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pairing_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>PAL</title>
           <link>/sessions/pal/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pal/</guid>
           <description></description>
         </item>
         <item>
           <title>PAPP_Impossibility</title>
           <link>/sessions/papp_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/papp_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Paraconsistency</title>
           <link>/sessions/paraconsistency/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/paraconsistency/</guid>
           <description></description>
         </item>
         <item>
           <title>Parity_Game</title>
           <link>/sessions/parity_game/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/parity_game/</guid>
           <description></description>
         </item>
         <item>
           <title>Partial_Function_MR</title>
           <link>/sessions/partial_function_mr/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/partial_function_mr/</guid>
           <description></description>
         </item>
         <item>
           <title>Partial_Order_Reduction</title>
           <link>/sessions/partial_order_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/partial_order_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Password_Authentication_Protocol</title>
           <link>/sessions/password_authentication_protocol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/password_authentication_protocol/</guid>
           <description></description>
         </item>
         <item>
           <title>PCF</title>
           <link>/sessions/pcf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pcf/</guid>
           <description></description>
         </item>
         <item>
           <title>Pell</title>
           <link>/sessions/pell/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pell/</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect_Fields</title>
           <link>/sessions/perfect_fields/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perfect_fields/</guid>
           <description></description>
         </item>
         <item>
           <title>Perfect-Number-Thm</title>
           <link>/sessions/perfect-number-thm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perfect-number-thm/</guid>
           <description></description>
         </item>
         <item>
           <title>Perron_Frobenius</title>
           <link>/sessions/perron_frobenius/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/perron_frobenius/</guid>
           <description></description>
         </item>
         <item>
           <title>pGCL</title>
           <link>/sessions/pgcl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pgcl/</guid>
           <description></description>
         </item>
         <item>
           <title>Physical_Quantities</title>
           <link>/sessions/physical_quantities/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/physical_quantities/</guid>
           <description></description>
         </item>
         <item>
           <title>Pi_Calculus</title>
           <link>/sessions/pi_calculus/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pi_calculus/</guid>
           <description></description>
         </item>
         <item>
           <title>Pi_Transcendental</title>
           <link>/sessions/pi_transcendental/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pi_transcendental/</guid>
           <description></description>
         </item>
         <item>
           <title>Planarity_Certificates</title>
           <link>/sessions/planarity_certificates/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/planarity_certificates/</guid>
           <description></description>
         </item>
         <item>
           <title>PLM</title>
           <link>/sessions/plm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/plm/</guid>
           <description></description>
         </item>
         <item>
           <title>Pluennecke_Ruzsa_Inequality</title>
           <link>/sessions/pluennecke_ruzsa_inequality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pluennecke_ruzsa_inequality/</guid>
           <description></description>
         </item>
         <item>
           <title>Poincare_Bendixson</title>
           <link>/sessions/poincare_bendixson/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poincare_bendixson/</guid>
           <description></description>
         </item>
         <item>
           <title>Poincare_Disc</title>
           <link>/sessions/poincare_disc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poincare_disc/</guid>
           <description></description>
         </item>
         <item>
           <title>Polygonal_Number_Theorem</title>
           <link>/sessions/polygonal_number_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polygonal_number_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Polylog</title>
           <link>/sessions/polylog/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polylog/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Crit_Geometry</title>
           <link>/sessions/polynomial_crit_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_crit_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Factorization</title>
           <link>/sessions/polynomial_factorization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_factorization/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomial_Interpolation</title>
           <link>/sessions/polynomial_interpolation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomial_interpolation/</guid>
           <description></description>
         </item>
         <item>
           <title>Polynomials</title>
           <link>/sessions/polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Pop_Refinement</title>
           <link>/sessions/pop_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pop_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>POPLmark-deBruijn</title>
           <link>/sessions/poplmark-debruijn/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/poplmark-debruijn/</guid>
           <description></description>
         </item>
         <item>
           <title>Posix-Lexing</title>
           <link>/sessions/posix-lexing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/posix-lexing/</guid>
           <description></description>
         </item>
         <item>
           <title>Possibilistic_Noninterference</title>
           <link>/sessions/possibilistic_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/possibilistic_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>Power_Sum_Polynomials</title>
           <link>/sessions/power_sum_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/power_sum_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Pratt_Certificate</title>
           <link>/sessions/pratt_certificate/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pratt_certificate/</guid>
           <description></description>
         </item>
         <item>
           <title>Prefix_Free_Code_Combinators</title>
           <link>/sessions/prefix_free_code_combinators/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prefix_free_code_combinators/</guid>
           <description></description>
         </item>
         <item>
           <title>Presburger-Automata</title>
           <link>/sessions/presburger-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/presburger-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Prim_Dijkstra_Simple</title>
           <link>/sessions/prim_dijkstra_simple/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prim_dijkstra_simple/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Distribution_Elementary</title>
           <link>/sessions/prime_distribution_elementary/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_distribution_elementary/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Harmonic_Series</title>
           <link>/sessions/prime_harmonic_series/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_harmonic_series/</guid>
           <description></description>
         </item>
         <item>
           <title>Prime_Number_Theorem</title>
           <link>/sessions/prime_number_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prime_number_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Priority_Queue_Braun</title>
           <link>/sessions/priority_queue_braun/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/priority_queue_braun/</guid>
           <description></description>
         </item>
         <item>
           <title>Priority_Search_Trees</title>
           <link>/sessions/priority_search_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/priority_search_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Noninterference</title>
           <link>/sessions/probabilistic_noninterference/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_noninterference/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Prime_Tests</title>
           <link>/sessions/probabilistic_prime_tests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_prime_tests/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_System_Zoo</title>
           <link>/sessions/probabilistic_system_zoo/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_system_zoo/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_Timed_Automata</title>
           <link>/sessions/probabilistic_timed_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_timed_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Probabilistic_While</title>
           <link>/sessions/probabilistic_while/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probabilistic_while/</guid>
           <description></description>
         </item>
         <item>
           <title>Probability_Inequality_Completeness</title>
           <link>/sessions/probability_inequality_completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/probability_inequality_completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Program-Conflict-Analysis</title>
           <link>/sessions/program-conflict-analysis/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/program-conflict-analysis/</guid>
           <description></description>
         </item>
         <item>
           <title>Progress_Tracking</title>
           <link>/sessions/progress_tracking/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/progress_tracking/</guid>
           <description></description>
         </item>
         <item>
           <title>Projective_Geometry</title>
           <link>/sessions/projective_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/projective_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Projective_Measurements</title>
           <link>/sessions/projective_measurements/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/projective_measurements/</guid>
           <description></description>
         </item>
         <item>
           <title>Promela</title>
           <link>/sessions/promela/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/promela/</guid>
           <description></description>
         </item>
         <item>
           <title>Proof_Strategy_Language</title>
           <link>/sessions/proof_strategy_language/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/proof_strategy_language/</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional_Logic_Class</title>
           <link>/sessions/propositional_logic_class/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/propositional_logic_class/</guid>
           <description></description>
         </item>
         <item>
           <title>Propositional_Proof_Systems</title>
           <link>/sessions/propositional_proof_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/propositional_proof_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>PropResPI</title>
           <link>/sessions/proprespi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/proprespi/</guid>
           <description></description>
         </item>
         <item>
           <title>Prpu_Maxflow</title>
           <link>/sessions/prpu_maxflow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/prpu_maxflow/</guid>
           <description></description>
         </item>
         <item>
           <title>PSemigroupsConvolution</title>
           <link>/sessions/psemigroupsconvolution/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/psemigroupsconvolution/</guid>
           <description></description>
         </item>
         <item>
           <title>PseudoHoops</title>
           <link>/sessions/pseudohoops/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pseudohoops/</guid>
           <description></description>
         </item>
         <item>
           <title>Psi_Calculi</title>
           <link>/sessions/psi_calculi/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/psi_calculi/</guid>
           <description></description>
         </item>
         <item>
           <title>Ptolemys_Theorem</title>
           <link>/sessions/ptolemys_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ptolemys_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Public_Announcement_Logic</title>
           <link>/sessions/public_announcement_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/public_announcement_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Pushdown_Systems</title>
           <link>/sessions/pushdown_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/pushdown_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Q0_Metatheory</title>
           <link>/sessions/q0_metatheory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/q0_metatheory/</guid>
           <description></description>
         </item>
         <item>
           <title>Q0_Soundness</title>
           <link>/sessions/q0_soundness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/q0_soundness/</guid>
           <description></description>
         </item>
         <item>
           <title>QBF_Solver_Verification</title>
           <link>/sessions/qbf_solver_verification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qbf_solver_verification/</guid>
           <description></description>
         </item>
         <item>
           <title>QHLProver</title>
           <link>/sessions/qhlprover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qhlprover/</guid>
           <description></description>
         </item>
         <item>
           <title>QR_Decomposition</title>
           <link>/sessions/qr_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/qr_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales</title>
           <link>/sessions/quantales/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantales/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantales_Converse</title>
           <link>/sessions/quantales_converse/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantales_converse/</guid>
           <description></description>
         </item>
         <item>
           <title>Quantifier_Elimination_Hybrid</title>
           <link>/sessions/quantifier_elimination_hybrid/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quantifier_elimination_hybrid/</guid>
           <description></description>
         </item>
         <item>
           <title>Quasi_Borel_Spaces</title>
           <link>/sessions/quasi_borel_spaces/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quasi_borel_spaces/</guid>
           <description></description>
         </item>
         <item>
           <title>Quaternions</title>
           <link>/sessions/quaternions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quaternions/</guid>
           <description></description>
         </item>
         <item>
           <title>Query_Optimization</title>
           <link>/sessions/query_optimization/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/query_optimization/</guid>
           <description></description>
         </item>
         <item>
           <title>Quick_Sort_Cost</title>
           <link>/sessions/quick_sort_cost/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/quick_sort_cost/</guid>
           <description></description>
         </item>
         <item>
           <title>Ramsey-Infinite</title>
           <link>/sessions/ramsey-infinite/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ramsey-infinite/</guid>
           <description></description>
         </item>
         <item>
           <title>Random_BSTs</title>
           <link>/sessions/random_bsts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/random_bsts/</guid>
           <description></description>
         </item>
         <item>
           <title>Random_Graph_Subgraph_Threshold</title>
           <link>/sessions/random_graph_subgraph_threshold/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/random_graph_subgraph_threshold/</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised_BSTs</title>
           <link>/sessions/randomised_bsts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/randomised_bsts/</guid>
           <description></description>
         </item>
         <item>
           <title>Randomised_Social_Choice</title>
           <link>/sessions/randomised_social_choice/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/randomised_social_choice/</guid>
           <description></description>
         </item>
         <item>
           <title>Rank_Nullity_Theorem</title>
           <link>/sessions/rank_nullity_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rank_nullity_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Impl</title>
           <link>/sessions/real_impl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_impl/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Power</title>
           <link>/sessions/real_power/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_power/</guid>
           <description></description>
         </item>
         <item>
           <title>Real_Time_Deque</title>
           <link>/sessions/real_time_deque/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/real_time_deque/</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion-Addition</title>
           <link>/sessions/recursion-addition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/recursion-addition/</guid>
           <description></description>
         </item>
         <item>
           <title>Recursion-Theory-I</title>
           <link>/sessions/recursion-theory-i/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/recursion-theory-i/</guid>
           <description></description>
         </item>
         <item>
           <title>Refine_Imperative_HOL</title>
           <link>/sessions/refine_imperative_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refine_imperative_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>Refine_Monadic</title>
           <link>/sessions/refine_monadic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refine_monadic/</guid>
           <description></description>
         </item>
         <item>
           <title>RefinementReactive</title>
           <link>/sessions/refinementreactive/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/refinementreactive/</guid>
           <description></description>
         </item>
         <item>
           <title>Regex_Equivalence</title>
           <link>/sessions/regex_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regex_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Region_Quadtrees</title>
           <link>/sessions/region_quadtrees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/region_quadtrees/</guid>
           <description></description>
         </item>
         <item>
           <title>Registers</title>
           <link>/sessions/registers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/registers/</guid>
           <description></description>
         </item>
         <item>
           <title>Regression_Test_Selection</title>
           <link>/sessions/regression_test_selection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regression_test_selection/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular_Algebras</title>
           <link>/sessions/regular_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular_Tree_Relations</title>
           <link>/sessions/regular_tree_relations/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular_tree_relations/</guid>
           <description></description>
         </item>
         <item>
           <title>Regular-Sets</title>
           <link>/sessions/regular-sets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/regular-sets/</guid>
           <description></description>
         </item>
         <item>
           <title>Relation_Algebra</title>
           <link>/sessions/relation_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relation_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Cardinality</title>
           <link>/sessions/relational_cardinality/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_cardinality/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Disjoint_Set_Forests</title>
           <link>/sessions/relational_disjoint_set_forests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_disjoint_set_forests/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Forests</title>
           <link>/sessions/relational_forests/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_forests/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Method</title>
           <link>/sessions/relational_method/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_method/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Minimum_Spanning_Trees</title>
           <link>/sessions/relational_minimum_spanning_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_minimum_spanning_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational_Paths</title>
           <link>/sessions/relational_paths/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational_paths/</guid>
           <description></description>
         </item>
         <item>
           <title>Relational-Incorrectness-Logic</title>
           <link>/sessions/relational-incorrectness-logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/relational-incorrectness-logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Rensets</title>
           <link>/sessions/rensets/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rensets/</guid>
           <description></description>
         </item>
         <item>
           <title>Rep_Fin_Groups</title>
           <link>/sessions/rep_fin_groups/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rep_fin_groups/</guid>
           <description></description>
         </item>
         <item>
           <title>Residuated_Lattices</title>
           <link>/sessions/residuated_lattices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/residuated_lattices/</guid>
           <description></description>
         </item>
         <item>
           <title>ResiduatedTransitionSystem</title>
           <link>/sessions/residuatedtransitionsystem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/residuatedtransitionsystem/</guid>
           <description></description>
         </item>
         <item>
           <title>Resolution_FOL</title>
           <link>/sessions/resolution_fol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/resolution_fol/</guid>
           <description></description>
         </item>
         <item>
           <title>Rewrite_Properties_Reduction</title>
           <link>/sessions/rewrite_properties_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rewrite_properties_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Rewriting_Z</title>
           <link>/sessions/rewriting_z/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rewriting_z/</guid>
           <description></description>
         </item>
         <item>
           <title>Ribbon_Proofs</title>
           <link>/sessions/ribbon_proofs/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ribbon_proofs/</guid>
           <description></description>
         </item>
         <item>
           <title>RIPEMD-160-SPARK</title>
           <link>/sessions/ripemd-160-spark/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/ripemd-160-spark/</guid>
           <description></description>
         </item>
         <item>
           <title>Risk_Free_Lending</title>
           <link>/sessions/risk_free_lending/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/risk_free_lending/</guid>
           <description></description>
         </item>
         <item>
           <title>Robbins-Conjecture</title>
           <link>/sessions/robbins-conjecture/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robbins-conjecture/</guid>
           <description></description>
         </item>
         <item>
           <title>ROBDD</title>
           <link>/sessions/robdd/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robdd/</guid>
           <description></description>
         </item>
         <item>
           <title>Robinson_Arithmetic</title>
           <link>/sessions/robinson_arithmetic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/robinson_arithmetic/</guid>
           <description></description>
         </item>
         <item>
           <title>Root_Balanced_Tree</title>
           <link>/sessions/root_balanced_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/root_balanced_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Roth_Arithmetic_Progressions</title>
           <link>/sessions/roth_arithmetic_progressions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/roth_arithmetic_progressions/</guid>
           <description></description>
         </item>
         <item>
           <title>Routing</title>
           <link>/sessions/routing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/routing/</guid>
           <description></description>
         </item>
         <item>
           <title>Roy_Floyd_Warshall</title>
           <link>/sessions/roy_floyd_warshall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/roy_floyd_warshall/</guid>
           <description></description>
         </item>
         <item>
           <title>RSAPSS</title>
           <link>/sessions/rsapss/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/rsapss/</guid>
           <description></description>
         </item>
         <item>
           <title>S_Finite_Measure_Monad</title>
           <link>/sessions/s_finite_measure_monad/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/s_finite_measure_monad/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_Distance</title>
           <link>/sessions/safe_distance/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_distance/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_OCL</title>
           <link>/sessions/safe_ocl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_ocl/</guid>
           <description></description>
         </item>
         <item>
           <title>Safe_Range_RC</title>
           <link>/sessions/safe_range_rc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/safe_range_rc/</guid>
           <description></description>
         </item>
         <item>
           <title>SATSolverVerification</title>
           <link>/sessions/satsolververification/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/satsolververification/</guid>
           <description></description>
         </item>
         <item>
           <title>Saturation_Framework</title>
           <link>/sessions/saturation_framework/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/saturation_framework/</guid>
           <description></description>
         </item>
         <item>
           <title>Saturation_Framework_Extensions</title>
           <link>/sessions/saturation_framework_extensions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/saturation_framework_extensions/</guid>
           <description></description>
         </item>
         <item>
           <title>Sauer_Shelah_Lemma</title>
           <link>/sessions/sauer_shelah_lemma/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sauer_shelah_lemma/</guid>
           <description></description>
         </item>
         <item>
           <title>SC_DOM_Components</title>
           <link>/sessions/sc_dom_components/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sc_dom_components/</guid>
           <description></description>
         </item>
         <item>
           <title>SCC_Bloemen_Sequential</title>
           <link>/sessions/scc_bloemen_sequential/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/scc_bloemen_sequential/</guid>
           <description></description>
         </item>
         <item>
           <title>Schutz_Spacetime</title>
           <link>/sessions/schutz_spacetime/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/schutz_spacetime/</guid>
           <description></description>
         </item>
         <item>
           <title>Schwartz_Zippel</title>
           <link>/sessions/schwartz_zippel/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/schwartz_zippel/</guid>
           <description></description>
         </item>
         <item>
           <title>SDS_Impossibility</title>
           <link>/sessions/sds_impossibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sds_impossibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Secondary_Sylow</title>
           <link>/sessions/secondary_sylow/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/secondary_sylow/</guid>
           <description></description>
         </item>
         <item>
           <title>Security_Protocol_Refinement</title>
           <link>/sessions/security_protocol_refinement/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/security_protocol_refinement/</guid>
           <description></description>
         </item>
         <item>
           <title>Selection_Heap_Sort</title>
           <link>/sessions/selection_heap_sort/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/selection_heap_sort/</guid>
           <description></description>
         </item>
         <item>
           <title>SenSocialChoice</title>
           <link>/sessions/sensocialchoice/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sensocialchoice/</guid>
           <description></description>
         </item>
         <item>
           <title>Separata</title>
           <link>/sessions/separata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separata/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Algebra</title>
           <link>/sessions/separation_algebra/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_algebra/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Logic_Imperative_HOL</title>
           <link>/sessions/separation_logic_imperative_hol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_logic_imperative_hol/</guid>
           <description></description>
         </item>
         <item>
           <title>Separation_Logic_Unbounded</title>
           <link>/sessions/separation_logic_unbounded/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/separation_logic_unbounded/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_Basic</title>
           <link>/sessions/sepref_basic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_basic/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_IICF</title>
           <link>/sessions/sepref_iicf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_iicf/</guid>
           <description></description>
         </item>
         <item>
           <title>Sepref_Prereq</title>
           <link>/sessions/sepref_prereq/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sepref_prereq/</guid>
           <description></description>
         </item>
         <item>
           <title>SequentInvertibility</title>
           <link>/sessions/sequentinvertibility/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sequentinvertibility/</guid>
           <description></description>
         </item>
         <item>
           <title>Shadow_DOM</title>
           <link>/sessions/shadow_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shadow_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Shadow_SC_DOM</title>
           <link>/sessions/shadow_sc_dom/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shadow_sc_dom/</guid>
           <description></description>
         </item>
         <item>
           <title>Shivers-CFA</title>
           <link>/sessions/shivers-cfa/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shivers-cfa/</guid>
           <description></description>
         </item>
         <item>
           <title>ShortestPath</title>
           <link>/sessions/shortestpath/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/shortestpath/</guid>
           <description></description>
         </item>
         <item>
           <title>Show</title>
           <link>/sessions/show/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/show/</guid>
           <description></description>
         </item>
         <item>
           <title>SIFPL</title>
           <link>/sessions/sifpl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sifpl/</guid>
           <description></description>
         </item>
         <item>
           <title>SIFUM_Type_Systems</title>
           <link>/sessions/sifum_type_systems/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sifum_type_systems/</guid>
           <description></description>
         </item>
         <item>
           <title>Sigma_Commit_Crypto</title>
           <link>/sessions/sigma_commit_crypto/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sigma_commit_crypto/</guid>
           <description></description>
         </item>
         <item>
           <title>Signature_Groebner</title>
           <link>/sessions/signature_groebner/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/signature_groebner/</guid>
           <description></description>
         </item>
         <item>
           <title>Simpl</title>
           <link>/sessions/simpl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simpl/</guid>
           <description></description>
         </item>
         <item>
           <title>Simple_Clause_Learning</title>
           <link>/sessions/simple_clause_learning/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simple_clause_learning/</guid>
           <description></description>
         </item>
         <item>
           <title>Simple_Firewall</title>
           <link>/sessions/simple_firewall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simple_firewall/</guid>
           <description></description>
         </item>
         <item>
           <title>Simplex</title>
           <link>/sessions/simplex/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplex/</guid>
           <description></description>
         </item>
         <item>
           <title>Simplicial_complexes_and_boolean_functions</title>
           <link>/sessions/simplicial_complexes_and_boolean_functions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplicial_complexes_and_boolean_functions/</guid>
           <description></description>
         </item>
         <item>
           <title>SimplifiedOntologicalArgument</title>
           <link>/sessions/simplifiedontologicalargument/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/simplifiedontologicalargument/</guid>
           <description></description>
         </item>
         <item>
           <title>Skew_Heap</title>
           <link>/sessions/skew_heap/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/skew_heap/</guid>
           <description></description>
         </item>
         <item>
           <title>Skip_Lists</title>
           <link>/sessions/skip_lists/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/skip_lists/</guid>
           <description></description>
         </item>
         <item>
           <title>Slicing</title>
           <link>/sessions/slicing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/slicing/</guid>
           <description></description>
         </item>
         <item>
           <title>Sliding_Window_Algorithm</title>
           <link>/sessions/sliding_window_algorithm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sliding_window_algorithm/</guid>
           <description></description>
         </item>
         <item>
           <title>SM</title>
           <link>/sessions/sm/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sm/</guid>
           <description></description>
         </item>
         <item>
           <title>SM_Base</title>
           <link>/sessions/sm_base/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sm_base/</guid>
           <description></description>
         </item>
         <item>
           <title>Smith_Normal_Form</title>
           <link>/sessions/smith_normal_form/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/smith_normal_form/</guid>
           <description></description>
         </item>
         <item>
           <title>Smooth_Manifolds</title>
           <link>/sessions/smooth_manifolds/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/smooth_manifolds/</guid>
           <description></description>
         </item>
         <item>
           <title>Solidity</title>
           <link>/sessions/solidity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/solidity/</guid>
           <description></description>
         </item>
         <item>
           <title>Sophomores_Dream</title>
           <link>/sessions/sophomores_dream/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sophomores_dream/</guid>
           <description></description>
         </item>
         <item>
           <title>Sort_Encodings</title>
           <link>/sessions/sort_encodings/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sort_encodings/</guid>
           <description></description>
         </item>
         <item>
           <title>Source_Coding_Theorem</title>
           <link>/sessions/source_coding_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/source_coding_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>SPARCv8</title>
           <link>/sessions/sparcv8/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sparcv8/</guid>
           <description></description>
         </item>
         <item>
           <title>SpecCheck</title>
           <link>/sessions/speccheck/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/speccheck/</guid>
           <description></description>
         </item>
         <item>
           <title>Special_Function_Bounds</title>
           <link>/sessions/special_function_bounds/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/special_function_bounds/</guid>
           <description></description>
         </item>
         <item>
           <title>Splay_Tree</title>
           <link>/sessions/splay_tree/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/splay_tree/</guid>
           <description></description>
         </item>
         <item>
           <title>Sqrt_Babylonian</title>
           <link>/sessions/sqrt_babylonian/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sqrt_babylonian/</guid>
           <description></description>
         </item>
         <item>
           <title>Stable_Matching</title>
           <link>/sessions/stable_matching/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stable_matching/</guid>
           <description></description>
         </item>
         <item>
           <title>Stalnaker_Logic</title>
           <link>/sessions/stalnaker_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stalnaker_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Standard_Borel_Spaces</title>
           <link>/sessions/standard_borel_spaces/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/standard_borel_spaces/</guid>
           <description></description>
         </item>
         <item>
           <title>Statecharts</title>
           <link>/sessions/statecharts/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/statecharts/</guid>
           <description></description>
         </item>
         <item>
           <title>Stateful_Protocol_Composition_and_Typing</title>
           <link>/sessions/stateful_protocol_composition_and_typing/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stateful_protocol_composition_and_typing/</guid>
           <description></description>
         </item>
         <item>
           <title>Stellar_Quorums</title>
           <link>/sessions/stellar_quorums/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stellar_quorums/</guid>
           <description></description>
         </item>
         <item>
           <title>Stern_Brocot</title>
           <link>/sessions/stern_brocot/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stern_brocot/</guid>
           <description></description>
         </item>
         <item>
           <title>Stewart_Apollonius</title>
           <link>/sessions/stewart_apollonius/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stewart_apollonius/</guid>
           <description></description>
         </item>
         <item>
           <title>Stirling_Formula</title>
           <link>/sessions/stirling_formula/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stirling_formula/</guid>
           <description></description>
         </item>
         <item>
           <title>Stochastic_Matrices</title>
           <link>/sessions/stochastic_matrices/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stochastic_matrices/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Algebras</title>
           <link>/sessions/stone_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Kleene_Relation_Algebras</title>
           <link>/sessions/stone_kleene_relation_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_kleene_relation_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Stone_Relation_Algebras</title>
           <link>/sessions/stone_relation_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stone_relation_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Store_Buffer_Reduction</title>
           <link>/sessions/store_buffer_reduction/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/store_buffer_reduction/</guid>
           <description></description>
         </item>
         <item>
           <title>Stream_Fusion_Code</title>
           <link>/sessions/stream_fusion_code/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stream_fusion_code/</guid>
           <description></description>
         </item>
         <item>
           <title>Stream-Fusion</title>
           <link>/sessions/stream-fusion/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stream-fusion/</guid>
           <description></description>
         </item>
         <item>
           <title>StrictOmegaCategories</title>
           <link>/sessions/strictomegacategories/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/strictomegacategories/</guid>
           <description></description>
         </item>
         <item>
           <title>Strong_Security</title>
           <link>/sessions/strong_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/strong_security/</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm_Sequences</title>
           <link>/sessions/sturm_sequences/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sturm_sequences/</guid>
           <description></description>
         </item>
         <item>
           <title>Sturm_Tarski</title>
           <link>/sessions/sturm_tarski/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sturm_tarski/</guid>
           <description></description>
         </item>
         <item>
           <title>Stuttering_Equivalence</title>
           <link>/sessions/stuttering_equivalence/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/stuttering_equivalence/</guid>
           <description></description>
         </item>
         <item>
           <title>Subresultants</title>
           <link>/sessions/subresultants/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/subresultants/</guid>
           <description></description>
         </item>
         <item>
           <title>Subset_Boolean_Algebras</title>
           <link>/sessions/subset_boolean_algebras/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/subset_boolean_algebras/</guid>
           <description></description>
         </item>
         <item>
           <title>Sumcheck_Protocol</title>
           <link>/sessions/sumcheck_protocol/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sumcheck_protocol/</guid>
           <description></description>
         </item>
         <item>
           <title>SumSquares</title>
           <link>/sessions/sumsquares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sumsquares/</guid>
           <description></description>
         </item>
         <item>
           <title>Sunflowers</title>
           <link>/sessions/sunflowers/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/sunflowers/</guid>
           <description></description>
         </item>
         <item>
           <title>SuperCalc</title>
           <link>/sessions/supercalc/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/supercalc/</guid>
           <description></description>
         </item>
         <item>
           <title>Suppes_Theorem</title>
           <link>/sessions/suppes_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/suppes_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Surprise_Paradox</title>
           <link>/sessions/surprise_paradox/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/surprise_paradox/</guid>
           <description></description>
         </item>
         <item>
           <title>Symmetric_Polynomials</title>
           <link>/sessions/symmetric_polynomials/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/symmetric_polynomials/</guid>
           <description></description>
         </item>
         <item>
           <title>Syntax_Independent_Logic</title>
           <link>/sessions/syntax_independent_logic/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/syntax_independent_logic/</guid>
           <description></description>
         </item>
         <item>
           <title>Synthetic_Completeness</title>
           <link>/sessions/synthetic_completeness/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/synthetic_completeness/</guid>
           <description></description>
         </item>
         <item>
           <title>Szemeredi_Regularity</title>
           <link>/sessions/szemeredi_regularity/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/szemeredi_regularity/</guid>
           <description></description>
         </item>
         <item>
           <title>Szpilrajn</title>
           <link>/sessions/szpilrajn/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/szpilrajn/</guid>
           <description></description>
         </item>
         <item>
           <title>Tail_Recursive_Functions</title>
           <link>/sessions/tail_recursive_functions/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tail_recursive_functions/</guid>
           <description></description>
         </item>
         <item>
           <title>Tarskis_Geometry</title>
           <link>/sessions/tarskis_geometry/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tarskis_geometry/</guid>
           <description></description>
         </item>
         <item>
           <title>Taylor_Models</title>
           <link>/sessions/taylor_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/taylor_models/</guid>
           <description></description>
         </item>
         <item>
           <title>TESL_Language</title>
           <link>/sessions/tesl_language/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tesl_language/</guid>
           <description></description>
         </item>
         <item>
           <title>Three_Circles</title>
           <link>/sessions/three_circles/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/three_circles/</guid>
           <description></description>
         </item>
         <item>
           <title>Three_Squares</title>
           <link>/sessions/three_squares/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/three_squares/</guid>
           <description></description>
         </item>
         <item>
           <title>Timed_Automata</title>
           <link>/sessions/timed_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/timed_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>TLA</title>
           <link>/sessions/tla/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tla/</guid>
           <description></description>
         </item>
         <item>
           <title>Topological_Semantics</title>
           <link>/sessions/topological_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/topological_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Topology</title>
           <link>/sessions/topology/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/topology/</guid>
           <description></description>
         </item>
         <item>
           <title>TortoiseHare</title>
           <link>/sessions/tortoisehare/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tortoisehare/</guid>
           <description></description>
         </item>
         <item>
           <title>Transcendence_Series_Hancl_Rucki</title>
           <link>/sessions/transcendence_series_hancl_rucki/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transcendence_series_hancl_rucki/</guid>
           <description></description>
         </item>
         <item>
           <title>Transformer_Semantics</title>
           <link>/sessions/transformer_semantics/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transformer_semantics/</guid>
           <description></description>
         </item>
         <item>
           <title>Transition_Systems_and_Automata</title>
           <link>/sessions/transition_systems_and_automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transition_systems_and_automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive_Models</title>
           <link>/sessions/transitive_models/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive_models/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive-Closure</title>
           <link>/sessions/transitive-closure/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive-closure/</guid>
           <description></description>
         </item>
         <item>
           <title>Transitive-Closure-II</title>
           <link>/sessions/transitive-closure-ii/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transitive-closure-ii/</guid>
           <description></description>
         </item>
         <item>
           <title>Transport</title>
           <link>/sessions/transport/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/transport/</guid>
           <description></description>
         </item>
         <item>
           <title>Treaps</title>
           <link>/sessions/treaps/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/treaps/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree_Decomposition</title>
           <link>/sessions/tree_decomposition/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree_decomposition/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree_Enumeration</title>
           <link>/sessions/tree_enumeration/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree_enumeration/</guid>
           <description></description>
         </item>
         <item>
           <title>Tree-Automata</title>
           <link>/sessions/tree-automata/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tree-automata/</guid>
           <description></description>
         </item>
         <item>
           <title>Triangle</title>
           <link>/sessions/triangle/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/triangle/</guid>
           <description></description>
         </item>
         <item>
           <title>Trie</title>
           <link>/sessions/trie/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/trie/</guid>
           <description></description>
         </item>
         <item>
           <title>TsirelsonBound</title>
           <link>/sessions/tsirelsonbound/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tsirelsonbound/</guid>
           <description></description>
         </item>
         <item>
           <title>Turans_Graph_Theorem</title>
           <link>/sessions/turans_graph_theorem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/turans_graph_theorem/</guid>
           <description></description>
         </item>
         <item>
           <title>Twelvefold_Way</title>
           <link>/sessions/twelvefold_way/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/twelvefold_way/</guid>
           <description></description>
         </item>
         <item>
           <title>Two_Generated_Word_Monoids_Intersection</title>
           <link>/sessions/two_generated_word_monoids_intersection/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/two_generated_word_monoids_intersection/</guid>
           <description></description>
         </item>
         <item>
           <title>Tycon</title>
           <link>/sessions/tycon/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/tycon/</guid>
           <description></description>
         </item>
         <item>
           <title>Types_Tableaus_and_Goedels_God</title>
           <link>/sessions/types_tableaus_and_goedels_god/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/types_tableaus_and_goedels_god/</guid>
           <description></description>
         </item>
         <item>
           <title>Types_To_Sets_Extension</title>
           <link>/sessions/types_to_sets_extension/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/types_to_sets_extension/</guid>
           <description></description>
         </item>
         <item>
           <title>Undirected_Graph_Theory</title>
           <link>/sessions/undirected_graph_theory/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/undirected_graph_theory/</guid>
           <description></description>
         </item>
         <item>
           <title>Universal_Hash_Families</title>
           <link>/sessions/universal_hash_families/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/universal_hash_families/</guid>
           <description></description>
         </item>
         <item>
           <title>Universal_Turing_Machine</title>
           <link>/sessions/universal_turing_machine/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/universal_turing_machine/</guid>
           <description></description>
         </item>
         <item>
           <title>UpDown_Scheme</title>
           <link>/sessions/updown_scheme/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/updown_scheme/</guid>
           <description></description>
         </item>
         <item>
           <title>UPF</title>
           <link>/sessions/upf/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/upf/</guid>
           <description></description>
         </item>
         <item>
           <title>UPF_Firewall</title>
           <link>/sessions/upf_firewall/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/upf_firewall/</guid>
           <description></description>
         </item>
         <item>
           <title>UTP</title>
           <link>/sessions/utp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/utp/</guid>
           <description></description>
         </item>
         <item>
           <title>UTP-Toolkit</title>
           <link>/sessions/utp-toolkit/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/utp-toolkit/</guid>
           <description></description>
         </item>
         <item>
           <title>Valuation</title>
           <link>/sessions/valuation/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/valuation/</guid>
           <description></description>
         </item>
         <item>
           <title>Van_der_Waerden</title>
           <link>/sessions/van_der_waerden/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/van_der_waerden/</guid>
           <description></description>
         </item>
         <item>
           <title>Van_Emde_Boas_Trees</title>
           <link>/sessions/van_emde_boas_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/van_emde_boas_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>VectorSpace</title>
           <link>/sessions/vectorspace/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/vectorspace/</guid>
           <description></description>
         </item>
         <item>
           <title>VeriComp</title>
           <link>/sessions/vericomp/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/vericomp/</guid>
           <description></description>
         </item>
         <item>
           <title>Verified_SAT_Based_AI_Planning</title>
           <link>/sessions/verified_sat_based_ai_planning/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/verified_sat_based_ai_planning/</guid>
           <description></description>
         </item>
         <item>
           <title>Verified-Prover</title>
           <link>/sessions/verified-prover/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/verified-prover/</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis2018</title>
           <link>/sessions/verifythis2018/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/verifythis2018/</guid>
           <description></description>
         </item>
         <item>
           <title>VerifyThis2019</title>
           <link>/sessions/verifythis2019/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/verifythis2019/</guid>
           <description></description>
         </item>
         <item>
           <title>Vickrey_Clarke_Groves</title>
           <link>/sessions/vickrey_clarke_groves/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/vickrey_clarke_groves/</guid>
           <description></description>
         </item>
         <item>
           <title>Virtual_Substitution</title>
           <link>/sessions/virtual_substitution/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/virtual_substitution/</guid>
           <description></description>
         </item>
         <item>
           <title>VolpanoSmith</title>
           <link>/sessions/volpanosmith/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/volpanosmith/</guid>
           <description></description>
         </item>
         <item>
           <title>VYDRA_MDL</title>
           <link>/sessions/vydra_mdl/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/vydra_mdl/</guid>
           <description></description>
         </item>
         <item>
           <title>WebAssembly</title>
           <link>/sessions/webassembly/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/webassembly/</guid>
           <description></description>
         </item>
         <item>
           <title>Weight_Balanced_Trees</title>
           <link>/sessions/weight_balanced_trees/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/weight_balanced_trees/</guid>
           <description></description>
         </item>
         <item>
           <title>Weighted_Arithmetic_Geometric_Mean</title>
           <link>/sessions/weighted_arithmetic_geometric_mean/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/weighted_arithmetic_geometric_mean/</guid>
           <description></description>
         </item>
         <item>
           <title>Weighted_Path_Order</title>
           <link>/sessions/weighted_path_order/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/weighted_path_order/</guid>
           <description></description>
         </item>
         <item>
           <title>Well_Quasi_Orders</title>
           <link>/sessions/well_quasi_orders/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/well_quasi_orders/</guid>
           <description></description>
         </item>
         <item>
           <title>Wetzels_Problem</title>
           <link>/sessions/wetzels_problem/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/wetzels_problem/</guid>
           <description></description>
         </item>
         <item>
           <title>WHATandWHERE_Security</title>
           <link>/sessions/whatandwhere_security/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/whatandwhere_security/</guid>
           <description></description>
         </item>
         <item>
           <title>Wieferich_Kempner</title>
           <link>/sessions/wieferich_kempner/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/wieferich_kempner/</guid>
           <description></description>
         </item>
         <item>
           <title>Winding_Number_Eval</title>
           <link>/sessions/winding_number_eval/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/winding_number_eval/</guid>
           <description></description>
         </item>
         <item>
           <title>WOOT_Strong_Eventual_Consistency</title>
           <link>/sessions/woot_strong_eventual_consistency/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/woot_strong_eventual_consistency/</guid>
           <description></description>
         </item>
         <item>
           <title>Word_Lib</title>
           <link>/sessions/word_lib/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
           <guid>/sessions/word_lib/</guid>
           <description></description>
         </item>
         <item>
           <title>WorkerWrapper</title>
           <link>/sessions/workerwrapper/</link>
           <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
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     <h2>Subject Classification</h2>
       <p>ACM: <a href="https://dl.acm.org/topic/ccs2012/10003752.10003809.10003636">Theory of computation~Approximation algorithms analysis</a></p>
       <p>AMS: <a href="https://mathscinet.ams.org/mathscinet/msc/msc2020.html?t=68W25">Computer science / Algorithms in computer science / Approximation algorithms</a></p>
+    <h2 class="head">2024</h2>
+      <article class="entry">
+        <div class="item-text">
+          <h5><a class="title" href="../../../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+          <br>
+            by <a href="../../../../authors/tan">Yong Kiam Tan</a> and <a href="../../../../authors/yang">Jiong Yang</a>
+
+        </div>
+        <span class="date">Mar 15</span>
+      </article>
     <h2 class="head">2023</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../../entries/Distributed_Distinct_Elements.html">Distributed Distinct Elements</a></h5>
           <br>
             by <a href="../../../../authors/karayel">Emin Karayel</a>
 
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         <span class="date">Apr 03</span>
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           <h5><a class="title" href="../../../../entries/Frequency_Moments.html">Formalization of Randomized Approximation Algorithms for Frequency Moments</a></h5>
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             by <a href="../../../../authors/karayel">Emin Karayel</a>
 
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           <h5><a class="title" href="../../../../entries/Approximation_Algorithms.html">Verified Approximation Algorithms</a></h5>
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             by <a href="../../../../authors/essmann">Robin Eßmann</a>, <a href="../../../../authors/nipkow">Tobias Nipkow</a>, <a href="../../../../authors/robillard">Simon Robillard</a> and <a href="../../../../authors/sulejmani">Ujkan Sulejmani</a>
 
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           <title>VerifyThis 2019 -- Polished Isabelle Solutions</title>
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           <title>Formalization of Multiway-Join Algorithms</title>
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           <title>Formalisation of an Adaptive State Counting Algorithm</title>
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           <title>Formalisation of an Adaptive State Counting Algorithm</title>
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           <title>Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</title>
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           <title>Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</title>
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           <title>VerifyThis 2018 - Polished Isabelle Solutions</title>
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           <title>The Median-of-Medians Selection Algorithm</title>
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           <title>The string search algorithm by Knuth, Morris and Pratt</title>
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         <item>
           <title>The string search algorithm by Knuth, Morris and Pratt</title>
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         </item>
         <item>
           <title>Lower bound on comparison-based sorting algorithms</title>
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         </item>
         <item>
           <title>Lower bound on comparison-based sorting algorithms</title>
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         </item>
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           <title>The number of comparisons in QuickSort</title>
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           <title>The number of comparisons in QuickSort</title>
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         </item>
         <item>
           <title>A formalisation of the Cocke-Younger-Kasami algorithm</title>
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           <title>A formalisation of the Cocke-Younger-Kasami algorithm</title>
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           <title>Algorithms for Reduced Ordered Binary Decision Diagrams</title>
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           <title>Algorithms for Reduced Ordered Binary Decision Diagrams</title>
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         <item>
           <title>The Tortoise and Hare Algorithm</title>
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           <description></description>
         </item>
         <item>
           <title>The Tortoise and Hare Algorithm</title>
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           <description></description>
         </item>
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           <title>Imperative Insertion Sort</title>
           <link>/entries/Imperative_Insertion_Sort.html</link>
           <pubDate>Thu, 25 Sep 2014 00:00:00 +0000</pubDate>
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           <title>Imperative Insertion Sort</title>
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           <description></description>
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         <item>
           <title>Boolean Expression Checkers</title>
           <link>/entries/Boolean_Expression_Checkers.html</link>
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           <title>Boolean Expression Checkers</title>
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           <description></description>
         </item>
         <item>
           <title>Verification of Selection and Heap Sort Using Locales</title>
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           <title>Verification of Selection and Heap Sort Using Locales</title>
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           <description></description>
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           <title>Efficient Mergesort</title>
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           <pubDate>Wed, 09 Nov 2011 00:00:00 +0000</pubDate>
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           <title>Efficient Mergesort</title>
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           <description></description>
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       <p>AMS: <a href="https://mathscinet.ams.org/mathscinet/msc/msc2020.html?t=68W20">Computer science / Algorithms in computer science / Randomized algorithms</a></p>
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+          <h5><a class="title" href="../../../../entries/Approximate_Model_Counting.html">Approximate Model Counting</a></h5>
+          <br>
+            by <a href="../../../../authors/tan">Yong Kiam Tan</a> and <a href="../../../../authors/yang">Jiong Yang</a>
+
+        </div>
+        <span class="date">Mar 15</span>
+      </article>
+      <article class="entry">
+        <div class="item-text">
           <h5><a class="title" href="../../../../entries/Sumcheck_Protocol.html">The Sumcheck Protocol</a></h5>
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             by <a href="../../../../authors/garvia">Azucena Garvia</a>, <a href="../../../../authors/sprenger">Christoph Sprenger</a> and <a href="../../../../authors/bootle">Jonathan Bootle</a>
 
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           <h5><a class="title" href="../../../../entries/Randomised_BSTs.html">Randomised Binary Search Trees</a></h5>
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       </article>
     <h2 class="head">2017</h2>
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           <br>
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\ No newline at end of file
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     <h2>
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-          <a href="../topics/mathematics/analysis">Analysis (57)</a>
+          <a href="../topics/mathematics/analysis">Analysis (58)</a>
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-        <a href="../topics/tools">Tools (23)</a>
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     <h2 class="head">2024</h2>
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+          <h5><a class="title" href="../../../entries/Continued_Fractions.html">Continued Fractions</a></h5>
+          <br>
+            by <a href="../../../authors/eberl">Manuel Eberl</a>
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+      <article class="entry">
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           <h5><a class="title" href="../../../entries/Fourier.html">Fourier Series</a></h5>
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         <span class="date">Sep 06</span>
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           <h5><a class="title" href="../../../entries/Laplace_Transform.html">Laplace Transform</a></h5>
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           <h5><a class="title" href="../../../entries/Transcendence_Series_Hancl_Rucki.html">The Transcendence of Certain Infinite Series</a></h5>
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           <h5><a class="title" href="../../../entries/Irrationality_J_Hancl.html">Irrational Rapidly Convergent Series</a></h5>
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           <h5><a class="title" href="../../../entries/Error_Function.html">The Error Function</a></h5>
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           <h5><a class="title" href="../../../entries/Green.html">An Isabelle/HOL formalisation of Green&#39;s Theorem</a></h5>
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           <h5><a class="title" href="../../../entries/Count_Complex_Roots.html">Count the Number of Complex Roots</a></h5>
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           <h5><a class="title" href="../../../entries/Zeta_Function.html">The Hurwitz and Riemann ζ Functions</a></h5>
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         <span class="date">Oct 12</span>
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           <h5><a class="title" href="../../../entries/Linear_Recurrences.html">Linear Recurrences</a></h5>
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         <span class="date">Oct 12</span>
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           <h5><a class="title" href="../../../entries/Euler_MacLaurin.html">The Euler–MacLaurin Formula</a></h5>
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           <h5><a class="title" href="../../../entries/Bernoulli.html">Bernoulli Numbers</a></h5>
           <br>
             by <a href="../../../authors/bulwahn">Lukas Bulwahn</a> and <a href="../../../authors/eberl">Manuel Eberl</a>
 
         </div>
         <span class="date">Jan 24</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/E_Transcendental.html">The Transcendence of e</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
         </div>
         <span class="date">Jan 12</span>
       </article>
     <h2 class="head">2016</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Deep_Learning.html">Expressiveness of Deep Learning</a></h5>
           <br>
             by <a href="../../../authors/bentkamp">Alexander Bentkamp</a>
 
         </div>
         <span class="date">Nov 10</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Lp.html">Lp spaces</a></h5>
           <br>
             by <a href="../../../authors/gouezel">Sebastien Gouezel</a>
 
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         <span class="date">Oct 05</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Stirling_Formula.html">Stirling&#39;s formula</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
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         <span class="date">Sep 01</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Cartan_FP.html">The Cartan Fixed Point Theorems</a></h5>
           <br>
             by <a href="../../../authors/paulson">Lawrence C. Paulson</a>
 
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         <span class="date">Mar 08</span>
       </article>
     <h2 class="head">2015</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Liouville_Numbers.html">Liouville numbers</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
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         <span class="date">Dec 28</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Descartes_Sign_Rule.html">Descartes&#39; Rule of Signs</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
         </div>
         <span class="date">Dec 28</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Akra_Bazzi.html">The Akra-Bazzi theorem and the Master theorem</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
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         <span class="date">Jul 14</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Landau_Symbols.html">Landau Symbols</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
         </div>
         <span class="date">Jul 14</span>
       </article>
     <h2 class="head">2014</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Sturm_Tarski.html">The Sturm–Tarski Theorem</a></h5>
           <br>
             by <a href="../../../authors/li">Wenda Li</a>
 
         </div>
         <span class="date">Sep 19</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Special_Function_Bounds.html">Real-Valued Special Functions: Upper and Lower Bounds</a></h5>
           <br>
             by <a href="../../../authors/paulson">Lawrence C. Paulson</a>
 
         </div>
         <span class="date">Aug 29</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Affine_Arithmetic.html">Affine Arithmetic</a></h5>
           <br>
             by <a href="../../../authors/immler">Fabian Immler</a>
 
         </div>
         <span class="date">Feb 07</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Real_Impl.html">Implementing field extensions of the form Q[sqrt(b)]</a></h5>
           <br>
             by <a href="../../../authors/thiemann">René Thiemann</a>
 
         </div>
         <span class="date">Feb 06</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Sturm_Sequences.html">Sturm&#39;s Theorem</a></h5>
           <br>
             by <a href="../../../authors/eberl">Manuel Eberl</a>
 
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         <span class="date">Jan 11</span>
       </article>
     <h2 class="head">2013</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Sqrt_Babylonian.html">Computing N-th Roots using the Babylonian Method</a></h5>
           <br>
             by <a href="../../../authors/thiemann">René Thiemann</a>
 
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         <span class="date">Jan 03</span>
       </article>
     <h2 class="head">2012</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Ordinary_Differential_Equations.html">Ordinary Differential Equations</a></h5>
           <br>
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         <span class="date">Apr 26</span>
       </article>
     <h2 class="head">2011</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Lower_Semicontinuous.html">Lower Semicontinuous Functions</a></h5>
           <br>
             by <a href="../../../authors/grechuk">Bogdan Grechuk</a>
 
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         <span class="date">Jan 08</span>
       </article>
     <h2 class="head">2010</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Polynomials.html">Executable Multivariate Polynomials</a></h5>
           <br>
             by <a href="../../../authors/sternagel">Christian Sternagel</a>, <a href="../../../authors/thiemann">René Thiemann</a>, <a href="../../../authors/maletzky">Alexander Maletzky</a>, <a href="../../../authors/immler">Fabian Immler</a>, <a href="../../../authors/haftmann">Florian Haftmann</a>, <a href="../../../authors/lochbihler">Andreas Lochbihler</a> and <a href="../../../authors/bentkamp">Alexander Bentkamp</a>
 
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         <span class="date">Aug 10</span>
       </article>
     <h2 class="head">2006</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Cauchy.html">Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</a></h5>
           <br>
             by <a href="../../../authors/porter">Benjamin Porter</a>
 
         </div>
         <span class="date">Mar 14</span>
       </article>
     <h2 class="head">2004</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../../entries/Integration.html">Integration theory and random variables</a></h5>
           <br>
             by <a href="../../../authors/richter">Stefan Richter</a>
 
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         <item>
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           <description></description>
         </item>
         <item>
           <title>Irrational Rapidly Convergent Series</title>
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         <item>
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         <item>
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         <item>
           <title>Count the Number of Complex Roots</title>
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           <title>Evaluate Winding Numbers through Cauchy Indices</title>
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           <title>The Hurwitz and Riemann ζ Functions</title>
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         </item>
         <item>
           <title>The Euler–MacLaurin Formula</title>
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           <title>The Euler–MacLaurin Formula</title>
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         <item>
           <title>Bernoulli Numbers</title>
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         <item>
           <title>The Transcendence of e</title>
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           <title>Stirling&#39;s formula</title>
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         <item>
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           <description></description>
         </item>
         <item>
           <title>The Akra-Bazzi theorem and the Master theorem</title>
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           <description></description>
         </item>
         <item>
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           <description></description>
         </item>
         <item>
           <title>The Sturm–Tarski Theorem</title>
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         </item>
         <item>
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         <item>
           <title>Real-Valued Special Functions: Upper and Lower Bounds</title>
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         </item>
         <item>
           <title>Real-Valued Special Functions: Upper and Lower Bounds</title>
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           <description></description>
         </item>
         <item>
           <title>Affine Arithmetic</title>
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           <description></description>
         </item>
         <item>
           <title>Implementing field extensions of the form Q[sqrt(b)]</title>
           <link>/entries/Real_Impl.html</link>
           <pubDate>Thu, 06 Feb 2014 00:00:00 +0000</pubDate>
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           <description></description>
         </item>
         <item>
           <title>Implementing field extensions of the form Q[sqrt(b)]</title>
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           <description></description>
         </item>
         <item>
           <title>Sturm&#39;s Theorem</title>
           <link>/entries/Sturm_Sequences.html</link>
           <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
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         <item>
           <title>Sturm&#39;s Theorem</title>
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         </item>
         <item>
           <title>Computing N-th Roots using the Babylonian Method</title>
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         <item>
           <title>Computing N-th Roots using the Babylonian Method</title>
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           <description></description>
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           <title>Ordinary Differential Equations</title>
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           <description></description>
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+          <h5><a class="title" href="../../entries/Go.html">Go Code Generation for Isabelle</a></h5>
+          <br>
+            by <a href="../../authors/stuebinger">Terru Stübinger</a> and <a href="../../authors/hupel">Lars Hupel</a>
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+        <span class="date">Jan 22</span>
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         <div class="item-text">
           <h5><a class="title" href="../../entries/Conditional_Transfer_Rule.html">Conditional Transfer Rule</a></h5>
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             by <a href="../../authors/milehins">Mihails Milehins</a>
 
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         <span class="date">Sep 06</span>
       </article>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Conditional_Simplification.html">Conditional Simplification</a></h5>
           <br>
             by <a href="../../authors/milehins">Mihails Milehins</a>
 
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         <span class="date">Sep 06</span>
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/SpecCheck.html">SpecCheck - Specification-Based Testing for Isabelle/ML</a></h5>
           <br>
             by <a href="../../authors/kappelmann">Kevin Kappelmann</a>, <a href="../../authors/bulwahn">Lukas Bulwahn</a> and <a href="../../authors/willenbrink">Sebastian Willenbrink</a>
 
         </div>
         <span class="date">Jul 01</span>
       </article>
     <h2 class="head">2020</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Automated_Stateful_Protocol_Verification.html">Automated Stateful Protocol Verification</a></h5>
           <br>
             by <a href="../../authors/hess">Andreas V. Hess</a>, <a href="../../authors/moedersheim">Sebastian Mödersheim</a>, <a href="../../authors/brucker">Achim D. Brucker</a> and <a href="../../authors/schlichtkrull">Anders Schlichtkrull</a>
 
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           <h5><a class="title" href="../../entries/Isabelle_C.html">Isabelle/C</a></h5>
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             by <a href="../../authors/tuong">Frédéric Tuong</a> and <a href="../../authors/wolff">Burkhart Wolff</a>
 
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Auto2_HOL.html">Auto2 Prover</a></h5>
           <br>
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/BNF_CC.html">Bounded Natural Functors with Covariance and Contravariance</a></h5>
           <br>
             by <a href="../../authors/lochbihler">Andreas Lochbihler</a> and <a href="../../authors/schneider">Joshua Schneider</a>
 
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         <span class="date">Apr 24</span>
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     <h2 class="head">2017</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/BNF_Operations.html">Operations on Bounded Natural Functors</a></h5>
           <br>
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Diophantine_Eqns_Lin_Hom.html">Homogeneous Linear Diophantine Equations</a></h5>
           <br>
             by <a href="../../authors/messner">Florian Messner</a>, <a href="../../authors/parsert">Julian Parsert</a>, <a href="../../authors/schoepf">Jonas Schöpf</a> and <a href="../../authors/sternagel">Christian Sternagel</a>
 
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Dict_Construction.html">Dictionary Construction</a></h5>
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Monad_Normalisation.html">Monad normalisation</a></h5>
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           <h5><a class="title" href="../../entries/Constructor_Funs.html">Constructor Functions</a></h5>
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           <br>
             by <a href="../../authors/hupel">Lars Hupel</a>
 
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Proof_Strategy_Language.html">Proof Strategy Language</a></h5>
           <br>
             by <a href="../../authors/nagashima">Yutaka Nagashima</a>
 
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           <h5><a class="title" href="../../entries/Separata.html">Separata: Isabelle tactics for Separation Algebra</a></h5>
           <br>
             by <a href="../../authors/hou">Zhe Hou</a>, <a href="../../authors/sanan">David Sanan</a>, <a href="../../authors/tiu">Alwen Tiu</a>, <a href="../../authors/gore">Rajeev Gore</a> and <a href="../../authors/clouston">Ranald Clouston</a>
 
         </div>
         <span class="date">Nov 16</span>
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     <h2 class="head">2015</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Case_Labeling.html">Generating Cases from Labeled Subgoals</a></h5>
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             by <a href="../../authors/noschinski">Lars Noschinski</a>
 
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       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/Nominal2.html">Nominal 2</a></h5>
           <br>
             by <a href="../../authors/urban">Christian Urban</a>, <a href="../../authors/berghofer">Stefan Berghofer</a> and <a href="../../authors/kaliszyk">Cezary Kaliszyk</a>
 
         </div>
         <span class="date">Feb 21</span>
       </article>
     <h2 class="head">2009</h2>
       <article class="entry">
         <div class="item-text">
           <h5><a class="title" href="../../entries/DPT-SAT-Solver.html">A Fast SAT Solver for Isabelle in Standard ML</a></h5>
           <br>
             by <a href="../../authors/heller">Armin Heller</a>
 
         </div>
         <span class="date">Dec 09</span>
       </article>
         
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     </div>
   </body>
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