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<div id="content" class="content">
<h1 class="title">Mathematical Components: Research Papers</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orge8a15c3">Mathematics</a></li>
<li><a href="#orge4b6d2e">Programming and Algorithms</a></li>
<li><a href="#org86926ee">Other Applications</a></li>
<li><a href="#org62dac1f">Tooling</a></li>
</ul>
</div>
</div>
<p>
This is a list of research papers and theses using the Mathematical
Components libraries and published (among others) in the following
venues:
</p>
<ul class="org-ul">
<li>ITP = Interactive Theorem Proving (was TPHOLs until 2009)</li>
<li>CPP = Certified Programs and Proofs</li>
<li>CICM = Conference on Intelligent Computer Mathematics</li>
<li>IJCAR = International Joint Conference on Automated Reasoning</li>
<li>ICFP = International Conference on Functional Programming</li>
<li>FSCD = International Conference on Formal Structures for Computation and Deduction</li>
<li>TACAS = International Conference on Tools and Algorithms for the Construction and Analysis of Systems</li>
<li>ESOP = European Symposium on Programming</li>
<li>POPL = Principles of Programming Languages</li>
<li>PPDP = Principles and Practice of Declarative Programming</li>
<li>JAR = Journal of Automated Reasoning</li>
<li>JFP = Journal of Functional Programming</li>
<li>LMCS = Logical Methods in Computer Science</li>
</ul>
<p>
Your paper/thesis is not in the list? You have a suggestion about the organization of this page?
Please, send <a href="mailto:[email protected]?subject=MathComp%20related%20paper">us</a> a message or <a href="https://github.com/math-comp/math-comp.github.io">issue/PR on github</a>.
</p>
<div id="outline-container-orge8a15c3" class="outline-2">
<h2 id="orge8a15c3">Mathematics</h2>
<div class="outline-text-2" id="text-orge8a15c3">
<ul class="org-ul">
<li>Reynald Affeldt, Zachary Stone.
<span class="underline">A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq</span>.
ITP 2024. <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.5/LIPIcs.ITP.2024.5.pdf">pdf</a></li>
<li>Assia Mahboubi, Matthieu Piquerez.
<span class="underline">A First Order Theory of Diagram Chasing</span>.
32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol288-csl2024/LIPIcs.CSL.2024.38/LIPIcs.CSL.2024.38.pdf">pdf</a></li>
<li>Benoît Guillemet, Assia Mahboubi, Matthieu Piquerez.
<span class="underline">Machine-Checked Categorical Diagrammatic Reasoning</span>.
FSCD 2024. <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol299-fscd2024/LIPIcs.FSCD.2024.7/LIPIcs.FSCD.2024.7.pdf">pdf</a></li>
<li>Yoshihiro Ishiguro, Reynald Affeldt.
<span class="underline">The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq</span>.
Computer Software 41(2), 2024. <a href="https://www.jstage.jst.go.jp/article/jssst/41/2/41_2_41/_pdf/-char/en">pdf</a></li>
<li>Reynald Affeldt, Cyril Cohen.
<span class="underline">Measure construction by extension in dependent type theory with application to integration</span>.
JAR 2023. <a href="https://arxiv.org/pdf/2209.02345.pdf">pdf</a></li>
<li>Pierre Pomeret-Coquot, Helene Fargier, Érik Martin-Dorel.
<span class="underline">Bel-Games: A Formal Theory of Games of Incomplete Information Based on Belief Functions in the Coq Proof Assistant</span>.
ITP 2023. <a href="https://drops.dagstuhl.de/opus/volltexte/2023/18400/pdf/LIPIcs-ITP-2023-25.pdf">pdf</a></li>
<li>Xavier Allamigeon, Quentin Canu, Pierre-Yves Strub.
<span class="underline">A Formal Disproof of Hirsch Conjecture</span>.
CPP 2023. <a href="https://arxiv.org/pdf/2301.04060.pdf">pdf</a></li>
<li>Xavier Allamigeon, Ricardo D. Katz, Pierre-Yves Strub.
<span class="underline">Formalizing the Face Lattice of Polyhedra</span>.
LMCS 18(2), 2022. <a href="https://lmcs.episciences.org/9570/pdf">pdf</a></li>
<li>Assia Mahboubi, Thomas Sibut-Pinote.
<span class="underline">A Formal Proof of the Irrationality of ζ(3)</span>.
LMCS 17(1), 2021. <a href="https://lmcs.episciences.org/7193/pdf">pdf</a></li>
<li>Sophie Bernard, Cyril Cohen, Assia Mahboubi, Pierre-Yves Strub.
<span class="underline">Unsolvability of the Quintic Formalized in Dependent Type Theory</span>
ITP 2021. <a href="https://hal.inria.fr/hal-03136002v3/document">pdf</a></li>
<li>Xavier Allamigeon, Ricardo D. Katz, Pierre-Yves Strub.
<span class="underline">Formalizing the Face Lattice of Polyhedra</span>.
IJCAR 2020. <a href="https://dx.doi.org/10.1007%2F978-3-030-51054-1_11">doi</a></li>
<li>Reynald Affeldt, Cyril Cohen, Marie Kerjean, Assia Mahboubi, Damien Rouhling, Kazuhiko Sakaguchi.
<span class="underline">Competing inheritance paths in dependent type theory: a case study in functional analysis</span>.
IJCAR 2020. <a href="https://hal.inria.fr/hal-02463336v2/document">pdf</a>, <a href="https://math-comp.github.io/competing-inheritance-paths-in-dependent-type-theory/">code</a></li>
<li>Xavier Allamigeon, Ricardo D. Katz.
<span class="underline">A Formalization of Convex Polyhedra Based on the Simplex Method</span>.
JAR 63(2), 2019. <a href="https://doi.org/10.1007/s10817-018-9477-1">doi</a></li>
<li>Florent Bréhard, Assia Mahboubi, Damien Pous. <span class="underline">A certificate-based
approach to formally verified approximations</span>. ITP 2019. <a href="https://hal.laas.fr/hal-02088529v2/document">pdf</a></li>
<li>Reynald Affeldt, Cyril Cohen, Damien Rouhling.
<span class="underline">Formalization techniques for asymptotic reasoning in classical analysis</span>.
Journal of Formalized Reasoning 11(1), 2018. <a href="https://jfr.unibo.it/article/view/8124/8407">pdf</a></li>
<li>Reynald Affeldt, Cyril Cohen, Assia Mahboubi, Damien Rouhling, Pierre-Yves Strub.
<span class="underline">Classical Analysis with Coq</span>. Coq Workshop 2018. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/coqws-reals.pdf">pdf</a></li>
<li>Xavier Allamigeon, Ricardo D. Katz.
<span class="underline">A formalization of convex polyhedra based on the simplex method</span>. ITP 2017. <a href="https://arxiv.org/pdf/1706.10269.pdf">pdf</a></li>
<li>Evmorfia-Iro Bartzia.
<span class="underline">A Formalization of Elliptic Curves for Cryptography</span>.
PhD thesis, Université Paris-Saclay, 2017. <a href="https://pastel.archives-ouvertes.fr/tel-01563979/document">pdf</a></li>
<li>Guillaume Cano, Cyril Cohen, Maxime Dénès, Anders Mörtberg, Vincent Siles.
<span class="underline">Formalized linear algebra over Elementary Divisor Rings in Coq</span>.
LMCS 12(2), 2016. <a href="https://hal.inria.fr/hal-01081908/document">pdf</a></li>
<li>Cyril Cohen, Boris Djalal.
<span class="underline">Formalization of a newton series representation of polynomials</span>. CPP 2016. <a href="https://hal.inria.fr/hal-01240469/document">pdf</a></li>
<li>Ken'ichi Kuga, Manabu Hagiwara, Mitsuharu Yamamoto.
<span class="underline">Formalization of Bing's Shrinking Method in Geometric Topology</span>. CICM 2016. <a href="https://doi.org/10.1007/978-3-319-42547-4_2">doi</a></li>
<li>Gallego Arias, Emilio Jesús, Pierre Jouvelot.
<span class="underline">Adventures in the (not so) Complex Space</span>. Coq Workshop 2015. <a href="https://github.com/ejgallego/mini-dft-coq">paper, code, slides</a></li>
<li>Frédéric Chyzak, Assia Mahboubi, Thomas Sibut-Pinote, Enrico Tassi.
<span class="underline">A Computer-Algebra-Based Formal Proof of the Irrationality of ζ(3)</span>. ITP 2014. <a href="https://hal.inria.fr/hal-00984057/document">pdf</a></li>
<li>Cyril Cohen, Anders Mörtberg.
<span class="underline">A Coq Formalization of Finitely Presented Modules</span>. ITP 2014. <a href="https://perso.crans.org/cohen/papers/fpmods.pdf">pdf</a></li>
<li>Anders Mörtberg.
<span class="underline">Formalizing Refinements and Constructive Algebra in Type Theory</span>.
PhD, University of Gothenburg, 2014. <a href="http://staff.math.su.se/anders.mortberg/thesis/thesis.pdf">pdf</a></li>
<li>Evmorfia-Iro Bartzia, Pierre-Yves Strub.
<span class="underline">A Formal Library for Elliptic Curves in the Coq Proof Assistant</span>. ITP 2014. <a href="https://hal.inria.fr/hal-01102288/file/A-Formal-Library-for-Elliptic-Curves-in-the-Coq-Proof-Assistant.pdf">pdf</a></li>
<li>Jónathan Heras, Thierry Coquand, Anders Mörtberg, Vincent Siles.
<span class="underline">Computing persistent homology within Coq/SSReflect</span>. ACM Transactions on Computational Logic 14(4), 2013. <a href="https://arxiv.org/pdf/1209.1905.pdf">pdf</a></li>
<li>Georges Gonthier, Andrea Asperti, Jeremy Avigad, Yves Bertot, Cyril
Cohen, François Garillot, Stéphane Le Roux, Assia Mahboubi, Russell
O'Connor, Sidi Ould Biha, Ioana Pasca, Laurence Rideau, Alexey
Solovyev, Enrico Tassi, Laurent Théry.
<span class="underline">A Machine-Checked Proof of the Odd Order Theorem</span>. ITP 2013. <a href="https://hal.inria.fr/hal-00816699/document">pdf</a></li>
<li>Cyril Cohen. <span class="underline">Pragmatic Quotient Types in Coq</span>. ITP 2013. <a href="https://hal.inria.fr/hal-01966714/document">pdf</a></li>
<li>Assia Mahboubi. <span class="underline">The Rooster and the Butterflies</span>. CICM 2013. <a href="https://hal.inria.fr/hal-00825074v3/document">pdf</a></li>
<li>Maxime Dénès, Anders Mörtberg, Vincent Siles.
<span class="underline">A Refinement-Based Approach to Computational Algebra in Coq</span>. ITP 2012. <a href="https://hal.inria.fr/hal-00734505/document">pdf</a></li>
<li>Jónathan Heras, Maxime Dénès, Gadea Mata, Anders Mörtberg, María Poza, Vincent Siles.
<span class="underline">Towards a Certified Computation of Homology Groups for Digital Images</span>.
4th International Workshop on Computational Topology in Image Context (CTIC 2012). <a href="https://hal.inria.fr/hal-00711385/document">pdf</a></li>
<li>Assia Mahboubi, Cyril Cohen.
<span class="underline">Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination</span>.
LMCS 8(1), 2012. <a href="https://hal.inria.fr/inria-00593738v4/document">pdf</a></li>
<li>Thierry Coquand, Anders Mörtberg, Vincent Siles.
<span class="underline">Coherent and Strongly Discrete Rings in Type Theory</span>. CPP 2012. <a href="https://staff.math.su.se/anders.mortberg/papers/coherent.pdf">pdf</a></li>
<li>Cyril Cohen.
<span class="underline">Formalized algebraic numbers: construction and first-order theory</span>.
PhD thesis, Ecole Polytechnique, 2012. <a href="https://pastel.archives-ouvertes.fr/pastel-00780446/file/main.pdf">pdf</a></li>
<li>Jónathan Heras, María Poza, Maxime Dénès, Laurence Rideau.
<span class="underline">Incidence Simplicial Matrices Formalized in Coq/SSReflect</span>.
18th Symposium on Symposium on the Integration of Symbolic Computation and Mechanized Reasoning (Calculemus 2011). <a href="https://hal.inria.fr/inria-00603208/file/ismfis.pdf">pdf</a></li>
<li>Georges Gonthier.
<span class="underline">Point-Free, Set-Free Concrete Linear Algebra</span>.
ITP 2011. <a href="https://hal.inria.fr/hal-00805966/document">pdf</a></li>
<li>Sidi Ould Biha.
<span class="underline">Finite groups representation theory with Coq</span>.
8th International Conference on Mathematical Knowledge Management (MKM 2009). <a href="https://hal.inria.fr/inria-00377431/document">pdf</a></li>
<li>Yves Bertot, Georges Gonthier, Sidi Ould Biha, Ioana Pasca.
<span class="underline">Canonical Big Operators</span>.
ITP 2008. <a href="https://hal.inria.fr/inria-00331193/document">pdf</a></li>
<li>Georges Gonthier, Assia Mahboubi, Laurence Rideau, Enrico Tassi, Laurent Théry.
<span class="underline">A Modular Formalisation of Finite Group Theory</span>.
TPHOLs 2007. <a href="https://hal.inria.fr/inria-00139131v2/document">pdf</a></li>
<li>Laurent Théry, Laurence Rideau. <span class="underline">Formalising Sylow’s theorems in Coq</span>.
RT-0327 INRIA 2006. <a href="https://hal.inria.fr/inria-00113750v2/document">pdf</a></li>
</ul>
</div>
<div id="outline-container-org384e522" class="outline-3">
<h3 id="org384e522">Graph Theory</h3>
<div class="outline-text-3" id="text-org384e522">
<ul class="org-ul">
<li>Christian Doczkal.
<span class="underline">A Variant of Wagner’s Theorem Based on Combinatorial Hypermaps</span>.
ITP 2021. <a href="https://hal.archives-ouvertes.fr/hal-03142192/document">pdf</a></li>
<li>Christian Doczkal, Damien Pous.
<span class="underline">Graph Theory in Coq: Minors, Treewidth, and Isomorphisms</span>.
JAR (special issue for ITP 2018), 2020. <a href="https://hal.archives-ouvertes.fr/hal-02316859/document">pdf</a></li>
<li>Christian Doczkal, Damien Pous.
<span class="underline">Completeness of an axiomatization of graph isomorphism via graph rewriting in Coq</span>.
CPP 2020. <a href="https://hal.archives-ouvertes.fr/hal-02333553/document">pdf</a></li>
<li>Daniel E. Severín.
<span class="underline">Formalization of the Domination Chain with Weighted Parameters</span>. ITP 2019. <a href="http://drops.dagstuhl.de/opus/volltexte/2019/11091/pdf/LIPIcs-ITP-2019-36.pdf">pdf</a></li>
<li>Christian Doczkal, Guillaume Combette, Damien Pous.
<span class="underline">A Formal Proof of the Minor-Exclusion Property for Treewidth-Two Graphs</span>. ITP 2018. <a href="https://hal.archives-ouvertes.fr/hal-01703922/document">pdf</a></li>
<li>George Gonthier.
<span class="underline">A computer-checked proof of the Four Colour Theorem</span>.
<a href="http://www2.tcs.ifi.lmu.de/~abel/lehre/WS07-08/CAFR/4colproof.pdf">pdf</a></li>
</ul>
</div>
</div>
<div id="outline-container-org1695762" class="outline-3">
<h3 id="org1695762">Robotics</h3>
<div class="outline-text-3" id="text-org1695762">
<ul class="org-ul">
<li>Yves Bertot,
<span class="underline">Safe Smooth Paths Between Straight Line Obstacles</span>.
Logics and Type Systems in Theory and Practice, LNCS 14560, Springer, 2024.
<a href="https://doi.org/10.1007/978-3-031-61716-4">doi</a>, <a href="https://inria.hal.science/hal-04312815">pdf</a></li>
<li>Cyril Cohen, Damien Rouhling.
<span class="underline">A Formal Proof in Coq of LaSalle's Invariance Principle</span>. ITP 2017. <a href="https://hal.inria.fr/hal-01612293/document">pdf</a></li>
<li>Reynald Affeldt, Cyril Cohen.
<span class="underline">Formal Foundations of 3D Geometry to Model Robot Manipulators</span>. CPP 2017. <a href="https://hal.inria.fr/hal-01414753/document">pdf</a></li>
</ul>
</div>
</div>
</div>
<div id="outline-container-orge4b6d2e" class="outline-2">
<h2 id="orge4b6d2e">Programming and Algorithms</h2>
<div class="outline-text-2" id="text-orge4b6d2e">
<ul class="org-ul">
<li>Cyril Cohen, Kazuhiko Sakaguchi.
<span class="underline">A bargain for mergesorts (functional pearl) – How to prove your mergesort correct and stable, almost for free</span>.
arXiv 2024. <a href="https://arxiv.org/pdf/2403.08173">pdf</a></li>
<li>Ana de Almeida Borges, Mireia González Bedmar, Juan Conejero Rodríguez, Eduardo Hermo Reyes, Joaquim Casals Buñuel, Joost J. Joosten.
<span class="underline">UTC time, formally verified</span>.
CPP 2024. <a href="https://arxiv.org/pdf/2209.14227.pdf">pdf</a></li>
<li>Philipp G. Haselwarter, Exequiel Rivas, Antoine Van Muylder, Théo Winterhalter,
Carmine Abate, Nikolaj Sidorenco, Cătălin Hriţcu, Kenji Maillard, Bas Spitters.
<span class="underline">SSProve: A Foundational Framework for Modular Cryptographic Proofs in Coq</span>.
ACM Transactions on Programming Languages and Systems 45(3), 2023. <a href="https://dl.acm.org/doi/pdf/10.1145/3594735">pdf</a></li>
<li>Ming-Hsien Tsai, Yu-Fu Fu, Jiaxiang Liu, Xiaomu Shi, Bow-Yaw Wang, Bo-Yin Yang.
<span class="underline">CoqCryptoLine: A Verified Model Checker with Certified Results</span>.
Conference on Computer-Aided Verification (CAV 2023). <a href="https://link.springer.com/chapter/10.1007/978-3-031-37703-7_11">doi</a></li>
<li>Ayumu Saito, Reynald Affeldt.
<span class="underline">Towards a Practical Library for Monadic Equational Reasoning in Coq</span>.
Mathematics of Program Construction (MPC 2022). <a href="https://staff.aist.go.jp/reynald.affeldt/documents/monae-mpc2022.pdf">pdf</a></li>
<li>Reynald Affeldt, David Nowak.
<span class="underline">Extending equational monadic reasoning with monad transformers</span>.
TYPES 2020. <a href="https://arxiv.org/pdf/2011.03463.pdf">pdf</a></li>
<li>Reynald Affeldt, David Nowak, Takafumi Saikawa.
<span class="underline">A Hierarchy of Monadic Effects for Program Verification Using Equational Reasoning</span>.
Mathematics of Program Construction (MPC 2019)</li>
<li>Ran Chen, Cyril Cohen, Jean-Jacques Levy, Stephan Merz, Laurent Thery.
<span class="underline">Formal Proof of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq, and Isabelle</span>.
ITP 2019. <a href="http://drops.dagstuhl.de/opus/volltexte/2019/11068/pdf/LIPIcs-ITP-2019-13.pdf">pdf</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, Kazunari Tanaka.
<span class="underline">Proving tree algorithms for succinct data structures</span>.
ITP 2019. <a href="https://arxiv.org/pdf/1904.02809.pdf">pdf</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Xuanrui Qi, Kazunari Tanaka.
<span class="underline">Experience Report: Type-Driven Development of Certified Tree Algorithms in Coq</span>.
Coq Workshop 2019. <a href="https://staff.aist.go.jp/reynald.affeldt/coq2019/coqws2019-affeldt-garrigue-qi-tanaka.pdf">pdf</a></li>
<li>Cyril Cohen, Damien Rouhling.
<span class="underline">A refinement-based approach to large scale reflection for algebra</span>.
28ème Journées Francophones des Langages Applicatifs (JFLA 2017). <a href="https://hal.inria.fr/hal-01414881/document">pdf</a></li>
<li>Timmy Weerwag.
<span class="underline">Verifying an elliptic curve cryptographic algorithm using Coq and the Ssreflect extension</span>.
Master’s thesis, Mathematics, Radboud University, 2016. <a href="https://www.ru.nl/publish/pages/813286/weerwag_timmy_-1a.pdf">pdf</a></li>
<li>Beta Ziliani, Derek Dreyer, Neelakantan R. Krishnaswami, Aleksandar Nanevski, Viktor Vafeiadis.
<span class="underline">Mtac: A Monad for Typed Tactic Programming in Coq</span>. JFP 25, 2015. <a href="https://people.mpi-sws.org/~dreyer/papers/mtac/journal.pdf">pdf</a></li>
<li>Cyril Cohen, Maxime Dénès, Anders Mörtberg.
<span class="underline">Refinements for free!</span>. CPP 2013. <a href="https://hal.inria.fr/hal-01113453/document">pdf</a></li>
<li>Andrew Kennedy, Nick Benton, Jonas B. Jensen, Pierre-Evariste Dagand.
<span class="underline">Coq: the world's best macro assembler?</span> PPDP 2013. <a href="http://nickbenton.name/coqasm.pdf">pdf</a></li>
<li>Germán Andrés Delbianco, Aleksandar Nanevski.
<span class="underline">Hoare-Style Reasoning with (Algebraic) Continuations</span>. ICFP 2013. <a href="https://doi.org/10.1145/2544174.2500593">doi</a></li>
<li>Beta Ziliani, Derek Dreyer, Neelakantan R. Krishnaswami, Aleksandar Nanevski, Viktor Vafeiadis.
<span class="underline">Mtac: A Monad for Typed Tactic Programming in Coq</span>. ICFP 2013. <a href="https://doi.org/10.1017/S0956796815000118">doi</a></li>
<li>Aleksandar Nanevski, Viktor Vafeiadis, Josh Berdine.
<span class="underline">Structuring the Verification of Heap-Manipulating Programs</span>. POPL 2010. <a href="https://doi.org/10.1145/1706299.1706331">doi</a></li>
</ul>
</div>
<div id="outline-container-org962e36d" class="outline-3">
<h3 id="org962e36d">Concurrency</h3>
<div class="outline-text-3" id="text-org962e36d">
<ul class="org-ul">
<li>Mohit Tekriwal, Avi Tachna-Fram, Jean-Baptiste Jeannin, Manos Kapritsos, Dimitra Panagou.
<span class="underline">Formally verified asymptotic consensus in robust networks</span>.
TACAS 2024. <a href="https://arxiv.org/pdf/2202.13833.pdf">pdf</a></li>
<li>Søren Eller Thomsen, Bas Spitters.
<span class="underline">Formalizing Nakamoto-Style Proof of Stake</span>.
34th IEEE Computer Security Foundations Symposium (CSF 2021). <a href="https://arxiv.org/pdf/2007.12105">pdf</a></li>
<li>Musab A. Alturki, Jing Chen, Victor Luchangco, Brandon Moore, Karl Palmskog, Lucas Peña, Grigore Roşu.
<span class="underline">Towards a Verified Model of the Algorand Consensus Protocol in Coq</span>.
1st Workshop on Formal Methods for Blockchains (FMBC 2019). <a href="https://arxiv.org/pdf/1907.05523">pdf</a></li>
<li>Joseph Tassarotti, Robert Harper.
<span class="underline">A Separation Logic for Concurrent Randomized Programs</span>.
POPL 2019. <a href="http://www.cs.bc.edu/~tassarot/papers/iris-prob-paper/paper.pdf">pdf</a></li>
<li>Ilya Sergey, James R. Wilcox, Zachary Tatlock.
<span class="underline">Programming and Proving with Distributed Protocols</span>. POPL 2018. <a href="https://dl.acm.org/citation.cfm?doid=3177123.3158116">pdf</a></li>
<li>George Pîrlea, Ilya Sergey. <span class="underline">Mechanising Blockchain Consensus</span>. CPP 2018. <a href="https://dl.acm.org/citation.cfm?id=3167086">pdf</a></li>
<li>Germán Andrés Delbianco, Ilya Sergey, Aleksandar Nanevski, Anindya Banerjee.
<span class="underline">Concurrent Data Structures Linked in Time</span>.
European Conference on Object-Oriented Programming (ECOOP 2017). <a href="https://drops.dagstuhl.de/opus/volltexte/2017/7255/pdf/LIPIcs-ECOOP-2017-8.pdf">pdf</a></li>
<li>Mitsuharu Yamamoto, Shogo Sekine, Saki Matsumoto.
<span class="underline">Formalization of Karp-Miller Tree Construction on Petri Nets</span>. CPP 2017. <a href="https://doi.org/10.1145/3018610.3018626">doi</a></li>
<li>Germán Andrés Delbianco.
<span class="underline">Hoare-style Reasoning with Higher-order Control: Continuations and Concurrency</span>.
PhD thesis, Computer Science, Universidad Politécnica de Madrid, 2017. <a href="http://oa.upm.es/47796/1/GERMAN_ANDRES_DELBIANCO.pdf">pdf</a></li>
<li>Ralf Jung, Robbert Krebbers, Lars Birkedal, Derek Dreyer.
<span class="underline">Higher-Order Ghost State</span>.
ICFP 2016. <a href="https://dl.acm.org/doi/pdf/10.1145/2951913.2951943">pdf</a></li>
<li>Ilya Sergey, Aleksandar Nanevski, Anindya Banerjee, Germán Andrés Delbianco.
<span class="underline">Hoare-style Specifications as Correctness Conditions for Non-linearizable Concurrent Objects</span>.
Object-oriented Programming, Systems, Languages, and Applications (OOPSLA 2016). <a href="https://arxiv.org/pdf/1509.06220.pdf">pdf</a></li>
<li>Ilya Sergey, Aleksandar Nanevski, Anindya Banerjee.
<span class="underline">Mechanized Verification of Fine-grained Concurrent Programs</span>.
Programming Language Design and Implementation (PLDI 2015). <a href="https://doi.org/10.1145/2737924.2737964">doi</a></li>
<li>Ilya Sergey, Aleksandar Nanevski, Anindya Banerjee.
<span class="underline">Specifying and Verifying Concurrent Algorithms with Histories and Subjectivity</span>.
ESOP 2015. <a href="https://arxiv.org/pdf/1410.0306.pdf">pdf</a></li>
<li>Aleksandar Nanevski, Ruy Ley-Wild, Ilya Sergey, Germán Andrés Delbianco.
<span class="underline">Communicating State Transition Systems for Fine-Grained Concurrent Resources</span>.
ESOP 2014. <a href="https://doi.org/10.1007/978-3-642-54833-8_16">doi</a></li>
<li>Ruy Ley-Wild, Aleksandar Nanevski.
<span class="underline">Subjective Auxiliary State for Coarse-Grained Concurrency</span>. POPL 2013. <a href="https://doi.org/10.1145/2429069.2429134">doi</a></li>
</ul>
</div>
</div>
<div id="outline-container-org4e00f44" class="outline-3">
<h3 id="org4e00f44">Information Flow</h3>
<div class="outline-text-3" id="text-org4e00f44">
<ul class="org-ul">
<li>Aleksandar Nanevski, Anindya Banerjee, Deepak Garg.
<span class="underline">Dependent Type Theory for Verification of Information Flow and Access Control Policies</span>.
ACM Transactions on Programming Languages and Systems, 35(2):6:1-6:41, 2013. <a href="https://doi.org/10.1145/2491522.2491523">doi</a></li>
<li>Gordon Stewart, Anindya Banerjee, Aleksandar Nanevski.
<span class="underline">Dependent Types for Enforcement of Information Flow and Erasure Policies in Heterogeneous Data Structures</span>.
PPDP 2013. <a href="https://doi.org/10.1145/2505879.2505895">doi</a></li>
<li>Aleksandar Nanevski, Anindya Banerjee, Deepak Garg.
<span class="underline">Verification of Information Flow and Access Control Policies with Dependent Types</span>.
2011 IEEE Symposium on Security and Privacy. <a href="https://ieeexplore.ieee.org/document/5958028">IEEE Xplore</a></li>
</ul>
</div>
</div>
<div id="outline-container-orge4396bf" class="outline-3">
<h3 id="orge4396bf">Probabilistic Reasoning</h3>
<div class="outline-text-3" id="text-orge4396bf">
<ul class="org-ul">
<li>Reynald Affeldt, Clark Barrett, Alessandro Bruni, Ieva Daukantas, Harun Khan, Takafumi Saikawa, Carsten Schürmann.
<span class="underline">Robust Mean Estimation by All Means (short paper)</span>.
ITP 2024. <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.39/LIPIcs.ITP.2024.39.pdf">pdf</a></li>
<li>Ayumu Saito, Reynald Affeldt.
<span class="underline">Experimenting with an Intrinsically-Typed Probabilistic Programming Language in Coq</span>.
Asian Symposium on Programming Languages and Systems (APLAS 2023). <a href="https://link.springer.com/chapter/10.1007/978-981-99-8311-7_9">doi</a></li>
<li>Reynald Affeldt, Cyril Cohen, Ayumu Saito.
<span class="underline">Semantics of Probabilistic Programs using s-Finite Kernels in Coq</span>.
CPP 2023. <a href="https://hal.inria.fr/hal-03917948/document">pdf</a></li>
<li>Ieva Daukantas, Alessandro Bruni, Carsten Schürmann.
<span class="underline">Trimming Data Sets: a Verified Algorithm for Robust Mean Estimation</span>.
PPDP 2021. <a href="https://doi.org/10.1145/3479394.3479412">doi</a></li>
<li>Reynald Affeldt, Jacques Garrigue, David Nowak, Takafumi Saikawa.
<span class="underline">A trustful monad for axiomatic reasoning with probability and nondeterminism</span>.
JFP 31(E17), 2021. <a href="https://arxiv.org/pdf/2003.09993.pdf">pdf</a></li>
<li>Kiran Gopinathan, Ilya Sergey.
<span class="underline">Certifying Certainty and Uncertainty in Approximate Membership Query Structures</span>.
32nd International Conference on Computer-Aided Verification (CAV 2020). <a href="https://arxiv.org/pdf/2004.13312.pdf">pdf</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa.
<span class="underline">Formal adventures in convex and conical spaces</span>.
CICM 2020. <a href="https://arxiv.org/pdf/2004.12713.pdf">pdf</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa.
<span class="underline">Reasoning with conditional probabilities and joint distributions</span>.
Computer Software 37(3):79-95, 2020. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/cproba_preprint.pdf">pdf</a></li>
<li>Joseph Tassarotti, Robert Harper.
<span class="underline">Verified Tail Bounds for Randomized Programs</span>. ITP 2018. <a href="https://www.cs.cmu.edu/~rwh/papers/tail-bounds/paper.pdf">pdf</a></li>
</ul>
</div>
</div>
<div id="outline-container-orge4a59df" class="outline-3">
<h3 id="orge4a59df">Quantum Computing</h3>
<div class="outline-text-3" id="text-orge4a59df">
<ul class="org-ul">
<li>Jacques Garrigue and Takafumi Saikawa.
<span class="underline">Typed compositional quantum computation with lenses</span>.
ITP 2024. <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.15/LIPIcs.ITP.2024.15.pdf">pdf</a></li>
<li>Li Zhou, Gilles Barthe, Pierre-Yves Strub, Junyi Liu, Mingsheng Ying.
<span class="underline">CoqQ: Foundational Verification of Quantum Programs</span>.
POPL 2023. <a href="https://arxiv.org/pdf/2207.11350.pdf">pdf</a></li>
</ul>
</div>
</div>
</div>
<div id="outline-container-org86926ee" class="outline-2">
<h2 id="org86926ee">Other Applications</h2>
<div class="outline-text-2" id="text-org86926ee">
<ul class="org-ul">
<li>Pierre-Léo Bégay, Pierre Crégut, Jean-François Monin.
<span class="underline">Developing and certifying Datalog optimizations in Coq/MathComp</span>. CPP 2021. <a href="https://hal.archives-ouvertes.fr/hal-03065304v1/document">pdf</a></li>
<li>Gallego Arias, Emilio Jesús, Olivier Hermant, Pierre Jouvelot.
<span class="underline">A Taste of Sound Reasoning in Faust</span>.
Linux Audio Conference 2015. <a href="https://github.com/ejgallego/mini-faust-coq">paper, code, slides</a></li>
<li>Maxime Dénès, Benjamin Lesage, Yves Bertot, Adrien Richard.
<span class="underline">Formal proof of theorems on genetic regulatory networks</span>.
11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNACS 2009).
<a href="https://ieeexplore.ieee.org/document/5460865">IEEE Xplore</a></li>
</ul>
</div>
<div id="outline-container-org4bad64f" class="outline-3">
<h3 id="org4bad64f">Logic, Types, and Verification</h3>
<div class="outline-text-3" id="text-org4bad64f">
<ul class="org-ul">
<li>Jan Bessai, Jakob Rehof, Boris Düdder.
<span class="underline">Fast Verified BCD Subtyping</span>.
Models, Mindsets, Meta: The What, the How, and the Why Not? LNCS 11200, 2019. <a href="https://doi.org/10.1007/978-3-030-22348-9_21">doi</a></li>
<li>Christian Doczkal, Gert Smolka.
<span class="underline">Regular Language Representations in the Constructive Type Theory of Coq</span>.
JAR 61, 2018. <a href="https://hal.archives-ouvertes.fr/hal-01832031/document">pdf</a></li>
<li>Christian Doczkal, Joachim Bard.
<span class="underline">Completeness and Decidability of Converse PDL in the Constructive Type Theory of Coq</span>.
CPP 2018. <a href="https://hal.archives-ouvertes.fr/hal-01646782/document">pdf</a></li>
<li>Angela Bonifati, Stefania Dumbrava, Emilio Jesús Gallego Arias.
<span class="underline">Certified Graph View Maintenance with Regular Datalog</span>.
34th International Conference on Logic Programming (ICLP 2018). <a href="https://hal.archives-ouvertes.fr/hal-01932818/document">pdf</a></li>
<li>Véronique Benzaken, Evelyne Contejean, Stefania Dumbrava.
<span class="underline">Certifying Standard and Stratified Datalog Inference Engines in SSReflect</span>. ITP 2017. <a href="https://hal.archives-ouvertes.fr/hal-01745566/file/ITP2017.pdf">pdf</a></li>
<li>Felipe Cerqueira, Felix Stutz, Björn Brandenburg.
<span class="underline">Prosa: A Case for Readable Mechanized Schedulability Analysis</span>.
28th Euromicro Conference on Real-Time Systems (ECRTS 2016). <a href="https://ieeexplore.ieee.org/document/7557887">IEEE Xplore</a></li>
<li>Christian Doczkal, Gert Smolka.
<span class="underline">Completeness and Decidability Results for CTL in Constructive Type Theory</span>.
JAR 56, 2016. <a href="https://doi.org/10.1007/s10817-016-9361-9">doi</a></li>
<li>Christian Doczkal, Gert Smolka.
<span class="underline">Completeness and Decidability Results for CTL in Coq</span>. ITP 2014. <a href="https://www.ps.uni-saarland.de/Publications/documents/DoczkalSmolka_2014_comp-dec-CTL.pdf">pdf</a></li>
<li>Christian Doczkal, Gert Smolka.
<span class="underline">Constructive Completeness for Modal Logic with Transitive Closure</span>. CPP 2012. <a href="https://doi.org/10.1007/978-3-642-35308-6_18">doi</a></li>
<li>Christian Doczkal, Gert Smolka.
<span class="underline">Constructive Formalization of Hybrid Logic with Eventualities</span>. CPP 2011. <a href="https://www.ps.uni-saarland.de/Publications/documents/DoczkalSmolka_2011_Constructive_0.pdf">pdf</a></li>
<li>Thierry Coquand, Vincent Siles.
<span class="underline">A Decision Procedure for Regular Expression Equivalence in Type Theory</span>. CPP 2011. <a href="https://doi.org/10.1007/978-3-642-25379-9_11">doi</a></li>
<li>Kasper Svendsen, Lars Birkedal, Aleksandar Nanevski.
<span class="underline">Partiality, State and Dependent Types</span>.
International Conference on Typed Lambda Calculi and Applications (TLCA 2011). <a href="https://doi.org/10.1007/978-3-642-21691-6_17">doi</a></li>
</ul>
</div>
</div>
<div id="outline-container-orga2611c6" class="outline-3">
<h3 id="orga2611c6">Information Theory</h3>
<div class="outline-text-3" id="text-orga2611c6">
<ul class="org-ul">
<li>Joshua M. Cohen, Qinshi Wang, Andrew W. Appel.
<span class="underline">Verified Erasure Correction in Coq with MathComp and VST</span>.
34th International Conference on Computer-Aided Verification (CAV 2022). <a href="https://www.cs.princeton.edu/~appel/papers/FECVerification.pdf">pdf</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa.
<span class="underline">A library for formalization of linear error-correcting codes</span>.
JAR 64:1123-1164, 2020. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/ecc.pdf">pdf</a></li>
<li>Kyosuke Nakano, Manabu Hagiwara.
<span class="underline">Formalization of binary symmetric erasure channel based on infotheo</span>.
International Symposium on Information Theory and its Application 2016 (ISITA 2016).
<a href="https://ieeexplore.ieee.org/document/7840477">IEEE Xplore</a></li>
<li>Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa.
<span class="underline">Formalization of Reed-Solomon codes and progress report on formalization of LDPC codes</span>.
International Symposium on Information Theory and its Application 2016 (ISITA 2016)</li>
<li>Reynald Affeldt, Jacques Garrigue.
<span class="underline">Formalization of error-correcting codes: from Hamming to modern coding theory</span>. ITP 2015. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/eccITP2015_authorsversion.pdf">pdf</a></li>
<li>Ryosuke Obi, Manabu Hagiwara, Reynald Affeldt.
<span class="underline">Formalization of the variable-length source coding theorem: Direct part</span>.
International Symposium on Information Theory and its Application 2014 (ISITA 2014). <a href="https://ieeexplore.ieee.org/document/6979832">IEEE Xplore</a></li>
<li>Reynald Affeldt, Manabu Hagiwara, Jonas Sénizergues.
<span class="underline">Formalization of Shannon's theorems</span>. JAR 53(1), 2014. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/shannon_theorems.pdf">pdf</a></li>
<li>Reynald Affeldt, Manabu Hagiwara.
<span class="underline">Formalization of Shannon's Theorems in SSReflect-Coq</span>. ITP 2012. <a href="https://staff.aist.go.jp/reynald.affeldt/documents/affeldt-itp2012-preprint.pdf">pdf</a></li>
</ul>
</div>
</div>
</div>
<div id="outline-container-org62dac1f" class="outline-2">
<h2 id="org62dac1f">Tooling</h2>
<div class="outline-text-2" id="text-org62dac1f">
<ul class="org-ul">
<li>Cyril Cohen, Enzo Crance, Assia Mahboubi.
<span class="underline">Trocq: Proof Transfer for Free, With or Without Univalence</span>.
ESOP 2024. <a href="https://arxiv.org/pdf/2310.14022">pdf</a></li>
<li>Xavier Allamigeon, Quentin Canu, Cyril Cohen, Kazuhiko Sakaguchi, Pierre-Yves Strub.
<span class="underline">Design patterns of hierarchies for order structures</span>.
HAL 2023. <a href="https://inria.hal.science/hal-04008820/document">pdf</a></li>
<li>Valentin Blot, Denis Cousineau, Enzo Crance, Louise Dubois de Prisque, Chantal Keller, Assia Mahboubi, Pierre Vial.
<span class="underline">Compositional Pre-processing for Automated Reasoning in Dependent Type Theory</span>.
CPP 2023. <a href="https://arxiv.org/pdf/2204.02643.pdf">pdf</a></li>
<li>Benjamin Grégoire, Jean-Christophe Léchenet, Enrico Tassi.
<span class="underline">Practical and sound equality tests, automatically</span>.
CPP 2023. <a href="https://hal.inria.fr/hal-03800154/document">pdf</a></li>
<li>Kazuhiko Sakaguchi. <span class="underline">Reflexive tactics for algebra, revisited</span>. ITP 2022. <a href="https://arxiv.org/pdf/2202.04330.pdf">pdf</a></li>
<li>Reynald Affeldt, Xavier Allamigeon, Yves Bertot, Quentin Canu, Cyril Cohen, Pierre Roux, Kazuhiko Sakaguchi, Enrico Tassi, Laurent Théry, Anton Trunov.
<span class="underline">Porting the Mathematical Components library to Hierarchy Builder</span>. Coq Workshop 2021. <a href="https://coq-workshop.gitlab.io/2021/abstracts/Coq2021-01-02-mathcomp-hierarchy-builder.pdf">pdf</a></li>
<li>Pierre-Léo Bégay, Pierre Crégut, Jean-Francois Monin.
<span class="underline">Developing sequence and tree fintypes in MathComp</span>. Coq Workshop 2020. <a href="https://coq-workshop.gitlab.io/2020/abstracts/Coq2020_03-03-seq-fintype.pdf">pdf</a></li>
<li>Xavier Allamigeon, Cyril Cohen, Kazuhiko Sakaguchi, Pierre-Yves Strub.
<span class="underline">A hierarchy of ordered types in Mathematical Components</span>. Coq Workshop 2020. <a href="https://coq-workshop.gitlab.io/2020/abstracts/Coq2020_03-02-ordered.pdf">pdf</a></li>
<li>Cyril Cohen, Kazuhiko Sakaguchi, Enrico Tassi.
<span class="underline">Hierarchy Builder: algebraic hierarchies made easy in Coq with Elpi</span>.
FSCD 2020. <a href="https://hal.inria.fr/hal-02478907v4/document">pdf</a></li>
<li>Karl Palmskog, Ahmet Celik, Milos Gligoric.
<span class="underline">Practical Machine-Checked Formalization of Change Impact Analysis</span>.
TACAS 2020. <a href="https://users.ece.utexas.edu/~gligoric/papers/PalmskogETAL20Chip.pdf">pdf</a></li>
<li>Kazuhiko Sakaguchi. <span class="underline">Validating Mathematical Structures</span>. IJCAR 2020. <a href="https://arxiv.org/pdf/2002.00620.pdf">pdf</a></li>
<li>Kazuhiko Sakaguchi. <span class="underline">Program extraction for mutable arrays</span>. Science of Computer Programming 191, 2020. <a href="https://doi.org/10.1016/j.scico.2019.102372">doi</a></li>
<li>Erik Martin-Dorel, Enrico Tassi. <span class="underline">SSReflect in Coq 8.10</span>. Coq Workshop 2019. <a href="https://staff.aist.go.jp/reynald.affeldt/coq2019/coqws2019-martindorel-tassi.pdf">pdf</a></li>
<li>Kazuhiko Sakaguchi. <span class="underline">Program Extraction for Mutable Arrays</span>.
15th International Symposium on Functional and Logic Programming (FLOPS 2018). <a href="https://doi.org/10.1007/978-3-319-90686-7_4">doi</a></li>
<li>Kazuhiko Sakaguchi, Yukiyoshi Kameyama.
<span class="underline">Efficient Finite-Domain Function Library for the Coq Proof Assistant</span>.
IPSJ Transactions on Programming 10(1), 2017. <a href="http://logic.cs.tsukuba.ac.jp/~sakaguchi/papers/ipsj-pro-2016-1-7.pdf">pdf (long, in Japanese)</a>, <a href="http://logic.cs.tsukuba.ac.jp/~sakaguchi/papers/ipsj-pro-2016-1-7.en.pdf">pdf (short, in English)</a></li>
<li>Georges Gonthier, Beta Ziliani, Aleksandar Nanevski, Derek Dreyer.
<span class="underline">How to make ad hoc proof automation less ad hoc</span>. JFP 23(4), 2013. <a href="https://doi.org/10.1017/S0956796813000051">doi</a></li>
<li>Vladimir Komendantsky, Alexander Konovalov, Steve Linton.
<span class="underline">Interfacing Coq + SSReflect with GAP</span>. Electronic Notes in Theoretical Computer Science 285, 2012. <a href="https://www.sciencedirect.com/science/article/pii/S1571066112000230">pdf</a></li>
<li>Iain Whiteside, David Aspinall, Gudmund Grov.
<span class="underline">An Essence of SSReflect</span>. CICM 2012. <a href="https://doi.org/10.1007/978-3-642-31374-5_13">doi</a></li>
<li>Georges Gonthier, Enrico Tassi.
<span class="underline">A Language of Patterns for Subterm Selection</span>. ITP 2012. <a href="https://hal.inria.fr/hal-00652286/file/rew.pdf">pdf</a></li>
<li>Georges Gonthier, Assia Mahboubi.
<span class="underline">An introduction to small scale reflection in Coq</span>. Journal of Formalized Reasoning 3(2), 2010. <a href="https://hal.inria.fr/inria-00515548v4/document">pdf</a></li>
<li>François Garillot, Georges Gonthier, Assia Mahboubi, Laurence Rideau.
<span class="underline">Packaging Mathematical Structures</span>. TPHOLs 2009. <a href="https://hal.inria.fr/inria-00368403v1/document">pdf</a></li>
</ul>
</div>
<div id="outline-container-org6defe0e" class="outline-3">
<h3 id="org6defe0e">Machine Learning</h3>
<div class="outline-text-3" id="text-org6defe0e">
<ul class="org-ul">
<li>Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, Kathrin Stark.
<span class="underline">Taming Differentiable Logics with Coq Formalisation</span>.
ITP 2024. <a href="https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.4/LIPIcs.ITP.2024.4.pdf">pdf</a></li>
<li>Pengyu Nie, Karl Palmskog, Junyi Jessy Li, Milos Gligoric.
<span class="underline">Deep Generation of Coq Lemma Names Using Elaborated Terms</span>. IJCAR 2020. <a href="https://arxiv.org/pdf/2004.07761.pdf">pdf</a></li>
<li>Jónathan Heras, Ekaterina Komendantskaya.
<span class="underline">Recycling Proof Patterns in Coq: Case Studies</span>. Mathematics in Computer Science 8(1), 2014. <a href="https://arxiv.org/pdf/1301.6039v4.pdf">pdf</a></li>
<li>Jónathan Heras, Ekaterina Komendantskaya.
<span class="underline">Proof Pattern Search in Coq/SSReflect</span>. <a href="https://arxiv.org/pdf/1402.0081.pdf">CoRR abs/1402.0081</a>, 2014</li>
<li>Jónathan Heras, Ekaterina Komendantskaya.
<span class="underline">ML4PG in Computer Algebra Verification</span>. CICM 2013. <a href="https://arxiv.org/pdf/1302.6421.pdf">pdf</a></li>
</ul>
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