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Coq for Homotopy Type Theory

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Publications

The MetaCoq Project

Author(s): Matthieu Sozeau, Abhishek Anand, Simon Boulier, Cyril Cohen, Yannick Forster, Fabian Kunze, Gregory Malecha, Nicolas Tabareau, Théo Winterhalter
Published in: Journal of Automated Reasoning, Issue 64/5, 2020, Page(s) 947-999, ISSN 0168-7433
DOI: 10.1007/s10817-019-09540-0

Model structure on the universe of all types in interval type theory

Author(s): Simon Boulier, Nicolas Tabareau
Published in: Mathematical Structures in Computer Science, 2020, Page(s) 1-32, ISSN 0960-1295
DOI: 10.1017/s0960129520000213

Foundations of dependent interoperability

Author(s): PIERRE-ÉVARISTE DAGAND, NICOLAS TABAREAU, ÉRIC TANTER
Published in: Journal of Functional Programming, Issue 28, 2018, ISSN 0956-7968
DOI: 10.1017/S0956796818000011

Lawvere-Tierney sheafification in Homotopy Type Theory

Author(s): Kevin Quirin and Nicolas Tabareau
Published in: Journal of Formalized Reasoning, 2016, ISSN 1972-5787
DOI: 10.6092/issn.1972-5787/6232

From Signatures to Monads in UniMath

Author(s): Benedikt Ahrens, Ralph Matthes, Anders Mörtberg
Published in: Journal of Automated Reasoning, Issue 63/2, 2019, Page(s) 285-318, ISSN 0168-7433
DOI: 10.1007/s10817-018-9474-4

Reduction monads and their signatures

Author(s): Benedikt Ahrens, André Hirschowitz, Ambroise Lafont, Marco Maggesi
Published in: Proceedings of the ACM on Programming Languages, Issue 4/POPL, 2020, Page(s) 1-29, ISSN 2475-1421
DOI: 10.1145/3371099

Definitional proof-irrelevance without K

Author(s): Gaëtan Gilbert, Jesper Cockx, Matthieu Sozeau, Nicolas Tabareau
Published in: Proceedings of the ACM on Programming Languages, Issue 3/POPL, 2019, Page(s) 1-28, ISSN 2475-1421
DOI: 10.1145/3290316

Equivalences for free: univalent parametricity for effective transport

Author(s): Nicolas Tabareau, Éric Tanter, Matthieu Sozeau
Published in: Proceedings of the ACM on Programming Languages, Issue 2/ICFP, 2018, Page(s) 1-29, ISSN 2475-1421
DOI: 10.1145/3236787

A reasonably exceptional type theory

Author(s): Pierre-Marie Pédrot, Nicolas Tabareau, Hans Jacob Fehrmann, Éric Tanter
Published in: Proceedings of the ACM on Programming Languages, Issue 3/ICFP, 2019, Page(s) 1-29, ISSN 2475-1421
DOI: 10.1145/3341712

Goodwillie's calculus of functors and higher topos theory

Author(s): M. Anel, G. Biedermann, E. Finster, A. Joyal
Published in: Journal of Topology, Issue 11/4, 2018, Page(s) 1100-1132, ISSN 1753-8416
DOI: 10.1112/topo.12082

Equations reloaded: high-level dependently-typed functional programming and proving in Coq

Author(s): Matthieu Sozeau, Cyprien Mangin
Published in: Proceedings of the ACM on Programming Languages, Issue 3/ICFP, 2019, Page(s) 1-29, ISSN 2475-1421
DOI: 10.1145/3341690

Static interpretation of higher-order modules in Futhark: functional GPU programming in the large

Author(s): Martin Elsman, Troels Henriksen, Danil Annenkov, Cosmin E. Oancea
Published in: Proceedings of the ACM on Programming Languages, Issue 2/ICFP, 2018, Page(s) 1-30, ISSN 2475-1421
DOI: 10.1145/3236792

Modular Specification of Monads Through Higher-Order Presentations

Author(s): Ahrens, Benedikt; Hirschowitz, André; Lafont, Ambroise; Maggesi, Marco
Published in: "FSCD 2019 - 4th International Conference on Formal Structures for Computation and Deduction, Jun 2019, Dortmund, Germany. pp.1-16, ⟨10.4230/LIPIcs.FSCD.2019.6⟩", Issue 3, 2019
DOI: 10.4230/lipics.fscd.2019.6

An effectful way to eliminate addiction to dependence

Author(s): Pierre-Marie Pedrot, Nicolas Tabareau
Published in: 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2017, Page(s) 1-12
DOI: 10.1109/LICS.2017.8005113

Displayed Categories

Author(s): Ahrens, Benedikt; Lumsdaine, Peter LeFanu
Published in: https://hal.inria.fr/hal-01584770, Issue 7, 2017
DOI: 10.4230/LIPIcs.FSCD.2017.5

Categorical Structures for Type Theory in Univalent Foundations

Author(s): Ahrens, Benedikt; Lumsdaine, Peter LeFanu; Voevodsky, Vladimir
Published in: 26th EACSL Annual Conference on Computer Science Logic (CSL 2017), Issue 6, 2017
DOI: 10.4230/LIPIcs.CSL.2017.8

The Definitional Side of the Forcing

Author(s): Guilhem Jaber, Gabriel Lewertowski, Pierre-Marie Pédrot, Matthieu Sozeau, Nicolas Tabareau
Published in: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16, 2016, Page(s) 367-376
DOI: 10.1145/2933575.2935320

The next 700 syntactical models of type theory

Author(s): Simon Boulier, Pierre-Marie Pédrot, Nicolas Tabareau
Published in: Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017, 2017, Page(s) 182-194
DOI: 10.1145/3018610.3018620

The HoTT library: a formalization of homotopy type theory in Coq

Author(s): Andrej Bauer, Jason Gross, Peter LeFanu Lumsdaine, Michael Shulman, Matthieu Sozeau, Bas Spitters
Published in: Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017, 2017, Page(s) 164-172
DOI: 10.1145/3018610.3018615

Formalising real numbers in homotopy type theory

Author(s): Gaëtan Gilbert
Published in: Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017, 2017, Page(s) 112-124
DOI: 10.1145/3018610.3018614

Partial type equivalences for verified dependent interoperability

Author(s): Pierre-Evariste Dagand, Nicolas Tabareau, Éric Tanter
Published in: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming - ICFP 2016, 2016, Page(s) 298-310
DOI: 10.1145/2951913.2951933

Cumulative Inductive Types in Coq

Author(s): Timany, Amin; Sozeau, Matthieu
Published in: FSCD 2018 - 3rd International Conference on Formal Structures for Computation and Deduction, Issue 1, 2018, Page(s) 29:1--29:16
DOI: 10.4230/LIPIcs.FSCD.2018.29

High-level signatures and initial semantics

Author(s): Ahrens, Benedikt; Hirschowitz, André; Lafont, Ambroise; Maggesi, Marco
Published in: 27th EACSL Annual Conference on Computer Science Logic (CSL 2018), Issue 1, 2018
DOI: 10.4230/lipics.csl.2018.4

Certified Compilation of Financial Contracts

Author(s): Danil Annenkov, Martin Elsman
Published in: Proceedings of the 20th International Symposium on Principles and Practice of Declarative Programming - PPDP '18, 2018, Page(s) 1-13
DOI: 10.1145/3236950.3236955

Modular Specification of Monads Through Higher-Order Presentations

Author(s): Ahrens, Benedikt; Hirschowitz, André; Lafont, Ambroise; Maggesi, Marco
Published in: 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019), Issue 1, 2019
DOI: 10.4230/LIPIcs.FSCD.2019.6

Every λ-Term is Meaningful for the Infinitary Relational Model

Author(s): Pierre Vial
Published in: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18, 2018, Page(s) 899-908
DOI: 10.1145/3209108.3209133

Eliminating reflection from type theory

Author(s): Théo Winterhalter, Matthieu Sozeau, Nicolas Tabareau
Published in: Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019, 2019, Page(s) 91-103
DOI: 10.1145/3293880.3294095

Heterogeneous Substitution Systems Revisited

Author(s): Ahrens, Benedikt; Matthes, Ralph
Published in: "Tarmo Uustalu. 21st International Conference on Types for Proofs and Programs (TYPES 2015), 69, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, pp.2:1-2:23, 2018, Leibniz International Proceedings in Informatics (LIPIcs), 978-3-95977-030-9. ⟨10.4230/LIPIcs.TYPES.2015.2⟩", Issue 1, 2018
DOI: 10.4230/LIPIcs.TYPES.2015.2

Towards Certified Meta-Programming with Typed Template-Coq

Author(s): Abhishek Anand, Simon Boulier, Cyril Cohen, Matthieu Sozeau, Nicolas Tabareau
Published in: Interactive Theorem Proving - 9th International Conference, ITP 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 9-12, 2018, Proceedings, Issue 10895, 2018, Page(s) 20-39
DOI: 10.1007/978-3-319-94821-8_2

Setoid Type Theory—A Syntactic Translation

Author(s): Thorsten Altenkirch, Simon Boulier, Ambrus Kaposi, Nicolas Tabareau
Published in: Mathematics of Program Construction - 13th International Conference, MPC 2019, Porto, Portugal, October 7–9, 2019, Proceedings, Issue 11825, 2019, Page(s) 155-196
DOI: 10.1007/978-3-030-33636-3_7

Failure is Not an Option

Author(s): Pierre-Marie Pédrot, Nicolas Tabareau
Published in: Programming Languages and Systems, Issue 10801, 2018, Page(s) 245-271
DOI: 10.1007/978-3-319-89884-1_9