Team, Visitors, External Collaborators
Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Major publications by the team in recent years
R. M. Amadio, Y. Régis-Gianas.
Certifying and reasoning about cost annotations of functional programs, in: Higher-Order and Symbolic Computation, January 2013.
Z. Ariola, H. Herbelin, A. Sabry.
A Type-Theoretic Foundation of Delimited Continuations, in: Higher Order and Symbolic Computation, 2007.
D. Baelde, A. Doumane, A. Saurin.
Infinitary proof theory : the multiplicative additive case , in: Proceedings of CSL 2016, September 2016.
C. Chenavier.
The lattice of reduction operators: applications to noncommutative Gröbner bases and homological algebra, Université paris Diderot, December 2016.
P.-L. Curien.
Operads, clones, and distributive laws, in: Operads and Universal Algebra : Proceedings of China-France Summer Conference, Tianjin, China, C. Bai, L. Guo, J.-L. Loday (editors), Nankai Series in Pure, Applied Mathematics and Theoretical Physics, Vol. 9, World Scientific, July 2010, pp. 25-50.
P.-L. Curien, R. Garner, M. Hofmann.
Revisiting the categorical interpretation of dependent type theory, in: Theoretical computer Science, 2014, vol. 546, pp. 99-119.
P.-L. Curien, H. Herbelin.
The duality of computation, in: Proceedings of the Fifth ACM SIGPLAN International Conference on Functional Programming (ICFP '00), Montreal, Canada, SIGPLAN Notices 35(9), ACM, September 18-21 2000, pp. 233–243. [ DOI : 10.1145/351240.351262 ]
P.-L. Curien, H. Herbelin.
Abstract machines for dialogue games, in: Interactive models of computation and program behavior, Panoramas et Synthèses, Société Mathématique de France, 2009, pp. 231-275.
P. Dehornoy, Y. Guiraud.
Quadratic normalization in monoids, in: Internat. J. Algebra Comput., 2016, vol. 26, no 5, pp. 935–972.
E. J. Gallego Arias, B. Pin, P. Jouvelot.
jsCoq: Towards Hybrid Theorem Proving Interfaces, in: Proceedings of the 12th Workshop on User Interfaces for Theorem Provers, Coimbra, Portugal, 2nd July 2016, S. Autexier, P. Quaresma (editors), Electronic Proceedings in Theoretical Computer Science, Open Publishing Association, 2017, vol. 239, pp. 15-27.
S. Gaussent, Y. Guiraud, P. Malbos.
Coherent presentations of Artin monoids, in: Compositio Mathematica, 2015, vol. 151, no 5, pp. 957-998. [ DOI : 10.1112/S0010437X14007842 ]
G. Gilbert, J. Cockx, M. Sozeau, N. Tabareau.
Definitional Proof-Irrelevance without K, in: 46th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2019, Lisbon, Portugal, POPL, January 2019.
T. Girka, D. Mentré, Y. Régis-Gianas.
Oracle-based Dierential Operational Semantics (long version), Université Paris Diderot / Sorbonne Paris Cité, October 2016.
Y. Guiraud, P. Malbos.
Higher-dimensional normalisation strategies for acyclicity, in: Advances in Mathematics, 2012, vol. 231, no 3-4, pp. 2294-2351. [ DOI : 10.1016/j.aim.2012.05.010 ]
Y. Guiraud, P. Malbos, S. Mimram.
A Homotopical Completion Procedure with Applications to Coherence of Monoids, in: RTA - 24th International Conference on Rewriting Techniques and Applications - 2013, Eindhoven, Netherlands, F. Van Raamsdonk (editor), Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, June 2013, vol. 21, pp. 223-238. [ DOI : 10.4230/LIPIcs.RTA.2013.223 ]
H. Herbelin.
On the Degeneracy of Sigma-Types in Presence of Computational Classical Logic, in: Proceedings of TLCA 2005, P. Urzyczyn (editor), Lecture Notes in Computer Science, Springer, 2005, vol. 3461, pp. 209–220.
H. Herbelin.
An intuitionistic logic that proves Markov's principle, in: Logic In Computer Science, Edinburgh, Royaume-Uni, IEEE Computer Society, 2010.
H. Herbelin.
A Constructive Proof of Dependent Choice, Compatible with Classical Logic, in: LICS 2012 - 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Dubrovnik, Croatia, Proceedings of the 27th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, 25-28 June 2012, Dubrovnik, Croatia, IEEE Computer Society, June 2012, pp. 365-374.
G. Jaber, N. Tabareau, M. Sozeau.
Extending Type Theory with Forcing, in: LICS 2012 : Logic In Computer Science, Dubrovnik, Croatia, June 2012.
P. Letouzey.
Hofstadter's problem for curious readers, Université Paris Diderot ; Inria Paris-Rocquencourt, September 2015, 29 p.
G. Munch-Maccagnoni.
Focalisation and Classical Realisability, in: Computer Science Logic '09, E. Grädel, R. Kahle (editors), Lecture Notes in Computer Science, Springer-Verlag, 2009, vol. 5771, pp. 409–423.
T. U. F. Program.
Homotopy type theory—univalent foundations of mathematics, The Univalent Foundations Program, Princeton, NJ; Institute for Advanced Study (IAS), Princeton, NJ, 2013, xiv+589 p.
Y. Régis-Gianas, F. Pottier.
A Hoare Logic for Call-by-Value Functional Programs, in: Proceedings of the Ninth International Conference on Mathematics of Program Construction (MPC'08), Lecture Notes in Computer Science, Springer, July 2008, vol. 5133, pp. 305–335.
A. Saurin.
Separation with Streams in the Λμ-calculus, in: Symposium on Logic in Computer Science (LICS 2005), Chicago, IL, USA, Proceedings, IEEE Computer Society, 26-29 June 2005, pp. 356-365.
B. Ziliani, M. Sozeau.
A comprehensible guide to a new unifier for CIC including universe polymorphism and overloading, in: Journal of Functional Programming, 2017, vol. 27. [ DOI : 10.1017/S0956796817000028 ]
Publications of the year

Doctoral Dissertations and Habilitation Theses

Y. Guiraud.
Rewriting methods in higher algebra, Université Paris 7, June 2019, Habilitation à diriger des recherches.
Y. Régis-Gianas.
About some Metamorphoses of Computer Programs, Université Paris Diderot, November 2019, Habilitation à diriger des recherches.
T. Zimmermann.
Challenges in the collaborative evolution of a proof language and its ecosystem, Université de Paris, December 2019.

Articles in International Peer-Reviewed Journals

C. Chenavier.
A Lattice Formulation of the F 4 Completion Procedure, in: International Journal of Algebra and Computation, 2019.
C. Chenavier.
Syzygies among reduction operators, in: Journal of Pure and Applied Algebra, 2019,
G. Gilbert, J. Cockx, M. Sozeau, N. Tabareau.
Definitional Proof-Irrelevance without K, in: Proceedings of the ACM on Programming Languages, January 2019, pp. 1-28. [ DOI : 10.1145/329031610.1145/3290316 ]
Y. Guiraud, E. Hoffbeck, P. Malbos.
Convergent presentations and polygraphic resolutions of associative algebras, in: Mathematische Zeitschrift, 2019, vol. 293, no 1-2, pp. 113-179, [ DOI : 10.1007/s00209-018-2185-z ]
Y. Jiang, J. Liu, G. Dowek, K. Ji.
Towards Combining Model Checking and Proof Checking, in: The Computer Journal, 2019, forthcoming. [ DOI : 10.1093/comjnl/bxy112 ]
G. Manzonetto, A. Polonsky, A. Saurin, J. G. Simonsen.
The fixed point property and a technique to harness double fixed point combinators, in: Journal of Logic and Computation, September 2019, vol. 29, no 5, pp. 831-880. [ DOI : 10.1093/logcom/exz013 ]
M. Sozeau, S. Boulier, Y. Forster, N. Tabareau, T. Winterhalter.
Coq Coq Correct! Verification of Type Checking and Erasure for Coq, in Coq, in: Proceedings of the ACM on Programming Languages, January 2020, pp. 1-28. [ DOI : 10.1145/3371076 ]
M. Sozeau, C. Mangin.
Equations reloaded, in: Proceedings of the ACM on Programming Languages, July 2019, vol. 3, no ICFP, pp. 1-29. [ DOI : 10.1145/3341690 ]

International Conferences with Proceedings

R. Chen, C. Cohen, J.-J. Levy, S. Merz, L. Théry.
Formal Proofs of Tarjan's Strongly Connected Components Algorithm in Why3, Coq and Isabelle, in: ITP 2019 - 10th International Conference on Interactive Theorem Proving, Portland, United States, J. Harrison, J. O'Leary, A. Tolmach (editors), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2019, vol. 141, pp. 13:1 - 13:19. [ DOI : 10.4230/LIPIcs.ITP.2019.13 ]
A. De, A. Saurin.
Infinets: The parallel syntax for non-wellfounded proof-theory, in: TABLEAUX 2019 - 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, London, United Kingdom, TABLEAUX 2019 - 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, September 2019.
P. G. Giarrusso, Y. Régis-Gianas, P. Schuster.
Incremental λ-Calculus in Cache-Transfer Style Static Memoization by Program Transformation, in: ESOP 2019 - European Symposium on Programming, Prague, Czech Republic, L. Caires (editor), Springer, April 2019.
T. Letan, Y. Régis-Gianas.
FreeSpec: Specifying, Verifying and Executing Impure Computations in Coq, in: CPP 2020 - 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Nouvelle-Orléans, United States, ACM, January 2020, pp. 1-15. [ DOI : 10.1145/3372885.3373812 ]
R. Nollet, A. Saurin, C. Tasson.
PSPACE-Completeness of a Thread Criterion for Cyclic Proofs in Linear Logic with Least and Greatest Fixed Points, in: TABLEAUX 2019 - 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, London, United Kingdom, Automated Reasoning with Analytic Tableaux and Related Methods - 28th International Conference, TABLEAUX 2019, London, UK, September 3-5, 2019, Proceedings, September 2019.
T. Winterhalter, M. Sozeau, N. Tabareau.
Eliminating Reflection from Type Theory : To the Legacy of Martin Hofmann, in: CPP 2019 - 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, Lisbonne, Portugal, ACM, January 2019, pp. 91-103. [ DOI : 10.1145/3293880.3294095 ]
T. Zimmermann, A. Casanueva Artís.
Impact of switching bug trackers: a case study on a medium-sized open source project, in: ICSME 2019 - International Conference on Software Maintenance and Evolution, Cleveland, United States, September 2019.

National Conferences with Proceedings

C. Bozman, B. Canou, R. Di Cosmo, P. Couderc, L. Gesbert, G. Henry, F. Le Fessant, M. Mauny, C. Morel, L. Peyrot, Y. Régis-Gianas.
Learn-OCaml : un assistant à l'enseignement d'OCaml, in: JFLA 2019 - Journées Francophones des Langages Applicatifs, Les Rousses, France, January 2019.

Conferences without Proceedings

C. Ho Thanh, P.-L. Curien, S. Mimram.
A Sequent Calculus for Opetopes, in: LICS 2019 - Logic in computer science 2019, Vancouver, Canada, June 2019.

Scientific Books (or Scientific Book chapters)

D. Baelde, A. Felty, G. Nadathur, A. Saurin.
A special issue on structural proof theory, automated reasoning and computation in celebration of Dale Miller’s 60th birthday, Cambridge University Press, September 2019, vol. 29, no 8, pp. 1007-1008. [ DOI : 10.1017/S0960129519000136 ]
Z. L. Dargaye, Y. Régis-Gianas.
31ème Journées Francophones des Langages Applicatifs, IRIF, January 2020.

Internal Reports

N. Jeannerod, C. Marché, Y. Régis-Gianas, M. Sighireanu, R. Treinen.
Specification of UNIX Utilities, ANR, October 2019.

Other Publications

P.-L. Curien, C. Ho Thanh, S. Mimram.
Syntactical approaches to opetopes, March 2019, working paper or preprint.
H. Herbelin, É. Miquey.
Continuation-and-environment-passing style translations: a focus on call-by-need, January 2019, working paper or preprint.
C. Ho Thanh, C. Leena Subramaniam.
Opetopic algebras I: Algebraic structures on opetopic sets, November 2019, 38 pages.
C. Ho Thanh, C. Leena Subramaniam.
Opetopic algebras III: Presheaf models of homotopy-coherent opetopic algebras, January 2020, working paper or preprint.
M. Milicevic, D. Baralic, J. Obradovic, Z. Petric, M. Zekic, R. Zivaljevic, P.-L. Curien.
Proofs and surfaces, December 2019, working paper or preprint.
M. Sozeau, A. Anand, S. Boulier, C. Cohen, Y. Forster, F. Kunze, G. Malecha, N. Tabareau, T. Winterhalter.
The MetaCoq Project, June 2019, working paper or preprint.
References in notes
Proverbot, a bot for proving, 2019, Accessed: 2019-12-09.
Waterproof: an educational environment for writing mathematical proofs in interactive notebooks, 2019, Accessed: 2019-12-09.
D. J. Anick.
On the Homology of Associative Algebras, in: Trans. Amer. Math. Soc., 1986, vol. 296, no 2, pp. 641–659.
D. Ara, F. Métayer.
The Brown-Golasiński Model Structure on strict -groupoids revisited, in: Homology, Homotopy and Applications, 2011, vol. 13, no 1, pp. 121–142.
J. Baez, A. Crans.
Higher-dimensional algebra. VI. Lie 2-algebras, in: Theory Appl. Categ., 2004, vol. 12, pp. 492–538.
H. P. Barendregt.
The Lambda Calculus: Its Syntax and Semantics, North Holland, Amsterdam, 1984.
Y. Bertot, P. Castéran.
Interactive Theorem Proving and Program Development Coq'Art: The Calculus of Inductive Constructions, Springer, 2004.
G. Bonfante, Y. Guiraud.
Polygraphic Programs and Polynomial-Time Functions, in: Logical Methods in Computer Science, 2009, vol. 5, no 2, pp. 1–37.
B. Buchberger.
Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal), Mathematical Institute, University of Innsbruck, Austria, 1965.
A. Burroni.
Higher-dimensional word problems with applications to equational logic, in: Theoretical Computer Science, jul 1993, vol. 115, no 1, pp. 43–62.
A. Celik, K. Palmskog, M. Parovic, E. J. Gallego Arias, M. Gligoric.
mCoq : Mutation Proving for Analysis of Verification Projects, in: Proceedings of the 34rd ACM/IEEE International Conference on Automated Software Engineering, ASE 2019, 2019.
A. Chlipala.
Certified Programming with Dependent Types - A Pragmatic Introduction to the Coq Proof Assistant, MIT Press, 2013.
A. Church.
A set of Postulates for the foundation of Logic, in: Annals of Mathematics, 1932, vol. 2, pp. 33, 346-366.
J. Cockx, D. Devriese.
Proof-relevant unification: Dependent pattern matching with only the axioms of your type theory, in: J. Funct. Program., 2018, vol. 28, e12 p.
T. Coquand.
Une théorie des Constructions, University Paris 7, January 1985.
T. Coquand, G. Huet.
Constructions : A Higher Order Proof System for Mechanizing Mathematics, in: EUROCAL'85, Linz, Lecture Notes in Computer Science, Springer Verlag, 1985, vol. 203.
T. Coquand, C. Paulin-Mohring.
Inductively defined types, in: Proceedings of Colog'88, P. Martin-Löf, G. Mints (editors), Lecture Notes in Computer Science, Springer Verlag, 1990, vol. 417.
H. B. Curry, R. Feys, W. Craig.
Combinatory Logic, North-Holland, 1958, vol. 1, §9E.
P. Dehornoy, Y. Lafont.
Homology of Gaussian groups, in: Ann. Inst. Fourier (Grenoble), 2003, vol. 53, no 2, pp. 489–540.
P. Deligne.
Action du groupe des tresses sur une catégorie, in: Invent. Math., 1997, vol. 128, no 1, pp. 159–175.
M. Felleisen, D. P. Friedman, E. Kohlbecker, B. F. Duba.
Reasoning with continuations, in: First Symposium on Logic and Computer Science, 1986, pp. 131-141.
A. Filinski.
Representing Monads, in: Conf. Record 21st ACM SIGPLAN-SIGACT Symp. on Principles of Programming Languages, POPL'94, Portland, OR, USA, ACM Press, 17-21 Jan 1994, pp. 446-457.
G. Gentzen.
Untersuchungen über das logische Schließen, in: Mathematische Zeitschrift, 1935, vol. 39, pp. 176–210,405–431.
J.-Y. Girard.
Une extension de l'interpretation de Gödel à l'analyse, et son application à l'élimination des coupures dans l'analyse et la théorie des types, in: Second Scandinavian Logic Symposium, J. Fenstad (editor), Studies in Logic and the Foundations of Mathematics, North Holland, 1971, no 63, pp. 63-92.
T. G. Griffin.
The Formulae-as-Types Notion of Control, in: Conf. Record 17th Annual ACM Symp. on Principles of Programming Languages, POPL '90, San Francisco, CA, USA, 17-19 Jan 1990, ACM Press, 1990, pp. 47–57.
Y. Guiraud.
Présentations d'opérades et systèmes de réécriture, Univ. Montpellier 2, 2004.
Y. Guiraud.
Termination Orders for 3-Dimensional Rewriting, in: Journal of Pure and Applied Algebra, 2006, vol. 207, no 2, pp. 341–371.
Y. Guiraud.
The Three Dimensions of Proofs, in: Annals of Pure and Applied Logic, 2006, vol. 141, no 1–2, pp. 266–295.
Y. Guiraud.
Two Polygraphic Presentations of Petri Nets, in: Theoretical Computer Science, 2006, vol. 360, no 1–3, pp. 124–146.
Y. Guiraud, E. Hoffbeck, P. Malbos.
Confluence of linear rewriting and homology of algebras, in: 3rd International Workshop on Confluence, Vienna, Austria, July 2014.
Y. Guiraud, P. Malbos.
Higher-dimensional categories with finite derivation type, in: Theory Appl. Categ., 2009, vol. 22, no 18, pp. 420-478.
Y. Guiraud, P. Malbos.
Identities among relations for higher-dimensional rewriting systems, in: Séminaires et Congrès, Société Mathématique de France, 2011, vol. 26, pp. 145-161.
Y. Guiraud, P. Malbos.
Coherence in monoidal track categories, in: Math. Structures Comput. Sci., 2012, vol. 22, no 6, pp. 931–969.
M. Hofmann, T. Streicher.
The groupoid interpretation of type theory, in: Twenty-five years of constructive type theory (Venice, 1995), Oxford Logic Guides, Oxford Univ. Press, New York, 1998, vol. 36, pp. 83–111.
W. A. Howard.
The formulae-as-types notion of constructions, in: to H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, 1980, Unpublished manuscript of 1969.
J. Kock, A. Joyal, M. Batanin, J.-F. Mascari.
Polynomial functors and opetopes, in: Advances in Mathematics, 2010, vol. 224, no 6, pp. 2690 - 2737. [ DOI : 10.1016/j.aim.2010.02.012 ]
J.-L. Krivine.
A call-by-name lambda-calculus machine, in: Higher Order and Symbolic Computation, 2005.
J.-L. Krivine.
Un interpréteur du lambda-calcul, 1986, Unpublished.
Y. Lafont.
Towards an Algebraic Theory of Boolean Circuits, in: Journal of Pure and Applied Algebra, 2003, vol. 184, pp. 257-310.
Y. Lafont, F. Métayer, K. Worytkiewicz.
A Folk Model Structure on Omega-Cat, in: Advances in Mathematics, 2010, vol. 224, no 3, pp. 1183–1231.
P. Landin.
The mechanical evaluation of expressions, in: The Computer Journal, January 1964, vol. 6, no 4, pp. 308–320.
P. Landin.
A generalisation of jumps and labels, UNIVAC Systems Programming Research, August 1965, no ECS-LFCS-88-66, Reprinted in Higher Order and Symbolic Computation, 11(2), 1998.
P. Malbos.
Critères de finitude homologique pour la non convergence des systèmes de réécriture de termes, Univ. Montpellier 2, 2004.
P. Martin-Löf.
A theory of types, University of Stockholm, 1971, no 71-3.
M. Parigot.
Free Deduction: An Analysis of "Computations" in Classical Logic, in: Logic Programming, Second Russian Conference on Logic Programming, St. Petersburg, Russia, A. Voronkov (editor), Lecture Notes in Computer Science, Springer, September 11-16 1991, vol. 592, pp. 361-380.
S. B. Priddy.
Koszul resolutions, in: Trans. Amer. Math. Soc., 1970, vol. 152, pp. 39–60.
J. C. Reynolds.
Definitional interpreters for higher-order programming languages, in: ACM '72: Proceedings of the ACM annual conference, New York, NY, USA, ACM Press, 1972, pp. 717–740.
J. C. Reynolds.
Towards a theory of type structure, in: Symposium on Programming, B. Robinet (editor), Lecture Notes in Computer Science, Springer, 1974, vol. 19, pp. 408-423.
T. Ringer, A. Sanchez-Stern, D. Grossman, S. Lerner.
REPLICA: REPL Analysis for Coq Instrumentation, in: Certified Programs and Proofs (CPP 2019), 2019.
C. Squier, F. Otto, Y. Kobayashi.
A finiteness condition for rewriting systems, in: Theoret. Comput. Sci., 1994, vol. 131, no 2, pp. 271–294.
C. C. Squier.
Word problems and a homological finiteness condition for monoids, in: J. Pure Appl. Algebra, 1987, vol. 49, no 1-2, pp. 201–217.
R. Street.
Limits Indexed by Category-Valued 2-Functors, in: Journal of Pure and Applied Algebra, 1976, vol. 8, pp. 149–181.
T. C. D. Team.
The Coq Proof Assistant, version 8.7.1, December 2017.
K. Yang, J. Deng.
Learning to Prove Theorems via Interacting with Proof Assistants, in: International Conference on Machine Learning, 2019.
N. de Bruijn.
AUTOMATH, a language for mathematics, Technological University Eindhoven, November 1968, no 66-WSK-05.