Coq swMATH ID: 161 Software Authors: Dehlinger, Christophe; Dufourd, Jean-François Description: Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. Typical applications include the formalization of programming languages semantics (e.g. the CompCert compiler certification project or Java Card EAL7 certification in industrial context), the formalization of mathematics (e.g. the full formalization of the 4 color theorem or constructive mathematics at Nijmegen) and teaching. Homepage: http://www.lix.polytechnique.fr/coq/ Keywords: Coq; Calculus of Inductive Constructions; Geometry modelling; Generalized maps; Surfaces; Specification; Proof Related Software: Isabelle/HOL; Isabelle; HOL; PVS; HOL Light; Nuprl; Mizar; Agda; GitHub; Automath; ML; Haskell; z3; Archive Formal Proofs; ACL2; OCaml; LEGO; Lean; Twelf; Coq/SSReflect Cited in: 2,069 Documents Standard Articles 3 Publications describing the Software, including 3 Publications in zbMATH Year 30 years of research and development around Coq. Zbl 1284.68517Huet, Gérard; Herbelin, Hugo 2014 Certified programming with dependent types. A pragmatic introduction to the Coq proof assistant. Zbl 1288.68001Chlipala, Adam 2013 Formalizing generalized maps in Coq. Zbl 1078.68136Dehlinger, Christophe; Dufourd, Jean-François 2004 all top 5 Cited by 2,217 Authors 27 Kaliszyk, Cezary 25 Geuvers, Jan Herman 25 Pichardie, David 24 Barthe, Gilles 24 Rabe, Florian 24 Sacerdoti Coen, Claudio 23 Théry, Laurent 22 Appel, Andrew W. 22 Bertot, Yves 20 Wiedijk, Freek 19 Felty, Amy P. 19 Leroy, Xavier 19 Mahboubi, Assia 19 Narboux, Julien 18 Smolka, Gert 17 Abel, Andreas M. 17 Affeldt, Reynald 17 Birkedal, Lars 17 Boldo, Sylvie 17 Melquiond, Guillaume 17 Paulson, Lawrence Charles 17 Tassi, Enrico 16 Ahrens, Benedikt 16 Luo, Zhaohui 16 Urban, Josef 15 Cohen, Cyril 15 Krebbers, Robbert 15 Nipkow, Tobias 15 Sozeau, Matthieu 14 Dubois, Catherine 14 Dufourd, Jean-François 14 Gonthier, Georges 14 Grégoire, Benjamin 14 Miculan, Marino 14 Paulin-Mohring, Christine 13 Blanchette, Jasmin Christian 13 Blazy, Sandrine 13 Kohlhase, Michael 13 Larchey-Wendling, Dominique 13 Myreen, Magnus O. 13 Pous, Damien 13 Shao, Zhong 12 Benzmüller, Christoph Ewald 12 Constable, Robert Lee 12 Coquand, Thierry 12 Corbineau, Pierre 12 Delahaye, David 12 Filliâtre, Jean-Christophe 12 Kirst, Dominik 12 Magaud, Nicolas 12 Pientka, Brigitte 12 Popescu, Andrei 12 Wenzel, Makarius 11 Doczkal, Christian 11 Kamareddine, Fairouz D. 11 Matthes, Ralph 11 Mörtberg, Anders 11 Norrish, Michael 11 Tabareau, Nicolas 11 Vafeiadis, Viktor 11 Werner, Benjamin 10 Asperti, Andrea 10 Ayala-Rincón, Mauricio 10 Beringer, Lennart 10 Bizjak, Aleš 10 Capretta, Venanzio 10 Charguéraud, Arthur 10 Courtieu, Pierre 10 Cruz-Filipe, Luís 10 Dreyer, Derek R. 10 Farmer, William M. 10 Forster, Yannick 10 Mayero, Micaela 10 Nanevski, Aleksandar 10 Niqui, Milad 10 Spitters, Bas 10 Strub, Pierre-Yves 10 Stump, Aaron 9 Barras, Bruno 9 Barrett, Clark W. 9 Ciaffaglione, Alberto 9 Heras, Jónathan 9 Honsell, Furio 9 Janičić, Predrag 9 Oliveira, Bruno C.d. S. 9 Owens, Scott 9 Pfenning, Frank 9 Rideau, Laurence 9 Rubio García, Julio Jesús 9 Schreck, Pascal 9 Weirich, Stephanie 9 Ziliani, Beta 8 Altenkirch, Thorsten 8 Cachera, David 8 Chlipala, Adam J. 8 Contejean, Evelyne 8 Koprowski, Adam 8 Kumar, Ramana 8 Lochbihler, Andreas 8 Luna, Carlos ...and 2,117 more Authors all top 5 Cited in 124 Serials 177 Journal of Automated Reasoning 67 Lecture Notes in Computer Science 60 Logical Methods in Computer Science 52 Journal of Functional Programming 45 Theoretical Computer Science 40 Mathematical Structures in Computer Science 31 Journal of Formalized Reasoning 24 Formal Aspects of Computing 24 Journal of Logical and Algebraic Methods in Programming 18 Journal of Symbolic Computation 16 Information and Computation 15 Annals of Mathematics and Artificial Intelligence 14 Formal Methods in System Design 11 Science of Computer Programming 11 Annals of Pure and Applied Logic 11 ACM Transactions on Computational Logic 11 Mathematics in Computer Science 10 Journal of Applied Logic 8 Higher-Order and Symbolic Computation 8 Fundamenta Informaticae 7 ACM Transactions on Mathematical Software 7 Journal of Logic and Computation 7 The Journal of Logic and Algebraic Programming 6 Formalized Mathematics 5 Acta Informatica 5 Journal of Logic, Language and Information 4 Information Processing Letters 4 Programming and Computer Software 4 Studia Logica 4 Bulletin of the American Mathematical Society. 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Theoretical Informatics and Applications 2 Logic and Logical Philosophy 2 Journal of Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Electronic Notes in Theoretical Computer Science 2 Logica Universalis 2 Scientific Annals of Computer Science 2 Frontiers of Computer Science in China 2 Computer Science Review 2 Journal of Applied Logics - IfCoLog Journal of Logics and their Applications 1 Artificial Intelligence 1 Communications in Mathematical Physics 1 International Journal of General Systems 1 International Journal for Numerical Methods in Fluids 1 International Journal of Systems Science 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Letters in Mathematical Physics 1 Acta Cybernetica 1 Archiv der Mathematik 1 BIT 1 The Computer Journal. Section A / Section B 1 Information Sciences 1 Journal of Computational and Applied Mathematics 1 Journal of Computer and System Sciences 1 Journal of the Korean Mathematical Society 1 Mathematics and Computers in Simulation 1 Notre Dame Journal of Formal Logic 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Bulletin of the Section of Logic 1 European Journal of Combinatorics 1 Annales Societatis Mathematicae Polonae. Series IV 1 New Generation Computing 1 Internationale Mathematische Nachrichten 1 International Journal of Approximate Reasoning 1 Journal of the American Mathematical Society 1 Japan Journal of Industrial and Applied Mathematics 1 Discrete Event Dynamic Systems 1 Numerical Algorithms 1 Pattern Recognition 1 Archive for Mathematical Logic 1 Experimental Mathematics 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Turkish Journal of Mathematics 1 The Electronic Journal of Combinatorics 1 Quadrature 1 Documenta Mathematica 1 Mathematical Problems in Engineering 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Discrete Mathematics and Theoretical Computer Science. DMTCS ...and 24 more Serials all top 5 Cited in 46 Fields 1,904 Computer science (68-XX) 702 Mathematical logic and foundations (03-XX) 96 General and overarching topics; collections (00-XX) 65 Numerical analysis (65-XX) 52 Category theory; homological algebra (18-XX) 41 Information and communication theory, circuits (94-XX) 39 Algebraic topology (55-XX) 33 Number theory (11-XX) 30 Combinatorics (05-XX) 26 Geometry (51-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Operations research, mathematical programming (90-XX) 13 Convex and discrete geometry (52-XX) 13 Systems theory; control (93-XX) 12 Real functions (26-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 10 Field theory and polynomials (12-XX) 10 Commutative algebra (13-XX) 10 Group theory and generalizations (20-XX) 9 History and biography (01-XX) 9 Partial differential equations (35-XX) 9 Quantum theory (81-XX) 8 General algebraic systems (08-XX) 8 Algebraic geometry (14-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Fluid mechanics (76-XX) 7 Biology and other natural sciences (92-XX) 6 Ordinary differential equations (34-XX) 4 General topology (54-XX) 4 Manifolds and cell complexes (57-XX) 4 Mathematics education (97-XX) 3 Functions of a complex variable (30-XX) 2 Associative rings and algebras (16-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Probability theory and stochastic processes (60-XX) 1 Nonassociative rings and algebras (17-XX) 1 \(K\)-theory (19-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) Citations by Year