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Software Open Access

The Coq Proof Assistant

The Coq Development Team

Emilio Jesús Gallego Arias; Théo Zimmermann
Abhishek Anand; Yves Bertot; Frédéric Besson; Lasse Blaauwbroek; Simon Boulier; Quentin Carbonneaux; Tej Chajed; Arthur Charguéraud; Cyril Cohen; Pierre Courtieu; Matthew Dempsky; Maxime Dénès; Andres Erbsen; Erika (@rrika); Nikita Eshkeev; Jim Fehrle; Paolo G. Giarrusso; Gaëtan Gilbert; Jason Gross; Samuel Gruetter; Attila Gáspár; Hugo Herbelin; Jasper Hugunin; Jan-Oliver Kaiser; Robbert Krebbers; Vincent Laporte; Olivier Laurent; Xavier Leroy; Thomas Letan; Yishuai Li; Kenji Maillard; Erik Martin-Dorel; Guillaume Melquiond; Ike Mulder; Guillaume Munch-Maccagnoni; Antonio Nikishaev; Karl Palmskog; Pierre-Marie Pédrot; Clément Pit-Claudel; Ramkumar Ramachandra; Lars Rasmusson; Daniel de Rauglaudre; Talia Ringer; Pierre Roux; Kazuhiko Sakaguchi; @scinart; Vincent Semeria; Kartik Singhal; Michael Soegtrop; Enrico Tassi; Laurent Théry; Ralf Treinen; Anton Trunov; Bernhard M. Wiedemann; Xia Li-yao; Nickolai Zeldovich
Project leader(s)
Matthieu Sozeau

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 certification of properties of programming languages (e.g. the CompCert compiler certification project, the Verified Software Toolchain for verification of C programs, or the Iris framework for concurrent separation logic), the formalization of mathematics (e.g. the full formalization of the Feit-Thompson theorem, or homotopy type theory), and teaching.

Coq version 8.12 integrates many usability improvements, in particular with respect to notations, scopes and implicit arguments, along with many bug fixes and major improvements to the reference manual. The main changes include:

  • New binder notation for non-maximal implicit arguments using [ ] allowing to set and see the implicit status of arguments immediately.

  • New notation Inductive I A | x : s := ... to distinguish the uniform from the non-uniform parameters in inductive definitions.

  • More robust and expressive treatment of implicit inductive parameters in inductive declarations.

  • Improvements in the treatment of implicit arguments and partially applied constants in notations, parsing of hexadecimal number notation and better handling of scopes and coercions for printing.

  • A correct and efficient coercion coherence checking algorithm, avoiding spurious or duplicate warnings.

  • An improved Search command which accepts complex queries. Note that this takes precedence over the now deprecated ssreflect search.

  • Many additions and improvements of the standard library.

  • Improvements to the reference manual include a more logical organization of chapters along with updated syntax descriptions that match Coq's grammar in most but not all chapters.

Additionally, the omega tactic is deprecated in this version of Coq, and we recommend users to switch to lia in new proof scripts (see also the warning message in the corresponding chapter).

See the Changes in 8.12+beta1 section and following sections for the detailed list of changes, including potentially breaking changes marked with Changed.

Coq's documentation is available at (reference manual), and (documentation of the standard library). Developer documentation of the ML API is available at

Maxime Dénès, Emilio Jesús Gallego Arias, Gaëtan Gilbert, Michael Soegtrop and Théo Zimmermann worked on maintaining and improving the continuous integration system and package building infrastructure.

Erik Martin-Dorel has maintained the Coq Docker images that are used in many Coq projects for continuous integration.

The OPAM repository for Coq packages has been maintained by Guillaume Claret, Karl Palmskog, Matthieu Sozeau and Enrico Tassi with contributions from many users. A list of packages is available at

Previously, most components of Coq had a single principal maintainer. This was changed in 8.12 (#11295) so that every component now has a team of maintainers, who are in charge of reviewing and merging incoming pull requests. This gave us a chance to significantly expand the pool of maintainters and provide faster feedback to contributors. Special thanks to all our maintainers!

Our current 31 maintainers are Yves Bertot, Frédéric Besson, Tej Chajed, Cyril Cohen, Pierre Corbineau, Pierre Courtieu, Maxime Dénès, Jim Fehrle, Julien Forest, Emilio Jesús Gallego Arias, Gaëtan Gilbert, Georges Gonthier, Benjamin Grégoire, Jason Gross, Hugo Herbelin, Vincent Laporte, Assia Mahboubi, Kenji Maillard, Guillaume Melquiond, Pierre-Marie Pédrot, Clément Pit-Claudel, Kazuhiko Sakaguchi, Vincent Semeria, Michael Soegtrop, Arnaud Spiwack, Matthieu Sozeau, Enrico Tassi, Laurent Théry, Anton Trunov, Li-yao Xia, Théo Zimmermann

The 59 contributors to this version are Abhishek Anand, Yves Bertot, Frédéric Besson, Lasse Blaauwbroek, Simon Boulier, Quentin Carbonneaux, Tej Chajed, Arthur Charguéraud, Cyril Cohen, Pierre Courtieu, Matthew Dempsky, Maxime Dénès, Andres Erbsen, Erika (@rrika), Nikita Eshkeev, Jim Fehrle, @formalize, Emilio Jesús Gallego Arias, Paolo G. Giarrusso, Gaëtan Gilbert, Jason Gross, Samuel Gruetter, Attila Gáspár, Hugo Herbelin, Jan-Oliver Kaiser, Robbert Krebbers, Vincent Laporte, Olivier Laurent, Xavier Leroy, Thomas Letan, Yishuai Li, Kenji Maillard, Erik Martin-Dorel, Guillaume Melquiond, Ike Mulder, Guillaume Munch-Maccagnoni, Antonio Nikishaev, Karl Palmskog, Pierre-Marie Pédrot, Clément Pit-Claudel, Ramkumar Ramachandra, Lars Rasmusson, Daniel de Rauglaudre, Talia Ringer, Pierre Roux, Kazuhiko Sakaguchi, Vincent Semeria, @scinart, Kartik Singhal, Michael Soegtrop, Matthieu Sozeau, Enrico Tassi, Laurent Théry, Ralf Treinen, Anton Trunov, Bernhard M. Wiedemann, Li-yao Xia, Nickolai Zeldovich and Théo Zimmermann.

Many power users helped to improve the design of this new version via the GitHub issue and pull request system, the Coq development mailing list, the mailing list, the Discourse forum and the new Coq Zulip chat (thanks to Cyril Cohen for organizing the move from Gitter).

Version 8.12's development spanned 6 months from the release of Coq 8.11.0. Emilio Jesus Gallego Arias and Théo Zimmermann are the release managers of Coq 8.12. This release is the result of ~500 PRs merged, closing ~100 issues.

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