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Published January 7, 2021 | Version 8.13
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The Coq Proof Assistant


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 8.13 ( integrates many usability improvements, as well as extensions of the core language. The main changes include:

  • Introduction of primitive persistent arrays in the core language, implemented using imperative persistent arrays.

  • Introduction of definitional proof irrelevance for the equality type defined in the SProp sort.

  • Cumulative record and inductive type declarations can now specify the variance of their universes.

  • Various bugfixes and uniformization of behavior with respect to the use of implicit arguments and the handling of existential variables in declarations, unification and tactics.

  • New warning for unused variables in catch-all match branches that match multiple distinct patterns.

  • New warning for Hint commands outside sections without a locality attribute, whose goal is to eventually remove the fragile default behavior of importing hints only when using Require. The recommended fix is to declare hints as export, instead of the current default global, meaning that they are imported through Require Import only, not Require. See the following rationale and guidelines for details.

  • General support for boolean attributes.

  • Many improvements to the handling of notations, including number notations, recursive notations and notations with bindings. A new algorithm chooses the most precise notation available to print an expression, which might introduce changes in printing behavior.

  • Tactic improvements in lia and its zify preprocessing step, now supporting reasoning on boolean operators such as Z.leb and supporting primitive integers Int63.

  • Typing flags can now be specified per-constant / inductive.

  • Improvements to the reference manual including updated syntax descriptions that match Coq's grammar in several chapters, and splitting parts of the tactics chapter to independent sections.

See the Changes in 8.13+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

Our current 32 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, Olivier Laurent, 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 and Théo Zimmermann.

The 52 contributors to this version are Reynald Affeldt, Tanaka Akira, Frédéric Besson, Lasse Blaauwbroek, Clément Blaudeau, Martin Bodin, Ali Caglayan, Tej Chajed, Cyril Cohen, Julien Coolen, Matthew Dempsky, Maxime Dénès, Andres Erbsen, Jim Fehrle, Emilio Jesús Gallego Arias, Paolo G. Giarrusso, Attila Gáspár, Gaëtan Gilbert, Jason Gross, Benjamin Grégoire, Hugo Herbelin, Wolf Honore, Jasper Hugunin, Ignat Insarov, Ralf Jung, Fabian Kunze, Vincent Laporte, Olivier Laurent, Larry D. Lee Jr, Thomas Letan, Yishuai Li, Xia Li-yao, James Lottes, Jean-Christophe Léchenet, Kenji Maillard, Erik Martin-Dorel, Yusuke Matsushita, Guillaume Melquiond, Carl Patenaude-Poulin, Clément Pit-Claudel, Pierre-Marie Pédrot, Pierre Roux, Kazuhiko Sakaguchi, Vincent Semeria, Michael Soegtrop, Matthieu Sozeau, Enrico Tassi, Anton Trunov, Edward Wang, Li-yao Xia, Beta Ziliani and Théo Zimmermann.

The Coq community at large helped 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 Coq Zulip chat.

Version 8.13's development spanned 5 months from the release of Coq 8.12.0. Enrico Tassi and Maxime Dénès are the release managers of Coq 8.13. This release is the result of 400 merged PRs, closing ~100 issues.



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