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 8.16 integrates changes to the Coq kernel and performance improvements along with a few new features. We highlight some of the most impactful changes here: The guard checker (see Guarded) now ensures strong normalization under any reduction strategy. Irrelevant terms (in the SProp sort) are now squashed to a dummy value during conversion, fixing a subject reduction issue and making proof conversion faster. Introduction of reversible coercions, which allow coercions relying on meta-level resolution such as type-classes or canonical structures. Also allow coercions that do not fullfill the uniform inheritance condition. Generalized rewriting support for rewriting with Type-valued relations and in Type contexts, using the Classes.CMorphisms library. Added the boolean equality scheme command for decidable inductive types. Added a Print Notation command. Incompatibilities in name generation for Program obligations, eauto treatment of tactic failure levels, use of ident in notations, parsing of module expressions. Standard library reorganization and deprecations. Improve the treatment of standard library numbers by Extraction. See the Changes in 8.16.0 section below for the detailed list of changes, including potentially breaking changes marked with Changed. Coq's reference manual for 8.16, documentation of the 8.16 standard library and developer documentation of the 8.16 ML API are also available. Ali Caglayan, Emilio Jesús Gallego Arias, Gaëtan Gilbert 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 https://coq.inria.fr/opam/www/. The Coq Platform has been maintained by Michael Soegtrop, with help from Karl Palmskog, Enrico Tassi and Théo Zimmermann. Our current maintainers are Yves Bertot, Frédéric Besson, Ana Borges, Ali Caglayan, 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, Pierre Roux, Kazuhiko Sakaguchi, Vincent Semeria, Michael Soegtrop, Arnaud Spiwack, Matthieu Sozeau, Enrico Tassi, Laurent Théry, Anton Trunov, Li-yao Xia and Théo Zimmermann. See the Coq Team face book page for more details. The 57 contributors to the 8.16 versions are Tanaka Akira, Frédéric Besson, Martin Bodin, Ana Borges, Ali Caglayan, Minki Cho, Cyril Cohen, Juan Conejero, "stop-cran", Adrian Dapprich, Maxime Dénès, Stéphane Desarzens, Christian Doczkal, Andrej Dudenhefner, Andres Erbsen, Jim Fehrle, Emilio Jesús Gallego Arias, Attila Gáspár, Paolo G. Giarrusso, Gaëtan Gilbert, Rudi Grinberg, Jason Gross, Hugo Herbelin, Wolf Honore, Jasper Hugunin, Bart Jacobs, Pierre Jouvelot, Ralf Jung, Grant Jurgensen, Jan-Oliver Kaiser, Wojciech Karpiel, Thomas Klausner, Ethan Kuefner, Fabian Kunze, Olivier Laurent, Yishuai Li, Erik Martin-Dorel, Guillaume Melquiond, Jean-Francois Monin, Pierre-Marie Pédrot, Rudy Peterson, Clément Pit-Claudel, Seth Poulsen, Ramkumar Ramachandra, Pierre Roux, Takafumi Saikawa, Kazuhiko Sakaguchi, Gabriel Scherer, Vincent Semeria, Kartik Singhal, Michael Soegtrop, Matthieu Sozeau, Enrico Tassi, Laurent Théry, Anton Trunov, Li-yao Xia and Théo Zimmermann. The Coq community at large helped improve this new version via the GitHub issue and pull request system, the coq-club@inria.fr mailing list, the Discourse forum and the Coq Zulip chat. Version 8.16's development spanned 6 months from the release of Coq 8.15.0. Pierre-Marie Pédrot is the release manager of Coq 8.16. This release is the result of 356 merged PRs, closing 99 issues