Awesome Coq ¶
A curated list of awesome Coq libraries, plugins, tools, and resources.
The Coq proof assistant provides a formal language to write mathematical definitions, executable algorithms, and theorems, together with an environment for semi-interactive development of machine-checked proofs.
Contributions welcome! Read the contribution guidelines first.
- CoqEAL - Framework to ease change of data representations in proofs.
- FCF - Framework for proofs of cryptography.
- Fiat - Mostly automated synthesis of correct-by-construction programs.
- FreeSpec - Framework for modularly verifying programs with effects and effect handlers.
- Iris - Higher-order concurrent separation logic framework.
- Q*cert - Platform for implementing and verifying query compilers.
- Verdi - Framework for formally verifying distributed systems implementations.
- VST - Toolchain for verifying C code inside Coq in a higher-order concurrent, impredicative separation logic that is sound w.r.t. the Clight language of the CompCert compiler.
- CoqIDE - Standalone graphical tool for interacting with Coq.
- Coqtail - Interface for Coq based on the Vim text editor.
- Proof General - Generic interface for proof assistants based on the extensible, customizable text editor Emacs.
- Company-Coq - IDE extensions for Proof General's Coq mode.
- Jupyter kernel for Coq - Coq support for the Jupyter Notebook web environment.
- VSCoq - Extension for the Visual Studio Code editor.
- ALEA - Library for reasoning on randomized algorithms.
- Bignums - Library of arbitrary large numbers.
- CoLoR - Library on rewriting theory, lambda-calculus and termination, with sub-libraries on common data structures extending the Coq standard library.
- coq-haskell - Library smoothing the transition to Coq for Haskell users.
- Coq record update - Library which provides a generic way to update Coq record fields.
- Coq-std++ - Extended alternative standard library for Coq.
- ExtLib - Collection of theories and plugins that may be useful in other Coq developments.
- FCSL-PCM - Formalization of partial commutative monoids as used in verification of pointer-manipulating programs.
- Flocq - Formalization of floating-point computations.
- Formalised Undecidable Problems - Library of undecidable problems and reductions between them.
- Hahn - Library for reasoning on lists and binary relations.
- Metalib - Library for programming language metatheory using locally nameless variable binding representations.
- Monae - Monadic effects and equational reasoning.
- Paco - Library for parameterized coinduction.
- Regular Language Representations - Translations between different definitions of regular languages, including regular expressions and automata.
- Relation Algebra - Modular formalization of algebras with heterogeneous binary relations as models.
- Simple IO - Input/output monad with user-definable primitive operations.
- TLC - Non-constructive alternative to Coq's standard library.
Package and Build Management¶
- coq_makefile - Build tool distributed with Coq and based on generating a makefile.
- Coq Package Index - OPAM-based collection of Coq packages.
- Coq Platform - Experimental curated collection of packages to support Coq use in industry, education, and research.
- Coq-community Templates - Templates for generating configuration files for Coq projects.
- Docker-Coq - Docker images for many versions of Coq.
- Docker-MathComp - Docker images for many combinations of versions of Coq and the Mathematical Components library.
- Docker-Coq-action - GitHub container action that can be used with Docker-Coq or Docker-MathComp.
- Dune - Composable and opinionated build system for Coq and OCaml (former jbuilder).
- Nix - Package manager for Linux and other Unix systems, supporting atomic upgrades and rollbacks.
- Nix Coq packages - Collection of Coq-related packages for Nix.
- OPAM - Flexible and Git-friendly package manager for OCaml with multiple compiler support.
- AAC Tactics - Tactics for rewriting universally quantified equations, modulo associativity and commutativity of some operator.
- Coq-Elpi - Plugin for the Embeddable Lambda Prolog Interpreter.
- CoqHammer - General-purpose automated reasoning hammer tool that combines learning from previous proofs with the translation of problems to automated provers and the reconstruction of found proofs.
- Equations - Function definition package for Coq.
- Gappa - Tactic for discharging goals about floating-point arithmetic and round-off errors.
- Hierarchy Builder - Collection of commands for declaring Coq hierarchies based on packed classes.
- Ltac2 - Experimental typed tactic language similar to Coq's classic Ltac language.
- MetaCoq - Project formalizing Coq in Coq and providing tools for manipulating Coq terms and developing certified plugins.
- Mtac2 - Plugin adding typed tactics for backward reasoning.
- Paramcoq - Plugin to generate parametricity translations of Coq terms.
- QuickChick - Plugin for randomized property-based testing.
- SMTCoq - Tool that checks proof witnesses coming from external SAT and SMT solvers.
- Unicoq - Plugin that replaces the existing unification algorithm with an enhanced one.
- CFML - Tool for proving properties of OCaml programs in separation logic.
- coq2html - Alternative HTML documentation generator for Coq.
- CoqOfOCaml - Tool for generating idiomatic Coq from OCaml code.
- coq-dpdgraph - Tool for building dependency graphs between Coq objects.
- coq-tools - Scripts to help construct small reproducing examples of bugs, remove unneeded imports, etc.
- Cosette - Automated solver for reasoning about SQL query equivalences.
- hs-to-coq - Converter from Haskell code to equivalent Coq code.
- lngen - Tool for generating locally nameless Coq definitions and proofs.
- Menhir - Parser generator that can output Coq code for verified parsers.
- mCoq - Mutation analysis tool for Coq projects.
- Ott - Tool for writing definitions of programming languages and calculi that can be translated to Coq.
- Roosterize - Tool for suggesting lemma names in Coq projects.
- SerAPI - Library and tools for (de)serialization of Coq code to and from JSON and S-expressions.
Type Theory and Mathematics¶
- Analysis - Library for classical real analysis compatible with Mathematical Components.
- Category Theory in Coq - Axiom-free formalization of category theory.
- Completeness and Decidability of Modal Logic Calculi - Soundness, completeness, and decidability for the logics K, K*, CTL, and PDL.
- CoqPrime - Library for certifying primality using Pocklington and Elliptic Curve certificates.
- CoRN - Library of constructive real analysis and algebra.
- Coqtail Math - Library of mathematical results ranging from arithmetic to real and complex analysis.
- Coquelicot - Formalization of classical real analysis compatible with the standard library and focusing on usability.
- Finmap - Extension of Mathematical Components with finite maps, sets, and multisets.
- Four Color Theorem - Formal proof of the Four Color Theorem, a landmark result of graph theory.
- Gaia - Implementation of books from Bourbaki's Elements of Mathematics, including set theory and number theory.
- GeoCoq - Formalization of geometry based on Tarski's axiom system.
- Graph Theory - Formalized graph theory results.
- Homotopy Type Theory - Development of homotopy-theoretic ideas.
- Infotheo - Formalization of information theory and linear error-correcting codes.
- Mathematical Components - Formalization of mathematical theories, focusing in particular on group theory.
- Math Classes - Abstract interfaces for mathematical structures based on type classes.
- Odd Order Theorem - Formal proof of the Odd Order Theorem, a landmark result of finite group theory.
- Puiseuxth - Proof of Puiseux's theorem and computation of roots of polynomials of Puiseux's series.
- UniMath - Library which aims to formalize a substantial body of mathematics using the univalent point of view.
- CompCert - High-assurance compiler for almost all of the C language (ISO C99), generating efficient code for the PowerPC, ARM, RISC-V and x86 processors.
- Fiat-Crypto - Cryptographic primitive code generation.
- Incremental Cycles - Verified OCaml implementation of an algorithm for incremental cycle detection in graphs.
- lambda-rust - Formal model of a Rust core language and type system, a logical relation for the type system, and safety proofs for some Rust libraries.
- Vélus - Verified compiler for a Lustre/Scade-like dataflow synchronous language.
- Verdi Raft - Implementation of the Raft distributed consensus protocol, verified in Coq using the Verdi framework.
- Official Coq website
- Official Coq manual
- Official Coq standard library
- Official Coq Discourse forum
- Official Coq Zulip chat
- Official Coq-Club mailing list
- Official Coq wiki
- Official Coq Twitter
- coq-community package maintenance project
- Coq subreddit
- Coq tag on Stack Overflow
- Coq tag on Theoretical Computer Science Stack Exchange
- Mathematical Components wiki
- Planet Coq link aggregator
- Coq Exchange: ideas and experiment reports about Coq
- Gregory Malecha's blog
- Guillaume Claret's Coq blog
- Joachim Breitner's blog posts on Coq
- MIT PLV blog posts on Coq
- PLClub Blog
- Poleiro: a Coq blog by Arthur Azevedo de Amorim
- Ralf Jung's blog posts on Coq
- Thomas Letan's blog posts on Coq
- Coq'Art - The first book dedicated to Coq.
- Software Foundations - Series of Coq-based textbooks on logic, functional programming, and foundations of programming languages, aimed at being accessible to beginners.
- Certified Programming with Dependent Types - Textbook about practical engineering with Coq which teaches advanced practical tricks and a very specific style of proof.
- Program Logics for Certified Compilers - Book that explains how to construct program logics using separation logic, accompanied by a formal model in Coq which is applied to the Clight programming language and other examples.
- Formal Reasoning About Programs - Book that simultaneously provides a general introduction to formal logical reasoning about the correctness of programs and to using Coq for this purpose.
- Programs and Proofs - Book that gives a brief and practically-oriented introduction to interactive proofs in Coq which emphasizes the computational nature of inductive reasoning about decidable propositions via a small set of primitives from the SSReflect proof language.
- Computer Arithmetic and Formal Proofs - Book that describes how to formally specify and verify floating-point algorithms in Coq using the Flocq library.
- The Mathematical Components book - Book oriented towards mathematically inclined users, focusing on the Mathematical Components library and the SSReflect proof language.
- Foundations of Separation Logic - Introduction to using separation logic to reason about sequential imperative programs in Coq.
- Introduction to Computational Logic - Introduction to basic logic principles, constructive type theory, and interactive theorem proving with Coq.
Tutorials and Hints¶
- CodeWars' Coq kata - Online proving challenges.
- Coq'Art Exercises and Tutorials - Coq code and exercises from the Coq'Art book, including additional tutorials.
- Coq in a Hurry - Introduction to how Coq can be used to define logical concepts and functions and reason about them.
- Lemma Overloading - Demonstration of design patterns for programming and proving with canonical structures.
- Mike Nahas's Coq Tutorial - Basics of using Coq to write formal proofs.
- Tricks in Coq - Tips, tricks, and features that are hard to discover.