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.
- 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.
- 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.