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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 GitHub Repo Stars GitHub last commit first.

Projects
Resources

Projects

Frameworks

ConCert - Framework for smart contract testing and verification featuring a code extraction pipeline to several smart contract languages.
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.
Hoare Type Theory - A shallow embedding of sequential separation logic formulated as a type theory.
Hybrid - System for reasoning using higher-order abstract syntax representations of object logics.
Iris - Higher-order concurrent separation logic framework.
Q*cert - Platform for implementing and verifying query compilers.
SSProve - Framework for modular cryptographic proofs based on the Mathematical Components library.
VCFloat - Framework for verifying C programs with floating-point computations.
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.

User Interfaces

CoqIDE - Standalone graphical tool for interacting with Coq.
Coqtail - Interface for Coq based on the Vim text editor.
Coq LSP - Language server and extension for the Visual Studio Code and VSCodium editors with custom document checking engine.
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.
opam-switch-mode - IDE extension for Proof General to locally change or reset the opam switch from a menu or using a command.
jsCoq - Port of Coq to JavaScript, which enables running Coq projects in a browser.
Jupyter kernel for Coq - Coq support for the Jupyter Notebook web environment.
VsCoq - Language server and extension for the Visual Studio Code and VSCodium editors.
VsCoq Legacy - Backwards-compatible extension for the Visual Studio Code and VSCodium editors using Coq’s legacy XML protocol.
Waterproof editor - Educational environment for writing mathematical proofs in interactive notebooks.

Libraries

ALEA - Library for reasoning on randomized algorithms.
Algebra Tactics $GitHub Repo Stars$ $GitHub last commit$ - Ring and field tactics for Mathematical Components.
Bignums - Library of arbitrarily large numbers.
Bedrock Bit Vectors - Library for reasoning on fixed precision machine words.
CertiGraph - Library for reasoning about directed graphs and their embedding in separation logic.
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-Kruskal - Collection of libraries related to rose trees and Kruskal’s tree theorem.
CoqInterval - Tactics for performing proofs of inequalities on expressions of real numbers.
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 numbers and computations.
Formalised Undecidable Problems - Library of undecidable problems and reductions between them.
Hahn - Library for reasoning on lists and binary relations.
Interaction Trees - Library for representing recursive and impure programs.
LibHyps - Library of Ltac tactics to manage and manipulate hypotheses in proofs.
MathComp Extra - Extra material for the Mathematical Components library, including the AKS primality test and RSA encryption and decryption.
Mczify $GitHub Repo Stars$ $GitHub last commit$ - Library enabling Micromega arithmetic solvers to work when using Mathematical Components number definitions.
Metalib - Library for programming language metatheory using locally nameless variable binding representations.
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 Nix Toolbox - Nix helper scripts to automate local builds and continuous integration for Coq.
Coq Package Index - Collection of Coq packages based on opam.
Coq Platform - Curated collection of packages to support Coq use in industry, education, and research.
coq-community Templates - Templates for generating configuration files for Coq projects.
Debian Coq packages - Coq-related packages available in the testing distribution of Debian.
Docker-Coq - Docker images for many versions of Coq.
Docker-MathComp $GitHub Repo Stars$ $GitHub last commit$ - Docker images for many combinations of versions of Coq and the Mathematical Components library.
Docker-Coq GitHub Action - GitHub container action that can be used with Docker-Coq or Docker-MathComp.
Dune - Composable and opinionated build system for OCaml and Coq (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 and Coq with multiple compiler support.

Plugins

AAC Tactics - Tactics for rewriting universally quantified equations, modulo associativity and commutativity of some operator.
Coinduction - Plugin for doing proofs by enhanced coinduction.
Coq-Elpi - Extension framework based on λProlog providing an extensive API to implement commands and tactics.
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 $GitHub Repo Stars$ $GitHub last commit$ - Collection of commands for declaring Coq hierarchies based on packed classes.
Itauto - SMT-like tactics for combined propositional reasoning about function symbols, constructors, and arithmetic.
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.
Tactician - Interactive tool which learns from previously written tactic scripts across all the installed Coq packages and suggests the next tactic to be executed or tries to automate proof synthesis fully.
Unicoq - Plugin that replaces the existing unification algorithm with an enhanced one.
Waterproof proof language - Plugin providing a language for writing proof scripts in a style that resembles non-mechanized mathematical proof.

Puzzles and Games

Coqoban - Coq implementation of Sokoban, the Japanese warehouse keepers’ game.
Hanoi - The Tower of Hanoi puzzle in Coq, including generalizations and theorems about configurations.
Mini-Rubik - Coq formalization and solver of the 2x2x2 version of the Rubik’s Cube puzzle.
Name the Biggest Number - Repository for submitting proven contenders for the title of biggest number in Coq.
Natural Number Game - Coq version of the natural number game developed for the Lean prover.
Sudoku - Formalization and solver of the Sudoku number-placement puzzle in Coq.
T2048 - Coq version of the 2048 sliding tile game.

Tools

Alectryon - Collection of tools for writing technical documents that mix Coq code and prose.
Autosubst 2 - Tool that generates Coq code for handling binders in syntax, such as for renaming and substitutions.
CFML - Tool for proving properties of OCaml programs in separation logic.
coq2html - Alternative HTML documentation generator for Coq.
coqdoc - Standard documentation tool that generates LaTeX or HTML files from Coq code.
CoqOfOCaml - Tool for generating idiomatic Coq from OCaml code.
coq-dpdgraph - Tool for building dependency graphs between Coq objects.
coq-scripts - Scripts for dealing with Coq files, including tabulating proof times.
coq-tools - Scripts for manipulating Coq developments.
- find-bug.py - Automatically minimizes source files producing an error, creating small test cases for Coq bugs.
- absolutize-imports.py - Processes source files to make loading of dependencies robust against shadowing of file names.
- inline-imports.py - Creates stand-alone source files from developments by inlining the loading of all dependencies.
- minimize-requires.py - Removes loading of unused dependencies.
- move-requires.py - Moves all dependency loading statements to the top of source files.
- move-vernaculars.py - Lifts many vernacular commands and inner lemmas out of proof script blocks.
- proof-using-helper.py - Modifies source files to include proof annotations for faster parallel proving.
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.
PyCoq - Set of bindings and libraries for interacting with Coq from inside Python 3.
Roosterize - Tool for suggesting lemma names in Coq projects.
Sail - Tool for specifying instruction set architecture (ISA) semantics of processors and generating Coq definitions.
SerAPI - Tools and OCaml library for (de)serialization of Coq code to and from JSON and S-expressions.
Trakt - Generic goal preprocessing tool for proof automation tactics.

Type Theory and Mathematics

Analysis $GitHub Repo Stars$ $GitHub last commit$ - 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 $GitHub Repo Stars$ $GitHub last commit$ - 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 $GitHub Repo Stars$ $GitHub last commit$ - 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 $GitHub Repo Stars$ $GitHub last commit$ - Abstract interfaces for mathematical structures based on type classes.
Monae - Monadic effects and equational reasoning.
Odd Order Theorem $GitHub Repo Stars$ $GitHub last commit$ - 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.

Verified Software

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.
Ceramist - Verified hash-based approximate membership structures such as Bloom filters.
CertiCoq - Verified compiler from Gallina, the internal language of Coq, down to CompCert’s Clight language.
Fiat-Crypto - Cryptographic primitive code generation.
Functional Algorithms Verified in SSReflect - Purely functional verified implementations of algorithms for searching, sorting, and other fundamental problems.
Incremental Cycles - Verified OCaml implementation of an algorithm for incremental cycle detection in graphs.
Jasmin - Formalized language and verified compiler for high-assurance and high-speed cryptography.
JSCert - Coq specification of ECMAScript 5 (JavaScript) with verified reference interpreter.
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.
Prosa - Definitions and proofs for real-time system schedulability analysis.
RISC-V Specification in Coq - Definition of the RISC-V processor instruction set architecture and extensions.
Stable sort algorithms in Coq - Generic and modular proofs of correctness, including stability, of mergesort functions.
Tarjan and Kosaraju $GitHub Repo Stars$ $GitHub last commit$ - Verified implementations of algorithms for topological sorting and finding strongly connected components in finite graphs.
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.
WasmCert-Coq - Formalization in Coq of the WebAssembly (aka Wasm) 1.0 specification.

Resources

Community

Blogs

Books

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.
Modeling and Proving in Computational Type Theory - Book covering topics in computational logic using Coq, including foundations, canonical case studies, and practical programming.
Hydras & Co. - Continuously in-progress book and library on Kirby and Paris’ hydra battles and other entertaining formalized mathematics in Coq, including a proof of the Gödel-Rosser first incompleteness theorem.

Course Material

An Introduction to MathComp-Analysis - Lecture notes on getting started with the Mathematical Components library and using it for classical reasoning and real analysis.
Foundations of Separation Logic - Introduction to using separation logic to reason about sequential imperative programs in Coq.
Floating-Point Numbers and Formal Proof - Introductory course on Coq real numbers and floating-point numbers from the Flocq library.
Introduction to the Theory of Computation - Formalization to support an undergraduate course on the theory of computation, including languages and Turing machines.
Lectures on Software Foundations - Material on the Software Foundations series of textbooks, including a series of YouTube videos.
MathComp School $GitHub Repo Stars$ $GitHub last commit$ - Coq sources for lessons and exercises that introduce the SSReflect proof language and the Mathematical Components library.
Mechanized Semantics - Companion Coq sources for a course on programming language semantics at Collège de France.
Program Logics - Companion Coq sources for a course on program logics at Collège de France.
Program verification with types and logic - Lectures and exercise material for a course in programming language semantics, type systems and program logics, using Coq, at Radboud University Nijmegen.
Proofs and Reliable Programming using Coq - Introduction to developing and verifying programs with Coq.

Tutorials and Hints

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.
Coq requirements in Common Criteria evaluations - Guide on how to write readable and reviewable Coq code in high assurance applications.
Coq Tactics in Plain English - Guide to Coq tactics with explanations and examples.
Lemma Overloading - Demonstration of design patterns for programming and proving with canonical structures.
MathComp Tutorial Materials $GitHub Repo Stars$ $GitHub last commit$ - Source code for Mathematical Components tutorials.
Mike Nahas’s Coq Tutorial - Basics of using Coq to write formal proofs.
Tricks in Coq - Tips, tricks, and features in Coq that are hard to discover.