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Awesome Coq Awesome

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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.

Contents

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 - 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 - 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 - 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 - 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 - 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.
  • Monae - Monadic effects and equational reasoning.
  • 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.

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 - 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.

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A curated list of awesome Coq libraries, plugins, tools, verification projects, and resources [maintainer=@palmskog]

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