awesome-coq

A curated list of awesome Coq libraries, plugins, tools, verification projects, and resources [maintainer=@palmskog]
https://github.com/rocq-community/awesome-coq

Last synced: 3 days ago
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Projects
- Frameworks
  - Hybrid - System for reasoning using higher-order abstract syntax representations of object logics.
  - Iris - Higher-order concurrent separation logic framework.
  - 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.
  - ConCert - Framework for smart contract testing and verification featuring a code extraction pipeline to several smart contract languages.
  - 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.
  - 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.
  - CoqEAL - Framework to ease change of data representations in proofs.
  - Hoare Type Theory - A shallow embedding of sequential separation logic formulated as a type theory.
  - CoqEAL - Framework to ease change of data representations in proofs.
  - 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.
- Libraries
  - CoqInterval - Tactics for performing proofs of inequalities on expressions of real numbers.
  - Coq-std++ - Extended alternative standard library for Coq.
  - Flocq - Formalization of floating-point numbers and computations.
  - Paco - Library for parameterized coinduction.
  - CertiGraph - Library for reasoning about directed graphs and their embedding in separation logic.
  - ALEA - Library for reasoning on randomized algorithms.
  - Algebra Tactics - Ring and field tactics for Mathematical Components.
  - Bedrock Bit Vectors - Library for reasoning on fixed precision machine words.
  - 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.
  - Coq record update - Library which provides a generic way to update Coq record fields.
  - FCSL-PCM - Formalization of partial commutative monoids as used in verification of pointer-manipulating programs.
  - 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.
  - Bignums - Library of arbitrarily large numbers.
  - CertiGraph - Library for reasoning about directed graphs and their embedding in separation logic.
  - 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.
  - ALEA - Library for reasoning on randomized algorithms.
  - Bignums - Library of arbitrarily large numbers.
  - Regular Language Representations - Translations between different definitions of regular languages, including regular expressions and automata.
- Package and Build Management
  - coq_makefile - Build tool distributed with Coq and based on generating a makefile.
  - Coq Package Index - Collection of Coq packages based on opam.
  - Debian Coq packages - Coq-related packages available in the testing distribution of Debian.
  - 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 Coq packages - Collection of Coq-related packages for Nix.
  - opam - Flexible and Git-friendly package manager for OCaml and Coq with multiple compiler support.
  - coq_makefile - Build tool distributed with Coq and based on generating a makefile.
  - Coq Platform - Curated collection of packages to support Coq use in industry, education, and research.
  - Docker-MathComp - Docker images for many combinations of versions of Coq and the Mathematical Components library.
  - coq-community Templates - Templates for generating configuration files for Coq projects.
  - Docker-Coq - Docker images for many versions of Coq.
  - Coq Nix Toolbox - Nix helper scripts to automate local builds and continuous integration for Coq.
  - coq_makefile - Build tool distributed with Coq and based on generating a makefile.
  - coq_makefile - Build tool distributed with Coq and based on generating a makefile.
- Plugins
  - Gappa - Tactic for discharging goals about floating-point arithmetic and round-off errors.
  - 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.
  - 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.
  - 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.
  - 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.
  - Mtac2 - Plugin adding typed tactics for backward reasoning.
  - 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.
  - Waterproof proof language - Plugin providing a language for writing proof scripts in a style that resembles non-mechanized mathematical proof.
  - AAC Tactics - Tactics for rewriting universally quantified equations, modulo associativity and commutativity of some operator.
  - Paramcoq - Plugin to generate parametricity translations of Coq terms.
  - MetaCoq - Project formalizing Coq in Coq and providing tools for manipulating Coq terms and developing certified plugins.
  - Ltac2 - Experimental typed tactic language similar to Coq's classic Ltac language.
  - Ltac2 - Experimental typed tactic language similar to Coq's classic Ltac language.
- Puzzles and Games
  - 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.
  - T2048 - Coq version of the 2048 sliding tile game.
  - Coqoban - Coq implementation of Sokoban, the Japanese warehouse keepers' game.
- Tools
  - CFML - Tool for proving properties of OCaml programs in separation logic.
  - coqdoc - Standard documentation tool that generates LaTeX or HTML files from Coq code.
  - `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.
  - Menhir - Parser generator that can output Coq code for verified parsers.
  - Alectryon - Collection of tools for writing technical documents that mix Coq code and prose.
  - Autosubst-ocaml - Tool that generates Coq code for handling binders in syntax, such as for renaming and substitutions.
  - 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-scripts - Scripts for dealing with Coq files, including tabulating proof times.
  - coq-tools - Scripts for manipulating Coq developments.
  - 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.
  - Rocqnavi - Fork of coq2html that adds indexes, clickable notations, Markdown and LaTeX formatting in comments, and more.
  - 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.
  - coq-dpdgraph - Tool for building dependency graphs between Coq objects.
  - coqdoc - Standard documentation tool that generates LaTeX or HTML files from Coq code.
  - coqdoc - Standard documentation tool that generates LaTeX or HTML files from Coq code.
- Type Theory and Mathematics
  - Coquelicot - Formalization of classical real analysis compatible with the standard library and focusing on usability.
  - Mathematical Components - Formalization of mathematical theories, focusing in particular on group theory.
  - Analysis - Library for classical real analysis compatible with Mathematical Components.
  - Category Theory in Coq - Axiom-free formalization of category theory.
  - CoqPrime - Library for certifying primality using Pocklington and Elliptic Curve certificates.
  - CoRN - Library of constructive real analysis and algebra.
  - Finmap - Extension of Mathematical Components with finite maps, sets, and multisets.
  - GeoCoq - Formalization of geometry based on Tarski's axiom system.
  - Homotopy Type Theory - Development of homotopy-theoretic ideas.
  - Infotheo - Formalization of information theory and linear error-correcting codes.
  - 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.
  - Graph Theory - Formalized graph theory results.
- User Interfaces
  - CoqIDE - Standalone graphical tool for interacting with Coq.
  - Proof General - Generic interface for proof assistants based on the extensible, customizable text editor Emacs.
  - VsCoq Legacy - Backwards-compatible extension for the Visual Studio Code and VSCodium editors using Coq's legacy XML protocol.
  - Coqtail - Interface for Coq based on the Vim text editor.
  - 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.
  - Waterproof editor - Educational environment for writing mathematical proofs in interactive notebooks.
  - VsCoq Legacy - Backwards-compatible extension for the Visual Studio Code and VSCodium editors using Coq's legacy XML protocol.
  - VsCoq Legacy - Backwards-compatible extension for the Visual Studio Code and VSCodium editors using Coq's legacy XML protocol.
  - Tree Sitter Rocq - Partial Rocq tree-sitter grammar useful for syntax highlighting in text editors like [Helix](https://github.com/helix-editor/helix), but not recommended for full parsing of Rocq code.
  - CoqIDE - Standalone graphical tool for interacting with Coq.
  - Coq LSP - Language server and extension for the Visual Studio Code and VSCodium editors with custom document checking engine.
  - VsCoq - Language server and extension for the Visual Studio Code and VSCodium editors.
  - CoqIDE - Standalone graphical tool for interacting with Coq.
  - CoqIDE - Standalone graphical tool for interacting with Coq.
- Verified Software
  - 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.
  - Prosa - Definitions and proofs for real-time system schedulability analysis.
  - Vélus - Verified compiler for a Lustre/Scade-like dataflow synchronous language.
  - CertiCoq - Verified compiler from Gallina, the internal language of Coq, down to CompCert's Clight language.
  - Fiat-Crypto - Cryptographic primitive code generation.
  - Jasmin - Formalized language and verified compiler for high-assurance and high-speed cryptography.
  - JSCert - Coq specification of ECMAScript 5 (JavaScript) with verified reference interpreter.
  - 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.
  - 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.
  - Functional Algorithms Verified in SSReflect - Purely functional verified implementations of algorithms for searching, sorting, and other fundamental problems.
Resources
- 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.
  - Volume 1: Logical Foundations - Introduction to functional programming, basic concepts of logic, and computer-assisted theorem proving.
  - Volume 2: Programming Language Foundations - Introduction to the theory of programming languages, including operational semantics, Hoare logic, and static type systems.
  - Volume 3: Verified Functional Algorithms - Demonstration of how a variety of fundamental data structures can be specified and verified.
  - Volume 4: QuickChick - Introduction to tools for combining randomized property-based testing with formal specification and proof.
  - Volume 5: Verifiable C - An extended tutorial on specifying and verifying C programs using the Verified Software Toolchain.
  - Volume 6: Separation Logic Foundations - An introduction to separation logic and how to build program verification tools on top of it.
  - Certified Programming with Dependent Types - Textbook about practical engineering with Coq which teaches advanced practical tricks and a very specific style of proof.
  - 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.
  - 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.
- Community

Programming Languages

Coq 51 Rocq Prover 5 OCaml 3 Python 3 Emacs Lisp 2 Dockerfile 1 Haskell 1 HTML 1 JavaScript 1 TypeScript 1

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Awesome

awesome-coq

Projects

Frameworks

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Puzzles and Games

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Resources

Blogs

Books

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