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.
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.
- 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.
- Coq-Elpi - Extension
framework based on λProlog providing an extensive API to implement
commands and tactics.
- Waterproof
proof language - Plugin providing a language for writing proof
scripts in a style that resembles non-mechanized mathematical
proof.
- 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.
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.
- 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 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.
- 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.
- 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
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
Tutorials and Hints