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Awesome Coq – Massive Collection of Resources

Awesome Coq Awesome

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.

Contents


Projects

Frameworks

  • 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.

User Interfaces

  • 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.
  • 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 – Extension for the Visual Studio Code editor.

Libraries

  • 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.

Plugins

  • 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.

Tools

  • 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.

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.
  • Fiat-Crypto – Cryptographic primitive code generation.
  • Incremental Cycles – Verified OCaml implementation of an algorithm for incremental cycle detection in graphs.
  • 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.
  • Verdi Raft – Implementation of the Raft distributed consensus protocol, verified in Coq using the Verdi framework.

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.

Course Material

Tutorials and Hints

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