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awesome-coq

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

Last synced: 5 days ago
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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.
  - Software Foundations - Series of Coq-based textbooks on logic, functional programming, and foundations of programming languages, aimed at being accessible to beginners.
- Course Material
  - Foundations of Separation Logic - Introduction to using separation logic to reason about sequential imperative programs in Coq.
  - Proofs and Reliable Programming using Coq - Introduction to developing and verifying programs with Coq.
  - An Introduction to MathComp-Analysis - Lecture notes on getting started with the Mathematical Components library and using it for classical reasoning and real analysis.
  - 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.
- Tutorials and Hints
  - 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.
  - Mike Nahas's Coq Tutorial - Basics of using Coq to write formal proofs.
  - Coq in a Hurry - Introduction to how Coq can be used to define logical concepts and functions and reason about them.
  - Mike Nahas's Coq Tutorial - Basics of using Coq to write formal proofs.
  - Coq requirements in Common Criteria evaluations - Guide on how to write readable and reviewable Coq code in high assurance applications.
  - Coq requirements in Common Criteria evaluations - Guide on how to write readable and reviewable Coq code in high assurance applications.
Projects
- Frameworks
  - 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.
  - Hybrid - System for reasoning using higher-order abstract syntax representations of object logics.
  - Iris - Higher-order concurrent separation logic framework.
  - CoqEAL - Framework to ease change of data representations in proofs.
  - 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.
  - 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.
  - 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.
- 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.
  - Proof General - Generic interface for proof assistants based on the extensible, customizable text editor Emacs.
  - 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.
  - 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.
  - Waterproof editor - Educational environment for writing mathematical proofs in interactive notebooks.
- Package and Build Management
  - 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 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 - Package manager for Linux and other Unix systems, supporting atomic upgrades and rollbacks.
  - Nix Coq packages - Collection of Coq-related packages for Nix.
  - 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.
  - opam - Flexible and Git-friendly package manager for OCaml and Coq with multiple compiler support.
- 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.
  - Bignums - Library of arbitrarily large numbers.
  - CertiGraph - Library for reasoning about directed graphs and their embedding in separation logic.
  - Paco - Library for parameterized coinduction.
  - 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.
  - 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.
  - 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.
  - 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.
  - CertiGraph - Library for reasoning about directed graphs and their embedding in separation logic.
- 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.
  - 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.
- 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.
  - CoqOfOCaml - Tool for generating idiomatic Coq from OCaml 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.
  - CoqOfOCaml - Tool for generating idiomatic Coq from OCaml 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.
  - Mathematical Components - Formalization of mathematical theories, focusing in particular on group theory.
- 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.
  - 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.
  - 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.
  - 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.

Programming Languages

Coq 26 Emacs Lisp 2 OCaml 2 Python 2 JavaScript 1 TypeScript 1

Ecosyste.ms: Awesome

awesome-coq

Resources

Community

Blogs

Books

Course Material

Tutorials and Hints

Projects

Frameworks

User Interfaces

Package and Build Management

Libraries

Plugins

Tools

Type Theory and Mathematics

Verified Software