Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. Typical applications include the certification of properties of programming languages (e.g. the CompCert compiler certification project, or the Bedrock verified low-level programming library), the formalization of mathematics (e.g. the full formalization of the Feit-Thompson theorem or homotopy type theory) and teaching.

Version 8.5 of Coq is available for beta testing. You can also download the current stable version, Coq 8.4. Released in August 2012, it features a uniform modular evolution of the arithmetical libraries, a new proof engine providing bullets, and various improvements of existing features, especially regarding CoqIDE, the tactics, the tactic language, the specification language.

The reference documentation for Coq are the Reference Manual and the documentation of the Standard Library. Other useful documents (tutorials, faq, ...) are available from the documentation page.

There is a strong and active community of users working with Coq. They are contributing formal developments (see Coq Users' Contributions), extensions of Coq, and tools based on Coq (see Related Tools).