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, the Verified Software Toolchain for verification of C programs, or the Iris framework for concurrent separation logic), the formalization of mathematics (e.g. the full formalization of the Feit-Thompson theorem, or homotopy type theory), and teaching.

The Reference Manual and the Standard Library documentation are the primary documentation for Coq. However, to learn about Coq, we recommend starting with a tutorial or book, such as those listed on the documentation page.

You don't need to install Coq to get started: you can run Coq in your browser using jsCoq!

Eventually you'll probably want to install the Coq platform on your system with a user interface of your choice.

Coq has a large and active user community. They contribute formal developments, Coq extensions (see Coq Package Index) and tools based on Coq (see Related Tools). We have a multi-lingual Discourse forum and a Zulip chat.

You can contribute to the development of Coq by reporting bugs, suggesting enhancements, submitting pull requests, improving the documentation and in many other ways.

Academic and industrial users are also encouraged to contribute financially to support the maintenance and evolution of Coq and its ecosystem through the Coq Consortium.