In automated theorem proving, Coq is a proof assistant which handles mathematical assertions, checks mechanically proofs of these assertions,
helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification. Coq works within the theory of the Calculus of Inductive Constructions, a derivative of the Calculus of Constructions.
It was developed in France, in the LogiCal project, jointly operated by INRIA, École Polytechnique, University Paris XI and CNRS (there was also formerly a group at École Normale Supérieure de Lyon). The team leaders are Pr Gilles Dowek and Pr Christine Paulin-Mohring. Coq is written in the Ocaml programming language.
Coq means "rooster" in French - and Thierry Coquand (along with Gérard Huet ) developed the aforementioned Calculus of Constructions.
Benjamin Werner (of INRIA) and Georges Gonthier (of Microsoft Research, in Cambridge, England) used Coq to create a surveyable proof of the Four color theorem, which was completed in September 2004.
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