Coq
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In computer science, Coq is a proof assistant application. It allows the expression of mathematical assertions, mechanically checks 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. Coq is not a theorem prover but includes automatic theorem proving tactics.
It is 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 Prof. Gilles Dowek and Prof. Christine Paulin-Mohring. Coq is implemented in Objective Caml.
The word coq means "rooster" in French. It is also a reference to Thierry Coquand, who developed the aforementioned calculus of constructions along with Gérard Huet.
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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