In computer science, Coq is an interactive theorem prover. 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 an automated theorem prover but includes automatic theorem proving tactics and various decision procedures.
Coq implements a dependently typed functional programming language.
It is developed in France, in the PI.R2 team of the PPS laboratory, jointly operated by INRIA, École Polytechnique, Paris-Sud 11 University, Paris Diderot University and CNRS. There was also formerly a group at École Normale Supérieure de Lyon. The project manager of Coq is Hugo Herbelin. Coq is implemented in OCaml.
The word coq means "rooster" in French, and stems from a tradition of naming French research development tools with animal names. It is also a reference to Thierry Coquand, who developed the aforementioned calculus of constructions along with Gérard Huet. Also, at first it was simply called Coc, the acronym of calculus of construction.
Read more about Coq: Four Color Theorem and Ssreflect Extension, Applications