The Rocq Prover (formerly named Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical checking of proofs of these assertions, assists in finding formal proofs using proof automation routines and extraction of a certified program from the constructive proof of its formal specification.
Rocq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions. Rocq is not an automated theorem prover but includes automatic theorem proving tactics (procedures) and various decision procedures.