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, or the Bedrock verified low-level programming library), the formalization of mathematics (e.g. the full formalization of the Feit-Thompson theorem or homotopy type theory) and teaching.
This package includes the Coq core binaries, plugins, and tools, but not the vernacular standard library.
Note that in this setup, Coq needs to be started with the -boot and -noinit options, as will otherwise fail to find the regular Coq prelude, now living in the coq-stdlib package.