From the website:

Developed in the LogiCal project, the Coq tool is a formal proof
management system: a proof done with Coq is mechanically checked
by the machine.

In particular, Coq allows:
* the definition of functions or predicates,
* to state mathematical theorems and software specifications,
* to develop interactively formal proofs of these theorems,
* to check these proofs by a small certification "kernel".

Coq is based on a logical framework called "Calculus of Inductive
Constructions" extended by a modular development system for
theories.
    
Coq is distributed under the GNU Lesser General Public Licence
Version 2.1 (LGPL).

CoqIde is installed if the x11-toolkits/ocaml-lablgtk2 port is installed.

WWW:    http://coq.inria.fr/