| Paradigm(s) | Functional |
|---|---|
| Stable release | 8.3 (October 2010) |
| Typing discipline | static, strong |
| Influenced by | ML and Standard ML |
| Influenced | Agda |
| OS | Cross-platform |
| License | LGPL 2.1 |
| Usual filename extensions | .v |
| Website | coq.inria.fr |
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.[1]
It is developed in France, in the TypiCal[2] (ex-LogiCal) project, jointly operated by INRIA, École Polytechnique, Paris-Sud 11 University and CNRS. There was also formerly a group at École Normale Supérieure de Lyon. The team leader is Senior Scientist Benjamin Werner. Coq is implemented in Objective Caml.
The word coq means "cock" (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.
Contents |
Georges Gonthier (of Microsoft Research, in Cambridge, England) and Benjamin Werner (of INRIA) used Coq to create a surveyable proof of the four color theorem, which was completed in September 2004.[3]
Based on this work, a significant extension to Coq was developed called Ssreflect (which stands for "small scale reflection"). Despite the name, most of the new features added to Coq by Ssreflect are general purpose features, useful not merely for the computational reflection style of proof. These include:
set tactic with more powerful matchingSsreflect 1.2 is freely available under the open source CeCill-B or Cecill-2.0 license (your choice), and is compatible with Coq 8.2pl1.[4]