When viewed as a programming language, Coq implements a dependently typedfunctional programming language; when viewed as a logical system, it implements a higher-ordertype theory. The development of Coq has been supported since 1984 by INRIA, now in collaboration with École Polytechnique, University of Paris-Sud, Paris Diderot University, and CNRS. In the 1990s, ENS Lyon was also part of the project. The development of Coq was initiated by Gérard Huet and Thierry Coquand, and more than 40 people, mainly researchers, have contributed features to the core system since its inception. The implementation team has successively been coordinated by Gérard Huet, Christine Paulin-Mohring, Hugo Herbelin, and Matthieu Sozeau. Coq is mainly implemented in OCaml with a bit of C. The core system can be extended by way of a plug-in mechanism. The name means "rooster" in French and stems from a French tradition of naming research development tools after animals. Up until 1991, Coquand was implementing a language called the Calculus of Constructions and it was simply called CoC at this time. In 1991, a new implementation based on the extended Calculus of Inductive Constructions was started and the name was changed from CoC to Coq in an indirect reference to Coquand, who developed the Calculus of Constructions along with Gérard Huet and contributed to the Calculus of Inductive Constructions with Christine Paulin-Mohring. Coq provides a specification language called Gallina. Programs written in Gallina have the weak normalization property, implying that they always terminate. This is a distinctive property of the language, since infinite loops are common in other programming languages, and is one way to avoid the halting problem.
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 2005. Their work led to the development of the SSReflect package, which was a significant extension to Coq. Despite its name, most of the features added to Coq by SSReflect are general-purpose features and are not limited to the computational reflection style of proof. These features include:
Additional convenient notations for irrefutable and refutable pattern matching, on inductive types with one or two constructors
Implicit arguments for functions applied to zero arguments, which is useful when programming with higher-order functions
Concise anonymous arguments
An improved set tactic with more powerful matching
Support for reflection
SSReflect 1.4 is freely available, dual-licensed under the open source CeCILL-B or CeCILL-2.0 license, and compatible with Coq 8.4.
