Implicit arguments for functions applied to zero arguments – which is useful when programming with higher-order functions.Additional convenient notations for irrefutable and refutable pattern matching, on inductive types with one or two constructors.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. īased on this work, a significant extension to Coq was developed called Ssreflect (which stands for 'small scale reflection'). 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. Four color theorem and ssreflect extension This may be surprising, since infinite loops (non-termination) are common in other programming languages. This is one way to avoid the halting problem. Programs written in Gallina have the weak normalization property – they always terminate. Ĭoq provides a specification language called Gallina (meaning hen in Spanish and Italian). In 1991, a new implementation based on the extended Calculus of Inductive Constructions was started and the name changed from CoC to Coq, also an indirect reference to Thierry Coquand who developed the Calculus of Constructions along with Gérard Pierre Huet and the Calculus of Inductive Constructions along with Christine Paulin-Mohring. Up to 1991, Coquand was implementing a language called the Calculus of Constructions and it was simply called CoC at this time. The word coq means ' rooster' in French, and stems from a local tradition of naming French research development tools with animal names. The core system can be extended due to a mechanism of plug-ins. Coq is for the most part implemented in OCaml with a bit of C. The implementation team was successively coordinated by Gérard Pierre Huet, Christine Paulin-Mohring and Hugo Herbelin. The development of Coq was initiated by Gérard Pierre Huet and Thierry Coquand, after which more than 40 people, mainly researchers, contributed features of the core system. In the 1990s, École Normale Supérieure de Lyon was also part of the project. 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. Seen as a programming language, Coq implements a dependently typed functional programming language, while seen as a logical system, it implements a higher-order type theory. 2 Four color theorem and ssreflect extension.

Coq programming language