The name "Coq" is a wordplay on the name of Thierry Coquand, Calculus of Constructions or "CoC" and follows the French computer science tradition of naming software after animals (coq in French meaning rooster).[2]
When viewed as a programming language, Coq implements a dependently typedfunctional programming language;[3] 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.[4]
The name coq means 'rooster' in French and stems from a French tradition of naming research development tools after animals.[5] 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.[6]
Coq provides a specification language called Gallina[7] ("hen" in Latin, Spanish, Italian and Catalan). 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 (non-terminating programs) are common in other programming languages,[8] and is one way to avoid the halting problem.
nat_ind stands for mathematical induction, eq_ind for substitution of equals, and f_equal for taking the same function on both sides of the equality. Earlier theorems are referenced showing and .
Notable uses
Four color theorem and SSReflect extension
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 2002.[9] Their work led to the development of the SSReflect ("Small Scale Reflection") package, which was a significant extension to Coq.[10] 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 1.11 is freely available, dual-licensed under the open source CeCILL-B or CeCILL-2.0 license, and compatible with Coq 8.11.[11]
Other applications
CompCert: an optimizing compiler for almost all of the C programming language which is largely programmed and proven correct in Coq.
^Avigad, Jeremy; Mahboubi, Assia (3 July 2018). Interactive Theorem Proving: 9th International Conference, ITP 2018, Held as ...ISBN9783319948218. Retrieved 21 October 2018.
Video tutorials for the Coq proof assistant by Andrej Bauer.
April 14, 2023
coenzyme, dietary, supplement, coenzyme, abbreviated, placename, uihalla, cockerel, rooster, interactive, theorem, prover, first, released, 1989, allows, expressing, mathematical, assertions, mechanically, checks, proofs, these, assertions, helps, find, formal. For the coenzyme and dietary supplement see Coenzyme Q10 For the abbreviated placename see Coquihalla For the cockerel see Rooster Coq is an interactive theorem prover first released in 1989 It allows for expressing mathematical assertions mechanically checks proofs of these assertions helps 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 procedures and various decision procedures Coq software Developer s The Coq development teamInitial release1 May 1989 33 years ago 1989 05 01 version 4 10 Stable release8 17 0 1 27 March 2023 18 days ago 27 March 2023 Repositorygithub wbr com wbr coq wbr coqWritten inOCamlOperating systemCross platformAvailable inEnglishTypeProof assistantLicenseLGPLv2 1Websitecoq wbr inria wbr frAn interactive proof session in CoqIDE showing the proof script on the left and the proof state on the right The Association for Computing Machinery awarded Thierry Coquand Gerard Huet Christine Paulin Mohring Bruno Barras Jean Christophe Filliatre Hugo Herbelin Chetan Murthy Yves Bertot and Pierre Casteran with the 2013 ACM Software System Award for Coq The name Coq is a wordplay on the name of Thierry Coquand Calculus of Constructions or CoC and follows the French computer science tradition of naming software after animals coq in French meaning rooster 2 Contents 1 Overview 2 Notable uses 2 1 Four color theorem and SSReflect extension 3 Other applications 4 See also 5 References 6 External linksOverview EditWhen viewed as a programming language Coq implements a dependently typed functional programming language 3 when viewed as a logical system it implements a higher order type theory The development of Coq has been supported since 1984 by INRIA now in collaboration with Ecole 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 Gerard 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 Gerard 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 4 The name coq means rooster in French and stems from a French tradition of naming research development tools after animals 5 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 Gerard Huet and contributed to the Calculus of Inductive Constructions with Christine Paulin Mohring 6 Coq provides a specification language called Gallina 7 hen in Latin Spanish Italian and Catalan 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 non terminating programs are common in other programming languages 8 and is one way to avoid the halting problem As an example a proof of commutativity of addition on natural numbers in Coq plus comm fun n m nat gt nat ind fun n0 nat gt n0 m m n0 plus n 0 m fun y nat H y m m y gt eq ind S m y fun n0 nat gt S y m n0 f equal S H m S y plus n Sm m y n forall n m nat n m m n span class n nat ind span stands for mathematical induction span class n eq ind span for substitution of equals and span class n f equal span for taking the same function on both sides of the equality Earlier theorems are referenced showing m m 0 displaystyle m m 0 and S m y m S y displaystyle S m y m Sy Notable uses EditFour color theorem and SSReflect extension Edit 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 2002 9 Their work led to the development of the SSReflect Small Scale Reflection package which was a significant extension to Coq 10 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 reflectionSSReflect 1 11 is freely available dual licensed under the open source CeCILL B or CeCILL 2 0 license and compatible with Coq 8 11 11 Other applications EditCompCert an optimizing compiler for almost all of the C programming language which is largely programmed and proven correct in Coq Disjoint set data structure correctness proof in Coq was published in 2007 12 Feit Thompson theorem formal proof using Coq was completed in September 2012 13 See also Edit Mathematics portal Free and open source software portalCalculus of constructions Curry Howard correspondence Intuitionistic type theory List of proof assistantsReferences Edit Release 8 17 0 27 March 2023 Retrieved 30 March 2023 Alternative names coq coq Wiki GitHub Retrieved 3 March 2023 A short introduction to Coq Avigad Jeremy Mahboubi Assia 3 July 2018 Interactive Theorem Proving 9th International Conference ITP 2018 Held as ISBN 9783319948218 Retrieved 21 October 2018 Frequently Asked Questions GitHub Retrieved 2019 05 08 Introduction to the Calculus of Inductive Constructions Retrieved 21 May 2019 Adam Chlipala Certified Programming with Dependent Types Library Universes Adam Chlipala Certified Programming with Dependent Types Library GeneralRec Library InductiveTypes Gonthier Georges 2008 Formal Proof The Four Color Theorem PDF Notices of the American Mathematical Society vol 55 no 11 pp 1382 1393 MR 2463991 Georges Gonthier Assia Mahboubi An introduction to small scale reflection in Coq Journal of Formalized Reasoning The Mathematical Components Library 1 11 0 GitHub Conchon Sylvain Filliatre Jean Christophe October 2007 A Persistent Union Find Data Structure ACM SIGPLAN Workshop on ML Freiburg Germany Feit Thompson theorem has been totally checked in Coq Msr inria inria fr 2012 09 20 Archived from the original on 2016 11 19 Retrieved 2012 09 25 External links Edit Wikimedia Commons has media related to Coq programming language The Coq proof assistant the official English website coq coq the project s source code repository on GitHub JsCoq Interactive Online System allows Coq to be run in a web browser without the need for any software installation Alectryon a library to process Coq snippets embedded in documents showing goals and messages for each Coq sentence Coq Wiki Mathematical Components library widely used library of mathematical structures part of which is the SSReflect proof language Constructive Coq Repository at Nijmegen Math Classes Coq at Open HubTextbooksThe Coq Art a book on Coq by Yves Bertot and Pierre Casteran Certified Programming with Dependent Types online and printed textbook by Adam Chlipala Software Foundations online textbook by Benjamin C Pierce et al An introduction to small scale reflection in Coq a tutorial on SSReflect by Georges Gonthier and Assia MahboubiTutorialsIntroduction to the Coq Proof Assistant video lecture by Andrew Appel at Institute for Advanced Study Video tutorials for the Coq proof assistant by Andrej Bauer Retrieved from https en wikipedia org w index php title Coq amp oldid 1149718097, wikipedia, wiki, book, books, library,
