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Coq received ACM SIGPLAN Programming Languages Software 2013 award The development of Coq has been initiated in 1984 at INRIA by Thierry Coquand and G�rard Huet, then joined by Christine Paulin-Mohring and more than 40 direct contributors. The first public release was CoC 4.10 in 1989. Extended with native inductive types, it was renamed Coq in 1991. Since then, a growing community of users has sh
Chapter 4 Calculus of Inductive Constructions 4.1 The terms 4.2 Typed terms 4.3 Conversion rules 4.4 Derived rules for environments 4.5 Inductive Definitions 4.6 Coinductive types 4.7 Cic: the Calculus of Inductive Construction with impredicative Set The underlying formal language of Coq is a Calculus of Constructions with Inductive Definitions. It is presented in this chapter. For Coq ver
Constructive Category Theory Authors Amokrane Saïbi Description Keywords category theory Available files ConCaT.CATEGORY_THEORY.FUNCTOR.FSC_inc.html ConCaT.CATEGORY_THEORY.CATEGORY.CONSTRUCTIONS.CCC.html ConCaT.CATEGORY_THEORY.NT.YONEDA_LEMMA.YonedaLemma.html ConCaT.CATEGORY_THEORY.LIMITS.Equalizers1.html ConCaT.CATEGORY_THEORY.ADJUNCTION.CCC.FunProd.html ConCaT.CATEGORY_THEORY.LIMITS.Iso_Limit.ht
Coq is a proof assistant. It means that it is designed to develop mathematical proofs, and especially to write formal specifications, programs and proofs that programs comply to their specifications. An interesting additional feature of Coq is that it can automatically extract executable programs from specifications, as either Objective Caml or Haskell source code. Properties, programs and proofs
Exploiting Hurkens's paradox [Hurkens95] for system U- so as to derive various contradictory contexts. The file is divided into various sub-modules which all follow the same structure: a section introduces the contradictory hypotheses and a theorem named paradox concludes the module with a proof of False. The Generic module contains the actual Hurkens's paradox for a postulated shallow encoding of
The Coq Proof Assistant A Tutorial Version 1 Gérard Huet, Gilles Kahn and Christine Paulin-Mohring LogiCal Project 1This research was partly supported by IST working group “Types” Getting started Coq is a Proof Assistant for a Logical Framework known as the Calculus of Inductive Constructions. It allows the interactive construction of formal proofs, and also the manipulation of functional programs
Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. Typical applications include the certification of properties of programming languages (e.g. the CompCert compiler certification project, the Verified Software Toolchain f
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