围绕Coq进行了30年的研发

G. Huet, Hugo Herbelin
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引用次数: 11

摘要

Coq Proof Assistant是一个基于高阶类型理论的交互式软件系统,由法国研究人员团队在过去30年中不断努力设计和实现。它实现了一个逻辑框架,称为归纳构造的演算,赋予了符号设施和模块化结构,允许它作为适合开发组合数学组件的高级语言使用。明确的潜在证明结构是通过执行ML战术和战术,以及选择证明方案组合来构建的。这允许广泛的推理粒度,从逐步推理到完整的决策过程和反射原则。这种潜在证明的有效性由一个独立的核心证明检查者验证,其元理论本身已经正式证明。Coq证明可以看作是高级函数表示法中的程序,由正确性断言修饰,并且可以翻译成现有的编程语言,如OCaml和Haskell。相反,专门的子系统允许开发具有逻辑断言的算法,其有效性由Coq检查。Coq Proof Assistant是一个开源软件开发,被大量用户社区所使用。在形式化数学(四色定理、奇阶定理)以及软件认证(Java Card处理环境、C编译的CompCert验证)方面取得了一些显著的成功。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
30 years of research and development around Coq
The Coq Proof Assistant is an interactive software system based on higher-order type theory, designed and implemented by a team of French researchers as a continuous effort over the last 30 years. It implements a logical framework, called the Calculus of Inductive Constructions, endowed with notational facilities and a modular structure, allowing its use as a high-level language fit for the development of compositional mathematical components. Explicit potential proof structures are built by execution of ML tactics and tacticals, along a choice of proof schemes combinators. This allows a wide spectrum of inference granularity, from step-by-step inference, to full decision procedures and reflection principles. The validity of such a potential proof is verified by an independent core proof checker, whose meta-theory has been itself formally justified. Coq proofs may be seen as programs in a high-level functional notation, decorated by correctness assertions, and translators into existing programming languages such as OCaml and Haskell are available. Conversely, specialized subsystems allow the development of algorithms with logical assertions, whose validity is checked by Coq. The Coq Proof Assistant, an open-source software development, is in use by a large community of users. Some notable successes have been achieved, in formalized mathematics (4 color theorem, odd order theorem), as well as in software certification (Java Card processing environment, CompCert verification of C compiling).
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