Reflexive toolbox for regular expression matching: verification of functional programs in Coq+Ssreflect

Vladimir Komendantsky
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引用次数: 8

Abstract

We study a derivative method allowing to prove termination of computations on regular expressions. A Coq formalisation of a canonical non-deterministic finite automaton construction on a regular expression is presented. The correctness of the functional definitions is formally verified in Coq using the libraries and the small-scale reflection tools of Ssreflect. We propose to extend the proofs further, and this is a work in progress, to study termination of containment and equivalence in terms of partial derivatives. This serves as a major motivation and intended application of the presented approach. A method that we develop in the paper, called shadowing, allows for a smooth program extraction from decision procedures whatever the complexity of the dependently typed proofs.
用于正则表达式匹配的反射工具箱:Coq+Ssreflect中函数程序的验证
我们研究了一种允许证明正则表达式计算终止的导数方法。给出了正则表达式上正则非确定性有限自动机构造的Coq形式化。使用库和Ssreflect的小规模反射工具,在Coq中正式验证了函数定义的正确性。我们打算进一步扩展证明,这是一项正在进行的工作,以研究在偏导数方面的包含终止和等价。这是本方法的主要动机和预期应用。我们在论文中开发的一种方法,称为阴影,允许从决策过程中顺利提取程序,无论依赖类型证明的复杂性如何。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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