Indexed and Fibred Structures for Hoare Logic

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-03-01 DOI:10.1016/j.entcs.2020.02.008

U.E. Wolter, A.R. Martini, E.H. Häusler

引用次数: 5

Abstract

Indexed and fibred categorical concepts are widely used in computer science as models of logical systems and type theories. Here we focus on Hoare logic and show that a comprehensive categorical analysis of its axiomatic semantics needs the languages of indexed category and fibred category theory. The structural features of the language are presented in an indexed setting, while the logical features of deduction are modeled in the fibred one. Especially, Hoare triples arise naturally as special arrows in a fibred category over a syntactic category of programs, while deduction in the Hoare calculus can be characterized categorically by the heuristic deduction = generation of cartesian arrows + composition of arrows.

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Hoare逻辑的索引和纤维结构

索引的和纤维化的范畴概念作为逻辑系统和类型理论的模型在计算机科学中被广泛使用。本文以霍尔逻辑为研究对象，指出对霍尔逻辑的公理化语义进行全面的范畴分析需要索引范畴论和纤维范畴论两种语言。语言的结构特征以索引的形式呈现，演绎的逻辑特征以纤维的形式建模。特别是，Hoare三元组作为特殊的箭头自然地出现在程序的语法范畴上的纤维范畴中，而Hoare演算中的演绎可以用启发式演绎=笛卡尔箭头的生成+箭头的组合来明确地表征。

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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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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