Indexed and fibered structures for partial and total correctness assertions

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2022-09-19 DOI:10.1017/S0960129522000275

Uwe Wolter, A. Martini, E. Haeusler

引用次数: 1

Abstract

Abstract Hoare Logic has a long tradition in formal verification and has been continuously developed and used to verify a broad class of programs, including sequential, object-oriented, and concurrent programs. Here we focus on partial and total correctness assertions within the framework of Hoare logic and show that a comprehensive categorical analysis of its axiomatic semantics needs the languages of indexed and fibered category theory. We consider Hoare formulas with local, finite contexts, of program and logical variables. The structural features of Hoare assertions are presented in an indexed setting, while the logical features of deduction are modeled in the fibered one.

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用于部分和全部正确性断言的索引结构和纤维结构

摘要Hoare逻辑在形式验证方面有着悠久的传统，并不断被开发和用于验证一系列程序，包括顺序程序、面向对象程序和并发程序。在这里，我们关注霍尔逻辑框架内的部分和完全正确性断言，并表明对其公理语义的全面分类分析需要索引和纤维化范畴理论的语言。我们考虑具有程序和逻辑变量的局部有限上下文的霍尔公式。霍尔断言的结构特征在索引环境中呈现，而推理的逻辑特征在纤维化环境中建模。

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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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.