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
{"title":"Indexed and fibered structures for partial and total correctness assertions","authors":"Uwe Wolter, A. Martini, E. Haeusler","doi":"10.1017/S0960129522000275","DOIUrl":null,"url":null,"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.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Structures in Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1017/S0960129522000275","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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。
求助全文
约1分钟内获得全文 去求助
来源期刊
Mathematical Structures in Computer Science
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
30
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.
期刊最新文献
On Hofmann–Streicher universes T0-spaces and the lower topology GADTs are not (Even partial) functors A linear linear lambda-calculus Countability constraints in order-theoretic approaches to computability
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1