{"title":"Up-to techniques for behavioural metrics via fibrations","authors":"Filippo Bonchi, Barbara König, Daniela Petrisan","doi":"10.1017/s0960129523000166","DOIUrl":null,"url":null,"abstract":"Abstract Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras, and we provide abstract results to prove their soundness in a compositional way. In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a fibrational sense. This observation enables us to reuse existing results about soundness of up-to techniques in a fibrational setting. We focus on the fibrations of predicates and relations valued in a quantale. To illustrate our approach, we provide an example on distances between regular languages.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"235 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Structures in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0960129523000166","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: 2
Abstract
Abstract Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras, and we provide abstract results to prove their soundness in a compositional way. In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a fibrational sense. This observation enables us to reuse existing results about soundness of up-to techniques in a fibrational setting. We focus on the fibrations of predicates and relations valued in a quantale. To illustrate our approach, we provide an example on distances between regular languages.
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.