{"title":"Type soundness of functional languages with subtyping in Lang-n-Prove","authors":"Matteo Cimini, Joan Montas","doi":"10.1016/j.scico.2025.103380","DOIUrl":null,"url":null,"abstract":"<div><div>Language verification is an important aspect in the cycle of programming language development, especially when such endeavor establishes properties of programming languages with mathematical proofs. Prior work proposed <figure><img></figure>, which is a domain-specific language for expressing language-parameterized proofs, that is, proofs that apply to classes of languages rather than a single language. Such work developed the language-parameterized proofs of type soundness (excluding the substitution lemmas) for a certain class of functional languages. In this paper, we extend that work to include subtyping. We have added new operations to <figure><img></figure> for expressing the proofs that are related to subtyping more naturally. We provide a semantics of our new system based on a compilation into proofs of the Abella proof assistant. Next, we develop language-parameterized proofs of type soundness (excluding the substitution lemmas) for the class of functional languages mentioned above, and of the equivalence between algorithmic and declarative subtyping. Our extended <figure><img></figure> generates Abella proofs that machine-check the type soundness of a nontrivial class of functional languages with declarative and algorithmic subtyping, when just a few simple lemmas are admitted.</div></div>","PeriodicalId":49561,"journal":{"name":"Science of Computer Programming","volume":"248 ","pages":"Article 103380"},"PeriodicalIF":1.4000,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science of Computer Programming","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167642325001194","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Language verification is an important aspect in the cycle of programming language development, especially when such endeavor establishes properties of programming languages with mathematical proofs. Prior work proposed , which is a domain-specific language for expressing language-parameterized proofs, that is, proofs that apply to classes of languages rather than a single language. Such work developed the language-parameterized proofs of type soundness (excluding the substitution lemmas) for a certain class of functional languages. In this paper, we extend that work to include subtyping. We have added new operations to for expressing the proofs that are related to subtyping more naturally. We provide a semantics of our new system based on a compilation into proofs of the Abella proof assistant. Next, we develop language-parameterized proofs of type soundness (excluding the substitution lemmas) for the class of functional languages mentioned above, and of the equivalence between algorithmic and declarative subtyping. Our extended generates Abella proofs that machine-check the type soundness of a nontrivial class of functional languages with declarative and algorithmic subtyping, when just a few simple lemmas are admitted.
期刊介绍:
Science of Computer Programming is dedicated to the distribution of research results in the areas of software systems development, use and maintenance, including the software aspects of hardware design.
The journal has a wide scope ranging from the many facets of methodological foundations to the details of technical issues andthe aspects of industrial practice.
The subjects of interest to SCP cover the entire spectrum of methods for the entire life cycle of software systems, including
• Requirements, specification, design, validation, verification, coding, testing, maintenance, metrics and renovation of software;
• Design, implementation and evaluation of programming languages;
• Programming environments, development tools, visualisation and animation;
• Management of the development process;
• Human factors in software, software for social interaction, software for social computing;
• Cyber physical systems, and software for the interaction between the physical and the machine;
• Software aspects of infrastructure services, system administration, and network management.