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A syntactic account of singleton types via hereditary substitution 通过遗传替换对单例类型的语法描述
International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice Pub Date : 2009-08-02 DOI: 10.1145/1577824.1577829
Karl Crary
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引用次数: 12
Higher-order constraint simplification in dependent type theory 依赖类型理论中的高阶约束简化
International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice Pub Date : 2009-08-02 DOI: 10.1145/1577824.1577832
J. Reed
{"title":"Higher-order constraint simplification in dependent type theory","authors":"J. Reed","doi":"10.1145/1577824.1577832","DOIUrl":"https://doi.org/10.1145/1577824.1577832","url":null,"abstract":"Higher-order unification is undecidable, but has fragments which admit practical algorithms, which are used extensively in logical frameworks. For example, it is decidable whether unification problems in the pattern fragment are solvable, and they enjoy unique most general unifiers when they are.\u0000 Often we wish to treat more general problems which are nonetheless solvable by incrementally reasoning about the parts of them that fall in the pattern fragment after more progress has been made --- to this end constraint simplification algorithms have been proposed, which work on the so-called dynamic pattern fragment. However, their theory turns out to be surprisingly subtle. The constraint simplification algorithm implemented in Twelf, for instance, is not terminating, despite the sketch of a proof of its termination in the literature. We describe and prove correct a new, terminating constraint simplification algorithm for a dynamic pattern fragment of higher-order unification in a dependent type system, and discuss its implementation.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123379048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 29
Coercive subtyping in lambda-free logical frameworks 无lambda逻辑框架中的强制子类型
International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice Pub Date : 2009-08-02 DOI: 10.1145/1577824.1577830
Robin Adams
{"title":"Coercive subtyping in lambda-free logical frameworks","authors":"Robin Adams","doi":"10.1145/1577824.1577830","DOIUrl":"https://doi.org/10.1145/1577824.1577830","url":null,"abstract":"We show how coercive subtyping may be added to a lambda-free logical framework, by constructing the logical framework TF<, an extension of the lambda-free logical framework TF with coercive subtyping. Instead of coercive application, TF< makes use of a typecasting operation. We develop the metatheory of the resulting framework, including providing some general conditions under which typecasting in an object theory with coercive subtyping is decidable. We show how TF< may be embedded in the logical framework LF, and hence how results about LF may be deduced from results about TF<.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130987365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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