{"title":"基于双模拟的递归数据类型的共归纳原理","authors":"M. Fiore","doi":"10.1109/LICS.1993.287595","DOIUrl":null,"url":null,"abstract":"The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result for the canonical model of the untyped call-by-value lambda -calculus is proved. The operations notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"52 1","pages":"110-119"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"64","resultStr":"{\"title\":\"A coinduction principle for recursive data types based on bisimulation\",\"authors\":\"M. Fiore\",\"doi\":\"10.1109/LICS.1993.287595\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result for the canonical model of the untyped call-by-value lambda -calculus is proved. The operations notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.<<ETX>>\",\"PeriodicalId\":6322,\"journal\":{\"name\":\"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science\",\"volume\":\"52 1\",\"pages\":\"110-119\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"64\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.1993.287595\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.1993.287595","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A coinduction principle for recursive data types based on bisimulation
The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result for the canonical model of the untyped call-by-value lambda -calculus is proved. The operations notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.<>
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