{"title":"内向性Martin-Löf类型理论中协数据类型的终端语义","authors":"B. Ahrens, Régis Spadotti","doi":"10.4230/LIPIcs.TYPES.2014.1","DOIUrl":null,"url":null,"abstract":"In this work, we study the notions of relative comonad and comodule over a relative comonad, and use these notions to give a terminal coalgebra semantics for the coinductive type families of streams and of infinite triangular matrices, respectively, in intensional Martin-L\\\"of type theory. Our results are mechanized in the proof assistant Coq.","PeriodicalId":131421,"journal":{"name":"Types for Proofs and Programs","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory\",\"authors\":\"B. Ahrens, Régis Spadotti\",\"doi\":\"10.4230/LIPIcs.TYPES.2014.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we study the notions of relative comonad and comodule over a relative comonad, and use these notions to give a terminal coalgebra semantics for the coinductive type families of streams and of infinite triangular matrices, respectively, in intensional Martin-L\\\\\\\"of type theory. Our results are mechanized in the proof assistant Coq.\",\"PeriodicalId\":131421,\"journal\":{\"name\":\"Types for Proofs and Programs\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Types for Proofs and Programs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.TYPES.2014.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Types for Proofs and Programs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.TYPES.2014.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory
In this work, we study the notions of relative comonad and comodule over a relative comonad, and use these notions to give a terminal coalgebra semantics for the coinductive type families of streams and of infinite triangular matrices, respectively, in intensional Martin-L\"of type theory. Our results are mechanized in the proof assistant Coq.
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