{"title":"的延展性","authors":"A. Polonsky","doi":"10.4230/LIPIcs.TYPES.2014.221","DOIUrl":null,"url":null,"abstract":"We prove an extensionality theorem for the \"type-in-type\" dependent type theory with Sigma-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.","PeriodicalId":131421,"journal":{"name":"Types for Proofs and Programs","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Extensionality of lambda-\",\"authors\":\"A. Polonsky\",\"doi\":\"10.4230/LIPIcs.TYPES.2014.221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove an extensionality theorem for the \\\"type-in-type\\\" dependent type theory with Sigma-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.\",\"PeriodicalId\":131421,\"journal\":{\"name\":\"Types for Proofs and Programs\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Types for Proofs and Programs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.TYPES.2014.221\",\"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.2014.221","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove an extensionality theorem for the "type-in-type" dependent type theory with Sigma-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.
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