{"title":"工作中的可实现性:分离两个建设性的有限性概念","authors":"M. Bezem, T. Coquand, Keiko Nakata, Erik Parmann","doi":"10.4230/LIPIcs.TYPES.2016.6","DOIUrl":null,"url":null,"abstract":"We elaborate in detail a realizability model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration of A contains a duplicate. 2012 ACM Subject Classification Theory of computation → Type theory, Theory of computation → Constructive mathematics","PeriodicalId":131421,"journal":{"name":"Types for Proofs and Programs","volume":"35 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Realizability at Work: Separating Two Constructive Notions of Finiteness\",\"authors\":\"M. Bezem, T. Coquand, Keiko Nakata, Erik Parmann\",\"doi\":\"10.4230/LIPIcs.TYPES.2016.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We elaborate in detail a realizability model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration of A contains a duplicate. 2012 ACM Subject Classification Theory of computation → Type theory, Theory of computation → Constructive mathematics\",\"PeriodicalId\":131421,\"journal\":{\"name\":\"Types for Proofs and Programs\",\"volume\":\"35 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Types for Proofs and Programs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.TYPES.2016.6\",\"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.2016.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Realizability at Work: Separating Two Constructive Notions of Finiteness
We elaborate in detail a realizability model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration of A contains a duplicate. 2012 ACM Subject Classification Theory of computation → Type theory, Theory of computation → Constructive mathematics
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