{"title":"数量类型理论的句法和语义","authors":"R. Atkey","doi":"10.1145/3209108.3209189","DOIUrl":null,"url":null,"abstract":"We present Quantitative Type Theory, a Type Theory that records usage information for each variable in a judgement, based on a previous system by McBride. The usage information is used to give a realizability semantics using a variant of Linear Combinatory Algebras, refining the usual realizability semantics of Type Theory by accurately tracking resource behaviour. We define the semantics in terms of Quantitative Categories with Families, a novel extension of Categories with Families for modelling resource sensitive type theories.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"86","resultStr":"{\"title\":\"Syntax and Semantics of Quantitative Type Theory\",\"authors\":\"R. Atkey\",\"doi\":\"10.1145/3209108.3209189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present Quantitative Type Theory, a Type Theory that records usage information for each variable in a judgement, based on a previous system by McBride. The usage information is used to give a realizability semantics using a variant of Linear Combinatory Algebras, refining the usual realizability semantics of Type Theory by accurately tracking resource behaviour. We define the semantics in terms of Quantitative Categories with Families, a novel extension of Categories with Families for modelling resource sensitive type theories.\",\"PeriodicalId\":389131,\"journal\":{\"name\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"86\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3209108.3209189\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3209108.3209189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We present Quantitative Type Theory, a Type Theory that records usage information for each variable in a judgement, based on a previous system by McBride. The usage information is used to give a realizability semantics using a variant of Linear Combinatory Algebras, refining the usual realizability semantics of Type Theory by accurately tracking resource behaviour. We define the semantics in terms of Quantitative Categories with Families, a novel extension of Categories with Families for modelling resource sensitive type theories.
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