{"title":"确定与sum和空类型的等价性","authors":"Gabriel Scherer","doi":"10.1145/3009837.3009901","DOIUrl":null,"url":null,"abstract":"The logical technique of focusing can be applied to the λ-calculus; in a simple type system with atomic types and negative type formers (functions, products, the unit type), its normal forms coincide with βη-normal forms. Introducing a saturation phase gives a notion of quasi-normal forms in presence of positive types (sum types and the empty type). This rich structure let us prove the decidability of βη-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and with set-theoretic equality in all finite models.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2016-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"Deciding equivalence with sums and the empty type\",\"authors\":\"Gabriel Scherer\",\"doi\":\"10.1145/3009837.3009901\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The logical technique of focusing can be applied to the λ-calculus; in a simple type system with atomic types and negative type formers (functions, products, the unit type), its normal forms coincide with βη-normal forms. Introducing a saturation phase gives a notion of quasi-normal forms in presence of positive types (sum types and the empty type). This rich structure let us prove the decidability of βη-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and with set-theoretic equality in all finite models.\",\"PeriodicalId\":20657,\"journal\":{\"name\":\"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3009837.3009901\",\"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 44th ACM SIGPLAN Symposium on Principles of Programming Languages","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3009837.3009901","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The logical technique of focusing can be applied to the λ-calculus; in a simple type system with atomic types and negative type formers (functions, products, the unit type), its normal forms coincide with βη-normal forms. Introducing a saturation phase gives a notion of quasi-normal forms in presence of positive types (sum types and the empty type). This rich structure let us prove the decidability of βη-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and with set-theoretic equality in all finite models.