{"title":"类型作为经典自然演绎的资源","authors":"D. Kesner, Pierre Vial","doi":"10.4230/LIPIcs.FSCD.2017.24","DOIUrl":null,"url":null,"abstract":"We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based on decreasing measures of type derivations– to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences. 1998 ACM Subject Classification F.4.1 Mathematical Logic","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"73 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":"{\"title\":\"Types as Resources for Classical Natural Deduction\",\"authors\":\"D. Kesner, Pierre Vial\",\"doi\":\"10.4230/LIPIcs.FSCD.2017.24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based on decreasing measures of type derivations– to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences. 1998 ACM Subject Classification F.4.1 Mathematical Logic\",\"PeriodicalId\":284975,\"journal\":{\"name\":\"International Conference on Formal Structures for Computation and Deduction\",\"volume\":\"73 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"32\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Conference on Formal Structures for Computation and Deduction\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.FSCD.2017.24\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Formal Structures for Computation and Deduction","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.FSCD.2017.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Types as Resources for Classical Natural Deduction
We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based on decreasing measures of type derivations– to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences. 1998 ACM Subject Classification F.4.1 Mathematical Logic
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