{"title":"正则类型的λ演算","authors":"B. Dundua, Mário Florido, Temur Kutsia","doi":"10.1109/SYNASC.2015.29","DOIUrl":null,"url":null,"abstract":"In this paper we introduce λR: A foundational calculus for sequence processing with regular expression types. Its term language is the lambda calculus extended with sequences of terms and its types are regular expressions over simple types. We provide a flexible notion of subtyping based on the semantic notion of nominal interpretation of a type. Then we prove that types are preserved by reduction (subject reduction), and that there exist no infinite reduction sequences starting at typed terms (strong normalization).","PeriodicalId":6488,"journal":{"name":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"370 ","pages":"129-136"},"PeriodicalIF":0.0000,"publicationDate":"2015-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Lambda Calculus with Regular Types\",\"authors\":\"B. Dundua, Mário Florido, Temur Kutsia\",\"doi\":\"10.1109/SYNASC.2015.29\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we introduce λR: A foundational calculus for sequence processing with regular expression types. Its term language is the lambda calculus extended with sequences of terms and its types are regular expressions over simple types. We provide a flexible notion of subtyping based on the semantic notion of nominal interpretation of a type. Then we prove that types are preserved by reduction (subject reduction), and that there exist no infinite reduction sequences starting at typed terms (strong normalization).\",\"PeriodicalId\":6488,\"journal\":{\"name\":\"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"volume\":\"370 \",\"pages\":\"129-136\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2015.29\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2015.29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we introduce λR: A foundational calculus for sequence processing with regular expression types. Its term language is the lambda calculus extended with sequences of terms and its types are regular expressions over simple types. We provide a flexible notion of subtyping based on the semantic notion of nominal interpretation of a type. Then we prove that types are preserved by reduction (subject reduction), and that there exist no infinite reduction sequences starting at typed terms (strong normalization).
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