{"title":"具有类型相等判断的Martin-Lof类型理论的评价归一化","authors":"Andreas Abel, T. Coquand, P. Dybjer","doi":"10.1109/LICS.2007.33","DOIUrl":null,"url":null,"abstract":"The decidability of equality is proved for Martin-Lof type theory with a universe a la Russell and typed beta-eta- equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"45","resultStr":"{\"title\":\"Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements\",\"authors\":\"Andreas Abel, T. Coquand, P. Dybjer\",\"doi\":\"10.1109/LICS.2007.33\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The decidability of equality is proved for Martin-Lof type theory with a universe a la Russell and typed beta-eta- equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.\",\"PeriodicalId\":137827,\"journal\":{\"name\":\"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"45\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2007.33\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2007.33","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements
The decidability of equality is proved for Martin-Lof type theory with a universe a la Russell and typed beta-eta- equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.