{"title":"非左线性非类型高阶重写理论中的合流","authors":"Gaspard Férey, J. Jouannaud","doi":"10.1145/3479394.3479403","DOIUrl":null,"url":null,"abstract":"We develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. We show that confluence is preserved for a large subset of terms that contains all pure lambda terms. Our results are applied to famous Klop’s examples of non-confluent behaviours in presence of convergent rewrite rules and to fragments of various encodings, in a dependent type theory with rewrite rules, of the Calculus of Constructions with polymorphic universes.","PeriodicalId":242361,"journal":{"name":"23rd International Symposium on Principles and Practice of Declarative Programming","volume":"66 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories\",\"authors\":\"Gaspard Férey, J. Jouannaud\",\"doi\":\"10.1145/3479394.3479403\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. We show that confluence is preserved for a large subset of terms that contains all pure lambda terms. Our results are applied to famous Klop’s examples of non-confluent behaviours in presence of convergent rewrite rules and to fragments of various encodings, in a dependent type theory with rewrite rules, of the Calculus of Constructions with polymorphic universes.\",\"PeriodicalId\":242361,\"journal\":{\"name\":\"23rd International Symposium on Principles and Practice of Declarative Programming\",\"volume\":\"66 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"23rd International Symposium on Principles and Practice of Declarative Programming\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3479394.3479403\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"23rd International Symposium on Principles and Practice of Declarative Programming","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3479394.3479403","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories
We develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. We show that confluence is preserved for a large subset of terms that contains all pure lambda terms. Our results are applied to famous Klop’s examples of non-confluent behaviours in presence of convergent rewrite rules and to fragments of various encodings, in a dependent type theory with rewrite rules, of the Calculus of Constructions with polymorphic universes.