{"title":"非循环递归类型论中的限制计算和参数","authors":"Roussanka Loukanova","doi":"10.14201/adcaij.29081","DOIUrl":null,"url":null,"abstract":"The paper extends the formal language and the reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative restrictions. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The extended type-theory of restricted recursion (TTRR) provides computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages.\nThe reduction calculi of TTRR provides a mathematical foundation of the work of compilers for reducing recursive programs to iterative ones. The type-theory of acyclic recursion (TTAR) has a special importance to syntax-semantics interfaces in computational grammars.","PeriodicalId":42597,"journal":{"name":"ADCAIJ-Advances in Distributed Computing and Artificial Intelligence Journal","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Restricted Computations and Parameters in Type-Theory of Acyclic Recursion\",\"authors\":\"Roussanka Loukanova\",\"doi\":\"10.14201/adcaij.29081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper extends the formal language and the reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative restrictions. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The extended type-theory of restricted recursion (TTRR) provides computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages.\\nThe reduction calculi of TTRR provides a mathematical foundation of the work of compilers for reducing recursive programs to iterative ones. The type-theory of acyclic recursion (TTAR) has a special importance to syntax-semantics interfaces in computational grammars.\",\"PeriodicalId\":42597,\"journal\":{\"name\":\"ADCAIJ-Advances in Distributed Computing and Artificial Intelligence Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ADCAIJ-Advances in Distributed Computing and Artificial Intelligence Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14201/adcaij.29081\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ADCAIJ-Advances in Distributed Computing and Artificial Intelligence Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14201/adcaij.29081","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Restricted Computations and Parameters in Type-Theory of Acyclic Recursion
The paper extends the formal language and the reduction calculus of Moschovakis type-theory of recursion, by adding a restrictor operator on terms with predicative restrictions. Terms with restrictions over memory variables formalise inductive algorithms with generalised, restricted parameters. The extended type-theory of restricted recursion (TTRR) provides computations for algorithmic semantics of mathematical expressions and definite descriptors, in formal and natural languages.
The reduction calculi of TTRR provides a mathematical foundation of the work of compilers for reducing recursive programs to iterative ones. The type-theory of acyclic recursion (TTAR) has a special importance to syntax-semantics interfaces in computational grammars.