{"title":"递归函数理论的起源","authors":"S. Kleene","doi":"10.1109/MAHC.1981.10004","DOIUrl":null,"url":null,"abstract":"For over two millennia mathematicians have used particular examples of algorithms for determining the values of functions. The notion of \"λ-definability\" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of all number-theoretic functions for which algorithms exist. This article explains the notion, and traces the investigation in 1931-3 by which quite unexpectedly it was so recognized. The Herbrand-Gödel notion of \"general recursiveness\" 1934, and the Turing notion of \"computability\" 1936 were the second and third of the equivalent notions. Techniques developed in the study of λ-definability were applied in the analysis of general recursiveness and Turing computability.","PeriodicalId":311166,"journal":{"name":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"123","resultStr":"{\"title\":\"Origins of recursive function theory\",\"authors\":\"S. Kleene\",\"doi\":\"10.1109/MAHC.1981.10004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For over two millennia mathematicians have used particular examples of algorithms for determining the values of functions. The notion of \\\"λ-definability\\\" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of all number-theoretic functions for which algorithms exist. This article explains the notion, and traces the investigation in 1931-3 by which quite unexpectedly it was so recognized. The Herbrand-Gödel notion of \\\"general recursiveness\\\" 1934, and the Turing notion of \\\"computability\\\" 1936 were the second and third of the equivalent notions. Techniques developed in the study of λ-definability were applied in the analysis of general recursiveness and Turing computability.\",\"PeriodicalId\":311166,\"journal\":{\"name\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"123\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MAHC.1981.10004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MAHC.1981.10004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For over two millennia mathematicians have used particular examples of algorithms for determining the values of functions. The notion of "λ-definability" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of all number-theoretic functions for which algorithms exist. This article explains the notion, and traces the investigation in 1931-3 by which quite unexpectedly it was so recognized. The Herbrand-Gödel notion of "general recursiveness" 1934, and the Turing notion of "computability" 1936 were the second and third of the equivalent notions. Techniques developed in the study of λ-definability were applied in the analysis of general recursiveness and Turing computability.