递归函数理论的起源

S. Kleene
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引用次数: 123

摘要

两千多年来,数学家们一直使用算法的特定例子来确定函数的值。“λ可定义性”的概念,是现在公认的,对所有存在算法的数论函数的等价精确数学描述的第一个概念。本文解释了这一概念,并追溯了1931年至1931年的调查,这一调查出乎意料地得到了人们的认可。1934年的Herbrand-Gödel“一般递归性”概念和1936年的图灵“可计算性”概念是第二和第三个等效概念。在λ可定义性研究中发展起来的技术被应用于一般递归性和图灵可计算性的分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Origins of recursive function theory
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.
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