The question of what is an effective process or algorithm arose form the statement of Hilbert's tenth problem. It was soon seen to be related to the question of which numerical functions N/sup n/ to N are computable. Among the early answers to this question the author singles out three. A numerical function is computable if and only if it is recursive, it is computable on a Turing machine, or it is definable in the untyped lambda -calculus. Some aspects of the relevance of these three notions of computability to linguistics and logic, in particular, categorial logic, are discussed.
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机译：出现了有效的过程或算法的问题是形成贝尔伯特第十个问题的陈述。很快就看到与哪个问题有关，其中数值函数n / sup n / t至n是可计算的。在这个问题的早期答案中，作者单打三个。如果且仅当它是递归而仅计算的数字功能，它是可在图灵机上可计算的，或者它是可定义的在没有型号的λ-calculus中。讨论了这三个概念对语言学和逻辑的可计算性的相关性的一些方面，特别是分类逻辑。
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