Confusion in the Church-Turing Thesis

Barry Jay; Jose Vergara

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arXiv · 1410.7103

Confusion in the Church-Turing Thesis

Barry Jay·Jose Vergara

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Abstract

The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is not equivalent to the Turing model. However, a modern combinatory calculus, the SF-calculus, can define equality of its closed normal forms, and so yields a model of computability that is equivalent to the Turing model. This has profound implications for programming language design.

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Barry Jay, Jose Vergara. 2014-10-27. Confusion in the Church-Turing Thesis. https://arxiv.org/abs/1410.7103

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