Confusion in the Church-Turing Thesis
Logic in Computer Science
2014-11-07 v2 Programming Languages
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.
Keywords
Cite
@article{arxiv.1410.7103,
title = {Confusion in the Church-Turing Thesis},
author = {Barry Jay and Jose Vergara},
journal= {arXiv preprint arXiv:1410.7103},
year = {2014}
}