Confusion in the Church-Turing Thesis [article]

Barry Jay, Jose Vergara
2014 arXiv   pre-print
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.
arXiv:1410.7103v2 fatcat:ybkzeatss5bdrpvhsj5c5p5bii