Computability and λ-definability

@article{Turing1937ComputabilityA,
  title={Computability and $\lambda$-definability},
  author={Alan M. Turing},
  journal={Journal of Symbolic Logic},
  year={1937},
  volume={2},
  pages={153 - 163}
}
  • A. Turing
  • Published 1 December 1937
  • Computer Science, Mathematics
  • Journal of Symbolic Logic
Several definitions have been given to express an exact meaning corresponding to the intuitive idea of ‘effective calculability’ as applied for instance to functions of positive integers. The purpose of the present paper is to show that the computable functions introduced by the author are identical with the λ-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene. It is shown that every λ-definable function is computable and that… 

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