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New Proofs of Important Theorems of Untyped Extensional λ Calculus

Abstract

This paper contains new proofs of the following two theorems of the untyped extensional λ-calculus: the Curry theorem stating that any λ-term has a βη-normal form if and only if it has a β-normal form and the normalization theorem for βη-reduction. The proposed approach is based on the following well-known results: the postponement theorem of η-reduction and the strong normalization property of η-reduction that allow one to naturally extend some propositions from the usual λ-calculus to the extensional case.

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Correspondence to A. A. Lyaletsky.

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 53–63, July–August, 2014.

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Lyaletsky, A.A. New Proofs of Important Theorems of Untyped Extensional λ Calculus. Cybern Syst Anal 50, 529–537 (2014). https://doi.org/10.1007/s10559-014-9641-5

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Keywords

  • untyped extensional λ-calculus
  • postponement of η-reduction
  • theorem on βη-normal form
  • normalization theorem for βη-reduction