ON CANONICAL NOTION OF $\delta$-REDUCTION AND ON TRANSLATION OF TYPED $\lambda$-TERMS INTO UNTYPED $\lambda$-TERMS

Authors

  • S.A. Nigiyan Chair of Programming and Information Technologies, YSU, Armenia
  • T.V. Khondkaryan Chair of Programming and Information Technologies, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2017.51.1.046

Keywords:

typed $\lambda$--term, untyped $\lambda$-term, translation, notion of $\delta$-reduction, $\lambda$-definability

Abstract

In the paper typed and untyped $\lambda$-terms are considered. Typed $\lambda$-terms use variables of any order and constants of order $\leq$1. Constants of order 1 are strong computable functions with indeterminate values of arguments and every function has an untyped $\lambda$-term that $\lambda$-defines it. The so-called canonical notion of $\delta$-reduction is introduced. This is the notion of $\delta$-reduction that is used in the implementation of functional programming languages. For the canonical notion of $\delta$-reduction the translation of typed $\lambda$-terms into untyped $\lambda$-terms is studied.

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Published

2017-03-20

How to Cite

Nigiyan, S., & Khondkaryan, T. (2017). ON CANONICAL NOTION OF $\delta$-REDUCTION AND ON TRANSLATION OF TYPED $\lambda$-TERMS INTO UNTYPED $\lambda$-TERMS. Proceedings of the YSU A: Physical and Mathematical Sciences, 51(1 (242), 46–52. https://doi.org/10.46991/PYSU:A/2017.51.1.046

Issue

Section

Informatics