ON CANONICAL NOTION OF δ-REDUCTION AND ON TRANSLATION OFTYPEDλ-TERMS INTO UNTYPED λ-TERMS

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ON CANONICAL NOTION OF δ-REDUCTION AND ON TRANSLATION OFTYPEDλ-TERMS INTO UNTYPED λ-TERMS Tigran Khondkaryan

In the paper typed and untyped λ-terms are considered. Typed λ-terms use variablesof any order and constants of order ≤1. Constants of order 1 are strong computablefunctions with indeterminate values of arguments and every function has an untyped λ-term that λ-defines it. The so-called canonical notion of δ-reduction is introduced.This is the notion of δ-reduction that is used in the implementation of functionalprogramming languages. For the canonical notion of δ-reduction the translation of typed λ-terms into untyped λ-terms is studied.

DOI: 10.46991/PYSU:A/2017.51.1.046 Physical and Mathematical Sciences, 51(1 (242) 46-52

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Keywords

typed λ-term, untyped λ-term, translation, notion of δ-reduction, λ-definability

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