ON CANONICAL NOTION OF δ-REDUCTION AND ON TRANSLATION OF TYPED λ-TERMS INTO UNTYPED λ-TERMS - Nigiyan, S.A.; Khondkaryan, T.V. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2017)
In the paper typed and untyped λ-terms are considered. Typed λ-terms use variables of any order and constants of order ≤1. Constants of order 1 are strong computable functions 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 functional programming languages. For the canonical notion of δ-reduction the translation of typed λ-terms into untyped λ-terms is studied.