2019; Physical and Mathematical Sciences, 53(1 (248): 28–36
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A NECESSARY AND SUFFICIENT CONDITION FOR THE UNIQUENESSOFβ δ-NORMAL FORM OF TYPEDλ-TERMS FOR THE CANONICALNOTION OFδ-REDUCTION

David GRIGORYAN*

Received: 2025-01-30 · Published: 2019-04-15

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CC BY-NC 4.0 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Original title
A NECESSARY AND SUFFICIENT CONDITION FOR THE UNIQUENESSOFβ δ-NORMAL FORM OF TYPEDλ-TERMS FOR THE CANONICALNOTION OFδ-REDUCTION
Author
David GRIGORYAN
Published
2019-04-15
Licence
Creative Commons Attribution-NonCommercial 4.0 International
Original
https://doi.org/10.46991/PYSU:A/2019.53.1.028

Abstract

n this paper the canonical notion ofδ-reduction is considered. Typedλ-terms use variables of any order and constants of order≤1, where theconstants of order 1 are strongly computable, monotonic functions with indeter-minate values of arguments. The canonical notion ofδ-reduction is the notionofδ-reduction that is used in the implementation of functional programminglanguages. It is shown that for canonical notion ofδ-reduction SI-property isthe necessary and sufficient condition for the uniqueness ofβ δ-normal form oftypedλ-terms.
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