A NECESSARY AND SUFFICIENT CONDITION FOR THE UNIQUENESS OF $ \beta\delta $-NORMAL FORM OF TYPED $ \lambda $-TERMS FOR THE CANONICAL NOTION OF $ \delta $-REDUCTION
DOI:
https://doi.org/10.46991/PYSU:A/2019.53.1.028Keywords:
canonical notion of $ \delta $-reduction, $ \beta\delta $-reduction, $ \beta\delta $-normal formAbstract
In this paper the canonical notion of $ \delta $-reduction is considered. Typed $ \lambda $-terms use variables of any order and constants of order $ \leq 1 $, where the constants of order 1 are strongly computable, monotonic functions with indeterminate values of arguments. The canonical notion of $ \delta $-reduction is the notion of $ \delta $-reduction that is used in the implementation of functional programming languages. It is shown that for canonical notion of $ \delta $-reduction SI-property is the necessary and sufficient condition for the uniqueness of $ \beta\delta $-normal form of typed $ \lambda $-terms.
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