ON THE UNIQUENESS OF $ \beta\delta $-NORMAL FORM OF TYPED $ \lambda $-TERMS FOR THE CANONICAL NOTION OF $ \delta $-REDUCTION

Abstract

In this paper we consider a substitution and inheritance property, which is the necessary and sufficient condition for the uniqueness of $ \beta\delta $-normal form of typed $ \lambda $-terms, for canonical notion of $ \delta $-reduction. 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.