Geodesic
A necessary and sufficient condition for the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 28-36.

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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 $\beta\delta$-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.
Keywords: Canonical notion of $\delta$-reduction, $\beta\delta$-reduction, $\beta\delta$-normal form. 
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L. Budaghyan; D. A. Grigoryan; L. H. Torosyan. A necessary and  sufficient condition for the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 28-36. http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a4/

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