Geodesic
On the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms for the canonical notion of $\delta$-reduction
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 37-46.

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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 $\leq1$, 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.
Keywords: Canonical notion of $\delta$-reduction, SI-property, $\beta\delta$-normal form. 
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D. A. Grigoryan. On the uniqueness of $\beta\delta$-normal form of typed $\lambda$-terms for the canonical notion of $\delta$-reduction. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 53 (2019) no. 1, pp. 37-46. http://geodesic.mathdoc.fr/item/UZERU_2019_53_1_a5/

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