Geodesic
On canonical notion of $\delta$-reduction and on translation of typed $\lambda$-terms into untyped $\lambda$-terms
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 46-52

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In the paper typed and untyped $\lambda$-terms are considered. Typed $\lambda$-terms use variables of any order and constants of order $\leq1$. Constants of order $1$ are strong computable functions with indeterminate values of arguments and every function has an untyped $\lambda$-term that $\lambda$-defines it. The so-called canonical notion of $\delta$-reduction is introduced. This is the notion of $\delta$-reduction that is used in the implementation of functional programming languages. For the canonical notion of $\delta$-reduction the translation of typed $\lambda$-terms into untyped $\lambda$-terms is studied.
Keywords: typed $\lambda$-term, untyped $\lambda$-term, translation, notion of $\delta$-reduction, $\lambda$-definability. 
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S. A. Nigiyan; T. V. Khondkaryan. On canonical notion of $\delta$-reduction and on translation of typed $\lambda$-terms into untyped $\lambda$-terms. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 1, pp. 46-52. http://geodesic.mathdoc.fr/item/UZERU_2017_51_1_a8/