Geodesic
On translation of typed functional programs into untyped functional programs
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 177-186.

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In this paper typed and untyped functional programs are considered. Typed functional programs use variables of any order and constants of order $\leq1$, where constants of order $1$ are strong computable, $\lambda$-definable functions with indeterminate values of arguments. The basic semantics of a typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. The basic semantics of an untyped functional program is an untyped $\lambda$-term, which is defined by means of a fixed point combinator. An algorithm that translates typed functional program $P$ into untyped functional program $P'$ is suggested. It is proved that the basic semantics of the program $P'$ $\lambda$-defines the basic semantics of the program $P$.
Keywords: typed functional program, untyped functional program, basic semantics, translation, $\lambda$-definability. 
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S. A. Nigiyan; T. V. Khondkaryan. On translation of typed functional programs into untyped functional programs. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 177-186. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a5/

[1] S. A. Nigiyan, “Functional Programming Languages.”, Programming and Computer Software, 1991, no. 5,, 77–86 | Zbl

[2] S. A. Nigiyan, “On Interpretation of Functional Programming Languages.”, Programming and Computer Software, 19:2 (1993), 71–78 | MR | Zbl

[3] S. A. Nigiyan, “On Non-classical Theory of Computability”, Proceedings of the YSU. Physical and Mathematical Sciences, 2015, no. 1, 52–60 | Zbl

[4] H. Barendregt, The Lambda Calculus. Its Syntax and Semantics, North-Holland Publishing Company, 1981 | MR | Zbl

[5] S. A. Nigiyan, S. A. Avetisyan, “Semantics of Untyped Functional Programs”, Programming and Computer Software, 28:3 (2002), 119–126 | DOI | MR | Zbl

[6] G. G. Hrachyan, “On Basic Semantics of Untyped Functional Programs”, Programming and Computer Software, 35:3 (2009), 121–135 | DOI | MR | Zbl

[7] L. E. Budaghyan Formalizing the Notion of $\delta$-Reduction in Monotonic Models of Typed $\lambda$-Calculus, Algebra, Geometry $\$ Their Applications, 1 (2002), 48–57 | MR

[8] 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 YSU. Physical and Mathematical Science, 51:1 (2017), 46–52