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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     title = {On translation of typed functional programs into untyped functional programs},
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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/