Geodesic
On interpretation of typed and untyped functional programs
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 2, pp. 119-133

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In this paper the interpretation algorithms for typed and untyped functional programs are considered. Typed functional programs use variables of any order and constants of order $\leq 1$, where constants of order $1$ are strongly computable, monotonic functions with indeterminate values of arguments. The basic semantics of the typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. The interpretation algorithms of typed functional programs are based on substitutions, $\beta$-reduction and canonical $\delta$-reduction. The basic semantics of the untyped functional program is the untyped $\lambda$-term, which is defined by means of the fixed point combinator. The interpretation algorithms of untyped functional programs are based on substitutions and $\beta$-reduction. Interpretation algorithms are examined for completeness and comparability. It is investigated how the “behavior” of the interpretation algorithm changes after translation of typed functional program into untyped functional program.
Keywords: typed functional program, untyped functional program, basic semantics, interpretation algorithm, completeness, comparability, translation. 
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     title = {On interpretation of typed and untyped functional programs},
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S. A. Nigiyan. On interpretation of typed and untyped functional programs. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 52 (2018) no. 2, pp. 119-133. http://geodesic.mathdoc.fr/item/UZERU_2018_52_2_a6/