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 Proceedings of the YSU, Physics & Mathematics, 2018, Volume 52, Issue 2, Pages 119–133 (Mi uzeru467)

Informatics

On interpretation of typed and untyped functional programs

S. A. Nigiyan

Chair of Programming and Information Technologies YSU, Armenia

Abstract: 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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Document Type: Article
MSC: 68N18
Language: English

Citation: S. A. Nigiyan, “On interpretation of typed and untyped functional programs”, Proceedings of the YSU, Physics & Mathematics, 52:2 (2018), 119–133

Citation in format AMSBIB
\Bibitem{Nig18} \by S.~A.~Nigiyan \paper On interpretation of typed and untyped functional programs \jour Proceedings of the YSU, Physics {\&} Mathematics \yr 2018 \vol 52 \issue 2 \pages 119--133 \mathnet{http://mi.mathnet.ru/uzeru467}