# On Dependence of Interpretation Algorithms of Typed Functional Programs on Canonical Notion of δ-Reduction

## DOI:

https://doi.org/10.51408/1963-0013## Keywords:

Typed functional program, Canonical δ-reduction, Interpretation algorithm, ┴-dependency## Abstract

In this paper the interpretation algorithms of typed functional programs are considered. The interpretation algorithm is based on substitutions, β-reduction and canonical δ-reduction. The basic semantics of typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. If the value of the basic semantics for some values of arguments is indeterminate, then the interpretation algorithm either stops with the value ┴, or works endlessly. It is shown that seven known interpretation algorithms are ┴-depend on canonical notion of δ-reduction. Here are these algorithms: FS (of full substitution), PES (of parallel external substitution), LES (of left external substitution), PIS (of parallel inner substitution), LIS (of left inner substitution), ACT (active algorithm), PAS (passive algorithm).

## References

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S. A. Nigiyan, “On non-classical theory of computabilit", Proceedings of the YSU, Physical and Mathematical Sciences, no. 1, pp. 5-60, 2015.

S. A. Nigiyan and T. V. Khondkaryan, “On canonical notion of δ-reduction and on translation of typed λ-terms into untyped λ-term", Proceedings of the YSU, Physical and Mathematical Sciences, no. 1, pp. 4-52, 2017.

R. Yu. Hakopian, “On procedural semantics of strong typed functional programs", Proceedings of YSU, Natural Sciences, (in Russian), no. 3, pp. 59-69, 2008.

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*Mathematical Problems of Computer Science*,

*49*, 103–109. https://doi.org/10.51408/1963-0013

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