Open AccessOn Dependence of Interpretation Algorithms of Typed Functional Programs on Canonical Notion of δ-Reduction
Author(s) -
D.A. Grigoryan
Publication year - 2015
Publication title -
mathematical problems of computer science
Language(s) - English
Resource type - Journals
eISSN - 2738-2788
pISSN - 2579-2784
DOI - 10.51408/1963-0013
Subject(s) - substitution (logic) , interpretation (philosophy) , algorithm , reduction (mathematics) , semantics (computer science) , abstract interpretation , value (mathematics) , computer science , indeterminate , basis (linear algebra) , mathematics , function (biology) , pure mathematics , programming language , machine learning , geometry , evolutionary biology , biology
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).