Primitive Programing Algebra of Computable Functions at Records

Тарас Леонідович Захарченко, Дмитро Ігорович Редько, Ігор Володимирович Редько, Петро Олексійович Яганов

Abstract


Background. The research is conducted in the context of compositional approach to programming. Problematic of the research is development of scientific foundations of programmer’s problems solution genesis. Its basis is concept of composition.

Objective. The objective of the research is general method development for function classes’ algebraic characteristics obtaining and application of the method for description of pragmatically important class of partially recursive functions on records.

Methods. Creations made in the paper are based on software analysis algebraic methods and compositional programming methodic. Problems of computable functions’ characteristics obtaining, problems of generative sets and bases finding, which are one of the most important questions in programmer’s problematic, are strictly stated and solved in the context of so called “program algebras”.

Results. In the paper method of mentioned problems solution was proposed in context of primitive program algebras (PPA) on different classes of computable functions. Received results are stated as sequence of original statements, lemmas, and theorems. They can be used for different classes of computable functions algebraic characteristics exploration in problems of programming languages semantics formalization.

Conclusions. Received results are foundations of adaptive programming environments development. Next steps in this direction will be connected with exploration of general concept of composition and development of related reduction methods of function exploration as environments of pragmatic depended programmer’s problems decomposition.

Keywords


Fullness of calculable functions; Fullness problem in PPA; Complete system; Pairs of natural numbers; Pr-functions; Pr-predicates

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DOI: https://doi.org/10.20535/1810-0546.2015.2.91092

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