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  5. Verification of interpreters of algebraic operations in expansions of multi-sorted algebras

Verification of interpreters of algebraic operations in expansions of multi-sorted algebras

M.S. Lvov
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Development of algorithms of algebraic computations implementation is one of basic tasks, which arise up during realization of mathematical systems, based on symbolic transformations. The mathematical model of this task is multi-sorted algebraic systems. In this work, the approach to verification of interpreters of multi-sorted algebraic operations by their specifications, based on structural clarification of expansion concept of multi-sorted algebraic system and proving the axioms of algebraic system is considered. This approach is illustrated by the examples of verification of interpreters of operations of rational numbers field, polynomial of one variable and propositional algebra. The practice of the use of this approach at the mathematical systems development of the educational destination shows its efficiency and even universality.
Keywords: mathematical systems, symbolic transformations, multi-sorted algebraic systems, expansions of algebraic systems, verification, interpreters of algebraic operations