2012•Formalized MathematicsOpen access

Program Algebra over an Algebra

Grzegorz Bancerek

Abstract

Summary We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms.

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Key concepts: Algebra over a field, Term algebra, Filtered algebra, Mathematics, Cellular algebra, Division algebra, Algebra representation, Symmetric algebra