An algebraic approach to semantics of programming languages

AbstractAn abstract language for a computer of von Neumann type is presented. This language is considered not only as a programming language, but as an algebraic one, whose semantics is defined by methods of model theory. Calculus of equivalencies of the abstract programs and techniques for solving equations within limits of this calculus are presented. An algebraic technique is described which allows to define the propositional semantics of programs. To construct such techniques it was necessary to use the data type representation by continuous lattices and the continuity of type and intertype operations and elementary relations. It is demonstrated how the proposed algebraic technique may be used