Abstract Semantic Algebras

A new approach to the formal description of programming language semantics is described and illustrated. ''Abstract semantic algebras'' are just algebraically-specified abstract data types whose operations correspond to fundamental concepts of programming languages. The values of abstract semantic algebras are taken as meanings of programs in Denotational (or Initial Algebra) Semantics, instead of using Scott domains. This leads to semantic descriptions that clearly exhibit the underlying conceptual analysis, and which are rather easy to modify and extend. Some basic abstract semantic algebras corresponding to fundamental concepts of programming languages are given; they could be used in the description of many different programming languages.