The author here continues his long-term project of trying to improve the modularity, modifiability, and comprehensibility of semantic descriptions by the use of “abstract semantic algebras” (i.e., axiomatically-specified algebraic structures whose models are domains of denotations and (continuous) operations on them, such as sequential composition). After some introductory material, this paper goes on to specify a basic semantic algebra which provides a basis for several extensions suitable for describing separate orthogonal facets of programming languages: functional, imperative, declarative, and so on. The problem of developing systematic ways of combining such various single-facet specifications is left to future work.

The paper concludes by sketching a demonstration of the correctness of one of the abstract specifications. This involves giving a concrete model of the axioms to show consistency and then proving limiting-completeness, a concept introduced by Wadsworth [1]. A set of axioms is limiting-complete relative to a model when they imply the validity of rewrite rules (which have the property that the denotation of a phrase is the limit of the denotations of its partial unfoldings). The details of these arguments are to appear in an expanded version of the paper.