An algebraic formulation of knuthian semantics

This paper presents a formulation, within the framework of initial algebra semantics, of Knuthian semantic systems (K-systems) which contain both synthesized and inherited attributes. This formulation permits a precise definition of K-systems, and combines their intuitive appeal with the theoretical power of algebraic methods. The basic approach consists of algebraically specifying the semantic portion of a given K-system, converting this K-system into another equivalent one which contains only synthesized attributes, and then defining the new equivalent K-system by means of an algebraic formulation. The practical implications of the algebraic definition of K-systems are discussed, and the combined use of Knuth's original formulation and the algebraic approach for the development of semantic definitions is advocated.