GOTOs — A Study in the Algebraic Specification of Programming Languages (Extended Abstract)

Abstract

During recent years the concept of algebraic specification (cf. e.g. /Guttag 75/, /Burstall, Goguen 77/, /Goguen et al. 78/, /Wirsing et al. 80/) has proved to be a powerful and flexible tool for the formal definition of data structures. Algebraic concepts have also been employed for the specification of programming language semantics, e.g. first-order identities (/Wand 77/) or continuous algebras (/Courcelle, Nivat 78/, /Goguen et al. 77/). In contrast to these “explicit” constructions of semantics, /Broy, Wirsing 80a/ have introduced a technique for characterizing the semantic models of a language by the axioms of an algebraic type without resorting to (the isomorphism class of) a fixed model. This approach is characterized by the following peculiarities (cf. /Wirsing et al. 80/, /Broy, Wirsing 80c/): (1) As semantic models, finitely generated (cf. /Bauer, Wossner 81/) heterogeneous algebras with partial operations are considered. (2) Their properties are specified in algebraic types using positive conditional equations and a definedness predicate D on the terms of the type. (3) Within the equations, the metasymbol = is interpreted as strong equality, and D is total, so that the underlying logic remains two-valued. (4) In general, the types are hierarchical, i.e. a type may be based on a subtype which is considered as the specification of primitive objects and operations. Models of hierarchical types are required to preserve the properties of the primitive type.