Semantics of Temporal Classes

A model theory of a typed, declarative, temporal object-oriented language system is presented. The declarative nature of the language makes it very different from the dominating procedural, strongly typed object-oriented programming languages. In this declarative system, methods are specified in a high-level, temporal constraint language. Two fundamental properties of these constraints are that they have an execution model and algebraic semantics. The model theory is based on temporal order-sorted algebras with predicates. A variety of orderings are explored in order to represent various types of inheritance, as well as the subtyping discipline. Temporal classes are viewed as temporal theories and some inheritance relationships as morphisms of temporal theories. A model of a temporal class is a temporal order-sorted structure with predicates which satisfies a set of temporal constraints specified in that class. Morphisms of those models are naturally required to preserve type coercions. A distinguished model of a temporal theory is constructed as a colimit of a suitably defined functor. This colimit construction reflects the temporal nature of the paradigm and generalizes the classical initial algebra semantics. In contradistinction to major difficulties in developing a model theory for full-fledged, typed procedural object-oriented languages, this paper shows that such a task becomes possible for a suitably defined declarative object-oriented language. This, in particular, leads to model-theoretic results on the preservation of the behavioral properties in the inheritance hierarchies. ] 2000 Academic Press