Abstract

In this paper we study the problem of semantic substitutability of objects. First we give semantics of classes, objects and inheritance in the presence of dynamic binding. For this purpose we extend Cook and Palsberg's denotational semantics of stateless classes and inheritance by adding state. We build our theory on the basis of the refinement calculus, which is a logic framework for reasoning about conformance of programs to their specifications and program refinement. We derive class refinement from the notion of abstract data type refinement as a criterion of object substitutability. We illustrate our model of classes and objects with an example and show how refinement between classes can be proved in practice.

Citations