Wrapper semantics of an object oriented programming language with state

Recently, several descriptions of object oriented programming languages with denotational semantics have been given. Cook presented an intuitive denotational semantics of class inheritance. This semantics abstracts from the internal state of objects, which is one of their salient characteristics. In this paper we show that Cooks denotational semantics of class inheritance is applicable to object oriented programming languages, where objects have a state. For this purpose we define a direct denotational semantics of a small example language. The insertion of state into class definitions can be done before or after the related fixed point operations. The choice of the alternative considerably influences the semantic domains and clauses. We claim that despite the introduction of state the resulting denotational semantics is clear and intuitive