Modular semantics and logics of classes

The semantics of class-based languages can be defined in terms of objects only [1, 7, 8] if classes are viewed as objects with a constructor method. One obtains a store in which method closures are held together with field values. Such a store is also called "higher-order" and does not come for free [13]. It is much harder to prove properties of such stores and as a consequence (soundness of) programming logics can become rather contrived (see [2]). A simpler semantics separates methods from the object store [4,12]. But again, there is a drawback. Once the semantics of a package of classes is computed it is impossible to add other classes in a compositional way. Modular reasoning principles are therefore not obtainable either. In this paper we improve a simple class-based semantics to deal with extensions compositionally and derive modular reasoning principles for a logic of classes. The domain theoretic reasoning principle behind this is fixpoint induction. Modularity is obtained by endowing the denotations of classes with an additional parameter that accounts for those classes added "later at linkage time." Local class definitions (inner classes) are possible but for dynamic class-loading one cannot do without higher-order store.