Computer Science Logic and 8th Kurt Gödel Colloquium
Bernhard Reus: Modular Semantics and Logics of Classes
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Denotational semantics for class-based languages is usually defined w.r.t. an environment of method suites obtained a ``global'' fixpoint. This reflects a closed world assumption. Once the semantics of a package of classes is computed it is impossible to add other classes in a compositional way.

In this paper we improve standard class-based semantics to obtain compositionality and modular reasoning principles for a logic of classes. The domain theoretic reasoning principle that drives this logic 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''. A mutual fixpoint establishes the link between old classes and new class.

One major advantage is that the method suites of classes can be kept separate from the heap that contains the objects' fields, avoiding the complications of higher-order store inherent in object-based languages. Local class definitions (inner classes) are possible but on-the-fly class-loading needs more advanced techniques.
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