Behavioral Subtyping Relations for Active Objects*

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In this paper we investigate the object-oriented notion of subtyping in the context of behavioral formalisms. Behavioral formalisms are used to describe the dynamic behavior of active objects, viz. the protocols of interaction that active objects have to obey.Subtyping in OO-formalisms is closely related to the concept of inheritance. The central issue in the choice of subtyping relations among classes is the principle of substitutability: an instance of the subtype should be usable wherever an instance of the supertype was expected. Depending on the interpretation of “usable”, we obtain a variety of subtyping relations: stronger relations, allowing sharing of subtype instances among different clients, and weaker relations, restricting the possibilities of interference of different clients on the subtype instance. The subtyping relations are taxonomically ordered in a hierarchy. Substitutability is formalized via testing scenarios, which provide alternative characterizations for the subtyping relations.

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