Subtyping patterns for active objects

Subtyping relations for object-oriented formalisms describe relationships between superand subclasses which satisfy the substitutability requirement imposed on types and their subtypes. For active objects with an associated behaviour description subtyping relations also have to guarantee substitutability with respect to the dynamic behaviour of classes. In this paper, we give subtyping patterns for integrated object-oriented formalisms, that is, with a description of a static as well as a dynamic part. The patterns can be used to obtain subtypes by construction without computing the semantics of classes at all.