Behavioural Subtyping and Property Preservation for Objects Oriented Formalisms

Behavioural typing and subtyping has proved to be a very useful concept for the support of incremental reuse in the area of object-oriented (O-O) languages. With the emergence of formalisms integrating the O-O approach and concurrency, the question arises how behavioural subtyping may be supported by such formalisms. We present a formal framework for the definition of behavioural subtyping in O-O concurrent systems. This framework is based upon the preorder relations which are considered in the study of concurrent systems, allowing to define various subtyping relations. We investigate the property preservation to the degree of change of these subtyping relations, safety and liveness properties are preserved up to different extents.