Weak refinement in Z

An important aspect in the specification of distributed systems is the role of the internal (or unobservable) operation. Such operations are not part of the user interface (i.e. the user cannot invoke them), however, they are essential to our understanding and correct modelling of the system. Various conventions have been employed to model internal operations when specifying distributed systems in Z. If internal operations are distinguished in the specification notation, then refinement needs to deal with internal operations in appropriate ways. However, in the presence of internal operations, standard Z refinement leads to undesirable implementations.

In this paper we present a generalization of Z refinement, called weak refinement, which treats internal operations differently from observable operations when refining a system. We illustrate some of the properties of weak refinement through a specification of a telecommunications protocol.