Weak Reenement in Z

An important aspect in the speciication 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 speciication notation, then reenement needs to deal with internal operations in appropriate ways. However, in the presence of internal operations, standard Z reenement leads to undesirable implementations. In this paper we present a generalization of Z reenement, called weak reenement, which treats internal operations diierently from observable operations when reening a system. We illustrate some of the properties of weak reenement through a speciication of a telecommunications protocol.