Coupling Schemas: Data Refinement and View(point) Composition

We define the notion of a coupling schema in Z, and describe the role it plays in data refinement, view composition, and viewpoint unification. In each case coupling schemas relate several state schemas. In data refinement they occur as retrieve relations (abstraction schemas). In specification by views, coupling schemas provide a link between the various views. For viewpoint specification, coupling schemas are closely related to correspondence relations between state schemas in the viewpoints. Simple properties of coupling schemas (e.g. totality, functionality, and consistency) are shown to have important consequences in the techniques listed, and to be very useful for exhibiting the relations between these techniques. It turns out that views and viewpoints can both be seen as variations on, or even as generalisations of, data refinement.