Relating Abstract Datatypes and Z-Schemata

In this paper we investigate formally the relationship between the notion of abstract datatypes in an arbitrary institution, found in algebraic specification languages like Clear, ASL, and CASL; and the notion of schemata from the model-oriented specification language Z. To this end the institution S of the logic underlying Z is defined, and a translation of Z-schemata to abstract datatypes over S is given. The notion of a schema is internal to the logic of Z, and thus specification techniques of Z relying on the notion of a schema can only be applied in the context of Z. By translating Z-schemata to abstract datatypes, these specification techniques can be transformed to specification techniques using abstract datatypes. Since the notion of abstract datatypes is institution independent, this results in a separation of these specification techniques from the specification language Z and allows them to be applied in the context of other, e.g. algebraic, specification languages.