From monolithic to modular formal specification

Formal specification using mathematical text provides a sound basis for developing complex systems, especially safety-critical systems. The paper discusses three formal specification styles for state-based systems from monolithic, through Z to modular each illustrated by the same simple example. In each case, formal text which is left implicit in practice is identified and discussed. The paper includes a denotational semantics for operations within a modular system, including their conjunctive, parallel, choice and sequential composition. The importance of extending the semantics to unwritten formal text implicit in Z and modular style specifications is emphasised because misinterpretation of the implicit can have serious consequences.