Using the language Z for more than specification is hindered by the fact that its algebra of schemas is not monotonic with respect to refinement; so specification is modular, but development is not. In this paper we isolate the reasons why Z suffers from these problems and we describe alternative models for specifications and schema operations which are monotonic. This leads us to explore a number of theoretical and pragmatic questions: the former concern logics for modular refinement; the latter explore the use of novel schema calculi in practice.
Moshe Deutsch, Martin C. Henson, Besnik Kajtazi