Modular refinement in novel schema calculi

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. 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.