Abstract

Compositional design is concerned with both constructing systems by composing components and with deconstructing systems into proposed sets of components. In bottom-up design, engineers prove system properties given properties of components and a compositional structure. In top-down design, they propose properties of components and a compositional structure given system properties. In this paper we show how the theory of predicate transformers, which has been used so successfully in sequential programming, can be applied to compositional design of systems. The rules of composition we study are more general than the rules employed in sequential programming, and the systems we study are not limited to programs. We exploit theorems about weakest and strongest solutions to equations to obtain a collection of useful predicate transformers, and then we exploit the theory of conjugate transformers to obtain more useful transformers. We show how these transformers are useful fo...

Citations