Horizontal Composability Revisited

Abstract

Abstract. We recall the contribution of Goguen and Burstall's 1980 CAT paper and its powerful influence on theories of specification implementation that were emerging at about the same time, via the introduction of the notions of vertical and horizontal composition of implementations. We then give a different view of implementation which we believe provides a more adequate reflection of the rather subtle interplay between implementation, specification structure and program structure.

The Foundational Legacy of ASL

“…The requirement of horizontal composition is missing a way of distinguishing between, on the one hand, the structure of the requirements specification used to facilitate its construction and understanding, and on the other hand, binding decisions made during the development process concerning the structure of the realisation. The latter fixes the design of the system architecture, and horizontal composition with respect to this structure is what really matters, see [ST06]. CASL [BM04] provides a way to capture designs of system architecture in the form of architectural specifications [BST02].…”

The role of logical interpretations in program development

“…Deductive systems, the basic tool in our approach, correspond to such classes. This means that the whole area of specification structuring [ST06] is, for the moment, left out. Our approach is not concerned with the fact that specifications describing the relevant classes of models are flat, i.e.…”