Horizontal composability revisited

Donald Sannella

Andrzej Tarlecki

pp. 296-316

in: Kokichi Futatsugi, Jean-Pierre Jouannaud, José Meseguer (eds), Algebra, meaning, and computation, Berlin, Springer, 2006

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.