Refinement by interpretation in π-institutions

Abstract

The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of π-institutions. This leads to a smooth generalization of the "refinement by interpretation" approach, recently introduced by the authors in more specific contexts. As a second, yet related contribution a basis is provided to build up a refinement calculus of structured specifications in and across arbitrary π-institutions.

Hybrid Specification of Reactive Systems: An Institutional Approach

“…Less conventional approaches to refinement may help to overcome this sort of situations. A possibility we are currently investigating is to resort to logical interpretations, instead of signature morphisms, to direct refinement as studied by the authors in [15,14,22]. Interpretations are multi-functions between the specifications formulas which preserve and reflect logical consequence.…”

The role of logical interpretations in program development

“…This entails the need for further research on how refinement by interpretation, which is entirely based on properties of arbitrary deductive systems, can be smoothly combined with concrete specification structuring operations. Preliminary work on this topic is reported in [RMMB11] in which the emphasis is shifted to specifications. Current work in this direction includes the development of a refinement calculus of structured specifications over a π-institution.…”

“…Clearly, the approach proposed in this paper can be tuned to specification refinement in a strict sense. In a recent publication [RMMB11] we showed how refinement by interpretation can be lifted to the level of structured specifications with the usual operators mentioned above. We believe, however, that by focussing on classes of models this piece of research acquires a broader scope of application and is worth on its own.…”