Interconnecting formalisms: supporting modularity, reuse and incrementality

The necessity to deal simultaneously with different formalisms seems to be intrinsic to the discipline of Software Engineering, particularly in relation to modularity, reusability and incremental ity. In order to accommodate this diversity of formalisms, some authors have proposed the adoption of a common semantic domain for the different specification languages, and their transla tion into a common style of predicate logic. In this paper, we suggest that an alternative approach may be taken where the different modelling approaches are formalised individually in a common mathematical framework – Category Theory, and relationships are established between them using functors. Several examples are adduced to support this view and the generality of the approach is illustrated by formalising reusability as a property of a functor relating two such formalisms.