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 incrementality. In order to accomodate this diversity of formalisms, some authors have proposed the adoption of a common semantic domain for the different specification languages, and their translation 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 formalized 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 formalizing reusability as a property of a functor relating two such formalisms.