Detecting Isomorphisms of Modular Specifications with Diagrams

We propose to detect isomorphisms of algebraic modular speci cations, by representing speci cations as diagrams over a category C0 of base speci cations and speci cation morphisms. We start with a formulation of modular speci cations as terms, which are interpreted as diagrams. This representation has the advantage of being more abstract, i.e. less dependent of one speci c construction than terms. For that, we de ne a category diagr (C0) of diagrams, which is a completion of C0 with nite colimits. The category diagr (C0) is nitely cocomplete, even if C0 is not nitely cocomplete. We de ne a functor D[[]] : Term (C0)! diagr (C0) which maps speci cations to diagrams, and speci cation morphisms to diagram morphisms. This interpretation is sound in that the colimit of a diagram representing a speci cation is isomorphic to this speci cation. The problem of isomorphisms of modular speci cations is solved by detecting isomorphisms of diagrams.