. We propose to detect isomorphisms of algebraic modular specifications, by representing specifications as diagrams over a category C0 of base specifications and specification morphisms. We start with a formulation of modular specifications as terms, which are interpreted as diagrams. This representation has the advantage of being more abstract, i.e. less dependent of one specific construction than terms. For that, we define a category diagr (C0) of diagrams, which is a completion of C0 with finite colimits. The category diagr (C0) is finitely cocomplete, even if C0 is not finitely cocomplete. We define a functor D[[]] : Term (C0) ! diagr (C0) which maps specifications to diagrams, and specification morphisms to diagram morphisms. This interpretation is sound in that the colimit of a diagram representing a specification is isomorphic to this specification. The problem of isomorphisms of modular specifications is solved by detecting isomorphisms of diagrams. 1 Introduction The specif...

: The composition of modular specifications can be modeled, in a category theoretic framework, by colimits of diagrams. Pushouts in particular describe the combination of two specifications sharing a common part. This work extends this classic idea along three lines. First, we define a term language to represent modular specifications built with colimit constructions over a category of base specifications. This language is formally characterized by a finitely cocomplete category. Then, we propose to associate with each term a diagram. This interpretation provides us with a more abstract representation of modular specifications because irrelevant steps of the construction are eliminated. We define a category of diagrams, which is a completion of the base category with finite colimits. We prove that the interpretation of terms as diagrams defines an equivalence between the corresponding categories, which shows the correctness of this interpretation. At last, we propose an algorithm to no...