# Etude des spécifications modulaires : constructions de colimites finies, diagrammes, isomorphismes

Abstract : The composition of modular specifications can be modeled, in a category theoretic framework, by means of colimits of diagrams. Pushouts in particular allow us to gather two specifications sharing a common part. Our work extends this classic idea along three lines. From a syntactic point of view, we define a language to represent modular specifications built from a category of base specifications and base specification morphisms. This language is formally characterized by a finitely cocomplete category of terms. From a semantic point of view, we propose to associate with each term a diagram. This interpretation allows us to abstract some choices made while constructing a modular specification. We thus define a concrete'' category of diagrams, in which arrows can actually be handled. Considering the quotient by a certain congruence relation, we get a completion of the base category with finite colimits. We prove that this calculus defines an equivalence between the category of terms and the category of diagrams, which shows the soundness of this interpretation. At last, we propose an algorithm to decide whether two diagrams are isomorphic, when the base category is finite and cycle free. This allows us to detect construction isomorphisms'' between modular specifications, i.e. isomorphisms which do not depend on the base specifications, but only on their combination.
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Submitted on : Monday, February 23, 2004 - 5:07:56 PM
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• HAL Id : tel-00005007, version 1

### Citation

Catherine Oriat. Etude des spécifications modulaires : constructions de colimites finies, diagrammes, isomorphismes. Autre [cs.OH]. Institut National Polytechnique de Grenoble - INPG, 1996. Français. ⟨tel-00005007⟩

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