. This paper is the result of a reflexion coming from the usage and learning of the language B. It tries to better explain and understand the assembly primitives includes and uses of the language. It presents a high-level notion of components and develops a "component algebra". This algebra is specialized to deal with the B-components. The B assembly primitives are re-expressed in this basic formalism. Some problems about independence of concepts in the B methodology are pointed out and are discussed. 1 Introduction Specifications, like programs, must be modular because very large formal texts are not understandable for a human being. So, the study of modules and modularization is one of the issues in software engineering. The three main objectives of modularization [BHK90] are : information hiding, compositionality of module operations and reusability of modules. If the specification methodology encompasses the need for formal proofs to ensure consistency, as it is the case in the B ...

: 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...