Superposing UML class diagrams

There is a close connection between superposition-based design and aspect-orientation [6, 7, 10]. In [11] three steps were identi ed when composing modules describing overlapping concerns: matching units describing the same concepts, reconciliation of their possible di erences, and integration of the units. These problems, as well as many concerning distribution, have already been studied in the context of superposition. A superposition step maps a speci cation into a new, augmented speci cation which is a renement of the original speci cation. The step describes cross-cutting concerns with respect to the module structure of the original speci cation. Moreover, in general, superposition steps are reusable design modules not speci c to some particular design. The original speci cation itself can be constructed using superposition. This leads to a speci cation process which is started with a superposition step mapping an empty speci cation to an initial speci cation. Subsequent steps may re ne the same speci cation to di erent augmented ones, resulting in separate branches of the speci cation. The branches correspond to di erent overlapping concerns, or aspects. This results in an aspect-oriented speci cation architecture comprised of the aspects built from superposition steps. The process can be formalized and composition of speci cation branches can be automated. However, the level of automation is governed by the rules of the superposition, i.e. how the mapping is restricted. The restrictions also dictate what properties of the original speci cation are preserved in the re ned one. Earlier work on superposition has focused on