A Proved Approach for Building Correct Instances of UML Associations: Multiplicities Satisfaction

In UML modeling, class diagrams permit to capture the entities involved in a system but also the associations they have with each other. These associations are characterized by a multiplicity on each role to state the min-max number of instances of the opposite class that can be linked to each instance of the class associated with the role. Since these multiplicities may be conflicting, it becomes necessary to check the global consistency of a class diagram. Such verification will ensure that it is possible to find an instantiation of the diagram that satisfies all the multiplicities. In this paper, we describe an automatized approach that permits to validate a class diagram by exhibiting a particular instance. Basically, this approach proceeds in two main steps: first, the multiplicities are represented as a mathematical model, then a constraint solver is used to determine whether it has at least one solution. The correctness of the approach, which is supported by an automatic tool, has been carried out using the B formal method.