Class Diagrams with Equated Association Chains

We investigate properties of class diagrams with multiplicity constraints - as they appear e.g. in model-based engineering or database design - augmented by equational constraints on association chains. Constraints are typically used to generate additional code that throws an exception when a constraint is violated during run-time. Our aim is different: We develop methods to check already at modelling time whether all constraints can be satisfied, to provide suitable user feedback, and to compute optimal instances of the model. In this paper we extend our approach by a family of constraints that has proven relevant in practice, namely equations between chains of associations. Such equational constraints are necessary if we want to specify that the objects reachable via one chain of associations should in fact be the same as reachable via another one.