Formalising model transformation rules for UML/MOF 2

Model-driven software development, today's state-of-the-art approach to the design of software, can be applied in various domains and thus demands a variety of domain-specific modelling languages. The specification of a domain-specific modelling language's syntax and semantics can in turn be specified based on models, which represent the approach of metamodelling as a special form of language engineering. The latest version of the unified modelling language 2 (UML 2) and its subset the meta object facility 2 (MOF 2) provide sufficient support for metamodelling, a modelling language's abstract syntax. Furthermore, based on the description of the abstract syntax, a language's static semantics can simply be specified by the object constraint language (OCL) as UML/MOF's natural constraint language, whereas the description of an MOF compliant language's dynamic semantics is still not covered. The authors try to close this gap by integrating MOF/OCL with graph transformations for the specification of dynamic aspects of modelling languages and tools. The formalisation of such an integration is non-trivial because of the fact that UML/MOF 2 offer a rather unusual and sophisticated association concept (graph model). Although there are many approaches, which formalise graph transformations in general and first approaches that offer a precise specification of the semantics of the association concepts of UML/MOF 2, there is still a lack in bringing both together. Here, the authors close this gap by formalising graph transformations that work on a UML/MOF 2 compatible graph model.