Pattern Matching In Metamodel-Based Model Transformation Systems

The vision of the OMG's Model-Driven Architecture (MDA) has necessitated the extensive research of model compilers, which are able to process graph-based visual models specified mainly in the Unified Modeling Language (UML). A possible mechanism for the realization of MDA model compilers can be graph rewriting-based transformation approach. Previous work has introduced the tool Visual Modeling and Transformation System, which uses graph rewriting as transformation mechanism, but the pattern language of the rewriting rules consists of UML class diagram elements instead of object diagram level patterns. This paper provides the algorithmic background for the application of these rules specified by the class diagram elements. To achieve that, it examines the allowed instantiation configuration based on the UML standard, and supplies a constructive algorithm to compute the allowed number of the objects participating in a valid instantiation of a class model. Furthermore, starting from the VF2 algorithm, the pattern matching algorithm for the left hand side of the metamodel-based rewriting rule is provided via several optimization steps examined.