Completeness and Correctness of Model Transformations based on Triple Graph Grammars with Negative Application Conditions

Model transformations are a key concept for modular and distributed model driven development. In this context, triple graph grammars have been investigated and applied to several case studies and they show a convenient combination of formal and intuitive specification abilities. Especially the automatic derivation of forward and backward transformations out of just one specified set of rules for the integrated model simplifies the specification and enhances usability as well as consistency. Since negative application conditions (NACs) are key ingredient for many model transformations based on graph transformation we embed them in the concept of triple graph grammars. As a first main result we can extend the composition/decomposition result for triple graph grammars to the case with NACs. This allows us to show completeness and correctness of model transformations based on rules with NACs and furthermore, we can extend the characterization of information preserving model transformations to the case with NACs. The presented results are applicable to several model transformations and in particular to the well known model transformation from class diagrams to relational data bases, which we present as running example with NACs.