Formal Analysis of Functional Behaviour for Model Transformations Based on Triple Graph Grammars - Extended Version

Triple Graph Grammars (TGGs) are a well-established concept for the specification of model transformations. In previous work we have formalized and analyzed already crucial properties of model transformations like termination, correctness and completeness, but functional behaviour - especially local confluence - is missing up to now. In order to close this gap we generate forward translation rules, which extend standard forward rules by translation attributes keeping track of the elements which have been translated already. In the first main result we show the equivalence of model transformations based on forward resp. forward translation rules. This way, an additional control structure for the forward transformation is not needed. This allows to apply critical pair analysis and corresponding tool support by the tool AGG. However, we do not need general local confluence because confluence for source graphs not belonging to the source language is not relevant for the functional behaviour of a model transformation. For this reason we only have to analyze a weaker property, called translation confluence. This leads to our second main result, the functional behaviour of model transformations, which is applied to our running example, the model transformation from class diagrams to database models.