Formal Analysis of Model Transformations Based on Triple Graph Rules with Kernels

Abstract

Triple graph transformation has become an important approach for model transformations. Triple graphs consist of a source, a target and a connection graph. The corresponding rules also contain these parts and describe the simultaneous construction of both the source and the target model. From these rules, forward rules can be derived which describe the model transformation from a given source model to a target model. The forward transformation must be source consistent in order to define a valid model transformation. Source consistency implies that the source and the target model correspond to each other according to a triple transformation.

In this paper, the relationship between the source consistency of forward transformations, and NAC consistency and termination used in other model transformation approaches is analysed from a formal point of view. We define the kernel of a forward rule and construct NACs based on this kernel. Then we give sufficient conditions such that source consistency implies NAC consistency and termination. Moreover, we analyse how to achieve local confluence independent of source consistency. Both results together provide sufficient conditions for functional behaviour of model transformations. Our results are illustrated by an example describing a model transformation from activity diagrams to CSP.