Compositionality of Model Transformations

Model transformations can be used not only for code or platform-specific model generation, but also for denotational semantics definition, e.g. using process algebras as semantics for visual modeling languages.Denotational semantics of programming languages are by definition compositional. In order to enjoy a similar property in the case of model transformations, every component of the source model should be distinguishable in the target model and the mapping compatible with syntactic and semantic composition. Since typed graphs are a natural representation of visual models, model transformations are often described by typed graph transformations. This paper proposes a formal definition of compositionality for mappings from typed graphs to semantic domains. To verify compositionality, syntactic criterion has been established for the implementation of the mappings by graph transformations with negative application conditions.An example compositional transformation is presented that maps architectural models described in UML component diagrams to CSP.