Triple Patterns: Compact Specifications for the Generation of Operational Triple Graph Grammar Rules

Triple Graph Grammars (TGGs) allow the specification of high-level rules modelling the synchronized creation of elements in two graphs related through a correspondence graph. Low-level operational rules are then derived to manipulate concrete graphs. TGGs are increasingly proposed as a way to specify model transformation, e.g. to perform bidirectional (possibly incremental) translations between different modelling languages, or to check the validity of the relations in the correspondence graph. However, TGG rules may become unnecessarily verbose, e.g. when elements have to be replicated from one graph to the other, and their actual derivation cannot exploit the presence of reoccurring patterns. Moreover they do not take advantage from situations in which a normal creation grammar for one of the graphs exists, from which a set of TGG operational rules can be derived to build the other graph. We present an approach to generating TGG operational rules from normal ones, reducing the information needed to derive them, through the definition of {\em Triple Patterns}, a high-level, compact, declarative, and visual notation for the description of admissible structures in a triple graph. Patterns can be expressed with respect to classes defined in a meta-model, and instantiated with derived classes at the model level, thus exploiting the inheritance hierarchies. The application of the generated rules results into the (synchronized or batch) creation of the structures specified in the patterns. We illustrate these concepts by showing their application to the synchronized incremental construction of visual models and of their semantics.