On the Relationship of Model Transformations Based on Triple and Plain Graph Grammars (Long Version)

Triple graph grammars have been applied and implemented as a formal basis for model transformations in a variety of application areas. They convince by special abilities in automatic derivation of forward, backward and several other transformations out of just one specified set of rules for the integrated model defined by a triple of graphs. While many case studies and all implementations, which state that they are using triple graph grammars, do not use triples of graphs, this paper presents the justification for many of them. It shows a one to one correspondence between triple graph grammars and suitable plain graph grammars, thus results and benefits of the triple case can be transferred to the plain case. Main results show the relationship between both graph transformation approaches, syntactical correctness of model transformations based on triple graph grammars and a sound and complete condition for functional behaviour. Theoretical results are elaborated on an intuitive case study for a model transformation from class diagrams to database models