Propagation of constraints along model transformations using triple graph grammars and borrowed context

• We show how graph constraints can be propagated from one domain towards another.
• Validity of a source constraint leads to validity of the target constraint.
• MT based on TGGs with borrowed context allows to transform model fragments using partial matches.
• As main contribution, we study propagation of partial constraints (model fragments).
• One running example and one compact example in its own section illustrate the theory.

Fundamental properties of model transformations based on triple graph grammars (TGGs) have been studied extensively including syntactical correctness, completeness, termination and functional behavior. But up to now, it is an open problem how domain specific properties that are valid for a source model can be preserved along model transformations such that the transformed properties are valid for the derived target model. This question shows up in enterprise modeling. Here, modeling activities related to different domains are handled by different parties, and their models need to be consistent and integrated into one holistic enterprise model later on. So, support for decentralized modeling processes is needed. One technical aspect of the needed support in this case is the (bidirectional) propagation of constraints because that enables one party to understand and check the constraints of another party. Therefore, we analyze in the framework of TGGs how to propagate constraints from a source model to an integrated model and, afterwards, to a target model, such that, whenever the source model satisfies the source constraint, also the integrated and target model satisfy the corresponding integrated and target constraint. In our main new results we show under which conditions this is possible.