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Model synchronization, i.e., the task of restoring consistency between two interrelated models after a model change, is a challenging task. Triple Graph Grammars (TGGs) specify model consistency by means of rules that describe how to create consistent pairs of models. These rules can be used to automatically derive further rules, which describe how to propagate changes from one model to the other or how to change one model in such a way that propagation is guaranteed to be possible. Restricting model synchronization to these derived rules, however, may lead to unnecessary deletion and recreation of model elements during change propagation. This is inefficient and may cause unnecessary information loss, i.e., when deleted elements contain information that is not represented in the second model, this information cannot be recovered easily. Short-cut rules have recently been developed to avoid unnecessary information loss by reusing existing model elements. In this paper, we show how to automatically derive (short-cut) repair rules from short-cut rules to propagate changes such that information loss is avoided and model synchronization is accelerated. The key ingredients of our rule-based model synchronization process are these repair rules and an incremental pattern matcher informing about suitable applications of them. We prove the termination and the correctness of this synchronization process and discuss its completeness. As a proof of concept, we have implemented this synchronization process in eMoflon, a state-of-the-art model transformation tool with inherent support of bidirectionality. Our evaluation shows that repair processes based on (short-cut) repair rules have considerably decreased information loss and improved performance compared to former model synchronization processes based on TGGs., 33 pages, 20 figures, 3 tables

A variety of restricted functor categories has been investigated independently and for different purposes to provide double-pushout-rewriting in the areas of model-driven development and graph transformation. We introduce S-cartesian functor categories as a unifying formal framework for these different examples. S-cartesian functor categories are certain subcategories of functor categories that preserve the adhesiveness of their base categories. We show the comprehensive theory of double-pushout-rewriting for S-cartesian functor categories which fulfill additional sufficient conditions. As a new application, we introduce the categories PTrG and APTrG of partial triple graphs and attributed partial triple graphs as S-cartesian functor categories and obtain all the classical results for double-pushout-rewriting in these categories by construction. Partial triple graphs have recently been used to improve model synchronization processes.

Synchronization and integration processes of correlated models that are formally based on triple graph grammars often suffer from the fact that elements are unnecessarily deleted and recreated losing information in the process. It has been shown that this undesirable loss of information can be softened by allowing partial correspondence morphisms in triple graphs. We provide a formal framework for this new synchronization process by introducing the category \(\mathbf {PTrG}\) of partial triple graphs and proving it to be adhesive. This allows for ordinary double pushout rewriting of partial triple graphs. To exhibit \(\mathbf {PTrG}\) as an adhesive category, we present a fundamental construction of subcategories of functor categories and show that these are adhesive HLR if the base category already is. Secondly, we consider an instantiation of this framework by triple graphs to illustrate its practical relevance and to have a concrete example at hand.

When using graph transformations to formalize model transformations, it is often desirable to design transformations that preserve consistency with respect to a given set of (model) integrity constraints. The standard approach is to equip transformations with suitable application conditions such that the introduction of constraint violations is prevented. This may lead to rules that are applicable seldom or even inapplicable at all, though. To supplement this approach, we present a new and systematic procedure to develop correct-by-construction transformations with respect to a special kind of constraints. Instead of controlling the applicability of a rule we complement its action in such a way that a given constraint holds after application: For every way in which the rule could introduce a violation of the constraint, we derive a supplementary action for the rule that remedies that violation. We formalize this construction in the setting of adhesive categories for monotonic rules and positive atomic constraints and present sufficient conditions for its correctness.