Constructing Constraint-Preserving Interaction Schemes in Adhesive Categories

Abstract

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.

Empowering model repair: A rule-based approach to graph repair without side effects -- Extended Version

“…There are several approaches to rule-based graph repair [25,6,8,26,9,10,11]. The approach closest to ours is that of Habel and Sandmann [8,9,10,11]: Similar to our approach, In [6], the authors formalize rule-based model repair on the basis of graphs and precisely characterize the type of constraints for which the repair algorithm terminates and results in consistent models.…”

Sustaining and improving graduated graph consistency: A static analysis of graph transformations

“…As the applicability of rules enhanced in that way can be severely restricted, improved constructions have been considered for specific forms of constraints. For constraints of the form ∀(C, ∃C ), for example, a suitable rule scheme is constructed in [25]. In [26], refactoring rules are checked for the preservation of constraints of nesting level ≤ 2.…”

Topological consistency preservation with graph transformation schemes

“…In [76], the authors developed an approach to bypass the loss of applicability of rules with application conditions. The authors guarantee that a constraint holds by construction after transformation.…”

“…In the sense of[76], the notation ∀(P, ∃C) means that each occurrence of P lies within an occurrence of C…”