A Formal Resolution Strategy for Operation-Based Conflicts in Model Versioning Using Graph Modifications

In model-driven engineering, models are primary artifacts and can evolve heavily during their life cycle. Hence, versioning of models is a key technique which has to be offered by an integrated development environment for model-driven engineering. In contrast to text-based versioning systems, our approach takes abstract syntax structures in model states and operational features into account. Considering the abstract syntax of models as graphs, we define a model revision by a span

$G \longleftarrow D \longrightarrow H$

, called graph modification, where

G

and

H

are the old and new versions, respectively, and

D

the common subgraph that remains unchanged. Based on notions of behavioural equivalence and parallel independence of graph modifications, we are able to show a Local-Church-Rosser Theorem for graph modifications. The main goal of the paper is to handle conflicts of graph modifications which may occur in the case of parallel dependent graph modifications. The main result is a general merge construction for graph modifications that resolves all conflicts simultaneously in the sense that for delete-insert conflicts insertion has priority over deletion.