Relabelling in Graph Transformation

The traditional double-pushout approach to graph transformation does not allow to change node labels in an arbitrary context. We propose a simple solution to this problem, namely to use rules with partially labelled interface graphs and to match rules injectively. In [8] we have shown that injective matching makes the double-pushout approach more expressive, and here we further generalise that approach. Besides solving the relabelling problem, our framework allows to write rules with partially labelled left-hand sides which are equivalent to (possibly infinite) sets of rules in the traditional setting. Unlike previous work on rules with partially labelled graphs, we do not need any labelling condition on matching morphisms, nor do we exclude node merging rules.