Graph Transformation with Variables

Variables make rule-based systems more abstract and expressive, as witnessed by term rewriting systems and two-level grammars. In this paper we show that variables can be used to define advanced ways of graph transformation as well. Taking the gluing approach to graph transformation [7, 3] as a basis, we consider extensions of rules with attribute variables, clone variables, and graph variables, respectively. In each case, the variables in a rule are instantiated in order to obtain a set of rule instances that in turn defines the transformation relation. By combining different kinds of variables, we define very expressive rules, and reduce them to plain rules by instantiation. Since gluing graph transformation has a well developed theory, this opens the door to lift results of that theory from instances to rules with variables.