Congruences for Contextual Graph-Rewriting

Abstract

We introduce a comprehensive operational semantic theory of graph rewriting. The central idea is recasting rewriting frameworks as Leifer and Milner's reactive systems. Consequently, graph rewriting systems are associated with canonical labelled transition systems, on which bisimulation equivalence is a congruence with respect to arbitrary graph contexts (cospans of graphs). This construction is derived from a more general theorem of much wider applicability. Expressed in abstract categorical terms, the central technical contribution of the paper is the construction of groupoidal relative pushouts, introduced and developed by the authors in recent work, in suitable cospan categories over arbitrary adhesive categories. As a consequence, we both generalise and shed light on rewriting via borrowed contexts due to Ehrig and König.