A Foundation for Functional Graph Programs: The Graph Transformation Control Algebra (GTA)

Applications of graph transformation (GT) systems often require control structures that can be used to direct GT processes. Most existing GT tools follow a stateful computational model, where a single graph is repeatedly modified "in-place" when GT rules are applied. The implementation of control structures in such tools is not trivial. Common challenges include dealing with the non-determinism inherent to rule application and transactional constraints when executing compositions of GTs, in particular atomicity and isolation. The complexity of associated transaction mechanisms and rule application search algorithms (e.g., backtracking) complicates the definition of a formal foundation for these control structures. Compared to these stateful approaches, functional graph rewriting presents a simpler (stateless) computational model, which simplifies the definition of a formal basis for (functional) GT control structures. In this paper, we propose the "Graph Transformation control Algebra" (GTA) as such a foundation. The GTA has been used as the formal basis for implementing the control structures in the (functional) GT tool "GrapeVine".