title: Graph Rewriting and Copying
authors: Erik Barendsen and Sjaak Smetsers
Graph rewrite systems play an important role in the implementation of
functional programming languages. This paper focusses on the theoretical
aspects of graph rewriting. Graph reduction is described in terms of
general operations on graphs, leading to a substitution-like mechanism called
graph replacement. Some basic theory on the interaction of these
operations is developed. The ordering induced by graph homomorphisms is
investigated. Equipped with this ordering, various sets of graphs have nice
domain theoretical properties. Moreover, a lazy copying mechanism is
added to the notion of graph reduction. This copying concept is
analyzed by splitting it into more elementary graph operations, leading to a
confluence result. Finally, some ideas are presented on the use of copying in
practice.