On graph rewriting, reduction, and evaluation in the presence of cycles

Abstract

We inter-derive two prototypical styles of graph reduction: reduction machines a la Turner and graph rewriting systems a la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of cyclic graphs. We also outline how to inter-derive a third style of graph reduction: a graph evaluator.