On Term-Graph Rewrite Strategies

We tackle the problem of cyclic term-graph rewriting. We first revisit the classical algorithmic approach to term-graph rewriting by providing a definition of rewrite rules of the form lhs -> rhs where the left-hand sides are term-graphs and the right-hand sides are sequences of actions. Such actions, which specify how to rewrite a term-graph in a stepwise manner, contribute to simplify substantially the definition of cyclic term-graph rewriting. Then we define a new class of term-graph rewrite systems which are confluent over the so-called admissible term-graphs. Finally, we provide an efficient rewrite strategy which contracts only needed redexes and give pointers to other results regarding optimal rewrite strategies of admissible term-graphs.