Higher-order Rewrite Systems and Their Connuence

We study Higher-Order Rewrite Systems (HRSs) which extend term rewriting to-terms. HRSs can describe computations over terms with bound variables. We show that rewriting with HRSs is closely related to undirected equational reasoning. We deene Pattern Rewrite Systems (PRSs) as a special case of HRSs and extend three connuence results from term rewriting to PRSs: the critical pair lemma by Knuth and Bendix, connuence of rewriting modulo equations a la Huet, and connuence of orthogonal PRSs.