TY - GEN

T1 - Partial order infinitary term rewriting and Böhm trees

AU - Bahr, Patrick

PY - 2010

Y1 - 2010

N2 - We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding B{"o}hm extensions. The B{"o}hm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the B{"o}hm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.

AB - We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding B{"o}hm extensions. The B{"o}hm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the B{"o}hm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.

KW - Faculty of Science

KW - infinitary term rewriting

KW - Böhm trees

KW - partial order

KW - confluence

KW - normalisation

U2 - 10.4230/LIPIcs.RTA.2010.67

DO - 10.4230/LIPIcs.RTA.2010.67

M3 - Article in proceedings

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 67

EP - 84

BT - Proceedings of the 21st International Conference on Rewriting Techniques and Applications

A2 - Lynch, Christopher

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Y2 - 11 July 2010 through 13 July 2010

ER -