10.4230/LIPICS.RTA.2010.49
Bahr, Patrick
Patrick
Bahr
Abstract Models of Transfinite Reductions
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2010
Infinitary rewriting
metric
partial order
abstract reduction system
axiomatic
term rewriting
graph rewriting
Lynch, Christopher
Christopher
Lynch
2010
2010-07-06
2010-07-06
2010-07-06
en
urn:nbn:de:0030-drops-26445
10.4230/LIPIcs.RTA.2010
978-3-939897-18-7
1868-8969
10.4230/LIPIcs.RTA.2010
LIPIcs, Volume 6, RTA 2010
Proceedings of the 21st International Conference on Rewriting Techniques and Applications
2013
6
7
49
66
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Lynch, Christopher
Christopher
Lynch
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2010
6
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
18 pages
207553 bytes
application/pdf
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
We investigate transfinite reductions in abstract reduction
systems. To this end, we study two abstract models for transfinite
reductions: a metric model generalising the usual metric approach to
infinitary term rewriting and a novel partial order model. For both
models we distinguish between a weak and a strong variant of
convergence as known from infinitary term rewriting. Furthermore, we
introduce an axiomatic model of reductions that is general enough to
cover all of these models of transfinite reductions as well as the
ordinary model of finite reductions. It is shown that, in this
unifying axiomatic model, many basic relations between termination and
confluence properties known from finite reductions still hold. The
introduced models are applied to term rewriting but also to term graph
rewriting. We can show that for both term rewriting as well as for
term graph rewriting the partial order model forms a conservative
extension to the metric model.
LIPIcs, Vol. 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications, pages 49-66