LIPIcs.RTA.2010.85.pdf
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Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting
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Proceedings of the 21st International Conference on Rewriting Techniques and Applications (RTA 2010)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Rewriting Techniques and Applications (RTA) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2010-07-06
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Joerg Endrullis, Clemens Grabmayer, Dimitri Hendriks, Jan Willem Klop, and Vincent van Oostrom. Unique Normal Forms in Infinitary Weakly Orthogonal Rewriting. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 85-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.RTA.2010.85
https://doi.org/10.4230/LIPIcs.RTA.2010.85
Abstract
We present some contributions to the theory of infinitary rewriting
for weakly orthogonal term rewrite systems, in which critical pairs
may occur provided they are trivial.
We show that the infinitary unique normal form property (UNinf)
fails by a simple example of a weakly orthogonal TRS with two
collapsing rules. By translating this example, we show that UNinf
also fails for the infinitary lambda-beta-eta-calculus.
As positive results we obtain the following: Infinitary confluence,
and hence UNinf, holds for weakly orthogonal TRSs that do not contain
collapsing rules. To this end we refine the compression lemma.
Furthermore, we consider the triangle and diamond properties
for infinitary developments in weakly orthogonal TRSs,
by refining an earlier cluster-analysis for the finite case.
Keywords
- Weakly orthogonal term rewrite systems
- unique normal form property
- infinitary rewriting
- infinitary lambda-beta-eta-calculus,
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