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arXiv · 0910.4081

Infinitary Combinatory Reduction Systems: Confluence

Jeroen Ketema·Jakob Grue Simonsen
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Abstract

We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fully-extended, orthogonal iCRSs are confluent modulo identification of hypercollapsing subterms. As a corollary, we obtain that fully-extended, orthogonal iCRSs have the normal form property and the unique normal form property (with respect to reduction). We also show that, unlike the case in first-order infinitary rewriting, almost non-collapsing iCRSs are not necessarily confluent.

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Jeroen Ketema, Jakob Grue Simonsen. 2009-10-21. Infinitary Combinatory Reduction Systems: Confluence. https://doi.org/10.2168/lmcs-5(4:3)2009

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