Infinitary Combinatory Reduction Systems: Confluence

Details Infinitary Combinatory Reduction Systems: Confluence Infinitary Combinatory Reduction Systems: Confluence

2009-10-21

arxiv.org/abs/0910.4081v2

LMCS 5 (4:3) 2009

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-5(4:3)2009

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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