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VOLUME 5, ISSUE 4, PAPER 3


Infinitary Combinatory Reduction Systems: Confluence

©Jeroen Ketema, Tohoku University
©Jakob Grue Simonsen, University of Copenhagen

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.

Publication date: December 20, 2009

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-5(4:3)2009

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