Infinitary Combinatory Reduction Systems: Confluence

Jeroen Ketema, Jakob Simonsen, Henk Barendregt
2009 Logical Methods in Computer Science  
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.
doi:10.2168/lmcs-5(4:3)2009 fatcat:vad2bu5bfvfldgkqmf6qvush2m