Infinitary Combinatory Reduction Systems: Confluence

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.

Keywords

• computer science - logic in computer science
• computer science - programming languages
• d.3.1
• f.3.2
• f.4.1
• f.4.2