TY - JOUR
T1 - Infinitary Combinatory Reduction Systems: Confluence
AU - Ketema, Jeroen
AU - Simonsen, Jakob Grue
PY - 2009
Y1 - 2009
N2 - We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fullyextended, 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.
AB - We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fullyextended, 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.
M3 - Journal article
SN - 1860-5974
VL - 5
SP - 1
EP - 29
JO - Logical Methods in Computer Science
JF - Logical Methods in Computer Science
IS - 4:3
ER -