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Infinitary Combinatory Reduction Systems: Confluence
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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.
Centre pour la Communication Scientifique Directe (CCSD)
Title: Infinitary Combinatory Reduction Systems: Confluence
Description:
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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