On Confluence of Infinitary Combinatory Reduction Systems
نویسندگان
چکیده
We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting.
منابع مشابه
Infinitary Combinatory Reduction Systems: Confluence
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 t...
متن کاملOn Normalisation of Infinitary Combinatory Reduction Systems
For fully-extended, orthogonal infinitary Combinatory Reduction Systems, we prove that terms with perpetual reductions starting from them do not have (head) normal forms. Using this, we show that 1. needed reduction strategies are normalising for fully-extended, orthogonal infinitary Combinatory Reduction Systems, and that 2. weak and strong normalisation coincide for such systems as a whole an...
متن کاملInfinitary Combinatory Reduction Systems
We define infinitary combinatory reduction systems (iCRSs). This provides the first extension of infinitary rewriting to higher-order rewriting. We lift two well-known results from infinitary term rewriting systems and infinitary λ-calculus to iCRSs: 1. every reduction sequence in a fully-extended left-linear iCRS is compressible to a reduction sequence of length at most ω, and 2. every complet...
متن کاملInfinitary Combinatory Reduction Systems: Normalising Reduction Strategies
We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly generalise a number of results on normalising strategies in first-order infinitary rewriting and provide the first examples of normalising strategies for infin...
متن کاملMeaningless Sets in Infinitary Combinatory Logic
In this paper we study meaningless sets in infinitary combinatory logic. So far only a handful of meaningless sets were known. We show that there are uncountably many meaningless sets. As an application to the semantics of finite combinatory logics, we show that there exist uncountably many combinatory algebras that are not a lambda algebra. We also study ways of weakening the axioms of meaning...
متن کامل