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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Skew and ω-Skew Confluence and Abstract Böhm Semantics
verfasst von : Zena M. Ariola, Stefan Blom
Erschienen in: Processes, Terms and Cycles: Steps on the Road to Infinity
Verlag: Springer Berlin Heidelberg
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Skew confluence was introduced as a characterization of non-confluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with
letrec
. We present a new notion called
ω
-skew confluence which constitutes a sufficient and necessary condition for uniqueness. We also present a theory that can lift uniqueness results from term rewriting systems to rewriting systems on terms with
letrec
. We present our results in the setting of Abstract Böhm Semantics, which is a generalization of Böhm like trees to abstract reduction systems.