Skew and ω-skew confluence and abstract Böhm semantics

  • Authors:
  • Zena M. Ariola;Stefan Blom

  • Affiliations:
  • University of Oregon;University of Innsbruck

  • Venue:
  • Processes, Terms and Cycles
  • Year:
  • 2005

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Abstract

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.