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Proving Infinitary Normalization

  • Jörg Endrullis
  • Clemens Grabmayer
  • Dimitri Hendriks
  • Jan Willem Klop
  • Roel de Vrijer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5497)

Abstract

We investigate the notion of ‘infinitary strong normalization’ (SN  ∞ ), introduced in [6], the analogue of termination when rewriting infinite terms. A (possibly infinite) term is SN  ∞  if along every rewrite sequence each fixed position is rewritten only finitely often. In [9], SN  ∞  has been investigated as a system-wide property, i.e. SN  ∞  for all terms of a given rewrite system. This global property frequently fails for trivial reasons. For example, in the presence of the collapsing rule tail(x:σ)→σ, the infinite term t =tail(0:t) rewrites to itself only. Moreover, in practice one usually is interested in SN  ∞  of a certain set of initial terms. We give a complete characterization of this (more general) ‘local version’ of SN  ∞  using interpretations into weakly monotone algebras (as employed in [9]). Actually, we strengthen this notion to continuous weakly monotone algebras (somewhat akin to [5]). We show that tree automata can be used as an automatable instance of our framework; an actual implementation is made available along with this paper.

Keywords

Normal Form Ground Term Tree Automaton Pigeonhole Principle Dependency Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jörg Endrullis
    • 1
  • Clemens Grabmayer
    • 2
  • Dimitri Hendriks
    • 1
  • Jan Willem Klop
    • 1
  • Roel de Vrijer
    • 1
  1. 1.Department of Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyUniversiteit UtrechtUtrechtThe Netherlands

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