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Computability Closure: Ten Years Later

  • Frédéric Blanqui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4600)

Abstract

The notion of computability closure has been introduced for proving the termination of higher-order rewriting with first-order matching by Jean-Pierre Jouannaud and Mitsuhiro Okada in a 1997 draft which later served as a basis for the author’s PhD. In this paper, we show how this notion can also be used for dealing with β-normalized rewriting with matching modulo βη (on patterns à la Miller), rewriting with matching modulo some equational theory, and higher-order data types (types with constructors having functional recursive arguments). Finally, we show how the computability closure can easily be turned into a reduction ordering which, in the higher-order case, contains Jean-Pierre Jouannaud and Albert Rubio’s higher-order recursive path ordering and, in the first-order case, is equal to the usual first-order recursive path ordering.

Keywords

Induction Hypothesis Equational Theory Dependency Pair Lambda Calculus Computable Term 
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 2007

Authors and Affiliations

  • Frédéric Blanqui
    • 1
  1. 1.INRIA, LORIA, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy CedexFrance

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