A Higher-Order Iterative Path Ordering

  title={A Higher-Order Iterative Path Ordering},
  author={Cynthia Kop and Femke van Raamsdonk},
The higher-order recursive path ordering ( HORPO ) defined by Jouannaud and Rubio provides a method to prove termination of higher-order rewriting. We present an iterative version of HORPO by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop. We study well-foundedness of the iterative definition, discuss its relationship with the original HORPO, and point out possible ways to strengthen the ordering. 
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This new order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work and appears promising as the basis of a higher-order superposition calculus.
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Coq formalization of the higher-order recursive path ordering
  • A. Koprowski
  • Computer Science
    Applicable Algebra in Engineering, Communication and Computing
  • 2009
This paper describes the undertaking of providing a complete, axiom-free, fully constructive formalization of results in the proof assistant Coq of the higher-order recursive path ordering, HORPO with a proof of its well-foundedness.
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The higher-order recursive path ordering
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  • Mathematics
    Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)
  • 1999
This paper extends the termination proof techniques based on reduction orderings to a higher-order setting, by adapting the recursive path ordering definition to terms of a typed lambda-calculus
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A family of recursive path orderings for terms of a typed lambda-calculus generated by a signature of polymorphic higher-order function symbols is defined, which can be generated from two given well-founded orderings, on the function symbols and on the type constructors.
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  • T. Nipkow
  • Computer Science
    [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
  • 1991
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