A Transfinite Knuth–Bendix Order for Lambda-Free Higher-Order Terms

  • Heiko Becker
  • Jasmin Christian Blanchette
  • Uwe Waldmann
  • Daniel Wand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10395)


We generalize the Knuth–Bendix order (KBO) to higher-order terms without \(\lambda \)-abstraction. The restriction of this new order to first-order terms coincides with the traditional KBO. The order has many useful properties, including transitivity, the subterm property, compatibility with contexts (monotonicity), stability under substitution, and well-foundedness. Transfinite weights and argument coefficients can also be supported. The order appears promising as the basis of a higher-order superposition calculus.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Heiko Becker
    • 1
  • Jasmin Christian Blanchette
    • 2
    • 3
    • 4
  • Uwe Waldmann
    • 4
  • Daniel Wand
    • 4
    • 5
  1. 1.Max-Planck-Institut für SoftwaresystemeSaarbrückenGermany
  2. 2.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  3. 3.Inria Nancy – Grand EstVillers-lès-NancyFrance
  4. 4.Max-Planck-Institut für InformatikSaarbrückenGermany
  5. 5.Technische Universität MünchenMunichGermany

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