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

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

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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Acknowledgment

We are grateful to Stephan Merz, Tobias Nipkow, and Christoph Weidenbach for making this research possible; to Mathias Fleury and Dmitriy Traytel for helping us formalize the syntactic ordinals; to Andrei Popescu and Christian Sternagel for advice with extending a partial well-founded order to a total one in the mechanized proof of Lemma 3; to Andrei Voronkov for the enlightening discussion about KBO at the IJCAR 2016 banquet; and to Carsten Fuhs, Mark Summerfield, and the anonymous reviewers for suggesting many textual improvements.

Blanchette has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 713999, Matryoshka). Wand is supported by the Deutsche Forschungsgemeinschaft (DFG) grant Hardening the Hammer (NI 491/14-1).

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Authors and Affiliations

  1. Max-Planck-Institut für Softwaresysteme, Saarbrücken, Germany

    Heiko Becker

  2. Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Jasmin Christian Blanchette

  3. Inria Nancy – Grand Est, Villers-lès-Nancy, France

    Jasmin Christian Blanchette

  4. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Jasmin Christian Blanchette, Uwe Waldmann & Daniel Wand

  5. Technische Universität München, Munich, Germany

    Daniel Wand

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  1. Heiko Becker
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  2. Jasmin Christian Blanchette
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  3. Uwe Waldmann
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  4. Daniel Wand
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Correspondence to Jasmin Christian Blanchette .

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  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Becker, H., Blanchette, J.C., Waldmann, U., Wand, D. (2017). A Transfinite Knuth–Bendix Order for Lambda-Free Higher-Order Terms. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_27

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