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

Heiko Becker (1) , Jasmin Christian Blanchette (2, 3) , Uwe Waldmann (2, 3) , Daniel Wand (2, 3, 4)

1 MPI-SWS - Max Planck Institute for Software Systems
2 MPII - Max-Planck-Institut für Informatik
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
4 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

We generalize the Knuth-Bendix order (KBO) to higher-order terms without λ-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.

Domaines: Logique en informatique [cs.LO]

Heiko Becker, Jasmin Christian Blanchette, Uwe Waldmann, Daniel Wand. A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms. CADE-26 - 26th International Conference on Automated Deduction, Aug 2017, Gothenburg, Sweden. pp.432-453, ⟨10.1007/978-3-319-63046-5_27⟩. ⟨hal-01592186⟩