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

@inproceedings{Becker2017ATK,
  title={A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms},
  author={Heiko Becker and Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
  booktitle={CADE},
  year={2017}
}
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… 
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