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

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.