### Abstract

This Isabelle/HOL formalization defines recursive path orders (RPOs) for higher-order terms without lambda-abstraction and proves many useful properties about them. The main order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. An optimized variant is formalized as well. It appears promising as the basis of a higher-order superposition calculus.

### License

### Topics

### Session Lambda_Free_RPOs

- Lambda_Free_Util
- Lambda_Free_Term
- Infinite_Chain
- Extension_Orders
- Lambda_Free_RPO_App
- Lambda_Free_RPO_Std
- Lambda_Free_RPO_Optim
- Lambda_Encoding
- Lambda_Free_RPOs

### Used by

- Substitutions for Lambda-Free Higher-Order Terms
- A Comprehensive Framework for Saturation Theorem Proving
- An Algebra for Higher-Order Terms
- A Verified Functional Implementation of Bachmair and Ganzinger’s Ordered Resolution Prover
- Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms
- Formalization of Knuthâ€“Bendix Orders for Lambda-Free Higher-Order Terms