### 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

BSD License

### Topics

- Logic/Rewriting

### 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

### Depends on

- Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

### 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 Knuth–Bendix Orders for Lambda-Free Higher-Order Terms

### Auto-related entries

- Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms
- Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms

## Cite

×

Lambda_Free_RPOs-AFP

    @article{Lambda_Free_RPOs-AFP,
      author  = {Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
      title   = {Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/Lambda_Free_RPOs.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 18, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Aug 16, 2018 : Isabelle2018
- Oct 10, 2017 : Isabelle2017
- Dec 17, 2016 : Isabelle2016-1