• Corpus ID: 53090076

# Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms

@article{Bentkamp2018FormalizationOT,
title={Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms},
author={Alexander Bentkamp},
journal={FLAP},
year={2018},
volume={8},
pages={2447-2470}
}
The embedding path order, introduced in this article, is a variant of the recursive path order (RPO) for untyped λ-free higher-order terms (also called applicative first-order terms). Unlike other higher-order variants of RPO, it is a groundtotal and well-founded simplification order, making it more suitable for the superposition calculus. I formally proved the order’s theoretical properties in Isabelle/HOL and evaluated the order in a prototype based on the superposition prover Zipperposition.
3 Citations
Superposition for Lambda-Free Higher-Order Logic
• Computer Science
IJCAR
• 2018
Refutationally complete superposition calculi for intentional and extensional $$\lambda$$-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.
Superposition with Lambdas
• Computer Science
• 2019
A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and implemented in the Zipperposition prover and evaluated on TPTP and Isabelle benchmarks.
Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)
This paper describes and reflects on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order logic.

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