# A Lambda-Free Higher-Order Recursive Path Order

@inproceedings{Blanchette2017ALH, title={A Lambda-Free Higher-Order Recursive Path Order}, author={Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand}, booktitle={FoSSaCS}, year={2017} }

We generalize the recursive path order RPO to higher-order terms without $$\lambda $$-abstraction. This new order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. It has many useful properties, including well-foundedness, transitivity, stability under substitution, and the subterm property. It appears promising as the basis of a higher-order superposition calculus.

## 14 Citations

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

- Computer ScienceArch. Formal Proofs
- 2018

The embedding path order is a variant of the recursive path order for untyped λ-free higher-order terms that is a groundtotal and well-founded simplification order, making it more suitable for the superposition calculus.

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

- MathematicsCADE
- 2017

The Knuth–Bendix order is generalized to higher-order terms without \(\lambda \)-abstraction and appears promising as the basis of a higher- order superposition calculus.

Superposition for Lambda-Free Higher-Order Logic

- Computer ScienceIJCAR
- 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 for Lambda-Free Higher-Order Logic ( Technical Report )

- Computer Science
- 2018

Refutationally complete superposition calculi for intentional and extensional λ-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 ScienceCADE
- 2019

A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and the results suggest that superposition is a suitable basis for higher- order reasoning.

Implementation of Lambda-Free Higher-Order Superposition

- Computer Science
- 2018

This thesis extends E, a state-of-the-art first-order ATP, to a fragment of HOL that is devoid of lambda abstractions (LFHOL), and devise generalizations of E’s indexing data structures to LFHOL, as well as algorithms like matching and unification to support HOL features in an efficient manner.

Extending a brainiac prover to lambda-free higher-order logic

- Computer ScienceInt. J. Softw. Tools Technol. Transf.
- 2022

This work proposes to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to higher- order logic, a formalism that supports partial application and applied variables.

Extending a Brainiac Prover to Lambda-Free Higher-Order Logic

- Computer ScienceTACAS
- 2019

This work proposes to start with the state-of-the-art superposition-based prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to \(\lambda \)-free higher- order logic, a formalism that supports partial application and applied variables.

A Knuth-Bendix-Like Ordering for Orienting Combinator Equations

- MathematicsIJCAR
- 2020

A number of desirable properties about the KBO are proved including it having the subterm property for ground terms, being transitive and being well-founded, and the ordering fails to be a reduction ordering as it lacks compatibility with certain contexts.

Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

- Mathematics, Computer ScienceFSCD
- 2017

Formal proofs of the main properties of the nested multiset order that are useful in applications are presented: preservation of well-foundedness and preservation of totality (linearity).

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