# Superposition for Lambda-Free Higher-Order Logic

@inproceedings{Bentkamp2018SuperpositionFL,
title={Superposition for Lambda-Free Higher-Order Logic},
author={Alexander Bentkamp and Jasmin Christian Blanchette and Simon Cruanes and Uwe Waldmann},
booktitle={IJCAR},
year={2018}
}
• Published in IJCAR 14 July 2018
• Computer Science
We introduce refutationally complete superposition calculi for intentional and extensional $$\lambda$$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the $$\lambda$$-free higher-order lexicographic path and Knuth–Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on TPTP benchmarks. They appear…
35 Citations
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## References

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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.
Extending a Brainiac Prover to Lambda-Free Higher-Order Logic
• Computer Science
TACAS
• 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.
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 the results suggest that superposition is a suitable basis for higher- order reasoning.
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