Superposition for Lambda-Free Higher-Order Logic

Bentkamp, Alexander; Blanchette, Jasmin Christian; Cruanes, Simon; Waldmann, Uwe

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Superposition for Lambda-Free Higher-Order Logic

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Waldmann, Uwe
Automation of Logic, MPI for Informatics, Max Planck Society;

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arXiv:2005.02094.pdf
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Bentkamp, A., Blanchette, J. C., Cruanes, S., & Waldmann, U. (2020). Superposition for Lambda-Free Higher-Order Logic. Retrieved from https://arxiv.org/abs/2005.02094.

Cite as: http://hdl.handle.net/21.11116/0000-0008-0A5F-4

Abstract

We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-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 Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.