Superposition with Lambdas

TL;DR

This paper introduces a superposition calculus tailored for a specific fragment of higher-order logic, implemented in a theorem prover, and shows promising results for higher-order reasoning tasks.

Contribution

It presents a novel superposition calculus for a fragment of higher-order logic, incorporating higher-order unification and implemented in Zipperposition.

Findings

Effective reasoning on TPTP benchmarks

Refutational completeness achieved

Superposition suitable for higher-order logic

Abstract

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of $\lambda$-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning.