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Superposition with Lambdas

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arxiv 2102.00453 v1 pith:24ZERJQN submitted 2021-01-31 cs.LO cs.AI

Alexander Bentkamp , Jasmin Blanchette , Sophie Tourret , Petar Vukmirović , Uwe Waldmann This is my paper · ORCID
classification cs.LOcs.AI
keywords higher-ordersuperpositioncalculusachieveanonymousbasisbenchmarksbeta
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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.

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