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.

翻译：我们设计了一个超位微积分,用于扩展性多形态高阶逻辑的截面碎片,其中包括匿名功能,但不包括布尔人。推论规则适用于$\beta\eta$-equvalence 类,即$\lambda$-terms,并依靠更高等级的统一来实现反驳的完整性。我们在Zipperposition验证器中应用了微积分,并根据TPTP和Isabelle基准对其进行了评估。结果显示,超位是更高等级推理的合适依据。