Abstract

Joint work with Alexander Bentkamp, Simon Cruanes, Visa Nummelin, Stephan Schulz, Sophie Tourret, Petar Vukmirović, and Uwe Waldmann

Isabelle’s Sledgehammer, the Lean Hammer, and other hammers are useful for automatically proving theorems from mathematics and computer science. But until a few years ago, Sledgehammer relied mostly on first-order automated theorem provers, which limited its usefulness. In this talk, I will describe my work, and especially my colleagues’ work, on native higher-order provers that can serve as hammer backends. We developed lambda-superposition, a proof calculus that generalizes the highly successful superposition calculus implemented by first-order provers such as E, SPASS , and Vampire to higher-order logic. This is the logic of HOL4 , HOL Light, and Isabelle/HOL and a fragment of Lean’s logic without dependent types. The calculus is implemented in Duper, E, slam, and Zipperposition. Sledgehammer’s success rate has gone up, and Zipperposition has won trophies at system competitions.

=== Online talk ===

Join Zoom Meeting https://cam-ac-uk.zoom.us/j/89856091954?pwd=Bba77QB2KuTideTlH6PjAmbXLO8HbY.1

Meeting ID: 898 5609 1954 Passcode: ITPtalk