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Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory

Authors Joshua Clune , Yicheng Qian, Alexander Bentkamp , Jeremy Avigad

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Author Details

Joshua Clune
  • Carnegie Mellon University, Pittsburgh, PA, USA
Yicheng Qian
  • Peking University, Beijing, China
Alexander Bentkamp
  • Heinrich-Heine-Universität Düsseldorf, Germany
Jeremy Avigad
  • Carnegie Mellon University, Pittsburgh, PA, USA

Acknowledgements

We thank Mario Carneiro, Rob Lewis, and Gabriel Ebner for their advice in the early stages of the project. We thank Lydia Kondylidou for her input on our evaluation section and Jasmin Blanchette for his feedback on this paper and input on our evaluation section. We also thank Haniel Barbosa and the anonymous reviewers for their feedback on this paper.

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Joshua Clune, Yicheng Qian, Alexander Bentkamp, and Jeremy Avigad. Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITP.2024.10

Abstract

We present Duper, a proof-producing theorem prover for Lean based on the superposition calculus. Duper can be called directly as a terminal tactic in interactive Lean proofs, but is also designed with proof reconstruction for a future Lean hammer in mind. In this paper, we describe Duper’s underlying approach to proof search and proof reconstruction with a particular emphasis on the challenges of working in a dependent type theory. We also compare Duper’s performance to Metis' on pre-existing benchmarks to give evidence that Duper is performant enough to be useful for proof reconstruction in a hammer.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
  • Theory of computation → Logic and verification
  • Theory of computation → Higher order logic
  • Theory of computation → Type theory
Keywords
  • proof search
  • automatic theorem proving
  • interactive theorem proving
  • Lean
  • dependent type theory

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Supplementary Materials

References

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