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.
@InProceedings{clune_et_al:LIPIcs.ITP.2024.10, author = {Clune, Joshua and Qian, Yicheng and Bentkamp, Alexander and Avigad, Jeremy}, title = {{Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory}}, booktitle = {15th International Conference on Interactive Theorem Proving (ITP 2024)}, pages = {10:1--10:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-337-9}, ISSN = {1868-8969}, year = {2024}, volume = {309}, editor = {Bertot, Yves and Kutsia, Temur and Norrish, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.10}, URN = {urn:nbn:de:0030-drops-207381}, doi = {10.4230/LIPIcs.ITP.2024.10}, annote = {Keywords: proof search, automatic theorem proving, interactive theorem proving, Lean, dependent type theory} }
Feedback for Dagstuhl Publishing