Lean Graph Search for Formal Theorem Proving
LeanGraphSearch retrieves supporting Lean lemmas via dependency graphs and lifts theorem-proving pass rates.
LeanGraphSearch builds a graph of Mathlib forward dependencies in Lean 4 and propagates relevance along multi-hop premise chains before reranking candidates against the query. Versus LeanSearch v2, recall improves by up to 12% on MathlibQR and complete annotated proof-route coverage rises by up to 3.7% of groups on MathlibMPR. Inside an iterative Lean-feedback prover, pass rates at 8, 16, and 32 reflection turns rise by as much as 40% over a vanilla prover and at most 10% over LeanSearch v2.
- LeanGraphSearch ranks lemmas via Mathlib multi-hop dependencies.
- Recall rises up to 12% over LeanSearch v2 on MathlibQR.
- It covers up to 3.7% more annotated proof-route groups.
- Pass rate improves by as much as 40% versus a vanilla prover.
- Gains versus LeanSearch v2 reach at most 10%.
From the original article
1 min read at arxiv.orgRetrieving relevant lemmas is crucial for formal theorem proving, enabling provers to build machine-checkable proofs from established mathematical results. Recent retrieval systems match library declarations to a target theorem or its intermediate proof steps, but make limited use of multi-hop dependencies among declarations.
By Yihan Xu · arxiv.org
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