Lean Graph Search for Formal Theorem Proving

Key points

• Retrieving relevant lemmas is crucial for formal theorem proving, enabling provers to build machine-checkable proofs from established mathematical results.1
• 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.1
• More importantly, we evaluate whether these retrieval gains translate into improved end-to-end theorem proving by integrating LeanGraphSearch into an iterative proving loop guided by Lean feedback.1
• These findings highlight the value of dependency graph search for theorem proving and motivate further research on structure-aware search for proof discovery.1

Sources (1)

• [1]Lean Graph Search for Formal Theorem Proving
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 05:55 PM

  To this end, we propose LeanGraphSearch, a graph-based retrieval method for Lean 4 that constructs a graph from Mathlib's forward dependencies and traverses it to uncover supporting lemmas through multi-hop dependency chains.

  Retrieving relevant lemmas is crucial for formal theorem proving, enabling provers to build machine-checkable proofs from established mathematical results.

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