Abstract:Automated theorem proving systems built on Lean 4 increasingly rely on parallel tactic search over partially specified proofs, such as those generated by Draft-Sketch-Prove (DSP) pipelines. In current systems, each search branch reconstructs a proof state by re-running elaboration, leading to substantial per-branch overhead. In Lean 4 with Mathlib, this cost has two components: (1) import loading, which deserializes pre-compiled libraries (~60 s per branch); and (2) theorem-body elaboration, which re-checks the theorem context up to the target goal (estimated 18-735 s depending on proof complexity). Together, these account for >99% of per-branch wall time, making portfolio-based search impractical at scale.
We observe that this overhead arises from a mismatch between the structure of proof search and its execution model: branching is implemented via repeated reconstruction of proof states rather than direct reuse. To address this, we introduce proof-state snapshotting, which captures the elaborated proof state once and reuses it across branches via a small extension to the Lean 4 language server.
Across 48 miniF2F-v2 problems (45 prove-phase benchmarks and 3 full end-to-end runs), our approach achieves a 5.6-50x wall-time speedup over the standard fallback (average 14x, median 9.7x). Speedup increases with the number of proof branches.
Our method is orthogonal to import-level caching (e.g., Kimina Lean Server), which avoids import loading but not theorem-body elaboration. The patched Lean binary and the Snapshot-DSP pipeline will be released as open source upon publication.
| Comments: | 10 pages, 1 figure |
| Subjects: | Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.25556 [cs.LO] |
| (or arXiv:2605.25556v1 [cs.LO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25556 arXiv-issued DOI via DataCite (pending registration) |
From: Austin Zi Jun Shen [view email]
[v1]
Mon, 25 May 2026 08:12:26 UTC (113 KB)
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