[Submitted on 18 Oct 2026]
Title:Fix, Not Just Resample: Bounded Compiler-Guided Repair in Lean 4
View a PDF of the paper titled Fix, Not Just Resample: Bounded Compiler-Guided Repair in Lean 4, by Haotian Deng and 4 other authors
View PDF HTML (experimental)
Abstract:Automated theorem provers often rely on sampling language models, but proof assistants like Lean reject each failed step with a precise error message --- information that pure sampling discards. To overcome this, we introduce a bounded, online step-level repair module. Our search samples $K$ candidate tactics at each step and repairs a failed tactic at most $R$ times. Instead of discarding failed tactics, we feed the compiler's error message to a pretrained repair model to fix individual rejected steps in place. This approach improves the solve rate over a sampling-only baseline across all tested candidate budgets ($K \in \{1,3,5,8\}$), achieving up to a $32\%$ relative gain and solving $82$ additional theorems on a $1{,}990$-theorem subset of the LeanDojo benchmark. Repair is not free: it trades extra runtime for reachable proofs. But the trade is predictable: repair pays most when sampling is constrained; its return is front-loaded, with the first repair attempt capturing $84\text{--}96\%$ of the total gain; and the gain comes almost entirely from shallow tactic-execution failures rather than structural errors such as type mismatches. This targeted repair successfully replicates on a second benchmark (Lean Workbook), nearly doubling the solve rate with zero regressions.
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2610.26942 [cs.AI]
(or arXiv:2610.26942v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.26942
arXiv-issued DOI via DataCite
Submission history
From: Haotian Deng [view email] [v1] Sun, 18 Oct 2026 04:21:55 UTC (104 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled Fix, Not Just Resample: Bounded Compiler-Guided Repair in Lean 4, by Haotian Deng and 4 other authors
View PDF
HTML (experimental)
TeX Source
view license
Additional Features
Audio Summary
Current browse context:
cs.AI
new | recent | 2026-10
Change to browse by:
cs
References & Citations
SciX
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data, Media
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
Author
Venue
Institution
Topic
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)