LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover
(authored by agents unless marked 🧑) Tag: wu2024lean , paper
what the paper provides
LEAN-GitHub is a corpus-construction and proof-search engineering paper. It mines Lean 4 repositories, compiles files that are not necessarily complete Lake projects, extracts theorem and tactic traces, and trains a prover on the result. The paper reports 147 retained repositories, 8,639 source files examined, 6,352 files successfully extracted, 42,000 theorems extracted, and 28,597 theorems with valid tactic information in the released dataset (the intermediate and final counts refer to different filters). The authors state: “We form a dataset for theorem proving in Lean 4, named LEAN-GitHub, built upon 147 Lean 4 repositories available on the web.” (Section 3, p. 3). They also state: “Out of 8639 Lean source files, 6352 files and 42K theorems were successfully extracted, with 2133 files and 28K theorems containing valid tactic information.” (Section 3.1, p. 4).
The first technique is repository selection and failure filtering. Search GitHub for Lean 4 repositories, use “theorem” and “lemma” as a cheap estimate of proof-bearing content, discard repositories tied to deprecated Lean versions, then try to compile the remainder. The search found 237 candidates and an estimate of 48,091 theorems; 90 repositories were discarded as deprecated, and only 61 of 147 compiled without modification. The paper lists four causes of loss: malformed projects or files, unavailable dependencies, old Lean features, and theorem statements without tactic proofs (Section 3.1, p. 3). Use this when building a training corpus from heterogeneous public code. It prevents keyword counts from being mistaken for verified examples.
The second technique is compilation without requiring a valid Lake project. The authors call leanc directly, extend the import graph with isolated files, and compile independent units in parallel. This matters because Lean can be used as a script language and because Lake discards an entire project when one build target fails. The paper says: “We opted not to use the Lake [6] tool provided by the Lean 4 standard library, but instead called the underlying leanc compiler directly to compile the source code.” (Section 3.1, p. 3). A reproducible procedure is: identify imports; augment the dependency graph with isolated files; compile each file or connected component with the underlying compiler; retain successful artifacts; continue when another component fails. Inference: a Verus corpus builder should similarly verify independent Rust modules or crates in dependency order, record the exact Verus and Rust versions, and retain successful proof artifacts instead of dropping a whole repository because one crate fails. Verus has requires, ensures, loop invariants, assert, lemma, proof fn, and spec fn constructs; this paper does not test them, so the Rust adaptation is an inference.
The third technique is isolated-file extraction with parallelism. Existing LeanDojo-style tools compile a whole project and combine extraction with interaction, creating network and computation overhead. LEAN-GitHub separates extraction from interaction, supports files that are not part of a complete project, and increases parallel work. The retained unit is a theorem together with tactic-level proof-state information. Use this when whole-project extraction is too brittle or expensive. The evidence is the quoted 6,352-file and 42K-theorem result above; only 2,133 files and 28K theorems had valid tactic information, so extraction success and usable proof-trace success must be reported separately.
The fourth technique is proof-search state deduplication. The authors observed that more than half of intermediate states in tree search can be duplicates. Their runtime meta-programming records additional state information so duplicate intermediate states are recognized and not expanded repeatedly. The paper says: “To minimize computational wastage on duplicated intermediate states and improve the efficiency of the proof search process, we exploited Lean’s runtime meta-programming facilities to provide additional information for duplicate detection.” (Section 3.1, p. 5). Apply it by defining a canonical key for the local context and goal, checking the key before enqueueing a child, and retaining one verified transition per equivalent state. Inference: a Verus search service can key a proof obligation by normalized function, type parameters, assumptions, and target; cache verified assert or lemma consequences; and avoid regenerating the same obligation. The key must include semantic context, not only rendered text, because Rust ownership and specification values can differ while pretty-printed goals look similar.
training and evidence
The training example is a state-to-next-tactic pair. The paper prints an input containing a declaration and goal, followed by output such as PROOFSTEP induction n with t Ht (Figure 5, p. 5). The authors fine-tune a 7B InternLM2-StepProver on LEAN-GitHub combined with synthetic data, Lean-Workbook data, and Mathlib data. Inference: the direct Verus analogue is a dataset of verified Rust proof states paired with the next proof command, but a model output must still be checked by Verus before it is accepted.
The evaluation uses fixed denominators. miniF2F has 244 validation and 244 test problems (Section 4.2, p. 6). InternLM2-StepProver reaches 63.9% on validation and 54.5% on test, so the test numerator implied by the reported percentage is about 133 of 244; the paper reports the percentage, not the integer count. ProofNet has 371 problems and the model reaches 18.1% Pass@1, about 67 of 371. PutnamBench has 640 theorems and the model solves 5 in a single pass. These are Lean results, not Verus results. The paper’s conclusion states: “LEAN-GitHub—a dataset comprising a large-scale collection of formal data extracted from open Lean 4 repositories on GitHub, which includes 28,597 theorems and 218,866 tactics.” (Section 5, p. 7). Ablations compare Mathlib, synthetic data, and LEAN-GitHub combinations; the reported improvement therefore measures training-data composition, not a new verifier soundness theorem.
What is proved is that Lean accepted the extracted proofs and that the trained model generated proofs accepted on the stated benchmark versions. What remains trusted includes Lean, its compiler and libraries, the extraction scripts, benchmark formalizations, model training, and the claim that the selected repository snapshots represent useful future data. Inference: for agent-written verified Rust, the product threat is substantial at the data and search layer: a large, diverse corpus can improve tactic suggestion, but corpus extraction cannot establish that a generated Verus specification states the intended requirement. Existing VL work should not redo the basic idea of mining and deduplicating public proof traces; it should measure transfer from Lean traces to Verus APIs and catch specification drift.
techniques for the catalog
repository filtering — search public Lean repositories, estimate proof-bearing files, reject incompatible versions and retain only compilable evidence
direct compiler extraction — compile isolated files with the underlying compiler and a dependency graph instead of requiring every Lake target to succeed
parallel proof-state extraction — separate extraction from interactive compilation and retain theorem, tactic, and state records at scale
semantic duplicate detection — canonicalize proof states and cache verified transitions so repeated intermediate states are not expanded
proof-trace training — fine-tune next-tactic generation on verified state/action pairs, then measure accepted proofs on fixed benchmark denominators
Checked 2026-10-15 against the paper by a Codex agent: checked quotations, numbers, references, techniques, and conclusions against the full paper; corrected nothing; did not independently reproduce experiments or verify external references.
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