| --- |
| pretty_name: Lean Transition Corpus |
| license: apache-2.0 |
| task_categories: |
| - text-generation |
| tags: |
| - lean |
| - lean4 |
| - automated-theorem-proving |
| - theorem-proving |
| - formal-mathematics |
| - mathematics |
| - code |
| configs: |
| - config_name: default |
| data_files: |
| - split: train |
| path: data/train/**/*.parquet |
| - split: dev |
| path: data/dev/**/*.parquet |
| - split: internal_test |
| path: data/internal_test/**/*.parquet |
| --- |
| |
| # LeanTransitionCorpus |
|
|
| LeanTransitionCorpus is a dataset for training and studying automated theorem |
| proving systems in Lean. Its unit of data is one tactic transition: the proof state |
| before a tactic, the tactic that was executed, and the resulting state. This makes |
| it suitable for tactic prediction, proof-state representation learning, premise |
| selection, retrieval, verification, and trajectory-level training. |
|
|
| Many Lean datasets expose a theorem, tactic, and pretty-printed goal strings. This |
| corpus retains those human-readable views, but also preserves richer information |
| from Lean's elaborator: the tactic `Syntax` tree, resolved identifiers, recursive |
| Lean `Expr` trees, local context, metavariables, universe metavariables, source |
| ranges, and premise/context information. The extra representations make it |
| possible to investigate models that use Lean's internal structure rather than |
| recovering it from printed text. |
|
|
| Original source and environment provenance are retained per row. The repository's |
| Apache-2.0 metadata applies to this packaging; source corpus licenses and restrictions |
| remain applicable and are not replaced by this card. |
|
|
| ## Source datasets |
|
|
| The extraction pipeline draws from pinned snapshots of the following Lean sources. |
| Rows identify their origin in `source_dataset`, `source_url`, `repo_commit`, and |
| toolchain columns. |
|
|
| The extraction uses immutable source revisions: Numina seed `1c12b9b8d6425f3c531c70601b1e70ccb5bc1e6a`, DeepSeek-Prover `1ee889f608fb12ba3596757ee91a60acd663ea81`, Goedel Lean Workbook `b731852af8d8ab11498fda27bce9020738c01c59`, Mathlib `29dcec074de168ac2bf835a77ef68bbe069194c5`, and OProver/OProofs `3bae0c06157639c0a673679635c669d19c99e906`. The Numina seed is retained in this repository as a frozen source snapshot so the packaged rows remain reproducible. |
|
|
| | Source | Role in the corpus | |
| |---|---| |
| | NuminaMath-CoT | Lean formalizations from the Numina mathematical reasoning corpus. This is the source of the initial uploaded seed. | |
| | DeepSeek-Prover | Lean proof data used to broaden theorem and tactic coverage. | |
| | Goedel Lean Workbook | Lean workbook proofs, retained as a separately attributable source. | |
| | Mathlib | The pinned Mathlib snapshot supplies the theorem-proving environment and contributes directly extracted Mathlib theorems. | |
| | OProver/OProofs | A large corpus of complete Lean proofs used as an additional source. | |
|
|
| ## How the data is produced |
|
|
| For each selected theorem, the extractor runs the matching pinned Lean and Mathlib |
| environment, records the sequence of tactic-state transitions, and canonicalizes |
| the result into one row per transition. It validates internal-state structure and |
| continuity between adjacent transitions, assigns deterministic splits, and keeps |
| provenance needed to trace a row back to its source theorem and environment. |
|
|
| Rows are written as Parquet shards. Before publication, every shard is checked |
| against its source rows; uploaded bytes are read back and verified at an immutable |
| Hugging Face revision. Batch manifests record shard hashes, source-batch identity, |
| and extraction evidence. |
|
|
| ## Evaluation contamination and quarantine |
|
|
| The clean splits are intended for training and analysis, not for preserving |
| benchmark answers. Before publication, source provenance and canonicalized |
| theorem statements are compared with a frozen registry of common Lean |
| benchmarks, including miniF2F, LeanDojo held-out splits, ProofNet, PutnamBench, |
| FIMO, ProverBench, and MathOlympiadBench. Exact source, statement, |
| expression-fingerprint, and provenance matches are excluded. Near-duplicate |
| statement matches are flagged for review rather than silently treated as |
| independent training examples. |
|
|
| Records that trigger these checks are quarantined during extraction and are not |
| part of the published `train`, `dev`, or `internal_test` splits. This policy is |
| applied before split assignment so that structurally equivalent theorems cannot |
| cross between clean splits. |
|
|
| ## Format |
|
|
| Zstandard-compressed Parquet shards, one row per transition. The physical encoding |
| is `leangpt-parquet-v3` with 31 columns. `step_index` is int64; `terminal` is |
| boolean; `imports` and `available_context` are lists of strings. Other columns are |
| nullable strings. |
|
|
| The following recursive/object columns contain lossless JSON text (parse with |
| `json.loads` when non-null): `provenance`, `source_start`, `source_end`, |
| `state_before_structured`, `state_after_structured`, `state_before_internal`, |
| `state_after_internal`, and `tactic_internal`. This prevents inference from |
| truncating recursive Lean trees or creating incompatible schemas between shards. |
| Null stays null; an empty object stays the JSON string `{}`. |
|
|
| `example_id` is globally unique and deterministic. It is the versioned SHA-256 |
| identity of the provenance-based proof key plus `step_index`, prefixed by |
| `ltc-v2:`. The earlier colliding source IDs are not retained in another column. |
|
|
| ## Schema in plain language |
|
|
| Each row is a single ordered step within a proof. The fields fall into these groups: |
|
|
| | Fields | Meaning | |
| |---|---| |
| | `example_id`, `proof_id`, `step_index`, `split` | Stable identity, position in the proof, and dataset split. `example_id` is globally unique; `proof_id` alone may not be. | |
| | `source_dataset`, `source_url`, `repo_commit`, `file_path`, `lean_version`, `mathlib_version`, `extractor_version`, `provenance` | Where the theorem came from and the environment and extraction provenance needed to reproduce or audit it. | |
| | `theorem_name`, `theorem_statement_raw`, `theorem_source_raw`, `imports` | The theorem and its surrounding Lean source context. | |
| | `state_before_raw`, `tactic_raw`, `state_after_raw` | The familiar human-readable goal display and tactic text for the transition. | |
| | `state_before_structured`, `state_after_structured` | Parsed versions of the displayed proof states. | |
| | `state_before_internal`, `state_after_internal` | Lean's detailed elaborator state: active goals, local declarations, targets, metavariables, universe metavariables, and recursive expressions. | |
| | `tactic_internal` | The tactic's full Lean `Syntax` representation, including atomic and nested tactic structure, identifier resolution, and premise references when available. | |
| | `available_context`, `source_start`, `source_end` | Candidate context and the tactic's source span. | |
| | `terminal` | Whether this step closes the proof. | |
| | `theorem_fingerprint`, `state_fingerprint`, `transition_fingerprint` | Deterministic hashes useful for deduplication, grouping, and integrity checks. | |
|
|
| The recursive structures are stored as lossless JSON strings in Parquet. Parse them |
| with `json.loads` when you need their tree structure; leave them as strings for |
| text-only training baselines. |
|
|
| Each shard is round-trip checked against its source records before publication, |
| and uploaded bytes are verified at an immutable Hugging Face revision. Split |
| assignments and provenance are retained so experiments can be reproduced and |
| results can be traced back to their source theorem and environment. |
|
|
| ## Read |
|
|
| ```python |
| from datasets import load_dataset |
| import json |
| |
| data = load_dataset( |
| "HyperCactus0/LeanTransitionCorpus", |
| revision="<immutable commit SHA>", |
| split="train", |
| streaming=True, |
| ) |
| row = next(iter(data)) |
| state = json.loads(row["state_before_internal"]) if row["state_before_internal"] else None |
| ``` |
|
|
| Use an immutable revision for experiments. The repository grows over time. |
|
|
| ## Identity |
|
|
| `example_id` is globally unique and deterministic. `proof_id` retains the source |
| identifier and may be reused by distinct Numina selections. Identify a proof by |
| `(source_dataset, repo_commit, file_path, provenance.source_sha256, |
| provenance.theorem_ordinal, theorem_name)`. Batch manifests expose these tuples as |
| JSON-encoded `proof_keys`, and the versioned `example_id` hashes that proof key plus |
| `step_index`. |
|
|
