| --- |
| license: mit |
| 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 |
|
|
| > **Status: incremental upload in progress.** This repository is useful now, but |
| > it is not the complete planned corpus. Counts, source coverage, and shard |
| > inventory will grow as verified batches are added. |
|
|
| 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 |
| MIT 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. Coverage is incremental: a source listed here may have less |
| published coverage than another at any point in time. |
|
|
| | 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. | |
|
|
| ## 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. A `replay_status` value records whether an additional |
| replay check was performed; publication alone does not mean replay certification. |
|
|
| ## Format |
|
|
| Zstandard-compressed Parquet shards, one row per transition, schema version 2. |
| The physical encoding is `leangpt-parquet-v2`: all 40 columns are retained. |
| `schema_version` and `step_index` are int64; `terminal` is boolean; |
| `imports`, `atomic_tactics`, `used_premises`, 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`, `schema_version` | Stable identity, position in the proof, dataset split, and format version. `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`, `pantograph_version`, `provenance` | Where the theorem came from and the exact environment and extraction provenance needed to reproduce or audit it. | |
| | `theorem_name`, `theorem_statement_raw`, `theorem_source_raw`, `namespace`, `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. | |
| | `atomic_tactics`, `tactic_internal` | The tactic's atomic view and its full Lean `Syntax` representation, including identifier resolution, premise references, and nested tactic structure when available. | |
| | `used_premises`, `available_context`, `source_start`, `source_end` | Referenced declarations, candidate context, and the tactic's source span. | |
| | `terminal`, `terminal_marker`, `terminal_raw` | Whether this step closes the proof and the source/display marker associated with closure. | |
| | `theorem_fingerprint`, `state_fingerprint`, `transition_fingerprint` | Deterministic hashes useful for deduplication, grouping, and integrity checks. | |
| | `replay_status`, `replay_error` | Result of optional replay validation; `not_run` means no independent replay was attempted. | |
|
|
| 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 compared against every original JSON row before upload. |
| Remote bytes are streamed back and checked for SHA-256 and size at a pinned commit. |
| `manifests/batches/` records verified shard hashes/revisions, original batch |
| fingerprints, extraction evidence, and retained proof IDs plus provenance-based proof keys. A batch manifest exists |
| only after all of its split shards are verified. Failed attempts are described in |
| batch evidence and must not be mistaken for successfully extracted proofs. |
|
|
| Quarantine artifacts, when present under `data/quarantine/`, are excluded from the |
| default configuration. They are archival evidence, not clean training examples. |
| Splits are inherited from the frozen extractor, not recomputed by the publisher. |
| Replay status is recorded per row; publication does not imply replay verification. |
|
|
| Frozen extraction inputs under `sources/` are also excluded from the default |
| configuration. They allow scratch-only workers to range-read deterministic chunks |
| when an original upstream revision is no longer available. Their paths, immutable |
| revisions, sizes, and SHA-256 digests are recorded by the extraction runner. |
|
|
| ## 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. |
|
|
| ## Local seed snapshot |
|
|
| The imported seed contains 285 completed Numina batches: 1,425 attempted proofs, |
| 1,378 extracted proofs, and 1,374 source-distinct proofs retained as 13,105 |
| transition rows. Four extracted proofs failed internal-state validation during |
| canonicalization; the batch evidence records these exclusions. |
|
|
| | Split | Transition rows | Source-distinct proofs | |
| |---|---:|---:| |
| | train | 11,182 | 1,159 | |
| | dev | 654 | 65 | |
| | internal_test | 1,269 | 150 | |
| |
| No quarantine transition rows are present in this seed. All transition rows have |
| `replay_status=not_run`. The local audit found no duplicate provenance-based |
| transition keys or theorem-fingerprint conflicts across splits. These checks do |
| not constitute independent Lean replay validation. |
| |
| ## 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`. |
|
|
