---
license: apache-2.0
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - lean4
  - standard-library
size_categories:
  - 10K<n<100K
dataset_info:
  features:
  - {name: statement, dtype: string}
  - {name: proof, dtype: string}
  - {name: type, dtype: string}
  - {name: symbolic_name, dtype: string}
  - {name: library, dtype: string}
  - {name: filename, dtype: string}
  - {name: imports, list: string}
  - {name: deps, list: string}
  - {name: docstring, dtype: string}
  - {name: source_url, dtype: string}
  - {name: commit, dtype: string}
  splits:
  - {name: train, num_examples: 52970}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Lean4-Stdlib

Structured dataset of definitions and theorems from the Lean 4 standard library (Init + Std).

## Source

- Repository: https://github.com/leanprover/lean4
- Commit: `d265d1ca745e7741a7e7f7366c22ce9c9dda57b6`
- Files: 1071
- License: apache-2.0

## Schema

| Column | Type | Description |
|--------|------|-------------|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level `Require`/`Import` modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |

## Statistics

- Entries: 52,970
- With proof: 51,596 (97.4%)
- With docstring: 7,626 (14.4%)
- Libraries: 165

### By type

| Type | Count |
|---|---|
| theorem | 42,996 |
| def | 7,688 |
| abbrev | 441 |
| structure | 426 |
| opaque | 383 |
| instance | 349 |
| class | 313 |
| inductive | 184 |
| macro | 172 |
| axiom | 15 |
| class inductive | 2 |
| class abbrev | 1 |

## Example

```
apply_dite (f : α → β) (P : Prop) [Decidable P] (x : P → α) (y : ¬P → α) :
    f (dite P x y) = dite P (fun h => f (x h)) (fun h => f (y h))
by
  by_cases h : P <;> simp [h]
```

- type: theorem | symbolic_name: `apply_dite` | src/Init/ByCases.lean

## Use

Each declaration is split into a `statement` (signature/claim) and a `proof` (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via `deps`.

## Citation

```bibtex
@misc{lean4_stdlib_dataset,
  title  = {Lean4-Stdlib},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/leanprover/lean4, commit d265d1ca745e},
  url    = {https://huggingface.co/datasets/phanerozoic/Lean4-Stdlib}
}
```