---
license: apache-2.0
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - lean4
  - batteries
  - standard-library
size_categories:
  - 1K<n<10K
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: 3061}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Lean4-Batteries

Structured dataset from Lean 4 Batteries - the community standard library extensions.

## Source

- Repository: https://github.com/leanprover-community/batteries
- Commit: `41680f5d84023c7406c841d08ef83bf15a9782a6`
- Files: 187
- 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: 3,061
- With proof: 2,965 (96.9%)
- With docstring: 1,199 (39.2%)
- Libraries: 35

### By type

| Type | Count |
|---|---|
| theorem | 1,874 |
| def | 1,005 |
| abbrev | 48 |
| structure | 37 |
| elab | 30 |
| inductive | 24 |
| class | 22 |
| macro | 11 |
| instance | 9 |
| opaque | 1 |

## Example

```
Function.id_def : @id α = fun x => x
rfl

/-! ## decidable -/

protected alias ⟨Decidable.exists_not_of_not_forall, _⟩ := Decidable.not_forall
```

- type: theorem | symbolic_name: `Function.id_def` | Batteries/Logic.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_batteries_dataset,
  title  = {Lean4-Batteries},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/leanprover-community/batteries, commit 41680f5d8402},
  url    = {https://huggingface.co/datasets/phanerozoic/Lean4-Batteries}
}
```