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---
license: apache-2.0
task_categories:
- text-generation
- feature-extraction
language:
- en
tags:
- theorem-proving
- formal-methods
- lean4
- mathlib
- mathematics
size_categories:
- 100K<n<1M
dataset_info:
features:
- name: fact
dtype: string
- name: type
dtype: string
- name: library
dtype: string
- name: imports
list: string
- name: filename
dtype: string
- name: symbolic_name
dtype: string
- name: docstring
dtype: string
splits:
- name: train
num_bytes: 110117432
num_examples: 193047
download_size: 26646919
dataset_size: 110117432
configs:
- config_name: default
data_files:
- split: train
path: data/train-*
---
# Mathlib4
Structured dataset of mathematical formalizations from the Mathlib4 library for Lean 4.
## Dataset Description
- **Source:** [leanprover-community/mathlib4](https://github.com/leanprover-community/mathlib4)
- **Entries:** 193,047
- **Files processed:** 6,943
- **License:** Apache 2.0
## Schema
| Column | Type | Description |
|--------|------|-------------|
| fact | string | Full declaration body |
| type | string | theorem, lemma, def, class, structure, instance, inductive, abbrev, axiom |
| library | string | Top-level Mathlib module (Algebra, Analysis, Topology, etc.) |
| imports | list | Import statements from source file |
| filename | string | Source file path within Mathlib |
| symbolic_name | string | Declaration identifier |
| docstring | string | Documentation comment (30% coverage) |
## Statistics
### By Type
| Type | Count | Percentage |
|------|-------|------------|
| theorem | 111,804 | 57% |
| lemma | 36,970 | 19% |
| def | 27,965 | 14% |
| instance | 10,322 | 5% |
| abbrev | 2,570 | 1% |
| class | 1,710 | 1% |
| structure | 1,387 | 1% |
| inductive | 310 | <1% |
### By Library (Top 10)
| Library | Count |
|---------|-------|
| Algebra | 30,936 |
| Analysis | 20,343 |
| Data | 20,327 |
| CategoryTheory | 18,553 |
| Topology | 16,800 |
| Order | 13,686 |
| RingTheory | 12,566 |
| LinearAlgebra | 9,279 |
| MeasureTheory | 8,927 |
| Combinatorics | 4,949 |
### Docstring Coverage
| Type | With Docstring |
|------|----------------|
| def | 98% |
| class | 98% |
| structure | 93% |
| theorem | 15% |
| lemma | 14% |
## Use Cases
- Retrieval / RAG for Lean 4 theorem proving
- Mathematical content search and exploration
- Training embeddings for formal mathematics
- Documentation generation
- Semantic search over mathematical definitions
## Example Entry
## Citation
If you use this dataset, please cite Mathlib:
|