metadata
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
Mathlib4
Structured dataset of mathematical formalizations from the Mathlib4 library for Lean 4.
Dataset Description
- Source: 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: