| --- |
| 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: |
| |
| |
| |
