| ---
|
| 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: 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: 232431}
|
| config_name: default
|
| configs:
|
| - config_name: default
|
| data_files:
|
| - split: train
|
| path: data/train-*
|
| ---
|
|
|
| # Lean4-Mathlib
|
|
|
| Structured dataset of mathematical formalizations from the Mathlib4 library for Lean 4.
|
|
|
| ## Source
|
|
|
| - Repository: https://github.com/leanprover-community/mathlib4
|
| - Commit: `b9f14353520df73472ae3825fb53f86559a01319`
|
| - Files: 8170
|
| - 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: 232,431
|
| - With proof: 228,818 (98.4%)
|
| - With docstring: 67,814 (29.2%)
|
| - Libraries: 1103
|
|
|
| ### By type
|
|
|
| | Type | Count |
|
| |---|---|
|
| | theorem | 125,463 |
|
| | lemma | 56,488 |
|
| | def | 31,961 |
|
| | instance | 10,971 |
|
| | abbrev | 3,379 |
|
| | class | 1,937 |
|
| | structure | 1,580 |
|
| | inductive | 326 |
|
| | elab | 168 |
|
| | macro | 147 |
|
| | class inductive | 6 |
|
| | class abbrev | 3 |
|
| | opaque | 2 |
|
|
|
| ## Example
|
|
|
| ```
|
| infinite_of_charZero (R A : Type*) [CommRing R] [Ring A] [Algebra R A]
|
| [CharZero A] : { x : A | IsAlgebraic R x }.Infinite
|
| by
|
| letI := MulActionWithZero.nontrivial R A
|
| exact infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
|
| ```
|
|
|
| - type: theorem | symbolic_name: `Algebraic.infinite_of_charZero` | Mathlib/Algebra/AlgebraicCard.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_mathlib_dataset,
|
| title = {Lean4-Mathlib},
|
| author = {Norton, Charles},
|
| year = {2026},
|
| note = {Extracted from https://github.com/leanprover-community/mathlib4, commit b9f14353520d},
|
| url = {https://huggingface.co/datasets/phanerozoic/Lean4-Mathlib}
|
| }
|
| ```
|
| |
