Datasets:
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license: other
license_name: cecill-b
license_link: https://cecill.info/licences/Licence_CeCILL-B_V1-en.html
task_categories:
- text-generation
- feature-extraction
language:
- en
tags:
- theorem-proving
- formal-methods
- coq
- mathcomp
- algebra
- mathematics
size_categories:
- 10K<n<100K
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: 23813}
config_name: default
configs:
- config_name: default
data_files:
- split: train
path: data/train-*
---
# Coq-MathComp
Structured dataset from the Mathematical Components library (MathComp) for Coq.
## Source
- Repository: https://github.com/math-comp/math-comp
- Commit: `91d97df9cf3204b4dab84f4e24bc633e84b6473d`
- Files: 139
- License: other
## 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: 23,813
- With proof: 23,468 (98.6%)
- With docstring: 847 (3.6%)
- Libraries: 10
### By type
| Type | Count |
|---|---|
| Lemma | 15,224 |
| Notation | 3,122 |
| Definition | 2,907 |
| Fact | 737 |
| Let | 557 |
| Canonical | 407 |
| Hypothesis | 202 |
| Fixpoint | 149 |
| Coercion | 119 |
| Variant | 116 |
| Theorem | 63 |
| Hypotheses | 51 |
| Inductive | 38 |
| Ltac | 26 |
| Structure | 24 |
| Record | 23 |
| Corollary | 18 |
| Example | 7 |
| Parameter | 5 |
| Proposition | 5 |
| Axiom | 4 |
| Instance | 3 |
| Remark | 3 |
| Class | 2 |
| Scheme | 1 |
## Example
```
floor_subproof n :
if n \is real_num then n%:~R <= n < (n + 1)%:~R else n == 0.
Proof. by rewrite num_real !intz ltzD1 lexx. Qed.
```
- type: Fact | symbolic_name: `floor_subproof` | algebra/archimedean.v
## 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{coq_mathcomp_dataset,
title = {Coq-MathComp},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/math-comp/math-comp, commit 91d97df9cf32},
url = {https://huggingface.co/datasets/phanerozoic/Coq-MathComp}
}
```
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