---
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: 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: 10218663
    num_examples: 19924
  download_size: 1831894
  dataset_size: 10218663
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Coq-MathComp

Structured dataset from the Mathematical Components library (MathComp) for Coq.

## Dataset Description

- **Source:** [math-comp/math-comp](https://github.com/math-comp/math-comp) (v2.5.0)
- **Entries:** 19,924
- **Files processed:** 115
- **License:** CeCILL-B

## Schema

| Column | Type | Description |
|--------|------|-------------|
| fact | string | Declaration body |
| type | string | Lemma, Definition, HB.structure, HB.mixin, Canonical, etc. |
| library | string | Module (algebra, boot, fingroup, character, etc.) |
| imports | list | Require/Import statements |
| filename | string | Source file path |
| symbolic_name | string | Declaration identifier |

## Statistics

### By Type
| Type | Count |
|------|-------|
| Lemma | 14,917 |
| Definition | 2,850 |
| Notation | 808 |
| Canonical | 425 |
| HB.instance | 247 |
| Fixpoint | 138 |
| Coercion | 116 |
| Variant | 104 |
| Theorem | 63 |
| HB.structure | 51 |
| HB.mixin | 50 |

### By Library
| Library | Count |
|---------|-------|
| algebra | 7,455 |
| boot | 4,591 |
| fingroup | 1,995 |
| character | 1,864 |
| solvable | 1,747 |
| order | 1,197 |
| field | 1,048 |

## About MathComp

Mathematical Components is a library of formalized mathematics for Coq, including algebra, number theory, and finite group theory. It uses the SSReflect proof language and Hierarchy Builder (HB) for structure definitions.

## Use Cases

- Retrieval/RAG for Coq/MathComp
- Learning SSReflect patterns
- Algebraic formalization research
- Training embeddings for formal proofs

## Related Datasets

- [Coq-HoTT](https://huggingface.co/datasets/phanerozoic/Coq-HoTT)
- [Coq-UniMath](https://huggingface.co/datasets/phanerozoic/Coq-UniMath)
- [Coq-Stdlib](https://huggingface.co/datasets/phanerozoic/Coq-Stdlib)
- [Coq-Iris](https://huggingface.co/datasets/phanerozoic/Coq-Iris)