---
license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - coq
  - unimath
  - univalent-mathematics
size_categories:
  - 10K<n<100K
---

# Coq-UniMath

Structured dataset of formalizations from the UniMath library (Univalent Mathematics in Coq).

## Dataset Description

- **Source:** [UniMath/UniMath](https://github.com/UniMath/UniMath)
- **Entries:** 48,240
- **Files processed:** 1,557
- **License:** UniMath License

## Schema

| Column | Type | Description |
|--------|------|-------------|
| fact | string | Full declaration (name, signature, body) |
| type | string | Definition, Lemma, Theorem, Proposition, etc. |
| library | string | Sub-library (Algebra, CategoryTheory, Foundations, etc.) |
| imports | list | Require Import statements |
| filename | string | Source file path |
| symbolic_name | string | Declaration identifier |
| docstring | string | Documentation comment (13% coverage) |

## Statistics

### By Type
| Type | Count |
|------|-------|
| Definition | 30,272 |
| Lemma | 10,231 |
| Proposition | 3,807 |
| Let | 2,878 |
| Theorem | 359 |
| Notation | 233 |
| Ltac | 229 |
| Corollary | 181 |
| Other | 50 |

### Docstring Coverage
- **6,648 entries (13%)** have documentation

## Example Entry



## Use Cases

- Retrieval / RAG for Coq theorem proving
- Univalent mathematics research
- Training embeddings for formal mathematics
- Documentation generation

## Citation



## Changelog

- **v2.0** (Jan 2025): Re-extraction with improved schema
  - 38,661 -> 48,240 entries (+25%)
  - Added docstring column (13% coverage)
  - Changed imports from string to list
  - Removed index_level column
  - fact now includes full signature
- **v1.0** (Dec 2024): Initial release