---
license: bsd-2-clause
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - coq
  - hott
  - homotopy-type-theory
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: 12715}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Coq-HoTT

Structured dataset of formalizations from the Coq-HoTT library (Homotopy Type Theory in Coq).

## Source

- Repository: https://github.com/HoTT/Coq-HoTT
- Commit: `b75eadc7cb2bc59dca415bf47662a9290f82dc5f`
- Files: 589
- License: bsd-2-clause

## 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: 12,715
- With proof: 12,537 (98.6%)
- With docstring: 5,206 (40.9%)
- Libraries: 92

### By type

| Type | Count |
|---|---|
| Definition | 6,820 |
| Instance | 2,406 |
| Lemma | 1,304 |
| Notation | 676 |
| Class | 371 |
| Ltac | 256 |
| Fixpoint | 140 |
| Record | 139 |
| Coercion | 120 |
| Let | 105 |
| Theorem | 103 |
| Proposition | 66 |
| Inductive | 48 |
| Axiom | 38 |
| Scheme | 37 |
| Hypothesis | 36 |
| Corollary | 26 |
| Example | 12 |
| Variant | 6 |
| Fact | 3 |
| Canonical | 1 |
| Parameters | 1 |
| Parameter | 1 |

## Example

```
ecompose_e_ee {A B C D} (e : A <~> B) (f : B <~> C) (g : C <~> D)
  : g oE (f oE e) = (g oE f) oE e.
Proof.
    apply path_equiv; reflexivity.
  Defined.
```

- type: Definition | symbolic_name: `ecompose_e_ee` | theories/EquivGroupoids.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_hott_dataset,
  title  = {Coq-HoTT},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/HoTT/Coq-HoTT, commit b75eadc7cb2b},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-HoTT}
}
```