---
license: lgpl-2.1
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - coq
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: 11669}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Coq-Prime

Structured dataset from **CoqPrime** — Primality certificates and number theory.

## Source

- Repository: https://github.com/thery/coqprime
- Commit: `3371791217c6f8dff53972a53f0c3e860d4b54dc`
- Files: 387
- License: lgpl-2.1

## 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: 11,669
- With proof: 11,596 (99.4%)
- With docstring: 147 (1.3%)
- Libraries: 21

### By type

| Type | Count |
|---|---|
| Lemma | 10,270 |
| Definition | 620 |
| Theorem | 420 |
| Let | 109 |
| Fixpoint | 75 |
| Hypothesis | 67 |
| Notation | 50 |
| Ltac | 33 |
| Inductive | 10 |
| Record | 7 |
| Coercion | 3 |
| Parameter | 3 |
| Structure | 1 |
| Hypotheses | 1 |

## Example

```
Zeq_iok: forall x y, x = y -> Zeq_bool x y = true.
intros x y H; subst. apply Zeq_is_eq_bool, eq_refl.
Qed.
```

- type: Theorem | symbolic_name: `Zeq_iok` | src/Coqprime/elliptic/GZnZ.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_prime_dataset,
  title  = {Coq-Prime},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/thery/coqprime, commit 3371791217c6},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Prime}
}
```