---
license: lgpl-2.1
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - coq
  - standard-library
size_categories:
  - 1K<n<10K
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: 18419}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Coq-Stdlib

Structured dataset of definitions and theorems from the Coq standard library.

## Source

- Repository: https://github.com/rocq-prover/stdlib
- Commit: `f76a666b0b2c28c671d4fdf6dd25bcab865b9c36`
- Files: 583
- 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: 18,419
- With proof: 17,842 (96.9%)
- With docstring: 2,948 (16.0%)
- Libraries: 44

### By type

| Type | Count |
|---|---|
| Lemma | 10,045 |
| Definition | 2,527 |
| Notation | 1,550 |
| Theorem | 1,386 |
| Instance | 736 |
| Ltac | 597 |
| Fixpoint | 512 |
| Parameter | 305 |
| Inductive | 182 |
| Axiom | 127 |
| Hypothesis | 107 |
| Let | 105 |
| Record | 60 |
| Class | 45 |
| Example | 42 |
| Corollary | 24 |
| Fact | 17 |
| Coercion | 12 |
| Remark | 11 |
| Scheme | 10 |
| Parameters | 6 |
| CoFixpoint | 5 |
| Variant | 3 |
| CoInductive | 3 |
| Proposition | 1 |
| Structure | 1 |

## Example

```
gt_pred_stt : forall n m, m > S n -> pred m > n
:= fun n m Hgt => proj1 (Nat.lt_succ_lt_pred n m) Hgt.
```

- type: Definition | symbolic_name: `gt_pred_stt` | theories/Arith/Arith_base.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_stdlib_dataset,
  title  = {Coq-Stdlib},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/rocq-prover/stdlib, commit f76a666b0b2c},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Stdlib}
}
```