---
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: fact, dtype: string}
  - {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: line_start, dtype: int64}
  - {name: line_end, dtype: int64}
  - {name: has_proof, dtype: bool}
  - {name: source_url, dtype: string}
  - {name: commit, dtype: string}
  splits:
  - {name: train, num_examples: 19736}
  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 |
|--------|------|-------------|
| fact | string | Complete verbatim declaration (keyword, signature, and body/proof) |
| statement | string | Signature with the leading keyword removed (verbatim slice) |
| proof | string | Verbatim proof/body, empty if 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, null if absent |
| line_start | int | First source line |
| line_end | int | Last source line |
| has_proof | bool | Whether a proof block was captured |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |

## Statistics

- Entries: 19,736
- With proof: 19,011 (96.3%)
- With docstring: 3,080 (15.6%)
- Libraries: 44

### By type

| Type | Count |
|---|---|
| Lemma | 10,586 |
| Definition | 2,880 |
| Notation | 1,716 |
| Theorem | 1,398 |
| Instance | 770 |
| Ltac | 662 |
| Fixpoint | 545 |
| Parameter | 364 |
| Inductive | 185 |
| Hypothesis | 133 |
| Axiom | 132 |
| Let | 116 |
| Record | 60 |
| Class | 45 |
| Example | 42 |
| Corollary | 24 |
| Fact | 17 |
| Coercion | 16 |
| Scheme | 15 |
| Remark | 11 |
| Parameters | 6 |
| CoFixpoint | 5 |
| Variant | 3 |
| CoInductive | 3 |
| Proposition | 1 |
| Structure | 1 |

## Example

```coq
#[local]
Definition gt_n_S_stt : forall n m, n > m -> S n > S m := fun n m Hgt => proj1 (Nat.succ_lt_mono m n) Hgt.
```

- type: Definition | symbolic_name: `gt_n_S_stt` | theories/Arith/Arith_base.v:137

## Use

Statement and proof are available both joined (`fact`) and split (`statement`, `proof`) for
proof-term 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}
}
```