---
license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - arend
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: 2690}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Arend

Declarations from Arend.

## Source

- Repository: https://github.com/JetBrains/arend-lib
- Commit: `373ed3c493f40a6b7b04a6b81c4e809338e568c4`
- Files: 280
- License: other

## 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: 2,690
- With proof: 2,682 (99.7%)
- With docstring: 0 (0.0%)
- Libraries: 53

### By type

| Type | Count |
|---|---|
| \func | 968 |
| \lemma | 920 |
| \class | 334 |
| \instance | 249 |
| \record | 93 |
| \data | 59 |
| \type | 37 |
| \sfunc | 12 |
| \cons | 9 |
| \meta | 7 |
| \axiom | 2 |

## Example

```
Mono
\extends Map
  | isMono {x : C} {g h : Hom x dom} : f ∘ g = f ∘ h -> g = h
  \where {
    \func comp {C : Precat} {x y z : C} (g : Mono {C} {y} {z}) (f : Mono {C} {x} {y}) : Mono {C} {x} {z} (g.f ∘ f) \cowith
      | isMono p => f.isMono (g.isMono (inv o-assoc *> p *> o-assoc))
  }
```

- type: \record | symbolic_name: `Mono` | src/Category.ard

## 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{arend_dataset,
  title  = {Arend},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/JetBrains/arend-lib, commit 373ed3c493f4},
  url    = {https://huggingface.co/datasets/phanerozoic/Arend}
}
```