---
license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - cooltt
  - cubical-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: 228}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# cooltt

Declarations from cooltt, a cubical/computational type theory system.

## Source

- Repository: https://github.com/RedPRL/cooltt
- Commit: `b39bf29900451cb43ae6fbd9af5aa33d59e18935`
- Files: 32
- 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: 228
- With proof: 221 (96.9%)
- With docstring: 31 (13.6%)
- Libraries: 1

### By type

| Type | Count |
|---|---|
| def | 221 |
| axiom | 7 |

## Example

```
+0R : (x : nat) → path nat {+ x 0} x
:=
  elim [
  | zero => +0L 0
  | suc {x => ih} =>
    equation nat begin
      + {suc x} 0 =[ +SL x 0 ]
      suc {+ x 0} =[ i => suc {ih i} ]
      suc x
    end
  ]
```

- type: def | symbolic_name: `+0R` | test/abstract.cooltt

## 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{cooltt_dataset,
  title  = {cooltt},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/RedPRL/cooltt, commit b39bf2990045},
  url    = {https://huggingface.co/datasets/phanerozoic/cooltt}
}
```