---
license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - cubicaltt
  - cubical-type-theory
  - homotopy-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: 1874}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# cubicaltt

Declarations from cubicaltt, an experimental cubical type theory.

## Source

- Repository: https://github.com/mortberg/cubicaltt
- Commit: `9baa6f2491cc61dbd4fd81d58323c04100381451`
- Files: 78
- 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: 1,874
- With proof: 1,874 (100.0%)
- With docstring: 316 (16.9%)
- Libraries: 3

### By type

| Type | Count |
|---|---|
| def | 1,829 |
| data | 44 |
| hdata | 1 |

## Example

```
propisAssociative (M : U) (sM : set M) (op : M -> M -> M)
  : prop (isAssociative M op)
= let
    B (a b c : M) : U
      = Path M (op a (op b c)) (op (op a b) c)
    h (a b c : M) : prop (B a b c)
      = sM (op a (op b c)) (op (op a b) c)
  in propPi3 M B h
```

- type: def | symbolic_name: `propisAssociative` | examples/algstruct.ctt

## 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{cubicaltt_dataset,
  title  = {cubicaltt},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/mortberg/cubicaltt, commit 9baa6f2491cc},
  url    = {https://huggingface.co/datasets/phanerozoic/cubicaltt}
}
```