---
license: other
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - redtt
  - cubical-type-theory
  - homotopy-type-theory
size_categories:
  - 10K<n<100K
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: 501}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# redtt

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

## Source

- Repository: https://github.com/RedPRL/redtt
- Commit: `ae76658873a647eb43d8cf84365a9d68e9a3273c`
- Files: 66
- License: other

## Schema

| Column | Type | Description |
|--------|------|-------------|
| fact | string | Verbatim declaration with the leading keyword removed: signature and body/proof joined |
| 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 `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: 501
- With proof: 501 (100.0%)
- With docstring: 19 (3.8%)
- Libraries: 6

### By type

| Type | Count |
|---|---|
| def | 478 |
| data | 23 |

## Example

```coq
biinv-equiv→iso (A B : type) : biinv-equiv A B → iso A B =
  λ (f,(g,α),h,β) →
  let β' (a : A) : path _ (g (f a)) a =
    λ i →
    comp 0 1 (h (α (f a) i)) [
    | i=0 j → β (g (f a)) j
    | i=1 j → β a j
    ]
  in
  (f,g,α,β')
```

- type: def | symbolic_name: `biinv-equiv→iso` | library/basics/biinv-equiv.red:12

## 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{redtt_dataset,
  title  = {redtt},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/RedPRL/redtt, commit ae76658873a6},
  url    = {https://huggingface.co/datasets/phanerozoic/redtt}
}
```