---
language: 
  - "en"
pretty_name: "Coq-HoTT Dataset"
tags:
  - "theorem-proving"
  - "formal-methods"
  - "hott"
  - "coq"
license: "bsd-2-clause"
task_categories:
- "text-generation"
- "feature-extraction"
- "other"
---

# Coq-HoTT Dataset

## Dataset Description

The Coq-HoTT Dataset is derived from the Coq-HoTT repository, focusing on the formalization of Homotopy Type Theory in the Coq proof assistant. This dataset processes `.v` files from the theories directory to extract mathematical content in a structured format.

This work builds upon the format established by Andreas Florath (@florath) in his Coq Facts, Propositions and Proofs dataset.

### Dataset Structure

The dataset includes the following fields:
- `fact`: The complete mathematical statement, including type (Definition/Lemma/Theorem), name, and body
- `imports`: The Require Import statements from the source file
- `filename`: The source file name within the theories directory
- `symbolic_name`: The identifier of the mathematical object
- `__index_level_0__`: Sequential index for the dataset

### Example Row

```
fact: "Definition minimal(n : nat) : Type := forall m : nat, P m -> n <= m."
imports: "Require Import HoTT.Basics HoTT.Types. Require Import HoTT.Truncations.Core. Require Import HoTT.Spaces.Nat.Core."
filename: "BoundedSearch.v"
symbolic_name: "minimal"
__index_level_0__: 0
```

### Source Code

The dataset was generated using a custom Python script that processes the Coq-HoTT repository's theories directory, extracting mathematical content while preserving the structure and relationships between definitions, imports, and their source files.
``` to clean and organize content. `.v` files were processed for mathematical content, while `.md` files were included to retain important documentation and context.

### Usage:

This dataset is designed for:
- Formal Methods Research: Analyzing formal proofs and definitions in Homotopy Type Theory.
- Machine Learning Applications: Training models on formal verification, code completion, and theorem proving tasks.
- Educational Purposes: Providing structured examples of Coq formalizations.

### License:

This dataset is distributed under the  BSD 2-clause licence, aligning with the license of the original Coq-HoTT repository.

### Acknowledgments:

- Original repository: Coq-HoTT (https://github.com/HoTT/Coq-HoTT)
- Inspiration: Hugging Face user Andreas Florath (@florath) and his dataset on Coq.