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Coq-HoTT

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theorem-proving
formal-methods
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metadata
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: