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Coq-UniMath

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Tags:
theorem-proving
formal-methods
univalent-mathematics
coq
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metadata
language:
  - en
pretty_name: UniMath Dataset
tags:
  - theorem-proving
  - formal-methods
  - univalent-mathematics
  - coq
license: bsd-2-clause
task_categories:
  - text-generation
  - feature-extraction
  - other

UniMath Dataset

Dataset Description

The UniMath Dataset is derived from the UniMath repository, focusing on the formalization of Univalent Mathematics in the Coq proof assistant. This dataset processes .v files from the core mathematical libraries 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, providing a more focused and structured view of the UniMath library specifically.

Dataset Structure

The dataset includes the following fields:

  • fact: The mathematical statement body
  • type: The statement type (Definition/Lemma/Theorem/etc.)
  • library: The originating library (Algebra/CategoryTheory/etc.)
  • imports: The Require Import statements from the source file
  • filename: The source file path within UniMath
  • symbolic_name: The identifier of the mathematical object
  • index_level_0: Sequential index for the dataset

Example Row

fact: "(X : abmonoid) {L : hrel X} (is : isbinophrel L) (isi : isinvbinophrel L) (isl : isdecrel L) : isdecrel (abgrdiffrel X is)" type: "Definition" library: "Algebra" imports: "Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Subtypes." filename: "Algebra/AbelianGroups.v" symbolic_name: "isdecabgrdiffrel" index_level_0: 55

Source Code

The dataset was generated using a custom Python script that processes core UniMath libraries including Algebra, CategoryTheory, Foundations, and others. The extraction focuses on mathematical content while preserving the structure and relationships between definitions, lemmas, and their source files.

Coverage

The dataset includes content from the following UniMath libraries:

  • Algebra
  • Bicategories
  • CategoryTheory
  • Combinatorics
  • Foundations
  • HomologicalAlgebra
  • Ktheory
  • MoreFoundations
  • NumberSystems
  • OrderTheory
  • PAdics
  • RealNumbers
  • SubstitutionSystems
  • Topology

Usage

This dataset is designed for:

  • Formal Methods Research: Analyzing formal proofs and definitions in Univalent Mathematics
  • Machine Learning Applications: Training models on formal verification, code completion, and theorem proving tasks
  • Educational Purposes: Providing structured examples of UniMath formalizations
  • Mathematical Analysis: Studying the structure and patterns in formalized mathematical content

License

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

Acknowledgments