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--- |
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language: |
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- "en" |
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pretty_name: "Coq-HoTT Dataset" |
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tags: |
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- "theorem-proving" |
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- "formal-methods" |
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- "hott" |
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- "coq" |
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license: "bsd-2-clause" |
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task_categories: |
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- "text-generation" |
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- "feature-extraction" |
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- "other" |
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--- |
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# Coq-HoTT Dataset |
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## Dataset Description |
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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. |
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This work builds upon the format established by Andreas Florath (@florath) in his Coq Facts, Propositions and Proofs dataset. |
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### Dataset Structure |
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The dataset includes the following fields: |
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- `fact`: The complete mathematical statement, including type (Definition/Lemma/Theorem), name, and body |
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- `imports`: The Require Import statements from the source file |
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- `filename`: The source file name within the theories directory |
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- `symbolic_name`: The identifier of the mathematical object |
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- `__index_level_0__`: Sequential index for the dataset |
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### Example Row |
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``` |
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fact: "Definition minimal(n : nat) : Type := forall m : nat, P m -> n <= m." |
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imports: "Require Import HoTT.Basics HoTT.Types. Require Import HoTT.Truncations.Core. Require Import HoTT.Spaces.Nat.Core." |
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filename: "BoundedSearch.v" |
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symbolic_name: "minimal" |
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__index_level_0__: 0 |
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``` |
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### Source Code |
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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. |
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``` to clean and organize content. `.v` files were processed for mathematical content, while `.md` files were included to retain important documentation and context. |
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### Usage: |
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This dataset is designed for: |
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- Formal Methods Research: Analyzing formal proofs and definitions in Homotopy Type Theory. |
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- Machine Learning Applications: Training models on formal verification, code completion, and theorem proving tasks. |
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- Educational Purposes: Providing structured examples of Coq formalizations. |
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### License: |
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This dataset is distributed under the BSD 2-clause licence, aligning with the license of the original Coq-HoTT repository. |
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### Acknowledgments: |
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- Original repository: Coq-HoTT (https://github.com/HoTT/Coq-HoTT) |
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- Inspiration: Hugging Face user Andreas Florath (@florath) and his dataset on Coq. |
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