---
license: other
language:
- code
task_categories:
- text-generation
tags:
- mathematics
- formal-proof
pretty_name: Coq Facts, Propositions and Proofs
size_categories:
- 100K<n<1M
source_datasets:
- https://github.com/coq-community/autosubst.git
- https://gitlab.inria.fr/fbesson/itauto.git
- https://github.com/coq-community/apery.git
- https://github.com/coq-contribs/dep-map.git
- https://github.com/coq-community/math-classes.git
- https://github.com/coq-contribs/amm11262.git
- https://gitlab.inria.fr/flocq/flocq.git
- https://github.com/uds-psl/coq-library-undecidability.git
- https://github.com/vafeiadis/hahn.git
- https://github.com/coq-community/trocq.git
- https://github.com/coq-community/tarjan.git
- https://github.com/coq-community/generic-environments.git
- https://github.com/imdea-software/htt.git
- https://gitlab.mpi-sws.org/iris/stdpp.git
- https://github.com/coq-contribs/coinductive-reals.git
- https://github.com/coq-community/bertrand.git
- https://github.com/coq-contribs/hoare-tut.git
- https://github.com/coq-contribs/cfgv.git
- https://github.com/artagnon/bonak.git
- https://github.com/coq-community/coq-ext-lib.git
- https://github.com/coq-contribs/checker.git
- https://gitlab.inria.fr/coqinterval/interval.git
- https://gitlab.inria.fr/gappa/coq.git
- https://github.com/imdea-software/fcsl-pcm.git
- https://github.com/coq-community/proviola.git
- https://gitlab.com/umb-svl/turing.git
- https://github.com/damien-pous/relation-algebra.git
- https://github.com/coq-community/HighSchoolGeometry.git
- https://github.com/coq-community/coqeal.git
- https://github.com/coq-community/semantics.git
- https://github.com/coq-contribs/algebra.git
- https://github.com/coq-contribs/abp.git
- https://github.com/coq/coq.git
- https://github.com/coq-contribs/demos.git
- https://github.com/coq-community/pocklington.git
- https://github.com/coq-contribs/cantor.git
- https://github.com/coq-community/notation-gallery.git
- https://github.com/coq-contribs/ctltctl.git
- https://github.com/HoTT/Coq-HoTT.git
- https://github.com/coq-community/corn.git
- https://github.com/affeldt-aist/monae.git
- https://github.com/coq-community/stalmarck.git
- https://github.com/coq-community/qarith-stern-brocot.git
- https://github.com/coq-contribs/bdds.git
- https://github.com/DeepSpec/InteractionTrees.git
- https://github.com/coq-community/lemma-overloading.git
- https://github.com/coq-community/coq-art.git
- https://github.com/coq-community/coq-performance-tests.git
- https://github.com/impermeable/coq-waterproof.git
- https://github.com/coq-contribs/dblib.git
- https://github.com/math-comp/algebra-tactics.git
- https://github.com/coq-community/zorns-lemma.git
- https://github.com/smtcoq/smtcoq.git
- https://gitlab.inria.fr/coquelicot/coquelicot.git
- https://github.com/coq-community/sudoku.git
- https://github.com/QuickChick/QuickChick.git
- https://github.com/coq-contribs/ails.git
- https://github.com/math-comp/math-comp.git
- https://github.com/plclub/metalib.git
- https://github.com/xavierleroy/cdf-mech-sem.git
- https://github.com/CertiGraph/CertiGraph.git
- https://github.com/math-comp/Coq-Combi.git
- https://github.com/coq-contribs/additions.git
- https://github.com/coq-community/regexp-Brzozowski.git
- https://github.com/math-comp/finmap.git
- https://github.com/coq-community/huffman.git
- https://github.com/mattam82/Coq-Equations.git
- https://github.com/math-comp/multinomials.git
- https://github.com/roglo/puiseuxth.git
- https://github.com/thery/FlocqLecture.git
- https://github.com/math-comp/odd-order.git
- https://github.com/uwplse/verdi.git
- https://github.com/mit-plv/fiat.git
- https://github.com/adampetcher/fcf.git
- https://github.com/uncomputable/natural-number-game.git
- https://github.com/mit-plv/bbv.git
- https://github.com/coq-community/fourcolor.git
- https://github.com/coq-community/coqtail-math.git
- https://github.com/coq-community/almost-full.git
- https://github.com/coq-contribs/dictionaries.git
- https://github.com/clarksmr/sf-lectures.git
- https://github.com/affeldt-aist/infotheo.git
- https://github.com/coq-community/gaia.git
- https://github.com/coq-contribs/circuits.git
- https://github.com/coq-contribs/coq-in-coq.git
- https://github.com/coq-community/hoare-tut.git
- https://github.com/thery/minirubik.git
- https://github.com/coq-contribs/coinductive-examples.git
- https://github.com/coq-community/bits.git
- https://github.com/coq-community/graph-theory.git
- https://github.com/coq-community/hydra-battles.git
- https://github.com/coq-community/coq-100-theorems.git
- https://github.com/coq-community/metaprogramming-rosetta-stone.git
- https://github.com/coq-community/buchberger.git
- https://github.com/math-comp/Abel.git
- https://github.com/thery/mathcomp-extra.git
- https://github.com/coq-contribs/coalgebras.git
- https://github.com/thery/coqprime.git
- https://github.com/coq-community/atbr.git
- https://github.com/coq-community/bignums.git
- https://github.com/coq-community/aac-tactics.git
- https://github.com/codyroux/name-the-biggest-number.git
- https://github.com/math-comp/trajectories.git
- https://github.com/coq-contribs/concat.git
- https://github.com/math-comp/real-closed.git
- https://github.com/lukaszcz/coqhammer.git
- https://github.com/jwiegley/category-theory.git
- https://github.com/math-comp/dioid.git
- https://github.com/jwiegley/coq-haskell.git
- https://github.com/math-comp/analysis.git
- https://github.com/coq-community/dblib.git
- https://github.com/coq-community/topology.git
- https://github.com/coq-contribs/automata.git
- https://github.com/coq-community/reglang.git
- https://github.com/thery/T2048.git
- https://github.com/lthms/FreeSpec.git
- https://github.com/charguer/tlc.git
- https://github.com/tchajed/coq-record-update.git
- https://github.com/coq-contribs/classical-realizability.git
- https://github.com/coq-community/comp-dec-modal.git
- https://github.com/coq-community/coqoban.git
- https://github.com/coq-community/parseque.git
- https://github.com/UniMath/UniMath.git
- https://github.com/coq-contribs/distributed-reference-counting.git
- https://github.com/coq-community/jmlcoq.git
- https://github.com/SSProve/ssprove.git
- https://github.com/coq-community/chapar.git
- https://github.com/coq-community/alea.git
- https://github.com/coq-community/paramcoq.git
- https://github.com/snu-sf/paco.git
- https://github.com/math-comp/mczify.git
- https://github.com/ilyasergey/pnp.git
- https://github.com/Mtac2/Mtac2.git
- https://github.com/Deducteam/coq-hol-light.git
- https://github.com/coq-community/coqffi.git
- https://github.com/math-comp/tutorial_material.git
- https://github.com/GeoCoq/GeoCoq.git
- https://github.com/math-comp/bigenough.git
- https://github.com/thery/hanoi.git
- https://github.com/coq-community/coq-mmaps.git
- https://github.com/fblanqui/color.git
- https://github.com/Matafou/LibHyps.git
---

# Dataset Name: Coq Facts, Propositions and Proofs

## Dataset Description

The CoqFactsPropsProofs dataset aims to enhance Large Language Models'
(LLMs) proficiency in interpreting and generating Coq code by
providing a comprehensive collection of over 10,000 Coq source
files. It encompasses a wide array of propositions, proofs, and
definitions, enriched with metadata including source references and
licensing information. This dataset is designed to facilitate the
development of models capable of generating syntactically correct and
semantically meaningful Coq constructs, thereby advancing automated
theorem proving.

A detailed description can be found in the paper
[Enhancing Formal Theorem Proving: A Comprehensive Dataset for Training AI Models on Coq Code](https://arxiv.org/abs/2403.12627).

## Composition

* Files: Over 10,000 Coq source files (`.v` files).
* Tables: Three distinct tables: facts (definitions or notations),
  propositions (theorems and lemmas alongside proofs), and
  licensing/repository information.
* Entries: 103,446 facts and 166,035 propositions with proofs.
* Size: Character length ranging from as short as 11 to as long as
  177,585 characters.
* Source and Collection Method: The Coq source files were collected
  from various internet sources, focusing on repositories pivotal
  within the Coq community. These sources range from foundational
  libraries and formalized mathematical theorems to computer science
  theories and algorithm implementations. The collection process
  prioritized quality, relevance, and the contribution of each source
  to the Coq ecosystem.

## Licenses

The dataset includes a diverse range of open-source licenses,
reflecting the variety in the Coq community and the broader
open-source ecosystem. Some of the licenses included are MIT, GPL
(versions 2.0 and 3.0), LGPL (versions 2.1 and 3.0), Apache 2.0, BSD
(2-Clause and 3-Clause), CECILL (versions 1.0, 2.1, B, C), MPL-2.0,
and the UniMath License. Each entry in the dataset links to detailed
license information, ensuring compliance and redistribution legality.

## Usage

This dataset is provided in three parquet files and can be employed in
a variety of ways depending on the use case. An example usage case
includes training or fine-tuning models to focus on proofs rather than
definitions and notations. The dataset also allows for filtering based
on specific licenses using the `info.parquet` file.

```python
import pandas as pd

df_facts_raw = pd.read_parquet("facts.parquet")
df_info = pd.read_parquet("info.parquet")

# This is the list of licenses which might be seen as permissive
permissive_licenses_list = [
    'Apache-2.0', 'BSD-2-Clause', 'BSD-3-Clause',
    'CECILL-B', 'CECILL-C', 
    'LGPL-2.1-only', 'LGPL-2.1-or-later', 'LGPL-3.0-only', 'LGPL-3.0-or-later', 
    'MIT', 'MPL-2.0', 'UniMath' ]

# Set the license-type to permissive based on the list
df_info['license-type'] = df_info['spdx-id'].apply(
    lambda x: 'permissive' if x in permissive_licenses_list else 'not permissive')

# Merge df_facts with df_info to get the license-type information
# 'symbolic_name' is the common key in both DataFrames
df_facts_merged = pd.merge(df_facts_raw, df_info, on='symbolic_name', how='left')

# Filter the merged DataFrame to only include entries with a permissive license
df_facts = df_facts_merged[df_facts_merged['license-type'] == 'permissive']
```

## Experiments and Findings

Initial experiments with the dataset have demonstrated its potential
in improving the accuracy of LLMs in generating Coq code. Fine-tuning
an existing base model with this dataset resulted in outputs
predominantly in Coq syntax, highlighting the dataset's efficacy in
specialized model training for formal theorem proving.

## Challenges and Limitations

* High standard deviations in fact, proposition, and proof lengths
  indicate the presence of outliers with significantly long content.
* The complexity of licensing and the manual process of license
  identification for each repository.

## Cite

```
@misc{florath2024enhancing,
      title={Enhancing Formal Theorem Proving: A Comprehensive Dataset for Training AI Models on Coq Code}, 
      author={Andreas Florath},
      year={2024},
      eprint={2403.12627},
      archivePrefix={arXiv},
      primaryClass={cs.AI}
}
```

## Legal Disclaimer
This dataset is provided 'as is' and without any warranty or guarantee of
accuracy, completeness, or compliance with any specific legal regime.  While 
every effort has been made to ensure that license information is accurate
and up-to-date, users of this dataset are responsible for verifying the
licensing information of each snippet and complying with all applicable
licenses and copyright laws.  Users should consider seeking legal advice
to ensure their use of these snippets complies with the original authors' 
licensing terms and any other applicable regulations.  The creators of this
dataset shall not be held liable for any infringements or legal challenges
arising from the use of or reliance on any materials contained within
this dataset.