metadata

annotations_creators:
  - no-annotation
language:
  - en
language_creators:
  - found
license: []
multilinguality:
  - monolingual
pretty_name: proof-pile
size_categories: []
source_datasets: []
tags:
  - math
  - mathematics
  - formal-mathematics
task_categories:
  - text-generation
task_ids:
  - language-modeling

Dataset Description

The proof-pile is a 40GB pre-training dataset of mathematical text that comprises roughly 15 billion tokens. The dataset is composed of diverse sources of both informal and formal mathematics, namely

ArXiv.math (37GB)
Open-source math textbooks (50MB)
Formal mathematics libraries (500MB)
- Lean mathlib and other Lean repositories
- Isabelle AFP
- Coq mathematical components and other Coq repositories
- HOL Light
- set.mm
- Mizar Mathematical Library
Math Overflow and Math Stack Exchange (500MB)
Wiki-style sources (50MB)
- ProofWiki
- Wikipedia math articles
MATH dataset (6MB)

Supported Tasks

This dataset is intended to be used for pre-training language models. We envision models pre-trained on the proof-pile will have many downstream applications, including informal quantitative reasoning, formal theorem proving, semantic search for formal mathematics, and autoformalization.

Languages

All informal mathematics in the proof-pile is written in English and LaTeX (arXiv articles in other languages are filtered out using languagedetect). Formal theorem proving languages represented in this dataset are Lean 3, Isabelle, Coq, HOL Light, Metamath, and Mizar.

Configurations

The data is sorted into "arxiv", "books", "formal", "stack-exchange", "wiki", and "math-dataset" configurations. This is so that it is easy to upsample particular configurations during pre-training with the datasets.interleave_datasets() function.

Evaluation

The version of set.mm in this dataset has 10% of proofs replaced with the ? character in order to preserve a validation and test set for Metamath provers pre-trained on the proof-pile. The precise split can be found here: validation and test.

The Lean mathlib commit used in this dataset is 6313863. Theorems created in subsequent commits can be used for evaluating Lean theorem provers.

This dataset contains only the training set of the MATH dataset. However, because this dataset contains ProofWiki, the Stacks Project, Trench's Analysis, and Stein's Number Theory, models trained on it cannot be evaluated on the NaturalProofs dataset.

Contributions

Authors: Zhangir Azerbayev, Edward Ayers, Bartosz Piotrowski.

We would like to thank Jeremy Avigad, Albert Jiang, and Wenda Li for their invaluable guidance, and the Hoskinson Center for Formal Mathematics for its support.