license: cc-by-4.0
task_categories:
- text-generation
language:
- en
size_categories:
- 1B<n<10B
pretty_name: ProofLang Corpus
dataset_info:
- config_name: proofs
num_bytes: 3197091800
num_examples: 3681901
features:
- name: fileID
dtype: string
- name: proof
dtype: string
- config_name: sentences
num_bytes: 3736579062
num_examples: 38899130
features:
- name: fileID
dtype: string
- name: sentence
dtype: string
download_size: 6933683563
dataset_size: 6933670862
Dataset Card for the ProofLang Corpus
Dataset Summary
The ProofLang Corpus includes 3.7M proofs (558 million words) mechanically extracted from papers that were posted on arXiv.org between 1992 and 2020.
The focus of this corpus is proofs, rather than the explanatory text that surrounds them, and more specifically on the language used in such proofs.
Specific mathematical content is filtered out, resulting in sentences such as Let MATH be the restriction of MATH to MATH.
This dataset reflects how people prefer to write (non-formalized) proofs, and is also amenable to statistical analyses and experiments with Natural Language Processing (NLP) techniques. We hope it can serve as an aid in the development of language-based proof assistants and proof checkers for professional and educational purposes.
Dataset Structure
There are multiple TSV versions of the data. Primarily, proofs
divides up the data proof-by-proof, and sentences
further divides up the same data sentence-by-sentence.
The raw
dataset is a less-cleaned-up version of proofs
. More usefully, the tags
dataset gives arXiv subject tags for each paper ID found in the other data files.
The data in
proofs
(andraw
) consists of apaper
ID (identifying where the proof was extracted from), and theproof
as a string.The data in
sentences
consists of apaper
ID, and thesentence
as a string.The data in
tags
consists of apaper
ID, and the arXiv subject tags for that paper as a single comma-separated string.
Further metadata about papers can be queried from arXiv.org using the paper ID.
In particular, each paper <id>
in the dataset can be accessed online at the url https://arxiv.org/abs/<id>
Dataset Size
proofs
is 3,094,779,182 bytes (unzipped) and has 3,681,893 examples.sentences
is 3,545,309,822 bytes (unzipped) and has 38,899,132 examples.tags
is 7,967,839 bytes (unzipped) and has 328,642 rows.raw
is 3,178,997,379 bytes (unzipped) and has 3,681,903 examples.
Dataset Statistics
The average length of
sentences
is 14.1 words.The average length of
proofs
is 10.5 sentences.
Dataset Usage
Data can be downloaded as (zipped) TSV files.
Accessing the data programmatically from Python is also possible using the Datasets
library.
For example, to print the first 10 proofs:
from datasets import load_dataset
dataset = load_dataset('proofcheck/prooflang', 'proofs', split='train', streaming='True')
for d in dataset.take(10):
print(d['paper'], d['proof'])
To look at individual sentences from the proofs,
dataset = load_dataset('proofcheck/prooflang', 'proofs', split='train', streaming='True')
for d in dataset.take(10):
print(d['paper'], d['sentence'])
To get a comma-separated list of arXiv subject tags for each paper,
from datasets import load_dataset
dataset = load_dataset('proofcheck/prooflang', 'tags', split='train', streaming='True')
for d in dataset.take(10):
print(d['paper'], d['tags'])
Finally, to look at a version of the proofs with less aggressive cleanup (straight from the LaTeX extraction),
dataset = load_dataset('proofcheck/prooflang', 'raw', split='train', streaming='True')
for d in dataset.take(10):
print(d['paper'], d['proof'])
Data Splits
There is currently no train/test split; all the data is in train
.
Dataset Creation
We started with the LaTeX source of 1.6M papers that were submitted to arXiv.org between 1992 and April 2022.
The proofs were extracted using a Python script simulating parts of LaTeX (including defining and expanding macros).
It does no actual typesetting, throws away output not between \begin{proof}...\end{proof}
, and skips math content. During extraction,
- Math-mode formulas (signalled by
$
,\begin{equation}
, etc.) becomeMATH
\ref{...}
and variants (autoref
,\subref
, etc.) becomeREF
\cite{...}
and variants (\Citet
,\shortciteNP
, etc.) becomeCITE
- Words that appear to be proper names become
NAME
\item
becomesCASE:
We then run a cleanup pass on the extracted proofs that includes
- Cleaning up common extraction errors (e.g., due to uninterpreted macros)
- Replacing more references by
REF
, e.g.,Theorem 2(a)
orPostulate (*)
- Replacing more citations with
CITE
, e.g.,Page 47 of CITE
- Replacing more proof-case markers with
CASE:
, e.g.,Case (a).
- Fixing a few common misspellings
Additional Information
This dataset is released under the Creative Commons Attribution 4.0 licence.
Copyright for the actual proofs remains with the authors of the papers on arXiv.org, but these simplified snippets are fair use under US copyright law.