---
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](https://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` (and `raw`) consists of a `paper` ID (identifying where the proof was extracted from), and the `proof` as a string.

* The data in `sentences` consists of a `paper` ID, and the `sentence` as a string.

* The data in `tags` consists of a `paper` 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:

```python
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, 

```python
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,
```python
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),

```python
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](https://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.) become `MATH`
* `\ref{...}` and variants (`autoref`, `\subref`, etc.) become `REF`
* `\cite{...}` and variants (`\Citet`, `\shortciteNP`, etc.) become `CITE`
* Words that appear to be proper names become `NAME`
* `\item` becomes `CASE:`

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)` or `Postulate (*)`
* 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](https://arXiv.org), but these simplified snippets are fair use under US copyright law.