MLFMF: Data Sets for Machine Learning for Mathematical Formalization

TL;DR

MLFMF introduces extensive datasets derived from formalized mathematics libraries in Agda and Lean, enabling benchmarking of recommendation systems to support mathematical formalization efforts.

Contribution

This work provides the largest collection of formalized mathematical data sets for machine learning, including network and syntax representations from major proof assistant libraries.

Findings

Baseline results with standard embeddings and algorithms demonstrate the datasets' utility.

The methodology is adaptable to other libraries and proof assistants.

The collection supports future research in machine learning for formalized mathematics.

Abstract

We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean~4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library. The network contains the (modular) structure of the library and the references between entries, while the s-expressions give complete and easily parsed information about every entry. We report baseline results using standard graph and word embeddings, tree ensembles, and instance-based learning algorithms. The MLFMF data sets provide solid benchmarking support for further investigation of the numerous machine learning approaches to formalized mathematics. The methodology used to extract the networks and the s-expressions readily applies to other libraries, and is applicable to other proof assistants. With more than $250\,000$ entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.