README.md

metadata

license: apache-2.0
task_categories:
  - graph-ml
language:
  - en
tags:
  - mathematics
  - lean4
  - mathlib
  - dependency-graph
  - formal-verification
size_categories:
  - 100K<n<1M

MathlibGraph: Mathlib Dependency Graph Dataset

Dependency graph of Mathlib (commit 534cf0b, 2 Feb 2026), the largest formal mathematics library for Lean 4.

Files

File	Rows	Unique entries	Description
mathlib_nodes.csv	317,655	308,129 declarations	Mathlib declarations (name, kind, module)
mathlib_edges.csv	8,436,366	8,436,366 edges	Mathlib dependencies (source, target, is_explicit)
nodes.csv	633,364	—	Full environment (Lean + Std + Mathlib)
edges.csv	10,889,011	—	Full environment edges

Note: mathlib_nodes.csv contains 9,526 duplicate name rows produced by @[to_additive] mirroring. After deduplication, there are 308,129 unique declarations — the figure used throughout the paper.

Statistics (308,129 unique Mathlib declarations)

Kind	Count	%
theorem	243,725	79.1%
definition	48,664	15.8%
abbrev	6,667	2.2%
constructor	4,755	1.5%
inductive	3,813	1.2%
opaque	499	0.2%
quotient	3	<0.1%
axiom	3	<0.1%

Quick Start

from datasets import load_dataset
import pandas as pd

nodes = load_dataset("MathNetwork/MathlibGraph",
                     data_files="mathlib_nodes.csv", split="train").to_pandas()
edges = load_dataset("MathNetwork/MathlibGraph",
                     data_files="mathlib_edges.csv", split="train").to_pandas()

# Deduplicate nodes (9,526 @[to_additive] mirrors)
nodes = nodes.drop_duplicates(subset="name", keep="first")

print(f"Declarations: {len(nodes):,}, Edges: {len(edges):,}")
# Output: Declarations: 308,129, Edges: 8,436,366

Extraction Pipeline

• Nodes: lean4export (official leanprover tool)
• Edges: lean-training-data premises (Kim Morrison, Mathlib maintainer)
• Filtering: premises whitelist method — lake exe premises Mathlib outputs only Mathlib declarations, which we use to filter the full lean4export output

Schema

mathlib_nodes.csv

Column	Type	Description
name	string	Fully qualified declaration name (e.g., CategoryTheory.Functor.comp_id)
kind	string	theorem, definition, abbrev, inductive, constructor, opaque, axiom, quotient
module	string	Lean module (e.g., CategoryTheory.Functor)

mathlib_edges.csv

Column	Type	Description
source	string	Dependent declaration
target	string	Dependency (premise)
is_explicit	bool	Appears in explicit arguments
is_simplifier	bool	Used by simplifier

Citation

Part of the MathlibGraph project — network analysis of formalized mathematics.

License

Apache 2.0