TL;DR
The paper presents mathlib, a comprehensive, community-driven library of formalized mathematics in Lean, emphasizing dependently typed foundations, classical mathematics, automation, and collaborative organization.
Contribution
It introduces the architecture, design, and social organization of mathlib, a large-scale, unified mathematical library in Lean, highlighting its unique features and development process.
Findings
Successful development of a large, unified mathematical library in Lean
Effective use of automation and hierarchical structures
Community-driven organization enabling continuous growth
Abstract
This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on classical mathematics, extensive hierarchy of structures, use of large- and small-scale automation, and distributed organization. We explain the architecture and design decisions of the library and the social organization that has led us here.
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