Related papers: The Network Structure of Mathlib
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…
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…
Following in the footsteps of the success of Mathlib - the centralised library of formalised mathematics in Lean - CSLib is a rapidly-growing centralised library of formalised computer science and software. In this paper, we present its…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
The Lean mathematical library Mathlib is one of the fastest-growing libraries of formalised mathematics. We describe various strategies to manage this growth, while allowing for change and avoiding maintainer overload. This includes dealing…
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,…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
We formalize the multi-graded Proj construction in Lean4, illustrating mechanized mathematics and formalization.
The Lean mathematical library mathlib is developed by a community of users with very different backgrounds and levels of experience. To lower the barrier of entry for contributors and to lessen the burden of reviewing contributions, we have…
We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…
We present ZFLean, a Lean 4 library for doing core mathematics inside a model of ZFC with the ergonomics expected of typed Mathlib developments. Building on Mathlib's ZFC model, we contribute a relational calculus for sets with rewriting…
This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formalize is a Taylor theorem for functions of several variables,…
Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often…
We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged…
We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped with formal verification tools, dependency-aware task…
Data science workflows often integrate functionalities from a diverse set of libraries and frameworks. Tasks such as debugging require data lineage that crosses library boundaries. The problem is that the way that "lineage" is represented…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
Current autoformalization benchmarks are largely focused on olympiad or undergraduate mathematics, while graduate and research-level mathematics remains underexplored. In this paper, we introduce MathAtlas, the first large-scale…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…