mathlib integration

This work addresses the absence of a centralized, reusable formal knowledge base in computer science, which hinders the development and verification of reliable systems. To this end, we propose CSLib—a modular formal library built on the Lean theorem prover—that enables systematic formalization of programming languages and computational models. CSLib is grounded in a unified semantic framework encompassing reduction systems and labeled transition systems, employs composable abstractions, and integrates engineering infrastructure compatible with Mathlib. The project incorporates automated proof support, continuous integration, and testing mechanisms. We have successfully established the core architecture of CSLib and completed the first formalizations of representative languages and models, thereby laying a scalable and maintainable foundation for formal computer science.

This work addresses the lack of a systematic, formalized knowledge base for computer science in Lean, which has hindered its adoption in education, research, and large-scale verification. To bridge this gap, we present CSLib—the first open-source library of formalized theorems and data structures specifically designed for computer science, built upon the Lean proof assistant and dependent type theory. CSLib establishes a reusable and composable formal infrastructure that significantly expands Lean’s foundational knowledge base in computer science. By providing a comprehensive and extensible collection of verified components, CSLib enables effective collaboration between human developers and AI systems in constructing large-scale formally verified software, thereby advancing the broader application and accessibility of formal methods within the field.

Mathlib faces sustainability challenges—including escalating maintenance overhead, difficulty managing breaking changes, and declining collaboration efficiency—due to rapid growth in scale and complexity. To address these, we propose a systematic governance framework comprising: (1) a declarative deprecation mechanism enabling gradual API evolution; (2) a customized toolchain integrating static analysis (linters), dependency-aware contribution routing, compilation performance diagnostics, and automated refactoring; and (3) a modular library rearchitecture coupled with quantitative technical debt management. Experimental evaluation demonstrates that our approach reduces average compilation time by 37%, shortens PR review cycles by 42%, and achieves a deprecation migration success rate exceeding 95%. These results significantly enhance maintainability, collaborative throughput, and evolutionary resilience of large-scale formalized mathematics libraries.

To address the difficulty users face in retrieving theorems from mathlib4 due to unfamiliarity with naming conventions and documentation, this paper introduces LeanSearch—the first semantic search engine tailored for the Lean mathematical library. Methodologically: (1) we construct the first evaluable cross-lingual semantic search benchmark mapping natural-language queries to formal theorems; (2) we propose a joint encoding strategy for theorems and their associated docstrings to build a customized dense semantic index over mathlib4; and (3) we implement an end-to-end embedded retrieval system. Our contributions include establishing the first reproducible, evaluable semantic search infrastructure for mathlib4; deploying a publicly accessible service (leansearch.net); and achieving significant improvements in retrieval accuracy and onboarding experience for novice users—thereby facilitating collaborative formalization within the Lean community.

Formal theorem proving is hindered by the scarcity of high-quality bilingual natural language–Lean 4 data. To address this, we propose the first bidirectional synthetic data construction framework tailored for mathematical theorem proving. Our method employs a large language model–driven iterative generation-and-filtering pipeline, integrating rule-guided filtering, mathematical semantic consistency verification, and proof-search feedback to ensure high-fidelity bidirectional translation between natural language and Lean 4. The resulting dataset introduces 21 newly curated International Mathematical Olympiad (IMO) problems and real-world forum proofs, and we publicly release an open-source dataset of 57K problem–proof pairs (on Hugging Face) alongside full implementation code (on GitHub). Experiments demonstrate substantial improvements in LLM performance across formalization translation, proposition understanding, and proof generation—establishing a foundational data resource for mathematical AI.

Existing infrastructure struggles to meet the demands of AI-driven mathematical research for Lean 4, particularly in high-throughput processing, scalable verification, multi-version support, and request-level isolation. This work proposes the first cloud-native Lean 4 service platform, which uniquely enables high concurrency, per-request isolation, and coexistence of multiple Lean 4 and Mathlib versions. The platform integrates 14 metaprogramming tools—including proof checking, semantic source code manipulation, deterministic repair, and lemma extraction—and provides seamless access via HTTP API, Python SDK, CLI, and a web UI, eliminating the need for local deployment. Already publicly deployed, it has processed over 500 million requests and powered Axiom Math’s perfect score in the 2025 Putnam Competition, thereby addressing a critical gap in scalable theorem-proving infrastructure.

This work addresses the challenge of subtle errors in mathematical reasoning by large language models through a novel multi-agent framework built upon general-purpose code-oriented large language models. The framework employs a coordinator to dynamically orchestrate a customized pipeline for automatically formalizing research-level mathematical theorems in Lean 4. Its key innovation lies in the ability to dynamically extend type definitions and verify auxiliary lemmas without introducing additional axioms. The approach successfully formalizes the core theorems of five STOC papers—two of which rely solely on the Lean kernel—and produces machine-verified proofs for 32 problems on PutnamBench. All formalizations have been expert-reviewed and are publicly released.

This work addresses the challenge of verifying mathematical proofs generated by large language models by formally encoding, for the first time, an entire advanced undergraduate probability textbook—including its measure-theoretic foundations—into Lean. To bridge the semantic gap between the textbook’s exposition and the abstract formalism of the Mathlib library, the authors introduce an “interface lemma” strategy. Combined with structured proof engineering and formalization techniques specific to measure theory, this approach yields a reusable, machine-verifiable infrastructure spanning fourteen textbook chapters. The resulting formalization not only provides rigorous verification of all stated theorems and explicit articulation of their assumptions but also establishes a robust foundation for reliable AI-assisted mathematics, educational applications, and future formalization efforts in probability theory.

This work addresses the challenge of large-scale automated translation of informal mathematical textbooks into machine-verifiable formal content. We propose AutoformBot, a multi-agent system comprising thousands of large language model agents equipped with Lean 4 verification tools, which leverages dependency-aware task scheduling and collaborative version control to achieve fully automated formalization of 26 graduate-level textbooks spanning analysis, algebra, topology, and related fields. The resulting Atlas formal mathematics library comprises over 45,000 theorem statements and 500,000 lines of Lean 4 code, demonstrating for the first time the technical and economic feasibility of large-scale automatic formalization of advanced mathematics. The complete framework and dataset are released as open-source resources.

This work addresses the absence of a formally verified foundational library in mathematical finance, which has hindered rigorous and reusable theoretical development. Building upon Mathlib and the BrownianMotion package in Lean 4, the authors construct a comprehensive formal library spanning eleven core areas, including continuous-time stochastic calculus, derivative pricing, and risk and portfolio theory. The library comprises over 200 theorems proved without gaps in assumptions. Notably, it presents the first formal construction of the L² Itô integral and derives the risk-neutral measure within a proof assistant. Additionally, a fidelity auditing mechanism is introduced to explicitly track the axioms and assumptions underlying each theorem. This effort establishes the most extensive machine-verified infrastructure for mathematical finance to date, enabling unified certification and reliable reuse of classical results.