LeanArchitect: Automating Blueprint Generation for Humans and AI

2026-01-30

AI Summary

This work addresses the challenges of maintaining informal LaTeX blueprints alongside formal Lean code in large-scale formalization projects, where discrepancies between the two hinder both maintenance and AI integration. To bridge this gap, the authors propose a declarative annotation mechanism that embeds metadata directly within Lean code to automatically infer dependencies and generate LaTeX blueprints synchronized with the formal proofs. This approach achieves, for the first time, bidirectional automatic synchronization between Lean code and blueprint documentation, eliminating redundancy, enabling fine-grained progress tracking, and providing a structured interface for AI-based theorem provers. Evaluations across multiple large-scale projects demonstrate that the method effectively resolves inconsistencies in existing blueprints, significantly improves maintainability, and validates the feasibility of human–AI collaborative formal development.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Humans and AI: Other Foundations of Human Computation & AI

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Large-scale formalization projects in Lean rely on blueprints: structured dependency graphs linking informal mathematical exposition to formal declarations. While blueprints are central to human collaboration, existing tooling treats the informal ($\LaTeX$) and formal (Lean) components as largely decoupled artifacts, leading to maintenance overhead and limiting integration with AI automation. We present LeanArchitect, a Lean package for extracting, managing, and exporting blueprint data directly from Lean code. LeanArchitect introduces a declarative annotation mechanism that associates formal declarations with blueprint metadata, automatically infers dependency information, and generates $\LaTeX$ blueprint content synchronized with the Lean development. This design eliminates duplication between formal and informal representations and eases fine-grained progress tracking for both human contributors and AI-based theorem provers. We demonstrate the practicality of LeanArchitect through the automated conversion of several large existing blueprint-driven projects, and through a human--AI collaboration case study formalizing a multivariate Taylor theorem. Our results show that LeanArchitect improves maintainability, exposes latent inconsistencies in existing blueprints, and provides an effective interface for integrating AI tools into real-world formalization workflows.

Problem

• blueprint
• formalization
• Lean
• AI automation
• dependency graph

Innovation

• LeanArchitect
• blueprint generation
• formalization
• human-AI collaboration
• declarative annotation