Overview

The Lean LSP MCP is a specialized Model Context Protocol server that bridges AI assistants with the Lean theorem prover through the Language Server Protocol (LSP). It enables conversational agents such as Claude, GPT‑4o, or other LLMs to interrogate Lean projects, retrieve diagnostics, explore goal states, and invoke theorem‑search tools—all within a single chat interface. By exposing Lean’s rich semantic information as MCP resources and tools, the server turns a complex proof environment into an interactive API that LLMs can query in natural language.

Problem Solved

Developers and researchers often struggle to get AI assistants to understand the intricacies of Lean proofs. Traditional LSP clients require manual navigation, command‑line interaction, or IDE overlays to surface information such as goal contexts, type hierarchies, and theorem dependencies. The Lean LSP MCP eliminates this friction by providing a unified, agent‑friendly endpoint that exposes all LSP capabilities as structured MCP resources. This allows an AI assistant to request, for example, the current proof goals or hover documentation without needing to run separate tooling or parse raw Lean output.

Core Functionality

• Rich Lean Interaction: The server offers diagnostics, goal states, term information, hover documentation, and other LSP features as MCP tools. An AI can ask for the type of a term or request the list of open goals, and receive machine‑readable responses that can be used to drive further reasoning or code generation.
• External Search Integration: Built‑in search tools such as , , , and allow the assistant to query Lean’s theorem libraries, find relevant lemmas, or locate missing proofs. These searches are exposed as simple MCP commands that return structured results.
• Seamless Client Support: The server is pre‑configured for popular IDEs and AI platforms, including VS Code (agent mode), Cursor, and Claude Code. Clients can add the MCP server with a single command or configuration file, after which they can invoke Lean operations directly from chat.

Use Cases

• Automated Proof Construction: An LLM can iteratively request the current goal, propose a tactic or lemma, and apply it via the MCP toolset. This workflow supports “auto proof” features in chat interfaces.
• Proof Exploration and Documentation: Developers can ask the assistant to explain a theorem, list its dependencies, or fetch hover information for any identifier. The server returns precise type signatures and documentation strings.
• Library Search: When a user needs to find an existing lemma that matches a pattern, the assistant can invoke or through MCP, receiving ranked results that can be directly inserted into the proof script.
• IDE Integration: In VS Code or Cursor, a user can switch to agent mode and let the assistant suggest edits, fix diagnostics, or generate new Lean code—all powered by the MCP server.

Unique Advantages

• Agent‑First Design: Unlike generic LSP servers, Lean LSP MCP is intentionally exposed as an MCP service. It serializes responses in JSON and provides a clean command interface, making it trivial for LLMs to parse and act upon the data.
• Zero‑Configuration Search Tools: The bundled search utilities are ready to use out of the box, eliminating the need for separate installation or configuration of external theorem‑search engines.
• Optimized Build Handling: The server automatically runs on the project root, ensuring that the language server has up‑to‑date information. This pre‑build step is also exposed as an MCP resource, allowing the assistant to trigger a rebuild when necessary.

By integrating Lean’s powerful proof engine with an LLM‑friendly protocol, the Lean LSP MCP transforms theorem proving from a manual, IDE‑centric activity into an interactive, conversational experience. It empowers developers to harness AI assistance for rapid proof development, exploration, and maintenance across Lean projects.