Lean Theorem Prover MCP

What is Lean Theorem Prover MCP about?

Lean Theorem Prover MCP provides an MCP server that connects AI agents to a Lean development environment via LSP. It exposes a rich set of tools—such as diagnostics, goal states, hover docs, code completions, and external theorem search—so agents can understand, analyze, and manipulate Lean projects programmatically.

How to use Lean Theorem Prover MCP?

1. Install the package using the Python package manager uv (e.g., uvx lean-lsp-mcp).
2. Build your Lean project with lake build to ensure fast LSP startup.
3. Configure your IDE (VSCode, Cursor, Claude Code, etc.) by adding an MCP server entry that runs uvx lean-lsp-mcp with the desired transport (stdio by default).
4. Invoke tools from the chat/agent interface (e.g., lean_goal, lean_hover_info, leansearch) to retrieve information or perform actions on the Lean code.

Key Features of Lean Theorem Prover MCP

• Rich Lean Interaction: diagnostics, goal inspection, term goals, hover docs, completions, file contents, and code execution.
• External Search Integration: leansearch, loogle, lean_state_search, and lean_hammer for theorem discovery.
• Multiple Transport Methods: stdio, streamable-http, and sse with optional bearer‑token authentication.
• Environment Variable Support: customize project path, authentication token, and self‑hosted search endpoints.
• Tool‑Only Interaction Model: all operations are exposed as discrete tools callable by agents.

Use Cases of Lean Theorem Prover MCP

• Automated Proof Assistance: agents can query goals, fetch lemmas, and iteratively construct proofs.
• Learning and Exploration: students can ask for hover explanations, diagnostics, and theorem searches while studying Lean code.
• Research Automation: batch‑run code snippets, evaluate expressions, or gather premises for large proof libraries.
• IDE Augmentation: enhance any MCP‑compatible editor with AI‑driven Lean features without writing custom extensions.

FAQ

Q: Do I need a successful lake build before running the server? A: A successful build is not required; warnings (e.g., sorry) are acceptable, but a quick build improves responsiveness.

Q: Which transport should I choose? A: stdio is the simplest and default. Use streamable‑http or sse if you need network access or want to enable bearer‑token authentication.

Q: How do I set a secret token for HTTP transports? A: Export LEAN_LSP_MCP_TOKEN="your_secret" before starting the server; clients then include it in the Authorization header.

Q: Can I point the server to a different Lean project? A: Yes, set LEAN_PROJECT_PATH to the root of the desired project.

Q: Are there rate limits on external search tools? A: All external tools are limited to 3 requests per 30 seconds; this may change based on provider feedback.

MCP server that allows agentic interaction with the Lean theorem prover via the Language Server Protocol using leanclient. This server provides a range of tools for LLM agents to understand, analyze and interact with Lean projects.

Currently beta testing: Please help us by submitting bug reports and feature requests!

Key Features

• Rich Lean Interaction: Access diagnostics, goal states, term information, hover documentation and more.
• External Search Tools: Use leansearch, loogle, lean_hammer and lean_state_search to find relevant theorems and definitions.
• Easy Setup: Simple configuration for various clients, including VSCode, Cursor and Claude Code.

Setup

Overview

1. Install uv, a Python package manager.
2. Make sure your Lean project builds quickly by running lake build manually.
3. Configure your IDE/Setup

1. Install uv

Install uv for your system.

E.g. on Linux/MacOS:

curl -LsSf https://astral.sh/uv/install.sh | sh

2. Run lake build

lean-lsp-mcp will run lake build in the project root to use the language server (for most tools). Some clients (e.g. Cursor) might timeout during this process. Therefore, it is recommended to run lake build manually before starting the MCP. This ensures a faster build time and avoids timeouts.

E.g. on Linux/MacOS:

cd /path/to/lean/project
lake build

Note: Your build does not necessarily need to be successful, some errors or warnings (e.g. declaration uses 'sorry') are OK.

3. a) VSCode Setup

VSCode and VSCode Insiders are supporting MCPs in agent mode. For VSCode you might have to enable Chat > Agent: Enable in the settings.

1. One-click config setup:

OR using the setup wizard:

Ctrl+Shift+P > "MCP: Add Server..." > "Command (stdio)" > "uvx lean-lsp-mcp" > "lean-lsp" (or any name you like) > Global or Workspace

OR manually add config to mcp.json:

{
    "servers": {
        "lean-lsp": {
            "type": "stdio",
            "command": "uvx",
            "args": [
                "lean-lsp-mcp"
            ]
        }
    }
}

2. Click "Start" above server config, open a Lean file, change to agent mode in the chat and run e.g. "auto proof" to get started.

3. b) Cursor Setup

1. Open MCP Settings (File > Preferences > Cursor Settings > MCP)

2. "+ Add a new global MCP Server" > ("Create File")

3. Paste the server config into mcp.json file:

{
    "mcpServers": {
        "lean-lsp": {
            "command": "uvx",
            "args": ["lean-lsp-mcp"]
        }
    }
}

3. c) Claude Code

Run one of these commands in the root directory of your Lean project (where lakefile.toml is located):

# Local-scoped MCP server
claude mcp add lean-lsp uvx lean-lsp-mcp

# OR project-scoped MCP server (creates or updates a .mcp.json file in the current directory)
claude mcp add lean-lsp -s project uvx lean-lsp-mcp

# OR If you run into issues with the project path (e.g. the language server directory cannot be found), you can also set it manually e.g.
claude mcp add lean-lsp uvx lean-lsp-mcp -e LEAN_PROJECT_PATH=$PWD

You can find more details about MCP server configuration for Claude Code here.

Other Setups

Other setups, such as Claude Desktop, OpenAI Agent SDK, Windsurf or Goose should work with similar configs.

Transport Methods

The Lean LSP MCP server supports the following transport methods:

• stdio: Standard input/output (default)
• streamable-http: HTTP streaming
• sse: Server-sent events (MCP legacy, use streamable-http if possible)

You can specify the transport method using the --transport argument when running the server:

uvx lean-lsp-mcp --transport stdio # Default transport
uvx lean-lsp-mcp --transport streamable-http # Available at http://127.0.0.1:8000/mcp
uvx lean-lsp-mcp --transport sse # Available at http://127.0.0.1:8000/sse

Bearer Token Authentication

Transport via streamable-http and sse supports bearer token authentication. This allows publicly accessible MCP servers to restrict access to authorized clients.

Set the LEAN_LSP_MCP_TOKEN environment variable (or see section 3 for setting env variables in MCP config) to a secret token before starting the server.

Example Linux/MacOS setup:

export LEAN_LSP_MCP_TOKEN="your_secret_token"
uvx lean-lsp-mcp --transport streamable-http

Clients should then include the token in the Authorization header.

Environment Variables

Some (optional) features and integrations of lean-lsp-mcp are configured using environment variables. These must be set in your shell or process environment before running the server.

• LEAN_PROJECT_PATH: (optional) Path to your Lean project root. Set this if the server cannot automatically detect your project.
• LEAN_LSP_MCP_TOKEN: (optional) Secret token for bearer authentication when using streamable-http or sse transport.
• LEAN_STATE_SEARCH_URL: (optional) URL for a self-hosted premise-search.com instance.
• LEAN_HAMMER_URL: (optional) URL for a self-hosted Lean Hammer Premise Search instance.

You can also often set these environment variables in your MCP client configuration:

{
    "servers": {
        "lean-lsp": {
            "type": "stdio",
            "command": "uvx",
            "args": [
                "lean-lsp-mcp"
            ],
            "env": {
                "LEAN_PROJECT_PATH": "/path/to/your/lean/project",
            }
        }
    }
}

Tools

Tools are currently the only way to interact with the MCP server.

File interactions (LSP)

lean_file_contents

Get the contents of a Lean file, optionally with line number annotations.

lean_diagnostic_messages

Get all diagnostic messages for a Lean file. This includes infos, warnings and errors.

l20c42-l20c46, severity: 1 simp made no progress

l21c11-l21c45, severity: 1 function expected at h_empty term has type T ∩ compl T = ∅

...

lean_goal

Get the proof goal at a specific location (line or line & column) in a Lean file.

lean_term_goal

Get the term goal at a specific position (line & column) in a Lean file.

lean_hover_info

Retrieve hover information (documentation) for symbols, terms, and expressions in a Lean file (at a specific line & column).

This is intended for stubbing-out incomplete parts of a proof while still having a syntactically correct proof skeleton. Lean will give a warning whenever a proof uses sorry, so you aren't likely to miss it, but you can double check if a theorem depends on sorry by looking for sorryAx in the output of the #print axioms my_thm command, the axiom used by the implementation of sorry.

lean_declaration_file

Get the file contents where a symbol or term is declared.

lean_completions

Code auto-completion: Find available identifiers or import suggestions at a specific position (line & column) in a Lean file.

lean_run_code

Run/compile an independent Lean code snippet/file and return the result or error message.

lean_multi_attempt

Attempt multiple lean code snippets on a line and return goal state and diagnostics for each snippet. This tool is useful to screen different proof attempts before using the most promising one.

External Search Tools

Currently all external tools are rate limited to 3 requests per 30 seconds. This will change based on provider feedback.

lean_leansearch

Search for theorems in Mathlib using leansearch.net (natural language search).

Github Repository | Arxiv Paper

• Supports natural language, mixed queries, concepts, identifiers, and Lean terms.
• Example: bijective map from injective, n + 1 <= m if n < m, Cauchy Schwarz, List.sum, {f : A → B} (hf : Injective f) : ∃ h, Bijective h

  {
    "module_name": "Mathlib.Logic.Function.Basic",
    "kind": "theorem",
    "name": "Function.Bijective.injective",
    "signature": " {f : α → β} (hf : Bijective f) : Injective f",
    "type": "∀ {α : Sort u_1} {β : Sort u_2} {f : α → β}, Function.Bijective f → Function.Injective f",
    "value": ":= hf.1",
    "informal_name": "Bijectivity Implies Injectivity",
    "informal_description": "For any function $f \\colon \\alpha \\to \\beta$, if $f$ is bijective, then $f$ is injective."
  },
  ...

lean_loogle

Search for Lean definitions and theorems using loogle.lean-lang.org.

Github Repository

• Supports queries by constant, lemma name, subexpression, type, or conclusion.
• Example: Real.sin, "differ", _ * (_ ^ _), (?a -> ?b) -> List ?a -> List ?b, |- tsum _ = _ * tsum _

[
  {
    "type": " (x : ℝ) : ℝ",
    "name": "Real.sin",
    "module": "Mathlib.Data.Complex.Trigonometric"
  },
  ...
]

lean_state_search

Search for applicable theorems for the current proof goal using premise-search.com.

Github Repository | Arxiv Paper

A self-hosted version is available and encouraged. You can set an environment variable LEAN_STATE_SEARCH_URL to point to your self-hosted instance. It defaults to https://premise-search.com.

Uses the first goal at a given line and column. Returns a list of relevant theorems.

[
  {
    "name": "Nat.mul_zero",
    "formal_type": "∀ (n : Nat), n * 0 = 0",
    "module": "Init.Data.Nat.Basic"
  },
  ...
]

lean_hammer_premise

Search for relevant premises based on the current proof state using the Lean Hammer Premise Search.

Github Repository | Arxiv Paper

A self-hosted version is available and encouraged. You can set an environment variable LEAN_HAMMER_URL to point to your self-hosted instance. It defaults to http://leanpremise.net.

Uses the first goal at a given line and column. Returns a list of relevant premises (theorems) that can be used to prove the goal.

Note: We use a simplified version, LeanHammer might have better premise search results.

[
  "MulOpposite.unop_injective",
  "MulOpposite.op_injective",
  "WellFoundedLT.induction",
  ...
]

Project-level tools

lean_build

Rebuild the Lean project and restart the Lean LSP server.

Disabling Tools

Many clients allow the user to disable specific tools manually (e.g. lean_build).

VSCode: Click on the Wrench/Screwdriver icon in the chat.

Cursor: In "Cursor Settings" > "MCP" click on the name of a tool to disable it (strikethrough).

Example Uses

Here are a few example prompts and interactions to try. All examples use VSCode (Agent Mode) and Gemini 2.5 Pro (Preview).

Use tools to assist with a proof

After installing the MCP, tools are automatically available to the agent. E.g. Open a Lean file with a sorry and run the following prompt: "Solve this sorry" The agent should use various tools such as lean_goal to understand and create a proof. You can also ask the agent to use tools explicitly, e.g. "Help me write this proof using tools." or "Use tools to analyze the goal and hover information, then write a proof."

Analyze a theorem

Open Algebra/Lie/Abelian.lean. Example prompt:

"Analyze commutative_ring_iff_abelian_lie_ring thoroughly using various tools such as goal, term goal, hover info. Explain the key proof steps in english.".

Design proof approaches

Open an incomplete proof such as putnam 1964 b2. Example prompt:

"First analyze the problem statement by checking the goal, hover info and looking up key declarations. Next use up to three queries to leansearch to design three different approaches to solve this problem. Very concisely present each approach and its key challenge."

Notes on MCP Security

There are many valid security concerns with the Model Context Protocol (MCP) in general!

This MCP server is meant as a research tool and is currently in beta. While it does not handle any sensitive data such as passwords or API keys, it still includes various security risks:

• Access to your local file system.
• No input or output validation.

Please be aware of these risks. Feel free to audit the code and report security issues!

For more information, you can use Awesome MCP Security as a starting point.

MCP Inspector

npx @modelcontextprotocol/inspector uvx --with-editable path/to/lean-lsp-mcp python -m lean_lsp_mcp.server

Related Projects

• LeanTool
• LeanExplore MCP

License & Citation

MIT licensed. See LICENSE for more information.

Citing this repository is highly appreciated but not required by the license.

@software{lean-lsp-mcp,
  author = {Oliver Dressler},
  title = {{Lean LSP MCP: Tools for agentic interaction with the Lean theorem prover}},
  url = {https://github.com/oOo0oOo/lean-lsp-mcp},
  month = {3},
  year = {2025}
}