lean-lsp-mcp

<h1 align="center"> lean-lsp-mcp </h1> <h3 align="center">Lean Theorem Prover MCP</h3> <p align="center"> <a href="https://pypi.org/project/lean-lsp-mcp/"> <img src="https://img.shields.io/pypi/v/lean-lsp-mcp.svg" alt="PyPI version" /> </a> <a href=""> <img src="https://img.shields.io/github/last-commit/oOo0oOo/lean-lsp-mcp" alt="last update" /> </a> <a href="https://github.com/oOo0oOo/lean-lsp-mcp/blob/master/LICENSE"> <img src="https://img.shields.io/github/license/oOo0oOo/lean-lsp-mcp.svg" alt="license" /> </a> </p> MCP server that allows agentic interaction with the [Lean theorem prover](https://lean-lang.org/) via the [Language Server Protocol](https://microsoft.github.io/language-server-protocol/specifications/lsp/3.17/specification/) using [leanclient](https://github.com/oOo0oOo/leanclient). This server provides a range of tools for LLM agents to understand, analyze and interact with Lean projects. ## Key Features * **Rich Lean Interaction**: Access diagnostics, goal states, term information, hover documentation and more. * **External Search Tools**: Use `LeanSearch`, `Loogle`, `Lean Finder`, `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](https://docs.astral.sh/uv/getting-started/installation/), a Python package manager. 2. Make sure your Lean project builds quickly by running `lake build` manually. 3. Configure your IDE/Setup 4. (Optional, highly recommended) Install [ripgrep](https://github.com/BurntSushi/ripgrep?tab=readme-ov-file#installation) (`rg`) to reduce hallucinations using local search. ### 1. Install uv [Install uv](https://docs.astral.sh/uv/getting-started/installation/) for your system. On Linux/MacOS: `curl -LsSf https://astral.sh/uv/install.sh | sh` ### 2. Run `lake build` `lean-lsp-mcp` will run `lake serve` 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. ### 3. Configure your IDE/Setup <details> <summary><b>VSCode (Click to expand)</b></summary> One-click config setup: [](https://insiders.vscode.dev/redirect/mcp/install?name=lean-lsp&config=%7B%22command%22%3A%22uvx%22%2C%22args%22%3A%5B%22lean-lsp-mcp%22%5D%7D) [](https://insiders.vscode.dev/redirect/mcp/install?name=lean-lsp&config=%7B%22command%22%3A%22uvx%22%2C%22args%22%3A%5B%22lean-lsp-mcp%22%5D%7D&quality=insiders) 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 adding config by opening `mcp.json` with: Ctrl+Shift+P > "MCP: Open User Configuration" and adding the following ```jsonc { "servers": { "lean-lsp": { "type": "stdio", "command": "uvx", "args": [ "lean-lsp-mcp" ] } } } ``` If you installed VSCode on Windows and are using WSL2 as your development environment, you may need to use this config instead: ```jsonc { "servers": { "lean-lsp": { "type": "stdio", "command": "wsl.exe", "args": [ "uvx", "lean-lsp-mcp" ] } } } ``` If that doesn't work, you can try cloning this repository and replace `"lean-lsp-mcp"` with `"/path/to/cloned/lean-lsp-mcp"`. </details> <details> <summary><b>Cursor (Click to expand)</b></summary> 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: ```jsonc { "mcpServers": { "lean-lsp": { "command": "uvx", "args": ["lean-lsp-mcp"] } } } ``` </details> <details> <summary><b>Claude Code (Click to expand)</b></summary> Run one of these commands in the root directory of your Lean project (where `lakefile.toml` is located): ```bash # 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 ``` You can find more details about MCP server configuration for Claude Code [here](https://docs.anthropic.com/en/docs/agents-and-tools/claude-code/tutorials#configure-mcp-servers). </details> #### Claude Skill: Lean4 Theorem Proving If you are using [Claude Desktop](https://modelcontextprotocol.io/quickstart/user) or [Claude Code](https://claude.ai/code), you can also install the [Lean4 Theorem Proving Skill](https://github.com/cameronfreer/lean4-skills/tree/main/plugins/lean4-theorem-proving). This skill provides additional prompts and templates for interacting with Lean4 projects and includes a section on interacting with the `lean-lsp-mcp` server. ### 4. Install ripgrep (optional but recommended) For the local search tool `lean_local_search`, install [ripgrep](https://github.com/BurntSushi/ripgrep?tab=readme-ov-file#installation) (`rg`) and make sure it is available in your PATH. ## MCP Tools ### File interactions (LSP) #### lean_file_outline Get a concise outline of a Lean file showing imports and declarations with type signatures (theorems, definitions, classes, structures). #### lean_file_contents (DEPRECATED) 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. <details> <summary>Example output</summary> ``` l20c42-l20c46, severity: 1 simp made no progress l21c11-l21c45, severity: 1 function expected at h_empty term has type T ∩ compl T = ∅ ... ``` </details> #### lean_goal Get the proof goal at a specific location (line or line & column) in a Lean file. <details> <summary>Example output (line)</summary> ``` Before: S : Type u_1 inst✝¹ : Fintype S inst✝ : Nonempty S P : Finset (Set S) hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅ hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅ compl : Set S → Set S := fun T ↦ univ \ T hcompl : ∀ T ∈ P, compl T ∉ P all_subsets : Finset (Set S) := Finset.univ h_comp_in_P : ∀ T ∉ P, compl T ∈ P h_partition : ∀ (T : Set S), T ∈ P ∨ compl T ∈ P ⊢ P.card = 2 ^ (Fintype.card S - 1) After: no goals ``` </details> #### 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). <details> <summary>Example output (hover info on a `sorry`)</summary> ``` The `sorry` tactic is a temporary placeholder for an incomplete tactic proof, closing the main goal using `exact sorry`. 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`. ``` </details> #### 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. <details> <summary>Example output (code snippet: `#eval 5 * 7 + 3`)</summary> ``` l1c1-l1c6, severity: 3 38 ``` </details> #### 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. <details> <summary>Example output (attempting `rw [Nat.pow_sub (Fintype.card_pos_of_nonempty S)]` and `by_contra h_neq`)</summary> ``` rw [Nat.pow_sub (Fintype.card_pos_of_nonempty S)]: S : Type u_1 inst✝¹ : Fintype S inst✝ : Nonempty S P : Finset (Set S) hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅ hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅ ⊢ P.card = 2 ^ (Fintype.card S - 1) l14c7-l14c51, severity: 1 unknown constant 'Nat.pow_sub' by_contra h_neq: S : Type u_1 inst✝¹ : Fintype S inst✝ : Nonempty S P : Finset (Set S) hPP : ∀ T ∈ P, ∀ U ∈ P, T ∩ U ≠ ∅ hPS : ¬∃ T ∉ P, ∀ U ∈ P, T ∩ U ≠ ∅ h_neq : ¬P.card = 2 ^ (Fintype.card S - 1) ⊢ False ... ``` </details> ### Local Search Tools #### lean_local_search Search for Lean definitions and theorems in the local Lean project and stdlib. This is useful to confirm declarations actually exist and prevent hallucinating APIs. This tool requires [ripgrep](https://github.com/BurntSushi/ripgrep?tab=readme-ov-file#installation) (`rg`) to be installed and available in your PATH. ### External Search Tools Currently most external tools are separately **rate limited to 3 requests per 30 seconds**. Please don't ruin the fun for everyone by overusing these amazing free services! Please cite the original authors of these tools if you use them! #### lean_leansearch Search for theorems in Mathlib using [leansearch.net](https://leansearch.net) (natural language search). [Github Repository](https://github.com/frenzymath/LeanSearch) | [Arxiv Paper](https://arxiv.org/abs/2403.13310) - 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` <details> <summary>Example output (query by LLM: `bijective map from injective`)</summary> ```json { "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." }, ... ``` </details> #### lean_loogle Search for Lean definitions and theorems using [loogle.lean-lang.org](https://loogle.lean-lang.org/). [Github Repository](https://github.com/nomeata/loogle) - Supports queries by constant, lemma name, subexpression, type, or conclusion. - Example: `Real.sin`, `"differ"`, `_ * (_ ^ _)`, `(?a -> ?b) -> List ?a -> List ?b`, `|- tsum _ = _ * tsum _` - **Local mode available**: Use `--loogle-local` to run loogle locally (avoids rate limits, see [Local Loogle](#local-loogle) section) <details> <summary>Example output (`Real.sin`)</summary> ```json [ { "type": " (x : ℝ) : ℝ", "name": "Real.sin", "module": "Mathlib.Data.Complex.Trigonometric" }, ... ] ``` </details> #### lean_leanfinder Semantic search for Mathlib theorems using [Lean Finder](https://huggingface.co/spaces/delta-lab-ai/Lean-Finder). [Arxiv Paper](https://arxiv.org/abs/2510.15940) - Supports informal descriptions, user questions, proof states, and statement fragments. - Examples: `algebraic elements x,y over K with same minimal polynomial`, `Does y being a root of minpoly(x) imply minpoly(x)=minpoly(y)?`, `⊢ |re z| ≤ ‖z‖` + `transform to squared norm inequality`, `theorem restrict Ioi: restrict Ioi e = restrict Ici e` <details> <summary>Example output</summary> Query: `Does y being a root of minpoly(x) imply minpoly(x)=minpoly(y)?` ```json [ [ "/-- If `y : L` is a root of `minpoly K x`, then `minpoly K y = minpoly K x`. -/\ntheorem eq_of_root {x y : L} (hx : IsAlgebraic K x)\n (h_ev : Polynomial.aeval y (minpoly K x) = 0) : minpoly K y = minpoly K x :=\n ((eq_iff_aeval_minpoly_eq_zero hx.isIntegral).mpr h_ev).symm", "Let $L/K$ be a field extension, and let $x, y \\in L$ be elements such that $y$ is a root of the minimal polynomial of $x$ over $K$. If $x$ is algebraic over $K$, then the minimal polynomial of $y$ over $K$ is equal to the minimal polynomial of $x$ over $K$, i.e., $\\text{minpoly}_K(y) = \\text{minpoly}_K(x)$. This means that if $y$ satisfies the polynomial equation defined by $x$, then $y$ shares the same minimal polynomial as $x$." ], ... ] ``` </details> #### lean_state_search Search for applicable theorems for the current proof goal using [premise-search.com](https://premise-search.com/). [Github Repository](https://github.com/ruc-ai4math/Premise-Retrieval) | [Arxiv Paper](https://arxiv.org/abs/2501.13959) A self-hosted version is [available](https://github.com/ruc-ai4math/LeanStateSearch) 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. <details> <summary>Example output (line 24, column 3)</summary> ```json [ { "name": "Nat.mul_zero", "formal_type": "∀ (n : Nat), n * 0 = 0", "module": "Init.Data.Nat.Basic" }, ... ] ``` </details> #### lean_hammer_premise Search for relevant premises based on the current proof state using the [Lean Hammer Premise Search](https://github.com/hanwenzhu/lean-premise-server). [Github Repository](https://github.com/hanwenzhu/lean-premise-server) | [Arxiv Paper](https://arxiv.org/abs/2506.07477) A self-hosted version is [available](https://github.com/hanwenzhu/lean-premise-server) 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](https://github.com/JOSHCLUNE/LeanHammer) might have better premise search results. <details><summary>Example output (line 24, column 3)</summary> ```json [ "MulOpposite.unop_injective", "MulOpposite.op_injective", "WellFoundedLT.induction", ... ] ``` </details> ### 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). ## MCP Configuration This MCP server works out-of-the-box without any configuration. However, a few optional settings are available. ### Environment Variables - `LEAN_LOG_LEVEL`: Log level for the server. Options are "INFO", "WARNING", "ERROR", "NONE". Defaults to "INFO". - `LEAN_PROJECT_PATH`: Path to your Lean project root. Set this if the server cannot automatically detect your project. - `LEAN_LSP_MCP_TOKEN`: Secret token for bearer authentication when using `streamable-http` or `sse` transport. - `LEAN_STATE_SEARCH_URL`: URL for a self-hosted [premise-search.com](https://premise-search.com) instance. - `LEAN_HAMMER_URL`: URL for a self-hosted [Lean Hammer Premise Search](https://github.com/hanwenzhu/lean-premise-server) instance. - `LEAN_LOOGLE_LOCAL`: Set to `true`, `1`, or `yes` to enable local loogle (see [Local Loogle](#local-loogle) section). - `LEAN_LOOGLE_CACHE_DIR`: Override the cache directory for local loogle (default: `~/.cache/lean-lsp-mcp/loogle`). You can also often set these environment variables in your MCP client configuration: <details> <summary><b>VSCode mcp.json Example</b></summary> ```jsonc { "servers": { "lean-lsp": { "type": "stdio", "command": "uvx", "args": [ "lean-lsp-mcp" ], "env": { "LEAN_PROJECT_PATH": "/path/to/your/lean/project", "LEAN_LOG_LEVEL": "NONE" } } } } ``` </details> ### 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. For `sse` and `streamable-http` you can also optionally specify the host and port: ```bash 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 --host localhost --port 12345 # Available at http://localhost:12345/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: ```bash 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. ### Local Loogle Run loogle locally to avoid the remote API's rate limit (3 req/30s). First run takes ~5-10 minutes to build; subsequent runs start in seconds. ```bash # Enable via CLI uvx lean-lsp-mcp --loogle-local # Or via environment variable export LEAN_LOOGLE_LOCAL=true ``` **Requirements:** `git`, `lake` ([elan](https://github.com/leanprover/elan)), ~2GB disk space. **Note:** Local loogle is currently only supported on Unix systems (Linux/macOS). Windows users should use WSL or the remote API. Falls back to remote API if local loogle fails. ## 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](https://github.com/Puliczek/awesome-mcp-security) as a starting point. ## Development ### MCP Inspector ```bash npx @modelcontextprotocol/inspector uvx --with-editable path/to/lean-lsp-mcp python -m lean_lsp_mcp.server ``` ### Run Tests ```bash uv sync --all-extras uv run pytest tests ``` ## Publications using lean-lsp-mcp - Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics [arxiv](https://arxiv.org/abs/2510.12787) ## Related Projects - [LeanTool](https://github.com/GasStationManager/LeanTool) - [LeanExplore MCP](https://www.leanexplore.com/docs/mcp) ## License & Citation **MIT** licensed. See [LICENSE](LICENSE) for more information. Citing this repository is highly appreciated but not required by the license. ```bibtex @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} } ```