Axle

An MCP server that exposes the AXLE (Axiom Lean Engine) CLI as tools for AI assistants like Claude.

AXLE is a remote API for Lean 4 proof engineering — it can check, repair, simplify, extract, and transform Lean theorems without requiring a local Lean installation.

Tools

Tool	Description
axle_environments	List available Lean environments (versions + Mathlib)
axle_check	Validate Lean code and report errors/warnings/info
axle_verify_proof	Check that a candidate proof matches a formal statement
axle_extract_theorems	Split a file into one-theorem-per-unit with rich metadata
axle_repair_proofs	Auto-repair broken proofs (replaces sorry with working tactics)
axle_simplify_theorems	Remove redundant tactics and clean up proof steps
axle_disprove	Find counterexamples to false theorems via property-based testing
axle_theorem2sorry	Replace proof bodies with sorry (create problem templates)
axle_have2sorry	Replace have proofs with sorry (targeted exercises)
axle_sorry2lemma	Lift sorry placeholders into standalone top-level lemmas
axle_have2lemma	Lift have statements into standalone top-level lemmas
axle_theorem2lemma	Convert between theorem and lemma keywords
axle_rename	Rename declarations and update all references
axle_merge	Combine multiple Lean snippets into one file
axle_normalize	Standardize Lean file formatting

Requirements

• Python 3.11+
• mcp Python package (pip install mcp)
• The axle CLI installed and accessible

Installation

1. Install dependencies

pip install mcp

2. Clone this repo

git clone https://github.com/Vilin97/axle-mcp
cd axle-mcp

3. Register with Claude Code

claude mcp add axle -s user \
  -e AXLE_BIN=/path/to/axle \
  -e AXLE_DEFAULT_ENVIRONMENT=lean-4.28.0 \
  -- python /path/to/axle-mcp/server.py

4. Register with Claude Desktop

Add to your claude_desktop_config.json:

{
  "mcpServers": {
    "axle": {
      "command": "python",
      "args": ["/path/to/axle-mcp/server.py"],
      "env": {
        "AXLE_BIN": "/path/to/axle",
        "AXLE_DEFAULT_ENVIRONMENT": "lean-4.28.0"
      }
    }
  }
}

Configuration

Environment variable	Default	Description
AXLE_BIN	axle	Path to the axle binary
AXLE_DEFAULT_ENVIRONMENT	lean-4.28.0	Default Lean environment for all tools

Usage examples

Once registered, Claude can use these tools directly. Some examples of what you can ask:

• "Check if this Lean theorem compiles" → axle_check
• "Repair the sorry'd proofs in this file" → axle_repair_proofs
• "Turn this proof into a problem set by replacing proofs with sorry" → axle_theorem2sorry
• "Does this theorem have a counterexample?" → axle_disprove
• "Extract each theorem into its own self-contained snippet" → axle_extract_theorems
• "Merge these two Lean files into one" → axle_merge

Common parameters

Most tools accept these optional parameters:

• environment — Lean environment to use (run axle_environments to list available ones)
• names — comma-separated declaration names to process (default: all)
• indices — comma-separated 0-based indices to process
• timeout — max execution time in seconds (default: 120)
• ignore_imports — ignore import mismatches between the code and the environment

How it works

Each MCP tool wraps the corresponding axle CLI command, passing Lean source code via stdin and returning the structured JSON response from the AXLE API. Tools that require multiple file arguments (verify-proof, merge) write temporary files automatically and clean them up after the call.