MCP-RoCQ MCP Server: Coq Reasoning Capabilities through Model Context Protocol

Overview: What is MCP-RoCQ MCP Server?

MCP-RoCQ (Coq Reasoning Server) is a specialized Model Context Protocol server designed to integrate advanced logical reasoning capabilities into AI applications. It leverages the Coq proof assistant for seamless verification, inductive type definition, and property proving tasks. By supporting custom tactics and automation, it provides robust tools for developers building complex formal systems.

🔧 Core Features & MCP Capabilities

MCP-RoCQ offers a suite of features optimized for AI workflows through Model Context Protocol (MCP):

• Automated Dependent Type Checking: Ensures that terms adhere to complex dependent types.
• Inductive Type Definition: Facilitates the creation and verification of custom inductive data types within Coq's rigorous framework.
• Property Proving: Enables logical property proofs using both predefined tactics and automated strategies, enhancing the reliability of formal systems.
• XML Protocol Integration: Provides a reliable, structured communication interface between MCP clients and the server.
• Rich Error Handling: Offers detailed feedback for type errors and failed proof attempts, streamlining development processes.

These capabilities make MCP-RoCQ an indispensable tool for AI applications that require robust logical reasoning and formal verification mechanisms.

⚙️ MCP Architecture & Protocol Implementation

MCP-RoCQ is built to fully comply with the Model Context Protocol (MCP), ensuring seamless integration with various AI clients. The server architecture is modular, allowing for easy expansion and customization. Communication between the client and server adheres strictly to MCP standards, ensuring interoperability.

The protocol flow diagram below illustrates how data flows through the system:

graph TD;
    A[AI Application] -->|MCP Client| B[MCP Protocol]
    B --> C[MCP Server]
    C --> D[Coq Proof Assistant]

This diagram shows that an AI application sends MCP requests over a client, which then interacts with the MCP server. The server processes these requests and communicates with Coq to perform necessary tasks like type checking, induction definition, or property proving.

🚀 Getting Started with Installation

Installing MCP-RoCQ involves setting up both Coq and its dependencies. Coq must be installed as a prerequisite, which can be found here:

• Coq Platform 8.19 (2024.10)

Step 1: Install Coq

Follow the instructions on the official Coq platform repository to install version 8.19.

git clone https://github.com/coq/platform

Step 2: Clone the Repository and Set Up Environment

Clone this repository:

git clone https://github.com/angrysky56/mcp-rocq.git
cd mcp-rocq
uv venv
./venv/Scripts/activate
pip install -e .

Step 3: Configure MCP Client for Usage

Set up the environment variables and paths specified in your MCP client configuration, such as Claude Desktop or Continue.

{
    "mcp-rocq": {
      "command": "uv",
      "args": [
        "--directory",
        "F:/GithubRepos/mcp-rocq",
        "run",
        "mcp_rocq",
        "--coq-path",
        "F:/Coq-Platform~8.19~2024.10/bin/coqtop.exe",
        "--lib-path",
        "F:/Coq-Platform~8.19~2024.10/lib/coq"
      ]
    },
}

💡 Key Use Cases in AI Workflows

MCP-RoCQ serves as a powerful tool for developers working on formal verification and automated reasoning tasks within complex AI systems. Here are two realistic use cases:

Use Case 1: Formal Verification of Code Logic

In software development, formal verification ensures the correctness of logical constructs like functions or algorithms. By integrating MCP-RoCQ, developers can automatically check code logic against specified types and properties.

{
    "tool": "type_check",
    "args": {
        "term": "<term to check>",
        "expected_type": "<type>",
        "context": ["relevant", "modules"]
    }
}

Use Case 2: Property Proving in Machine Learning Models

In machine learning, property proving can validate certain behaviors or properties of models. For instance, proving that a model's outputs meet specific constraints is critical for building reliable systems.

{
    "tool": "prove_property",
    "args": {
        "property": "<statement>",
        "tactics": ["<tactic sequence>"],
        "use_automation": true
    }
}

🔌 Integration with MCP Clients

MCP-RoCQ is compatible with several AI clients, including:

MCP Client	Resources	Tools	Prompts
Claude Desktop	✅	✅	✅
Continue	✅	✅	✅
Cursor	❌	✅	❌

This matrix highlights that while certain tools are universally supported, not all features are compatible with every client. Specifically, resources and prompts require full support only from Claude Desktop and Continue.

📊 Performance & Compatibility Matrix

The following table outlines the performance and compatibility of MCP-RoCQ across various AI platforms:

Feature	Coq Platform 8.19 (2024.10)	Python Environment
Type Checking	✅	✅
Inductive Definition	✅	✅
Property Proving	✅	✅
XML Protocol	✅	✅

🛠️ Advanced Configuration & Security

Configuration and security settings can be adjusted by modifying the server's environment variables or command-line arguments. For example, you can set up API keys for enhanced security.

Example Configuration:

{
    "mcp-rocq": {
      "command": "uv",
      "args": [
        "--directory",
        "F:/GithubRepos/mcp-rocq",
        "run",
        "mcp_rocq",
        "--coq-path",
        "F:/Coq-Platform~8.19~2024.10/bin/coqtop.exe",
        "--lib-path",
        "F:/Coq-Platform~8.19~2024.10/lib/coq"
      ],
      "env": {
        "API_KEY": "your-api-key"
      }
    },
}

❓ Frequently Asked Questions (FAQ)

Q: Can MCP-RoCQ be used with other AI clients besides Claude Desktop and Continue?

A: Currently, Coq Platform 8.19 (2024.10) supports a limited number of clients, primarily focusing on Claude Desktop and Continue for full resource, tool, and prompt support.

Q: How do I ensure that my proof scripts are compatible with MCP-RoCQ?

A: Ensure your Coq scripts follow the standards and guidelines provided by Coq to avoid syntax errors or incompatibilities.

Q: Are there specific tactics that work better for property proving in complex systems?

A: Yes, certain tactics like rewrite, simpl, and solve are particularly useful for automating proofs in intricate logical structures. Experimenting with different tactic sequences can improve performance.

Q: How do I integrate MCP-RoCQ into my existing development process?

A: Integrate MCP-RoCQ by setting it up as a service alongside your application, configuring the relevant paths and environment variables to ensure seamless interaction between your code logic and the formal verification system.

Q: Can MCP-RoCQ handle real-time proofs during runtime?

A: MCP-RoCQ supports both batch and real-time modes. Real-time proof checking can be enabled by setting up specific environment configurations for handling ongoing or dynamic data inputs.

👨‍💻 Development & Contribution Guidelines

Contributions to MCP-RoCQ are encouraged to improve its robustness and usability. To contribute, follow these steps:

1. Fork the Repository: Visit the GitHub repository and fork it.
2. Set Up Your Environment: Clone your repository and set up the environment as outlined in the "Getting Started" section.
3. Make Changes: Develop new features or improve existing ones.
4. Run Tests: Ensure that all test cases pass before opening a pull request.

🌐 MCP Ecosystem & Resources

For more information on Model Context Protocol and related projects, visit:

• Model Context Protocol Official Site

Explore the extensive documentation and community resources available to build robust AI applications with MCP-RoCQ.