MCP-RoCQ

MCP‑RoCQ: Coq Reasoning Server

MCP‑RoCQ is a Model Context Protocol (MCP) server that bridges the powerful formal verification capabilities of the Coq proof assistant with AI assistants such as Claude. By exposing Coq’s type‑checking engine, inductive data‑type definition facilities, and automated proof tactics as MCP tools, it allows developers to embed rigorous logical reasoning directly into conversational AI workflows. The server solves the common pain point of having to manually invoke Coq from a command line or IDE: it presents Coq’s complex functionality through a clean, JSON‑based interface that AI assistants can call with simple tool requests.

At its core, MCP‑RoCQ offers three principal services. First, automated dependent type checking lets the AI validate that a given term conforms to an expected dependent type, returning detailed diagnostics if mismatches occur. Second, the inductive type definition capability enables dynamic creation of custom data structures—such as trees or lists—with optional verification that the constructors satisfy Coq’s strict typing rules. Finally, property proving allows the assistant to request proof of logical statements using supplied tactic sequences or automated tactics, with the server handling Coq’s proof search and reporting success or failure back to the client.

The server’s design emphasizes reliability and clarity. It communicates over an XML‑based protocol that ensures structured, error‑free exchanges with Coq, and it provides rich error handling that surfaces type errors or proof failures in an easily consumable format. This transparency is invaluable when debugging proofs or integrating Coq checks into larger development pipelines, as developers can see exactly why a proof failed rather than receiving opaque failure messages.

Real‑world scenarios that benefit from MCP‑RoCQ include automated verification of safety properties in embedded systems, formal validation of cryptographic protocols within a conversational interface, and educational tools where students can query an AI assistant for step‑by‑step type checks or proof guidance. By exposing Coq’s formal engine through MCP, developers can weave deep mathematical guarantees into AI‑driven code reviews, documentation generation, or interactive tutoring without leaving the familiar chat environment.

What sets MCP‑RoCQ apart is its tight coupling with Coq’s latest platform (currently 8.19), ensuring access to the newest language features and automation tactics, while maintaining a lightweight MCP interface that requires minimal configuration. This combination of formal rigor, ease of integration, and AI‑friendly tooling makes MCP‑RoCQ a standout solution for teams that need dependable logical reasoning embedded in their AI workflows.