Introduction to GPT-Coq Assistant

Welcome to GPT-Coq Assistant, your specialized mathematician in utilizing the Coq Proof Assistant. This tool is dedicated to aiding the development of definitions, lemmas, examples, and theorems within Coq’s robust framework. It provides the same look and feel as the build-in code interpreter: the GPT is able to execute Coq source code and directly fix it when there are problems.

Key Features

  1. Expertise in Mathematics and Coq: Tailored assistance in creating and understanding mathematical proofs, definitions, and lemmas using Coq’s language and tools.
  2. Formal and Concise Communication: Maintains a formal tone and adheres to a concise 80-character line length to promote readability and standard coding practices.
  3. Structured Problem Solving: Emphasizes a top-down approach, breaking down goals into manageable tasks and highlighting errors or contradictions immediately.
  4. Import Management: Ensures all necessary imports are included in the Coq source code, prompting for any missing or suggesting alternatives.

Usage Guidelines

  • Initiating Coq Code: Clearly demarcate your Coq source code between [COQ] and [/COQ], hypothesis between [HYP] and [/HYP], and any error messages between [ERR] and [/ERR] for clear processing.
  • Interactive Dialogue: Provide your familiarity level with Coq or mathematics to receive tailored assistance. Don’t hesitate to ask for clarification or provide additional context for ambiguous requests.
  • Safety and Security: Respect the safety and security protocols in place for the code interpreter to ensure a secure environment for all users.
  • Responsible Use: Adhere to the assistant’s capabilities and avoid non-mathematical or irrelevant queries for optimal performance.

Current Shortcomings and Possible Problems

1. Experimental Implementation:

The current iteration of the GPT-Coq Assistant is purely experimental and subject to change. Users should be aware that functionalities, features, and the overall approach may evolve over time as improvements and updates are made. This experimental nature means that the tool should be used with an understanding of its provisional status.

Be prepared that the interaction with GPT runs into “network problems” which typically is the way to state, that the iterative process of one interaction took too long.

2. Limited Coq Environment:

The Coq environment provided within the GPT-Coq Assistant is limited and may not encompass the full range of features, libraries, or capabilities found in a complete, standalone Coq environment. Users might encounter restrictions in terms of available tactics, libraries, or functionality that can impact the proof development process.

3. Varied Quality in Coq Handling:

While GPT has been trained on a wide range of languages and disciplines, its handling of Coq proofs may not be as robust or nuanced as its handling of other programming languages or simpler mathematical tasks. As such, users might find that achieving a successful proof requires several iterations, refinements, or rephrasings of the problem at hand to guide the assistant towards a useful solution.

As an example GPT tries to proof the commutativity of addition. It presents a theorem and the proof, but the proof is wrong. A “Check it.” prompt let’s GTP execute a remote coq environment, checks the proof and returns possible errors. GPT analysis the error, fixes the problem and tries again until a valid proof is found.

4. Need for Problem Decomposition:

Given the complex nature of proofs and the limitations of the GPT’s understanding of Coq, users are advised to be prepared to break down larger problems into smaller, more manageable ones. Mid-sized proofs or those of considerable complexity may exceed the assistant’s current capabilities, necessitating a more granular approach where each component of the proof is tackled individually. This strategy not only aligns better with the assistant’s capabilities but also fosters a more methodical and thorough approach to problem-solving.

Privacy Policy for GPT-Coq Assistant Service

Effective Date: 2024-01-07

Welcome to the Coq Compiler Service. We are committed to protecting your privacy and ensuring a secure service. Please read the following to learn more about our privacy policy.

1. No Personal Data:

The Coq Compiler Service is designed exclusively for compiling Coq source code files. Users are strictly prohibited from submitting any personal data to the service, including but not limited to names, addresses, phone numbers, or any information that can be used to identify or contact a person.

2. Use of the Service:

When using our service, ensure that the content of the Coq files does not contain any personal or sensitive data. We are not responsible for any personal data submitted to our service, and we have the right to delete any content that we suspect may contain such information.

3. Data Collection:

We may collect non-personally identifying information that is typically made available by web servers and browsers, such as the browser type, language preference, referring site, and the date and time of each visitor request. Our purpose in collecting non-personally identifying information is to better understand how visitors use our service.

4. Your Responsibilities:

As a user of the Coq Compiler Service, it is your responsibility to ensure that no personal data is included in the files you submit for compilation. Always review and sanitize the content before submission.

5. Changes to the Privacy Policy:

We may update this policy from time to time. We will notify you of any changes by posting the new policy on this page. You are advised to review this Privacy Policy periodically for any changes.