Description
Summary of our discussion:
Project Goal:
Utilize a large language model (LLM) to explore and potentially create a "class of classes" within a self-descriptive hierarchy using Coq.
Derive methods and descriptions for these classes through LLM prompts and feedback loops.
Key Points:
LLM Capabilities: Consider the limitations and strengths of the chosen LLM, especially in understanding type classes and formal languages like Coq.
Prompt Design: Provide clear, concise, and iterative prompts with relevant context (e.g., previous/next items, function purpose, evaluation criteria).
Feedback Loop: Establish clear criteria for evaluating generated functions and use the feedback to adapt prompts and guide the LLM.
Data Representation: Choose a consistent format for representing classes, methods, descriptions, and context for efficient processing.
Additional Considerations:
Scaling for large hierarchies
Ethical implications of LLM bias
Human oversight and explainability
Computational resources
Potential Benefits:
Exploring relationships and insights within the hierarchy
Generating creative and diverse methods for different classes
Automating some aspects of method development
Challenges and Limitations:
LLMs might not always generate correct or functional Coq code.
The iterative process requires careful design and human intervention.
Scaling to large hierarchies might be computationally expensive.
Next Steps:
Define specific use cases and desired outcomes for the "class of classes" concept.
Choose a specific LLM and experiment with different prompt formats and feedback mechanisms.
Start with simple examples and gradually increase complexity as you gain confidence.
Monitor the LLM's performance and adapt your approach based on the results.
Additional Resources:
Coq libraries: CoqAssist, Coq extraction
Research on LLMs for code generation and formal verification
I hope this summary is helpful! Please let me know if you have any further questions or want to explore specific aspects in more detail.