Add Lean 4 Theorem Prover plugin

[ImHangLi]

Integrate Lean 4 Theorem Prover for Advanced Logical Reasoning

Is your feature request related to a problem? Please describe.

Eliza excels with conversational patterns but struggles with formal or mathematical reasoning.

The motivations can be:

• Enhanced Conversation: Beyond classic Eliza patterns, users could ask logical or mathematical questions, and Eliza could leverage Lean 4 to provide validated answers or insights.
• Educational Value: A Lean 4 integration could serve as an educational tool for users learning formal reasoning and proof techniques.
• Differentiation: Incorporating a theorem prover sets Eliza apart from traditional chatbot frameworks, offering unique capabilities for advanced or specialized use cases.

Describe the solution you’d like.

• Integrate Lean 4 so Eliza can pass user statements or questions to a theorem-proving engine. Whether in natural language, e.g., “Eliza, can you prove that the sum of two even numbers is even?”, or in Lean code snippet.
• Define specific triggers or keywords in Eliza’s pattern-matching system.
• When triggered, Eliza calls the Lean 4 plugin to validate or prove statements.
• If a statement can’t be proved, Eliza gracefully handles the error or explains the reason.

Describe alternatives you’ve considered.

• Using different theorem provers (e.g., Coq, Isabelle).
• Simpler pattern-based approaches that lack robust logic handling.

Additional context.

• Using external APIs or embedding Lean 4 directly?

[github-actions]

Hello @ImHangLi! Welcome to the elizaOS community. Thank you for opening your first issue; we appreciate your contribution. You are now an elizaOS contributor!