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discussion_partner

Get proof strategy suggestions and alternative reasoning paths for Lean 4 code and math problems by querying Gemini or GPT models. Discuss approaches, compare suggestions, and debug stuck proofs.

Instructions

Use this tool to interact with a specialized partner model for proof strategies, reasoning, and formalization.

You can send Lean 4 code, natural language math problems, or proof strategies to different models
and get their suggestions. This is useful for:
- Discussing proof strategies and approaches
- Getting alternative reasoning paths
- Comparing suggestions from different models
- Debugging stuck proofs

Args:
    question (str): Lean code, math problem, or any question you want to discuss.
    model (str): Choose "gemini" (Google gemini-3-pro-preview) or "gpt" (OpenAI gpt-5.2-pro). Default is "gemini".

Returns:
    str: The model's response.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
modelNogemini
questionYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the transparency burden. It explains that the tool sends questions to external models and returns a string, and it documents model choices. However, it omits caveats about response variability, latency, or the potential for inaccurate answers, which are relevant when invoking external LLMs.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is well-structured: it opens with a purpose statement, uses a bulleted list for use cases, and clearly labels Args and Returns. It is somewhat verbose but every section adds value, and the formatting improves scannability.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple tool with 2 parameters and a string output, the description is complete. It covers purpose, use cases, parameter semantics, model options, and return type, leaving no major gaps. The explicit return description is a nice touch.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema descriptions are absent (0% coverage), but the description fully explains both parameters: question (with examples of acceptable content) and model (with allowed values and default). This adds crucial meaning beyond the raw schema definitions.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's function ('interact with a specialized partner model') and specifies the domain (proof strategies, reasoning, formalization). It lists concrete use cases, including comparing suggestions from different models, which distinguishes it from sibling Lean-specific and model-specific tools.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides a clear list of when the tool is useful (discussing strategies, getting alternative paths, comparing models, debugging stuck proofs). However, it does not explicitly mention alternatives or exclusions relative to sibling tools like gemini_informal_prover or gpt_informal_prover.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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