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gleachkr
by gleachkr

prove_informal_text

Formalizes and proves mathematical statements expressed in natural language using the Aristotle API, returning a Project ID for tracking.

Instructions

Submits natural language mathematics directly to be formalized and proved. Returns the Project ID immediately.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
textYes
formal_context_pathNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • main.py:147-168 (handler)
    The handler function for the 'prove_informal_text' tool. It is decorated with @mcp.tool(), which registers it as an MCP tool. The function submits informal text to Aristotle via Project.prove_from_file and returns the project ID.
    @mcp.tool()
    async def prove_informal_text(
        text: str,
        formal_context_path: Optional[str] = None,
        ctx: Context | None = None,
    ) -> str:
        """
        Submits natural language mathematics directly to be formalized and proved.
        Returns the Project ID immediately.
        """
        if ctx:
            await ctx.info("Submitting informal text to Aristotle...")
        
        project_id = await Project.prove_from_file( # type: ignore
            input_content=text,
            project_input_type=ProjectInputType.INFORMAL,
            formal_input_context=formal_context_path,
            wait_for_completion=False
        )
        
        monitored_projects.add(project_id)
        return f"Project started with ID: {project_id}."
Behavior2/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states the tool 'submits' content and 'returns the Project ID immediately', implying an asynchronous operation with a quick initial response. However, it lacks details on permissions, rate limits, error handling, or what 'formalized and proved' entails in terms of time or resources.

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

Conciseness5/5

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

The description is highly concise with two sentences that are front-loaded and waste no words. Each sentence adds value: the first explains the core action, and the second clarifies the immediate return, making it efficient and well-structured.

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

Completeness3/5

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

Given the tool's complexity (asynchronous proof submission with 2 parameters), no annotations, and an output schema present (which handles return values), the description is minimally adequate. It covers the basic purpose and immediate response but lacks details on parameter usage, behavioral traits, and differentiation from siblings, leaving gaps for an agent to infer correctly.

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

Parameters2/5

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

Schema description coverage is 0%, so the schema provides no parameter details. The description mentions 'natural language mathematics' which hints at the 'text' parameter, but doesn't explain the 'formal_context_path' parameter at all. It adds minimal meaning beyond the bare schema, failing to compensate for the low coverage.

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

Purpose4/5

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

The description clearly states the action ('Submits natural language mathematics directly to be formalized and proved') and the resource (mathematical content), making the purpose understandable. However, it doesn't explicitly differentiate from sibling tools like 'prove_informal' or 'prove_lean_code', which likely handle similar proof tasks but with different input formats or contexts.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions 'natural language mathematics' but doesn't specify scenarios where this is preferred over other proof tools like 'prove_lean_code' or 'prove_lean_file', nor does it mention prerequisites or exclusions.

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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