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gleachkr
by gleachkr

prove_informal

Formalizes and proves mathematical statements from natural language files using Lean theorem proving, returning a Project ID for tracking.

Instructions

Submits a file containing natural language mathematics (Text, Markdown, LaTeX) to be formalised and proved. Returns the Project ID immediately.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
file_pathYes
formal_context_pathNo

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Implementation Reference

  • main.py:39-64 (handler)
    The handler function for the 'prove_informal' tool. It is registered via the @mcp.tool() decorator and handles submitting an informal mathematics file to Aristotle for formalization and proof using Project.prove_from_file, returning the project ID.
    @mcp.tool()
    async def prove_informal(
        file_path: str,
        formal_context_path: Optional[str] = None,
        ctx: Context | None = None,
    ) -> str:
        """
        Submits a file containing natural language mathematics (Text, Markdown, LaTeX) to be formalised and proved.
        Returns the Project ID immediately.
        """
        path = Path(file_path)
        if not path.exists():
            raise FileNotFoundError(f"File not found: {file_path}")
    
        if ctx:
            await ctx.info(f"Submitting informal file {file_path} to Aristotle...")
    
        project_id = await Project.prove_from_file( # type: ignore
            input_file_path=path,
            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}."
  • main.py:147-168 (handler)
    A related handler for submitting informal text directly (without file), similar to prove_informal.
    @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?

No annotations are provided, so the description carries full burden for behavioral disclosure. It mentions that the tool 'Returns the Project ID immediately,' which is useful context about response timing. However, it doesn't disclose critical behavioral traits: whether this is a long-running operation, what happens to the submitted file, authentication requirements, rate limits, or error conditions. For a tool that submits files for processing, this is a significant gap.

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 appropriately concise with two clear sentences. The first sentence explains the core functionality, and the second provides important behavioral context about immediate Project ID return. There's no wasted language, though it could be slightly more structured with explicit parameter mentions.

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 that an output schema exists (which presumably documents the Project ID return), the description doesn't need to explain return values. However, for a tool with 2 parameters (one undocumented), no annotations, and multiple sibling tools, the description is incomplete. It covers the basic purpose and immediate response but misses parameter explanations, usage differentiation, and important behavioral context about the formalization/proof process.

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?

With 0% schema description coverage for both parameters, the description must compensate but fails to do so. It mentions 'file_path' implicitly through 'file containing natural language mathematics' but doesn't explain what format or constraints this path should have. It doesn't mention 'formal_context_path' at all, leaving this parameter completely undocumented. The description adds minimal value beyond what's implied by the tool name.

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 tool's purpose: 'Submits a file containing natural language mathematics... to be formalised and proved.' It specifies the action (submits), resource (file with mathematics content), and outcome (formalization and proof). However, it doesn't explicitly differentiate from siblings like 'prove_informal_text' which likely serves a similar purpose with text input instead of file input.

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. With siblings like 'prove_informal_text', 'prove_lean_code', and 'prove_lean_file', there's no indication of when file-based informal proof is preferred over text-based or Lean-based alternatives. The description only states what the tool does, not when to choose it.

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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