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

No annotations are provided, so the description bears full behavioral disclosure. It describes return content but omits read-only safety, side effects, authentication needs, error behavior, or what happens if the theorem is not found.

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

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

A single front-loaded sentence that wastes no words and puts the core resource first. It is a sentence fragment rather than a complete sentence, which slightly hurts readability.

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

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

With no annotations, no output schema, and 0% parameter coverage, the description should carry more of the load. It covers return values reasonably well but leaves parameters and usage context undocumented.

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

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

Schema description coverage is 0% for two required parameters. The phrase 'One theorem in a Lean program' loosely maps 'program' to a Lean program and 'name' to a theorem, but adds no format, syntax, or validation detail beyond the bare property names.

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

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

The description names a specific resource (a theorem in a Lean program) and enumerates what the tool returns: statement, proof status, and prior attempts with blockers. This distinguishes it from get_program and other siblings, though it never states the retrieval verb explicitly.

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

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

There is no guidance on when to use this tool versus get_program, list_programs, or search_notebook. The description only describes content, leaving the agent to infer usage context.

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