verify-commutativity

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

With no annotations provided, the description carries full burden and does well by explaining the tool's behavior: it generates premises/conclusion for proving path equality, mentions the output format (premises and conclusion to pass to prove tool), and includes an example. However, it doesn't cover potential limitations like error conditions or computational constraints.

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?

Well-structured with clear sections: purpose statement, usage guidelines, example, and output description. Every sentence adds value without redundancy, and the information is front-loaded with the core purpose first.

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?

For a tool with no annotations and no output schema, the description provides good context: purpose, usage boundaries, example, and output format. It could be more complete by explaining what happens with the 'with_category_axioms' parameter or potential failure modes, but covers the essential behavioral aspects well.

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 100%, so the schema already documents all 6 parameters thoroughly. The description adds minimal value beyond the schema through the example showing how path_a, path_b, object_start, and object_end work together. This meets the baseline for high schema coverage.

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 clearly states the specific verb ('verify') and resource ('categorical diagram commutes'), explaining it generates FOL premises and conclusion for path equality. It distinguishes from sibling tools like 'prove' by focusing specifically on diagram verification rather than general proving.

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?

Explicitly provides 'When to use' (for categorical diagram verification) and 'When NOT to use' (for non-categorical reasoning, directing to 'prove' instead). This gives clear guidance on when to select this tool versus alternatives among siblings.

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