is_catalan_number

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

No annotations are provided, so the description carries the full burden. It mentions the tool 'checks' a number, implying a read-only operation, but doesn't disclose behavioral traits like error handling (e.g., for non-integer inputs), performance characteristics, or what the output looks like (e.g., boolean or detailed result). This leaves significant gaps for an agent to understand how to invoke it correctly.

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?

The description is extremely concise—two sentences with zero waste. The first sentence states the purpose, and the second adds domain context. It's front-loaded and efficiently structured, making it easy to parse.

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?

Given the tool's complexity (a mathematical check with one parameter), no annotations, no output schema, and 0% schema coverage, the description is incomplete. It doesn't explain the return value, error conditions, or parameter semantics, which are essential for correct usage. The domain/category hint is insufficient to fill these gaps.

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?

The input schema has one parameter 'n' with 0% description coverage. The tool description adds no information about what 'n' represents (e.g., an integer to test) or its constraints (e.g., non-negative, range limits). This fails to compensate for the lack of schema documentation, leaving the parameter's meaning ambiguous.

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 tool's purpose: 'Check if a number is a Catalan number.' It specifies the verb ('Check') and resource ('a number'), and the domain/category context helps clarify it's about combinatorial numbers. However, it doesn't explicitly differentiate from sibling tools like 'catalan' or 'catalan_number', which might have overlapping functionality.

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?

The description provides no guidance on when to use this tool versus alternatives. With many sibling tools (e.g., 'catalan', 'catalan_number', 'catalan_sequence'), there's no indication of how this tool differs or when it's preferred. The domain/category hint is minimal and doesn't address usage context.

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