stirling_first

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It mentions 'FIXED IMPLEMENTATION', which hints at a stable or deterministic calculation, but does not elaborate on computational characteristics (e.g., performance, limitations for large inputs), error handling, or output format. For a mathematical computation tool with zero annotation coverage, this leaves significant behavioral gaps.

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 brief and to the point, consisting of a single sentence that states the core function. The additional note 'FIXED IMPLEMENTATION' and domain/category are somewhat extraneous but not overly verbose. It is front-loaded with the main purpose, though could be more structured.

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 complexity of a combinatorial number calculation, the description is insufficient. There are no annotations, no output schema, and the input parameters are poorly documented. The description does not cover important aspects like the mathematical definition, typical use cases, or example outputs, leaving the agent with inadequate context to use the tool effectively.

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 0% description coverage, with parameters 'n' and 'k' documented only by type (integer). The description does not explain what these parameters represent (e.g., that 'n' and 'k' are non-negative integers with k ≤ n for Stirling numbers of the first kind), their constraints, or typical usage ranges. It fails to compensate for the lack of schema descriptions.

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: 'Calculate Stirling number of the first kind s(n,k)'. It specifies both the verb ('Calculate') and the mathematical resource ('Stirling number of the first kind'), making the function unambiguous. However, it does not explicitly differentiate from its sibling tool 'stirling_second', though the naming implies a distinction between first and second kind Stirling numbers.

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. While it mentions 'FIXED IMPLEMENTATION' and a domain/category, these do not indicate specific contexts, prerequisites, or comparisons with sibling tools like 'stirling_second'. There is no explicit when-to-use or when-not-to-use information.

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