factorial

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It reveals that the computation is exact (not an approximation), the valid input range (0-1000), and the return type (decimal string, implying support for large numbers). This adds valuable context beyond the input schema, which only specifies the parameter constraints. For a pure mathematical function, this level of detail is sufficient.

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 a single sentence that front-loads the core action and includes all essential details: operation, exactness, input range, and output format. Every word contributes meaning, with no redundancy or filler. It exemplifies conciseness while being fully informative.

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 low complexity and the absence of an output schema, the description covers the critical aspects: what the tool does, its input constraints, and its output format. It does not mention error handling or performance, but for a straightforward mathematical function, these omissions are acceptable. The description is complete enough for an AI agent to use the tool correctly.

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 single parameter 'value' is described in the input schema as an integer with min 0 and max 1000. The description complements this by clarifying that 'value' is the integer for which factorial is computed, and it explicitly repeats the valid range ('integer from 0 through 1000'). Since schema description coverage is 0%, the description effectively compensates by providing the necessary meaning.

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 explicitly states the action ('Calculates n! exactly'), the resource ('factorial of an integer'), the valid input range ('0 through 1000'), and the output format ('returns a decimal string'). This uniquely identifies the tool's functionality and clearly distinguishes it from sibling tools, which cover other mathematical operations.

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 clearly implies when to use the tool (for exact factorial calculations within the specified range). Although it does not explicitly state when not to use it or name alternatives, the context of sibling tools (e.g., combinations, permutations) makes the appropriate usage obvious. The lack of explicit exclusions is minor given the tool's straightforward purpose.

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