factorial

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 states the mathematical operation but doesn't mention important behavioral aspects: input constraints (e.g., n must be non-negative integer, potential overflow for large n), error handling, performance characteristics, or return format. The description is mathematically correct but operationally incomplete.

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 efficiently structured in two parts: the mathematical definition and domain/category metadata. Both sentences earn their place - the first defines the operation, the second provides classification. It's appropriately sized for a simple mathematical function, though it could be slightly more front-loaded with usage context.

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 mathematical computation tool with no annotations and no output schema, the description is insufficient. It explains what factorial is mathematically but doesn't cover: input validation (what happens with negative n?), output format (integer, potential overflow), error conditions, or performance considerations. The context signals show 1 parameter with 0% schema coverage - the description doesn't fully compensate for 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 1 parameter with 0% description coverage (just 'n' as integer). The description adds the mathematical meaning of 'n' in the factorial formula, which provides essential semantic context beyond the bare schema. However, it doesn't specify constraints like n ≥ 0 or handling of edge cases (n=0, negative n). Given the low schema coverage, the description partially compensates but not fully.

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 mathematical operation: 'Calculate factorial n! = n × (n-1) × ... × 2 × 1.' It specifies the verb ('calculate') and resource ('factorial') with the mathematical definition. However, it doesn't explicitly differentiate from sibling tools like 'double_factorial' or 'subfactorial', which are related but distinct 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 provides no guidance on when to use this tool versus alternatives. It mentions 'Domain: arithmetic, Category: basic_sequences' which gives some context but doesn't specify use cases, prerequisites, or comparisons to sibling tools like 'double_factorial' or 'fibonacci'. There's 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.