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IBM

MCP Math Server

by IBM

catalan_sequence

Calculate the first n Catalan numbers for combinatorial mathematics applications. This tool generates sequences used in counting problems, binary trees, and other mathematical structures.

Instructions

Generate the first n Catalan numbers. (Domain: arithmetic, Category: combinatorial_numbers)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
Behavior2/5

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 tool generates numbers but does not describe output format (e.g., list of integers), performance characteristics (e.g., computational limits for large n), error handling, or any side effects. For a tool with no annotations, this leaves significant gaps in understanding how it behaves.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and front-loaded with the core purpose in the first sentence. The additional domain and category information is brief and relevant. There is no wasted text, making it efficient for quick understanding, though it could be slightly more structured with bullet points or examples.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the lack of annotations and output schema, the description is incomplete. It does not explain what the tool returns (e.g., a list of Catalan numbers), any limitations (e.g., maximum n), or error conditions. For a tool with no structured support, the description should provide more context to ensure the agent can use it correctly.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 0% description coverage, so the description must compensate. It mentions 'n' as the parameter but does not explain its meaning beyond 'first n'. No details on constraints (e.g., n must be positive integer), default values, or examples are provided. The description adds minimal semantics, so it meets the baseline for a tool with one parameter but does not fully address the coverage gap.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Generate the first n Catalan numbers.' It specifies the verb ('Generate'), resource ('Catalan numbers'), and scope ('first n'), which is specific and unambiguous. However, it does not explicitly distinguish this tool from sibling tools like 'catalan' or 'catalan_number', which might serve similar functions, so it falls short of a perfect score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

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 the domain ('arithmetic') and category ('combinatorial_numbers'), but this is too generic to help an agent choose between this and sibling tools like 'catalan' or 'catalan_number'. There are no explicit instructions on prerequisites, constraints, or comparative use cases.

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

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