ackermann

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

No annotations are provided, so the description carries the full burden. 'Compute the Ackermann function' says nothing about cost, recursion depth, or the practical explosion of values even at m=3-4, which is the single most important behavioral trait of this function. The schema's 'max 4' constraint is left unexplained rather than justified by compute cost.

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?

A single front-loaded sentence with no waste. It is efficient, though its brevity reflects under-specification rather than disciplined conciseness.

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 pure-compute tool with no annotations and no output schema, the description should at minimum warn about the computational blowup and what the return value looks like. Neither is present, so an agent could plausibly call it with values that stall or return astronomically large integers without warning.

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?

Schema description coverage is 100%: m is documented as a non-negative integer with max 4, and n as a non-negative integer. The description adds no meaning beyond the schema, so baseline 3 applies.

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?

Names a specific verb ('Compute') and a specific well-known mathematical function with its canonical notation A(m, n). No sibling is confusable (ack_handoff is an unrelated dispatch concept), but the description does nothing to distinguish scope or differentiate from other math compute tools like is_even or fibonacci_sequence beyond the name itself.

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?

There is no guidance on when to use this tool versus alternatives, no prerequisites, and no caution about the function's extreme growth rate. The agent must infer everything from the name alone.

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