prove

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

With no annotations, the description bears full responsibility for behavioral disclosure. It explains the logical process (proving by showing negation unsatisfiable) and mentions Z3. However, it does not specify side effects, authorization requirements, or what happens on success/failure. The absence of output schema exacerbates the gap, as return value behavior is unclear.

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 concise: three sentences and an example. It front-loads the purpose, then explains the method, and ends with a concrete example. Every sentence is purposeful with no redundant information.

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 no output schema, the description should clarify what the tool returns. It only states the logical condition for proof ('If negation is unsatisfiable, the theorem is proven'), but does not specify the output format (e.g., boolean, proof object, or error). It also lacks information on error handling, timeout outcomes, or how variables are used. This is incomplete for an agent to properly invoke the tool.

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 coverage is 100%, so each parameter has a description in the schema. The tool description adds minimal value: it explains that the theorem is a Z3 expression and provides an example, but does not elaborate on the 'variables' parameter format or the timeout behavior beyond what is in the schema. The example omits variables, so no extra clarity is given for nested objects.

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: 'Attempt to prove a theorem by showing its negation is unsatisfiable.' It specifies the resource (a theorem) and the method (Z3 expression). The example reinforces usage, and it distinguishes itself from siblings like 'check_sat' (satisfiability check) and 'solve' (model finding).

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 explains when to use the tool (to prove a theorem) but does not explicitly state when not to use it or compare with alternatives. There is no guidance on when to choose this over siblings like 'check_sat' or 'solve', leaving the agent to infer context. The example is helpful but lacks exclusion criteria.

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