lean_leansearch

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

Adds rate limit information beyond annotations (readOnlyHint, idempotentHint, openWorldHint). No contradictions. However, does not describe response behavior or error conditions.

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?

Very concise, front-loaded with rate limit, then purpose, then examples. Every sentence adds value with no redundancy.

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 simple search tool with output schema, the description covers purpose, parameters, examples, and rate limit. No gaps given the context.

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%. Description provides example queries for the 'query' parameter, adding practical meaning. No additional detail for 'num_results' but schema is clear.

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?

Explicitly states it searches Mathlib via leansearch.net using natural language. Provides concrete examples distinguishing it from sibling search tools like lean_loogle or lean_local_search.

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?

Mentions rate limit (90req/30s) but does not clarify when to use this tool vs alternatives like lean_leanfinder or lean_loogle. No explicit exclusions or selection criteria.

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