Lean LSP MCP

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

The description adds valuable behavioral context beyond annotations: it discloses a rate limit ('Limit: 3req/30s'), which is not covered by the annotations (readOnlyHint, openWorldHint, idempotentHint). This helps the agent understand operational constraints. No contradiction with annotations exists, as the description aligns with the read-only, open-world nature implied by searching.

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 highly concise and well-structured: it front-loads key information (rate limit and purpose), uses bullet-like examples for clarity, and avoids redundant sentences. Every sentence adds value, such as the rate limit warning and query examples, making it efficient for agent comprehension.

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 the tool's complexity (search with rate limits), rich annotations (readOnlyHint, openWorldHint, idempotentHint), and the presence of an output schema, the description is mostly complete. It covers purpose, usage, and behavioral constraints like rate limits. However, it could briefly mention the output format or error handling to enhance completeness, though the output schema mitigates this gap.

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%, so the schema fully documents the parameters (query and num_results). The description adds minimal semantic value beyond the schema, such as implying query types through examples (natural language or Lean terms), but does not elaborate on parameter interactions or advanced usage. This meets the baseline for high schema coverage.

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: 'Search Mathlib via leansearch.net using natural language.' It specifies the verb ('Search'), resource ('Mathlib'), and method ('via leansearch.net using natural language'), distinguishing it from siblings like lean_local_search or lean_loogle by emphasizing natural language queries.

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 clear context for when to use this tool: for searching Mathlib with natural language queries. It includes examples like 'sum of two even numbers is even' to illustrate appropriate queries. However, it does not explicitly state when not to use it or name alternatives among the many sibling tools, such as lean_loogle for different search methods.

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