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lean_leanfinder

Read-onlyIdempotent

Search for theorems and mathematical concepts by describing their meaning or providing a proof state. Uses semantic understanding to find relevant results from the Lean library.

Instructions

Limit: 10req/30s. Semantic search by mathematical meaning via Lean Finder.

Examples: "commutativity of addition on natural numbers",
"I have h : n < m and need n + 1 < m + 1", proof state text.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
queryYesMathematical concept or proof state
num_resultsNoMax results

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
itemsNoList of Lean Finder results
Behavior4/5

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

Discloses a rate limit of 10 requests per 30 seconds, which is not provided by annotations. Annotations already indicate readOnly, openWorld, and idempotent behavior, and the description adds this practical constraint without contradiction.

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

Conciseness5/5

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

Two concise sentences plus examples. Every element is useful: rate limit, core semantic search purpose, and concrete query examples. No wasted words.

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

Completeness4/5

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

Despite multiple sibling tools and no output schema shown, the description covers rate limit, search behavior, and example queries. The presence of an output schema (not shown but indicated) means return format is handled externally. Minor gap: no explanation of what Lean Finder is or how results are ranked.

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?

Schema coverage is 100%, so baseline is 3. The description adds partial value with examples for the query parameter but does not elaborate on num_results beyond the schema's 'Max results'.

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 it performs semantic search by mathematical meaning via Lean Finder, which differentiates it from other search tools. However, it does not explicitly distinguish from siblings like lean_leansearch or lean_loogle.

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?

No guidance on when to use this tool versus the many similar sibling tools (e.g., lean_leansearch, lean_local_search). Examples are given but no conditional usage advice.

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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