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lean_leanfinder

Read-onlyIdempotent

Search Lean mathematical statements by semantic meaning using natural language queries or proof state text, with selectable mathlib versions.

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.

The `version` argument selects which mathlib snapshot to query
(v4.19.0, v4.24.0, or v4.28.0). Default: v4.28.0.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`query`	Yes	Mathematical concept or proof state
`version`	No	Mathlib version index to search	v4.28.0
`num_results`	No	Max results

Output Schema

TableJSON Schema

Name	Required	Description	Default
`items`	No	List of Lean Finder results

Schema Changelog

Changes observed during successful MCP inspections.

Changed11 schema fields changedv0.28.0Jul 11, 2026

addedInput schema / properties / version

Added value: +{
+  "default": "v4.28.0",
+  "description": "Mathlib version index to search",
+  "enum": [
+    "v4.19.0",
+    "v4.24.0",
+    "v4.28.0"
+  ],
+  "title": "Version",
+  "type": "string"
+}

addedOutput schema / $defs / LeanFinderResult / properties / formal_name

Added value: +{
+  "description": "Fully qualified Lean declaration name",
+  "title": "Formal Name",
+  "type": "string"
+}

removedOutput schema / $defs / LeanFinderResult / properties / formal_statement

Removed value: -{
-  "description": "Lean type signature",
-  "title": "Formal Statement",
-  "type": "string"
-}

removedOutput schema / $defs / LeanFinderResult / properties / full_name

Removed value: -{
-  "description": "Full qualified name",
-  "title": "Full Name",
-  "type": "string"
-}

addedOutput schema / $defs / LeanFinderResult / properties / informal_description

Added value: +{
+  "description": "Natural-language description of the statement",
+  "title": "Informal Description",
+  "type": "string"
+}

addedOutput schema / $defs / LeanFinderResult / properties / informal_name

Added value: +{
+  "description": "Short natural-language name for the statement",
+  "title": "Informal Name",
+  "type": "string"
+}

removedOutput schema / $defs / LeanFinderResult / properties / informal_statement

Removed value: -{
-  "description": "Natural language description",
-  "title": "Informal Statement",
-  "type": "string"
-}

addedOutput schema / $defs / LeanFinderResult / properties / kind

Added value: +{
+  "description": "Declaration kind (theorem, def, instance, etc.)",
+  "title": "Kind",
+  "type": "string"
+}

addedOutput schema / $defs / LeanFinderResult / properties / path

Added value: +{
+  "description": "Mathlib module path, dot-separated (e.g. Mathlib.Data.Nat.Basic)",
+  "title": "Path",
+  "type": "string"
+}

addedOutput schema / $defs / LeanFinderResult / properties / type

Added value: +{
+  "description": "Lean type signature / formal statement",
+  "title": "Type",
+  "type": "string"
+}

changedOutput schema / $defs / LeanFinderResult / required

Previous value: -[
-  "full_name",
-  "formal_statement",
-  "informal_statement"
-]New value: +[
+  "formal_name",
+  "informal_name",
+  "kind",
+  "type",
+  "informal_description",
+  "path"
+]

Addedv0.10.0May 1, 2026
Removedv0.23.1May 1, 2026
First observedJan 26, 2026

TDQS

A3.9/5.0

Behavior4/5

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

Beyond annotations (readOnly, openWorld, idempotent), description adds rate limit, version behavior (default and options), and that it performs semantic search. No contradictions.

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?

Extremely concise: two short paragraphs with rate limit, purpose, examples, and parameter explanation. No wasted sentences, information is front-loaded.

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

Completeness5/5

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

Given the tool's simplicity, description covers purpose, usage constraints, parameter details, and examples. Output schema exists, so return values are covered. No gaps for an agent to select or invoke this tool.

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 minimal extra needed. Description adds example queries for the 'query' parameter and explains version options, but adds no new semantic info for 'num_results'. Baseline 3 is appropriate.

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?

Description clearly states 'semantic search by mathematical meaning via Lean Finder' with examples. Purpose is specific and distinguishable from siblings, but does not explicitly differentiate from similar tools like lean_leansearch or lean_state_search.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Provides rate limit (10req/30s) and examples of queries, implying usage for semantic search. However, no explicit guidance on when to use this tool versus alternatives among the many sibling tools.

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