Moogle 
Moogle is a semantic search engine for mathlib4, helping Lean users find relevant theorems, definitions, and formal mathematics results.
Starting price Free
Tool Information
Moogle is a semantic search engine for mathlib4, helping Lean users find relevant theorems, definitions, and formal mathematics results.
Users enter a mathematical concept, inspect matched declarations and source locations, verify types and assumptions in mathlib, and test proofs in the appropriate Lean environment.
The public search service is free and no paid plan was verified.
Semantic search can return irrelevant or outdated declarations and does not prove a result automatically. Source inspection, version compatibility, formal checking, and mathematical understanding remain necessary.
F.A.Q (3)
Pros and Cons
Pros
- Moogle provides semantic search over the Lean mathlib4 library
- Queries can be written in ordinary mathematical language
- Semantic matching helps when the exact theorem name is not known
- The engine can connect informal wording with formal library terminology
- Search results expose candidate declarations for use in Lean proofs
- It reduces time spent manually browsing a very large theorem collection
- The focused scope avoids unrelated general-web search results
- Moogle is useful to students learning mathlib naming conventions
- Experienced formalizers can use it to rediscover forgotten lemmas
- A Lean 4 VS Code command can launch Moogle searches from the editor
- The service complements exact-name and type-pattern search tools
- Natural-language queries allow exploration before a proof statement is fully formalized
- It can suggest related theorems even when a query uses synonyms
- The web interface requires no local model installation
- The underlying mathlib collection is open source and community maintained
- Each candidate can be checked against formal types in Lean rather than trusted blindly
Cons
- Moogle searches only mathlib4 rather than arbitrary mathematical literature
- It finds theorems but does not construct or verify a complete proof for the user
- Semantic ranking may place the most relevant declaration below weaker matches
- Ambiguous natural-language questions can retrieve unrelated results
- A useful theorem can be missed even when it exists in the library
- Community documentation describes Moogle as somewhat outdated beside newer search tools
- An index can lag behind rapid changes in mathlib
- Users must verify that a result exists in their installed mathlib version
- Suggested declarations may require imports not present in the current Lean file
- Understanding theorem types still requires familiarity with Lean syntax
- The public homepage contains very little usage documentation
- No public service-level commitment is displayed
- A stable public API is not documented on the main site
- Technical details of the ranking system have not been fully published
- Feedback-based ranking can favor common queries over niche formalizations
- LeanSearch; Loogle; documentation search; or local grep may work better for some queries
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Overview
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