Loogle Search
- 465 installs
- 3.9k repo stars
- Updated January 26, 2026
- parcadei/continuous-claude-v3
loogle-search is a Claude Code skill that runs Mathlib type-signature pattern searches for developers who know lemma shapes but not Mathlib lemma names.
About
loogle-search is a Mathlib search skill from parcadei/continuous-claude-v3 that finds Lean lemmas by type signature pattern instead of by name. Developers run loogle-search with quoted patterns such as "Nontrivial _ ↔ _" or function-type shapes like "(?a → ?b) → List ?a → List ?b", optionally passing --json for structured output. A companion loogle-server command keeps the index in memory for faster repeat queries during proof sessions. Reach for loogle-search when doing type-directed proof search, exploring lemmas available for a type, or pairing unknown type shapes with existing Mathlib entries.
- Enables agents to run precise Google-style searches with domain and time filters
- Returns clean, citation-ready results directly into the agent context
- Reduces hallucinated references by grounding answers in live web results
- Works across any coding, research, or planning workflow
- 429 developers have installed this skill
Loogle Search by the numbers
- 465 all-time installs (skills.sh)
- +2 installs in the week ending Aug 4, 2026 (Skillselion tracking)
- Ranked #1,858 of 16,546 AI & Agent Building skills by installs in the Skillselion catalog
- Data as of Aug 5, 2026 (Skillselion catalog sync)
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| Installs | 465 |
|---|---|
| repo stars | ★ 3.9k |
| Last updated | January 26, 2026 |
| Repository | parcadei/continuous-claude-v3 ↗ |
How do you find Mathlib lemmas by type signature?
Give their Claude or Cursor agent the ability to perform accurate, scoped web and documentation searches during development.
Who is it for?
Lean or Mathlib developers who know the type shape they need but not the exact lemma identifier and want CLI-driven discovery inside an agent session.
Skip if: JavaScript or Python projects with no Lean/Mathlib codebase, or developers who already know exact lemma names and only need import statements.
When should I use this skill?
A developer or agent is proving a Lean theorem and needs lemmas matching a known type pattern or connector like Nontrivial ↔.
What you get
Matching Mathlib lemma names, JSON search results, and optionally a warmed loogle-server index for faster repeat queries
- Lemma name matches
- JSON search payloads
Files
Loogle Search - Mathlib Type Signature Search
Search Mathlib for lemmas by type signature pattern.
When to Use
- Finding a lemma when you know the type shape but not the name
- Discovering what's available for a type (e.g., all
Nontrivial ↔ _lemmas) - Type-directed proof search
Commands
# Search by pattern (uses server if running, else direct)
loogle-search "Nontrivial _ ↔ _"
loogle-search "(?a → ?b) → List ?a → List ?b"
loogle-search "IsCyclic, center"
# JSON output
loogle-search "List.map" --json
# Start server for fast queries (keeps index in memory)
loogle-server &Query Syntax
| Pattern | Meaning |
|---|---|
_ | Any single type |
?a, ?b | Type variables (same variable = same type) |
Foo, Bar | Must mention both Foo and Bar |
Foo.bar | Exact name match |
Examples
# Find lemmas relating Nontrivial and cardinality
loogle-search "Nontrivial _ ↔ _ < Fintype.card _"
# Find map-like functions
loogle-search "(?a → ?b) → List ?a → List ?b"
# → List.map, List.pmap, ...
# Find everything about cyclic groups and center
loogle-search "IsCyclic, center"
# → commutative_of_cyclic_center_quotient, ...
# Find Fintype.card lemmas
loogle-search "Fintype.card"Performance
- With server running: ~100-200ms per query
- Cold start (no server): ~10s per query (loads 343MB index)
Setup
Loogle must be built first:
cd ~/tools/loogle && lake build
lake build LoogleMathlibCache # or use --write-indexIntegration with Proofs
When stuck in a Lean proof: 1. Identify what type shape you need 2. Query Loogle to find the lemma name 3. Apply the lemma in your proof
-- Goal: Nontrivial G from 1 < Fintype.card G
-- Query: loogle-search "Nontrivial _ ↔ 1 < Fintype.card _"
-- Found: Fintype.one_lt_card_iff_nontrivial
exact Fintype.one_lt_card_iff_nontrivial.mpr hRelated skills
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Pick loogle-search over generic web search when the goal is Mathlib lemma discovery by type signature rather than documentation pages or package READMEs.
FAQ
How do you search Mathlib with loogle-search?
loogle-search accepts quoted type patterns on the command line, for example loogle-search "Nontrivial _ ↔ _", uses a running loogle-server when available, and falls back to direct queries otherwise, with --json for machine-readable results.
When should agents invoke loogle-search?
Agents should invoke loogle-search when a Lean proof needs a lemma matching a known type shape, such as function types or bi-implications, but the Mathlib name is unknown during type-directed proof search.