Vibecosystem loogle-search

Search Mathlib for lemmas by type signature pattern using Loogle.

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/loogle-search" ~/.claude/skills/vibeeval-vibecosystem-loogle-search && rm -rf "$T"

manifest: skills/loogle-search/SKILL.md

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-index

Integration with Proofs

When stuck in a Lean proof:

Identify what type shape you need
Query Loogle to find the lemma name
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 h