Loogle searches Lean and Mathlib definitions and theorems.
You can use Loogle from witin the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the CLI version, the Loogle VS Code extension, the lean.nvim
integration or the Zulip bot.
Loogle finds definitions and lemmas in various ways:
-
By constant:
🔍Real.sin
finds all lemmas whose statement somehow mentions the sine function. -
By lemma name substring:
🔍"differ"
finds all lemmas that have"differ"
somewhere in their lemma name. -
By subexpression:
🔍_ * (_ ^ _)
finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.The pattern can also be non-linear, as in
🔍Real.sqrt ?a * Real.sqrt ?a
If the pattern has parameters, they are matched in any order. Both of these will find
List.map
:
🔍 [(?a -> ?b) -> List ?a -> List ?b
](?q=(?a -> ?b) -> List ?a -> List ?b)
🔍 [List ?a -> (?a -> ?b) -> List ?b
](?q=List ?a -> (?a -> ?b) -> List ?b) -
By main conclusion:
🔍 [|- tsum _ = _ * tsum _
](?q=|- tsum _ = _ * tsum _)
finds all lemmas where the conclusion (the subexpression to the right of all→
and∀
) has the given shape.As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
🔍 [|- _ < _ → tsum _ < tsum _
](?q=|- _ < _ → tsum _ < tsum _)
will findtsum_lt_tsum
even though the hypothesisf i < g i
is not the last.
If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them.
The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
woould find all lemmas which mention the constants Real.sin
and tsum
, have "two"
as a
substring of the lemma name, include a product and a power somewhere in the type, and have a
hypothesis of the form _ < _
(if there were any such lemmas). Metavariables (?a
) are assigned independently in each filter.
The #lucky
button will directly send you to the documentation of the first hit.
You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.