Loogle!

Result

Found 10556 definitions mentioning List. Of these, 16 match your pattern(s).

• List.modifyHead 📋 Init.Data.List.Basic
  {α : Type u} (f : α → α) : List α → List α
• List.map 📋 Init.Data.List.Basic
  {α : Type u} {β : Type v} (f : α → β) : List α → List β
• List.mapTR 📋 Init.Data.List.Basic
  {α : Type u} {β : Type v} (f : α → β) (as : List α) : List β
• List.modify 📋 Init.Data.List.Basic
  {α : Type u} (f : α → α) : ℕ → List α → List α
• List.mapTR.loop 📋 Init.Data.List.Basic
  {α : Type u} {β : Type v} (f : α → β) : List α → List β → List β
• List.map_eq_mapTR 📋 Init.Data.List.Basic
  : @List.map = @List.mapTR
• List.mapMono 📋 Init.Data.List.BasicAux
  {α : Type u_1} (as : List α) (f : α → α) : List α
• List.modifyTR 📋 Init.Data.List.Impl
  {α : Type u_1} (f : α → α) (n : ℕ) (l : List α) : List α
• List.modifyTR.go 📋 Init.Data.List.Impl
  {α : Type u_1} (f : α → α) : List α → ℕ → Array α → List α
• List.modify_eq_modifyTR 📋 Init.Data.List.Impl
  : @List.modify = @List.modifyTR
• List.modifyLast 📋 Batteries.Data.List.Basic
  {α : Type u_1} (f : α → α) (l : List α) : List α
• List.modifyNth 📋 Batteries.Data.List.Basic
  {α : Type u} (f : α → α) : ℕ → List α → List α
• List.modifyLast.go 📋 Batteries.Data.List.Basic
  {α : Type u_1} (f : α → α) : List α → Array α → List α
• Lean.SCC.scc 📋 Lean.Util.SCC
  {α : Type} [BEq α] [Hashable α] (vertices : List α) (successorsOf : α → List α) : List (List α)
• List.iterateTR.loop 📋 Mathlib.Data.List.Defs
  {α : Type u_1} (f : α → α) (a : α) (n : ℕ) (l : List α) : List α
• List.mapAsyncChunked 📋 Mathlib.Data.List.Defs
  {α : Type u_7} {β : Type u_8} (f : α → β) (xs : List α) (chunk_size : ℕ := 1024) : List β

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. 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
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- 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 _
   will find tsum_lt_tsum even though the hypothesis f 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.

Source code

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.

This is Loogle revision 4e1aab0 serving mathlib revision 79ca167