Loogle!

Result

Found 7 declarations mentioning Array.mapM.map.

• Array.mapM.map 📋 Init.Data.Array.Basic
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) (i : ℕ) (bs : Array β) : m (Array β)
• Array.mapM.map.eq_def 📋 Init.Data.Array.Basic
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) (i : ℕ) (bs : Array β) : Array.mapM.map f as i bs = if hlt : i < as.size then do let __do_lift ← f as[i] Array.mapM.map f as (i + 1) (bs.push __do_lift) else pure bs
• Array.mapM.eq_1 📋 Init.Data.Array.Lemmas
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) : Array.mapM f as = Array.mapM.map f as 0 (Array.emptyWithCapacity as.size)
• Array.mapM_map_eq_foldl 📋 Init.Data.Array.Lemmas
  {α : Type u_1} {β : Type u_2} {b : Array β} {as : Array α} {f : α → β} {i : ℕ} : Array.mapM.map f as i b = Array.foldl (fun acc a => acc.push (f a)) b as i
• Array.mapM_eq_foldlM.aux 📋 Init.Data.Array.Lemmas
  {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} [Monad m] [LawfulMonad m] {f : α → m β} {xs : Array α} (i : ℕ) (bs : Array β) : Array.mapM.map f xs i bs = List.foldlM (fun bs a => bs.push <$> f a) bs (List.drop i xs.toList)
• Array.mapM.map.eq_1 📋 Init.Data.Array.Lemmas
  {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) (i : ℕ) (bs : Array β) : Array.mapM.map f as i bs = if hlt : i < as.size then do let __do_lift ← f as[i] Array.mapM.map f as (i + 1) (bs.push __do_lift) else pure bs
• Vector.toArray_mapM_go 📋 Init.Data.Vector.Lemmas
  {m : Type u_1 → Type u_2} {α : Type u_3} {β : Type u_1} {n : ℕ} [Monad m] [LawfulMonad m] {f : α → m β} {xs : Vector α n} {i : ℕ} (h : i ≤ n) {acc : Vector β i} : Vector.toArray <$> Vector.mapM.go f xs i h acc = Array.mapM.map f xs.toArray i acc.toArray

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, _ * _, _ ^ _, |- _ < _ → _
would 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 19971e9 serving mathlib revision bce1d65