Loogle!

Result

Found 28 declarations mentioning Std.Iterators.IterM.map.

• Std.Iterators.IterM.map 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Monad m] (f : β → γ) (it : Std.IterM m β) : Std.IterM m γ
• Std.Iterators.IterM.map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Monad m] (f : β → γ) (it : Std.IterM m β) : Std.Iterators.IterM.map f it = Std.Iterators.IterM.mapWithPostcondition (fun b => pure (f b)) it
• Std.Iterators.IterM.toListRev_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] [Std.Iterators.Finite α m] {f : β → γ} (it : Std.IterM m β) : (Std.Iterators.IterM.map f it).toListRev = (fun x => List.map f x) <$> it.toListRev
• Std.Iterators.IterM.count_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Monad m] [Std.Iterators.IteratorLoop α m m] [Std.Iterators.Finite α m] [LawfulMonad m] [Std.Iterators.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} : (Std.Iterators.IterM.map f it).count = it.count
• Std.Iterators.IterM.all_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.Iterators.IteratorLoop α m m] [LawfulMonad m] [Std.Iterators.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → Bool} : Std.Iterators.IterM.all p (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.all (fun x => p (f x)) it
• Std.Iterators.IterM.any_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.Iterators.IteratorLoop α m m] [LawfulMonad m] [Std.Iterators.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → Bool} : Std.Iterators.IterM.any p (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.any (fun x => p (f x)) it
• Std.Iterators.IterM.allM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.Iterators.IteratorLoop α m m] [LawfulMonad m] [Std.Iterators.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → m (ULift.{w, 0} Bool)} : Std.Iterators.IterM.allM p (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.allM (fun x => p (f x)) it
• Std.Iterators.IterM.anyM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.Iterators.IteratorLoop α m m] [LawfulMonad m] [Std.Iterators.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → m (ULift.{w, 0} Bool)} : Std.Iterators.IterM.anyM p (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.anyM (fun x => p (f x)) it
• Std.Iterators.IterM.fold_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Std.Iterators.IteratorLoop α m m] [Std.Iterators.LawfulIteratorLoop α m m] {f : β → γ} {g : δ → γ → δ} {init : δ} {it : Std.IterM m β} : Std.Iterators.IterM.fold g init (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.fold (fun d b => g d (f b)) init it
• Std.Iterators.IterM.toArray_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] [Std.Iterators.Finite α m] {f : β → γ} (it : Std.IterM m β) : (Std.Iterators.IterM.map f it).toArray = (fun x => Array.map f x) <$> it.toArray
• Std.Iterators.IterM.toList_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] [Std.Iterators.Finite α m] {f : β → β'} (it : Std.IterM m β) : (Std.Iterators.IterM.map f it).toList = (fun x => List.map f x) <$> it.toList
• Std.Iterators.IterM.foldM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Monad n] [LawfulMonad m] [LawfulMonad n] [Std.Iterators.IteratorLoop α m m] [Std.Iterators.IteratorLoop α m n] [Std.Iterators.LawfulIteratorLoop α m m] [Std.Iterators.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → γ} {g : δ → γ → n δ} {init : δ} {it : Std.IterM m β} : Std.Iterators.IterM.foldM g init (Std.Iterators.IterM.map f it) = Std.Iterators.IterM.foldM (fun d b => g d (f b)) init it
• Std.Iterators.IterM.toListRev_map_eq_toListRev_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toListRev = (Std.Iterators.IterM.mapM (fun b => pure (f b)) it).toListRev
• Std.Iterators.IterM.toListRev_map_eq_toListRev_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toListRev = (Std.Iterators.IterM.filterMapM (fun b => pure (some (f b))) it).toListRev
• Std.Iterators.IterM.toArray_map_eq_toArray_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toArray = (Std.Iterators.IterM.mapM (fun b => pure (f b)) it).toArray
• Std.Iterators.IterM.toList_map_eq_toList_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toList = (Std.Iterators.IterM.mapM (fun b => pure (f b)) it).toList
• Std.Iterators.IterM.toArray_map_eq_toArray_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toArray = (Std.Iterators.IterM.filterMapM (fun b => pure (some (f b))) it).toArray
• Std.Iterators.IterM.toList_map_eq_toList_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {it : Std.IterM m β} : (Std.Iterators.IterM.map f it).toList = (Std.Iterators.IterM.filterMapM (fun b => pure (some (f b))) it).toList
• Std.Iterators.IterM.toListRev_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.Iterators.IterM.mapM g (Std.Iterators.IterM.map f it)).toListRev = (Std.Iterators.IterM.mapM (fun b => g (f b)) it).toListRev
• Std.Iterators.IterM.toListRev_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.Iterators.IterM.filterMapM g (Std.Iterators.IterM.map f it)).toListRev = (Std.Iterators.IterM.filterMapM (fun b => g (f b)) it).toListRev
• Std.Iterators.IterM.toList_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.Iterators.IterM.filterMapM g (Std.Iterators.IterM.map f it)).toList = (Std.Iterators.IterM.filterMapM (fun b => g (f b)) it).toList
• Std.Iterators.IterM.toArray_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.Iterators.IterM.filterMapM g (Std.Iterators.IterM.map f it)).toArray = (Std.Iterators.IterM.filterMapM (fun b => g (f b)) it).toArray
• Std.Iterators.IterM.toArray_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m n] [Std.Iterators.LawfulIteratorCollect α m n] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.Iterators.IterM.mapM g (Std.Iterators.IterM.map f it)).toArray = (Std.Iterators.IterM.mapM (fun b => g (f b)) it).toArray
• Std.Iterators.IterM.toList_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m n] [Std.Iterators.LawfulIteratorCollect α m n] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.Iterators.IterM.mapM g (Std.Iterators.IterM.map f it)).toList = (Std.Iterators.IterM.mapM (fun b => g (f b)) it).toList
• Std.Iterators.IterM.step_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] {it : Std.IterM m β} [Monad m] [LawfulMonad m] {f : β → β'} : (Std.Iterators.IterM.map f it).step = do let __do_lift ← it.step match __do_lift.inflate with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => let out' := f out; pure (Std.Shrink.deflate (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.map f it') out' ⋯)) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.map f it') ⋯)) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.Iterators.PlausibleIterStep.done ⋯))
• Std.Iterators.Iter.map_eq_toIter_map_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {f : β → γ} : Std.Iterators.Iter.map f it = (Std.Iterators.IterM.map f it.toIterM).toIter
• Std.Iterators.Iter.map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.FlatMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] (f : β → γ) (it : Std.Iter β) : Std.Iterators.Iter.map f it = (Std.Iterators.IterM.map f it.toIterM).toIter
• Std.Iterators.IterM.Equiv.map 📋 Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α₁ α₂ β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α₁ m β] [Std.Iterators.Iterator α₂ m β] {f : β → γ} {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : (Std.Iterators.IterM.map f ita).Equiv (Std.Iterators.IterM.map f itb)

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 6ff4759 serving mathlib revision edaf32c