Loogle!

Result

Found 36 declarations mentioning Std.Iterators.Map.

• Std.Iterators.Map 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  (α : Type w) {β γ : Type w} (m : Type w → Type w') (n : Type w → Type w'') (lift : ⦃α : Type w⦄ → m α → n α) [Functor n] (f : β → Std.Iterators.PostconditionT n γ) : Type w
• Std.Iterators.instIteratorMap 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.Iterator (Std.Iterators.Map α m n lift f) n γ
• Std.Iterators.IterM.InternalCombinators.map 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] (lift : ⦃α : Type w⦄ → m α → n α) [Std.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.IterM n γ
• Std.Iterators.IterM.mapWithPostcondition 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [MonadLiftT m n] [Std.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.IterM n γ
• Std.Iterators.instFiniteMap 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.Finite α m] : Std.Iterators.Finite (Std.Iterators.Map α m n lift f) n
• Std.Iterators.instIteratorSizeMap 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.IteratorSize α m] : Std.Iterators.IteratorSize (Std.Iterators.Map α m n lift f) n
• Std.Iterators.instIteratorSizePartialMap 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.IteratorSizePartial α m] : Std.Iterators.IteratorSizePartial (Std.Iterators.Map α m n lift f) n
• Std.Iterators.Map.instIteratorLoop 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type x} [Monad n] [Monad o] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.IteratorLoop (Std.Iterators.Map α m n lift f) n o
• Std.Iterators.Map.instIteratorLoopPartial 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type x} [Monad n] [Monad o] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.IteratorLoopPartial (Std.Iterators.Map α m n lift f) n o
• Std.Iterators.Map.instProductive 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.Productive α m] : Std.Iterators.Productive (Std.Iterators.Map α m n lift f) n
• 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.Map.instIteratorCollectPartial 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type x} [Monad n] [Monad o] [Std.Iterators.Iterator α m β] {lift₁ : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.IteratorCollectPartial α m o] : Std.Iterators.IteratorCollectPartial (Std.Iterators.Map α m n lift₁ f) n o
• Std.Iterators.Map.instIteratorCollect 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type x} [Monad n] [Monad o] [Std.Iterators.Iterator α m β] {lift₁ : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} [Std.Iterators.IteratorCollect α m o] [Std.Iterators.Finite α m] : Std.Iterators.IteratorCollect (Std.Iterators.Map α m n lift₁ f) n o
• Std.Iterators.Iter.mapWithPostcondition 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {m : Type w → Type w'} [Monad m] (f : β → Std.Iterators.PostconditionT m γ) (it : Std.Iter β) : Std.IterM m γ
• Std.Iterators.Iter.map 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] (f : β → γ) (it : Std.Iter β) : Std.Iter γ
• Std.Iterators.Map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  (α : Type w) {β γ : Type w} (m : Type w → Type w') (n : Type w → Type w'') (lift : ⦃α : Type w⦄ → m α → n α) [Functor n] (f : β → Std.Iterators.PostconditionT n γ) : Std.Iterators.Map α m n lift f = Std.Iterators.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)
• Std.Iterators.IterM.mapWithPostcondition.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [MonadLiftT m n] [Std.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.Iterators.IterM.mapWithPostcondition f it = Std.Iterators.IterM.InternalCombinators.map (fun {x} => monadLift) f it
• 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.InternalCombinators.map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] (lift : ⦃α : Type w⦄ → m α → n α) [Std.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.Iterators.IterM.InternalCombinators.map lift f it = Std.Iterators.toIterM { inner := it } n γ
• Std.Iterators.instIteratorMap.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.instIteratorMap = inferInstanceAs (Std.Iterators.Iterator (Std.Iterators.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)) n γ)
• Std.Iterators.instLawfulIteratorCollectMapOfLawfulMonadOfLawfulMonadLiftFunction 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type x} [Monad m] [Monad n] [Monad o] [LawfulMonad n] [LawfulMonad o] [Std.Iterators.Iterator α m β] [Std.Iterators.Finite α m] [Std.Iterators.IteratorCollect α m o] [Std.Iterators.LawfulIteratorCollect α m o] {lift : ⦃δ : Type w⦄ → m δ → n δ} {f : β → Std.Iterators.PostconditionT n γ} [Std.Internal.LawfulMonadLiftFunction lift] : Std.Iterators.LawfulIteratorCollect (Std.Iterators.Map α m n lift f) n o
• 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) <$> it.toListRev
• Std.Iterators.IterM.toArray_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterators.Iterator α m β] [Std.Iterators.IteratorCollect α m m] [Std.Iterators.LawfulIteratorCollect α m m] [Std.Iterators.Finite α m] {f : β → γ} (it : Std.IterM m β) : (Std.Iterators.IterM.map f it).toArray = (fun x => Array.map f x) <$> 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.step_mapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterators.Iterator α m β] {it : Std.IterM m β} {γ : Type w} {f : β → Std.Iterators.PostconditionT n γ} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iterators.IterM.mapWithPostcondition f it).step = do let __do_lift ← liftM it.step match __do_lift with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.mapWithPostcondition f it') ↑out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.mapWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• 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 with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => let out' := f out; pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.map f it') out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.map f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.Iter.mapWithPostcondition_eq_toIter_mapWithPostcondition_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} [Monad m] {f : β → Std.Iterators.PostconditionT m γ} : Std.Iterators.Iter.mapWithPostcondition f it = Std.Iterators.IterM.mapWithPostcondition f it.toIterM
• 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.toListRev_map 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} [Std.Iterators.IteratorCollect α Id Id] [Std.Iterators.LawfulIteratorCollect α Id Id] [Std.Iterators.Finite α Id] {f : β → γ} : (Std.Iterators.Iter.map f it).toListRev = List.map f it.toListRev
• Std.Iterators.Iter.toArray_map 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} [Std.Iterators.IteratorCollect α Id Id] [Std.Iterators.LawfulIteratorCollect α Id Id] [Std.Iterators.Finite α Id] {f : β → γ} : (Std.Iterators.Iter.map f it).toArray = Array.map f it.toArray
• Std.Iterators.Iter.toList_map 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} [Std.Iterators.IteratorCollect α Id Id] [Std.Iterators.LawfulIteratorCollect α Id Id] [Std.Iterators.Finite α Id] {f : β → γ} : (Std.Iterators.Iter.map f it).toList = List.map f it.toList
• Std.Iterators.Iter.step_mapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} {n : Type w → Type w''} {f : β → Std.Iterators.PostconditionT n γ} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iterators.Iter.mapWithPostcondition f it).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.mapWithPostcondition f it') ↑out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.mapWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.Iter.step_map 📋 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).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.map f it') (f out) ⋯ | ⟨Std.Iterators.IterStep.skip it', h⟩ => Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.map f it') ⋯ | ⟨Std.Iterators.IterStep.done, h⟩ => Std.Iterators.PlausibleIterStep.done ⋯
• Std.Slice.Array.toList_internalIter 📋 Init.Data.Slice.Array.Lemmas
  {α : Type u} {s : Subarray α} : (Std.Slice.Internal.iter s).toList = List.map (fun i => s.array[↑i]) ({ lower := s.start, upper := s.stop }.toList.attachWith (fun x => x < s.array.size) ⋯)
• Std.Iterators.IterM.Equiv.mapWithPostcondition 📋 Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α₁ α₂ β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.Iterators.Iterator α₁ m β] [Std.Iterators.Iterator α₂ m β] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → Std.Iterators.PostconditionT n γ} {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : (Std.Iterators.IterM.mapWithPostcondition f ita).Equiv (Std.Iterators.IterM.mapWithPostcondition f itb)
• 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 ff04530 serving mathlib revision 8623f65