Documentation

Init.Data.Vector.OfFn

Theorems about Vector.ofFn #

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@[simp]
theorem Vector.getElem_ofFn {i : Nat} {α : Type u_1} {n : Nat} {f : Fin n → α} (h : i < n) :
(ofFn f)[i] = f ⟨i, h⟩
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@[simp]
theorem Vector.getElem?_ofFn {i : Nat} {α : Type u_1} {n : Nat} {f : Fin n → α} :
(ofFn f)[i]? = if h : i < n then some (f ⟨i, h⟩) else none
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@[simp]
theorem Vector.mem_ofFn {α : Type u_1} {n : Nat} {f : Fin n → α} {a : α} :
a ∈ ofFn f ↔ ∃ (i : Fin n), f i = a
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@[simp]
theorem Vector.map_ofFn {n : Nat} {α : Type u_1} {β : Type u_2} {f : Fin n → α} {g : α → β} :
map g (ofFn f) = ofFn (g ∘ f)
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theorem Vector.back_ofFn {α : Type u_1} {n : Nat} [NeZero n] {f : Fin n → α} :
(ofFn f).back = f ⟨n - 1, ⋯⟩
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theorem Vector.ofFn_succ {n : Nat} {α : Type u_1} {f : Fin (n + 1) → α} :
ofFn f = (ofFn fun (i : Fin n) => f i.castSucc).push (f ⟨n, ⋯⟩)
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theorem Vector.ofFn_add {α : Type u_1} {n m : Nat} {f : Fin (n + m) → α} :
ofFn f = (ofFn fun (i : Fin n) => f (Fin.castLE ⋯ i)) ++ ofFn fun (i : Fin m) => f (Fin.natAdd n i)
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theorem Vector.ofFn_succ' {n : Nat} {α : Type u_1} {f : Fin (n + 1) → α} :
ofFn f = Vector.cast ⋯ (#v[f 0] ++ ofFn fun (i : Fin n) => f i.succ)
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@[simp]
theorem Vector.ofFn_getElem {α : Type u_1} {n : Nat} {xs : Vector α n} :
(ofFn fun (i : Fin n) => xs[↑i]) = xs

ofFnM #

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def Vector.ofFnM {m : Type u_1 → Type u_2} {α : Type u_1} {n : Nat} [Monad m] (f : Fin n → m α) :
m (Vector α n)

Construct (in a monadic context) a vector by applying a monadic function to each index.

Instances For
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    @[simp]
    theorem Vector.ofFnM_zero {m : Type u_1 → Type u_2} {α : Type u_1} [Monad m] {f : Fin 0 → m α} :
    ofFnM f = pure #v[]
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    theorem Vector.ofFnM_succ {m : Type u_1 → Type u_2} {α : Type u_1} {n : Nat} [Monad m] [LawfulMonad m] {f : Fin (n + 1) → m α} :
    ofFnM f = do let as ← ofFnM fun (i : Fin n) => f i.castSucc let a ← f (Fin.last n) pure (as.push a)
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    theorem Vector.ofFnM_add {k : Nat} {α : Type u_1} {n : Nat} {m : Type u_1 → Type u_2} [Monad m] [LawfulMonad m] {f : Fin (n + k) → m α} :
    ofFnM f = do let as ← ofFnM fun (i : Fin n) => f (Fin.castLE ⋯ i) let bs ← ofFnM fun (i : Fin k) => f (Fin.natAdd n i) pure (as ++ bs)
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    @[simp]
    theorem Vector.toArray_ofFnM {m : Type u_1 → Type u_2} {n : Nat} {α : Type u_1} [Monad m] [LawfulMonad m] {f : Fin n → m α} :
    toArray <$> ofFnM f = Array.ofFnM f
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    @[simp]
    theorem Vector.toList_ofFnM {m : Type u_1 → Type u_2} {n : Nat} {α : Type u_1} [Monad m] [LawfulMonad m] {f : Fin n → m α} :
    toList <$> ofFnM f = List.ofFnM f
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    theorem Vector.ofFnM_succ' {m : Type u_1 → Type u_2} {α : Type u_1} {n : Nat} [Monad m] [LawfulMonad m] {f : Fin (n + 1) → m α} :
    ofFnM f = do let a ← f 0 let as ← ofFnM fun (i : Fin n) => f i.succ pure (Vector.cast ⋯ (#v[a] ++ as))
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    @[simp]
    theorem Vector.ofFnM_pure_comp {m : Type u_1 → Type u_2} {α : Type u_1} [Monad m] [LawfulMonad m] {n : Nat} {f : Fin n → α} :
    ofFnM (pure ∘ f) = pure (ofFn f)
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    theorem Vector.ofFnM_pure {m : Type u_1 → Type u_2} {α : Type u_1} [Monad m] [LawfulMonad m] {n : Nat} {f : Fin n → α} :
    (ofFnM fun (i : Fin n) => pure (f i)) = pure (ofFn f)
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    @[simp]
    theorem Vector.idRun_ofFnM {n : Nat} {α : Type u_1} {f : Fin n → Id α} :
    (ofFnM f).run = ofFn fun (i : Fin n) => (f i).run