Documentation

Init.Data.Array.OfFn

Theorems about Array.ofFn #

ofFn #

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@[simp]
theorem Array.ofFn_zero {α : Type u_1} {f : Fin 0 → α} :
ofFn f = #[]
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theorem Array.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 Array.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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@[simp]
theorem List.toArray_ofFn {n : Nat} {α : Type u_1} {f : Fin n → α} :
(ofFn f).toArray = Array.ofFn f
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@[simp]
theorem Array.toList_ofFn {n : Nat} {α : Type u_1} {f : Fin n → α} :
(ofFn f).toList = List.ofFn f
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theorem Array.ofFn_succ' {n : Nat} {α : Type u_1} {f : Fin (n + 1) → α} :
ofFn f = #[f 0] ++ ofFn fun (i : Fin n) => f i.succ
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@[simp]
theorem Array.ofFn_eq_empty_iff {n : Nat} {α : Type u_1} {f : Fin n → α} :
ofFn f = #[] ↔ n = 0
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@[simp]
theorem Array.mem_ofFn {α : Type u_1} {n : Nat} {f : Fin n → α} {a : α} :
a ∈ ofFn f ↔ ∃ (i : Fin n), f i = a

ofFnM #

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

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

Equations
    Instances For
      source
      @[simp]
      theorem Array.ofFnM_zero {m : Type u_1 → Type u_2} {α : Type u_1} [Monad m] {f : Fin 0 → m α} :
      ofFnM f = pure #[]
      source
      theorem Array.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 (#[a] ++ as)
      source
      theorem Array.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)
      source
      theorem Array.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)
      source
      @[simp]
      theorem Array.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
      source
      @[simp]
      theorem Array.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)
      source
      theorem Array.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)
      source
      @[simp]
      theorem Array.idRun_ofFnM {n : Nat} {α : Type u_1} {f : Fin n → Id α} :
      (ofFnM f).run = ofFn fun (i : Fin n) => (f i).run