def Fin.clamp (n m : Nat) : Fin (m + 1)

min n m as an element of Fin (m + 1)

Equations

• Fin.clamp n m = ⟨min n m, ⋯⟩

@[deprecated Array.finRange (since := "2024-11-15")]

def Fin.enum (n : Nat) : Array (Fin n)

Alias of Array.finRange.

---

finRange n is the array of all elements of Fin n in order.

Equations

• Fin.enum = Array.finRange

@[deprecated List.finRange (since := "2024-11-15")]

def Fin.list (n : Nat) : List (Fin n)

Alias of List.finRange.

---

finRange n lists all elements of Fin n in order

Equations

• Fin.list = List.finRange

@[inline]

def Fin.dfoldrM {m : Type u_1 → Type u_2} [Monad m] (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.succ → m (α i.castSucc)) (init : α (last n)) : m (α 0)

Heterogeneous monadic fold over Fin n from right to left:

Fin.foldrM n f xₙ = do
  let xₙ₋₁ : α (n-1) ← f (n-1) xₙ
  let xₙ₋₂ : α (n-2) ← f (n-2) xₙ₋₁
  ...
  let x₀ : α 0 ← f 0 x₁
  pure x₀

This is the dependent version of Fin.foldrM.

Equations

• Fin.dfoldrM n α f init = Fin.dfoldrM.loop n α f n ⋯ init

@[specialize #[]]

def Fin.dfoldrM.loop {m : Type u_1 → Type u_2} [Monad m] (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.succ → m (α i.castSucc)) (i : Nat) (h : i < n + 1) (x : α ⟨i, h⟩) : m (α 0)

Inner loop for Fin.dfoldrM.

Fin.dfoldrM.loop n f i h xᵢ = do
  let xᵢ₋₁ ← f (i-1) xᵢ
  ...
  let x₁ ← f 1 x₂
  let x₀ ← f 0 x₁
  pure x₀

Equations

• Fin.dfoldrM.loop n α f i_2.succ h_2 x_2 = f ⟨i_2, ⋯⟩ x_2 >>= Fin.dfoldrM.loop n α f i_2 ⋯
• Fin.dfoldrM.loop n α f 0 h_2 x_2 = pure x_2

@[inline]

def Fin.dfoldr (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.succ → α i.castSucc) (init : α (last n)) : α 0

Heterogeneous fold over Fin n from the right: foldr 3 f x = f 0 (f 1 (f 2 x)), where f 2 : α 3 → α 2, f 1 : α 2 → α 1, etc.

This is the dependent version of Fin.foldr.

Equations

• Fin.dfoldr n α f init = Fin.dfoldrM n α f init

@[inline]

def Fin.dfoldlM {m : Type u_1 → Type u_2} [Monad m] (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.castSucc → m (α i.succ)) (init : α 0) : m (α (last n))

Heterogeneous monadic fold over Fin n from left to right:

Fin.foldlM n f x₀ = do
  let x₁ : α 1 ← f 0 x₀
  let x₂ : α 2 ← f 1 x₁
  ...
  let xₙ : α n ← f (n-1) xₙ₋₁
  pure xₙ

This is the dependent version of Fin.foldlM.

Equations

• Fin.dfoldlM n α f init = Fin.dfoldlM.loop n α f 0 ⋯ init

@[specialize #[]]

def Fin.dfoldlM.loop {m : Type u_1 → Type u_2} [Monad m] (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.castSucc → m (α i.succ)) (i : Nat) (h : i < n + 1) (x : α ⟨i, h⟩) : m (α (last n))

Inner loop for Fin.dfoldlM.

Fin.foldM.loop n α f i h xᵢ = do
let xᵢ₊₁ : α (i+1) ← f i xᵢ
...
let xₙ : α n ← f (n-1) xₙ₋₁
pure xₙ

Equations

• Fin.dfoldlM.loop n α f i h x = if h' : i < n then f ⟨i, h'⟩ x >>= Fin.dfoldlM.loop n α f (i + 1) ⋯ else cast ⋯ (pure x)

@[inline]

def Fin.dfoldl (n : Nat) (α : Fin (n + 1) → Type u_1) (f : (i : Fin n) → α i.castSucc → α i.succ) (init : α 0) : α (last n)

Heterogeneous fold over Fin n from the left: foldl 3 f x = f 0 (f 1 (f 2 x)), where f 0 : α 0 → α 1, f 1 : α 1 → α 2, etc.

This is the dependent version of Fin.foldl.

Equations

• Fin.dfoldl n α f init = Fin.dfoldlM n α f init