Array literal syntax

def «term#[_,]» : Lean.ParserDescr

Syntax for Array α.

Conventions for notations in identifiers:

• The recommended spelling of #[] in identifiers is empty.

• The recommended spelling of #[x] in identifiers is singleton.

Preliminary theorems

@[simp]

theorem Array.size_set {α : Type u} {xs : Array α} {i : Nat} {v : α} (h : i < xs.size) : (xs.set i v h).size = xs.size

@[simp]

theorem Array.size_push {α : Type u} {xs : Array α} (v : α) : (xs.push v).size = xs.size + 1

theorem Array.ext {α : Type u} {xs ys : Array α} (h₁ : xs.size = ys.size) (h₂ : ∀ (i : Nat) (hi₁ : i < xs.size) (hi₂ : i < ys.size), xs[i] = ys[i]) : xs = ys

theorem Array.ext.extAux {α : Type u} (as bs : List α) (h₁ : as.length = bs.length) (h₂ : ∀ (i : Nat) (hi₁ : i < as.length) (hi₂ : i < bs.length), as[i] = bs[i]) : as = bs

theorem Array.ext' {α : Type u} {xs ys : Array α} (h : xs.toList = ys.toList) : xs = ys

@[simp]

theorem Array.toArrayAux_eq {α : Type u} {as : List α} {acc : Array α} : (as.toArrayAux acc).toList = acc.toList ++ as

@[simp]

theorem Array.toArray_toList {α : Type u} {xs : Array α} : xs.toList.toArray = xs

@[simp]

theorem Array.getElem_toList {α : Type u} {xs : Array α} {i : Nat} (h : i < xs.size) : xs.toList[i] = xs[i]

@[simp]

theorem Array.getElem?_toList {α : Type u} {xs : Array α} {i : Nat} : xs.toList[i]? = xs[i]?

structure Array.Mem {α : Type u} (as : Array α) (a : α) : Prop

a ∈ as is a predicate which asserts that a is in the array as.

• val : a ∈ as.toList

instance Array.instMembership {α : Type u} : Membership α (Array α)

theorem Array.mem_def {α : Type u} {a : α} {as : Array α} : a ∈ as ↔ a ∈ as.toList

@[simp]

theorem Array.mem_toArray {α : Type u} {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l

@[simp]

theorem Array.getElem_mem {α : Type u} {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i] ∈ xs

@[simp]

theorem Array.emptyWithCapacity_eq {α : Type u_1} {n : Nat} : emptyWithCapacity n = #[]

@[simp]

theorem Array.mkEmpty_eq {α : Type u_1} {n : Nat} : mkEmpty n = #[]

@[reducible, inline, deprecated Array.toArray_toList (since := "2025-02-17")]

abbrev List.toArray_toList {α : Type u_1} {xs : Array α} : xs.toList.toArray = xs

theorem List.toList_toArray {α : Type u} {as : List α} : as.toArray.toList = as

@[reducible, inline, deprecated List.toList_toArray (since := "2025-02-17")]

abbrev Array.toList_toArray {α : Type u_1} {as : List α} : as.toArray.toList = as

@[simp]

theorem List.size_toArray {α : Type u} {as : List α} : as.toArray.size = as.length

@[reducible, inline, deprecated List.size_toArray (since := "2025-02-17")]

abbrev Array.size_toArray {α : Type u_1} {as : List α} : as.toArray.size = as.length

@[simp]

theorem List.getElem_toArray {α : Type u} {xs : List α} {i : Nat} (h : i < xs.toArray.size) : xs.toArray[i] = xs[i]

@[simp]

theorem List.getElem?_toArray {α : Type u} {xs : List α} {i : Nat} : xs.toArray[i]? = xs[i]?

@[simp]

theorem List.getElem!_toArray {α : Type u} [Inhabited α] {xs : List α} {i : Nat} : xs.toArray[i]! = xs[i]!

theorem Array.size_eq_length_toList {α : Type u} {xs : Array α} : xs.size = xs.toList.length

Externs

@[extern lean_array_size]

def Array.usize {α : Type u} (a : Array α) : USize

Returns the size of the array as a platform-native unsigned integer.

This is a low-level version of Array.size that directly queries the runtime system's representation of arrays. While this is not provable, Array.usize always returns the exact size of the array since the implementation only supports arrays of size less than USize.size.

@[extern lean_array_uget]

def Array.uget {α : Type u} (a : Array α) (i : USize) (h : i.toNat < a.size) : α

Low-level indexing operator which is as fast as a C array read.

This avoids overhead due to unboxing a Nat used as an index.

@[extern lean_array_uset]

def Array.uset {α : Type u} (xs : Array α) (i : USize) (v : α) (h : i.toNat < xs.size) : Array α

Low-level modification operator which is as fast as a C array write. The modification is performed in-place when the reference to the array is unique.

This avoids overhead due to unboxing a Nat used as an index.

@[extern lean_array_pop]

def Array.pop {α : Type u} (xs : Array α) : Array α

Removes the last element of an array. If the array is empty, then it is returned unmodified. The modification is performed in-place when the reference to the array is unique.

Examples:

• #[1, 2, 3].pop = #[1, 2]
• #["orange", "yellow"].pop = #["orange"]
• (#[] : Array String).pop = #[]

@[simp]

theorem Array.size_pop {α : Type u} {xs : Array α} : xs.pop.size = xs.size - 1

@[extern lean_mk_array]

def Array.replicate {α : Type u} (n : Nat) (v : α) : Array α

Creates an array that contains n repetitions of v.

The corresponding List function is List.replicate.

Examples:

• Array.replicate 2 true = #[true, true]
• Array.replicate 3 () = #[(), (), ()]
• Array.replicate 0 "anything" = #[]

@[extern lean_mk_array, deprecated Array.replicate (since := "2025-03-18")]

def Array.mkArray {α : Type u} (n : Nat) (v : α) : Array α

Creates an array that contains n repetitions of v.

The corresponding List function is List.replicate.

Examples:

• Array.mkArray 2 true = #[true, true]
• Array.mkArray 3 () = #[(), (), ()]
• Array.mkArray 0 "anything" = #[]

@[extern lean_array_fswap]

def Array.swap {α : Type u} (xs : Array α) (i j : Nat) (hi : i < xs.size := by get_elem_tactic) (hj : j < xs.size := by get_elem_tactic) : Array α

Swaps two elements of an array. The modification is performed in-place when the reference to the array is unique.

Examples:

• #["red", "green", "blue", "brown"].swap 0 3 = #["brown", "green", "blue", "red"]
• #["red", "green", "blue", "brown"].swap 0 2 = #["blue", "green", "red", "brown"]
• #["red", "green", "blue", "brown"].swap 1 2 = #["red", "blue", "green", "brown"]
• #["red", "green", "blue", "brown"].swap 3 0 = #["brown", "green", "blue", "red"]

@[simp]

theorem Array.size_swap {α : Type u} {xs : Array α} {i j : Nat} {hi : i < xs.size} {hj : j < xs.size} : (xs.swap i j hi hj).size = xs.size

@[extern lean_array_swap]

def Array.swapIfInBounds {α : Type u} (xs : Array α) (i j : Nat) : Array α

Swaps two elements of an array, returning the array unchanged if either index is out of bounds. The modification is performed in-place when the reference to the array is unique.

Examples:

• #["red", "green", "blue", "brown"].swapIfInBounds 0 3 = #["brown", "green", "blue", "red"]
• #["red", "green", "blue", "brown"].swapIfInBounds 0 2 = #["blue", "green", "red", "brown"]
• #["red", "green", "blue", "brown"].swapIfInBounds 1 2 = #["red", "blue", "green", "brown"]
• #["red", "green", "blue", "brown"].swapIfInBounds 0 4 = #["red", "green", "blue", "brown"]
• #["red", "green", "blue", "brown"].swapIfInBounds 9 2 = #["red", "green", "blue", "brown"]

GetElem instance for USize, backed by uget

instance Array.instGetElemUSizeLtNatToNatSize {α : Type u} : GetElem (Array α) USize α fun (xs : Array α) (i : USize) => i.toNat < xs.size

Definitions

instance Array.instEmptyCollection {α : Type u} : EmptyCollection (Array α)

instance Array.instInhabited {α : Type u} : Inhabited (Array α)

def Array.isEmpty {α : Type u} (xs : Array α) : Bool

Checks whether an array is empty.

An array is empty if its size is 0.

Examples:

• (#[] : Array String).isEmpty = true
• #[1, 2].isEmpty = false
• #[()].isEmpty = false

@[specialize #[]]

def Array.isEqvAux {α : Type u} (xs ys : Array α) (hsz : xs.size = ys.size) (p : α → α → Bool) (i : Nat) : i ≤ xs.size → Bool

@[inline]

def Array.isEqv {α : Type u} (xs ys : Array α) (p : α → α → Bool) : Bool

Returns true if as and bs have the same length and they are pairwise related by eqv.

Short-circuits at the first non-related pair of elements.

Examples:

• #[1, 2, 3].isEqv #[2, 3, 4] (· < ·) = true
• #[1, 2, 3].isEqv #[2, 2, 4] (· < ·) = false
• #[1, 2, 3].isEqv #[2, 3] (· < ·) = false

instance Array.instBEq {α : Type u} [BEq α] : BEq (Array α)

def Array.ofFn {α : Type u} {n : Nat} (f : Fin n → α) : Array α

Creates an array by applying f to each potential index in order, starting at 0.

Examples:

• Array.ofFn (n := 3) toString = #["0", "1", "2"]
• Array.ofFn (fun i => #["red", "green", "blue"].get i.val i.isLt) = #["red", "green", "blue"]

def Array.ofFn.go {α : Type u} {n : Nat} (f : Fin n → α) (acc : Array α) (i : Nat) : i ≤ n → Array α

Auxiliary for ofFn. ofFn.go f acc i h = acc ++ #[f (n - i), ..., f(n - 1)]

def Array.range (n : Nat) : Array Nat

Constructs an array that contains all the numbers from 0 to n, exclusive.

Examples:

• Array.range 5 := #[0, 1, 2, 3, 4]
• Array.range 0 := #[]
• Array.range 1 := #[0]

def Array.range' (start size : Nat) (step : Nat := 1) : Array Nat

Constructs an array of numbers of size size, starting at start and increasing by step at each element.

In other words, Array.range' start size step is #[start, start+step, ..., start+(len-1)*step].

Examples:

• Array.range' 0 3 (step := 1) = #[0, 1, 2]
• Array.range' 0 3 (step := 2) = #[0, 2, 4]
• Array.range' 0 4 (step := 2) = #[0, 2, 4, 6]
• Array.range' 3 4 (step := 2) = #[3, 5, 7, 9]

@[inline]

def Array.singleton {α : Type u} (v : α) : Array α

Constructs a single-element array that contains v.

Examples:

• Array.singleton 5 = #[5]
• Array.singleton "one" = #["one"]

def Array.back! {α : Type u} [Inhabited α] (xs : Array α) : α

Returns the last element of an array, or panics if the array is empty.

Safer alternatives include Array.back, which requires a proof the array is non-empty, and Array.back?, which returns an Option.

def Array.back {α : Type u} (xs : Array α) (h : 0 < xs.size := by get_elem_tactic) : α

Returns the last element of an array, given a proof that the array is not empty.

See Array.back! for the version that panics if the array is empty, or Array.back? for the version that returns an option.

def Array.back? {α : Type u} (xs : Array α) : Option α

Returns the last element of an array, or none if the array is empty.

See Array.back! for the version that panics if the array is empty, or Array.back for the version that requires a proof the array is non-empty.

@[deprecated "Use `a[i]?` instead." (since := "2025-02-12")]

def Array.get? {α : Type u} (xs : Array α) (i : Nat) : Option α

@[inline]

def Array.swapAt {α : Type u} (xs : Array α) (i : Nat) (v : α) (hi : i < xs.size := by get_elem_tactic) : α × Array α

Swaps a new element with the element at the given index.

Returns the value formerly found at i, paired with an array in which the value at i has been replaced with v.

Examples:

• #["spinach", "broccoli", "carrot"].swapAt 1 "pepper" = ("broccoli", #["spinach", "pepper", "carrot"])
• #["spinach", "broccoli", "carrot"].swapAt 2 "pepper" = ("carrot", #["spinach", "broccoli", "pepper"])

@[inline]

def Array.swapAt! {α : Type u} (xs : Array α) (i : Nat) (v : α) : α × Array α

Swaps a new element with the element at the given index. Panics if the index is out of bounds.

Returns the value formerly found at i, paired with an array in which the value at i has been replaced with v.

Examples:

• #["spinach", "broccoli", "carrot"].swapAt! 1 "pepper" = (#["spinach", "pepper", "carrot"], "broccoli")
• #["spinach", "broccoli", "carrot"].swapAt! 2 "pepper" = (#["spinach", "broccoli", "pepper"], "carrot")

def Array.shrink {α : Type u} (xs : Array α) (n : Nat) : Array α

Returns the first n elements of an array. The resulting array is produced by repeatedly calling Array.pop. If n is greater than the size of the array, it is returned unmodified.

If the reference to the array is unique, then this function uses in-place modification.

Examples:

• #[0, 1, 2, 3, 4].shrink 2 = #[0, 1]
• #[0, 1, 2, 3, 4].shrink 0 = #[]
• #[0, 1, 2, 3, 4].shrink 10 = #[0, 1, 2, 3, 4]

def Array.shrink.loop {α : Type u} : Nat → Array α → Array α

@[reducible, inline]

abbrev Array.take {α : Type u} (xs : Array α) (i : Nat) : Array α

Returns a new array that contains the first i elements of xs. If xs has fewer than i elements, the new array contains all the elements of xs.

The returned array is always a new array, even if it contains the same elements as the input array.

Examples:

• #["red", "green", "blue"].take 1 = #["red"]
• #["red", "green", "blue"].take 2 = #["red", "green"]
• #["red", "green", "blue"].take 5 = #["red", "green", "blue"]

@[simp]

theorem Array.take_eq_extract {α : Type u} {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i

@[reducible, inline]

abbrev Array.drop {α : Type u} (xs : Array α) (i : Nat) : Array α

Removes the first i elements of xs. If xs has fewer than i elements, the new array is empty.

The returned array is always a new array, even if it contains the same elements as the input array.

Examples:

• #["red", "green", "blue"].drop 1 = #["green", "blue"]
• #["red", "green", "blue"].drop 2 = #["blue"]
• #["red", "green", "blue"].drop 5 = #[]

@[simp]

theorem Array.drop_eq_extract {α : Type u} {xs : Array α} {i : Nat} : xs.drop i = xs.extract i

@[inline]

unsafe def Array.modifyMUnsafe {α : Type u} {m : Type u → Type u_1} [Monad m] (xs : Array α) (i : Nat) (f : α → m α) : m (Array α)

@[implemented_by Array.modifyMUnsafe]

def Array.modifyM {α : Type u} {m : Type u → Type u_1} [Monad m] (xs : Array α) (i : Nat) (f : α → m α) : m (Array α)

Replaces the element at the given index, if it exists, with the result of applying the monadic function f to it. If the index is invalid, the array is returned unmodified and f is not called.

Examples:

#eval #[1, 2, 3, 4].modifyM 2 fun x => do
  IO.println s!"It was {x}"
  return x * 10

It was 3

#[1, 2, 30, 4]

#eval #[1, 2, 3, 4].modifyM 6 fun x => do
  IO.println s!"It was {x}"
  return x * 10

#[1, 2, 3, 4]

@[inline]

def Array.modify {α : Type u} (xs : Array α) (i : Nat) (f : α → α) : Array α

Replaces the element at the given index, if it exists, with the result of applying f to it. If the index is invalid, the array is returned unmodified.

Examples:

• #[1, 2, 3].modify 0 (· * 10) = #[10, 2, 3]
• #[1, 2, 3].modify 2 (· * 10) = #[1, 2, 30]
• #[1, 2, 3].modify 3 (· * 10) = #[1, 2, 3]

@[inline]

def Array.modifyOp {α : Type u} (xs : Array α) (idx : Nat) (f : α → α) : Array α

Replaces the element at the given index, if it exists, with the result of applying f to it. If the index is invalid, the array is returned unmodified.

Examples:

• #[1, 2, 3].modifyOp 0 (· * 10) = #[10, 2, 3]
• #[1, 2, 3].modifyOp 2 (· * 10) = #[1, 2, 30]
• #[1, 2, 3].modifyOp 3 (· * 10) = #[1, 2, 3]

@[inline]

unsafe def Array.forIn'Unsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β

We claim this unsafe implementation is correct because an array cannot have more than usizeSz elements in our runtime.

This kind of low level trick can be removed with a little bit of compiler support. For example, if the compiler simplifies as.size < usizeSz to true.

@[specialize #[]]

unsafe def Array.forIn'Unsafe.loop {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (a : α) → a ∈ as → β → m (ForInStep β)) (sz i : USize) (b : β) : m β

@[implemented_by Array.forIn'Unsafe]

def Array.forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (b : β) (f : (a : α) → a ∈ as → β → m (ForInStep β)) : m β

Reference implementation for forIn'

def Array.forIn'.loop {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (a : α) → a ∈ as → β → m (ForInStep β)) (i : Nat) (h : i ≤ as.size) (b : β) : m β

instance Array.instForIn'InferInstanceMembership {α : Type u} {m : Type u_1 → Type u_2} : ForIn' m (Array α) α inferInstance

@[simp]

theorem Array.forIn'_eq_forIn' {α : Type u} {m : Type u_1 → Type u_2} {β : Type u_1} [Monad m] : Array.forIn' = forIn'

@[inline]

unsafe def Array.foldlMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m β

See comment at forIn'Unsafe

@[specialize #[]]

unsafe def Array.foldlMUnsafe.fold {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (as : Array α) (i stop : USize) (b : β) : m β

@[implemented_by Array.foldlMUnsafe]

def Array.foldlM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m β

Folds a monadic function over a list from the left, accumulating a value starting with init. The accumulated value is combined with the each element of the list in order, using f.

The optional parameters start and stop control the region of the array to be folded. Folding proceeds from start (inclusive) to stop (exclusive), so no folding occurs unless start < stop. By default, the entire array is folded.

Examples:

example [Monad m] (f : α → β → m α) :
    Array.foldlM (m := m) f x₀ #[a, b, c] = (do
      let x₁ ← f x₀ a
      let x₂ ← f x₁ b
      let x₃ ← f x₂ c
      pure x₃)
  := by rfl

example [Monad m] (f : α → β → m α) :
    Array.foldlM (m := m) f x₀ #[a, b, c] (start := 1) = (do
      let x₁ ← f x₀ b
      let x₂ ← f x₁ c
      pure x₂)
  := by rfl

def Array.foldlM.loop {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (as : Array α) (stop : Nat) (h : stop ≤ as.size) (i j : Nat) (b : β) : m β

@[inline]

unsafe def Array.foldrMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Array α) (start : Nat := as.size) (stop : Nat := 0) : m β

See comment at forIn'Unsafe

@[specialize #[]]

unsafe def Array.foldrMUnsafe.fold {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (as : Array α) (i stop : USize) (b : β) : m β

@[implemented_by Array.foldrMUnsafe]

def Array.foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Array α) (start : Nat := as.size) (stop : Nat := 0) : m β

Folds a monadic function over an array from the right, accumulating a value starting with init. The accumulated value is combined with the each element of the list in reverse order, using f.

The optional parameters start and stop control the region of the array to be folded. Folding proceeds from start (exclusive) to stop (inclusive), so no folding occurs unless start > stop. By default, the entire array is folded.

Examples:

example [Monad m] (f : α → β → m β) :
  Array.foldrM (m := m) f x₀ #[a, b, c] = (do
    let x₁ ← f c x₀
    let x₂ ← f b x₁
    let x₃ ← f a x₂
    pure x₃)
  := by rfl

example [Monad m] (f : α → β → m β) :
  Array.foldrM (m := m) f x₀ #[a, b, c] (start := 2) = (do
    let x₁ ← f b x₀
    let x₂ ← f a x₁
    pure x₂)
  := by rfl

def Array.foldrM.fold {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (as : Array α) (stop : Nat := 0) (i : Nat) (h : i ≤ as.size) (b : β) : m β

@[inline]

unsafe def Array.mapMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) : m (Array β)

See comment at forIn'Unsafe

@[specialize #[]]

unsafe def Array.mapMUnsafe.map {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (sz i : USize) (bs : Array NonScalar) : m (Array PNonScalar)

@[implemented_by Array.mapMUnsafe]

def Array.mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) : m (Array β)

Applies the monadic action f to every element in the array, left-to-right, and returns the array of results.

def Array.mapM.map {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m β) (as : Array α) (i : Nat) (bs : Array β) : m (Array β)

@[inline]

def Array.mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (i : Nat) → α → i < as.size → m β) : m (Array β)

Applies the monadic action f to every element in the array, along with the element's index and a proof that the index is in bounds, from left to right. Returns the array of results.

@[specialize #[]]

def Array.mapFinIdxM.map {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : (i : Nat) → α → i < as.size → m β) (i j : Nat) (inv : i + j = as.size) (bs : Array β) : m (Array β)

@[inline]

def Array.mapIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : Nat → α → m β) (as : Array α) : m (Array β)

Applies the monadic action f to every element in the array, along with the element's index, from left to right. Returns the array of results.

@[inline]

def Array.firstM {β : Type v} {α : Type u} {m : Type v → Type w} [Alternative m] (f : α → m β) (as : Array α) : m β

Maps f over the array and collects the results with <|>. The result for the end of the array is failure.

Examples:

• #[[], [1, 2], [], [2]].firstM List.head? = some 1
• #[[], [], []].firstM List.head? = none
• #[].firstM List.head? = none

@[irreducible]

def Array.firstM.go {β : Type v} {α : Type u} {m : Type v → Type w} [Alternative m] (f : α → m β) (as : Array α) (i : Nat) : m β

@[inline]

def Array.findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β)

Returns the first non-none result of applying the monadic function f to each element of the array, in order. Returns none if f returns none for all elements.

Example:

#eval #[7, 6, 5, 8, 1, 2, 6].findSomeM? fun i => do
  if i < 5 then
    return some (i * 10)
  if i ≤ 6 then
    IO.println s!"Almost! {i}"
  return none

Almost! 6
Almost! 5

some 10

@[inline]

def Array.findM? {m : Type → Type u_1} {α : Type} [Monad m] (p : α → m Bool) (as : Array α) : m (Option α)

Returns the first element of the array for which the monadic predicate p returns true, or none if no such element is found. Elements of the array are checked in order.

The monad m is restricted to Type → Type to avoid needing to use ULift Bool in p's type.

Example:

#eval #[7, 6, 5, 8, 1, 2, 6].findM? fun i => do
  if i < 5 then
    return true
  if i ≤ 6 then
    IO.println s!"Almost! {i}"
  return false

Almost! 6
Almost! 5

some 1

@[inline]

def Array.findIdxM? {α : Type u} {m : Type → Type u_1} [Monad m] (p : α → m Bool) (as : Array α) : m (Option Nat)

Finds the index of the first element of an array for which the monadic predicate p returns true. Elements are examined in order from left to right, and the search is terminated when an element that satisfies p is found. If no such element exists in the array, then none is returned.

@[inline]

unsafe def Array.anyMUnsafe {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m Bool

@[specialize #[]]

unsafe def Array.anyMUnsafe.any {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (i stop : USize) : m Bool

@[implemented_by Array.anyMUnsafe]

def Array.anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m Bool

Returns true if the monadic predicate p returns true for any element of as.

Short-circuits upon encountering the first true. The elements in as are examined in order from left to right.

The optional parameters start and stop control the region of the array to be checked. Only the elements with indices from start (inclusive) to stop (exclusive) are checked. By default, the entire array is checked.

def Array.anyM.loop {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (stop : Nat) (h : stop ≤ as.size) (j : Nat) : m Bool

@[inline]

def Array.allM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m Bool

Returns true if the monadic predicate p returns true for every element of as.

Short-circuits upon encountering the first false. The elements in as are examined in order from left to right.

The optional parameters start and stop control the region of the array to be checked. Only the elements with indices from start (inclusive) to stop (exclusive) are checked. By default, the entire array is checked.

@[inline]

def Array.findSomeRevM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β)

Returns the first non-none result of applying the monadic function f to each element of the array in reverse order, from right to left. Once a non-none result is found, no further elements are checked. Returns none if f returns none for all elements of the array.

Examples:

#eval #[1, 2, 0, -4, 1].findSomeRevM? (m := Except String) fun x => do
  if x = 0 then throw "Zero!"
  else if x < 0 then return (some x)
  else return none

Except.ok (some (-4))

#eval #[1, 2, 0, 4, 1].findSomeRevM? (m := Except String) fun x => do
  if x = 0 then throw "Zero!"
  else if x < 0 then return (some x)
  else return none

Except.error "Zero!"

@[specialize #[]]

def Array.findSomeRevM?.find {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) (i : Nat) : i ≤ as.size → m (Option β)

@[inline]

def Array.findRevM? {α : Type} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Array α) : m (Option α)

Returns the last element of the array for which the monadic predicate p returns true, or none if no such element is found. Elements of the array are checked in reverse, from right to left..

The monad m is restricted to Type → Type to avoid needing to use ULift Bool in p's type.

Example:

#eval #[7, 5, 8, 1, 2, 6, 5, 8].findRevM? fun i => do
  if i < 5 then
    return true
  if i ≤ 6 then
    IO.println s!"Almost! {i}"
  return false

Almost! 5
Almost! 6

some 2

@[inline]

def Array.forM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m PUnit

Applies the monadic action f to each element of an array, in order.

The optional parameters start and stop control the region of the array to which f should be applied. Iteration proceeds from start (inclusive) to stop (exclusive), so f is not invoked unless start < stop. By default, the entire array is used.

instance Array.instForM {α : Type u} {m : Type u_1 → Type u_2} : ForM m (Array α) α

@[simp]

theorem Array.forM_eq_forM {α : Type u} {m : Type u_1 → Type u_2} {as : Array α} [Monad m] {f : α → m PUnit} : Array.forM f as = forM as f

@[inline]

def Array.forRevM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Array α) (start : Nat := as.size) (stop : Nat := 0) : m PUnit

Applies the monadic action f to each element of an array from right to left, in reverse order.

The optional parameters start and stop control the region of the array to which f should be applied. Iteration proceeds from start (exclusive) to stop (inclusive), so no f is not invoked unless start > stop. By default, the entire array is used.

@[inline]

def Array.foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : β

Folds a function over an array from the left, accumulating a value starting with init. The accumulated value is combined with the each element of the array in order, using f.

The optional parameters start and stop control the region of the array to be folded. Folding proceeds from start (inclusive) to stop (exclusive), so no folding occurs unless start < stop. By default, the entire array is used.

Examples:

• #[a, b, c].foldl f z = f (f (f z a) b) c
• #[1, 2, 3].foldl (· ++ toString ·) "" = "123"
• #[1, 2, 3].foldl (s!"({·} {·})") "" = "((( 1) 2) 3)"

@[inline]

def Array.foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : Array α) (start : Nat := as.size) (stop : Nat := 0) : β

Folds a function over an array from the right, accumulating a value starting with init. The accumulated value is combined with the each element of the array in reverse order, using f.

The optional parameters start and stop control the region of the array to be folded. Folding proceeds from start (exclusive) to stop (inclusive), so no folding occurs unless start > stop. By default, the entire array is used.

Examples:

• #[a, b, c].foldr f init = f a (f b (f c init))
• #[1, 2, 3].foldr (toString · ++ ·) "" = "123"
• #[1, 2, 3].foldr (s!"({·} {·})") "!" = "(1 (2 (3 !)))"

@[inline]

def Array.sum {α : Type u_1} [Add α] [Zero α] : Array α → α

Computes the sum of the elements of an array.

Examples:

• #[a, b, c].sum = a + (b + (c + 0))
• #[1, 2, 5].sum = 8

@[inline]

def Array.countP {α : Type u} (p : α → Bool) (as : Array α) : Nat

Counts the number of elements in the array as that satisfy the Boolean predicate p.

Examples:

• #[1, 2, 3, 4, 5].countP (· % 2 == 0) = 2
• #[1, 2, 3, 4, 5].countP (· < 5) = 4
• #[1, 2, 3, 4, 5].countP (· > 5) = 0

@[inline]

def Array.count {α : Type u} [BEq α] (a : α) (as : Array α) : Nat

Counts the number of times an element occurs in an array.

Examples:

• #[1, 1, 2, 3, 5].count 1 = 2
• #[1, 1, 2, 3, 5].count 5 = 1
• #[1, 1, 2, 3, 5].count 4 = 0

@[inline]

def Array.map {α : Type u} {β : Type v} (f : α → β) (as : Array α) : Array β

Applies a function to each element of the array, returning the resulting array of values.

Examples:

• #[a, b, c].map f = #[f a, f b, f c]
• #[].map Nat.succ = #[]
• #["one", "two", "three"].map (·.length) = #[3, 3, 5]
• #["one", "two", "three"].map (·.reverse) = #["eno", "owt", "eerht"]

instance Array.instFunctor : Functor Array

@[inline]

def Array.mapFinIdx {α : Type u} {β : Type v} (as : Array α) (f : (i : Nat) → α → i < as.size → β) : Array β

Applies a function to each element of the array along with the index at which that element is found, returning the array of results. In addition to the index, the function is also provided with a proof that the index is valid.

Array.mapIdx is a variant that does not provide the function with evidence that the index is valid.

@[inline]

def Array.mapIdx {α : Type u} {β : Type v} (f : Nat → α → β) (as : Array α) : Array β

Applies a function to each element of the array along with the index at which that element is found, returning the array of results.

Array.mapFinIdx is a variant that additionally provides the function with a proof that the index is valid.

def Array.zipIdx {α : Type u} (xs : Array α) (start : Nat := 0) : Array (α × Nat)

Pairs each element of an array with its index, optionally starting from an index other than 0.

Examples:

• #[a, b, c].zipIdx = #[(a, 0), (b, 1), (c, 2)]
• #[a, b, c].zipIdx 5 = #[(a, 5), (b, 6), (c, 7)]

@[reducible, inline, deprecated Array.zipIdx (since := "2025-01-21")]

abbrev Array.zipWithIndex {α : Type u_1} (xs : Array α) (start : Nat := 0) : Array (α × Nat)

@[inline]

def Array.find? {α : Type u} (p : α → Bool) (as : Array α) : Option α

Returns the first element of the array for which the predicate p returns true, or none if no such element is found.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].find? (· < 5) = some 1
• #[7, 6, 5, 8, 1, 2, 6].find? (· < 1) = none

@[inline]

def Array.findSome? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β

Returns the first non-none result of applying the function f to each element of the array, in order. Returns none if f returns none for all elements.

Example:

#eval #[7, 6, 5, 8, 1, 2, 6].findSome? fun i =>
  if i < 5 then
    some (i * 10)
  else
    none

some 10

@[inline]

def Array.findSome! {α : Type u} {β : Type v} [Inhabited β] (f : α → Option β) (xs : Array α) : β

Returns the first non-none result of applying the function f to each element of the array, in order. Panics if f returns none for all elements.

Example:

#eval #[7, 6, 5, 8, 1, 2, 6].findSome? fun i =>
  if i < 5 then
    some (i * 10)
  else
    none

some 10

@[inline]

def Array.findSomeRev? {α : Type u} {β : Type v} (f : α → Option β) (as : Array α) : Option β

Returns the first non-none result of applying f to each element of the array in reverse order, from right to left. Returns none if f returns none for all elements of the array.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].findSome? (fun x => if x < 5 then some (10 * x) else none) = some 10
• #[7, 6, 5, 8, 1, 2, 6].findSome? (fun x => if x < 1 then some (10 * x) else none) = none

@[inline]

def Array.findRev? {α : Type} (p : α → Bool) (as : Array α) : Option α

Returns the last element of the array for which the predicate p returns true, or none if no such element is found.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].findRev? (· < 5) = some 2
• #[7, 6, 5, 8, 1, 2, 6].findRev? (· < 1) = none

@[inline]

def Array.findIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option Nat

Returns the index of the first element for which p returns true, or none if there is no such element.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].findIdx (· < 5) = some 4
• #[7, 6, 5, 8, 1, 2, 6].findIdx (· < 1) = none

def Array.findIdx?.loop {α : Type u} (p : α → Bool) (as : Array α) (j : Nat) : Option Nat

@[inline]

def Array.findFinIdx? {α : Type u} (p : α → Bool) (as : Array α) : Option (Fin as.size)

Returns the index of the first element for which p returns true, or none if there is no such element. The index is returned as a Fin, which guarantees that it is in bounds.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].findFinIdx? (· < 5) = some (4 : Fin 7)
• #[7, 6, 5, 8, 1, 2, 6].findFinIdx? (· < 1) = none

def Array.findFinIdx?.loop {α : Type u} (p : α → Bool) (as : Array α) (j : Nat) : Option (Fin as.size)

@[irreducible]

theorem Array.findIdx?_loop_eq_map_findFinIdx?_loop_val {α : Type u} {xs : Array α} {p : α → Bool} {j : Nat} : findIdx?.loop p xs j = Option.map (fun (x : Fin xs.size) => ↑x) (findFinIdx?.loop p xs j)

theorem Array.findIdx?_eq_map_findFinIdx?_val {α : Type u} {xs : Array α} {p : α → Bool} : findIdx? p xs = Option.map (fun (x : Fin xs.size) => ↑x) (findFinIdx? p xs)

@[inline]

def Array.findIdx {α : Type u} (p : α → Bool) (as : Array α) : Nat

Returns the index of the first element for which p returns true, or the size of the array if there is no such element.

Examples:

• #[7, 6, 5, 8, 1, 2, 6].findIdx (· < 5) = 4
• #[7, 6, 5, 8, 1, 2, 6].findIdx (· < 1) = 7

def Array.idxOfAux {α : Type u} [BEq α] (xs : Array α) (v : α) (i : Nat) : Option (Fin xs.size)

@[reducible, inline, deprecated Array.idxOfAux (since := "2025-01-29")]

abbrev Array.indexOfAux {α : Type u_1} [BEq α] (xs : Array α) (v : α) (i : Nat) : Option (Fin xs.size)

def Array.finIdxOf? {α : Type u} [BEq α] (xs : Array α) (v : α) : Option (Fin xs.size)

Returns the index of the first element equal to a, or the size of the array if no element is equal to a. The index is returned as a Fin, which guarantees that it is in bounds.

Examples:

• #["carrot", "potato", "broccoli"].finIdxOf? "carrot" = some 0
• #["carrot", "potato", "broccoli"].finIdxOf? "broccoli" = some 2
• #["carrot", "potato", "broccoli"].finIdxOf? "tomato" = none
• #["carrot", "potato", "broccoli"].finIdxOf? "anything else" = none

@[reducible, inline, deprecated "`Array.indexOf?` has been deprecated, use `idxOf?` or `finIdxOf?` instead." (since := "2025-01-29")]

abbrev Array.indexOf? {α : Type u_1} [BEq α] (xs : Array α) (v : α) : Option (Fin xs.size)

def Array.idxOf {α : Type u} [BEq α] (a : α) : Array α → Nat

Returns the index of the first element equal to a, or the size of the array if no element is equal to a.

Examples:

• #["carrot", "potato", "broccoli"].idxOf "carrot" = 0
• #["carrot", "potato", "broccoli"].idxOf "broccoli" = 2
• #["carrot", "potato", "broccoli"].idxOf "tomato" = 3
• #["carrot", "potato", "broccoli"].idxOf "anything else" = 3

def Array.idxOf? {α : Type u} [BEq α] (xs : Array α) (v : α) : Option Nat

Returns the index of the first element equal to a, or none if no element is equal to a.

Examples:

• #["carrot", "potato", "broccoli"].idxOf? "carrot" = some 0
• #["carrot", "potato", "broccoli"].idxOf? "broccoli" = some 2
• #["carrot", "potato", "broccoli"].idxOf? "tomato" = none
• #["carrot", "potato", "broccoli"].idxOf? "anything else" = none

@[inline]

def Array.any {α : Type u} (as : Array α) (p : α → Bool) (start : Nat := 0) (stop : Nat := as.size) : Bool

Returns true if p returns true for any element of as.

Short-circuits upon encountering the first true.

The optional parameters start and stop control the region of the array to be checked. Only the elements with indices from start (inclusive) to stop (exclusive) are checked. By default, the entire array is checked.

Examples:

• #[2, 4, 6].any (· % 2 = 0) = true
• #[2, 4, 6].any (· % 2 = 1) = false
• #[2, 4, 5, 6].any (· % 2 = 0) = true
• #[2, 4, 5, 6].any (· % 2 = 1) = true

@[inline]

def Array.all {α : Type u} (as : Array α) (p : α → Bool) (start : Nat := 0) (stop : Nat := as.size) : Bool

Returns true if p returns true for every element of as.

Short-circuits upon encountering the first false.

The optional parameters start and stop control the region of the array to be checked. Only the elements with indices from start (inclusive) to stop (exclusive) are checked. By default, the entire array is checked.

Examples:

• #[a, b, c].all p = (p a && (p b && p c))
• #[2, 4, 6].all (· % 2 = 0) = true
• #[2, 4, 5, 6].all (· % 2 = 0) = false

def Array.contains {α : Type u} [BEq α] (as : Array α) (a : α) : Bool

Checks whether a is an element of as, using == to compare elements.

Array.elem is a synonym that takes the element before the array.

Examples:

• #[1, 4, 2, 3, 3, 7].contains 3 = true
• Array.contains #[1, 4, 2, 3, 3, 7] 5 = false

def Array.elem {α : Type u} [BEq α] (a : α) (as : Array α) : Bool

Checks whether a is an element of as, using == to compare elements.

Array.contains is a synonym that takes the array before the element.

For verification purposes, Array.elem is simplified to Array.contains.

Example:

• Array.elem 3 #[1, 4, 2, 3, 3, 7] = true
• Array.elem 5 #[1, 4, 2, 3, 3, 7] = false

@[export lean_array_to_list_impl]

def Array.toListImpl {α : Type u} (as : Array α) : List α

Convert a Array α into an List α. This is O(n) in the size of the array.

@[inline]

def Array.toListAppend {α : Type u} (as : Array α) (l : List α) : List α

Prepends an array to a list. The elements of the array are at the beginning of the resulting list.

Equivalent to as.toList ++ l.

Examples:

• #[1, 2].toListAppend [3, 4] = [1, 2, 3, 4]
• #[1, 2].toListAppend [] = [1, 2]
• #[].toListAppend [3, 4, 5] = [3, 4, 5]

def Array.append {α : Type u} (as bs : Array α) : Array α

Appends two arrays. Normally used via the ++ operator.

Appending arrays takes time proportional to the length of the second array.

Examples:

• #[1, 2, 3] ++ #[4, 5] = #[1, 2, 3, 4, 5].
• #[] ++ #[4, 5] = #[4, 5].
• #[1, 2, 3] ++ #[] = #[1, 2, 3].

instance Array.instAppend {α : Type u} : Append (Array α)

def Array.appendList {α : Type u} (as : Array α) (bs : List α) : Array α

Appends an array and a list.

Takes time proportional to the length of the list..

Examples:

• #[1, 2, 3].appendList [4, 5] = #[1, 2, 3, 4, 5].
• #[].appendList [4, 5] = #[4, 5].
• #[1, 2, 3].appendList [] = #[1, 2, 3].

instance Array.instHAppendList {α : Type u} : HAppend (Array α) (List α) (Array α)

@[inline]

def Array.flatMapM {α : Type u} {m : Type u_1 → Type u_2} {β : Type u_1} [Monad m] (f : α → m (Array β)) (as : Array α) : m (Array β)

Applies a monadic function that returns an array to each element of an array, from left to right. The resulting arrays are appended.

@[inline]

def Array.flatMap {α : Type u} {β : Type u_1} (f : α → Array β) (as : Array α) : Array β

Applies a function that returns an array to each element of an array. The resulting arrays are appended.

Examples:

• #[2, 3, 2].flatMap Array.range = #[0, 1, 0, 1, 2, 0, 1]
• #[['a', 'b'], ['c', 'd', 'e']].flatMap List.toArray = #['a', 'b', 'c', 'd', 'e']

@[inline]

def Array.flatten {α : Type u} (xss : Array (Array α)) : Array α

Appends the contents of array of arrays into a single array. The resulting array contains the same elements as the nested arrays in the same order.

Examples:

• #[#[5], #[4], #[3, 2]].flatten = #[5, 4, 3, 2]
• #[#[0, 1], #[], #[2], #[1, 0, 1]].flatten = #[0, 1, 2, 1, 0, 1]
• (#[] : Array Nat).flatten = #[]

def Array.reverse {α : Type u} (as : Array α) : Array α

Reverses an array by repeatedly swapping elements.

The original array is modified in place if there are no other references to it.

Examples:

• (#[] : Array Nat).reverse = #[]
• #[0, 1].reverse = #[1, 0]
• #[0, 1, 2].reverse = #[2, 1, 0]

theorem Array.reverse.termination {i j : Nat} (h : i < j) : j - 1 - (i + 1) < j - i

@[irreducible]

def Array.reverse.loop {α : Type u} (as : Array α) (i : Nat) (j : Fin as.size) : Array α

@[inline]

def Array.filter {α : Type u} (p : α → Bool) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Array α

Returns the array of elements in as for which p returns true.

Only elements from start (inclusive) to stop (exclusive) are considered. Elements outside that range are discarded. By default, the entire array is considered.

Examples:

• #[1, 2, 5, 2, 7, 7].filter (· > 2) = #[5, 7, 7]
• #[1, 2, 5, 2, 7, 7].filter (fun _ => false) = #[]
• #[1, 2, 5, 2, 7, 7].filter (fun _ => true) = #[1, 2, 5, 2, 7, 7]
• #[1, 2, 5, 2, 7, 7].filter (· > 2) (start := 3) = #[7, 7]
• #[1, 2, 5, 2, 7, 7].filter (fun _ => true) (start := 3) = #[2, 7, 7]
• #[1, 2, 5, 2, 7, 7].filter (fun _ => true) (stop := 3) = #[1, 2, 5]

@[inline]

def Array.filterM {m : Type → Type u_1} {α : Type} [Monad m] (p : α → m Bool) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m (Array α)

Applies the monadic predicate p to every element in the array, in order from left to right, and returns the array of elements for which p returns true.

Only elements from start (inclusive) to stop (exclusive) are considered. Elements outside that range are discarded. By default, the entire array is checked.

Example:

#eval #[1, 2, 5, 2, 7, 7].filterM fun x => do
  IO.println s!"Checking {x}"
  return x < 3

Checking 1
Checking 2
Checking 5
Checking 2
Checking 7
Checking 7

#[1, 2, 2]

@[inline]

def Array.filterRevM {m : Type → Type u_1} {α : Type} [Monad m] (p : α → m Bool) (as : Array α) (start : Nat := as.size) (stop : Nat := 0) : m (Array α)

Applies the monadic predicate p on every element in the array in reverse order, from right to left, and returns those elements for which p returns true. The elements of the returned list are in the same order as in the input list.

Only elements from start (exclusive) to stop (inclusive) are considered. Elements outside that range are discarded. Because the array is examined in reverse order, elements are only examined when start > stop. By default, the entire array is considered.

Example:

#eval #[1, 2, 5, 2, 7, 7].filterRevM fun x => do
  IO.println s!"Checking {x}"
  return x < 3

Checking 7
Checking 7
Checking 2
Checking 5
Checking 2
Checking 1

#[1, 2, 2]

@[specialize #[]]

def Array.filterMapM {α : Type u} {m : Type u_1 → Type u_2} {β : Type u_1} [Monad m] (f : α → m (Option β)) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : m (Array β)

Applies a monadic function that returns an Option to each element of an array, collecting the non-none values.

Only elements from start (inclusive) to stop (exclusive) are considered. Elements outside that range are discarded. By default, the entire array is considered.

Example:

#eval #[1, 2, 5, 2, 7, 7].filterMapM fun x => do
  IO.println s!"Examining {x}"
  if x > 2 then return some (2 * x)
  else return none

Examining 1
Examining 2
Examining 5
Examining 2
Examining 7
Examining 7

#[10, 14, 14]

@[inline]

def Array.filterMap {α : Type u} {β : Type u_1} (f : α → Option β) (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Array β

Applies a function that returns an Option to each element of an array, collecting the non-none values.

Example:

#eval #[1, 2, 5, 2, 7, 7].filterMap fun x =>
  if x > 2 then some (2 * x) else none

#[10, 14, 14]

@[specialize #[]]

def Array.getMax? {α : Type u} (as : Array α) (lt : α → α → Bool) : Option α

Returns the largest element of the array, as determined by the comparison lt, or none if the array is empty.

Examples:

• (#[] : Array Nat).getMax? (· < ·) = none
• #["red", "green", "blue"].getMax? (·.length < ·.length) = some "green"
• #["red", "green", "blue"].getMax? (· < ·) = some "red"

@[inline]

def Array.partition {α : Type u} (p : α → Bool) (as : Array α) : Array α × Array α

Returns a pair of arrays that together contain all the elements of as. The first array contains those elements for which p returns true, and the second contains those for which p returns false.

as.partition p is equivalent to (as.filter p, as.filter (not ∘ p)), but it is more efficient since it only has to do one pass over the array.

Examples:

• #[1, 2, 5, 2, 7, 7].partition (· > 2) = (#[5, 7, 7], #[1, 2, 2])
• #[1, 2, 5, 2, 7, 7].partition (fun _ => false) = (#[], #[1, 2, 5, 2, 7, 7])
• #[1, 2, 5, 2, 7, 7].partition (fun _ => true) = (#[1, 2, 5, 2, 7, 7], #[])

def Array.popWhile {α : Type u} (p : α → Bool) (as : Array α) : Array α

Removes all the elements that satisfy a predicate from the end of an array.

The longest contiguous sequence of elements that all satisfy the predicate is removed.

Examples:

• #[0, 1, 2, 3, 4].popWhile (· > 2) = #[0, 1, 2]
• #[3, 2, 3, 4].popWhile (· > 2) = #[3, 2]
• (#[] : Array Nat).popWhile (· > 2) = #[]

@[simp]

theorem Array.popWhile_empty {α : Type u} {p : α → Bool} : popWhile p #[] = #[]

def Array.takeWhile {α : Type u} (p : α → Bool) (as : Array α) : Array α

Returns a new array that contains the longest prefix of elements that satisfy the predicate p from an array.

Examples:

• #[0, 1, 2, 3, 2, 1].takeWhile (· < 2) = #[0, 1]
• #[0, 1, 2, 3, 2, 1].takeWhile (· < 20) = #[0, 1, 2, 3, 2, 1]
• #[0, 1, 2, 3, 2, 1].takeWhile (· < 0) = #[]

def Array.takeWhile.go {α : Type u} (p : α → Bool) (as : Array α) (i : Nat) (acc : Array α) : Array α

def Array.eraseIdx {α : Type u} (xs : Array α) (i : Nat) (h : i < xs.size := by get_elem_tactic) : Array α

Removes the element at a given index from an array without a run-time bounds check.

This function takes worst-case O(n) time because it back-shifts all elements at positions greater than i.

Examples:

• #["apple", "pear", "orange"].eraseIdx 0 = #["pear", "orange"]
• #["apple", "pear", "orange"].eraseIdx 1 = #["apple", "orange"]
• #["apple", "pear", "orange"].eraseIdx 2 = #["apple", "pear"]

@[simp]

theorem Array.size_eraseIdx {α : Type u} {xs : Array α} (i : Nat) (h : i < xs.size) : (xs.eraseIdx i h).size = xs.size - 1

def Array.eraseIdxIfInBounds {α : Type u} (xs : Array α) (i : Nat) : Array α

Removes the element at a given index from an array. Does nothing if the index is out of bounds.

This function takes worst-case O(n) time because it back-shifts all elements at positions greater than i.

Examples:

• #["apple", "pear", "orange"].eraseIdxIfInBounds 0 = #["pear", "orange"]
• #["apple", "pear", "orange"].eraseIdxIfInBounds 1 = #["apple", "orange"]
• #["apple", "pear", "orange"].eraseIdxIfInBounds 2 = #["apple", "pear"]
• #["apple", "pear", "orange"].eraseIdxIfInBounds 3 = #["apple", "pear", "orange"]
• #["apple", "pear", "orange"].eraseIdxIfInBounds 5 = #["apple", "pear", "orange"]

def Array.eraseIdx! {α : Type u} (xs : Array α) (i : Nat) : Array α

Removes the element at a given index from an array. Panics if the index is out of bounds.

This function takes worst-case O(n) time because it back-shifts all elements at positions greater than i.

def Array.erase {α : Type u} [BEq α] (as : Array α) (a : α) : Array α

Removes the first occurrence of a specified element from an array, or does nothing if it is not present.

This function takes worst-case O(n) time because it back-shifts all later elements.

Examples:

• #[1, 2, 3].erase 2 = #[1, 3]
• #[1, 2, 3].erase 5 = #[1, 2, 3]
• #[1, 2, 3, 2, 1].erase 2 = #[1, 3, 2, 1]
• (#[] : List Nat).erase 2 = #[]

def Array.eraseP {α : Type u} (as : Array α) (p : α → Bool) : Array α

Removes the first element that satisfies the predicate p. If no element satisfies p, the array is returned unmodified.

This function takes worst-case O(n) time because it back-shifts all later elements.

Examples:

• #["red", "green", "", "blue"].eraseP (·.isEmpty) = #["red", "green", "blue"]
• #["red", "green", "", "blue", ""].eraseP (·.isEmpty) = #["red", "green", "blue", ""]
• #["red", "green", "blue"].eraseP (·.length % 2 == 0) = #["red", "green"]
• #["red", "green", "blue"].eraseP (fun _ => true) = #["green", "blue"]
• (#[] : Array String).eraseP (fun _ => true) = #[]

@[inline]

def Array.insertIdx {α : Type u} (as : Array α) (i : Nat) (a : α) : autoParam (i ≤ as.size) _auto✝ → Array α

Inserts an element into an array at the specified index. If the index is greater than the size of the array, then the array is returned unmodified.

In other words, the new element is inserted into the array as after the first i elements of as.

This function takes worst case O(n) time because it has to swap the inserted element into place.

Examples:

• #["tues", "thur", "sat"].insertIdx 1 "wed" = #["tues", "wed", "thur", "sat"]
• #["tues", "thur", "sat"].insertIdx 2 "wed" = #["tues", "thur", "wed", "sat"]
• #["tues", "thur", "sat"].insertIdx 3 "wed" = #["tues", "thur", "sat", "wed"]

def Array.insertIdx.loop {α : Type u} (i : Nat) (as : Array α) (j : Fin as.size) : Array α

def Array.insertIdx! {α : Type u} (as : Array α) (i : Nat) (a : α) : Array α

Inserts an element into an array at the specified index. Panics if the index is greater than the size of the array.

In other words, the new element is inserted into the array as after the first i elements of as.

This function takes worst case O(n) time because it has to swap the inserted element into place. Array.insertIdx and Array.insertIdxIfInBounds are safer alternatives.

Examples:

• #["tues", "thur", "sat"].insertIdx! 1 "wed" = #["tues", "wed", "thur", "sat"]
• #["tues", "thur", "sat"].insertIdx! 2 "wed" = #["tues", "thur", "wed", "sat"]
• #["tues", "thur", "sat"].insertIdx! 3 "wed" = #["tues", "thur", "sat", "wed"]

def Array.insertIdxIfInBounds {α : Type u} (as : Array α) (i : Nat) (a : α) : Array α

Inserts an element into an array at the specified index. The array is returned unmodified if the index is greater than the size of the array.

In other words, the new element is inserted into the array as after the first i elements of as.

This function takes worst case O(n) time because it has to swap the inserted element into place.

Examples:

• #["tues", "thur", "sat"].insertIdxIfInBounds 1 "wed" = #["tues", "wed", "thur", "sat"]
• #["tues", "thur", "sat"].insertIdxIfInBounds 2 "wed" = #["tues", "thur", "wed", "sat"]
• #["tues", "thur", "sat"].insertIdxIfInBounds 3 "wed" = #["tues", "thur", "sat", "wed"]
• #["tues", "thur", "sat"].insertIdxIfInBounds 4 "wed" = #["tues", "thur", "sat"]

def Array.isPrefixOfAux {α : Type u} [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : Nat) : Bool

def Array.isPrefixOf {α : Type u} [BEq α] (as bs : Array α) : Bool

Return true if as is a prefix of bs, or false otherwise.

Examples:

• #[0, 1, 2].isPrefixOf #[0, 1, 2, 3] = true
• #[0, 1, 2].isPrefixOf #[0, 1, 2] = true
• #[0, 1, 2].isPrefixOf #[0, 1] = false
• #[].isPrefixOf #[0, 1] = true

@[specialize #[]]

def Array.zipWithAux {α : Type u} {β : Type u_1} {γ : Type u_2} (as : Array α) (bs : Array β) (f : α → β → γ) (i : Nat) (cs : Array γ) : Array γ

@[inline]

def Array.zipWith {α : Type u} {β : Type u_1} {γ : Type u_2} (f : α → β → γ) (as : Array α) (bs : Array β) : Array γ

Applies a function to the corresponding elements of two arrays, stopping at the end of the shorter array.

Examples:

• #[1, 2].zipWith (· + ·) #[5, 6] = #[6, 8]
• #[1, 2, 3].zipWith (· + ·) #[5, 6, 10] = #[6, 8, 13]
• #[].zipWith (· + ·) #[5, 6] = #[]
• #[x₁, x₂, x₃].zipWith f #[y₁, y₂, y₃, y₄] = #[f x₁ y₁, f x₂ y₂, f x₃ y₃]

def Array.zip {α : Type u} {β : Type u_1} (as : Array α) (bs : Array β) : Array (α × β)

Combines two arrays into an array of pairs in which the first and second components are the corresponding elements of each input array. The resulting array is the length of the shorter of the input arrays.

Examples:

• #["Mon", "Tue", "Wed"].zip #[1, 2, 3] = #[("Mon", 1), ("Tue", 2), ("Wed", 3)]
• #["Mon", "Tue", "Wed"].zip #[1, 2] = #[("Mon", 1), ("Tue", 2)]
• #[x₁, x₂, x₃].zip #[y₁, y₂, y₃, y₄] = #[(x₁, y₁), (x₂, y₂), (x₃, y₃)]

def Array.zipWithAll {α : Type u} {β : Type u_1} {γ : Type u_2} (f : Option α → Option β → γ) (as : Array α) (bs : Array β) : Array γ

Applies a function to the corresponding elements of both arrays, stopping when there are no more elements in either array. If one array is shorter than the other, the function is passed none for the missing elements.

Examples:

• #[1, 6].zipWithAll min #[5, 2] = #[some 1, some 2]
• #[1, 2, 3].zipWithAll Prod.mk #[5, 6] = #[(some 1, some 5), (some 2, some 6), (some 3, none)]
• #[x₁, x₂].zipWithAll f #[y] = #[f (some x₁) (some y), f (some x₂) none]

@[irreducible]

def Array.zipWithAll.go {α : Type u} {β : Type u_1} {γ : Type u_2} (f : Option α → Option β → γ) (as : Array α) (bs : Array β) (i : Nat) (cs : Array γ) : Array γ

def Array.unzip {α : Type u} {β : Type u_1} (as : Array (α × β)) : Array α × Array β

Separates an array of pairs into two arrays that contain the respective first and second components.

Examples:

• #[("Monday", 1), ("Tuesday", 2)].unzip = (#["Monday", "Tuesday"], #[1, 2])
• #[(x₁, y₁), (x₂, y₂), (x₃, y₃)].unzip = (#[x₁, x₂, x₃], #[y₁, y₂, y₃])
• (#[] : Array (Nat × String)).unzip = ((#[], #[]) : List Nat × List String)

def Array.replace {α : Type u} [BEq α] (xs : Array α) (a b : α) : Array α

Replaces the first occurrence of a with b in an array. The modification is performed in-place when the reference to the array is unique. Returns the array unmodified when a is not present.

Examples:

• #[1, 2, 3, 2, 1].replace 2 5 = #[1, 5, 3, 2, 1]
• #[1, 2, 3, 2, 1].replace 0 5 = #[1, 2, 3, 2, 1]
• #[].replace 2 5 = #[]

Lexicographic ordering

instance Array.instLT {α : Type u} [LT α] : LT (Array α)

instance Array.instLE {α : Type u} [LT α] : LE (Array α)

Auxiliary functions used in metaprogramming.

We do not currently intend to provide verification theorems for these functions.

leftpad and rightpad

def Array.leftpad {α : Type u} (n : Nat) (a : α) (xs : Array α) : Array α

Pads xs : Array α on the left with repeated occurrences of a : α until it is of size n. If xs already has at least n elements, it is returned unmodified.

Examples:

• #[1, 2, 3].leftpad 5 0 = #[0, 0, 1, 2, 3]
• #["red", "green", "blue"].leftpad 4 "blank" = #["blank", "red", "green", "blue"]
• #["red", "green", "blue"].leftpad 3 "blank" = #["red", "green", "blue"]
• #["red", "green", "blue"].leftpad 1 "blank" = #["red", "green", "blue"]

def Array.rightpad {α : Type u} (n : Nat) (a : α) (xs : Array α) : Array α

Pads xs : Array α on the right with repeated occurrences of a : α until it is of length n. If l already has at least n elements, it is returned unmodified.

Examples:

• #[1, 2, 3].rightpad 5 0 = #[1, 2, 3, 0, 0]
• #["red", "green", "blue"].rightpad 4 "blank" = #["red", "green", "blue", "blank"]
• #["red", "green", "blue"].rightpad 3 "blank" = #["red", "green", "blue"]
• #["red", "green", "blue"].rightpad 1 "blank" = #["red", "green", "blue"]

@[inline]

def Array.reduceOption {α : Type u} (as : Array (Option α)) : Array α

Drop nones from a Array, and replace each remaining some a with a.

eraseReps

def Array.eraseReps {α : Type u_1} [BEq α] (as : Array α) : Array α

Erases repeated elements, keeping the first element of each run.

O(|as|).

Example:

• #[1, 3, 2, 2, 2, 3, 3, 5].eraseReps = #[1, 3, 2, 3, 5]

allDiff

def Array.allDiff {α : Type u} [BEq α] (as : Array α) : Bool

Returns true if no two elements of as are equal according to the == operator.

Examples:

• #["red", "green", "blue"].allDiff = true
• #["red", "green", "red"].allDiff = false
• (#[] : Array Nat).allDiff = true

getEvenElems

@[inline]

def Array.getEvenElems {α : Type u} (as : Array α) : Array α

Returns a new array that contains the elements at even indices in as, starting with the element at index 0.

Examples:

• #[0, 1, 2, 3, 4].getEvenElems = #[0, 2, 4]
• #[1, 2, 3, 4].getEvenElems = #[1, 3]
• #["red", "green", "blue"].getEvenElems = #["red", "blue"]
• (#[] : Array String).getEvenElems = #[]

Repr and ToString

def Array.Array.repr {α : Type u} [Repr α] (xs : Array α) : Std.Format

instance Array.instRepr {α : Type u} [Repr α] : Repr (Array α)

instance Array.instToString {α : Type u} [ToString α] : ToString (Array α)