Definitions on Arrays

This file contains various definitions on Array. It does not contain proofs about these definitions, those are contained in other files in Batteries.Data.Array.

def Array.equalSet {α : Type u_1} [BEq α] (xs ys : Array α) : Bool

Check whether xs and ys are equal as sets, i.e. they contain the same elements when disregarding order and duplicates. O(n*m)! If your element type has an Ord instance, it is asymptotically more efficient to sort the two arrays, remove duplicates and then compare them elementwise.

Equations

• xs.equalSet ys = ((xs.all fun (x : α) => ys.contains x) && ys.all fun (x : α) => xs.contains x)

@[inline]

def Array.minWith {α : Type u_1} [ord : Ord α] (xs : Array α) (d : α) (start : Nat := 0) (stop : Nat := xs.size) : α

Returns the first minimal element among d and elements of the array. If start and stop are given, only the subarray xs[start:stop] is considered (in addition to d).

Equations

• xs.minWith d start stop = Array.foldl (fun (min x : α) => if (compare x min).isLT = true then x else min) d xs start stop

@[inline]

def Array.minD {α : Type u_1} [ord : Ord α] (xs : Array α) (d : α) (start : Nat := 0) (stop : Nat := xs.size) : α

Find the first minimal element of an array. If the array is empty, d is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.minD d start stop = if h : start < xs.size ∧ start < stop then xs.minWith xs[start] (start + 1) stop else d

@[inline]

def Array.min? {α : Type u_1} [ord : Ord α] (xs : Array α) (start : Nat := 0) (stop : Nat := xs.size) : Option α

Find the first minimal element of an array. If the array is empty, none is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.min? start stop = if h : start < xs.size ∧ start < stop then some (xs.minD xs[start] start stop) else none

@[inline]

def Array.minI {α : Type u_1} [ord : Ord α] [Inhabited α] (xs : Array α) (start : Nat := 0) (stop : Nat := xs.size) : α

Find the first minimal element of an array. If the array is empty, default is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.minI start stop = xs.minD default start stop

@[inline]

def Array.maxWith {α : Type u_1} [ord : Ord α] (xs : Array α) (d : α) (start : Nat := 0) (stop : Nat := xs.size) : α

Returns the first maximal element among d and elements of the array. If start and stop are given, only the subarray xs[start:stop] is considered (in addition to d).

Equations

• xs.maxWith d start stop = xs.minWith d start stop

@[inline]

def Array.maxD {α : Type u_1} [ord : Ord α] (xs : Array α) (d : α) (start : Nat := 0) (stop : Nat := xs.size) : α

Find the first maximal element of an array. If the array is empty, d is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.maxD d start stop = xs.minD d start stop

@[inline]

def Array.max? {α : Type u_1} [ord : Ord α] (xs : Array α) (start : Nat := 0) (stop : Nat := xs.size) : Option α

Find the first maximal element of an array. If the array is empty, none is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.max? start stop = xs.min? start stop

@[inline]

def Array.maxI {α : Type u_1} [ord : Ord α] [Inhabited α] (xs : Array α) (start : Nat := 0) (stop : Nat := xs.size) : α

Find the first maximal element of an array. If the array is empty, default is returned. If start and stop are given, only the subarray xs[start:stop] is considered.

Equations

• xs.maxI start stop = xs.minI start stop

Safe Nat Indexed Array functions

The functions in this section offer variants of Array functions which use Nat indices instead of Fin indices. All these functions have as parameter a proof that the index is valid for the array. But this parameter has a default argument by get_elem_tactic which should prove the index bound.

@[reducible, inline]

abbrev Array.setN {α : Type u_1} (a : Array α) (i : Nat) (x : α) (h : i < a.size := by get_elem_tactic) : Array α

setN a i h x sets an element in a vector using a Nat index which is provably valid. A proof by get_elem_tactic is provided as a default argument for h. This will perform the update destructively provided that a has a reference count of 1 when called.

Equations

• a.setN i x h = a.set i x h

@[inline]

def Subarray.isEmpty {α : Type u_1} (as : Subarray α) : Bool

Check whether a subarray is empty.

Equations

• as.isEmpty = (as.start == as.stop)

@[inline]

def Subarray.contains {α : Type u_1} [BEq α] (as : Subarray α) (a : α) : Bool

Check whether a subarray contains an element.

Equations

• as.contains a = Subarray.any (fun (x : α) => x == a) as

def Subarray.popHead? {α : Type u_1} (as : Subarray α) : Option (α × Subarray α)

Remove the first element of a subarray. Returns the element and the remaining subarray, or none if the subarray is empty.

Equations

• One or more equations did not get rendered due to their size.