structure Std.DList (α : Type u) : Type u

A difference List is a Function that, given a List, returns the original contents of the difference List prepended to the given List. This structure supports O(1) append and concat operations on lists, making it useful for append-heavy uses such as logging and pretty printing.

• apply : List α → List α

  "Run" a DList by appending it on the right by a List α to get another List α.

• invariant : ∀ (l : List α), self.apply l = self.apply [] ++ l

  The apply function of a DList is completely determined by the list apply [].

theorem Std.DList.invariant {α : Type u} (self : Std.DList α) (l : List α) : self.apply l = self.apply [] ++ l

The apply function of a DList is completely determined by the list apply [].

def Std.DList.ofList {α : Type u} (l : List α) : Std.DList α

O(1) (apply is O(|l|)). Convert a List α into a DList α.

Equations

• Std.DList.ofList l = { apply := fun (x : List α) => l ++ x, invariant := ⋯ }

def Std.DList.empty {α : Type u} : Std.DList α

O(1) (apply is O(1)). Return an empty DList α.

Equations

• Std.DList.empty = { apply := id, invariant := ⋯ }

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

Equations

• Std.DList.instEmptyCollection = { emptyCollection := Std.DList.empty }

def Std.DList.toList {α : Type u} : Std.DList α → List α

O(apply()). Convert a DList α into a List α by running the apply function.

Equations

• x.toList = match x with | { apply := f, invariant := invariant } => f []

def Std.DList.singleton {α : Type u} (a : α) : Std.DList α

O(1) (apply is O(1)). A DList α corresponding to the list [a].

Equations

• Std.DList.singleton a = { apply := fun (t : List α) => a :: t, invariant := ⋯ }

def Std.DList.cons {α : Type u} : α → Std.DList α → Std.DList α

O(1) (apply is O(1)). Prepend a on a DList α.

Equations

• Std.DList.cons x✝ x = match x✝, x with | a, { apply := f, invariant := h } => { apply := fun (t : List α) => a :: f t, invariant := ⋯ }

def Std.DList.append {α : Type u} : Std.DList α → Std.DList α → Std.DList α

O(1) (apply is O(1)). Append two DList α.

Equations

• x✝.append x = match x✝, x with | { apply := f, invariant := h₁ }, { apply := g, invariant := h₂ } => { apply := f ∘ g, invariant := ⋯ }

def Std.DList.push {α : Type u} : Std.DList α → α → Std.DList α

O(1) (apply is O(1)). Append an element at the end of a DList α.

Equations

• x✝.push x = match x✝, x with | { apply := f, invariant := h }, a => { apply := fun (t : List α) => f (a :: t), invariant := ⋯ }

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

Equations

• Std.DList.instAppend = { append := Std.DList.append }