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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,70 +1,2 @@ | ||
| /- | ||
| Copyright (c) 2018 Microsoft Corporation. All rights reserved. | ||
| Released under Apache 2.0 license as described in the file LICENSE. | ||
| Authors: Leonardo de Moura | ||
| -/ | ||
| namespace Batteries | ||
| /-- | ||
| 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. | ||
| -/ | ||
| structure DList (α : Type u) where | ||
| /-- "Run" a `DList` by appending it on the right by a `List α` to get another `List α`. -/ | ||
| apply : List α → List α | ||
| /-- The `apply` function of a `DList` is completely determined by the list `apply []`. -/ | ||
| invariant : ∀ l, apply l = apply [] ++ l | ||
|
|
||
| namespace DList | ||
| variable {α : Type u} | ||
| open List | ||
|
|
||
| /-- `O(1)` (`apply` is `O(|l|)`). Convert a `List α` into a `DList α`. -/ | ||
| def ofList (l : List α) : DList α := | ||
| ⟨(l ++ ·), fun t => by simp⟩ | ||
|
|
||
| /-- `O(1)` (`apply` is `O(1)`). Return an empty `DList α`. -/ | ||
| def empty : DList α := | ||
| ⟨id, fun _ => rfl⟩ | ||
|
|
||
| instance : EmptyCollection (DList α) := ⟨DList.empty⟩ | ||
|
|
||
| /-- `O(apply())`. Convert a `DList α` into a `List α` by running the `apply` function. -/ | ||
| def toList : DList α → List α | ||
| | ⟨f, _⟩ => f [] | ||
|
|
||
| /-- `O(1)` (`apply` is `O(1)`). A `DList α` corresponding to the list `[a]`. -/ | ||
| def singleton (a : α) : DList α where | ||
| apply := fun t => a :: t | ||
| invariant := fun _ => rfl | ||
|
|
||
| /-- `O(1)` (`apply` is `O(1)`). Prepend `a` on a `DList α`. -/ | ||
| def cons : α → DList α → DList α | ||
| | a, ⟨f, h⟩ => { | ||
| apply := fun t => a :: f t | ||
| invariant := by intro t; simp; rw [h] | ||
| } | ||
|
|
||
| /-- `O(1)` (`apply` is `O(1)`). Append two `DList α`. -/ | ||
| def append : DList α → DList α → DList α | ||
| | ⟨f, h₁⟩, ⟨g, h₂⟩ => { | ||
| apply := f ∘ g | ||
| invariant := by | ||
| intro t | ||
| show f (g t) = (f (g [])) ++ t | ||
| rw [h₁ (g t), h₂ t, ← append_assoc (f []) (g []) t, ← h₁ (g [])] | ||
| } | ||
|
|
||
| /-- `O(1)` (`apply` is `O(1)`). Append an element at the end of a `DList α`. -/ | ||
| def push : DList α → α → DList α | ||
| | ⟨f, h⟩, a => { | ||
| apply := fun t => f (a :: t) | ||
| invariant := by | ||
| intro t | ||
| show f (a :: t) = f (a :: nil) ++ t | ||
| rw [h [a], h (a::t), append_assoc (f []) [a] t] | ||
| rfl | ||
| } | ||
|
|
||
| instance : Append (DList α) := ⟨DList.append⟩ | ||
| import Batteries.Data.DList.Basic | ||
| import Batteries.Data.DList.Lemmas |
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