74 lines
1.6 KiB
Text
74 lines
1.6 KiB
Text
/-
|
||
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
|
||
Released under Apache 2.0 license as described in the file LICENSE.
|
||
Author: Leonardo de Moura
|
||
-/
|
||
prelude
|
||
import init.logic init.nat
|
||
open decidable list
|
||
|
||
universe variables u v
|
||
|
||
instance (A : Type u) : inhabited (list A) :=
|
||
⟨list.nil⟩
|
||
|
||
notation h :: t := cons h t
|
||
notation `[` l:(foldr `, ` (h t, cons h t) nil `]`) := l
|
||
|
||
namespace list
|
||
variables {A : Type u} {B : Type v}
|
||
|
||
def append : list A → list A → list A
|
||
| [] l := l
|
||
| (h :: s) t := h :: (append s t)
|
||
|
||
def length : list A → nat
|
||
| [] := 0
|
||
| (a :: l) := length l + 1
|
||
|
||
open option nat
|
||
|
||
def nth : list A → nat → option A
|
||
| [] n := none
|
||
| (a :: l) 0 := some a
|
||
| (a :: l) (n+1) := nth l n
|
||
|
||
def head [inhabited A] : list A → A
|
||
| [] := default A
|
||
| (a :: l) := a
|
||
|
||
def tail : list A → list A
|
||
| [] := []
|
||
| (a :: l) := l
|
||
|
||
def concat : Π (x : A), list A → list A
|
||
| a [] := [a]
|
||
| a (b :: l) := b :: concat a l
|
||
|
||
def reverse : list A → list A
|
||
| [] := []
|
||
| (a :: l) := concat a (reverse l)
|
||
|
||
def map (f : A → B) : list A → list B
|
||
| [] := []
|
||
| (a :: l) := f a :: map l
|
||
|
||
def for : list A → (A → B) → list B :=
|
||
flip map
|
||
|
||
def join : list (list A) → list A
|
||
| [] := []
|
||
| (l :: ls) := append l (join ls)
|
||
|
||
def filter (p : A → Prop) [h : decidable_pred p] : list A → list A
|
||
| [] := []
|
||
| (a::l) := if p a then a :: filter l else filter l
|
||
|
||
def dropn : ℕ → list A → list A
|
||
| 0 a := a
|
||
| (succ n) [] := []
|
||
| (succ n) (x::r) := dropn n r
|
||
end list
|
||
|
||
instance {A : Type u} : has_append (list A) :=
|
||
⟨list.append⟩
|