lean4-htt/library/init/list.lean
2016-09-24 16:38:39 -07:00

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/-
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
notation h :: t := cons h t
notation `[` l:(foldr `, ` (h t, cons h t) nil `]`) := l
universe variables u v
instance (A : Type u) : inhabited (list A) :=
⟨list.nil⟩
variables {A : Type u} {B : Type v}
namespace list
def append : list A → list A → list A
| [] l := l
| (h :: s) t := h :: (append s t)
instance : has_append (list A) :=
⟨append⟩
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 : → list A → list A
| 0 a := a
| (succ n) [] := []
| (succ n) (x::r) := dropn n r
end list