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