84 lines
2.4 KiB
Text
84 lines
2.4 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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protected definition list.is_inhabited [instance] (A : Type) : inhabited (list A) :=
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inhabited.mk list.nil
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definition list.has_decidable_eq [instance] {A : Type} [H : decidable_eq A] (l₁ : list A) : ∀ l₂ : list A, decidable (l₁ = l₂) :=
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list.rec_on l₁
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(λ l₂, list.cases_on l₂
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(tt rfl)
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(λ b l₂, ff (λ H, list.no_confusion H)))
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(λ a l₁ ih l₂, list.cases_on l₂
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(ff (λ H, list.no_confusion H))
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(λ b l₂,
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decidable.cases_on (H a b)
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(λ Hnab : a ≠ b, ff (λ H, list.no_confusion H (λ Hab Hl₁l₂, absurd Hab Hnab)))
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(λ Hab : a = b,
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decidable.cases_on (ih l₂)
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(λ Hne : l₁ ≠ l₂, ff (λ H, list.no_confusion H (λ Hab Hl₁l₂, absurd Hl₁l₂ Hne)))
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(λ He : l₁ = l₂, tt (congr (congr_arg cons Hab) He)))))
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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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variable {A : Type}
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definition 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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definition 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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definition nth : list A → nat → option A
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| [] _ := 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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definition head {A : Type} [inhabited A] : list A → A
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| [] := default A
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| (a :: l) := a
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definition tail : list A → list A
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| [] := []
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| (a :: l) := l
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definition 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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definition reverse : list A → list A
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| [] := []
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| (a :: l) := concat a (reverse l)
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definition map {B : Type} (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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definition join : list (list A) → list A
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| [] := []
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| (l :: ls) := append l (join ls)
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definition 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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definition 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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definition list_has_append [instance] {A : Type} : has_append (list A) :=
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has_append.mk list.append
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