141 lines
3.3 KiB
Text
141 lines
3.3 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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notation h :: t := cons h t
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notation `[` l:(foldr `, ` (h t, cons h t) nil `]`) := l
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universe variables u v
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instance (A : Type u) : inhabited (list A) :=
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⟨list.nil⟩
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variables {A : Type u} {B : Type v}
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namespace list
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protected 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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instance : has_append (list A) :=
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⟨list.append⟩
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protected def mem : A → list A → Prop
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| a [] := false
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| a (b :: l) := a = b ∨ mem a l
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instance : has_mem A list :=
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⟨list.mem⟩
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instance decidable_mem [decidable_eq A] (a : A) : ∀ (l : list A), decidable (a ∈ l)
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| [] := is_false not_false
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| (b::l) :=
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if h₁ : a = b then is_true (or.inl h₁)
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else match decidable_mem l with
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| is_true h₂ := is_true (or.inr h₂)
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| is_false h₂ := is_false (not_or h₁ h₂)
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end
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def concat : list A → A → list A
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| [] a := [a]
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| (b::l) a := b :: concat l a
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instance : has_emptyc (list A) :=
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⟨list.nil⟩
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protected def insert [decidable_eq A] (a : A) (l : list A) : list A :=
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if a ∈ l then l else concat l a
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instance [decidable_eq A] : has_insert A list :=
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⟨list.insert⟩
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protected def union [decidable_eq A] : list A → list A → list A
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| l₁ [] := l₁
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| l₁ (a::l₂) := union (insert a l₁) l₂
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instance [decidable_eq A] : has_union (list A) :=
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⟨list.union⟩
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protected def inter [decidable_eq A] : list A → list A → list A
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| [] l₂ := []
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| (a::l₁) l₂ := if a ∈ l₂ then a :: inter l₁ l₂ else inter l₁ l₂
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instance [decidable_eq A] : has_inter (list A) :=
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⟨list.inter⟩
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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 reverse : list A → list A
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| [] := []
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| (a :: l) := concat (reverse l) a
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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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definition foldl (f : A → B → A) : A → list B → A
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| a [] := a
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| a (b :: l) := foldl (f a b) l
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definition foldr (f : A → B → B) : B → list A → B
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| b [] := b
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| b (a :: l) := f a (foldr b l)
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definition any (l : list A) (p : A → bool) : bool :=
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foldr (λ a r, p a || r) ff l
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definition all (l : list A) (p : A → bool) : bool :=
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foldr (λ a r, p a && r) tt l
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def zip : list A → list B → list (prod A B)
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| [] _ := []
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| _ [] := []
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| (x::xs) (y::ys) := (prod.mk x y) :: zip xs ys
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def repeat (a : A) : ℕ → list A
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| 0 := []
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| (succ n) := a :: repeat n
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def iota : ℕ → list ℕ
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| 0 := []
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| (succ n) := iota n ++ [succ n]
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end list
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