182 lines
4.4 KiB
Text
182 lines
4.4 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.data.nat.basic
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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 w
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instance (α : Type u) : inhabited (list α) :=
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⟨list.nil⟩
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variables {α : Type u} {β : Type v} {γ : Type w}
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namespace list
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protected def append : list α → list α → list α
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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 α) :=
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⟨list.append⟩
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protected def mem : α → list α → 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 α (list α) :=
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⟨list.mem⟩
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instance decidable_mem [decidable_eq α] (a : α) : ∀ (l : list α), 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 α → α → list α
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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 α) :=
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⟨list.nil⟩
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protected def insert [decidable_eq α] (a : α) (l : list α) : list α :=
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if a ∈ l then l else concat l a
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instance [decidable_eq α] : has_insert α list :=
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⟨list.insert⟩
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protected def union [decidable_eq α] : list α → list α → list α
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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 α] : has_union (list α) :=
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⟨list.union⟩
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protected def inter [decidable_eq α] : list α → list α → list α
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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 α] : has_inter (list α) :=
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⟨list.inter⟩
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def length : list α → nat
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| [] := 0
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| (a :: l) := length l + 1
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def empty : list α → bool
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| [] := tt
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| (_ :: _) := ff
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open option nat
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def nth : list α → nat → option α
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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 update_nth : list α → ℕ → α → list α
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| (x::xs) 0 a := a :: xs
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| (x::xs) (i+1) a := x :: update_nth xs i a
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| [] _ _ := []
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def remove_nth : list α → ℕ → list α
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| [] _ := []
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| (x::xs) 0 := xs
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| (x::xs) (i+1) := x :: remove_nth xs i
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def head [inhabited α] : list α → α
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| [] := default α
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| (a :: l) := a
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def tail : list α → list α
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| [] := []
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| (a :: l) := l
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def reverse_core : list α → list α → list α
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| [] r := r
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| (a::l) r := reverse_core l (a::r)
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def reverse : list α → list α :=
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λ l, reverse_core l []
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def map (f : α → β) : list α → list β
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| [] := []
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| (a :: l) := f a :: map l
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def for : list α → (α → β) → list β :=
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flip map
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def join : list (list α) → list α
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| [] := []
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| (l :: ls) := append l (join ls)
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def filter (p : α → Prop) [decidable_pred p] : list α → list α
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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 α → list α
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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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def taken : ℕ → list α → list α
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| 0 a := []
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| (succ n) [] := []
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| (succ n) (x :: r) := x :: taken n r
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definition foldl (f : α → β → α) : α → list β → α
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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 : α → β → β) : β → list α → β
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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 α) (p : α → bool) : bool :=
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foldr (λ a r, p a || r) ff l
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definition all (l : list α) (p : α → bool) : bool :=
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foldr (λ a r, p a && r) tt l
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def bor (l : list bool) : bool := any l id
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def band (l : list bool) : bool := all l id
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def zip_with (f : α → β → γ) : list α → list β → list γ
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| (x::xs) (y::ys) := f x y :: zip_with xs ys
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| _ _ := []
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def zip : list α → list β → list (prod α β) :=
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zip_with prod.mk
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def repeat (a : α) : ℕ → list α
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| 0 := []
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| (succ n) := a :: repeat n
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def range_core : ℕ → list ℕ → list ℕ
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| 0 l := l
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| (succ n) l := range_core n (n :: l)
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def range (n : ℕ) : list ℕ :=
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range_core n []
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def iota_core : ℕ → list ℕ → list ℕ
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| 0 l := reverse l
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| (succ n) l := iota_core n (succ n :: l)
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def iota : ℕ → list ℕ :=
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λ n, iota_core n []
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def sum [has_add α] [has_zero α] : list α → α :=
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foldl add zero
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end list
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