93 lines
3.1 KiB
Text
93 lines
3.1 KiB
Text
/-
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Copyright (c) 2017 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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Authors: Leonardo de Moura
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-/
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prelude
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import init.data.nat
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universes u w
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structure array (α : Type u) (n : nat) :=
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(data : fin n → α)
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def mk_array {α} (n) (v : α) : array α n :=
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{data := λ _, v}
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namespace array
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variables {α : Type u} {β : Type w} {n : nat}
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def read (a : array α n) (i : fin n) : α :=
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a^.data i
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def read' [inhabited α] (a : array α n) (i : nat) : α :=
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if h : i < n then a^.read ⟨i,h⟩ else default α
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def write (a : array α n) (i : fin n) (v : α) : array α n :=
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{data := λ j, if i = j then v else a^.read j}
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def write' (a : array α n) (i : nat) (v : α) : array α n :=
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if h : i < n then a^.write ⟨i, h⟩ v else a
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lemma push_back_idx {j n} : j < n + 1 → j ≠ n → j < n :=
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λ h₁ h₂, nat.lt_of_le_and_ne (nat.le_of_lt_succ h₁) h₂
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def push_back (a : array α n) (v : α) : array α (n+1) :=
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{data := λ ⟨j, h₁⟩, if h₂ : j = n then v else a^.read ⟨j, push_back_idx h₁ h₂⟩}
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lemma pop_back_idx {j n} : j < n → j < n + 1 :=
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λ h, nat.lt.step h
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def pop_back (a : array α (n+1)) : array α n :=
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{data := λ ⟨j, h⟩, a^.read ⟨j, pop_back_idx h⟩}
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lemma foreach_lt {a b c : nat} : a + c < b → a < b :=
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λ h, lt_of_le_of_lt (nat.le_add_right a c) h
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def foreach_aux (f : fin n → α → α) : Π (i : nat), i < n → array α n → array α n
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| 0 h a :=
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let z : fin n := ⟨0, h⟩ in
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a^.write z (f z (a^.read z))
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| (j+1) h a :=
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let i : fin n := ⟨j+1, h⟩ in
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have h' : j < n, from foreach_lt h,
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foreach_aux j h' (a^.write i (f i (a^.read i)))
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def foreach : Π {n}, array α n → (fin n → α → α) → array α n
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| 0 a f:= a
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| (n+1) a f := foreach_aux f n (nat.lt_succ_self _) a
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def map {α} {n} (f : α → α) (a : array α n) : array α n :=
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foreach a (λ _, f)
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def map₂ {α} {n} (f : α → α → α) (a b : array α n) : array α n :=
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foreach b (λ i, f (a^.read i))
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lemma fold_lt₁ {n} : n > 0 → n - 1 < n :=
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assume h,
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have h₁ : 1 > 0, from dec_trivial,
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nat.sub_lt h h₁
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lemma fold_lt₂ {n i} : i + 1 < n → n - 2 - i < n :=
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assume h,
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have h₁ : 2 > 0, from dec_trivial,
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have h₂ : n > 0, from lt.trans (nat.zero_lt_succ i) h,
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have h₃ : n - 2 < n, from nat.sub_lt h₂ h₁,
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have h₄ : n - 2 - i ≤ n - 2, from nat.sub_le _ _,
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lt_of_le_of_lt h₄ h₃
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def fold_aux (f : α → β → β) : Π (i : nat), i < n → array α n → β → β
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| 0 h a b := f (a^.read ⟨n - 1, fold_lt₁ h⟩) b
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| (i+1) h a b := fold_aux i (foreach_lt h) a (f (a^.read ⟨n - 2 - i, fold_lt₂ h⟩) b)
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def fold : Π {n}, array α n → β → (α → β → β) → β
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| 0 a b fn := b
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| (n+1) a b fn := fold_aux fn n (nat.lt_succ_self _) a b
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protected def to_string [has_to_string α] (a : array α n) : string :=
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let p : string × bool := a^.fold ("", tt) (λ v ⟨r, first⟩, (r ++ if first then to_string v else ", " ++ to_string v, ff))
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in "[" ++ p.1 ++ "]"
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instance [has_to_string α] : has_to_string (array α n) :=
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⟨array.to_string⟩
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end array
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