36 lines
1.3 KiB
Text
36 lines
1.3 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: Gabriel Ebner
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-/
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prelude
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import init.data.nat init.data.array.basic init.data.nat.lemmas
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universes u
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variables {α : Type u} {n : nat}
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namespace array
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def slice (a : array α n) (k l : nat) (h₁ : k ≤ l) (h₂ : l ≤ n) : array α (l - k) :=
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⟨ λ ⟨ i, hi ⟩, a.read ⟨ i + k,
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calc i + k < (l - k) + k : add_lt_add_right hi _
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... = l : nat.sub_add_cancel h₁
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... ≤ n : h₂⟩ ⟩
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def take (a : array α n) (m : nat) (h : m ≤ n) : array α m :=
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cast (by simp) $ a.slice 0 m (nat.zero_le _) h
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def drop (a : array α n) (m : nat) (h : m ≤ n) : array α (n-m) :=
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a.slice m n h (le_refl _)
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private lemma sub_sub_cancel (m n : ℕ) (h : m ≤ n) : n - (n - m) = m :=
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calc n - (n - m) = (n - m) + m - (n - m) : by rw nat.sub_add_cancel; assumption
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... = m : nat.add_sub_cancel_left _ _
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def take_right (a : array α n) (m : nat) (h : m ≤ n) : array α m :=
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cast (by simp [*, sub_sub_cancel]) $ a.drop (n - m) (nat.sub_le _ _)
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def reverse (a : array α n) : array α n :=
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⟨ λ ⟨ i, hi ⟩, a.read ⟨ n - (i + 1),
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begin apply nat.sub_lt_of_pos_le, apply nat.zero_lt_succ, assumption end ⟩ ⟩
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end array
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