14 lines
586 B
Text
14 lines
586 B
Text
def List.bubblesort [LT α] [DecidableRel (. < . : α → α → Prop)] (l : List α) : {l' : List α // l.length = l'.length} :=
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match l with
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| [] => ⟨[], rfl⟩
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| x :: xs =>
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match bubblesort xs with
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| ⟨[], h⟩ => ⟨[x], by simp[h]⟩
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| ⟨y :: ys, h⟩ =>
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if y < x then
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have : Nat.succ (length ys) < Nat.succ (length xs) := by rw [h, List.length_cons]; apply Nat.lt_succ_self
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let ⟨zs, he⟩ := bubblesort (x :: ys)
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⟨y :: zs, by simp[h, ← he]⟩
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else
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⟨x :: y :: ys, by simp[h]⟩
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termination_by _ => l.length
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