9a24db4e86
This commit also improves the `▸` notation a bit. It now tries `subst` (if applicable) before failing.
39 lines
1.6 KiB
Text
39 lines
1.6 KiB
Text
namespace Ex1
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variable (a : Nat) (i : Fin a) (h : 1 = a)
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example : i < a := h ▸ i.2 -- `▸` uses `subst` here
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end Ex1
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namespace Ex2
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def heapifyDown' (a : Array α) (i : Fin a.size) : Array α := sorry
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def heapifyDown (a : Array α) (i : Fin a.size) : Array α :=
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heapifyDown' a ⟨i.1, a.size_swap i i ▸ i.2⟩ -- Error, failed to compute motive, `subst` is not applicable here
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end Ex2
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namespace Ex3
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def heapifyDown (a : Array α) (i : Fin a.size) : Array α :=
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have : i < i := sorry
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heapifyDown a ⟨i.1, a.size_swap i i ▸ i.2⟩ -- Error, failed to compute motive, `subst` is not applicable here
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termination_by measure fun ⟨_, a, i⟩ => i.1
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decreasing_by assumption
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end Ex3
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namespace Ex4
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def heapifyDown (lt : α → α → Bool) (a : Array α) (i : Fin a.size) : Array α :=
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let left := 2 * i.1 + 1
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let right := left + 1
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have left_le : i ≤ left := sorry
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have right_le : i ≤ right := sorry
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have i_le : i ≤ i := Nat.le_refl _
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have j : {j : Fin a.size // i ≤ j} := if h : left < a.size then
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if lt (a.get i) (a.get ⟨left, h⟩) then ⟨⟨left, h⟩, left_le⟩ else ⟨i, i_le⟩ else ⟨i, i_le⟩
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have j := if h : right < a.size then
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if lt (a.get j) (a.get ⟨right, h⟩) then ⟨⟨right, h⟩, right_le⟩ else j else j
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if h : i ≠ j then
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let a' := a.swap i j
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have : a'.size - j < a.size - i := sorry
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heapifyDown lt a' ⟨j.1.1, a.size_swap i j ▸ j.1.2⟩ -- Error, failed to compute motive, `subst` is not applicable here
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else
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a
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termination_by measure fun ⟨_, _, a, i⟩ => a.size - i.1
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decreasing_by assumption
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end Ex4
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