3bd39ed8b6
The performance issue at #4413 is due to our `Fin.sub` definition. ``` def sub : Fin n → Fin n → Fin n | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + (n - b)) % n, mlt h⟩ ``` Thus, the following runs out of stack space ``` example (a : UInt64) : a - 1 = a := rfl ``` at the `isDefEq` test ``` (a.val.val + 18446744073709551615) % 18446744073709551616 =?= a.val.val ``` From the user's perspective, this timeout is unexpected since they are using small numerals, and none of the other `Fin` basic operations (such as `Fin.add` and `Fin.mul`) suffer from this problem. This PR implements an inelegant solution for the performance issue. It redefines `Fin.sub` as ``` def sub : Fin n → Fin n → Fin n | ⟨a, h⟩, ⟨b, _⟩ => ⟨((n - b) + a) % n, mlt h⟩ ``` This approach is unattractive because it relies on the fact that `Nat.add` is defined using recursion on the second argument. The impact on this repo was small, but we want to evaluate the impact on Mathlib. closes #4413
49 lines
1.1 KiB
Text
49 lines
1.1 KiB
Text
structure Note where
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pitch : UInt64
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start : Nat
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def Note.containsNote (n1 n2 : Note) : Prop :=
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n1.start ≤ n2.start
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def Note.lowerSemitone (n : Note) : Note :=
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{ n with pitch := n.pitch - 1 }
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theorem Note.self_containsNote_lowerSemitone_self (n : Note) :
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n.containsNote (Note.lowerSemitone n) := by
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simp [Note.containsNote, Note.lowerSemitone]
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/--
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error: type mismatch
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rfl
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has type
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n = n : Prop
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but is expected to have type
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n = n - 1 : Prop
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-/
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#guard_msgs in
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set_option maxRecDepth 100 in
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set_option maxHeartbeats 100 in
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example (n : UInt64) : n = n - 1 :=
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rfl
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namespace Ex2
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def lowerSemitone := fun (n : Note) => Note.mk (n.1 - 0) n.2
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set_option maxRecDepth 100 in
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theorem Note.self_containsNote_lowerSemitone_self (n : Note) :
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0 ≤ (lowerSemitone n).start :=
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(Nat.zero_le (Note.start n))
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end Ex2
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namespace Ex3
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def lowerSemitone := fun (n : Note) => Note.mk (n.1 + 100) n.2
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set_option maxRecDepth 200 in
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theorem Note.self_containsNote_lowerSemitone_self (n : Note) :
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0 ≤ (lowerSemitone n).start :=
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(Nat.zero_le (Note.start n))
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end Ex3
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