647a5e9492
This modification improves the performance of the example in issue #4861. It no longer times out but is still expensive. Here is the analysis of the performance issue: Given `(x : Int)`, to elaborate `x ^ 1`, a few default instances have to be tried. First, the homogeneous instance is tried and fails since `Int` does not implement `Pow Int`. Then, the `NatPow` instance is tried, and it also fails. The same process is performed for each term of the form `p ^ 1`. There are seveal of them at #4861. After all of these fail, the lower priority default instance for numerals is tried, and `x ^ 1` becomes `x ^ (1 : Nat)`. Then, `HPow Int Nat Int` can be applied, and the elaboration succeeds. However, this process has to be repeated for every single term of the form `p ^ 1`. The elaborator tries all homogeneous `HPow` and `NatPow` instances for all `p ^ 1` terms before trying the lower priority default instance `OfNat`. This commit ensures `Int` has a `NatPow` instance instead of `HPow Int Nat Int`. This change shortcuts the process, but it still first tries the homogeneous `HPow` instance, fails, and then tries `NatPow`. The elaboration can be made much more efficient by writing `p ^ (1 : Nat)`.
55 lines
2.4 KiB
Text
55 lines
2.4 KiB
Text
set_option maxHeartbeats 210000 in
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theorem foo (x y z p q : Int) : False :=
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have : (1 * x ^ 1 + z ^ 1 * p) *
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(1 / 1 * p ^ 1 * x ^ 1 + 1 * q * p ^ 1 * x * z + 1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * x ^ 1 -
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1 * q ^ 1 * p * y ^ 1) +
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z * (1 * y) *
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(-(1 / 1 * p ^ 1 * x * y) + 1 * q * p ^ 1 * z * y - 1 * q ^ 1 * p ^ 1 * x * y +
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1 * q ^ 1 * p ^ 1 * z * y -
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1 * q ^ 1 * p ^ 1 * x * y +
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1 * q ^ 1 * p ^ 1 * z * y -
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1 * q ^ 1 * p ^ 1 * x * y +
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1 / 1 * q ^ 1 * p ^ 1 * z * y) +
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(-y ^ 1 + p * x * (1 * z) + q * (1 * z ^ 1)) *
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(-(1 / 1 * p ^ 1 * x * z) - 1 * q * p ^ 1 * x ^ 1 - 1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * x ^ 1 -
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * x ^ 1 -
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p * x ^ 1) =
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1 *
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(1 / 1 * p ^ 1 * x ^ 1 + 1 * q * p ^ 1 * x * z + 1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * p ^ 1 * x ^ 1 +
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * y ^ 1 +
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1 * q ^ 1 * x ^ 1 -
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1 * q ^ 1 * p * y ^ 1) +
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1 *
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(-(1 / 1 * p ^ 1 * x * y) + 1 * q * p ^ 1 * z * y - 1 * q ^ 1 * p ^ 1 * x * y +
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1 * q ^ 1 * p ^ 1 * z * y -
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1 * q ^ 1 * p ^ 1 * x * y +
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1 * q ^ 1 * p ^ 1 * z * y -
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1 * q ^ 1 * p ^ 1 * x * y +
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1 / 1 * q ^ 1 * p ^ 1 * z * y) +
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1 *
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(-(1 / 1 * p ^ 1 * x * z) - 1 * q * p ^ 1 * x ^ 1 - 1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * x ^ 1 -
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p ^ 1 * x ^ 1 -
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1 * q ^ 1 * p ^ 1 * x * z -
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1 * q ^ 1 * p * x ^ 1) := sorry
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sorry
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