08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
36 lines
1.1 KiB
Text
36 lines
1.1 KiB
Text
namespace Nat
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def ascFactorial (n : Nat) : Nat → Nat
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| 0 => 1
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| k + 1 => (n + k) * ascFactorial n k
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def descFactorial (n : Nat) : Nat → Nat
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| 0 => 1
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| k + 1 => (n - k) * descFactorial n k
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theorem descFactorial_of_lt {n : Nat} : ∀ {k : Nat}, n < k → n.descFactorial k = 0 := by sorry
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theorem add_descFactorial_eq_ascFactorial' (n : Nat) :
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∀ k : Nat, (n + k - 1).descFactorial k = n.ascFactorial k := by sorry
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def ascFactorialBinary (n k : Nat) : Nat :=
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match k with
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| 0 => 1
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| 1 => n
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| k@(_ + 2) => ascFactorialBinary n (k / 2) * ascFactorialBinary (n + k / 2) ((k + 1) / 2)
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theorem ascFactorial_eq_ascFactorialBinary : ascFactorial = ascFactorialBinary := sorry
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def descFactorialBinary (n k : Nat) : Nat :=
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if n < k then 0
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else ascFactorialBinary (n - k + 1) k
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theorem descFactorial_eq_descFactorialBinary : descFactorial = descFactorialBinary := by
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ext n k
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rw [descFactorialBinary]
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split <;> rename_i h
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· rw [descFactorial_of_lt h]
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· rw [← ascFactorial_eq_ascFactorialBinary, ← add_descFactorial_eq_ascFactorial']
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grind
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end Nat
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