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.
22 lines
851 B
Text
22 lines
851 B
Text
class Semigroup (M : Type u) extends Mul M where
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mul_assoc (a b c : M) : (a * b) * c = a * (b * c)
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export Semigroup (mul_assoc)
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class CommSemigroup (M : Type u) extends Semigroup M where
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mul_comm (a b : M) : a * b = b * a
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export CommSemigroup (mul_comm)
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class Monoid (M : Type u) extends Semigroup M, OfNat M 1 where
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mul_one (m : M) : m * 1 = m
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one_mul (m : M) : 1 * m = m
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class CommMonoid (M : Type u) extends Monoid M, CommSemigroup M
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theorem mul_left_comm {M} [CommSemigroup M] (a b c : M) : a * (b * c) = b * (a * c) := by
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rw [← mul_assoc, mul_comm a b, mul_assoc]
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example {M} [CommMonoid M] (a b c d : M) : a * (b * (c * d)) = (a * c) * (b * d) := by
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simp only [mul_left_comm, mul_comm, mul_assoc]
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example {M} [CommMonoid M] (a b c d : M) : (b * (c * d)) = (c) * (b * d) := by
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simp only [mul_left_comm, mul_comm, mul_assoc]
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