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.
35 lines
1.4 KiB
Text
35 lines
1.4 KiB
Text
module
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axiom R : Type
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instance : Lean.Grind.CommRing R := sorry
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axiom cos : R → R
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axiom sin : R → R
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axiom trig_identity : ∀ x, (cos x)^2 + (sin x)^2 = 1
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grind_pattern trig_identity => cos x
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grind_pattern trig_identity => sin x
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-- Whenever `grind` sees `cos` or `sin`, it adds `(cos x)^2 + (sin x)^2 = 1` to the blackboard.
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-- That's a polynomial, so it is sent to the Grobner basis module.
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-- And we can prove equalities modulo that relation!
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example : (cos x + sin x)^2 = 2 * cos x * sin x + 1 := by
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grind
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-- `grind` notices that the two arguments of `f` are equal,
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-- and hence the function applications are too.
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example (f : R → Nat) : f ((cos x + sin x)^2) = f (2 * cos x * sin x + 1) := by
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grind
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-- After that, we can use basic modularity conditions:
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-- this reduces to `4 * x ≠ 2 + x` for some `x : ℕ`
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example (f : R → Nat) : 4 * f ((cos x + sin x)^2) ≠ 2 + f (2 * cos x * sin x + 1) := by
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grind
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-- A bit of case splitting is also fine.
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-- If `max = 3`, then `f _ = 0`, and we're done.
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-- Otherwise, the previous argument applies.
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example (f : R → Nat) : max 3 (4 * f ((cos x + sin x)^2)) ≠ 2 + f (2 * cos x * sin x + 1) := by
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grind
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-- See https://github.com/leanprover-community/mathlib4-nightly-testing/blob/nightly-testing/MathlibTest/grind/trig.lean
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-- for the Mathlib version of this test, using the real `ℝ`, `cos`, `sin`, and `cos_sq_and_sin_sq` declarations.
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