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.
101 lines
2 KiB
Text
101 lines
2 KiB
Text
def f (x y : Nat) : Nat :=
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match x, y with
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| 0, 0 => 1
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| 0, y => y
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| x+1, 5 => 2 * f x 0
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| x+1, y => 2 * f x y
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/--
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trace: x y : Nat
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h : y ≠ 5
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⊢ ∃ z, 2 * f x y = 2 * z
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-/
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#guard_msgs in
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theorem ex1 (x : Nat) (y : Nat) (h : y ≠ 5) : ∃ z, f (x+1) y = 2 * z := by
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simp [f]
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trace_state
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apply Exists.intro
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rfl
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@[simp] def g (x y : Nat) : Nat :=
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match x, y with
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| 0, 0 => 1
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| 0, y => y
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| x+1, 5 => 2 * g x 0
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| x+1, y => 2 * g x y
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/--
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trace: x y : Nat
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h : y ≠ 5
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⊢ ∃ z, 2 * g x y = 2 * z
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-/
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#guard_msgs in
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theorem ex2 (x : Nat) (y : Nat) (h : y ≠ 5) : ∃ z, g (x+1) y = 2 * z := by
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simp
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trace_state
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apply Exists.intro
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rfl
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/--
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trace: x y : Nat
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h : y = 5 → False
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⊢ ∃ z, 2 * f x y = 2 * z
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-/
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#guard_msgs in
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theorem ex3 (x : Nat) (y : Nat) (h : y = 5 → False) : ∃ z, f (x+1) y = 2 * z := by
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simp [f]
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trace_state
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apply Exists.intro
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rfl
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@[simp] def f2 (x y z : Nat) : Nat :=
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match x, y, z with
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| 0, 0, 0 => 1
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| 0, y, _ => y
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| x+1, 5, 6 => 2 * f2 x 0 1
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| x+1, y, z => 2 * f2 x y z
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#check f2.eq_4
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/--
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trace: x y z : Nat
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h : y = 5 → z = 6 → False
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⊢ ∃ w, 2 * f2 x y z = 2 * w
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-/
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#guard_msgs in
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theorem ex4 (x y z : Nat) (h : y = 5 → z = 6 → False) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2]
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trace_state
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apply Exists.intro
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rfl
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theorem ex5 (x y z : Nat) (h1 : y ≠ 5) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2, h1]
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apply Exists.intro
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rfl
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theorem ex6 (x y z : Nat) (h2 : z ≠ 6) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2, h2]
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apply Exists.intro
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rfl
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@[simp] def f3 (x y z : Nat) : Nat :=
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match x, y, z with
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| 0, 0, 0 => 1
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| 0, y, _ => y
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| x+1, 5, 6 => 4 * f3 x 0 1
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| x+1, 6, 4 => 3 * f3 x 0 1
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| x+1, y, z => 2 * f3 x y z
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#check f3.eq_5
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theorem ex7 (x y z : Nat) (h2 : z ≠ 6) (h3 : y ≠ 6) : ∃ w, f3 (x+1) y z = 2 * w := by
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simp [f3, h2, h3]
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apply Exists.intro
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rfl
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theorem ex8 (x y z : Nat) (h2 : y = 5 → z = 6 → False) (h3 : y = 6 → z = 4 → False) : ∃ w, f3 (x+1) y z = 2 * w := by
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simp [f3]
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apply Exists.intro
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rfl
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