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.
96 lines
3.1 KiB
Text
96 lines
3.1 KiB
Text
module
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set_option warningAsError false
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set_option grind.debug true
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set_option grind.debug.proofs true
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example (a b : Nat) (f : Nat → Nat) : (h₁ : a = b) → f a = f b := by
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grind
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example (a b : Nat) (f : Nat → Nat) : (h₁ : a = b) → (h₂ : f a ≠ f b) → False := by
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grind
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example (a b : Nat) (f : Nat → Nat) : a = b → f (f a) ≠ f (f b) → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat) : a = b → c = b → f (f a) ≠ f (f c) → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat → Nat) : a = b → c = b → f (f a b) a ≠ f (f c c) c → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat → Nat) : a = b → c = b → f (f a b) a = f (f c c) c := by
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grind
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example (a b c d : Nat) : a = b → b = c → c = d → a = d := by
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grind
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example (a b c d : Nat) : a ≍ b → b = c → c ≍ d → a ≍ d := by
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grind
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example (a b c d : Nat) : a = b → b = c → c ≍ d → a ≍ d := by
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grind
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opaque f {α : Type} : α → α → α := fun a _ => a
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opaque g : Nat → Nat
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example (a b c : Nat) : a = b → g a ≍ g b := by
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grind
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example (a b c : Nat) : a = b → c = b → f (f a b) (g c) = f (f c a) (g b) := by
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grind
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example (a b c d e x y : Nat) : a = b → a = x → b = y → c = d → c = e → c = b → a = e := by
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grind
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namespace Ex1
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opaque f (a b : Nat) : a > b → Nat
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opaque g : Nat → Nat
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example (a₁ a₂ b₁ b₂ c d : Nat)
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(H₁ : a₁ > b₁)
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(H₂ : a₂ > b₂) :
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a₁ = c → a₂ = c →
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b₁ = d → d = b₂ →
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g (g (f a₁ b₁ H₁)) = g (g (f a₂ b₂ H₂)) := by
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grind
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end Ex1
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namespace Ex2
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def f (α : Type) (a : α) : α := a
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example (a : α) (b : β) : (h₁ : α = β) → (h₂ : a ≍ b) → f α a ≍ f β b := by
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grind
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end Ex2
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example (f g : (α : Type) → α → α) (a : α) (b : β) : (h₁ : α = β) → (h₂ : a ≍ b) → (h₃ : f = g) → f α a ≍ g β b := by
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grind
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set_option trace.grind.debug.proof true in
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example (f : {α : Type} → α → Nat → Bool → Nat) (a b : Nat) : f a 0 true = v₁ → f b 0 true = v₂ → a = b → v₁ = v₂ := by
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grind
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set_option trace.grind.debug.proof true in
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example (f : {α : Type} → α → Nat → Bool → Nat) (a b : Nat) : f a b x = v₁ → f a b y = v₂ → x = y → v₁ = v₂ := by
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grind
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set_option trace.grind.debug.proof true in
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theorem ex1 (f : {α : Type} → α → Nat → Bool → Nat) (a b c : Nat) : f a b x = v₁ → f c b y = v₂ → a = c → x = y → v₁ = v₂ := by
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grind
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#print ex1
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example (n1 n2 n3 : Nat) (v1 w1 : Vector Nat n1) (w1' : Vector Nat n3) (v2 w2 : Vector Nat n2) :
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n1 = n3 → v1 = w1 → w1 ≍ w1' → v2 = w2 → v1 ++ v2 ≍ w1' ++ w2 := by
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grind
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example (n1 n2 n3 : Nat) (v1 w1 : Vector Nat n1) (w1' : Vector Nat n3) (v2 w2 : Vector Nat n2) :
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n1 ≍ n3 → v1 = w1 → w1 ≍ w1' → v2 ≍ w2 → v1 ++ v2 ≍ w1' ++ w2 := by
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grind
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theorem ex2 (n1 n2 n3 : Nat) (v1 w1 v : Vector Nat n1) (w1' : Vector Nat n3) (v2 w2 w : Vector Nat n2) :
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n1 ≍ n3 → v1 = w1 → w1 ≍ w1' → v2 ≍ w2 → w1' ++ w2 ≍ v ++ w → v1 ++ v2 ≍ v ++ w := by
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grind
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#print ex2
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