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.
65 lines
2.2 KiB
Text
65 lines
2.2 KiB
Text
universe u
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def f1 (n m : Nat) (x : Fin n) (h : n = m) : Fin m :=
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h ▸ x
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def f2 (n m : Nat) (x : Fin n) (h : m = n) : Fin m :=
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h ▸ x
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theorem ex1 {α : Sort u} {a b c : α} (h₁ : a = b) (h₂ : b = c) : a = c :=
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h₂ ▸ h₁
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theorem ex2 {α : Sort u} {a b : α} (h : a = b) : b = a :=
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h ▸ rfl
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theorem ex3 {α : Sort u} {a b c : α} (r : α → α → Prop) (h₁ : r a b) (h₂ : b = c) : r a c :=
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h₂ ▸ h₁
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theorem ex3b {α : Sort u} {a b c : α} (r : α → α → Prop) (h₁ : r a b) (h₂ : b = c) : r a c :=
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h₂.symm ▸ h₁
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theorem ex3c {α : Sort u} {a b c : α} (r : α → α → Prop) (h₁ : r a b) (h₂ : b = c) : r a c :=
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h₂.symm.symm ▸ h₁
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theorem ex4 {α : Sort u} {a b c : α} (r : α → α → Prop) (h₁ : a = b) (h₂ : r b c) : r a c :=
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h₁ ▸ h₂
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theorem ex5 {p : Prop} (h : p = True) : p :=
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h ▸ trivial
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theorem ex6 {p : Prop} (h : p = False) : ¬p :=
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fun hp => h ▸ hp
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theorem ex7 {α} {a b c d : α} (h₁ : a = c) (h₂ : b = d) (h₃ : c ≠ d) : a ≠ b :=
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h₁ ▸ h₂ ▸ h₃
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theorem ex8 (n m k : Nat) (h : Nat.succ n + m = Nat.succ n + k) : Nat.succ (n + m) = Nat.succ (n + k) :=
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Nat.succ_add .. ▸ Nat.succ_add .. ▸ h
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theorem ex9 (a b : Nat) (h₁ : a = a + b) (h₂ : a = b) : a = b + a :=
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h₂ ▸ h₁
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theorem ex10 (a b : Nat) (h : a = b) : b = a :=
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h ▸ rfl
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def ex11 {α : Type u} {n : Nat} (a : Array α) (i : Nat) (h₁ : a.size = n) (h₂ : i < n) : α :=
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a[i]
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theorem ex12 {α : Type u} {n : Nat}
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(a b : Array α)
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(hsz₁ : a.size = n) (hsz₂ : b.size = n)
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(h : ∀ (i : Nat) (hi : i < n), a.getLit i hsz₁ hi = b.getLit i hsz₂ hi) : a = b :=
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Array.ext (hsz₁.trans hsz₂.symm) fun i hi₁ hi₂ => h i (hsz₁ ▸ hi₁)
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def toArrayLit {α : Type u} (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
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List.toArray $ Array.toListLitAux a n hsz n (hsz ▸ Nat.le_refl _) []
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partial def isEqvAux {α} (a b : Array α) (hsz : a.size = b.size) (p : α → α → Bool) (i : Nat) : Bool :=
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if h : i < a.size then
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let aidx : Fin a.size := ⟨i, h⟩
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let bidx : Fin b.size := ⟨i, hsz ▸ h⟩
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match p a[aidx] b[bidx] with
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| true => isEqvAux a b hsz p (i+1)
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| false => false
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else
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true
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