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.
72 lines
1.9 KiB
Text
72 lines
1.9 KiB
Text
example (x : α × β) : x = (x.1, x.2) :=
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rfl -- Should work with eta for structures
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example (x : Unit) : x = ⟨⟩ :=
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rfl -- Should work with eta for structures
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structure Equiv (α : Sort u) (β : Sort v) where
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toFun : α → β
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invFun : β → α
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left_inv : ∀ x, invFun (toFun x) = x
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right_inv : ∀ x, toFun (invFun x) = x
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infix:50 "≃" => Equiv
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def Equiv.symm (e : α ≃ β) : β ≃ α :=
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{ toFun := e.invFun
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invFun := e.toFun
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left_inv := e.right_inv
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right_inv := e.left_inv }
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theorem Equiv.symm.symm (e : α ≃ β) : e.symm.symm = e :=
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rfl -- Should work with eta for structures
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structure Bla where
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x : Nat
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def Bla.toNat (b : Bla) : Nat := b.x
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def Nat.toBla (x : Nat) : Bla := { x }
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example (b : Bla) : b.toNat.toBla = b :=
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rfl -- Should work with eta for structures
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example (b : Bla) : b.toNat.toBla = b := by
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cases b
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rfl
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example (x : Unit × α) : x = ((), x.2) := rfl
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example (x : (_ : True ∨ False) ×' α) : x = ⟨Or.inl ⟨⟩, x.2⟩ := rfl
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example (p : α × α → Prop) (h : ∀ x y, p (x, y)) : p z := h z.1 _
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class TopologicalSpace (α : Type)
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structure Homeomorph (α β : Type) [TopologicalSpace α] [TopologicalSpace β] extends Equiv α β where
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continuousToFun : True
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continuousInv : True
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def Homeomorph.symm [TopologicalSpace α] [TopologicalSpace β] (f : Homeomorph α β) : Homeomorph β α where
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toFun := f.invFun
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invFun := f.toFun
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left_inv := sorry
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right_inv := sorry
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continuousToFun := f.continuousInv
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continuousInv := sorry
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example [TopologicalSpace α] [TopologicalSpace β] (f : Homeomorph α β) :
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f.symm.symm = f := rfl -- fails
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def frob : Nat × Nat → Nat × Nat
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| (x, y) => (x + y, 42)
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example (x : Nat × Nat) : (frob x).2 = 42 := rfl
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example (x y : Unit) : x = y := rfl
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opaque f : Nat → Unit
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opaque g : Nat → Unit
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example (x y : Nat) : f x = f y := rfl
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example (x y : Nat) : f x = g y := rfl
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