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.
34 lines
1.6 KiB
Text
34 lines
1.6 KiB
Text
class Preorder (α : Type u) extends LE α where
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le_refl (a : α) : a ≤ a
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le_trans {a b c : α} : a ≤ b → b ≤ c → a ≤ c
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instance {α : Type u} {β : α → Type v} [(a : α) → Preorder (β a)] : Preorder ((a : α) → β a) where
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le f g := ∀ a, f a ≤ g a
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le_refl f := fun a => Preorder.le_refl (f a)
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le_trans := fun h₁ h₂ a => Preorder.le_trans (h₁ a) (h₂ a)
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-- In Lean 3, we defined `monotone` using the strict implicit notation `{{ ... }}`.
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-- Implicit lambdas in Lean 4 allow us to use the regular `{...}`
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def Monotone [Preorder α] [Preorder β] (f : α → β) :=
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∀ {a b}, a ≤ b → f a ≤ f b
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theorem monotone_id [Preorder α] : Monotone (α := α) id :=
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fun h => h
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theorem monotone_id' [Preorder α] : Monotone (α := α) id :=
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@fun a b h => h -- `@` disables implicit lambdas
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theorem monotone_id'' [Preorder α] : Monotone (α := α) id :=
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fun {a b} (h : a ≤ b) => h -- `{a b}` disables implicit lambdas
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theorem monotone_const [Preorder α] [Preorder β] (b : β) : Monotone (fun a : α => b) :=
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fun _ => Preorder.le_refl b
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theorem monotone_comp [Preorder α] [Preorder β] [Preorder γ] {g : β → γ} {f : α → β} (m_g : Monotone g) (m_f : Monotone f) : Monotone (g ∘ f) :=
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fun h => m_g (m_f h)
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theorem monotone_fun {α : Type u} {β : Type v} [Preorder α] [Preorder γ] {f : α → β → γ} (m : (b : β) → Monotone (fun a => f a b)) : Monotone f :=
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fun h b => m b h
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theorem ex [Preorder α] {f g h : α → α} (m_h : Monotone h) (m_g : Monotone g) (m_f : Monotone f) : Monotone (h ∘ g ∘ f) :=
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monotone_comp m_h (monotone_comp m_g m_f) -- implicit lambdas in action here
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