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.
49 lines
4.1 KiB
Text
49 lines
4.1 KiB
Text
axiom testSorry : α
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def is_smooth {α β} (f : α → β) : Prop := testSorry
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class IsSmooth {α β} (f : α → β) : Prop where
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(proof : is_smooth f)
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instance identity : IsSmooth fun a : α => a := testSorry
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instance const (b : β) : IsSmooth fun a : α => b := testSorry
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instance swap (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := testSorry
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instance parm (f : α → β → γ) [IsSmooth f] (b : β) : IsSmooth (λ a => f a b) := testSorry
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instance comp (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (fun a => f (g a)) := testSorry
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instance diag (f : β → δ → γ) (g : α → β) (h : α → δ) [IsSmooth f] [∀ b, IsSmooth (f b)] [IsSmooth g] [IsSmooth h] : IsSmooth (λ a => f (g a) (h a)) := testSorry
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example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (d : δ) : IsSmooth (λ a => f (g a) d) := by infer_instance
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example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => f (g a) d) := by infer_instance
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example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (h : α → α) [IsSmooth h] (d : δ) : IsSmooth (λ a => f (g (h a)) d) := by infer_instance
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example (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := by infer_instance
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example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c b a => f a b c) := by infer_instance
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example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c a b => f a b c) := by infer_instance
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example (f : α → β → γ → δ → ε) [∀ a b c, IsSmooth (f a b c)] : IsSmooth (λ d a b c => f a b c d) := by infer_instance
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example (f : α → β → γ) [IsSmooth f] (b : β) : IsSmooth (λ a => f a b) := by infer_instance
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example (f : α → β → γ → δ) [IsSmooth f] (b : β) (c : γ) : IsSmooth (λ a => f a b c) := by infer_instance
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example (f : α → β → γ → δ) [IsSmooth f] (b : β) : IsSmooth (λ a c => f a b c) := by infer_instance
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example (f : α → β → γ → δ) [IsSmooth f] (c : γ) : IsSmooth (λ a b => f a b c) := by infer_instance
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example (f : α → β → γ → δ) (b : β) [IsSmooth (λ a => f a b)] : IsSmooth (λ a c => f a b c) := by infer_instance
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example (f : α → β → γ) (g : δ → ε → α) (h : δ → ε → β) [IsSmooth f] [∀ a, IsSmooth (f a)] [IsSmooth g] [IsSmooth h] : IsSmooth (λ x y => f (g x y) (h x y)) := by infer_instance
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example (f : β → δ → γ) (g : α → β) [IsSmooth f] [∀ b, IsSmooth (f b)] [IsSmooth g] (a : α): IsSmooth (λ (h : α → δ) => f (g a) (h a)) := by infer_instance
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example (f : β → δ → γ) (h : α → δ) [IsSmooth f] : IsSmooth (λ (g : α → β) a => f (g a) (h a)) := by infer_instance
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example (f : β → δ → γ) [IsSmooth f] (d : δ) : IsSmooth (λ (g : α → β) a => f (g a) d) := by infer_instance
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example (f : β → γ) (g : β → β) [IsSmooth f] [IsSmooth g] : IsSmooth (fun x => f (g (g x))) := by infer_instance
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example (f : α → β → γ) [∀ a, IsSmooth (f a)] : IsSmooth (λ b a => f a b) := by infer_instance
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example (f : α → β → γ → δ) [∀ a b, IsSmooth (f a b)] : IsSmooth (λ c a b => f a b c) := by infer_instance
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example (f : α → β → γ → δ → ε) [∀ a b c, IsSmooth (f a b c)] : IsSmooth (λ d a b c => f a b c d) := by infer_instance
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example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] (d : δ) : IsSmooth (λ a => f (g a) d) := by infer_instance
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example (f : β → δ → γ) [IsSmooth f] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => f (g a) d) := by infer_instance
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example (f : δ → β → γ) [∀ d, IsSmooth (f d)] (g : α → β) [IsSmooth g] : IsSmooth (λ a d => (f d (g a))) := by infer_instance
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-- Recall Function.comp is not reducible anymore
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instance (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (f ∘ g) := by
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delta Function.comp
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infer_instance
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example (f : β → γ) (g : α → β) [IsSmooth f] [IsSmooth g] : IsSmooth (f ∘ g) := by infer_instance
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example (f : β → γ) [IsSmooth f] : IsSmooth λ (g : α → β) => (f ∘ g) := by
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delta Function.comp
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infer_instance
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