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
1.8 KiB
Text
49 lines
1.8 KiB
Text
module
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universe v v₁ v₂ u u₁ u₂
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public section
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namespace CategoryTheory
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class Quiver (V : Type u) where
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Hom : V → V → Sort v
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infixr:10 " ⟶ " => Quiver.Hom
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class CategoryStruct (obj : Type u) : Type max u (v + 1) extends Quiver.{v + 1} obj where
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/-- The identity morphism on an object. -/
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id : ∀ X : obj, Hom X X
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/-- Composition of morphisms in a category, written `f ≫ g`. -/
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comp : ∀ {X Y Z : obj}, (X ⟶ Y) → (Y ⟶ Z) → (X ⟶ Z)
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notation "𝟙" => CategoryStruct.id -- type as \b1
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infixr:80 " ≫ " => CategoryStruct.comp -- type as \gg
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class Category (obj : Type u) : Type max u (v + 1) extends CategoryStruct.{v} obj where
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id_comp : ∀ {X Y : obj} (f : X ⟶ Y), 𝟙 X ≫ f = f
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comp_id : ∀ {X Y : obj} (f : X ⟶ Y), f ≫ 𝟙 Y = f
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assoc : ∀ {W X Y Z : obj} (f : W ⟶ X) (g : X ⟶ Y) (h : Y ⟶ Z), (f ≫ g) ≫ h = f ≫ g ≫ h
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structure Prefunctor (V : Type u₁) [Quiver.{v₁} V] (W : Type u₂) [Quiver.{v₂} W] where
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obj : V → W
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map : ∀ {X Y : V}, (X ⟶ Y) → (obj X ⟶ obj Y)
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structure Functor (C : Type u₁) [Category.{v₁} C] (D : Type u₂) [Category.{v₂} D] : Type max v₁ v₂ u₁ u₂
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extends Prefunctor C D where
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map_id : ∀ X : C, map (𝟙 X) = 𝟙 (obj X)
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map_comp : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), map (f ≫ g) = map f ≫ map g
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set_option trace.grind.ematch.pattern true
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/--
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trace: [grind.ematch.pattern] Functor.map_id: [@Prefunctor.map #5 _ #3 _ (@Functor.toPrefunctor _ #4 _ #2 #1) #0 #0 (@CategoryStruct.id _ _ #0)]
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-/
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#guard_msgs in
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grind_pattern Functor.map_id => self.map (𝟙 X)
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/--
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trace: [grind.ematch.pattern] Functor.map_comp: [@Prefunctor.map #9 _ #7 _ (@Functor.toPrefunctor _ #8 _ #6 #5) #4 #2 (@CategoryStruct.comp _ _ #4 #3 #2 #1 #0)]
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-/
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#guard_msgs in
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grind_pattern Functor.map_comp => self.map (f ≫ g)
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