e74ba14f4c
@Kha It felt odd that we can write ``` map f x := ... ``` in instances, but we had to write ``` map (f x) := ... ``` when setting the field default value in a class.
22 lines
1.1 KiB
Text
22 lines
1.1 KiB
Text
universes u v
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class Bind2 (m : Type u → Type v) where
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bind : ∀ {α β : Type u}, m α → (α → m β) → m β
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class Monad2 (m : Type u → Type v) extends Applicative m, Bind2 m : Type (max (u+1) v) where
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map := fun f x => Bind2.bind x (pure ∘ f)
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seq := fun f x => Bind2.bind f fun y => Functor.map y x
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seqLeft := fun x y => Bind2.bind x fun a => Bind2.bind y fun _ => pure a
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seqRight := @fun β x y => Bind2.bind x fun _ => y -- Recall that `@` disables implicit lambda support
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class Monad3 (m : Type u → Type v) extends Applicative m, Bind2 m : Type (max (u+1) v) where
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map (f x) := Bind2.bind x (pure ∘ f)
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seq (f x) := Bind2.bind f fun y => Functor.map y x
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seqLeft (x y) := Bind2.bind x fun a => Bind2.bind y fun _ => pure a
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seqRight (x y) := Bind2.bind x fun _ => y
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class Monad4 (m : Type u → Type v) extends Applicative m, Bind2 m : Type (max (u+1) v) where
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map f x := Bind2.bind x (pure ∘ f)
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seq f x := Bind2.bind f fun y => Functor.map y x
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seqLeft x y := Bind2.bind x fun a => Bind2.bind y fun _ => pure a
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seqRight x y := Bind2.bind x fun _ => y
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