16 lines
826 B
Text
16 lines
826 B
Text
universes u v
|
||
|
||
class Bind2 (m : Type u → Type v) where
|
||
bind : ∀ {α β : Type u}, m α → (α → m β) → m β
|
||
|
||
class Monad2 (m : Type u → Type v) extends Applicative m, Bind2 m : Type (max (u+1) v) where
|
||
map := fun f x => Bind2.bind x (pure ∘ f)
|
||
seq := fun f x => Bind2.bind f fun y => Functor.map y x
|
||
seqLeft := fun x y => Bind2.bind x fun a => Bind2.bind y fun _ => pure a
|
||
seqRight := @fun β x y => Bind2.bind x fun _ => y -- Recall that `@` disables implicit lambda support
|
||
|
||
class Monad3 (m : Type u → Type v) extends Applicative m, Bind2 m : Type (max (u+1) v) where
|
||
map (f x) := Bind2.bind x (pure ∘ f)
|
||
seq (f x) := Bind2.bind f fun y => Functor.map y x
|
||
seqLeft (x y) := Bind2.bind x fun a => Bind2.bind y fun _ => pure a
|
||
seqRight (x y) := Bind2.bind x fun _ => y
|