如何将Monoid r =>光学折叠类型的Const r推广到Contravariant + Applicative？

Question

Starting from this Getter type

type Getter s a = forall r. (a -> Const r a) -> s -> Const r s

we need an additional Monoid constraint to obtain a Fold :

type Fold s a = forall r. Monoid r => (a -> Const r a) -> s -> Const r s

But Fold 's actual and more general type is

type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s

I understand that Contravariant is used to exclude Identity and thus ensure that we can only get the value. But I don't understand how Monoid r corresponds to Applicative ? Sure, Const is also an Applicative but where is the monoid hidden?

Sorry for this confusing question.

Answer 1

The Monoid instance is hidden in the constraint of the Applicative instance for Const r .

Const r is only an instance of Applicative if r is an instance of Monoid :

instance Monoid m => Applicative (Const m) where
   ...