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.
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
...