Foldable, Monoid and Monad

Question

Consider the following signature of foldMap

foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

This is very

Answer 1

When a container is Foldable, there is a relationship between foldMap and Applicative (which is a superclass of Monad).

Foldable has a function called traverse_, with signature:

traverse_ :: Applicative f => (a -> f b) -> t a -> f ()

One possible Applicative is Constant. To be an Applicative, it requires the "accumulator" parameter to be a Monoid:

newtype Constant a b = Constant { getConstant :: a } -- no b value at the term level!

Monoid a => Applicative (Constant a)

for example:

gchi> Constant (Sum 1) <*> Constant (Sum 2) :: Constant (Sum Int) whatever
Constant (Sum {getSum = 3})

We can define foldMap in terms of traverse_ and Constant this way:

foldMap' :: (Monoid m, Foldable t) => (a -> m) -> t a -> m
foldMap' f = getConstant . traverse_ (Constant . f)

We use traverse_ to go through the container, accumulating values with Constant, and then we use getConstant to get rid of the newtype.