Hi Cafe,
I was playing with the classic example of a Foldable structure: Trees.
So the code you can find both on Haskell Wiki and LYAH is the following:
data Tree a = Empty | Node (Tree a) a (Tree a) deriving (Show, Eq)
instance Foldable Tree where
foldMap f (Node l p r) = foldMap f l `mappend` f p `mappend` foldMap f r
treeSum :: Tree Int -> Int
treeSum = Data.Foldable.foldr (+) 0
What this code does is straighforward. I was struck from the following sentences in LYAH:
Notice that we didn't have to provide the function that takes a value and returns a monoid value.
We receive that function as a parameter to foldMap and all we have to decide is where to apply
that function and how to join up the resulting monoids from it.
This is obvious, so in case of (+) f = Sum, so f 3 = Sum 3 which is a Monoid.
What I was wondering about is how Haskell knows that it has to pass, for example, Sum in case of (+) and Product in case of (*)?
In other term, I'm missing the logical piece of the puzzle which maps the associative binary function passed to fold up to our foldMap declaration.
Thanks for any explanation :)
Cheers,
A.