I've started to wrap my head around it, and rather like using it for simple situations in which I can essentially pipe the values from one output to one input. A simple example of a pointfree composition I'm comfortable with would be:
let joinLines = foldr (++) "" . intersperse "\n"
While playing with GHCI today, I wanted to see if I could compose not and (==) to replicate (/=), but I wasn't really able to reason it out. (==) take two inputs, and not takes one. I thought that this might work:
let ne = not . (==)
With the assumption that the single Bool output of (==) would go to not, but it won't compile, citing the following error:
<interactive>:1:16:
Couldn't match expected type `Bool' with actual type `a0 -> Bool'
Expected type: a0 -> Bool
Actual type: a0 -> a0 -> Bool
In the second argument of `(.)', namely `(==)'
In the expression: not . (==)
I wish I could say it meant much to me, but all I'm getting is that maybe the second argument that's passed to (==) is mucking things up for not? Can anybody help me understand a little better the logic behind this composition?
If you start to remove one argument at the time, you get
ne x y = not (x == y)
= (not . (x ==)) y
ne x = not . (x ==)
= not . ((==) x)
= ((not .) . (==)) x
ne = (not .) . (==)
basically, for every argument you need one (.), properly associated.
The type of (==) is Eq a => a -> a -> Bool. So if you write whatever . (==), and pass a value x to that, you get whatever ((==) x), but (==) x is a function a -> Bool (where a is the type of x, and an instance of Eq). So the whatever must accept arguments of function type.