Dot Operator in Haskell: need more explanation

Question

I\'m trying to understand what the dot operator is doing in this Haskell code:

sumEuler = sum . (map euler) . mkList

The entire source code

Answer 1

sum is a function in the Haskell Prelude, not an argument to sumEuler. It has the type

Num a => [a] -> a

The function composition operator . has type

(b -> c) -> (a -> b) -> a -> c

So we have

           euler           ::  Int -> Int
       map                 :: (a   -> b  ) -> [a  ] -> [b  ]
      (map euler)          ::                 [Int] -> [Int]
                    mkList ::          Int -> [Int]
      (map euler) . mkList ::          Int ->          [Int]
sum                        :: Num a =>                 [a  ] -> a
sum . (map euler) . mkList ::          Int ->                   Int

Note that Int is indeed an instance of the Num typeclass.