Haskell - how to count elements in nested list

Question

Lets say I have nested lsit: [1, [2, 3, 4], [5, [6]]] and I want to count how many elements it has. In this case it is six elements. I have written such code for doing this:

totalElems :: [a] -> Int
totalElems (x:xs) = case (x, xs) of
                    (_, []) -> 0
                    (y:ys, _) -> 1 + totalElems ys + totalElems xs
                    (_, _) -> 1 + totalElems xs

But I've got an error:

a.hs:4:42:
    Couldn't match expected type ‘a’ with actual type ‘[a0]’
      ‘a’ is a rigid type variable bound by
          the type signature for totalElems :: [a] -> Int at a.hs:1:15
    Relevant bindings include
      xs :: [a] (bound at a.hs:2:15)
      x :: a (bound at a.hs:2:13)
      totalElems :: [a] -> Int (bound at a.hs:2:1)
    In the pattern: y : ys
    In the pattern: (y : ys, _)
    In a case alternative:
        (y : ys, _) -> 1 + totalElems ys + totalElems xs

How I can do this in Haskell?

Answer 1

You can't make freeform lists-within-lists like that in Haskell. Dynamically typed langues will tolerate silliness like that, but strongly-typed Haskell won't.

1 is of type Int, and [2,3,4] is of a different type [Int]. Things in a list have to be of the same type.

However, you could do something like this:

data Nest a = Elem a | List [Nest a]

example ::Nest Int
example = List [Elem 1, List [Elem 2, Elem 3, Elem 4], List [Elem 5, List [Elem 6]]]

countNest :: Nest a -> Int
countNest (Elem x) = 1
countNest (List xs) = sum $ map countNest xs

Answer 2

Let's say I have nested lsit: [1, [2, 3, 4], [5, [6]]]

You can't have that list. It won't type-check. Try typing it by itself in GHCi; it'll just spit an error message at you. Since this input can't exist in the first place, trying to write a function to process it is a doomed endeavor.

Instead, you need to define a custom data type for this. See the other answers.