understanding data type in haskell

Question

I am a haskell new bee. I can't just wrap my head around what is going on here

 data NestedList a=Elem a | List [NestedList a] deriving Show

 append::NestedList a->NestedList a->Either String (NestedList a)
 append (Elem x) (Elem y) = Right $ List [Elem x, Elem y]
 append (_) (Elem _)=Left "Elements are not allowed"
 append (Elem _) (_)=Left "Elements are not allowed"
 append (List a) (List b)=List(a++b)`

it gives me error

Couldn't match expected type Either String (NestedList a)' with actual typeNestedList a' In the return type of a call of List' In the expression: List (a ++ b) In an equation forappend': append (List a) (List b) = List (a ++ b).

But data NestedList a=Elem a | List [NestedList a] doesn't it mean that NestedList is of type Elem or List of NestedList and

 append::NestedList a->NestedList a->Either String (NestedList a)

that append can return either String or NestedList. Now when I do List(a++b) I am returning List. It should work isn't it?

My other function flatten

flatten ::NestedList a->[a]
flatten (Elem x)=[x]
flatten (List(x:xs))=flatten(x)++flatten(List xs)
--flatten NestedList (x:xs)=flatten(x)++flatten(List xs)
flatten(List [])=[]

works fine while its input parameter is also NestedList but ghc is fine with flatten (List(x:xs)) where List(x:xs) is also just List. why doesn't it complain here? Any inputs?

Answer 1

In order to return Either a b, you have to use either Left y or Right x, where y :: a and x :: b. You correctly used Left "...." and Right in all but the last pattern:

data NestedList a=Elem a | List [NestedList a] deriving Show

append::NestedList a->NestedList a->Either String (NestedList a)
append (Elem x) (Elem y) = Right $ List [Elem x, Elem y]
append (_) (Elem _)      = Left  $ "Elements are not allowed"
append (Elem _) (_)      = Left  $ "Elements are not allowed"
append (List a) (List b) = Right $ List(a++b)
--                         ^^^^^