Question

here is my ADT:

data Tree a = Val Integer
            |Tree a
            |Variable a

I have two questions:

Question 1: use Tree String type to represent some trees?

Question 2: define a function for converting a tree, an element of the datatype Tree String to string: showTree::Tree String -> String

Answer 1

With respect to your second question, coverting a tree into a string, just derive Show and use the show function:

data Tree a = Val Integer
            | Tree a
            | Variable a
    deriving (Eq, Ord, Show)

showTree :: (Show a) => Tree a -> String
showTree = show

I don’t understand your first question, so I’m just going to talk a bit in hopes that something I say helps you.

Understand that your “tree” data type is not really a tree at all, it’s just a sum data type that can be instantiated by an integer or some type that matches the type variable, a. The second constructor, Tree, is actually not making your data type recursive – its just a constructor name in the same way Variable is a constructor name. I think you probably wanted to have subtrees (by using Tree as a type, not a constructor) – so let’s define your type as:

data Tree a = Val Integer
            | Branch (Tree a) (Tree a)
            | Variable a

Now you have a constructor named Branch that has a left and a right sub-tree. If your variables are supposed to be Strings then you certainly can use Tree String to represent this:

myTree :: Tree String
myTree =
    let leftBranch = Variable "x"
        rightBranch = Branch (Val 3) (Variable "y")
    in Branch leftBranch rightBranch