Algebraic data type

This is a type where we specify the shape of each of the elements.

Tree examples

Suppose we want to represent the following tree:

              5
             / \
            3   7
           / \
          1   4

We may actually use a variety of Haskell data declarations that will handle this.

Binary search tree

In this example, values are stored at each node, with smaller values to the left, greater to the right.

data Stree a = Tip | Node (Stree a) a (Stree a)

and then our example tree would be:

  etree = Node (Node (Node Tip 1 Tip) 3 (Node Tip 4 Tip)) 5 (Node Tip 7 Tip)

To maintain the order, such a tree structure is usually paired with a smart constructor.

Rose tree

Alternatatively, it may be represented in what appears to be a totally different stucture.

data Rose a = Rose a [Rose a]

In this case, the examlple tree would be:

retree = Rose 5 [Rose 3 [Rose 1 [], Rose 4[]], Rose 7 []]

The two representations are almost equivalent, with the exception that the binary search tree Tip is not representable in this Rose type declaration. Also, due to laziness, I believe we could represent infinite trees with the above declaration.