Algebraic data type

(Difference between revisions)

Revision as of 13:09, 25 July 2008

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

Suppose we want to represent the following tree:

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

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.

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 differences between the two are that the (empty) binary search tree

Tip

is not representable as a

Rose

tree, and a Rose tree can have arbitrary an dinternally varying branching factor (0,1,2, or more).

@@ Line 36: / Line 36: @@
 </haskell>
-The two representations are almost equivalent, with the exception that the
+The differences between the two are that the (empty) binary search tree <hask>Tip</hask> is not representable as a <hask>Rose</hask>tree, and a Rose tree can have arbitrary an dinternally varying branching factor (0,1,2, or more).
-binary search tree <hask>Tip</hask> is not representable in this <hask>Rose</hask> type declaration. Also, due to laziness, I believe we could represent infinite trees with the above declaration.
 ==See also==
 *[[Abstract data type]]