# Difference between revisions of "Algebraic data type"

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− | 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 | + | 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 an arbitrary and internally varying branching factor (0,1,2, or more). |

==See also== | ==See also== |

## Revision as of 16:45, 19 November 2008

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 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 an arbitrary and internally varying branching factor (0,1,2, or more).