# Difference between revisions of "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.