Algebraic data type

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

1 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.

1.1 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.

1.2 Rose tree

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

`data Rose a = Rose a [Rose a]`

In this case, the example 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).