# Factory function

If you need more intelligence from your constructor functions, use a real function instead. Also known as smart constructors.

## Examples

### Expression type

Consider the following data type:

```data Expr = EAdd Expr Expr | EMult Expr Expr | EInt Int | EVar String
```

Keeping an expression in a relatively simplified form can be difficult if it is modified a lot. One simple way is to write replacements for the constructor functions:

```eInt i = EInt i

eAdd (EInt i1) (EInt i2) = eInt (i1+i2)
eAdd (EInt 0)  e2        = e2
eAdd e1        (EInt 0)  = e1

eMult (EInt 0) e2        = eInt 0
{- etc -}
```

Then if you need to construct an expression, use the factory functions:

```derivative :: String -> Expr -> Expr
derivative x (EMult e1 e2)
= eAdd (eMult (derivative x e1) e2) (eMult e1 (derivative x e2))
{- etc -}
```

This is actually a special kind of worker wrapper where the wrapper does more work than the worker.

The factory function idiom is especially useful when you have a data structure with invariants that you need to preserve, such as a binary search tree which needs to stay balanced.

### Red-black trees example

This form of balanced tree is a perfect example of the use of this idiom. The type declaration for a Red-Black tree is:

```data Colour = R | B
deriving (Eq, Show, Ord)

data RBSet a = Empty |
RBTip Colour (RBSet a) a (RBSet a)
deriving Show
```

However, this must satisfy these invariants:

1. The children of a red node are black.
2. There are the same number of black nodes on every path from root to leaf.

To do this, we create a factory function, `balance` that ensures the invariants are met.

```balance :: Colour -> RBSet a -> a -> RBSet a -> RBSet a
balance B (RBTip R (RBTip R a x b) y c) z d
= RBTip R (RBTip B a x b) y (RBTip B c z d)
balance B (RBTip R a x (RBTip R b y c)) z d
= RBTip R (RBTip B a x b) y (RBTip B c z d)
balance B a x (RBTip R (RBTip R b y c) z d)
= RBTip R (RBTip B a x b) y (RBTip B c z d)
balance B a x (RBTip R b y (RBTip R  c z d))
= RBTip R (RBTip B a x b) y (RBTip B c z d)
balance c a x b = RBTip c a x b
```

(See Red-black trees in a functional setting by Chris Okasaki)