# Difference between revisions of "Factory function"

BrettGiles (talk | contribs) (HaWiki conversion) |
(Added a link to "Red-black trees in a functional setting" and a link to Wikipedia article Red-black_tree) |
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<haskell> |
<haskell> |
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data Expr = EAdd Expr Expr | EMult Expr Expr | EInt Int | EVar String |
data Expr = EAdd Expr Expr | EMult Expr Expr | EInt Int | EVar String |
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− | }}} |
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+ | </haskell> |
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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: |
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: |
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<haskell> |
<haskell> |
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===Red-black trees example=== |
===Red-black trees example=== |
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− | This form of balanced tree is a perfect example of the use of this idiom. The type declaration for a Red-Black tree is: |
+ | This form of balanced tree is a perfect example of the use of this idiom. The type declaration for a [http://en.wikipedia.org/wiki/Red-black_tree Red-Black tree] is: |

<haskell> |
<haskell> |
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balance c a x b = RBTip c a x b |
balance c a x b = RBTip c a x b |
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</haskell> |
</haskell> |
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− | (See Red-black trees in a functional setting by Chris Okasaki) |
+ | (See [http://www.eecs.usma.edu/webs/people/okasaki/jfp99.ps Red-black trees in a functional setting] by Chris Okasaki) |

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

## Latest revision as of 20:29, 5 December 2008

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
eAdd e1 e2 = EAdd e1 e2
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:

- The children of a red node are black.
- 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)