# Difference between revisions of "Haskell a la carte"

From HaskellWiki

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fourthPower = square . square |
fourthPower = square . square |
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</haskell> |
</haskell> |
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− | ::The dot <hask>f . g</hask> is good old function composition <math>f \circ g</math> |
+ | ::The dot <hask>f . g</hask> is good old function composition <math>f \circ g</math>. First apply g, then apply f. Use it for squaring something twice. |

== Plats principaux == |
== Plats principaux == |

## Revision as of 13:46, 14 December 2007

New to Haskell? This menu will give you a first impression. Don't read all the explanations, or you'll be starved before the meal.

## Apéritifs

Foretaste of an excellent meal.

```
qsort :: Ord a => [a] -> [a]
qsort [] = []
qsort (x:xs) = qsort (filter (<x) xs) ++ [x] ++ qsort (filter (>=x) xs))
```

- Quicksort in three lines (!). Sorts not only integers but anything that can be compared.

```
fibs = 1:1:zipWith (+) fibs (tail fibs)
```

- The
*infinite*list of fibonacci numbers. Just don't try to print all of it.

- The

```
linecount = interact $ show . length . lines
wordcount = interact $ show . length . words
```

- Count the number of lines or words from standard input.

## Entrées

How to start eating?

```
square x = x*x
```

- The function which maps a number to its square. While we commonly write parenthesis around function arguments in mathematics and most programming languages, a simple space is enough in Haskell. We're going to apply functions to arguments all around, so why clutter the notation with unnecessary ballast?

```
square :: Integer -> Integer
square x = x*x
```

- Squaring again, this time with a
*type signature*which says that squaring maps integers to integers. In mathematics, we'd write . Every expression in Haskell has a type and the compiler will automatically infer (= figure out) one for you if you're too lazy to write down a type signature yourself. Of course, parenthesis are allowed for grouping, like in`square (4+2)`

which is 36 compared to`square 4 + 2`

which is 16+2=18.

- Squaring again, this time with a

```
square :: Num a => a -> a
square x = x*x
```

- Squaring yet again, this time with a more general type signature. After all, we can square anything (
`a`

) that looks like a number (`Num a`

). By the way, this general type is the one that the compiler will infer for`square`

if you omit an explicit signature.

- Squaring yet again, this time with a more general type signature. After all, we can square anything (

```
average x y = (x+y)/2
```

- The average of two numbers. Multiple arguments are separated by spaces.

```
average :: Double -> Double -> Double
average x y = (x+y)/2
```

- Average again, this time with a type signature. Looks a bit strange, but that's the spicey
*currying*. In fact,`average`

is a function that takes only one argument (`Double`

) but returns a function with one argument (`Double -> Double`

).

- Average again, this time with a type signature. Looks a bit strange, but that's the spicey

## Potages

The best soup is made by combining the available ingredients.

```
(.) :: (b -> c) -> (a -> b) -> (a -> c)
(.) f g x = f (g x)
fourthPower = square . square
```

- The dot
`f . g`

is good old function composition . First apply g, then apply f. Use it for squaring something twice.

- The dot