# Haskell a la carte

### From HaskellWiki

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− | [[Categories:Tutorials]] |
+ | [[Category:Tutorials]] |

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+ | 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. |
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== Apéritifs == |
== Apéritifs == |
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qsort :: Ord a => [a] -> [a] |
qsort :: Ord a => [a] -> [a] |
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qsort [] = [] |
qsort [] = [] |
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− | qsort (x:xs) = qsort (filter (<x) xs) ++ [x] ++ qsort (filter (>x) xs)) |
+ | qsort (x:xs) = qsort (filter (<x) xs) ++ [x] ++ qsort (filter (>=x) xs)) |

</haskell> |
</haskell> |
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::Quicksort in three lines (!). Sorts not only integers but anything that can be compared. |
::Quicksort in three lines (!). Sorts not only integers but anything that can be compared. |
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== Entrées == |
== Entrées == |
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− | How to eat? |
+ | How to start eating? |

* |
* |
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square x = x*x |
square x = x*x |
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</haskell> |
</haskell> |
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− | ::The function <math>f(x)=x\cdot x</math> 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 supply arguments all around, so why clutter the notation with unnecessary ballast? |
+ | ::The function <math>f(x)=x\cdot x</math> 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? |

+ | |||

+ | * |
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+ | <haskell> |
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+ | square :: Integer -> Integer |
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+ | square x = x*x |
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+ | </haskell> |
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+ | :: Squaring again, this time with a ''type signature'' which says that squaring maps integers to integers. In mathematics, we'd write <math>f:\mathbb{Z}\to\mathbb{Z},\ f(x)=x\cdot x</math>. 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 <hask>square (4+2)</hask> which is 36 compared to <hask>square 4 + 2</hask> which is 16+2=18. |
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+ | |||

+ | * |
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+ | <haskell> |
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+ | square :: Num a => a -> a |
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+ | square x = x*x |
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+ | </haskell> |
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+ | :: Squaring yet again, this time with a more general type signature. After all, we can square anything (<hask>a</hask>) that looks like a number (<hask>Num a</hask>). By the way, this general type is the one that the compiler will infer for <hask>square</hask> if you omit an explicit signature. |
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+ | |||

+ | * |
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+ | <haskell> |
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+ | average x y = (x+y)/2 |
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+ | </haskell> |
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+ | :: The average of two numbers. Multiple arguments are separated by spaces. |
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+ | |||

+ | * |
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+ | <haskell> |
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+ | average :: Double -> Double -> Double |
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+ | average x y = (x+y)/2 |
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+ | </haskell> |
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+ | ::Average again, this time with a type signature. Looks a bit strange, but that's the spicey ''currying''. In fact, <hask>average</hask> is a function that takes only one argument (<hask>Double</hask>) but returns a function with one argument (<hask>Double -> Double</hask>). |
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+ | |||

+ | == Potages == |
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+ | The best soup is made by combining well-known ingredients. |
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+ | |||

+ | * |
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+ | <haskell> |
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+ | (.) :: (b -> c) -> (a -> b) -> (a -> c) |
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+ | (.) f g x = f (g x) |
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+ | |||

+ | fourthPower = square . square |
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+ | </haskell> |
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+ | ::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. |
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+ | |||

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

## Revision as of 13:44, 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.

## Contents |

## 1 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.

## 2 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 inwhich is 36 compared tosquare (4+2)which is 16+2=18.square 4 + 2

- 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 () that looks like a number (a). By the way, this general type is the one that the compiler will infer forNum aif you omit an explicit signature.square

- 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,is a function that takes only one argument (average) but returns a function with one argument (Double).Double -> Double

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

## 3 Potages

The best soup is made by combining well-known ingredients.

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

- The dot is good old function composition : first apply g, then apply f. Use it for squaring something twice.f . g

- The dot