# Haskell a la carte

### From HaskellWiki

(Difference between revisions)

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− | [[ | + | [[Category:Tutorials]] |

+ | |||

+ | 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 == | == Apéritifs == | ||

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qsort :: Ord a => [a] -> [a] | qsort :: Ord a => [a] -> [a] | ||

qsort [] = [] | qsort [] = [] | ||

− | 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> | ||

::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 == | ||

− | How to | + | How to start eating? |

* | * | ||

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square x = x*x | square x = x*x | ||

</haskell> | </haskell> | ||

− | ::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 | + | ::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? |

+ | |||

+ | * | ||

+ | <haskell> | ||

+ | square :: Integer -> Integer | ||

+ | square x = x*x | ||

+ | </haskell> | ||

+ | :: 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. | ||

+ | |||

+ | * | ||

+ | <haskell> | ||

+ | square :: Num a => a -> a | ||

+ | square x = x*x | ||

+ | </haskell> | ||

+ | :: 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. | ||

+ | |||

+ | * | ||

+ | <haskell> | ||

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

+ | </haskell> | ||

+ | :: The average of two numbers. Multiple arguments are separated by spaces. | ||

+ | |||

+ | * | ||

+ | <haskell> | ||

+ | average :: Double -> Double -> Double | ||

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

+ | </haskell> | ||

+ | ::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>). | ||

+ | |||

+ | == Potages == | ||

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

+ | |||

+ | * | ||

+ | <haskell> | ||

+ | (.) :: (b -> c) -> (a -> b) -> (a -> c) | ||

+ | (.) f g x = f (g x) | ||

+ | |||

+ | fourthPower = square . square | ||

+ | </haskell> | ||

+ | ::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 13:44, 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