# Difference between revisions of "Haskell a la carte"

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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.

## 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.
  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 $f(x)=x\cdot x$ 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 $f:\mathbb{Z}\to\mathbb{Z},\ f(x)=x\cdot x$. 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.
  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.
  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).

## 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 f . g is good old function composition $f \circ g$: first apply g, then apply f. Use it for squaring something twice.