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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.

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.
  linecount = interact $ show . length . lines
  wordcount = interact $ show . length . words
Count the number of lines or words from standard input.

2 Entrées

How to read the dishes.

  square x = x*x
is 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 :: Int -> Int
  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
).
  power a n = if n == 0 then 1 else a * power a (n-1)
an, defined with recursion. Assumes that the exponent
n
is not negative, that is
n >= 0
.
Recursion is the basic building block for iteration in Haskell, there are no for or while-loops. Well, there are functions like
map
or
foldr
that provide something similar. There is no need for special built-in control structures, you can define them yourself as ordinary functions (later).
  power a 0 = 1
  power a n = a * power a (n-1)
Exponentiation again, this time with pattern matching. The first equation that matches will be chosen.
  length []     = 0
  length (x:xs) = 1 + length xs
Calculate the length of a list. What's a list? Well, a list may either be empty (
[]
) or be an element (
x
) prepended (
:
) to another list (
xs
). Read "
xs
" as the plural of "
x
", that is as "ex-es". It's a list of other such elements
x
, after all.
  length :: [a] -> Int
  length []     = 0
  length (x:xs) = 1 + length xs
Length of a list again, this time with type signature. What type must the elements be of? It doesn't matter, length will work for any such type
a
.
  sum []     = 0
  sum (x:xs) = x + sum xs
Sum all elements in a list. Similar to the previous one.
  average xs = sum xs / (fromIntegral (length xs))
Arithmetic mean.
fromIntegral
converts the integer result of
length
into a decimal number for the division
/
.

3 Soupes

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 f \circ g. First apply g, then apply f. Use it for squaring something twice.

4 Plats principaux

5 Desserts

6 Vins