Haskell a la carte: Difference between revisions
m (→Potages) |
|||
Line 28: | Line 28: | ||
== Entrées == | == Entrées == | ||
How to | How to read the dishes. | ||
* | * | ||
Line 34: | Line 34: | ||
square x = x*x | square x = x*x | ||
</haskell> | </haskell> | ||
:: | ::is 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? | ||
* | * | ||
Line 62: | Line 62: | ||
</haskell> | </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>). | ::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>). | ||
* | |||
<haskell> | |||
power a n = if n == 0 then 1 else a * power a (n-1) | |||
</haskell> | |||
::<math>a^n</math>, defined with ''recursion''. Assumes that the exponent <hask>n</hask> is not negative, that is <hask>n >= 0</hask>. | |||
:: Recursion is the basic building block for iteration in Haskell, there are no <code>for</code> or <code>while</code>-loops. Well, there are ordinary functions like <hask>map</hask> or <hask>foldr</hask> that provide something similar. There is no need for special built-in control structures, you can define them yourself as ordinary functions (later). | |||
* | |||
<haskell> | |||
power a 0 = 1 | |||
power a n = a * power a (n-1) | |||
</haskell> | |||
::Exponentiation again, this time with ''pattern matching''. The first equation that matches will be chosen. | |||
== Potages == | == Potages == |
Revision as of 16:30, 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.
linecount = interact $ show . length . lines
wordcount = interact $ show . length . words
- Count the number of lines or words from standard input.
Entrées
How to read the dishes.
square x = x*x
- is 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 tosquare 4 + 2
which is 16+2=18.
- 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 :: 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 forsquare
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 currying. In fact,
power a n = if n == 0 then 1 else a * power a (n-1)
- , defined with recursion. Assumes that the exponent
n
is not negative, that isn >= 0
. - Recursion is the basic building block for iteration in Haskell, there are no
for
orwhile
-loops. Well, there are ordinary functions likemap
orfoldr
that provide something similar. There is no need for special built-in control structures, you can define them yourself as ordinary functions (later).
- , defined with recursion. Assumes that the exponent
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.
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