I have a function
f :: Int -> Int -> Int
and I have a list of arbitrary length but for the sake of the example:
[x1,x2,x3]
I need to apply f to the list such that the resulting list looks like this:
[f x1 x1 + f x1 x2 + f x1 x3 , f x2 x1 + f x2 x2 + f x2 x3 , f x3 x1 + f x3 x2 + f x3 x3]
I know that
map f [x1,x2,x3] will give [f x1, f x2, f x3]
but this doesn't seem like much help here. What's the best way to do it?
You could use a list comprehension, to illustrate try the following expression under ghci,
fun f xs = map sum [[ f x y | y <- xs] | x <- xs]
A solution without list comprehensions:
Use map twice.
map (\x -> sum $ map (f x) xs) xs
You can use applicative functors to do it this way :
import Control.Applicative
let l = ["a", "b", "c"]
(++) <$> l <*> l
That will return ["aa","ab","ac","ba","bb","bc","ca","cb","cc"].
To explain a little bit further, (++) <$> l will map the function (++) on every element of l, thus returning [("a"++), ("b"++), ("c"++)]. Then, using <*> will apply all of these functions to all of the elements of l.
See the documentation about applicative functors for more details. http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Applicative.html