Haskell equivalent to Scala's groupBy

Question

Scala has a function groupBy on lists that accepts a function for extracting keys from list items, and returns another list where the items are tuples consisting of

Answer 1

Putting a trace in f reveals that, with @Niklas solution, f is evaluated 3 times for each element on any list of length 2 or more. I took the liberty of modifying it so that f is applied to each element only once. It's not clear however whether the cost of creating and destroying tuples is less than the cost of evaluating f multiple times (since f can be arbitrary).

import Control.Arrow ((&&&))
import Data.List
import Data.Function

myGroupBy' :: (Ord b) => (a -> b) -> [a] -> [(b, [a])]
myGroupBy' f = map (fst . head &&& map snd)
                   . groupBy ((==) `on` fst)
                   . sortBy (compare `on` fst)
                   . map (f &&& id)