Introduction/Direct Translation

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import Control.Monad (when)
import Control.Monad.ST
import Data.Array.ST
import Data.Array.IArray
import Data.Array.MArray
import System.IO.Unsafe

qsort :: (IArray a e,Ix i,Enum i,Ord e) => a i e -> a i e
qsort arr = processArray quickSort arr

    :: (IArray a e,IArray b e,Ix i) 
    => (forall s. (STArray s) i e -> ST s ()) -> a i e -> b i e
processArray f (arr :: a i e) = runST (do
                arr' <- thaw arr :: ST s (STArray s i e)
                f arr'
                unsafeFreeze arr')

quickSort :: (MArray a e m, Ix i, Enum i, Ord e) => a i e -> m ()
quickSort arr = case bounds arr of (lo,hi) -> qsort lo hi
    where qsort lo hi | lo >= hi  = return ()
                      | otherwise = do
              p <- readArray arr hi
              l <- mainLoop p lo hi
              swap l hi
              qsort lo (pred l)
              qsort (succ l) hi
          mainLoop p l h | l >= h    = return l
                         | otherwise = do
              l' <- doTil (\l' b -> l' < h && b <= p) succ l                  
              h' <- doTil (\h' b -> h' > l' && b >= p) pred h
              when (l' < h') $
                  swap l' h'
              mainLoop p l' h'
          doTil pred op ix = do
              b <- readArray arr ix
              if pred ix b then doTil pred op (op ix) else return ix

          swap xi yi = do
              x <- readArray arr xi
              readArray arr yi >>= writeArray arr xi
              writeArray arr yi x

This uses various extensions to make the types ridiculously general, but the actual algorithm (quickSort) is plain Haskell.