Haskell: Multi-property sort is not generic enough - sorting

Question

I was trying to implement a ranked multi-property sort that works on lists of anything.
import Data.Ord (Ordering, Down (..), comparing)
import Data.List (sortBy)
import Data.Monoid (mconcat)
data Order a = ASC a | DESC a
orderBy :: Ord b => [Order (a -> b)] -> [a] -> [a]
orderBy rankedProperties unsorted =
sortBy rankedCompare unsorted
where
rankedCompare x y =
mconcat $ map
(\property ->
case property of
ASC f -> comparing f x y
DESC f -> comparing (Down . f) x y
) rankedProperties
It works now for tuples and records, however I've discovered a problem. The problem is that the b in orderBy has to be the same. That is consider this:
data Row = Row { shortListed :: Bool, cost :: Float, distance1 :: Int, distance2 :: Int } deriving (Show, Eq)
I want to be able to say: orderBy [ASC shortListed, DESC cost] listofrows.
But the error that comes back is:
<interactive>:1:31:
Couldn't match type ‘Float’ with ‘Bool’
Expected type: Row -> Bool
Actual type: Row -> Float
In the first argument of ‘ASC’, namely ‘cost’
In the expression: ASC cost
I need a way to make the b type generic, as the b only really has to be acceptable by the comparing function comparing :: Ord a => (b -> a) -> b -> b -> Ordering.
I've read a little bit about existential types and heterogenous lists, but I'm not sure how to proceed.

Answer 1

Since we have Monoid Ordering and instance Monoid b => Monoid (a -> b) in Prelude, we also have Monoid (a -> a -> Ordering) by iterating the function instance twice. This lets us solve the issue quite simply, without existentials:
import Data.Ord (Ordering, comparing)
import Data.List (sortBy)
import Data.Monoid ((<>), mconcat)
data Row = Row {
shortListed :: Bool,
cost :: Float,
distance1 :: Int,
distance2 :: Int
} deriving (Show, Eq)
asc, desc :: Ord b => (a -> b) -> a -> a -> Ordering
asc = comparing
desc = flip . asc
list :: [Row]
list = [Row False 0 10 20, Row True 10 30 40]
list' :: [Row]
list' = sortBy (asc shortListed <> desc cost <> asc distance1) list
Alternatively:
orderBy :: [a -> a -> Ordering] -> [a] -> [a]
orderBy = sortBy . mconcat
list'' :: [Row]
list'' = orderBy [asc shortListed, desc cost, asc distance1] list