CompOnSnd.hs

import Data.List (minimum)
import Data.Function (on)
import Data.Ratio ((%))

-- return minimum element compared by given function
-- (return value used by compare, too)
-- another implementation (more generic ver.)

newtype CompOnSnd a b = CompOnSnd { fromCompOnSnd :: (a, b) }

-- for implementation, get snd from CompOnSnd
sndFromCompOnSnd = snd . fromCompOnSnd

instance Eq b => Eq (CompOnSnd a b) where
  (==) = (==) `on` sndFromCompOnSnd

instance Ord b => Ord (CompOnSnd a b) where
  compare = compare `on` sndFromCompOnSnd

minimumOn :: (Ord b) => (a -> b) -> [a] -> (a, b)
minimumOn f xs = fromCompOnSnd $ minimum $ [ CompOnSnd (x, f x) | x <- xs ]

main = do
  let xs = [(1, 2), (2, 3), (4, 5)]
  print $ minimumOn (\(a, b) -> a % b) xs

MinimumOn.hs

import Data.List (minimumBy)
import Data.Function (on)
import Data.Ratio ((%))

-- return minimum element compared by given function
-- (return value used by compare, too)
minimumOn :: (Ord b) => (a -> b) -> [a] -> (a, b)
minimumOn f xs = minimumBy (compare `on` snd) $ [(x, f x) | x <- xs]

main = do
  let xs = [(1, 2), (2, 3), (4, 5)]
  print $ minimumOn (\(a, b) -> a % b) xs