On over-engineered example of FizzBuzz in Haskell

FizzBuzz.hs

-- This is an over-engineered example of using the `Either a` monad to implement
-- a FizzBuzz. This exercise was inspired by "The Power of Composition" by Scott
-- Wlaschin (https://youtu.be/WhEkBCWpDas?t=2489).
module FizzBuzz where

main :: IO ()
main = mapM_ printAsFizzBuzz [1..100]
    where printAsFizzBuzz :: Int -> IO ()
          printAsFizzBuzz = putStrLn . fizzBuzz

fizzBuzz :: Int -> String
fizzBuzz i = either id show $ computeFizzBuzz i

-- The key here is to realize that in the Either monad, if the value on the left
-- side of the bind is tagged with the Left data constructor, then
-- evaluation stops; if the value is instead tagged with the Right data
-- constructor, evaluation continues with that value in scope:
-- Left  v >>= _ = Left v
-- Right v >>= f = f v
-- Therefore, if we return a value tagged with Left, the rest of the computation
-- will be short-circuited.
computeFizzBuzz :: Int -> Either String Int
computeFizzBuzz i = handle15 >> handle5 >> handle3 >> notDivisible
    where handle15 = if i `divisibleBy` 15
                     then Left "FizzBuzz"
                     else Right i
          handle5 = if i `divisibleBy` 5
                    then Left "Fizz"
                    else Right i
          handle3 = if i `divisibleBy` 3
                    then Left "Buzz"
                    else Right i
          notDivisible = Left (show i)
          divisibleBy numerator denominator = numerator `mod` denominator == 0