Implementation of "Kleisli Category" for "Optional" type! (based on the challenge at the end of this article -> http://bartoszmilewski.com/2014/12/23/kleisli-categories/)

klesli_category_for_optional.hs

data Optional a = Invalid | Valid a 
  deriving (Show)

optionalToString :: (Show a) => Optional a -> String
optionalToString Invalid       = "Not Valid"
optionalToString (Valid value) = show value

safeRoot :: Double -> Optional Double
safeRoot x
  | x >= 0    = Valid (sqrt x)
  | otherwise = Invalid

safeReciprocal :: Double -> Optional Double
safeReciprocal 0   = Invalid
safeReciprocal num = Valid (1/num)

(>=>) :: (a -> Optional b) -> (b -> Optional c) -> (a -> Optional c)
f1 >=> f2 = \x ->
  let fstResult = f1 x
  in case fstResult of
    Valid value -> f2 value
    Invalid     -> Invalid

safeRootReciprocal :: Double -> Optional Double
safeRootReciprocal = safeReciprocal >=> safeRoot

main :: IO ()
main = putStrLn $ show $ safeRootReciprocal 0