Multiple dispatch (double dispatch) in Haskell

multiple_dispatch.hs

main = do
  putStrLn $ show $ add (MyInt 1) (MyInt 3)
    -- MyInt 4
  putStrLn $ show $ add (MyInt 13) (MyString "B")
    -- MyString "13B"
  putStrLn $ show $ add (MyString "B") (MyInt 13)
    -- MyString "B13"
  putStrLn $ show $ add (MyString "a") (MyString "b")
    -- MyString "ab"
  putStrLn $ show $ add' $ IntInt 1 3
    -- MyInt'' 4
  putStrLn $ show $ add' $ IntString 13 "B"
    -- MyString'' "13B"
  putStrLn $ show $ add' $ StringInt "B" 13
    -- MySring'' "B13"
  putStrLn $ show $ add' $ StringString "a" "b"
    -- MyString'' "ab"


-- version 1

data MyObj = MyInt Int | MyString String
  deriving Show

add :: MyObj -> MyObj -> MyObj
add x y =
  case (x, y) of
    (MyInt a, MyInt b) -> MyInt $ a + b
    (MyInt a, MyString b) -> MyString $ show a ++ b
    (MyString a, MyInt b) -> MyString $ a ++ show b
    (MyString a, MyString b) -> MyString $ a ++ b


-- version 2

data MyObj' =
  IntInt Int Int |
  IntString Int String |
  StringInt String Int |
  StringString String String

data MyObj'' = MyInt'' Int | MyString'' String
  deriving Show

add' :: MyObj' -> MyObj''
add' x =
  case x of
    IntInt a b -> MyInt'' $ a + b
    IntString a b -> MyString'' $ show a ++ b
    StringInt a b -> MyString'' $ a ++ show b
    StringString a b -> MyString'' $ a ++ b

multiple_dispatch_via_typeclass.hs

-- version 3
-- inspired by https://stackoverflow.com/a/26305824

{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}

module Main where

main = do
  putStrLn $ show (add (1 :: Integer) (3 :: Integer) :: Integer)
    -- 4
  putStrLn $ show (add (13 :: Integer) ("B" :: String) :: String)
    -- "13B"
  putStrLn $ show (add ("B" :: String) (13 :: Integer)  :: String)
    -- "B13"
  putStrLn $ show (add ("a" :: String) ("b" :: String) :: String)
    -- "ab"

class Adder a b c where
  add :: a -> b -> c

instance Adder Integer Integer Integer where
  add = (+)

instance Adder Integer String String where
  add a b = show a ++ b

instance Adder String Integer String where
  add a b = a ++ show b

instance Adder String String String where
  add a b = a ++ b