[Haskell-cafe] [Haskell-Cafe] How to deal with looped references inside instances?

[Daneel Yaitskov]

{-
Hi,

I am trying to translate a Java sample
with looped references below to Haskell.
I've found 2 solutions, but both of them look ugly,
because they require a helper class.
So I am looking for an advice for best practices on working
with looped references in polymorphic types.

interface Engine {
   String showEng();
}

class Car<E extends Engine> {
   int id;
   E eng;

   String show() {
     return "Car with " + eng.showEng();
   }

   int getId() { return id; }
}

class Steam implements Engine {
   Car<Steam> car;
   Stream(Car<Steam> car) { this.car = car; }
   String showEng() {
     return "id " + car.getId();
   }
}

Car<Steam> car = new Car<>();
car.id = 42;
car.eng = new Stream(car);
car.show();

-}

{-# LANGUAGE UndecidableInstances #-} -- Fix2 shortcoming

class Car c where
    getId :: c -> Int

class Engine e where
    showEng :: e -> String

data SteamEng c = SteamEng c

instance (Car c) => Engine (SteamEng c) where
    showEng (SteamEng c) = "id " ++ show (getId c)

{-

First solution is via ShowEng class.
I don't know how to tell type checker
that the type which is got after application of type function
is instantiating Engine class??

  instance (Engine eng) => Show (Car1 eng) where
      show (Car1 _ eng) = "Car1 with " ++ showEng eng

-}


data Car1 eng = Car1 Int (eng (Car1 eng))

class ShowEng f where
    showEng2 :: (Car a) => f a -> String

instance ShowEng SteamEng where
    showEng2 = showEng

{-
A side note. Intuitive alternative for ShowEng which is not working!
showEng2 = showEng means showEng2 gets Engine, but

class HaveEngine f where
    cast :: (Car a) => f a -> f a

instance HaveEngine SteamEng where
    cast = id

...

instance (HaveEngine eng) => Show (Car1 eng) where
    show (Car1 _ eng) = "Car1 with " ++ (showEng (cast eng))

nor

instance (HaveEngine eng) => Show (Car1 eng) where
    show (Car1 _ eng) = "Car1 with " ++ (showEng eng)

-}

instance Car (Car1 e) where
    getId (Car1 id _) = id

instance (ShowEng eng) => Show (Car1 eng) where
    show (Car1 _ eng) = "Car1 with " ++ (showEng2 eng)

c1 = Car1 42 (SteamEng c1)

{-
Second solution is removing argument from engine type parameter.
-}

data Car0 eng = Car0 Int eng

instance Car (Car0 e) where
    getId (Car0 id _) = id

instance (Engine eng) => Show (Car0 eng) where
    show (Car0 _ eng) = "Car0 with " ++ showEng eng


{-
in this case I have to avoid infinite type and introducing
an extra wrapper and instantiating business logic classes for him.

  λ c0 = Car0 42 (SteamEng c0)

  <interactive>:30:6: error:
     • Occurs check: cannot construct the infinite type:
         car ~ Car0 (SteamEng car)
     • In the expression: Car0 (SteamEng c0)
       In an equation for ‘c0’: c0 = Car0 42 (SteamEng c0)
     • Relevant bindings include c0 :: car (bound at <interactive>:30:1)

-}


newtype Fix2 f g = Fix2 (f (g (Fix2 f g)))

instance (Show (f (g (Fix2 f g)))) => Show (Fix2 f g) where
    show (Fix2 a) = show a

{-
  λ c0 = Car0 42 (SteamEng (Fix2 c0))

  <interactive>:62:1: error:
     • No instance for (Car (Fix2 Car0 SteamEng))
         arising from a use of ‘print’
     • In a stmt of an interactive GHCi command: print it
-}

instance (Car (f (g (Fix2 f g)))) => Car (Fix2 f g) where
    getId (Fix2 a) = getId a

c0 = Car0 42 (SteamEng (Fix2 c0))

{-
Thanks,
Daniil
-}