[Haskell] Object-Orientation and Haskell

[Ashley Yakeley]

Here's a simple test for object orientation (for some reasonable 
definition):

  Define a type A such that for any type B you can define

    up :: B -> A
    down :: A -> Maybe B

  such that

    down . up = Just

You can do this quite easily in Java or C++, mutatis mutandis. You can't 
do this in Haskell, I don't think. You can't actually do this in 
O'Haskell either, it seems the O' essentially amounts to syntactic sugar.

You can do a weaker form of this with Haskell's Dynamic, where you only 
have to deal with Bs that are instances of Typeable. But even with that, 
note that Dynamic/Typeable/TypeRep are a bit messy, with instances for 
Typeable defined for a wide range of known types.

An alternative approach would be to identify your "B" within "A" not 
per-B but per-(up,down). This would allow for instance separate 
(up,down) for the same B such that

  down1 . up2 = Nothing
  down2 . up1 = Nothing

Of course this can be done with Dynamic too, by defining dummy types. 
But it's ugly. A better extension is something like extensible 
data-types. This allows a type to be defined as "open", which can later 
be extended by disjoint union. Here's a sample syntax that achieves my 
OO test:

  module P where
  data A = ..

  module Q where
  import P

  A |= MkB B

  up = MkB
  down (MkB b) = Just b
  down _ = Nothing

Actually, it is possible to define Dynamic in this way. Here's a naive 
attempt:

  data Dynamic = ..

  class Typeable' a where
    toDyn :: a -> Dynamic
    fromDynamic :: Dynamic -> Maybe a

  -- for each type...

  Dynamic |= MkBool Bool

  instance Typeable' Bool where
    toDyn = MkBool
    fromDynamic (MkBool b) = Just b
    fromDynamic _ = Nothing

This attempt however doesn't allow easy creation of Typeable1, Typeable2 
etc. A better way is to use type-constructor parameters:

  data Dynamic0 (f :: * -> *) = ..

  data Dynamic1 (g :: (* -> *) -> *) = ..

  type Dynamic = Dynamic0 Identity

  data Type a = MkType

  type TypeRep = Dynamic0 Type

  class Typeable0 a where
    toDyn0 :: f a -> Dynamic0 f
    fromDynamic0 :: Dynamic0 f -> Maybe (f a)

  class Typeable1 p where
    toDyn1 :: g p -> Dynamic1 g
    fromDynamic1 :: Dynamic1 g -> Maybe (g p)

  data Compose p q a = MkCompose (p (q a))
  data Compose1 d0 f p = MkCompose1 (d0 (Compose f p))

  Dynamic0 f |= MkDynamic1 (Dynamic1 (Compose1 Dynamic0 f))
  
  unDynamic1 :: Dynamic0 f -> Maybe (Dynamic1 (Compose1 Dynamic0 f))
  unDynamic1 (MkDynamic1 xx) = Just xx
  unDynamic1 _ = Nothing

  instance (Typeable1 p,Typeable0 a) => Typeable0 (p a)
    -- toDyn0 :: f (p a) -> Dynamic0 f
    toDyn0 = MkDynamic1 . toDyn1 . MkCompose1 . toDyn0 . MkCompose
    -- fromDynamic0 :: Dynamic0 f -> Maybe (f (p a))
    fromDynamic0 dyn = do
      dcdf <- unDynamic1 dyn
      (MkCompose1 dcfp) <- fromDynamic1 dcdf
      (MkCompose fpa) <- fromDynamic0 dcfp
      return fpa

  -- for each type

  Dynamic0 f |= MkInt (f Int)

  instance Typeable0 Int where
     toDyn0 = MkInt
     fromDynamic0 (MkInt fi) = Just fi
     fromDynamic0 _ = Nothing

  Dynamic1 g |= MkMaybe (g Maybe)

  instance Typeable1 Maybe where
     toDyn1 = MkMaybe
     fromDynamic1 (MkMaybe gm) = Just gm
     fromDynamic1 _ = Nothing

I submit that this is "hairy" rather than "ugly", but I suspect the 
Type-Constructors Of Unusual Kind (TCOUKs) get even hairier for 
Typeable2, Typeable3 etc...

-- 
Ashley Yakeley, Seattle WA