[Haskell-cafe] Functional Dependencies conflicts

[Daniel Fischer]

Am Samstag 17 April 2010 22:01:23 schrieb Limestraël:
> Yes! Sorry, I forgot a bit:
> Binary types are automatically made instances of
> Binarizable/Unbinarizable (that's my line 16):
>
> instance (Binary a) => Binarizable a a where
>   toBinary = id
>
> instance (Binary a, Monad m) => Unbinarizable a a m where
>   fromBinary = return
>

And that is your problem.
The compiler only looks at the context (Binary a) *after* it has chosen an 
instance.
When somewhere in the code it encounters "toBinary x", it looks for an 
instance declaration "instance Binarizable a b where" which matches x's 
type. Since you have "instance Binarizable a a", you have a matching 
instance and that is selected. *Now* the compiler looks at the context and 
barfs if x's type is not an instance of Binary.

>
> To me, the functional dependency in:
> class (Binary b) => Binarizable a b | a -> b
> meant that for each a, there only one type b that can match.

Yes, that's what the functional dependency says.

>
> That's what I want: for every Binary type 'a', the matching Binary is
> also 'a'

And that instance says "for every type 'a', the matching type is also 'a', 
and furthermore, 'a' is an instance of Binary".

Contexts on a class and functional dependencies don't work as one would 
naively expect.

> And for GameObject, the sole matching type is String.
> In other words, GameObject implies String.
> I would have undestood the error if GameObject was also an instance of
> Binary (then the two instances would match), but it's not the case...

The context isn't considered until after matching.

>
> Is my FunDep wrong?

At least, the FunDep plus the generic instance is not what you want.
Probably, what you want can be done with some type wizardry, but I don't 
know how.

Perhaps the following will work:

{-# LANGUAGE OverlappingInstances, TypeFamilies, MultiParamTypeClasses #-}

class Binarizable a where
    type ToBin a
    toBinary :: a -> ToBin a

class (Monad m) => Unbinarizable a m where
    type FromBin a
    fromBinary :: FromBin a -> m a

instance Binarizable GameObject where
    type ToBin GameObject = String
    toBinary g = ...

instance (Binary a) => Binarizable a where
    type ToBin a = a
    toBinary x = x

instance (MonadReader [GameObject] m) => Unbinarizable GameObject m where
    type FromBin GameObject = String
    fromBinary s = ...

instance (Monad m, Binary a) => Unbinarizable a m where
    type FromBin a = a
    fromBinary x = return x

With OverlappingInstances, the most specific match is chosen, so for 
GameObjects, the special instance is selected.

>
> I done this especially because I didn't wanted to declare each type one
> by one instance of Binarizable,
> Haskell type system normally enables me to automatically define a Binary
> as an instance of Binarizable.