[Haskell-cafe] do we need types?

[John Meacham]

On Fri, Feb 26, 2010 at 04:23:52PM +0300, Miguel Mitrofanov wrote:
> I'd say we don't really need subclasses. I mean, what's the difference:
>
> class Eq a where (==) :: a -> a -> Bool
> instance Eq a => Eq (Maybe a) where
>   Nothing == Nothing = True
>   Just x == Just y = x == y
>   _ == _ = False
> sort :: Eq a => [a] -> [a]
>
> or
>
> data Eq a = Eq {eq :: a -> a -> Bool}
> eqMaybe :: Eq a -> Eq (Maybe a)
> eqMaybe e = Eq {eq = eqM} where
>   eqM Nothing Nothing = True
>   eqM (Just x) (Just y) = eq e x y
>   eqM _ _ = False
> sort :: Eq a -> [a] -> [a]
>
> Replacing classes with types, we only lose one thing: the compiler won't deduce the right instances for us. I'll trade it for the ability to abstract over them. After all, we CAN deduce the right
> instances by hand, it's just a finite amount of work (not very big, in my experience).

But then we would lose the invarient that there is a unique pairing
between a type and a given class. for instance, you would no longer be
able to implement things like Set and Map,

For instance if you called the two following functions with different
ord arguments, you would suddenly break all the invarients of what 'Set'
means.

insert :: Ord a -> a -> Set a -> Set a
member :: Ord a -> a -> Set a -> Bool

The unique correspondence between types and classes (i.e. no local
instances) is a main _feature_ of type classes. Often when people think
they need local instances, they are just applying type classes when they
should be using a different idiom, such as the one you mention.

        John

-- 
John Meacham - ⑆repetae.net⑆john⑈ - http://notanumber.net/