[Haskell-cafe] Type families again

[Antoine Latter]

On Thu, Dec 2, 2010 at 3:29 PM, Andrew Coppin
<andrewcoppin at btinternet.com> wrote:
> Yes, it's me. And yes, I come with yet more questions.
>
> With Haskell 98 (or, indeed, Haskell 2010) it is impossible to define a
> polymorphic version of "head" that works for [], Set and ByteString. You can
> use a higher-kinded type class for [], but that fails for Set (because you
> can't specify the Ord constraint) and fails spectacularly for ByteString
> (because it has the wrong kind). The basic problem is that the function's
> type needs to refer to the type of the container and the type of elements it
> contains, but the relationship between these types can be arbitrary.
>
> Type families allow you to neatly and cleanly fix the problem:
>
>  class Head c where
>    type Element c :: *
>    head :: c -> Element c
>
> It's simple, comprehensible, and it /actually works/.
>
> Following this success, we can define functions such as tail, join, and so
> forth.
>
> What we /can't/ do is define a polymorphic map function. One might try to do
> something like
>
>  class Functor f where
>    type Element f :: *
>    fmap :: (Element f2 ~ y) => (x -> y) -> f -> f2
>
>  instance Functor [x] where
>    type Element [x] = x
>    fmap = map
>
> However, this fails. Put simply, the type for fmap fails to specify that f
> and f2 must be /the same type of thing/, just with different element types.
>
> The trouble is, after spending quite a bit of brainpower, I literally cannot
> think of a way of writing such a constraint. Does anybody have any
> suggestions?
>

Does this do what you need?

http://hackage.haskell.org/packages/archive/rmonad/0.6/doc/html/Control-RMonad.html#t:RFunctor

Antoine

>
>
> Second, what's the difference between using "type", "newtype" and "data" in
> a class definition?
>
>
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>