On Thu, Dec 2, 2010 at 3:29 PM, Andrew Coppin
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-RMon... Antoine
Second, what's the difference between using "type", "newtype" and "data" in a class definition?
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