Hi Markus, On 07/06/2011 03:04 PM, Markus Läll wrote:
[...]
import Control.Arrow import Control.Category
type X a b = [a] -> [b]
instance Category X where id = map Prelude.id g . f = g Prelude.. f
instance Arrow X where arr f = map f first f = unzip>>> first f>>> uncurry zip
The problem is that it's not allowed to use partially applied type synonyms. It is however possible to define a type synonym which value is a partially applied type, but I haven't been able to figure out if I could somehow use that fact in defining the X... Is it at all possible, or is a newtype the only way to do it?
You should really use a newtype for that. Allowing partially applied type synonyms would greatly increase the expressiveness of the type language. (too much, actually) In fact, you could write arbitrary type level lambdas, like that:
type Y b a = [a] -> [b]
But now, given instances like this:
instance Category X where ...
instance Category Y where ... -- uh, yeah, does it make sense in this case? Whatever, we *could* have an instance.
, any function of type [a] -> [b] will match both instances. So which instance to choose? We have two solutions: a) The compiler discovers itself that we have overlaps here and complains. This seems hard to me (is it even possible in finite time?). Note that it is easy if type synonyms are always fully applied because the compiler just has to fill in the definition of all the types and can then proceed to compare just the instance *heads*. b) You somehow annotate which instance to choose for each specific case. But that's exactly what newtypes are for! The problem does indeed occur in your example: What is (id :: [a] -> [b]) supposed to be, Prelude.id (as given by the general instance for functions) or map Prelude.id (given by your instance)? -- Steffen