On Wed, 14 Apr 2010, Ashley Yakeley wrote:
Joe Fredette wrote:
this is bounded, enumerable, but infinite.
The question is whether there are types like this. If so, we would need a new class:
class Finite a where allValues :: [a]
instance (Finite a,Eq b) => Eq (a -> b) where p == q = fmap p allValues == fmap q allValues
As ski noted on #haskell we probably want to extend this to work on Compact types and not just Finite types instance (Compact a, Eq b) => Eq (a -> b) where ... For example (Int -> Bool) is a perfectly fine Compact set that isn't finite and (Int -> Bool) -> Int has a decidable equality in Haskell (which Oleg claims that everyone knows ;). I don't know off the top of my head what the class member for Compact should be. I'd guess it should have a member search :: (a -> Bool) -> a with the specificaiton that p (search p) = True iff p is True from some a. But I'm not sure if this is correct or not. Maybe someone know knows more than I do can claify what the member of the Compact class should be. http://math.andrej.com/2007/09/28/seemingly-impossible-functional-programs/ -- Russell O'Connor http://r6.ca/ ``All talk about `theft,''' the general counsel of the American Graphophone Company wrote, ``is the merest claptrap, for there exists no property in ideas musical, literary or artistic, except as defined by statute.''