[Haskell-cafe] Re: instance Eq (a -> b)

[Ashley Yakeley]

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

   instance (Finite a,Eq a) => Traversable (a -> b) where
      sequenceA afb = fmap lookup
        (sequenceA (fmap (\a -> fmap (b -> (a,b)) (afb a)) allValues))
       where
        lookup :: [(a,b)] -> a -> b
        lookup (a,b):_ a' | a == a' = b
        lookup _:r a' = lookup r a'
        lookup [] _ = undefined

   instance Finite () where
     allValues = [()]

   data Nothing

   instance Finite Nothing where
     allValues = []

-- 
Ashley Yakeley