Henning Thielemann wrote:
? However 'foldMap' cannot utilize the additional information, namely Position and (Maybe e), respectively. In the first case this is sad, in the second case I consider this bad, since it is too easy to throw away and thus ignore the exception (Maybe e). Some kind of fold is always useful on these structures, but 'foldMap' is too limited.
I'm not sure what you mean, but if you define Traversable in a sensible way, then you can define Foldable with Data.Traversable.foldMapDefault and get a sensible definition.
Even more, consider a data structure like StorableVector which requires certain properties of its elements. StorableVector is intended for Int, Double and other Storable types, but you cannot store (IO Double) values. This example is not practical, because the Storable restriction disallows to define both Traversable and FunctorM instances. However you see, that one cannot even imagine 'sequence' on StorableVector, whereas 'mapM' is possible, yet very inefficient (needs copying the entire vector for each added element).
Sure you can define 'sequence'... because you cannot construct a StorableVector with elements that are not Storable. (You could save this information inside the StorableVector using existentials/GADTs.) Except...
My conclusion is, that FunctorM was better than its reputation, and that Traversable as it is, is not what I need most of the time. What are the experiences of other Traversable users?
that the fundamental complaint is that Traversables must be in Functor which requires to accomodate all types of kind *. On the other hand, as you note, either FunctorM or Traversable instance requires that property as well. (cf. Data.Traversable.fmapDefault, which uses "traverse" to define it) Basically, if you can make a type Traversable by defining (Traversable t) : traverse :: Applicative f => (a -> f b) -> t a -> f (t b) then this is almost always just as easy as defining (FunctorM f) : fmapM :: Monad m => (a -> m b) -> f a -> m (f b) for that type. (note that the type signatures are almost the same, and have almost equal power. Assuming you didn't want to do weird monadic more-complicated-than- Applicative things, that is.) In other words, my experience is that Traversable is more beautiful and no less usable. -Isaac