Thomas Tuegel
And since Foldable is a superclass of Traversable, it rules out a good degree of the things we want to be Traversable.
This is a radical position, but I don't think we do want these things to be Traversable or Foldable. Let me explain.
For example, Set is a very good example of something we want to be Foldable. But it can't be made an Alternative.
Foldable implies a notion of structural direction through the associativity of its members. Set is different from the well-behaved Foldables because its notion of direction or order is not structural, i.e. not preserved by operations on Set.
Something we want to traverse often (and fold sometimes) is Map. Map is not something that can be made an Alternative either.
Because it is not Applicative? Yes. For the same reason as Set, though, I do not think it should be Foldable or Traversable. It is convenient, but unsound. Or at least, less-sound. To fold or traverse Set and Map, I think the sound thing to do is to use one of the provided functions to convert them to a type where ordering is reflected structurally.
What about adding unstructural fold/traversal under different names? That way we could have the convenience when we truly don't care about the directionality property, and the benefits of pure folding at the same time. -- с уважениeм / respectfully, Косырев Сергей