Gershom,
Thank you for taking the time to write such a thoughtful response. I appreciate
that you gave concrete examples; I think the discussion will be more meaningful
for it.
On Wed, Feb 24, 2016 at 10:34 PM, Gershom B
This sounds appealing until one realizes that Alternative doesn't just rule out _some_ but _nearly all_ the things we may want to be Foldable. Especially so since Alternative is a subclass of Applicative.
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.
Another example: Maybe is something that _is_ an Alternative.
But it cannot be made Foldable under this set of laws, since it would fail them. In fact, all alternative instances that have a "choice-like" rather than "concat-like" <|> would fail this law. And alternative instances are rare enough as is.
Yes, exactly. I am suggesting we curtail the scope of Foldable severely in order to expand its power vastly. Regards, Tom