Is the Set instance of ix a well-behaved optic?

[marick]

profunctor-lenses has the ix function to produce 0-or-1 (“affine”) Traversals. It’s nice for arrays and maps. I noticed it also has an instance for Set. Fooling around, I saw the following:

     > result = set (ix "foo") unit Set.empty
     > result
     (fromFoldable ("foo" : Nil))

    > preview (ix "foo") result
    Nothing

This is peculiar in several ways:

1. You cannot use (ix “foo”) to insert a new value into a Map:

   > set (ix "foo") "bar" Map.empty
   (fromFoldable [])

   … and yet you can with a Set.

2. I’m not sure what form the set-get optics law should take with ix optics. But you can’t get what you can set, which seems odd. Actually, as far as I can tell, you can’t view or preview anything in a Set:

   > preview (ix "foo") (Set.singleton "foo")
   Nothing
   
   > view (ix "foo") (Set.singleton "foo")
   unit

Is the instance for Set a well-behaved optic? Should it be?