Improve tagging

[puffnfresh]

I found this out over the past few weeks:

scala> Monoid[Int].append(Tags.Multiplication(2), Tags.Multiplication(3))
res0: Int = 5

The tags are lost!

This is probably more obvious for seeing what's happening:

scala> val x: Option[Int] @@ Tags.First = Tag(Some(1))
x: scalaz.@@[Option[Int],scalaz.Tags.First] = Some(1)

scala> val y: Option[Int] = x
y: Option[Int] = Some(1)

Tags are a subtype of the type they're tagging 👎

This comes down to how tags are implemented:

type @@[+T, Tag] = T with Tagged[Tag]

But we don't need the T on the right hand side to have unboxed tagging - here's an experiment I tried:

https://gist.github.com/puffnfresh/9377378

Would it be a problem to make tags not be a subtype?

[puffnfresh]

Another I accidentally found:

<puffnfresh> ! Tags.Zip(List(1, 2, 3)) *> Tags.Zip(List(3, 4, 5))
<multibot_>  List[Int] = List(3, 4, 5, 3, 4, 5, 3, 4, 5)

[larsrh]

Your Zip example doesn't compile any more, so I guess this issue is resolved.

[oxbowlakes]

"Tags are a subtype of the type they are tagging"

One advantage of this is that an Array[Double @@ V] can be represented by an Array[Double] - post scalaz 7.1, our code has just fallen off a performance cliff :-(

Here's 7.0:

scala> import scalaz._; import Scalaz._; import Tags._; trait V
import scalaz._
import Scalaz._
import Tags._
defined trait V

scala> new Array[Double @@ V](1)
res0: Array[scalaz.@@[Double,V]] = Array(0.0)

scala> res0.getClass
res1: Class[_ <: Array[scalaz.@@[Double,V]]] = class [D

And here is 7.1

scala> new Array[Double @@ V](1)
res0: Array[scalaz.@@[Double,V]] = Array(null)

scala> res0.getClass
res1: Class[_ <: Array[scalaz.@@[Double,V]]] = class [Ljava.lang.Object;

[larsrh]

Sounds like a case of correctness or performance: pick one. Unfortunately, I have no idea how to safely fix that.