scalaz.Process and Free equiv. using simple structure encoding

proc.scala

sealed trait Free[F[_], A]
case class Return[F[_], A](v: A) extends Free[F, A]
case class Suspend[F[_], A](s: F[Free[F, A]]) extends Free[F, A]

sealed trait ProcessB[T[_], O, B]
case class Emit[T[_], O, B](o: O, next: B) extends ProcessB[T, O, B]
case class Await[T[_], A, O, B](ta: T[A], k: A => B) extends ProcessB[T, O, B]
case class Stop[T[_], O, B] extends ProcessB[T, O, B]

type Process[T[_], O] = Free[({ type F[x] = ProcessB[T,O,x] })#F, O]

Anyway, this makes me rethink about the Iteratee being just a function and the Process being interpreted...
Don't you think an iteratee as a Free becomes interpreted in some way?

Yes, but I see no benefit.

The more I look at Process vs Iteratee, the more I believe one important difference is that Process awaits the result of T[_] whereas the Iteratee uses T[_] to generate next step

That's the key. Process abstracts the way you get an 'A', allowing a lot of reuse (ex: Process1, Tye, Wye). Process also lets its driver (i.e interpreter) decides how it want to deal the result. ex:

• I want to execute that process sequentially
• I want to execute that process in parallel
• I want to do crazy stuff !

Ok I agree with you!
But what can't you do with iteratee from these 3 points? (trying to find the bad arguments :))
you don't really control the source in iteratee, but you can control the output!