First of all, having a default (zero) value for someProperty makes things a bit easier. In your case, I guess you could choose Must or MustNot, depending on the specifics of your problem.
I'll assume the following definition of T and its default:
sealed trait T
object T {
final val Default: T = Must
}
case object Must extends T
case object MustNot extends T
case object Should extends T
You can have the following implementation for MySet, deferring most operations to its set attribute, and some to its companion object. Also, note that some methods like filter don't use CanBuildFrom, so you have to override newBuilder method for them.
class MySet[A](val someProperty: T, set: Set[A])
extends Set[A] with SetLike[A, MySet[A]] {
def +(elem: A): MySet[A] = new MySet[A](someProperty, set + elem)
def -(elem: A): MySet[A] = new MySet[A](someProperty, set - elem)
def contains(elem: A): Boolean = set contains elem
def iterator: Iterator[A] = set.iterator
override def companion = MySet
override def empty: MySet[A] = MySet.empty[A]
// Required for `filter`, `take`, `drop`, etc. to preserve `someProperty`.
override def newBuilder: mutable.Builder[A, MySet[A]] =
MySet.newBuilder[A](someProperty)
}
As for the companion object MySet, it's possible to extend SetFactory[MySet] or some other base class of collection companion objects. This gives implementations of MySet.empty[A] and MySet.apply[A](as: A*), which create MySet using the default value of someProperty.
object MySet extends SetFactory[MySet] {
// For the builder you can defer to the standard `mutable.SetBuilder`
class MySetBuilder[A](someProperty: T) extends
mutable.SetBuilder[A, MySet[A]](new MySet(someProperty, Set.empty))
def newBuilder[A] = newBuilder[A](T.Default)
// Additional method for creating a builder with a known value of `someProperty`
def newBuilder[A](someProperty: T) = new MySetBuilder[A](someProperty)
// You may also want to define `apply` and `empty` methods
// that take a known `someProperty`.
// `CanBuildFrom` from `MySet[_]` to `MySet[A]`.
implicit def canBuildFrom[A]: CanBuildFrom[Coll, A, MySet[A]] =
new CanBuildFrom[Coll, A, MySet[A]] {
// This is the method that makes
// e.g. `map`, `flatMap`, `collect` preserve `someProperty`
def apply(from: Coll): mutable.Builder[A, MySet[A]] =
newBuilder[A](from.someProperty)
def apply(): mutable.Builder[A, MySet[A]] = newBuilder[A]
}
}