queryenc1.scala

trait Rep {
  type Base
}

class Query[E] extends Rep { self =>
  type C[_] <: Iterable[_]
  type Base = C[E]
  def map[F](f: E => F): Query[F] { type C[X] = self.C[X] } = ???
  def to[D[_] <: Iterable[_]]: Query[E] { type C[X] = D[X] } = ???
}

object Query {
  def apply[D[_] <: Iterable[_], T]: Query[T] { type C[X] = D[X] } = ???
}

def run[E](q: Rep { type Base = E }): E = ???

def elem[E](q: Query[E]): E = ???

val q1 = Query[Vector, Int]
val q2 = q1.map(_.toString).to[Set]
val r = run(q2)
val rt: Set[String] = r
val r2 = elem(q2)
val r2t: String = r2

queryenc2.scala

trait Rep[T]

class Query[C[_], E] extends Rep[C[E]] { self =>
  def map[F](f: E => F): Query[C, F] = ???
  def to[D[_] <: Iterable[_]]: Query[D, E] = ???
}

object Query {
  def apply[D[_] <: Iterable[_], T]: Query[D, T] = ???
}

def run[E](q: Rep[E]): E = ???

def elem[E](q: Query[X, E] forSome { type X[_] }): E = ???

val q1 = Query[Vector, Int]
val q2 = q1.map(_.toString).to[Set]
val r = run(q2)
val rt: Set[String] = r
val r2 = elem(q2)
val r2t: String = r2