scala> class Bar1 extends Bar { protected def f(): Int = 5 }
defined class Bar1

scala> class Bar2 extends Bar { protected def f(): Int = 5 }
defined class Bar2

scala> List(new Bar1, new Bar2)
res1: List[Bar{protected def f(): Int}] = List(Bar1@55661f7b, Bar2@239cf00a)

scala> type BarF = { def f(): Int }
defined type alias BarF

scala> var x: BarF = _
x: BarF = null

scala> x = res1.head
x: BarF = Bar1@55661f7b

scala> x.f
res2: Int = 5

scala> (new Bar1).f
<console>:10: error: method f in class Bar1 cannot be accessed in Bar1
 Access to protected method f not permitted because
 enclosing object $iw is not a subclass of 
 class Bar1 where target is defined
              (new Bar1).f
                         ^

scala> type Foo = { protected def f(): Int }
<console>:1: error: illegal start of declaration
       type Foo = { protected def f(): Int }
                    ^

scala> class A {
     |   abstract class Bar { protected[this] def f(): Any }
     |   class Bar1 extends Bar { protected[this] def f(): Int = 5 }
     |   class Bar2 extends Bar { protected[this] def f(): Int = 5 }
     |   
     |   def f = List(new Bar1, new Bar2)
     | }
defined class A

scala> (new A).f _
res0: () => List[A#Bar{protected def f(): Int}] = <function0>

package bippy {
  package dingus {
    abstract class Bar { protected[dingus] def f(): Any }
    class Bar1 extends Bar { protected[bippy] def f(): Int = 5 }
    class Bar2 extends Bar { protected[bippy] def f(): Int = 5 }
    // Infers List[Bar{protected[bippy] def f(): Int}]
    
    abstract class Bar { protected[dingus] def f(): Int } // note no return type refinement
    class Bar1 extends Bar { protected[bippy] def f(): Int = 5 }
    class Bar2 extends Bar { protected[bippy] def f(): Int = 5 }
    // Infers List[Bar]
  }
  import dingus._
  object A { def g2 = List(new Bar1, new Bar2) }
}

scala> object A {
     |   abstract class Bar { protected def f(): Any }
     |   class Bar1 extends Bar { protected def f(): Int = 5 }
     |   class Bar2 extends Bar { protected def f(): Int = 5 ; def h = g map (_.f()) }
     |   
     |   def g = List(new Bar1, new Bar2)
     | }
<console>:10: error: method f cannot be accessed in A.Bar{protected def f(): Int}
 Access to protected method f not permitted because
 enclosing class Bar2 in object A is not a subclass of 
 A in object A where target is defined
         class Bar2 extends Bar { protected def f(): Int = 5 ; def h = g map (_.f()) }
                                                                                ^                                                                                      ^