type-container.scala

trait TypeContainer {
  type A
  type B
  type ABPlus
  type C
}

trait TypeProjector[TC <: TypeContainer] {
  type A = TC#A
  type B = TC#B
  type ABPlus = TC#ABPlus
  type C = TC#C
}

trait API[TC <: TypeContainer] extends TypeProjector[TC] {
  def addAB(a: A, b: B): ABPlus
}

class FirstContainer extends TypeContainer {
  type A = String
  type B = Int
  type ABPlus = String
  type C = Boolean
}

class FirstAPI extends API[FirstContainer] {
  def addAB(a: String, b: Int): String = a + b
}