import scala.language.higherKinds
trait Foo[A] {
  type Out[_]
  def apply[T](t: T): Out[T]
}

object Foo {

  type Aux[A, Out0[_]] = Foo[A] { type Out[A] = Out0[A] }

  implicit val fooInt: Aux[Int, List] = new Foo[Int] {
    type Out[A] = List[A]
    def apply[T](t: T): List[T] = List(t)
  }

  implicit val fooString: Aux[String, Option] = new Foo[String] {
    type Out[A] = Option[A]
    def apply[T](t: T): Option[T] = Option(t)
  }

}

def works[A, T](a: A, t: T)(implicit
  foo: Foo[A]
): foo.Out[T] = foo(t)

def fails[A, FooOut[_], T](a: A, t: T)(implicit
  foo: Foo.Aux[A, FooOut]
): FooOut[T] = foo(t)

works(10, true)
// res0: Foo.fooInt.Out[Boolean] = List(true)

fails(10, true)
// error: could not find implicit value for parameter foo: Foo.Aux[Int,FooOut]