test.scala

import annotation.implicitNotFound

@implicitNotFound(msg = "This message can never appear!")
trait ~>[A, B] { self =>
  def apply(a: A): B
  def invert(b: B): A = inverse.apply(b)
  def inverse: B ~> A = new ~>[B,A] {
    def apply(b: B) = self.invert(b)
    override def invert(a: A) = self(a)
  }
}

object ~> {
  implicit def inverseOf[A, B](implicit forward: A ~> B): B ~> A = forward.inverse 
}