StateChange.scala

    // we notice  S => (S,A) is useful, almost composable and testable, but awkward... lets do better
    // Lets create a type that wraps the computation, and add some useful combinators: mapResult, doAgainWithResultAndNewState
    case class StateChange[S,A](run: S => (S,A)){

      def mapResult[B](f:A => B):StateChange[S,B] = StateChange{ (s:S) =>
          val(s2,a) = run(s)
          (s2,f(a))
        }

      /*
       A magical moment!!!!!!  Now I can stick 2 StateChange's together: the resulting
       StateChange runs the first one, then uses the resulting state a the param for
       the second one: I have now threaded my state through 2 computations.
       */

      def doWithNewState[B](f: A => StateChange[S,B]):StateChange[S,B] = StateChange{ (s:S) =>
          val(s2,a) = run(s)
          val stateChangeToB = f(a)
          val (s3,b) = stateChangeToB.run(s2)
          (s3,b)
        }
    }