TypeFamily example

TypeFamily.scala

package typefamily

import scala.language._

/* From the paper: 
 * http://research.microsoft.com/en-us/um/people/simonpj/papers/assoc-types/fun-with-type-funs/typefun.pdf
 *
 * class Mutation m where
 *  type Ref m :: * -> *
 *  newRef :: a -> m (Ref m a)
 *  readRef :: Ref m a -> m a
 *  writeRef :: Ref m a -> a -> m ()
 * 
 * instance Mutation IO where
 *  type Ref IO = IORef
 *  newRef = newIORef
 *  readRef = readIORef
 *  writeRef = writeIORef
 *
 * instance Mutation (ST s) where
 *  type Ref (ST s) = STRef s
 *  newRef = newSTRef
 *  readRef = readSTRef
 *  writeRef = writeSTRef
 */

/* Associated Type Instance */
trait Mutation[M[_]] {
  type Ref[M[_], A]
  def newRef[A](a: A): M[Ref[M, A]]
  def readRef[A](r: Ref[M, A]): M[A]
  def writeRef[A](r: Ref[M, A])(a: A): M[Unit]
}

trait IO[A]
trait IORef[A]
trait ST[S, A]
trait STRef[S, A]


object Instances {
  implicit val mutationIO = new Mutation[IO] {
    /* not sure how to do this without the bound */
    type Ref[M[_] <: IO[_], A] = IORef[A]
    def newRef[A](a: A): IO[Ref[IO, A]] = ???
    def readRef[A](r: Ref[IO, A]): IO[A] = ???
    def writeRef[A](r: Ref[IO, A])(a: A): IO[Unit] = ???
  }

  implicit def mutationST[S] = new Mutation[({ type λ[A] = ST[S, A] })#λ] {
    /* Make the Type Lambda less annoying */
    type STWithS[A] = ST[S, A]
    type Ref[M[_] <: STWithS[_], A] = STRef[S, A]
    def newRef[A](a: A): STWithS[Ref[STWithS, A]] = ???
    def readRef[A](r: Ref[STWithS, A]): STWithS[A] = ???
    def writeRef[A](r: Ref[STWithS, A])(a: A): STWithS[Unit] = ???
  }
}