Slightly simpler example of typed transducers in Scala. See http://blog.podsnap.com/ducers2.html for more context.

transducers.scala

object Transducer {
  type RF[R, A] = (R, A) => R
  def apply[A, B](f: A => B) =
    new Transducer[B, A] {
      def apply[R](rf: RF[R, B]) = (r, a) => rf(r, f(a))
    }
}

import Transducer.RF

trait Transducer[A, B] { self =>
  def apply[R](f: RF[R, A]): RF[R, B]
  def ∘[Z](that: Transducer[Z, A]) =
    new Transducer[Z, B] {
      def apply[R](rf: RF[R, Z]) = self(that(rf))
    }
}

object Test {
  val parseI = Transducer((s: String) => s.toInt)
  val root2 = Transducer((n: Int) => math.pow(2.0, 1.0 / n))

  def repeat[A] =
    new Transducer[A, A] {
      def apply[R](rf: RF[R, A]) = (r, a) => rf(rf(r, a), a)
    }

  def main(args: Array[String]) {
    val lst = List("1","2","3")
    println(lst.foldLeft(0)(parseI(_ + _)))
    println(lst.foldLeft(0.0)((parseI ∘ repeat ∘ root2)(_ + _)))
  }
}