Garden Hoses as a Category in Scala

Hose.scala

// Category
//
trait Category[Arrow[_,_]] {
  def compose[A,B,C](c1: Arrow[B,C], c2: Arrow[A,B]): Arrow[A,C]
  def id[A]: Arrow[A,A]
}

object Category {
  implicit object FunctionCat extends Category[Function1] {
    def compose[A,B,C](f: B => C, g: A => B): A => C = f compose g 
    def id[A]: A => A = identity
  }
}



// Connection types
// In order of water flow
trait WaterSupply
trait TapScrew 
trait FemaleMale
trait MaleHose
trait HoseFemale
trait Exit



sealed trait Hose[In, Out] {
  def leaks: Int
  def kinked: Boolean

  final def <<[A](in: Hose[A, In]): Hose[A, Out] = 
    in >> this

  final def >>[A](out: Hose[Out, A]): Hose[In, A] = (this, out) match {
    case (_, _) => new >>[In, Out, A](this, out)
  }
}


// Fills in some fields for hard gadgety hose components
trait HoseGadget[In, Out] extends Hose[In, Out] {
  def leaky: Boolean
  override final def kinked = false
  override final def leaks: Int = if (leaky) 1 else 0
}


case class Tap(leaky: Boolean) extends HoseGadget[WaterSupply, TapScrew]
case class TapNozzle(leaky: Boolean) extends HoseGadget[TapScrew, FemaleMale]
case class MaleNozzle(leaky: Boolean) extends HoseGadget[FemaleMale, MaleHose]
case class HosePipe(leaks: Int, kinked: Boolean) extends Hose[MaleHose, HoseFemale]
case class FemaleNozzle(leaky: Boolean) extends HoseGadget[HoseFemale, FemaleMale]
case class SprayGun(leaky: Boolean) extends HoseGadget[FemaleMale, Exit]
case class Sprinkler(leaky: Boolean) extends HoseGadget[FemaleMale, Exit]

// Identity hose
case class EmptyHose[A] extends Hose[A, A] {
  def leaks = 0 
  def kinked = false
}

// Composition of two hoses
case class >>[In, Mid, Out](
    in: Hose[In, Mid], 
    out: Hose[Mid, Out]) extends Hose[In, Out] {

  def kinked = in.kinked || out.kinked
  def leaks = in.leaks + out.leaks
  override def toString: String = s"$in >> $out"
}

object Hose {

  implicit object HoseCategory extends Category[Hose] {
    def compose[A,B,C](c1: Hose[B,C], c2: Hose[A,B]): Hose[A,C] = 
      c1 << c2

    def id[A]: Hose[A,A] = EmptyHose[A]
  }

  def empty[A]: Hose[A,A] = EmptyHose[A]

  def newHose: Hose[FemaleMale, FemaleMale] = 
    MaleNozzle(false) >> HosePipe(0, false) >> FemaleNozzle(false)

  def oldHose(leaks: Int, kinked: Boolean) = 
    MaleNozzle(false) >> HosePipe(leaks, kinked) >> FemaleNozzle(false)

  def newSprayGun = SprayGun(false)

  def newSprinkler = Sprinkler(false)

  def newFittedTap = Tap(false) >> TapNozzle(false)
}