List.sum per user class

Question

I have the following code that represents a GF2 field:

trait GF2 {
  def unary_- = this
  def + (that: GF2): GF2
  def * (that: GF2): GF2

  def / (that: GF2) = that match {
    case Zero => throw new IllegalArgumentException("Div by 0")
    case _ => this
  }
}

object Zero extends GF2 {
  override def toString = "Zero"
  def + (that: GF2) = that
  def * (that: GF2) = this
}

object One extends GF2 {
  override def toString = "One"
  def + (that: GF2) = that match { case One => Zero ; case _ => this }
  def * (that: GF2) = that match { case One => this ; case _ => that }
}

And now I would like to call this function: List(One, One, Zero, One).sumto be GF2._+called for summation, how can I do this? Should I GF2extend any interface or should I use a type class method?

Answer 1

You need a numeric [GF2] implicit:

trait GF2IsNumeric extends Numeric[GF2] {
  def plus(x: GF2, y: GF2): GF2 = x + y
  def minus(x: GF2, y: GF2): GF2 = x + (-y)
  def times(x: GF2, y: GF2): GF2 = x * y
  def negate(x: GF2): GF2 = -x
  def fromInt(x: Int): GF2 = ???
  def toInt(x: GF2): Int = ???
  def toLong(x: GF2): Long = ???
  def toFloat(x: GF2): Float = ???
  def toDouble(x: GF2): Double = ???
  override def zero = Zero
  override def one = One
}

trait GF2Ordering extends scala.math.Ordering[GF2] {
  override def compare(a: GF2, b: GF2) = if (a == b) 0 else if (b == One) 1 else -1
}

implicit object GF2IsNumeric extends GF2IsNumeric with GF2Ordering

Then you can do:

println(List(One, One, Zero, One).sum)
// One

Answer 2

Look at the signature sum:

def sum[B >: A](implicit num: Numeric[B]): B

, GF2 Numeric, Numeric[GF2], Numeric , , , .

, , sum typeclass (, ?).

, , ( Numeric) - reduce ( ), fold:

yourList.reduce(_ + _)
yourList.fold(Zero)(_ + _)

Answer 3

Numeric , . . , .

 object InScope{
   implicit object GF2Numeric extends Numeric[GF2]{
     //..your implementation here
   }
 }

The full signature sumon a Listactually is:

 def sum(implicit num: Numeric[A])

Where Ais the type List[A].