自定义类上的 List.sum

我有以下代表 GF2 字段的代码：

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 }
}

现在我想调用这个函数：List(One, One, Zero, One).sum这样GF2._+会要求求和，我该如何实现呢？应该GF2扩展一些接口还是应该实现类型类技术？

您需要一个隐式的 Numeric[GF2]：

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

然后你可以这样做：

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