Scala: abstracting over a path-dependent type in impilicit parameter

Question

Let's say I have a class:

abstract class NumericCombine[A:Numeric,B:Numeric]{
        type AB <: AnyVal
    }

I want to define a function that returns a value of type NumericCombine[A,B].AB. for instance:

def plus[A: Numeric,B:Numeric](x: A, y: B): NumericCombine[A,B].AB

but the compiler doesn't let me reference .AB in plus.

FYI, this is the context of this question.

I want to provide:

implicit object IntFloat extends NumericCombine[Int,Float]{override type AB = Float}
implicit object FloatInt extends NumericCombine[Float,Int]{override type AB = Float}

and its other 44 friends (7*6-2) so that I can define my plus as below:

def plus[A: Numeric,B:Numeric](x: A, y: B): NumericCombine[A,B].AB =
{
type AB = Numeric[NumericCombine[A,B].AB]
implicitly[AB].plus(x.asInstanceOf[AB],y.asInstanceOf[AB])
}

plus(1f,2)//=3f
plus(1,2f)//=3f

I am aware of the fact that value conversions in Scala allows me to define

def plus[T](a: T, b: T)(implicit ev:Numeric[T]): T = ev.plus(a,b)

and achieve the behaviour above as suggested here, but since I want to use this function as part of a bigger function (which is described in the link mentioned as the context of this question), I need to parametrize the function with both A and B.

Update:

I made some good progress with this.

My NumericCombine now looks like this:

abstract class NumericCombine[A: Numeric, B: Numeric] {
        type AB <: AnyVal

        def fromA(x: A): AB
        def fromB(y: B): AB

        val numeric: Numeric[AB]

        def plus(x: A, y: B): AB = numeric.plus(fromA(x), fromB(y))
        def minus(x: A, y: B): AB = numeric.minus(fromA(x), fromB(y))
        def times(x: A, y: B): AB = numeric.times(fromA(x), fromB(y))
    }

and My plus function looks like:

def plus[A: Numeric, B: Numeric](x: A, y: B)(implicit ev:NumericCombine[A,B])
        : ev.AB = ev.plus(x, y)

The weighted average function requiring plus ended up becoming a bit more complicated:

def accumulateWeightedValue[A: Numeric,B: Numeric]
            (accum: (A, NumericCombine[A, B]#AB), ValueWithWeight: (A, B))
            (implicit combine: NumericCombine[A, B], timesNumeric: Numeric[NumericCombine[A, B]#AB])
            :(A,NumericCombine[A, B]#AB)=

this is a function that takes (A,AB),(A,B) and returns (A,AB). I use it internally inside weightedSum which just aggregates over this:

def weightedSum[A: Numeric,B: Numeric](weightedValues: GenTraversable[(A, B)])
(implicit numericCombine: NumericCombine[A, B], plusNumeric: Numeric[NumericCombine[A, B]#AB])
: (A, NumericCombine[A, B]#AB)

Now, this compiles fine. It does seem to have a problem with the second implicit parameter. ie Numeric[AB] when I run it with implicit values for say NumericCombine[Int,Float] present. It gives me:

could not find implicit value for parameter plusNumeric: Numeric[NumericCombine[Int,Float]#AB]

note that in NumericCombine, I have a Numeric[AB] which should be available for implicit look-up. storing it locally, in the case of [Int,Float]:

val lst: Seq[(Int, Float)] =List((1,3f),(1,4f))
implicit val num: Numeric[Float] = IntFloat.numeric //IntFloat extends NumericCombine[Int,Float]
weightedSum(lst)

in a local variable before invoking the function needing it doesn't seem to have any impact. So why is it being picked up by the implicit system.

Answer 1

Just use

def plus[A: Numeric,B:Numeric](x: A, y: B): NumericCombine[A,B]#AB

Note the # (hash) instead of . (dot). This is called "type projection". Dot notation is called "path dependent type". I'm telling you these names so that you can google for more info easily. Simply put, # is used for accessing types from classes/traits, and . is used for accessing types from objects/values.

Example:

trait Foo {
    type T   
}

val fooObj: Foo = new Foo {
    type T = Int
}

type t1 = fooObj.T
type t2 = Foo#T

Answer 2

An alternative to @slouc's answer is

def plus[A, B](x: A, y: B)(implicit ev: NumericCombine[A, B]): ev.AB

I'd also enhance NumericCombine:

trait NumericCombine[A, B] {
  type AB <: AnyVal
  def fromA(a: A): AB
  def fromB(b: B): AB
  val num: Numeric[AB]
}

abstract class NumericCombineImpl[A, B, R](implicit val num: Numeric[R], f1: A => R, f2: B => R) {
  type AB = R
  def fromA(a: A) = f1(a)
  def fromB(b: B) = f2(b)
}

implicit object IntFloat extends NumericCombineImpl[Int,Float,Float]
...

This would allow to actually implement plus, no casts required:

def plus[A, B](x: A, y: B)(implicit ev: NumericCombine[A, B]): ev.AB = 
  ev.num.plus(ev.fromA(x), ev.fromB(y))

Answer 3

* 18 Apr 2017: updated base on the latest code from author *

* 19 Apr 2017 *

• Add NumericCombine#Implicits for convinence
• Remove AnyVal constraints to support any Numeric types e.g. BigInt
• Refactor NumericCombine

You need Aux pattern:

import scala.collection.GenSeq

trait NumericCombine[A, B] {
  type AB

  def fromA(x: A): AB

  def fromB(y: B): AB

  val numericA: Numeric[A]
  val numericB: Numeric[B]
  val numericAB: Numeric[AB]

  // For convenience, caller can 'import combine.Implicits._'
  // to bring the Numeric's into the current scope
  object Implicits {
    implicit def implicitNumericA = numericA

    implicit def implicitNumericB = numericB

    implicit def implicitNumericAB = numericAB
  }

  def plus(x: A, y: B): AB = numericAB.plus(fromA(x), fromB(y))

  def minus(x: A, y: B): AB = numericAB.minus(fromA(x), fromB(y))

  def times(x: A, y: B): AB = numericAB.times(fromA(x), fromB(y))
}

object NumericCombine {
  type Aux[A, B, _AB] = NumericCombine[A, B] {
    type AB = _AB
  }

  private def combine[A, B, _AB](fa: A => _AB, fb: B => _AB)
                               (implicit
                                _numericA: Numeric[A],
                                _numericB: Numeric[B],
                                _numericAB: Numeric[_AB]
                               ): NumericCombine[A, B] = new NumericCombine[A, B] {
      override type AB = _AB

      override def fromA(x: A): AB = fa(x)

      override def fromB(y: B): AB = fb(y)

      override val numericA: Numeric[A] = _numericA
      override val numericB: Numeric[B] = _numericB
      override val numericAB: Numeric[AB] = _numericAB
    }

  implicit lazy val IntFloat  = combine[Int, Float, Float](_.toFloat, identity)
  implicit lazy val BigIntBigDecimal  = combine[BigInt, BigDecimal, BigDecimal](i => BigDecimal(i), identity)

}

implicit class ValuesWithWeight[A, B](val weightedValue: (A, B)) {
  def weight: A = weightedValue._1

  def value: B = weightedValue._2
}

def weightedSum[A, B, AB]
(valuesWithWeight: GenSeq[(A, B)])
(implicit combine: NumericCombine.Aux[A, B, AB]):
(A, AB) = {

  import combine.Implicits._

  val z: (A, AB) =
    (combine.numericA.zero, combine.numericAB.zero)

  def accumulateWeightedValue(accum: (A, AB), valueWithWeight: (A, B)): (A, AB) = {
    val weightedValue = combine.times(valueWithWeight.weight, valueWithWeight.value)
    (
      combine.numericA.plus(accum.weight, valueWithWeight.weight),
      combine.numericAB.plus(accum.value, weightedValue)
    )
  }

  valuesWithWeight.aggregate(z)(
    accumulateWeightedValue,
    // dataOps.tuple2.plus[A,AB]
    {
      case ((a1, ab1), (a2, ab2)) =>
        (combine.numericA.plus(a1, a2) ->
          combine.numericAB.plus(ab1, ab2))
    }
  )
}

weightedSum(Seq(1 -> 1.5f, 2 -> 1f, 3 -> 1.7f))
weightedSum(Seq(BigInt(1) -> BigDecimal("1.5"), BigInt(2) -> BigDecimal("1"), BigInt(3) -> BigDecimal("1.7")))