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

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

* 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")))

Answer 3

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))