Extending generic type with Ordered trait makes sbt compiler issue 'diverging implicit expansion for type' error

Question

I've got a trait implementing an Ordered trait of Scala:

package stackQuestions

trait ValueTrait[TYPE] extends Ordered[ValueTrait[TYPE]]{
  def value: Double
}

and a subclass:

package stackQuestions

class Value[A](list: List[A], function: (A, A) => Double) extends ValueTrait[A] {
  private val _value: Double = list.zip(list.tail).map(pair => function(pair._1, pair._2)).sum

  override def value: Double = _value

  override def compare(that: ValueTrait[A]): Int = {
    (this.value - that.value).signum
  }
}

Basically, when an object of Value is created with provided function, the value is calculated. What I want to achieve is to sort a collection of Value objects based on their value. This should be guaranteed by Ordered trait. I've written some simple tests for this:

package stackQuestions

import org.scalatest.FunSpec

class ValueTest extends FunSpec {
  def evaluationFunction(arg1: Int, arg2: Int): Double = {
    if (arg1 == 1 && arg2 == 2) return 1.0
    if (arg1 == 2 && arg2 == 1) return 10.0
    0.0
  }

  val lesserValue = new Value(List(1, 2), evaluationFunction) // value will be: 1.0
  val biggerValue = new Value(List(2, 1), evaluationFunction) // value will be: 10.0

  describe("When to Value objects are compared") {
    it("should compare by calculated value") {
      assert(lesserValue < biggerValue)
    }
  }
  describe("When to Value objects are stored in collection") {
    it("should be able to get max value, min value, and get sorted") {
      val collection = List(biggerValue, lesserValue)

      assertResult(expected = lesserValue)(actual = collection.min)
      assertResult(expected = biggerValue)(actual = collection.max)

      assertResult(expected = List(lesserValue, biggerValue))(actual = collection.sorted)
    }
  }
}

However, when sbt test -Xlog-implicits I've get error messages:

[info] Compiling 1 Scala source to /project/target/scala-2.11/test-classes ...
[error] /project/src/test/scala/stackQuestions/ValueTest.scala:24:64: diverging implicit expansion for type Ordering[stackQuestions.Value[Int]]
[error] starting with method $conforms in object Predef
[error]       assertResult(expected = lesserValue)(actual = collection.min)
[error]                                                                ^
[error] /project/src/test/scala/stackQuestions/ValueTest.scala:25:64: diverging implicit expansion for type Ordering[stackQuestions.Value[Int]]
[error] starting with method $conforms in object Predef
[error]       assertResult(expected = biggerValue)(actual = collection.max)
[error]                                                                ^
[error] /project/src/test/scala/stackQuestions/ValueTest.scala:27:83: diverging implicit expansion for type scala.math.Ordering[stackQuestions.Value[Int]]
[error] starting with method $conforms in object Predef
[error]       assertResult(expected = List(lesserValue, biggerValue))(actual = collection.sorted)
[error]                                                                                   ^
[error] three errors found
[error] (Test / compileIncremental) Compilation failed
[error] Total time: 1 s, completed 2018-09-01 08:36:18

I've dug for similar problems and after reading:

• What's a “diverging implicit expansion” scalac message mean?,
• Why am I getting a “ diverging implicit expansion” error when trying to sort instances of an ordered class?,
• How can I solve the Diverging implicit expansion for type,
• scala - Confusing “diverging implicit expansion” error when using “sortBy”,

I get to know that the compiler is confused about how to choose the proper function for comparison. I know that I can circumvent this using sortBy(obj => obj.fitness) but is there any way to use less verbose sorted method?

Answer 1

Scala uses Ordering[T] trait for methods sorted, min and max of a collection of type T. It can generate instances of Ordering[T] automatically for T's that extend Ordered[T].

Because of Java compatibility Ordering[T] extends java.util.Comparator[T], which is invariant in T, so Ordering[T] has to be invariant in T as well. See this issue: SI-7179.

This means that Scala can't generate instances of Ordering[T] for T's that are subclasses of classes that implement Ordered.

---

In your code you have val collection = List(biggerValue, lesserValue), which has type List[Value[Int]]. Value doesn't have its own Ordered or Ordering, so Scala can't sort this collection.

To fix you can specify collection to have type List[ValueTrait[Int]]:

val collection = List[ValueTrait[Int]](biggerValue, lesserValue)

Or define an explicit Ordering for Value[T]:

object Value {
  implicit def ord[T]: Ordering[Value[T]] = 
    Ordering.by(t => t: ValueTrait[T])
}

---

You can also consider using a different design in this problem, if it suits your other requirements:

In your code all instances of ValueTrait[TYPE] have a value of type Double, and the distinctions in subclass and TYPE don't seem to be important at runtime. So you can just define a case class Value(value: Double) and have different factory methods to create Value's from different kinds of arguments.

case class Value(value: Double) extends Ordered[Value] {
  override def compare(that: Value): Int = this.value compareTo that.value
}

object Value {
  def fromList[A](list: List[A], function: (A, A) => Double): Value =
    Value((list, list.tail).zipped.map(function).sum)
} 

And the usage:

scala> val lesserValue = Value.fromList(List(1, 2), evaluationFunction)
lesserValue: Value = Value(1.0)

scala> val biggerValue = Value.fromList(List(2, 1), evaluationFunction)
biggerValue: Value = Value(10.0)

scala> val collection = List(biggerValue, lesserValue)
collection: List[Value] = List(Value(10.0), Value(1.0))

scala> (collection.min, collection.max, collection.sorted)
res1: (Value, Value, List[Value]) = (Value(1.0),Value(10.0),List(Value(1.0), Value(10.0)))