PartialOrderOrEq

If you are using the Cats library, you can define a PartialOrder type class for any data type.

Scala 3

// Simplified definition.
// See https://typelevel.org/cats/api/cats/kernel/PartialOrder.html for further details
trait PartialOrder[A]:
  def partialCompare(x: A, y: A): Double

Scala 2.13

// Simplified definition.
// See https://typelevel.org/cats/api/cats/kernel/PartialOrder.html for further details
trait PartialOrder[A] {
  def partialCompare(x: A, y: A): Double
}

The PartialOrder type provides a method for comparing two objects of the given type, returning a double value of:

• 0.0 if the two objects are equivalent
• -1.0 if x < y
• 1.0 if x < y
• NaN if x and y cannot be compared.

Cats is also kind enough to provide implicit <, <=, ===, >= and > operators if the given type does not provide them already.

That's all nice, but not every type comes with a given PartialOrder for us to use.

But logically, it must be possible to define a PartialOrder for every type; even if it is very partial!

The couldbe-cats package provides a ready implementation of PartialOrderOrEq:

Scala 3

trait PartialOrderOrEq[A: CouldHave[PartialOrder]: EqOrEquals]:
  def p(x: A, y: A): Double =
    CouldHave[PartialOrder, A]
      .act(_.partialCompare(x, y))
          (if EqOrEquals.e(x, y) then 0.0 else Double.NaN)

Scala 2.13

trait PartialOrderOrEq[A: EqOrEquals](A: CouldHave[PartialOrder, A]) {
  def p(x: A, y: A): Double =
    CouldHave[PartialOrder, A]
      .act(_.partialCompare(x, y))
          (if (EqOrEquals.e(x, y)) 0.0 else Double.NaN)
}

This is a "best attempt" at a partial order for any given type.

In the following function

Scala 3

def yourFunction[A: PartialOrderOrEq](x: A, y: A):
  // ...
  PartialOrderOrEq.p(x, y)
  // ...

Scala 2.13

def yourFunction[A: PartialOrderOrEq](x: A, y: A) {
  // ...
  PartialOrderOrEq.p(x, y)
  // ...
}

the following rules will be applied:

1. if a given PartialOrder (or a complete Order, which extends the trait) exists, then that instance will be used to perform the comparison
2. otherwise, if a given Eq (Cats Equality) instance exists, then the function will return 0.0 if x === y; NaN otherwise
3. finally, if we still have no comparison, the two values will be compared using the JVM .equals() method; returning 0.0 if x.equals(y) or NaN otherwise.