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Comparable/Ordered

In java there’s a Comparable interface that defines a compareTo method used for sorting/comparing objects.

For the unaware, comparing in Java works as follows - the compareTo method returns a value $x$ such that: $x > 0 \iff this > that$,

$x < 0 \iff this < that$

and $x = 0$ otherwise.

On the other hand Scala, defines a Ordered trait that extends the Java Comparable interface. Because mixin composition in Scala is possible, the Ordered trait defines some additional concrete methods that depend on the compare method.

trait Ordered[T] extends Comparable[T] {
  abstract def compare(that: T): Int
  def <(that: T): Boolean = // ...
  def <=(that: T): Boolean = // ...
  def >(that: T): Boolean = // ...
  def >=(that: T): Boolean = // ...
  def compareTo(that: T): Int = // ...
}

By default the compareTo method is an alias for the abstract compare method (this is mostly because in Scala &lt 2.8 Ordered didn’t extend Comparable).

As you can see, Ordered[T] in scala gives us comparison methods and we don’t have to resort to ugly this.compareTo(that) > 0 kludges.

Anyway, let’s define a simple Value case class that holds integers:

case class Value(i: Int) extends Ordered[Value] {
  def compare(that: Value) = this.i - that.i
}

Because Value extends Ordered we can use methods that expect a natural ordering of objects - look at this interpreter session:

scala> val valueList = List(Value(1), Value(2), Value(3), Value(2), Value(1))
valueList: List[Value] = List(Value(1), Value(2), Value(3), Value(2), Value(1))
scala> valueList.sorted

res0: List[Value] = List(Value(1), Value(1), Value(2), Value(2), Value(3))
scala> valueList.min
res1: Value = Value(1)

By contrast, we can’t sort on classes not defining the Ordered trait:

scala> case class UnOrderedValue(i: Int) 
scala> val unOrderedValueList = List(UnOrderedValue(1), UnOrderedValue(2),
     | UnOrderedValue(3), UnOrderedValue(2), UnOrderedValue(1))
unOrderedValueList: List[UnOrderedValue] = List(UnOrderedValue(1), UnOrderedVal
ue(2), UnOrderedValue(3), UnOrderedValue(2), UnOrderedValue(1))
scala> unOrderedValueList.sorted
<console>:11: error: No implicit Ordering defined for UnOrderedValue.
              unOrderedValueList.sorted
scala> unOrderedValueList.min
<console>:11: error: No implicit Ordering defined for UnOrderedValue.
              unOrderedValueList.sorted

Ordering/Comparator

Java/Scala also defines another kind of abstraction which is used to compare two values. In java this interface is called Comparator and in scala it’s Ordering:

trait Ordering[T] extends Comparator[T] {
  abstract def compare(x: T, y: T): Int
  // concrete methods
}

Ordering can be thought as a more general interface then Ordered - you can have many Orderings available for a class, which for Ordered isn’t possible without subtyping.

Generic sorting

Let’s create a generic container:

trait Box[T] {
  def value: T
}

We can sort on it using this sort class:

class Sort[T](ordering: Ordering[Box[T]]) {
  def apply(boxes: Seq[Box[T]]) = {
    boxes.sorted(ordering)
  }
}

For Sort to work, we have to define an Ordering on Boxes:

class BoxOrdering[T](ordering: Ordering[T]) extends Ordering[Box[T]] {
  def compare(x: Box[T], y: Box[T]): Int = ordering.compare(x.value, y.value)
}

Now we can define a trivial box type:

case class IntBox(value: Int) extends Box[Int]

And we can sort sequences of IntBox using:

scala> val list = List(IntBox(1), IntBox(2), IntBox(3), IntBox(2), IntBox(1))
list: List[IntBox] = List(IntBox(1), IntBox(2), IntBox(3), IntBox(2), IntBox(1))

scala> val sort = new Sort(new BoxOrdering(scala.math.Ordering.Int))
sort: Sort[Int] = Sort@5e0e9cd0

scala> sort(list)
res5: Seq[Box[Int]] = List(IntBox(1), IntBox(1), IntBox(2), IntBox(2), IntBox(3))

This isn’t good as we can make it more general, but now let’s talk implicits.

Implicits 101

Implicit parameters

An implicit parameter T of a method, can be omitted when the argument can be deduced by the compiler - when an implicit instance of the type T is in scope.

Trivial example for Ints:

scala> def add(x: Int)(implicit y: Int) = x + y
add: (x: Int)(implicit y: Int)Int

scala> add(3)(4)
res9: Int = 7

scala> implicit val x: Int = 4
x: Int = 4

scala> add(3)
res10: Int = 7

Implicit definitions

Another type of implicits are implicit definitions which are used to create conversions between objects of type A to B. If we have a method that expects a parameter of type B we can give it an instance of A if there exists a implicit method in scope:

implicit def aToB(a: A): B = ???

Concretely, lets go back and modify the IntBox class giving it a + method:

case class IntBox(value: Int) extends Box[Int] {
  def +(other: IntBox) = IntBox(value + other.value)
}

If we wanted + to work on ints we could extend the functionality by defining an implicit conversion between Int and IntBox

implicit def intToIntBox(int: Int): IntBox = IntBox(int)

Now both versions will work:

scala> val a = IntBox(3)
a: IntBox = IntBox(3)

scala> val b = IntBox(4)
b: IntBox = IntBox(4)

scala> a + b.value
res16: IntBox = IntBox(7)

scala> a + b
res17: IntBox = IntBox(7)

Sorting on Ordered

Coming back to our Box example - the scala library defines an implicit conversion between Ordered[T] and Ordering[T] and vice-versa. We can use this to define a universal sorting function on Boxes:

object boxSort {
  def apply[T](boxes: Seq[Box[T]])(implicit ordering: Ordering[T]) = {
    val boxOrdering = new BoxOrdering(ordering)
    boxes.sorted(boxOrdering)
  }
}

And now, sorting works as expected:

scala> val list = List(IntBox(1), IntBox(2), IntBox(3), IntBox(2), IntBox(1))
list: List[IntBox] = List(IntBox(1), IntBox(2), IntBox(3), IntBox(2), IntBox(1))

scala> boxSort(list)
res18: Seq[Box[Int]] = List(IntBox(1), IntBox(1), IntBox(2), IntBox(2), IntBox(3))

Type classes

I’ve written a little post about typeclasses (Ordering is in fact a type class) you can check it out here

Edit history

2013-03-28

2016-03-15