Order Type Class | NO SEA. I SEE.

Notes

This article was translated by GPT-5.2-Codex. The original is here.

`Order`

Order is a type class that represents total ordering.

Cats' Order is defined as a trait with a compare method.

1trait Order[@sp A] extends Any with PartialOrder[A] { self =>
2
3  def compare(x: A, y: A): Int
4
5  def comparison(x: A, y: A): Comparison = Comparison.fromInt(compare(x, y))
6
7  def partialCompare(x: A, y: A): Double = compare(x, y).toDouble
8
9  def min(x: A, y: A): A = if (lt(x, y)) x else y
10
11  def max(x: A, y: A): A = if (gt(x, y)) x else y
12
13  override def eqv(x: A, y: A): Boolean =
14    compare(x, y) == 0
15
16  override def neqv(x: A, y: A): Boolean = !eqv(x, y)
17
18  override def lteqv(x: A, y: A): Boolean =
19    compare(x, y) <= 0
20
21  override def lt(x: A, y: A): Boolean =
22    compare(x, y) < 0
23
24  override def gteqv(x: A, y: A): Boolean =
25    compare(x, y) >= 0
26
27  override def gt(x: A, y: A): Boolean =
28    compare(x, y) > 0
29
30  def toOrdering: Ordering[A] =
31    compare(_, _)

All methods other than compare are default implementations that rely on compare. In the Cats type class diagram, PartialOrder is not highlighted, so I looked at Order first. However, you must still know what PartialOrder requires to implement. PartialOrder requires partialCompare, but Order can implement partialCompare and eqv via compare, so if you can define compare for Order, it can also serve as instances of Eq and PartialOrder.

Unlike Eq.fromUniversalEquals, there doesn’t seem to be a method that returns an Order instance just by calling it, so you must define the instance yourself or use derives.

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To derive instances with derives, all fields must already have Order instances defined.

If you know the mathematical definition of total order, there is nothing particularly noteworthy about Order. However, partial order (PartialOrder) is a concept taught in discrete math (not in high school math, I guess), so it might be unfamiliar to those who haven't studied university math. That might be why it isn't highlighted.

`Order` syntax

Type Class	Syntax	Description
`Order`	`compare`	Compares left and right; returns a negative value if left is smaller, positive if larger, 0 if equal.
`Order`	`min`	Returns the smaller of left and right.
`Order`	`max`	Returns the larger of left and right.
`Order`	`comparison`	Returns `Comparison`, equivalent to Haskell's `Ordering`.
`PartialOrder`	`>`	Returns `true` if left is greater than right.
`PartialOrder`	`>=`	Returns `true` if left is greater than or equal to right.
`PartialOrder`	`<`	Returns `true` if left is less than right.
`PartialOrder`	`<=`	Returns `true` if left is less than or equal to right.
`PartialOrder`	`partialCompare`	Same as `compare`.
`PartialOrder`	`partialComparison`	Same as `Comparison`.

##Order

###Order syntax

`Order`

`Order` syntax