# scala.math.PartialOrdering

A trait for representing partial orderings. It is important to distinguish between a type that has a partial order and a representation of partial ordering on some type. This trait is for representing the latter.

A partial ordering is a binary relation on a type `T` , exposed as the `lteq` method of this trait. This relation must be:

• reflexive: `lteq(x, x) == true` , for any `x` of type `T` .
• anti-symmetric: if `lteq(x, y) == true` and `lteq(y, x) == true` then `equiv(x, y) == true` , for any `x` and `y` of type `T` .
• transitive: if `lteq(x, y) == true` and `lteq(y, z) == true` then `lteq(x, z) == true` , for any `x` , `y` , and `z` of type `T` .

Additionally, a partial ordering induces an equivalence relation on a type `T` : `x` and `y` of type `T` are equivalent if and only if `lteq(x, y) && lteq(y, x) == true` . This equivalence relation is exposed as the `equiv` method, inherited from the Equiv trait.

• Self Type
• PartialOrdering [T]
• Source
• Version
• 1.0, 2008-04-0-3
• Since
• 2.7

### `abstract def lteq(x: T, y: T): Boolean`

Returns `true` iff `x` comes before `y` in the ordering.

(defined at scala.math.PartialOrdering)

### `abstract def tryCompare(x: T, y: T): Option[Int]`

Result of comparing `x` with operand `y` . Returns `None` if operands are not comparable. If operands are comparable, returns `Some(r)` where

• `r < 0` iff `x < y`
• `r == 0` iff `x == y`
• `r > 0` iff `x > y`

(defined at scala.math.PartialOrdering)

### `def equiv(x: T, y: T): Boolean`

Returns `true` iff `x` is equivalent to `y` in the ordering.

• Definition Classes
• PartialOrdering → Equiv

(defined at scala.math.PartialOrdering)

### `def gt(x: T, y: T): Boolean`

Returns `true` iff `y` comes before `x` in the ordering and is not the same as `x` .

(defined at scala.math.PartialOrdering)

### `def gteq(x: T, y: T): Boolean`

Returns `true` iff `y` comes before `x` in the ordering.

(defined at scala.math.PartialOrdering)

### `def lt(x: T, y: T): Boolean`

Returns `true` iff `x` comes before `y` in the ordering and is not the same as `y` .

(defined at scala.math.PartialOrdering)

### `def reverse: PartialOrdering[T]`

(defined at scala.math.PartialOrdering)