# PartialOrdering

#### trait PartialOrdering[T] extends Equiv[T]

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 that is also an equivalence relation on values of type T. This relation is exposed as the lteq method of the PartialOrdering trait. This relation must be:

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

known subclasses: Ordering
source: PartialOrdering.scala
version
1. 1 . 0, 2008-04-0-3

since
1. 2 . 7

authors:
1. Geoffrey Washburn

1. Hide All
2. Show all
1. Equiv
2. AnyRef
3. Any

1. Public
2. All

### Value Members

1. #### def !=(arg0: AnyRef): Boolean

attributes: final
definition classes: AnyRef
2. #### def !=(arg0: Any): Boolean

`o != arg0` is the same as `!(o == (arg0))`.

`o != arg0` is the same as `!(o == (arg0))`.

arg0

the object to compare against this object for dis-equality .

returns

`false` if the receiver object is equivalent to the argument; `true` otherwise.

attributes: final
definition classes: Any
3. #### def ##(): Int

attributes: final
definition classes: AnyRef → Any
4. #### def \$asInstanceOf[T0](): T0

attributes: final
definition classes: AnyRef
5. #### def \$isInstanceOf[T0](): Boolean

attributes: final
definition classes: AnyRef
6. #### def ==(arg0: AnyRef): Boolean

`o == arg0` is the same as `if (o eq null) arg0 eq null else o.equals(arg0)`.

`o == arg0` is the same as `if (o eq null) arg0 eq null else o.equals(arg0)`.

arg0

the object to compare against this object for equality .

returns

`true` if the receiver object is equivalent to the argument; `false` otherwise.

attributes: final
definition classes: AnyRef
7. #### def ==(arg0: Any): Boolean

`o == arg0` is the same as `o.equals(arg0)`.

`o == arg0` is the same as `o.equals(arg0)`.

arg0

the object to compare against this object for equality .

returns

`true` if the receiver object is equivalent to the argument; `false` otherwise.

attributes: final
definition classes: Any
8. #### def asInstanceOf[T0]: T0

This method is used to cast the receiver object to be of type `T0`.

This method is used to cast the receiver object to be of type `T0`.

Note that the success of a cast at runtime is modulo Scala's erasure semantics. Therefore the expression`1.asInstanceOf[String]` will throw a `ClassCastException` at runtime, while the expression`List(1).asInstanceOf[List[String]]` will not. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the requested typed.

returns

the receiver object .

attributes: final
definition classes: Any
9. #### def clone(): AnyRef

This method creates and returns a copy of the receiver object .

This method creates and returns a copy of the receiver object .

The default implementation of the `clone` method is platform dependent.

returns

a copy of the receiver object .

attributes: protected
definition classes: AnyRef
10. #### def eq(arg0: AnyRef): Boolean

This method is used to test whether the argument (`arg0`) is a reference to the receiver object (`this`).

This method is used to test whether the argument (`arg0`) is a reference to the receiver object (`this`).

The `eq` method implements an [http://en.wikipedia.org/wiki/Equivalence_relation equivalence relation] on non-null instances of `AnyRef`: * It is reflexive: for any non-null instance `x` of type `AnyRef`, `x.eq(x)` returns `true`. * It is symmetric: for any non-null instances `x` and `y` of type `AnyRef`, `x.eq(y)` returns `true` if and only if `y.eq(x)` returns `true`. * It is transitive: for any non-null instances `x`, `y`, and `z` of type `AnyRef` if `x.eq(y)` returns `true` and `y.eq(z)` returns `true`, then `x.eq(z)` returns `true`.

Additionally, the `eq` method has three other properties. * It is consistent: for any non-null instances `x` and `y` of type `AnyRef`, multiple invocations of `x.eq(y)` consistently returns `true` or consistently returns `false`. * For any non-null instance `x` of type `AnyRef`, `x.eq(null)` and `null.eq(x)` returns `false`. * `null.eq(null)` returns `true`.

When overriding the `equals` or `hashCode` methods, it is important to ensure that their behavior is consistent with reference equality. Therefore, if two objects are references to each other (`o1 eq o2`), they should be equal to each other (`o1 == o2`) and they should hash to the same value (`o1.hashCode == o2.hashCode`).

arg0

the object to compare against this object for reference equality .

returns

`true` if the argument is a reference to the receiver object; `false` otherwise.

attributes: final
definition classes: AnyRef
11. #### def equals(arg0: Any): Boolean

This method is used to compare the receiver object (`this`) with the argument object (`arg0`) for equivalence.

This method is used to compare the receiver object (`this`) with the argument object (`arg0`) for equivalence.

The default implementations of this method is an [http://en.wikipedia.org/wiki/Equivalence_relation equivalence relation]: * It is reflexive: for any instance `x` of type `Any`, `x.equals(x)` should return `true`. * It is symmetric: for any instances `x` and `y` of type `Any`, `x.equals(y)` should return `true` if and only if `y.equals(x)` returns `true`. * It is transitive: for any instances `x`, `y`, and `z` of type `AnyRef` if `x.equals(y)` returns `true` and `y.equals(z)` returns `true`, then `x.equals(z)` should return `true`.

If you override this method, you should verify that your implementation remains an equivalence relation. Additionally, when overriding this method it is often necessary to override `hashCode` to ensure that objects that are "equal" (`o1.equals(o2)` returns `true`) hash to the same scala.Int (`o1.hashCode.equals(o2.hashCode)`).

arg0

the object to compare against this object for equality .

returns

`true` if the receiver object is equivalent to the argument; `false` otherwise.

definition classes: AnyRef → Any
12. #### def equiv(x: T, y: T): Boolean

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

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

definition classes: PartialOrderingEquiv
13. #### def finalize(): Unit

This method is called by the garbage collector on the receiver object when garbage collection determines that there are no more references to the object .

This method is called by the garbage collector on the receiver object when garbage collection determines that there are no more references to the object .

The details of when and if the `finalize` method are invoked, as well as the interaction between `finalize`and non-local returns and exceptions, are all platform dependent.

attributes: protected
definition classes: AnyRef
14. #### def getClass(): java.lang.Class[_ <: java.lang.Object]

Returns a representation that corresponds to the dynamic class of the receiver object .

Returns a representation that corresponds to the dynamic class of the receiver object .

The nature of the representation is platform dependent.

returns

a representation that corresponds to the dynamic class of the receiver object .

attributes: final
definition classes: AnyRef
15. #### def gt(x: T, y: T): Boolean

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

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

16. #### def gteq(x: T, y: T): Boolean

Returns true iff y comes before x in the ordering .

Returns true iff y comes before x in the ordering .

17. #### def hashCode(): Int

Returns a hash code value for the object .

Returns a hash code value for the object .

The default hashing algorithm is platform dependent.

Note that it is allowed for two objects to have identical hash codes (`o1.hashCode.equals(o2.hashCode)`) yet not be equal (`o1.equals(o2)` returns `false`). A degenerate implementation could always return `0`. However, it is required that if two objects are equal (`o1.equals(o2)` returns `true`) that they have identical hash codes (`o1.hashCode.equals(o2.hashCode)`). Therefore, when overriding this method, be sure to verify that the behavior is consistent with the `equals` method.

returns

the hash code value for the object .

definition classes: AnyRef → Any
18. #### def isInstanceOf[T0]: Boolean

This method is used to test whether the dynamic type of the receiver object is `T0`.

This method is used to test whether the dynamic type of the receiver object is `T0`.

Note that the test result of the test is modulo Scala's erasure semantics. Therefore the expression`1.isInstanceOf[String]` will return `false`, while the expression `List(1).isInstanceOf[List[String]]` will return `true`. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the requested typed.

returns

`true` if the receiver object is an instance of erasure of type `T0`; `false` otherwise.

attributes: final
definition classes: Any
19. #### def lt(x: T, y: T): Boolean

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

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

20. #### def lteq(x: T, y: T): Boolean

Returns true iff x comes before y in the ordering .

Returns true iff x comes before y in the ordering .

attributes: abstract
21. #### def ne(arg0: AnyRef): Boolean

`o.ne(arg0)` is the same as `!(o.eq(arg0))`.

`o.ne(arg0)` is the same as `!(o.eq(arg0))`.

arg0

the object to compare against this object for reference dis-equality .

returns

`false` if the argument is not a reference to the receiver object; `true` otherwise.

attributes: final
definition classes: AnyRef
22. #### def notify(): Unit

Wakes up a single thread that is waiting on the receiver object's monitor .

Wakes up a single thread that is waiting on the receiver object's monitor .

attributes: final
definition classes: AnyRef
23. #### def notifyAll(): Unit

Wakes up all threads that are waiting on the receiver object's monitor .

Wakes up all threads that are waiting on the receiver object's monitor .

attributes: final
definition classes: AnyRef

25. #### def synchronized[T0](arg0: T0): T0

attributes: final
definition classes: AnyRef
26. #### def toString(): String

Returns a string representation of the object .

Returns a string representation of the object .

The default representation is platform dependent.

returns

a string representation of the object .

definition classes: AnyRef → Any
27. #### def tryCompare(x: T, y: T): Option[Int]

Result of comparing x with operand y .

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

attributes: abstract
28. #### def wait(): Unit

attributes: final
definition classes: AnyRef
29. #### def wait(arg0: Long, arg1: Int): Unit

attributes: final
definition classes: AnyRef
30. #### def wait(arg0: Long): Unit

attributes: final
definition classes: AnyRef