# 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`.
Self Type
PartialOrdering[T]
Source
PartialOrdering.scala
Version

1.0, 2008-04-0-3

Since

2.7

Linear Supertypes
Equiv[T], Serializable, java.io.Serializable, AnyRef, Any
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. PartialOrdering
2. Equiv
3. Serializable
4. Serializable
5. AnyRef
6. Any
Implicitly
2. by any2stringfmt
3. by any2ArrowAssoc
4. by any2Ensuring
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Visibility
1. Public
2. All

### Abstract Value Members

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

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

2. #### abstract 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`

### Concrete Value Members

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

Definition Classes
AnyRef
2. #### final def !=(arg0: Any): Boolean

Test two objects for inequality.

Test two objects for inequality.

returns

`true` if !(this == that), false otherwise.

Definition Classes
Any
3. #### final def ##(): Int

Equivalent to `x.hashCode` except for boxed numeric types and `null`.

Equivalent to `x.hashCode` except for boxed numeric types and `null`. For numerics, it returns a hash value which is consistent with value equality: if two value type instances compare as true, then ## will produce the same hash value for each of them. For `null` returns a hashcode where `null.hashCode` throws a `NullPointerException`.

returns

a hash value consistent with ==

Definition Classes
AnyRef → Any
4. #### def +(other: String): String

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to StringAdd performed by method any2stringadd in scala.Predef.
Definition Classes
5. #### def ->[B](y: B): (PartialOrdering[T], B)

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]] performed by method any2ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc
Annotations
()
6. #### final def ==(arg0: AnyRef): Boolean

Definition Classes
AnyRef
7. #### final def ==(arg0: Any): Boolean

Test two objects for equality.

Test two objects for equality. The expression `x == that` is equivalent to `if (x eq null) that eq null else x.equals(that)`.

returns

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

Definition Classes
Any
8. #### final def asInstanceOf[T0]: T0

Cast the receiver object to be of type `T0`.

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 type.

returns

Definition Classes
Any
Exceptions thrown
ClassCastException

if the receiver object is not an instance of the erasure of type `T0`.

9. #### def clone(): AnyRef

Create a copy of the receiver object.

Create 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[java.lang]
Definition Classes
AnyRef
Annotations
()
Note

not specified by SLS as a member of AnyRef

10. #### def ensuring(cond: (PartialOrdering[T]) ⇒ Boolean, msg: ⇒ Any): PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method any2Ensuring in scala.Predef.
Definition Classes
Ensuring
11. #### def ensuring(cond: (PartialOrdering[T]) ⇒ Boolean): PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method any2Ensuring in scala.Predef.
Definition Classes
Ensuring
12. #### def ensuring(cond: Boolean, msg: ⇒ Any): PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method any2Ensuring in scala.Predef.
Definition Classes
Ensuring
13. #### def ensuring(cond: Boolean): PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method any2Ensuring in scala.Predef.
Definition Classes
Ensuring
14. #### final def eq(arg0: AnyRef): Boolean

Tests whether the argument (`arg0`) is a reference to the receiver object (`this`).

Tests whether the argument (`arg0`) is a reference to the receiver object (`this`).

The `eq` method implements an equivalence relation on non-null instances of `AnyRef`, and has three additional 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`).

returns

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

Definition Classes
AnyRef
15. #### def equals(arg0: Any): Boolean

The equality method for reference types.

The equality method for reference types. Default implementation delegates to `eq`.

See also `equals` in scala.Any.

returns

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

Definition Classes
AnyRef → Any
16. #### 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
17. #### def finalize(): Unit

Called by the garbage collector on the receiver object when there are no more references to the object.

Called by the garbage collector on the receiver object when there are no more references to the object.

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

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
()
Note

not specified by SLS as a member of AnyRef

18. #### def formatted(fmtstr: String): String

Returns string formatted according to given `format` string.

Returns string formatted according to given `format` string. Format strings are as for `String.format` (@see java.lang.String.format).

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to StringFormat performed by method any2stringfmt in scala.Predef.
Definition Classes
StringFormat
Annotations
()
19. #### final def getClass(): Class[_]

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

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.

Definition Classes
AnyRef → Any
Note

not specified by SLS as a member of AnyRef

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

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

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

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

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

The hashCode method for reference types.

The hashCode method for reference types. See hashCode in scala.Any.

returns

the hash code value for this object.

Definition Classes
AnyRef → Any
23. #### final def isInstanceOf[T0]: Boolean

Test whether the dynamic type of the receiver object is `T0`.

Test whether the dynamic type of the receiver object is `T0`.

Note that the 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 specified type.

returns

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

Definition Classes
Any
24. #### def lt(x: T, y: T): Boolean

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

25. #### final def ne(arg0: AnyRef): Boolean

Equivalent to `!(this eq that)`.

Equivalent to `!(this eq that)`.

returns

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

Definition Classes
AnyRef
26. #### final 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.

Definition Classes
AnyRef
Note

not specified by SLS as a member of AnyRef

27. #### final 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.

Definition Classes
AnyRef
Note

not specified by SLS as a member of AnyRef

29. #### final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
30. #### def toString(): String

Creates a String representation of this object.

Creates a String representation of this object. The default representation is platform dependent. On the java platform it is the concatenation of the class name, "@", and the object's hashcode in hexadecimal.

returns

a String representation of the object.

Definition Classes
AnyRef → Any
31. #### final def wait(): Unit

Definition Classes
AnyRef
Annotations
()
32. #### final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
()
33. #### final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
()
34. #### def →[B](y: B): (PartialOrdering[T], B)

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]] performed by method any2ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc

### Shadowed Implict Value Members

1. #### val self: Any

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to StringAdd performed by method any2stringadd in scala.Predef.
This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
To access this member you can use a type ascription:
`(partialOrdering: StringAdd).self`
Definition Classes
2. #### val self: Any

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to StringFormat performed by method any2stringfmt in scala.Predef.
This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
To access this member you can use a type ascription:
`(partialOrdering: StringFormat).self`
Definition Classes
StringFormat

### Deprecated Value Members

1. #### def x: PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]] performed by method any2ArrowAssoc in scala.Predef.
This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
To access this member you can use a type ascription:
`(partialOrdering: ArrowAssoc[PartialOrdering[T]]).x`
Definition Classes
ArrowAssoc
Annotations
Deprecated

(Since version 2.10.0) Use `leftOfArrow instead`

2. #### def x: PartialOrdering[T]

Implicit information
This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method any2Ensuring in scala.Predef.
This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
To access this member you can use a type ascription:
`(partialOrdering: Ensuring[PartialOrdering[T]]).x`
Definition Classes
Ensuring
Annotations
Deprecated

(Since version 2.10.0) Use `resultOfEnsuring instead`