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]
Version: 1.0, 2008-04-0-3
Since: 2.7

Linear Supertypes

Equiv[T], Serializable, java.io.Serializable, AnyRef, Any

Known Subclasses

BigDecimal, BigDecimalAsIfIntegral, BigDecimalAsIfIntegral, BigDecimalIsConflicted, BigDecimalIsFractional, BigDecimalIsFractional, BigDecimalOrdering, BigInt, BigIntIsIntegral, BigIntIsIntegral, BigIntOrdering, Boolean, BooleanOrdering, Byte, ByteIsIntegral, ByteIsIntegral, ByteOrdering, Char, CharIsIntegral, CharIsIntegral, CharOrdering, DeadlineIsOrdered, Double, DoubleAsIfIntegral, DoubleAsIfIntegral, DoubleIsConflicted, DoubleIsFractional, DoubleIsFractional, DoubleOrdering, DurationIsOrdered, FiniteDurationIsOrdered, Float, FloatAsIfIntegral, FloatAsIfIntegral, FloatIsConflicted, FloatIsFractional, FloatIsFractional, FloatOrdering, Fractional, Int, IntIsIntegral, IntIsIntegral, IntOrdering, Integral, Long, LongIsIntegral, LongIsIntegral, LongOrdering, Numeric, OptionOrdering, Ordering, Short, ShortIsIntegral, ShortIsIntegral, ShortOrdering, String, StringOrdering, Unit, UnitOrdering, ValueOrdering

Abstract Value Members

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

Returns true iff x comes before y in the ordering.
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

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
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
PartialOrdering → Equiv
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def gt(x: T, y: T): Boolean

Returns true iff y comes before x in the ordering and is not the same as x.
def gteq(x: T, y: T): Boolean

Returns true iff y comes before x in the ordering.
def hashCode(): Int

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

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

Returns true iff x comes before y in the ordering and is not the same as y.
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def reverse: PartialOrdering[T]
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )

Related Doc: package math

trait PartialOrdering[T] extends Equiv[T]

Abstract Value Members

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

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

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def clone(): AnyRef

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

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

def finalize(): Unit

final def getClass(): Class[_]

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

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

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

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

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def reverse: PartialOrdering[T]

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

Inherited from Equiv[T]

Inherited from Serializable

Inherited from java.io.Serializable

Inherited from AnyRef

Inherited from Any

Ungrouped