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scala.math

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, 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
PartialOrdering.scala
Version

1.0, 2008-04-0-3

Since

2.7

Linear Supertypes
Equiv[T], Serializable, java.io.Serializable, AnyRef, Any
Known Subclasses
ValueOrdering, DeadlineIsOrdered, DurationIsOrdered, FiniteDurationIsOrdered, Fractional, Integral, Numeric, BigDecimalAsIfIntegral, BigDecimalAsIfIntegral, BigDecimalIsConflicted, BigDecimalIsFractional, BigDecimalIsFractional, BigIntIsIntegral, BigIntIsIntegral, ByteIsIntegral, ByteIsIntegral, CharIsIntegral, CharIsIntegral, DoubleAsIfIntegral, DoubleAsIfIntegral, DoubleIsConflicted, DoubleIsFractional, DoubleIsFractional, FloatAsIfIntegral, FloatAsIfIntegral, FloatIsConflicted, FloatIsFractional, FloatIsFractional, IntIsIntegral, IntIsIntegral, LongIsIntegral, LongIsIntegral, ShortIsIntegral, ShortIsIntegral, Ordering, BigDecimal, BigDecimalOrdering, BigInt, BigIntOrdering, Boolean, BooleanOrdering, Byte, ByteOrdering, Char, CharOrdering, Double, DoubleOrdering, Float, FloatOrdering, Int, IntOrdering, Long, LongOrdering, OptionOrdering, Short, ShortOrdering, String, StringOrdering, Unit, UnitOrdering
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. PartialOrdering
  2. Equiv
  3. Serializable
  4. Serializable
  5. AnyRef
  6. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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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: Any): Boolean

    Test two objects for inequality.

    Test two objects for inequality.

    returns

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

    Definition Classes
    AnyRef → Any
  2. 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
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to any2stringadd[PartialOrdering[T]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (PartialOrdering[T], B)
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

    The expression x == that is equivalent to if (x eq null) that eq null else x.equals(that).

    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
    AnyRef → Any
  6. 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

    the receiver object.

    Definition Classes
    Any
    Exceptions thrown

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

  7. 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
    @native() @throws( ... )
    Note

    not specified by SLS as a member of AnyRef

  8. def ensuring(cond: (PartialOrdering[T]) ⇒ Boolean, msg: ⇒ Any): PartialOrdering[T]
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  9. def ensuring(cond: (PartialOrdering[T]) ⇒ Boolean): PartialOrdering[T]
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  10. def ensuring(cond: Boolean, msg: ⇒ Any): PartialOrdering[T]
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: Boolean): PartialOrdering[T]
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to Ensuring[PartialOrdering[T]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. final def eq(arg0: AnyRef): Boolean

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

    Tests whether the argument (that) 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
  13. 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
  14. 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
  15. 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
    @throws( classOf[java.lang.Throwable] )
    Note

    not specified by SLS as a member of AnyRef

  16. 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
    This member is added by an implicit conversion from PartialOrdering[T] to StringFormat[PartialOrdering[T]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. final def getClass(): Class[_]

    Returns the runtime class representation of the object.

    Returns the runtime class representation of the object.

    returns

    a class object corresponding to the runtime type of the receiver.

    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  18. def gt(x: T, y: T): Boolean

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

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

    Returns true iff y comes before x in the ordering.

  20. 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
    Annotations
    @native()
  21. 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
  22. def lt(x: T, y: T): Boolean

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

  23. 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
  24. 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
    Annotations
    @native()
    Note

    not specified by SLS as a member of AnyRef

  25. 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
    Annotations
    @native()
    Note

    not specified by SLS as a member of AnyRef

  26. def reverse: PartialOrdering[T]
  27. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  28. 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
  29. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  30. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  32. def →[B](y: B): (PartialOrdering[T], B)
    Implicit
    This member is added by an implicit conversion from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Equiv[T]

Inherited from Serializable

Inherited from java.io.Serializable

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from PartialOrdering[T] to any2stringadd[PartialOrdering[T]]

Inherited by implicit conversion StringFormat from PartialOrdering[T] to StringFormat[PartialOrdering[T]]

Inherited by implicit conversion Ensuring from PartialOrdering[T] to Ensuring[PartialOrdering[T]]

Inherited by implicit conversion ArrowAssoc from PartialOrdering[T] to ArrowAssoc[PartialOrdering[T]]

Ungrouped