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.
Attributes
- Companion
- object
- Source
- PartialOrdering.scala
- Graph
-
- Supertypes
- Known subtypes
-
trait Ordering[T]object DeadlineIsOrderedobject DurationIsOrderedobject FiniteDurationIsOrderedobject ValueOrderingtrait Numeric[T]trait Fractional[T]trait BigDecimalIsFractionalobject BigDecimalIsFractionaltrait DoubleIsFractionalobject DoubleIsFractionaltrait FloatIsFractionalobject FloatIsFractionaltrait Integral[T]trait BigDecimalAsIfIntegralobject BigDecimalAsIfIntegraltrait BigIntIsIntegralobject BigIntIsIntegraltrait ByteIsIntegralobject ByteIsIntegraltrait CharIsIntegralobject CharIsIntegraltrait IntIsIntegralobject IntIsIntegraltrait LongIsIntegralobject LongIsIntegraltrait ShortIsIntegralobject ShortIsIntegraltrait BigDecimalIsConflictedtrait BigDecimalOrderingobject BigDecimaltrait BigIntOrderingobject BigInttrait BooleanOrderingobject Booleantrait ByteOrderingobject Bytetrait CachedReverse[T]object Inttrait CharOrderingobject Chartrait IeeeOrderingobject IeeeOrderingtrait TotalOrderingobject DeprecatedDoubleOrderingobject TotalOrderingtrait IeeeOrderingobject IeeeOrderingtrait TotalOrderingobject DeprecatedFloatOrderingobject TotalOrderingtrait IntOrderingtrait LongOrderingobject Longtrait OptionOrdering[T]trait ShortOrderingobject Shorttrait StringOrderingobject Stringtrait SymbolOrderingobject Symboltrait UnitOrderingobject Unit
- Self type