PartialOrdering

trait PartialOrdering[T] extends Equiv[T]

A trait for representing partial orderings.

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.

Companion: object

trait Equiv[T]

trait Serializable

class Object

trait Matchable

class Any

trait Ordering[T]

trait Numeric[T]

trait Fractional[T]

trait FloatIsFractional

object FloatIsFractional

trait DoubleIsFractional

object DoubleIsFractional

trait BigDecimalIsFractional

object BigDecimalIsFractional

trait Integral[T]

trait BigIntIsIntegral

object BigIntIsIntegral

trait IntIsIntegral

object IntIsIntegral

trait ShortIsIntegral

object ShortIsIntegral

trait ByteIsIntegral

object ByteIsIntegral

trait CharIsIntegral

object CharIsIntegral

trait LongIsIntegral

object LongIsIntegral

trait BigDecimalAsIfIntegral

object BigDecimalAsIfIntegral

trait BigDecimalIsConflicted

trait CachedReverse[T]

object Int

trait UnitOrdering

object Unit

trait BooleanOrdering

object Boolean

trait ByteOrdering

object Byte

trait CharOrdering

object Char

trait ShortOrdering

object Short

trait IntOrdering

trait LongOrdering

object Long

trait TotalOrdering

object TotalOrdering

object DeprecatedFloatOrdering

trait IeeeOrdering

object IeeeOrdering

trait TotalOrdering

object TotalOrdering

object DeprecatedDoubleOrdering

trait IeeeOrdering

object IeeeOrdering

trait BigIntOrdering

object BigInt

trait BigDecimalOrdering

object BigDecimal

trait StringOrdering

object String

trait SymbolOrdering

object Symbol

trait OptionOrdering[T]

Value members

Abstract methods

Returns true iff x comes before y in the ordering.

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 methods

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

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.

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