scala

trait PartialOrdering

`trait` PartialOrdering[T]
` extends `Equiv[T]` with `AnyRef
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`.
Author
Geoffrey Washburn
Version
1.0, 2008-04-0-3
Direct Known Subclasses:
Ordering

 Method Summary ` def` equiv (x : T, y : T) : Boolean Returns `true` iff `x` is equivalent to `y` in the ordering. ` 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` lt (x : T, y : T) : Boolean Returns `true` iff `x` comes before `y` in the ordering and is not the same as `y`. `abstract def` lteq (x : T, y : T) : Boolean Returns `true` iff `x` comes before `y` in the ordering.
 Methods inherited from AnyRef getClass, hashCode, equals, clone, toString, notify, notifyAll, wait, wait, wait, finalize, ==, !=, eq, ne, synchronized
 Methods inherited from Any ==, !=, isInstanceOf, asInstanceOf
 Method Details
`abstract` `def` lteq(x : T, y : T) : Boolean
Returns `true` iff `x` comes before `y` in the ordering.

`def` gteq(x : T, y : T) : Boolean
Returns `true` iff `y` comes before `x` in the ordering.

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

`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` equiv(x : T, y : T) : Boolean
Returns `true` iff `x` is equivalent to `y` in the ordering.
Overrides
Equiv.equiv