de.rwth.domains
Interface CompletePOSet

All Superinterfaces:

POSet, Set

All Known Subinterfaces:

CompleteLattice

All Known Implementing Classes:

LiftedCompletePOSet, TupleCompletePOSet, FunctionCompletePOSet

public interface CompletePOSet

extends POSet

Interface for complete partially ordered sets. Complete partially ordered sets are partially ordered sets with a least element and the property that every infinite directed set has a least upper bound.

Version:

$Id: CompletePOSet.java,v 1.2 2002/09/17 06:53:53 mohnen Exp $

Author:

Markus Mohnen

Inner classes inherited from class de.rwth.domains.Set

Set.Default

Method Summary

java.lang.Object

bottom() Gets the least element of this CompletePOSet.

Methods inherited from interface de.rwth.domains.POSet

le, lt

Methods inherited from interface de.rwth.domains.Set

equals, isElement, iterator, iteratorSkel, size, sizeSkel

Method Detail

bottom

public java.lang.Object bottom()

Gets the least element of this CompletePOSet.

Implementations should guarantee that bottom is indeed least element of this set, this is to say that isElement recognises the value returned by bottom and lt(bottom(),e)==true for all elements e.

Returns:

the least element in this set

See Also:

Domain.checkProperties(CompletePOSet cposet)