TotallyOrdered.java

package com.github.vincentk.dedekind.sets.ordered;

import com.github.vincentk.dedekind.sets.Cardinality;
import com.github.vincentk.dedekind.sets.binary.relation.homogeneous.TotalOrder;

/**
 * Set with a total order.
 * 
 * @param <C> cardinality
 * @param <T> implementation type
 * 
 * @see https://en.wikipedia.org/wiki/Partially_ordered_set#Derived_notions
 */
public interface TotallyOrdered<
E extends TotallyOrdered.Oe<E>,
C extends Cardinality,
T extends TotallyOrdered<E, C, T>
>
extends Lattice<E, C, T>{

    interface Oe<T extends Oe<T>>
    extends
    Lattice.Le<T>, TotalOrder<T> 
    {	
	@Override
	default boolean leq(T that) {
	    return compareTo(that) <= 0;
	}

	@SuppressWarnings("unchecked")
	@Override
	default T join(T that) {
	    return leq(that) ? that : (T) this;
	}

	@Override
	default T upperBound(T that) {
	    return join(that);
	}

	@SuppressWarnings("unchecked")
	@Override
	default T meet(T that) {
	    return leq(that) ? (T) this : that;
	}
    }
}