package ordering;

/**
 * Represents an total order relation, "less or equal to", in a set.
 * @author Dung X. Nguyen - Copyright 2001 - All rights reserved.
 */
public abstract class AOrder {
    /**
     * defines a "less than" strict ordering.
     */
    public abstract boolean lt (Object x, Object y);

    /**
     * defines equality.
     */
    public abstract boolean eq (Object x, Object y);

    public boolean ne (Object x, Object y) {
        return !eq(x, y);
    }

    public boolean le (Object x, Object y) {
        return lt(x, y) || eq(x, y);
    }

    public boolean gt (Object x, Object y) {
        return !le(x, y);
    }

    public boolean ge (Object x, Object y) {
        return !lt(x, y);
    }
}