Set operations for Array

/*
 * Set operations for Array: https://pastebin.com/yMY0Q4AE
 * This snippet adds the following functions to Array.prototype:
 * 1. isProperSubsetOf(Array) -> Boolean
 *    - Checks whether this Array is a proper subset of the passed one
 * 2. isProperSupersetOf(Array) -> Boolean
 *    - Checks whether this Array is a proper superset of the passed one
 * 3. isSameSetAs(Array) -> Boolean
 *    - Checks whether this Array is the same set of the passed one
 * 4. isSupersetOf(Array) -> Boolean
 *    - Checks whether this Array is a superset of the passed one
 * 5. isSubsetOf(Array) -> Boolean
 *    - Checks whether this Array is a subset of the passed one
 * 6. isEmptySet() -> Boolean
 *    - Checks whether this Array is an empty set
 * 7. symmetricDifference(Array) -> Array
 *    - Returns the symmetric difference from this Array and the passed one
 * 8. union(Array) -> Array
 *    - Returns the union from this Array and the passed one
 * 9. difference(Array) -> Array
 *    - Returns the difference of this Array with respect to the passed one
 * 10. intersection(Array) -> Array
 *     - Returns the intersection from this Array and the passed one
 * 11. excludes(arrayElement) -> Boolean
 *    - Checks whether this Array doesn't have element arrayElement
 * 12. includes(arrayElement) -> Boolean
 *    - Checks whether this Array has element arrayElement
 * If any of the above function are already defined before running this snippet,
 * this snippet won't define those already defined ones
 */

(function() {

    "use strict";

    var $ = Array.prototype;

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isProperSubsetOf = $.isProperSubsetOf || function(array) {
        return this.isSubsetOf(array) && !array.isSubsetOf(this);
    }; // $.isProperSubsetOf

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isProperSupersetOf = $.isProperSupersetOf || function(array) {
        return this.isSupersetOf(array) && !array.isSupersetOf(this);
    }; // $.isProperSupersetOf

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isSameSetAs = $.isSameSetAs || function(array) {
        return this.isSubsetOf(array) && this.isSupersetOf(array);
    }; // $.isSameSetAs

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isSupersetOf = $.isSupersetOf || function(array) {
        return array.isSubsetOf(this);
    }; // $.isSupersetOf

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isSubsetOf = $.isSubsetOf || function(array) {
        return this.difference(array).isEmptySet();
    }; // $.isSubsetOf

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.isEmptySet = $.isEmptySet || function() { return this.length <= 0; };

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to have symmetric difference with
     * @returns {Array} The requested symmetric difference
     * @since v1.00a
     * @version v1.00a
     */
    $.symmetricDifference = $.symmetricDifference || function(array) {
        return this.difference(array).union(array.difference(this));
    }; // $.symmetricDifference

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to have union with this array
     * @returns {Array} The requested union
     * @since v1.00a
     * @version v1.00a
     */
    $.union = $.union || function(array) {
        return this.concat(array.difference(this));
    }; // $.union

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to have difference with this array
     * @returns {Array} The requested difference
     * @since v1.00a
     * @version v1.00a
     */
    $.difference = $.difference || function(array) {
        return this.filter(this.excludes, array);
    }; // $.difference

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {Array} array - The array to have intersection with this array
     * @returns {Array} The requested intersection
     * @since v1.00a
     * @version v1.00a
     */
    $.intersection = $.intersection || function(array) {
        return this.filter(this.includes, array);
    }; // $.intersection

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {} element - The element to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.excludes = $.excludes || function(element) {
        return !this.includes(element);
    }; // $.excludes

    /**
     * Pure function
     * @author DoubleX
     * @interface
     * @param {} element - The element to be checked against
     * @returns {Boolean} The check result
     * @since v1.00a
     * @version v1.00a
     */
    $.includes = $.includes || function(element) {
        return this.indexOf(element) >= 0;
    }; // $.includes

})();