JavaScript map, reduce, group, distinct

gistfile1.js

Object.properties = function(obj, includeFunctions)
{
    var props = [];
    for (var prop in obj)
    {
        if (true === includeFunctions || 'function' !== typeof obj[prop])
            props.push(prop);
    }
    return props;
}

Array.prototype.reduce = function(acc, callback/*(accumulator, element, index)*/, finalizer)
{
    for (var i = 0; i < this.length; i++)
        acc = callback(acc, this[i], i);
    return 'function' === typeof finalizer ? finalizer(acc) : acc;
}

Array.prototype.map = function(callback/*(element, index)*/)
{
    return this.reduce([], function(arr, e, i) { arr.push(callback(e, i)); return arr; });
}

Array.prototype.group = (function()
{
    function Grouping() { }
    Grouping.prototype.keys = function() { return Object.properties(this); };

    return function(fkey/*(element, index)*/, fvalue/*(element, index)*/)
    {
        if ('function' !== typeof fvalue)
            fvalue = function(e) { return e; };
        return this.reduce(
            new Grouping(),
            function(grouping, e, i)
            {
                var key = fkey(e, i);
                if (!(key in grouping))
                {
                    var g = [];
                    g.key = key;
                    grouping[key] = g;
                }
                grouping[key].push(fvalue(e, i));
                return grouping;
            }
        );
    };
})();

Array.prototype.distinct = function(callback/*(element, index)*/)
{
    return this.group('function' === typeof callback ? callback : function(e) { return e; }).keys();
}