local ipairs, pairs, setmetatable, next, tostring = 

      ipairs, pairs, setmetatable, next, tostring;

local t_concat = table.concat;

module "set"

local set_mt = {};

function set_mt.__call(set, _, k)

	return next(set._items, k);

end

function set_mt.__add(set1, set2)

	return _M.union(set1, set2);

end

function set_mt.__sub(set1, set2)

	return _M.difference(set1, set2);

end

function set_mt.__div(set, func)

	local new_set, new_items = _M.new();

	local items, new_items = set._items, new_set._items;

	for item in pairs(items) do

		if func(item) then

			new_items[item] = true;

		end

	end

	return new_set;

end

function set_mt.__eq(set1, set2)

	local set1, set2 = set1._items, set2._items;

	for item in pairs(set1) do

		if not set2[item] then

			return false;

		end

	end

	for item in pairs(set2) do

		if not set1[item] then

			return false;

		end

	end

	return true;

end

function set_mt.__tostring(set)

	local s, items = { }, set._items;

	for item in pairs(items) do

		s[#s+1] = tostring(item);

	end

	return t_concat(s, ", ");

end

local items_mt = {};

function items_mt.__call(items, _, k)

	return next(items, k);

end

function new(list)

	local items = setmetatable({}, items_mt);

	local set = { _items = items };

	function set:add(item)

		items[item] = true;

	end

	function set:contains(item)

		return items[item];

	end

	function set:items()

		return items;

	end

	function set:remove(item)

		items[item] = nil;

	end

	function set:add_list(list)

		for _, item in ipairs(list) do

			items[item] = true;

		end

	end

	function set:include(otherset)

		for item in pairs(otherset) do

			items[item] = true;

		end

	end

	function set:exclude(otherset)

		for item in pairs(otherset) do

			items[item] = nil;

		end

	end

	function set:empty()

		return not next(items);

	end

	if list then

		set:add_list(list);

	end

	return setmetatable(set, set_mt);

end

function union(set1, set2)

	local set = new();

	local items = set._items;

	for item in pairs(set1._items) do

		items[item] = true;

	end

	for item in pairs(set2._items) do

		items[item] = true;

	end

	return set;

end

function difference(set1, set2)

	local set = new();

	local items = set._items;

	for item in pairs(set1._items) do

		items[item] = (not set2._items[item]) or nil;

	end

	return set;

end

function intersection(set1, set2)

	local set = new();

	local items = set._items;

	set1, set2 = set1._items, set2._items;

	for item in pairs(set1) do

		items[item] = (not not set2[item]) or nil;

	end

	return set;

end

function xor(set1, set2)

	return union(set1, set2) - intersection(set1, set2);

end

return _M;