def overloaded(func):
    """
    Introduces a new overloaded function and registers its first implementation.
    """
    fn = unwrap(func)
    ensure_function(fn)

    def dispatcher(*args, **kwargs):

        resolved = None
        if dispatcher.__complex_parameters:
            cache_key_pos = []
            cache_key_kw = []
            for argset in (0, 1) if kwargs else (0,):
                if argset == 0:
                    arg_pairs = enumerate(args)
                    complexity_mapping = dispatcher.__complex_positions
                else:
                    arg_pairs = kwargs.items()
                    complexity_mapping = dispatcher.__complex_parameters
                for id, arg in arg_pairs:
                    type_ = type(arg)
                    element_type = None
                    if id in complexity_mapping:
                        try:
                            element = next(iter(arg))
                        except TypeError:
                            pass
                        except StopIteration:
                            element_type = _empty
                        else:
                            complexity = complexity_mapping[id]
                            if complexity & 8 and isinstance(arg, tuple):
                                element_type = tuple(type(el) for el in arg)
                            elif complexity & 4 and hasattr(arg, 'keys'):
                                element_type = (type(element), type(arg[element]))
                            else:
                                element_type = type(element)
                    if argset == 0:
                        cache_key_pos.append((type_, element_type))
                    else:
                        cache_key_kw.append((id, type_, element_type))
        else:
            cache_key_pos = (type(arg) for arg in args)
            cache_key_kw = ((name, type(arg)) for (name, arg) in kwargs.items()) if kwargs else None

        cache_key = (tuple(cache_key_pos),
                     tuple(sorted(cache_key_kw)) if kwargs else None)

        try:
            resolved = dispatcher.__cache[cache_key]
        except KeyError:
            resolved = find(dispatcher, args, kwargs)
            if resolved:
                dispatcher.__cache[cache_key] = resolved
        if resolved:
            before = dispatcher.__hooks['before']
            after = dispatcher.__hooks['after']
            if before:
                before(*args, **kwargs)
            result = resolved(*args, **kwargs)
            if after:
                after(*args, **kwargs)
            return result
        else:
            return error(dispatcher.__name__)

    dispatcher.__dict__.update(
        __functions = [],
        __hooks = {'before': None, 'after': None},
        __cache = {},
        __complex_positions = {},
        __complex_parameters = {},
        __maxlen = 0,
    )
    for attr in ('__module__', '__name__', '__qualname__', '__doc__'):
        setattr(dispatcher, attr, getattr(fn, attr, None))
    if is_void(fn):
        update_docstring(dispatcher, fn)
        return dispatcher
    else:
        update_docstring(dispatcher)
        return register(dispatcher, func)
Introduces a new overloaded function and registers its first implementation.