Truth value of empty set

I am interested in the truth value of Python sets like {'a', 'b'}, or the empty set set() (which is not the same as the empty dictionary {}). In particular, I would like to know whether bool(my_set) is False if and only if the set my_set is empty.

Ignoring primitive (such as numerals) as well as user-defined types, https://docs.python.org/3/library/stdtypes.html#truth says:

The following values are considered false:

[...]

any empty sequence, for example, '', (), [].

any empty mapping, for example, {}.

[...]

All other values are considered true

According to https://docs.python.org/3/library/stdtypes.html#sequence-types-list-tuple-range, a set is not a sequence (it is unordered, its elements do not have indices, etc.):

There are three basic sequence types: lists, tuples, and range objects.

And, according to https://docs.python.org/3/library/stdtypes.html#mapping-types-dict,

There is currently only one standard mapping type, the dictionary.

So, as far as I understand, the set type is not a type that can ever be False. However, when I try, bool(set()) evaluates to False.

Questions:

Is this a documentation problem, or am I getting something wrong?
Is the empty set the only set whose truth value is False?

Solution

After looking at the source code for CPython, I would guess this is a documentation error, however, it could be implementation dependent and therefore would be a good issue to raise on the Python bug tracker.

Specifically, object.c defines the truth value of an item as follows:

int
PyObject_IsTrue(PyObject *v)
{
    Py_ssize_t res;
    if (v == Py_True)
        return 1;
    if (v == Py_False)
        return 0;
    if (v == Py_None)
        return 0;
    else if (v->ob_type->tp_as_number != NULL &&
             v->ob_type->tp_as_number->nb_bool != NULL)
        res = (*v->ob_type->tp_as_number->nb_bool)(v);
    else if (v->ob_type->tp_as_mapping != NULL &&
             v->ob_type->tp_as_mapping->mp_length != NULL)
        res = (*v->ob_type->tp_as_mapping->mp_length)(v);
    else if (v->ob_type->tp_as_sequence != NULL &&
             v->ob_type->tp_as_sequence->sq_length != NULL)
        res = (*v->ob_type->tp_as_sequence->sq_length)(v);
    else
        return 1;
    /* if it is negative, it should be either -1 or -2 */
    return (res > 0) ? 1 : Py_SAFE_DOWNCAST(res, Py_ssize_t, int);
}

We can clearly see that the value is value would be always true if it is not a boolean type, None, a sequence, or a mapping type, which would require tp_as_sequence or tp_as_mapping to be set.

Fortunately, looking at setobject.c shows that sets do implement tp_as_sequence, suggesting the documentation seems to be incorrect.

PyTypeObject PySet_Type = {
    PyVarObject_HEAD_INIT(&PyType_Type, 0)
    "set",                              /* tp_name */
    sizeof(PySetObject),                /* tp_basicsize */
    0,                                  /* tp_itemsize */
    /* methods */
    (destructor)set_dealloc,            /* tp_dealloc */
    0,                                  /* tp_print */
    0,                                  /* tp_getattr */
    0,                                  /* tp_setattr */
    0,                                  /* tp_reserved */
    (reprfunc)set_repr,                 /* tp_repr */
    &set_as_number,                     /* tp_as_number */
    &set_as_sequence,                   /* tp_as_sequence */
    0,                                  /* tp_as_mapping */
    /* ellipsed lines */
};

Dicts also implement tp_as_sequence, so it seems that although it is not a sequence type, it sequence-like, enough to be truthy.

In my opionion, the documentation should clarify this: mapping-like types, or sequence-like types will be truthy dependent on their length.

Edit As user2357112 correctly points out, tp_as_sequence and tp_as_mapping do not mean the type is a sequence or a map. For example, dict implements tp_as_sequence, and list implements tp_as_mapping.