How come regex match objects aren't iterable even though they implement getitem?

As you may know, implementing a __getitem__ method makes a class iterable:

    class IterableDemo:
        def __getitem__(self, index):
            if index > 3:
                raise IndexError

            return index

    demo = IterableDemo()
    print(demo[2])  # 2
    print(list(demo))  # [0, 1, 2, 3]
    print(hasattr(demo, '__iter__'))  # False

However, this doesn't hold true for regex match objects:

    >>> import re
    >>> match = re.match('(ab)c', 'abc')
    >>> match[0]
    >>> match[1]
    >>> list(match)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: '_sre.SRE_Match' object is not iterable

It's worth noting that this exception isn't thrown in the __iter__ method, because that method isn't even implemented:

    >>> hasattr(match, '__iter__')

So, how is it possible to implement __getitem__ without making the class iterable?

There are lies, damned lies and then there is Python documentation.

Having __getitem__ for a class implemented in C is not enough for it to be iterable. That is because there are actually 2 places in the PyTypeObject where the __getitem__ can be mapped to: tp_as_sequence and tp_as_mapping. Both have a slot for __getitem__ ([1], [2]).

Looking at the source of the SRE_Match, tp_as_sequence is initialized to NULL whereas tp_as_mapping is defined.

The iter() built-in function, if called with one argument, will call the PyObject_GetIter, which has the following code:

    f = t->tp_iter;
    if (f == NULL) {
        if (PySequence_Check(o))
            return PySeqIter_New(o);
        return type_error("'%.200s' object is not iterable", o);

It first checks the tp_iter slot (obviously NULL for _SRE_Match objects); and failing that, then if PySequence_Check returns true, a new sequence iterator, else a TypeError is raised.

PySequenceCheck first checks if the object is a dict or a dict subclass - and returns false in that case. Otherwise it returns the value of

    s->ob_type->tp_as_sequence &&
        s->ob_type->tp_as_sequence->sq_item != NULL;

and since s->ob_type->tp_as_sequence was NULL for a _SRE_Match instance, 0 will be returned, and PyObject_GetIter raises TypeError: '_sre.SRE_Match' object is not iterable.