Non-heap types, aka builtin types, cannot have their
attributes changed by Python code -- see
Objects/typeobject.c: type_setattro().  This limitation
is good for Python's core builtin types (int, float,
list, dict, ...), but not necessarily for non-heap
types in extension modules.  The attached patch allows
for non-heap types to mutate iff the
Py_TPFLAGS_MUTABLE_BUILTIN flag is set.

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Why can't you create such a type as a heap type?

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One reason that the type wasn't a heap type was because I
didn't find an example in the Python documentation.  And
because when I was looking through typeobject.c, I saw code,
like type_get_doc(), that ignores the (tp_doc) slot when it
is a heap type -- exactly what I don't want (looking closer,
it may be the only one).  I also like most of the
restrictions a non-heap type has, like being unable to
change its name.  So if heap types are as fast as non-heap
types, then I have no objection to switching.  I'm also
concerned about the additional startup time switching to
heap types would cost since I currently have 75 types in my
module.

The python code that prompted this patch was code that
reached in and added extra keyword arguments to a method,
sort of like a decorator, for additional bookkeeping. 
Subclassing is out because the C (C++) object factory
function only returns the instances of the original type.

FYI, I was able to work around this and use an unmodified Python by
subtyping type and overriding the setattr method as shown below.  It's a
lot messier than patching Python.

static int
Mutable_SetAttr(PyObject *obj, PyObject *name, PyObject *value)
{
        // Can't just call PyObject_GenericSetAttr because
        // we need to able to update the __str__ slot as well.
        PyTypeObject *type = reinterpret_cast<PyTypeObject*>(obj);
        type->tp_flags |= Py_TPFLAGS_HEAPTYPE;
        int result = PyType_Type.tp_setattro(obj, name, value);
        type->tp_flags &= ~Py_TPFLAGS_HEAPTYPE;
        return result;
}