Maybe. If update() were added, would it mean adding intersection() and intersection_update() too (and maybe others)? For some reason the MutableSet ABC in https://docs.python.org/3/library/collections.abc.html#collections-abstract-base-classes prefers the binary operators rather than the method names. For example:

$ ipython
Python 3.8.4 (v3.8.4:dfa645a65e, Jul 13 2020, 10:45:06) 
Type 'copyright', 'credits' or 'license' for more information
IPython 7.16.1 -- An enhanced Interactive Python. Type '?' for help.

In [1]: from sortedcollections import OrderedSet                                         

In [2]: s = OrderedSet()                                                                 

In [3]: s.update([1, 2, 3, 4])                                                           
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-3-a5458f946adc> in <module>
----> 1 s.update([1, 2, 3, 4])

AttributeError: 'OrderedSet' object has no attribute 'update'

In [4]: s |= [1, 2, 3, 4]                                                                

In [5]: s                                                                                
Out[5]: OrderedSet([1, 2, 3, 4])

I once knew why but have since forgotten. It's probably as simple as adding update = MutableSet.__ior__ to the class definition (which I did not do ... again I can't recall why).

I would also add that OrderedSet has only the advantage of random-access indexing. Now that Python's dictionary maintains insertion order, a much faster version of OrderedSet could simply be implemented atop the dictionary data type.

from collections.abc import MutableSet

class OrderedSet(MutableSet):
    def __init__(self, iterable=()):
        self._values = dict()
        for element in iterable:
            self.add(element)

    def __contains__(self, key):
        return key in self._values

    def __iter__(self):
        return iter(self._values)

    def __len__(self):
        return len(self._values)

    def add(self, value):
        self._values[value] = None

    def discard(self, value):
        self._values.pop(value)

OrderedSet.update #17

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