Why aren't Python sets hashable?

I stumbled across a blog post detailing how to implement a powerset function in Python. So I went about trying my own way of doing it, and discovered that Python apparently cannot have a set of sets, since set is not hashable. This is irksome, since the definition of a powerset is that it is a set of sets, and I wanted to implement it using actual set operations.

>>> set([ set() ])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'set'

Is there a good reason Python sets are not hashable?

Generally, only immutable objects are hashable in Python. The immutable variant of set() -- frozenset() -- is hashable.

Because they're mutable.

If they were hashable, a hash could silently become "invalid", and that would pretty much make hashing pointless.

From the Python docs:

> hashable
> An object is hashable if it > has a hash value which never changes > during its lifetime (it needs a > hash() method), and can be compared to other objects (it needs an > eq() or cmp() method). Hashable objects which compare equal > must have the same hash value. > > Hashability makes an object usable as > a dictionary key and a set member, > because these data structures use the > hash value internally. > > All of Python’s immutable built-in > objects are hashable, while no mutable > containers (such as lists or > dictionaries) are. Objects which are > instances of user-defined classes are > hashable by default; they all compare > unequal, and their hash value is their > id().

In case this helps... if you really need to convert unhashable things into hashable equivalents for some reason you might do something like this:

from collections import Hashable, MutableSet, MutableSequence, MutableMapping

def make_hashdict(value):
    """
    Inspired by https://stackoverflow.com/questions/1151658/python-hashable-dicts
     - with the added bonus that it inherits from the dict type of value
       so OrderedDict's maintain their order and other subclasses of dict() maintain their attributes
    """
    map_type = type(value)

    class HashableDict(map_type):
        def __init__(self, *args, **kwargs):
            super(HashableDict, self).__init__(*args, **kwargs)
        def __hash__(self):
            return hash(tuple(sorted(self.items())))

    hashDict = HashableDict(value)

    return hashDict


def make_hashable(value):
    if not isinstance(value, Hashable):
        if isinstance(value, MutableSet):
            value = frozenset(value)
        elif isinstance(value, MutableSequence):
            value = tuple(value)
        elif isinstance(value, MutableMapping):
            value = make_hashdict(value)

        return value

my_set = set()
my_set.add(make_hashable(['a', 'list']))
my_set.add(make_hashable({'a': 1, 'dict': 2}))
my_set.add(make_hashable({'a', 'new', 'set'}))

print my_set

My HashableDict implementation is the simplest and least rigorous example from here. If you need a more advanced HashableDict that supports pickling and other things, check the many other implementations. In my version above I wanted to preserve the original dict class, thus preserving the order of OrderedDicts. I also use AttrDict from here for attribute-like access.

My example above is not in any way authoritative, just my solution to a similar problem where I needed to store some things in a set and needed to "hashify" them first.