sets¶

Classes to represent arbitrary sets (including sets of sets).

This module implements sets using dictionaries whose values are ignored. The usual operations (union, intersection, deletion, etc.) are provided as both methods and operators.

Important: sets are not sequences! While they support ‘x in s’, ‘len(s)’, and ‘for x in s’, none of those operations are unique for sequences; for example, mappings support all three as well. The characteristic operation for sequences is subscripting with small integers: s[i], for i in range(len(s)). Sets don’t support subscripting at all. Also, sequences allow multiple occurrences and their elements have a definite order; sets on the other hand don’t record multiple occurrences and don’t remember the order of element insertion (which is why they don’t support s[i]).

The following classes are provided:

BaseSet – All the operations common to both mutable and immutable

sets. This is an abstract class, not meant to be directly instantiated.

Set – Mutable sets, subclass of BaseSet; not hashable.

ImmutableSet – Immutable sets, subclass of BaseSet; hashable.

An iterable argument is mandatory to create an ImmutableSet.

_TemporarilyImmutableSet – A wrapper around a Set, hashable,

giving the same hash value as the immutable set equivalent would have. Do not use this class directly.

Only hashable objects can be added to a Set. In particular, you cannot really add a Set as an element to another Set; if you try, what is actually added is an ImmutableSet built from it (it compares equal to the one you tried adding).

When you ask if `x in y’ where x is a Set and y is a Set or ImmutableSet, x is wrapped into a _TemporarilyImmutableSet z, and what’s tested is actually `z in y’.