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:
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'.