eset

Extended sets - support for set complement

Overview

An eset works like a normal python set except that you can invert it to generate its complement. For example, let's say you have the following:

>>> from esets import eset
>>> s = eset(['hello', 'there'])
>>> s_invert = ~s
>>> s_invert
~eset(['hello', 'there'])

In this example, s_invert contains everything except 'hello' and 'there'.

Logic

All the logic operations you'd expect from sets are available in esets, including intersection, union, difference, and symmetric difference. Use the &, |, -, and ^ operators respectively.

Similarly, conditional expressions are available to determine subset relationships. If A <= B, that A is a subset of B.

The named forms of these operations are there too -- union, intersection, difference, symmetric_difference, isdisjoint, issubset, issuperset -- along with their in-place counterparts (update, intersection_update, difference_update, symmetric_difference_update) and the usual add, discard, remove, pop, clear and copy. As with the builtin set, the operators accept only sets, dicts and esets, while the named methods raise TypeError on anything else.

Membership is what mutates

Mutation is defined in terms of membership, not storage, so it reads the same either side of an inversion: after s.add(x), x in s is always true, and after s.discard(x) it is always false -- even when s is a complement, where the item is dropped from (or added to) the excluded items to make that hold.

>>> s = ~eset(['hello'])
>>> s.add('hello')
~eset()
>>> 'hello' in s
True

Iteration and length

A complement eset has infinitely many members, so it can neither be iterated nor measured with len(); both raise TypeError. Invert it to walk the finite set of items it excludes, and use abs() for its cardinality.

>>> list(~~eset(['hello', 'there']))
['hello', 'there']

Frozen esets

frozen() returns an immutable eset, which -- unlike a plain one -- is hashable and so can be a dict key or live inside another set. A frozen eset hashes the same as the frozenset it compares equal to.

>>> from esets import frozen
>>> frozen(['hello']) in {frozen(['hello'])}
True

Anything that would mutate one -- add, discard, clear, update and the other *_update methods -- raises TypeError. The augmented operators are the exception, and behave as they do for frozenset: f &= x never mutated anything to begin with, it rebound the name, so it yields a new frozen eset and leaves the original alone.

>>> f = frozen(['hello', 'there'])
>>> f &= {'hello'}
>>> f
frozen(eset(['hello']))

Use freeze() and thaw() to flip an existing eset between the two states.

Infinities

You'll note there's an inf.py module that implement א0 and א1 infinities, that is, countable and uncountable infinities. This was implemented so that cardinality calculations would be correct for complement sets: discussed below.

>>> from esets import inf
>>> inf.countable, inf.uncountable
(א0, א1)
>>> inf.countable < inf.uncountable
True

Indeterminate forms such as א0 - א0 yield inf.nan, which propagates through any further arithmetic and compares False against everything ordered -- but, unlike float('nan'), equals itself so results can be checked against it.

>>> inf.countable - inf.countable
nan
>>> inf.countable - inf.countable == inf.nan
True

Cardinality

The abs expression (also cardinality method) will return a countably infinite scalar if in complement mode; otherwise it returns the count of items in set.

>>> from esets import eset, inf
>>> s = eset(['hello', 'there'])
>>> abs(s)
2
>>> abs(~s)
א0