Set Expressions¶

A SetExpr represents either a named set, or a set computed from various unary or binary operations applied to other set expressions.

A SetExpr is a completely abstract representation of such an expression, but can be evaluated by providing a way to look up a set’s value from its name.

It is used by setvis to filter based on matching intersections (see setvis.membership.Membership.matching_intersections()).

A SetExpr is either:

A named set, Set
A Union (set union), Intersect (set intersection), Diff (set difference) or SymDiff (symmetric set difference) instance, formed from two SetExpr
A Complement instance, formed from one SetExpr.

A set expression can be built using boolean set notation:

| Union
& Intersect
- Diff
^ SymDiff
~ Complement

For example:

>>> (Set('A') & Set('B')) | ~Set('C')
Union(a=Intersect(a=Set(name='A'), b=Set(name='B')), b=Complement(a=Set(name='C')))

For a SetExpr to be evaluated with SetExpr.evaluate(): the lookup_name argument to evaluate must be a function (or other callable) that returns values supporting boolean set operations. The required methods are:

__or__ (|) set union
__and__ (&) set intersection
__xor__ (^) symmetric difference
__invert__ (~) set complement

Note that __sub__ (-) for set difference is not needed, and __invert__ is required only for evaluating Complement (the builtin python set does not support this operation).

Examples

>>> Set('A')
Set(name='A')
>>> U = Set('A') | Set('B')
>>> U
Union(a=Set(name='A'), b=Set(name='B'))
>>> I = Set('A') & Set('B')
>>> I
Intersect(a=Set(name='A'), b=Set(name='B'))

Associate named sets with values and evaluate the expression. In this case, the values have type python set, which support | and & operators for union and intersection.

>>> set_dict1 = {'A': {1,2,3}, 'B': {1,3,4}}}
>>> U.evaluate(lookup_name=set_dict1.get)
{1,2,3,4}
>>> I.evaluate(lookup_name=set_dict1.get)
{1,3}

The same expressions can be evaluated in a different context. Here, set membership is represented as a bit field, and the various set operations are computed via bitwise operators on integers (| and &).

>>> set_dict2 = {'A': 0b1110, 'B': 0b1011}
>>> bin(U.evaluate(lookup_name=set_dict2.get))
'0b1111'
>>> bin(I.evaluate(lookup_name=set_dict2.get))
'0b1010'