How to do boolean algebra on missing values?

boolean-expression, python

Solution

As other have said, you can define your own class.

class NA_(object):
    instance = None # Singleton (so `val is NA` will work)
    def __new__(self):
        if NA_.instance is None:
            NA_.instance = super(NA_, self).__new__(self)
        return NA_.instance
    def __str__(self): return "NA"
    def __repr__(self): return "NA_()"
    def __and__(self, other):
        if self is other or other:
            return self
        else:
            return other
    __rand__ = __and__
    def __or__(self, other):
        if self is other or other:
            return other
        else:
            return self
    __ror__ = __or__
    def __xor__(self, other):
        return self
    __rxor__ = __xor__
    def __eq__(self, other):
        return self is other
    __req__ = __eq__
    def __nonzero__(self):
        raise TypeError("bool(NA) is undefined.")
NA = NA_()

Use:

>>> print NA & NA
NA
>>> print NA & True
NA
>>> print NA & False
False
>>> print NA | True
True
>>> print NA | False
NA
>>> print NA | NA
NA
>>> print NA ^ True
NA
>>> print NA ^ NA
NA
>>> if NA: print 3
...
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 28, in __nonzero__
TypeError: bool(NA) is undefined.
>>> if NA & False: print 3
...
>>>
>>> if NA | True: print 3
...
3
>>>

Problem

I want to replicate boolean `NA` values as they behave in R: NA is a valid logical object. Where a component of x or y is NA, the result will be NA if the outcome is ambiguous. In other words NA & TRUE evaluates to NA, but NA & FALSE evaluates to FALSE. http://stat.ethz.ch/R-manual/R-devel/library/base/html/Logic.html I have seen `None` being recommended for missing values, but Python converts `None` to `False` when evaluating boolean expressions, and computes `None or False` to `False`. The result should of course have been `None`, as no conclusions can be made given the missing value. How do I achieve this in Python? EDIT Accepted answer computes correctly with bitwise boolean operators, but to achieve the same behavior with logical operators `not`, `or` and `and`, seems to require a change in the Python programming language.

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