Question about None
Steven D'Aprano
steve at REMOVETHIS.cybersource.com.au
Sun Jun 14 15:25:20 CEST 2009
John Yeung wrote:
> Paul LaFollette is probably thinking along the lines of formal logic
> or set theory. It's a little bit confused because programming isn't
> quite the same as math, and so it's a common question when designing
> and implementing programming languages how far to take certain
> abstractions. In some languages, nil, null, or none will try to
> behave as mathematically close to "nothing" (complete absence of
> anything) as possible, even though in reality they have to have some
> concrete implementation, such as perhaps being a singleton object.
> But mathematically speaking, it's intuitive that "nothing" would match
> any type.
I think you're wrong. Mathematically, you can't mix types like real numbers
and sets: while 1+0 = 1, you can't expect to get a sensible result from
1+{} or {1}∩0. (If that character between the set and zero ends up missing,
it's meant to be INTERSECTION u'\u2229'.)
Similarly, you can't add a scalar to a vector or matrix, even if one or the
other is null.
> I find that it's somewhat like the confusion that often occurs
> regarding the all() function. Some people are surprised that all([])
> returns True, but it's the same logic behind the truth of the
> statement "every element of the empty set is an integer". It's also
> true that every element of the empty set is a float. Or an elephant.
So-called "vacuous truth". It's often useful to have all([]) return true,
but it's not *always* useful -- there are reasonable cases where the
opposite behaviour would be useful:
if all(the evidence points to the Defendant's guilt) then:
the Defendant is guilty
execute(the Defendant)
sadly means that if there is no evidence that a crime has been committed,
the person accused of committing the imaginary crime will be executed.
--
Steven
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