NaN, Null, and Sorting

[Steven D'Aprano]

On Fri, 13 Jan 2012 11:04:48 -0800, Ethan Furman wrote:

> With NaN, it is possible to get a list that will not properly sort:
> 
> --> NaN = float('nan')
> --> spam = [1, 2, NaN, 3, NaN, 4, 5, 7, NaN] --> sorted(spam)
> [1, 2, nan, 3, nan, 4, 5, 7, nan]
> 
> I'm constructing a Null object with the semantics that if the returned
> object is Null, it's actual value is unknown.
>
> From a purist point of view if it is unknown then comparison results
> are also unknown since the actual value might be greater, lesser, or the
> same as the value being compared against.

>From a purist point of view, NANs are unordered with respect to numbers, 
and so one of two behaviours should occur:

(1) nan OP x should raise an exception, for all comparison operators 
except == and != 

(2) nan OP x should return False for all OPs except != 

I believe the current version of the standard supports operators for both 
sets of behaviour; the 1990s version of Apple's numeric framework (SANE) 
included both.

I think Python chooses the second behaviour, although it may be version 
and platform dependent. This is from Python 2.6:

>>> float('nan') < 0
False
>>> float('nan') > 0
False


I would expect the same behaviour for your Null objects. But as you say:


> From a practical point of view a list with Nulls scattered throughout
> is a pain in the backside.

And this is why sorting should be defined in terms of a separate sorting 
operator, not < or >, so that lists containing unordered values like NANs, 
Nulls, and complex numbers, can be sorted. "Sorted" is a property of the 
list, not the values within the list.


> So I am strongly leaning towards implementing the comparisons such that
> Null objects are less than other objects so they will always sort
> together.
> 
> Thoughts/advice/criticisms/etc?

Possibly the least-worst solution.


-- 
Steven