[Python-ideas] Automatic total ordering

[Arnaud Delobelle]

On 15 Oct 2008, at 19:35, George Sakkis wrote:

> On Wed, Oct 15, 2008 at 2:11 PM, Guido van Rossum <guido at python.org>  
> wrote:
>
> On Wed, Oct 15, 2008 at 11:03 AM, Terry Reedy <tjreedy at udel.edu>  
> wrote:
> > George Sakkis wrote:
> >>
> >> Now that 3.x fixes the arbitrary object comparison wart and drops  
> (?)
> >> __cmp__,
> >
> > An entry for __cmp__ was in the 3.0c1 doc, which confused me.
> > It is now gone in
> > http://docs.python.org/dev/3.0/reference/datamodel.html#special-method-names
> >
> > Since rich comparisons are defined on object and are inherited by  
> all
> > classes, it would be difficult to make them not defined.
>
> I should also note that part of George's proposal has already been
> implemented: if you define __eq__, you get a complementary __ne__ for
> free. However it doesn't work the other way around (defining __ne__
> doesn't give you __eq__ for free), and there is no similar
> relationship for the ordering operators. The reason for the freebie is
> that it's *extremely* unlikely to want to define != as something other
> than the complement of == (the only use case is IEEE compliant NaNs);
> however it's pretty common to define non-total orderings (e.g. set
> inclusion).
>
> Partial orderings are certainly used, but I believe they are far  
> less common than total ones. Regardless, a partially ordered class  
> has to explicitly define the supported methods with the desired  
> semantics anyway; the proposed change wouldn't make this any harder.

I don't understand.  In a mathematical ordering,

* x > y means the same as y < x
* x <= y means the same as x < y or x = y
* x >= y means the same as x > y or x = y

and this is irrespective of whether the ordering is partial or total.

So, given __eq__ and __lt__, all the rest follows. E.g.

def __gt__(self, other):
     return other.__lt__(self)
etc...

Where am I going wrong?

-- 
Arnaud