Re: fixing infinities and ranges etc

On 2016-10-30 4:11 PM, Darren Duncan wrote:
> On 2016-10-30 5:45 AM, yary wrote:
>> Before/AfterEverything are also easy to understand, and would be as natural to
>> use for sorting strings, eg. for saying if a database NULL should go before the
>> empty string or after everything else. On the other hand, if I'doing something
>> with tangents and handling pi/2, I'd rather be thinking about PosInf as my
>> exception and not AfterEverything.
>
> So, the main thing that I think should exist is a generic
> before/after-everything concept so that it can be used to indicate that generic
> intervals are unbounded at either end and that generic 'cmp' etc are
> automatically defined for every other type and them and use as identity values
> for min/max.

So, following up on this, ...

I went with the singleton names Before_All_Others and After_All_Others in my 
abstract database protocol API for Perl 6, and explicitly documented that these 
are a type-agnostic analogy to negative/positive infinity whose sole purpose is 
to canonically sort before or after every other value in the type system, and 
they expressly do NOT represent any mathematical or physical concept of 
infinity, including those in IEEE floating point, which should be defined 
separately where useful.  Example uses of these singletons are to represent the 
endpoints of partially or totally unbounded intervals/ranges, or be the identity 
values for "min" and "max", or be the result when one calls "pred" or "succ" on 
the first/last value of an orderable type.

And so, I also want to propose that Perl 6 add the 2 singletons 
X::BeforeAllOthers and X::AfterAllOthers for similar type-generic use cases. 
Yet other singletons or values can exist to meaningfully represent mathematical 
infinities etc such as the IEEE floats support so appropriate semantics exist in 
peoples' code.

-- Darren Duncan