Waldek Hebisch <hebi...@math.uni.wroc.pl> writes:

> Martin Rubey wrote:
>> 
>> I have a request: please document the difference between
>> 
>> \section{category COMPAR Comparable}
>> <<category COMPAR Comparable>>=
>> )abbrev category COMPAR Comparable
>> 
>> and 
>> 
>> \section{category ORDSET OrderedSet}
>> <<category ORDSET OrderedSet>>=
>> )abbrev category ORDSET OrderedSet
>
> OrderedSet should be a natural order, Comparable is just some
> order which not necessarly makes any sense from user point of
> view.

Sorry for bothering you (actually: everybody!) again:

    is there any (at least: vague) definition of "natural"?

I appreciate the work you have put into this.  But I think that your
commit would be even more beneficial if we could clear this up.

Things that come to mind:

* it seems that we need to have ordering even if no "natural" order is
  available, as in EXPR INT.  

* Possibly we also want to have two different orders: a fast one, and a
  mathematical one...

* in python, as far as I know, any two things are comparable, and it's
  (if I remember correctly) expressively designed for hashing etc.,
  i.e. for exactly the same functionality you have in mind for
  Comparable.

  I think I would be nice to reflect this intention very clearly even in
  the name of the category.  Brainstorming: OrderedDatastructure.

In any case: I'm very happy to see all this happening: new-lambda,
removing <: (%,%) -> Boolean from EXPR INT, etc.

Martin

PS: one final personal thing:  I strongly prefer

    Expression(R: Comparable): Exports 

over

    Expression(R : Comparable): Exports 


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