Re: Partial OSA

[pdmosses@brics.dk]

Don,

You wrote:

> Could you please briefly explain why
> 
> > the only way to have Nat as a subsort of Int is to specify naturals
> > and integers in the same module (similarly for rationals Rat, etc.)
> 
> I don't see this, myself.  (I'm not sure that I know what you mean by
> "module", but I assume that it is synonymous with "specification".)
> What's wrong with
> 
>   INT = ... specification of Int ...
> 
>   NAT = enrich INT by ... specification of Nat as subsort of Int ...

Ah, I hadn't imagined anyone wanting to do it that way round; thanks.
So I'd overstated my claim.  It should now be more like:

  The only ways that I can see to have Nat as a subsort of Int are 
  (i) to specify naturals and integers in the same specification body,
  or (ii - thanks, Don) to first specify integers and then extend with
  the specification of naturals as a subsort.  If one ever wants
  integers to be a subsort of rationals, however, one has to start with
  Rat as the primary sort instead.  Moreover, (ii) wouldn't cater for
  using naturals without integers around - although one could provide
  an alternative version of NAT as well, I suppose.

> If your assertion is indeed false, then I don't see the problem with
> the present CL treatment of subsorts.  I like it because it's so
> simple.  And as you said on Wed, 19 Jun 1996:
> 
> > I can't hide
> > a personal preference for simplicity!

I still can't - and I was quite happy with the present CL treatment,
until I noticed the extension problem.  I still think it is a problem,
despite your suggestion.

Cheers

Peter