A clarification...

[Jan-Willem Maessen]

qrczak@knm.org.pl (Marcin 'Qrczak' Kowalczyk) further clarifies my
clarification: 
> >        case ERROR of x -> expr  =>   ERROR glb expr[?/x]
> 
> The subject of errors vs. bottoms is discussed in
> http://research.microsoft.com/~simonpj/papers/imprecise-exceptions.ps.gz

Indeed.  I crawled through my stack of electronic papers, and couldn't
find the reference.  As I noted in my earlier messages, I was
deliberately dodging the issue of *catching* exceptions, as it really
requires a thorough treatment. :-) The "?"  in the above reduction is
their special 0 term.  They equate divergence with exceptional
convergence within the functional calculus for the reasons I outlined
[I reconstructed those reasons from memory and my own experience, so
differences are due to my faulty recollection].  Their notion of
refinement justifies the reduction I mentioned in my mail:

> >        case ERROR of x -> expr  =>   ERROR

In all, an excellent paper for those who are interested in this topic.

-Jan-Willem Maessen