Not lazy/smart enough

[Hans Aberg]

At 10:11 -0700 2001/11/01, Alastair David Reid wrote:
>>>>>> "Sohrab" == Sohrab Saran <sohrabsaran@hotmail.com> writes:
>
>> If at the Hugs interpreter prompt I type:
>> 3/4 == 3/4
>> ...I get "True"
>> If I now type:
>> 3/0 == 3/0
>> ...I should get "True" but I get a divide-by-zero error
>> instead. Anyone ready to fix this, or should I fix this myself?
>
>I don't believe this is a bug.

I think that in the (denotational semantics) theory that Haskell
(originally) relies on, errors are identified with non-termination, and it
is not determinable to decide whether something is a non-termination. Thus,
equations like
  3/0 == 4/0
cannot de decided from that viewpoint: All one knows that if the values 3/0
and 4/0 are needed by "==", then they will be computed; but they then
generate errors.

The problem is that divide-by-zero is not represented as a _value_, or not
all closures can be treated as values. It would be fully possible to give
3/0 and 4/0 values: In math, suppose we choose a projective space P^1, they
would have the same value infinity value oo.

An alternative approach is to let them produce an exception, which can be
picked up. This way to can let n/0 have say a projective value by
redefining "/": a thrown divide-by-zero is caught and converted to a
special oo value.

  Hans Aberg