[Haskell-cafe] Are bottoms ever natural?

[Alexey Muranov]

Siddharth,

are you aware that the question whether a given element belongs to the 
domain of a given computable function is algorithmically undecidable?

Alexey.

On Tue, 2017-12-19 at 16:51 +0000, Siddharth Bhat wrote:
> > So, I have two opinions to share on this:
> > Regarding the plane example, it is wrong to attempt to graph it on a
> > plane, precisely because the domain is not the plane.
> > I am confused by your assertion that it is impossible to avoid
> > divergence in mathematics: we do not define division as a *partial*
> > function. Rather we define it as a *total* function on a *restricted
> > domain*.
> > So, what one would need is the ability to create these restricted
> > domains, which certain languages have as far as I am aware.
> > At that point, now that we track our domains and codomains 
> correctly,
> > all should work out?
> > I would still like an answer to interesting transformations that are
> > enabled by having purity and laziness and are not encumbered by the
> > presence of bottoms.
> > Cheers,
> > Siddharth
> >