[Haskell-cafe] Are bottoms ever natural?

[Baa]

Pure functions can return "undefined" for some arguments values. So,
such function is partially-defined. Its domain has "gaps". This can be
coded in math, to avoid "undefined" (bottom), like

  x = {-100..100, 105, 107..200}

It's impossible in Haskell, but IMHO its possible in F*, due to DepTypes
and RefTypes ;)

IMHO this is the reason to have bottom: possibility to return
"undefined" w/ simple correct type in signature (hidden bottom). If you
have a way to code arguments domains, no need to have bottom for pure
functions to "signal" gaps - gaps happen in run-time :) This is the one
of reasons for bottom to exist, as far as I understand. May be there are
other reasons :)

===
Best regards, Paul

> Siddharth,
> 
> how would you deal with functions that terminate for some 
> arguments/inputs but do not terminate for the others ?
> 
> Alexey.
> 
> On Tue, 2017-12-19 at 07:20 +0000, (IIIT) Siddharth Bhat wrote:
> > > Is that really true, though?
> > > Usually when you have an infinite loop, you have progress of some
> > > sort. Infinite loops with no side effects can be removed from the
> > > program according to the C standard, for example. So, in general,
> > > we should allow programmers to express termination / progress,
> > > right?   
> > At  
> > > that point, no computation ever "bottoms out"?
> > > Shouldn't a hypothetical purely functional programming language
> > > better control this (by eg. Forcing totality?) It seems like we
> > > lose much of the benefits of purity by muddying the waters with
> > > divergence.
> > > From an optimising compiler perspective, Haskell is on some weird
> > > lose-lose space, where you lose out on traditional compiler
> > > techniques that work on strict code, but it also does not allow
> > > the awesome stuff you could do with "pure" computation because
> > > bottom lurks everywhere.
> > > What neat optimisations can be done on Haskell that can't be done
> > > in a traditional imperative language? I genuinely want to know.
> > > What are your thoughts on this?
> > > Cheers
> > > Siddharth
> > >
> > > On Tue 19 Dec, 2017, 08:09 Brandon Allbery, <allbery.b at gmail.com>
> > > wrote:  
> >> > > Define "natural".
> >> > >
> >> > > You might want to look into the concept of Turing
> >> > > completeness.   
> >> One  
> >> > > could define a subset of Haskell in which bottoms cannot
> >> > > occur... but it turns out there's a lot of useful things you
> >> > > can't do in such a language. (In strict languages, these often
> >> > > are expressed   
> >> as  
> >> > > infinite loops of one kind or another. Note also that any
> >> > > dependency on external input is an infinite loop from the
> >> > > perspective of the language, since it can only be broken by the
> >> > > external entity providing the input.)
> >> > >
> >> > > On Tue, Dec 19, 2017 at 1:47 AM, (IIIT) Siddharth Bhat   
> >> <siddharth.b  
> >> > > hat at research.iiit.ac.in> wrote:  
> >>> > > > I've been thinking about the issue of purity and speculation
> >>> > > > lately, and from what little I have read, it looks like the
> >>> > > > presence of bottom hiding inside a lazy value is a huge
> >>> > > > issue.
> >>> > > >
> >>> > > > How "natural" is it for bottoms to exist? If one were to   
> >>> change  
> >>> > > > Haskell and declare that any haskell value can be speculated
> >>> > > > upon, what ramifications does this have?
> >>> > > >
> >>> > > > Is it totally broken? Is it "correct" but makes programming
> >>> > > > unpleasant? What's the catch?
> >>> > > >
> >>> > > > Thanks,
> >>> > > > Siddharth  
> 
> _______________________________________________
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> Only members subscribed via the mailman list are allowed to post.