John O'Donnell <[EMAIL PROTECTED]>:
> There have been several papers on exact real arithmetic ... The
> idea is to use lazy representations of unbounded data structures.
>
> I'm not sure what the current state of this research is, but
> we should look into it. There may be serious limitations on what
> you can do with exact real numbers in a computer, but some useful
> applications have been reported.
Over here at Edinburgh, Martin Escardo and Alex Simpson have both done
work on this. I'm not sure about the "serious limitations" --- I
was quite surprised to learn that there are functional algorithms
for maximum and integration over exact reals. And yes, they give
exact answers.
http://www.dcs.ed.ac.uk/home/mhe/
http://www.dcs.ed.ac.uk/home/als/
Alex Simpson: Lazy Functional Algorithms for Exact Real Functionals.
To appear in the proceedings of MFCS 1998.
http://www.dcs.ed.ac.uk/home/als/Research/lazy.ps.gz
Phil Wadler:
> I believe that David A. Turner (of Miranda fame) has an EPSRC
> grant to develop arbitrary precision real libraries in Haskell.
Is "arbitrary precision" the same as true real numbers --- or does
it just mean "for this run of the program I would like to use 10^5
digits" ?
Ian Stark
.....................................................................
Ian Stark http://www.dcs.ed.ac.uk/home/stark
Department of Computer Science, The University of Edinburgh, Scotland
