[Haskell-cafe] Re: Why purely in haskell?

[Achim Schneider]

Jonathan Cast <jonathanccast at fastmail.fm> wrote:

> On 10 Jan 2008, at 7:55 AM, Achim Schneider wrote:
> 
> > "Daniel Yokomizo" <daniel.yokomizo at gmail.com> wrote:
> >
> >> On Jan 10, 2008 3:36 PM, Achim Schneider <barsoap at web.de> wrote:
> >>> jerzy.karczmarczuk at info.unicaen.fr wrote:
> >>>
> >>>> Niko Korhonen writes:
> >>>>
> >>>> ...
> >>>>> Although it could be argued that laziness is the cause of some
> >>>>> very obscure bugs... <g>
> >>>>> Niko
> >>>>
> >>>> Example, PLEASE.
> >>>>
> >>> [1..] == [1..]
> >>>
> >>> , for assumed operational semantics of ones own axiomatic
> >>> semantics. Bugs are only a misunderstanding away.
> >>
> >> It has nothing to do with laziness, but with using an algebraic
> >> function (==) with a codata structure (stream). If Haskell kept
> >> laziness but enforced separation of data and codata such code  
> >> wouldn't
> >> compile. Lazy lists or streams never are a problem, but you can't
> >> (generically) fold codata.
> >>
> > Exactly. Denotationally it hasn't, but axiomatically it has.  
> > Because it
> > looks like mathematical terms one can easily get lost in believing
> > it reduces like mathematics, too.
> 
> What kind of mathematics?  I don't know of any mathematics where  
> algebraic simplifications are employed without proof of the  
> underlying equations (in some denotational model).
> 
Mathematics as, as my professor put it, "Solving by staring".


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