[Agda] fast DecTotalOrder

[Sergei Meshveliani]

On Tue, 2015-03-24 at 14:42 +0100, Andrea Vezzosi wrote:
> It seemed like you only wanted the decision procedure to be fast, not
> the relation itself?
> 
> (2) _≤?_ to perform fast,

Thank you.
Probably, yes.
Because the sorting function applies  _≤?_ for the proper result, and
applies _≤_ only may be in proofs.

So, may be, this my first approach will do :

   _≤_ : Rel Bin 0ℓ
   x ≤ y =  x < y ⊎ x ≡ y

   _≤?_ : Decidable _≤_
   x ≤? y  with  compare x y
   ... | tri< x<y _   _   =  yes $ inj₁ x<y
   ... | tri≈ _   x≡y _   =  yes $ inj₂ x≡y
   ... | tri> x≮y x≢y x>y =  no x≰y
                             where x≰y : ¬ x ≤ y
                                   x≰y (inj₁ x<y) = x≮y x<y
                                   x≰y (inj₂ x≡y) = x≢y x≡y
   ...
?

I have 1-2 days to accomplish the performance test for sorting.
Everything is ready, but I do not see the result on a real data! 
Because I need fast  DecTotalOrder  and many different elements which
are put fast in a list.
Such a simple thing to arrange, and it resists ...

Thanks,

------
Sergei



> On Tue, Mar 24, 2015 at 2:30 PM, Sergei Meshveliani <mechvel at botik.ru> wrote:
> > On Tue, 2015-03-24 at 14:05 +0100, Nils Anders Danielsson wrote:
> >> On 2015-03-24 13:51, Sergei Meshveliani wrote:
> >> > And as `compare' is O(bit length) for Bin, why does not Standard library
> >> > implement _<_ for Bin via `compare' ?
> >>
> >> _<_ is used in the specification of compare:
> >>
> >>    _<_     : Bin → Bin → Set
> >>    compare : Trichotomous _≡_ _<_
> >>
> >
> >
> > This looks like a pitfall.
> > Probably, there are many applications which use a generic
> > StrictTotalOrder._<_.
> > And as soon as  A = Bin  is substituted, their performance cost will
> > explode unexpectedly.
> >
> > Regards,
> >
> > ------
> > Sergei
> >
> >
> >
> > _______________________________________________
> > Agda mailing list
> > Agda at lists.chalmers.se
> > https://lists.chalmers.se/mailman/listinfo/agda
>