[Agda] fast DecTotalOrder

[Sergei Meshveliani]

On Tue, 2015-03-24 at 15:36 +0100, Andrea Vezzosi wrote:
> That implementation of  _≤?_ looks like it should be as fast as compare.
> 
> How are you running the benchmarks however? Some inefficiencies might
> be a result of problems in the backends as well.
> 

  agda -c $agdaLibOpt +RTS -K200m -M9G -H9G -RTS SortingTest.agda

  ./SortingTest

I think, it is all right. 
The problem is in that the arithmetic of  ℕ  always creeps in.
I try  Bin,  but then, see that the arithmetic of  ℕ  has already
intruded somewhere there, to Standard.
Currently I am going to try the above _≤?_ and its DecTotalOrder 
instance for  Bin.

Regards,

------
Sergei



> On Tue, Mar 24, 2015 at 3:31 PM, Sergei Meshveliani <mechvel at botik.ru> wrote:
> > 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
> >> >
> >> >
> >> >
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> >>
> >
> >
>