[Agda] fast DecTotalOrder

[Andrea Vezzosi]

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.

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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>
>