Should try semi-deep Prolog argument indexing (Was: Relation of the practical to the mathematical oracle)

From	Mild Shock <janburse@fastmail.fm>
Newsgroups	comp.lang.prolog
Subject	Should try semi-deep Prolog argument indexing (Was: Relation of the practical to the mathematical oracle)
Date	2025-07-10 21:43 +0200
Message-ID	<104p54q$22e7j$1@solani.org> (permalink)
References	<vpceij$is1s$1@solani.org> <104osio$2281u$1@solani.org> <104p3so$22dce$1@solani.org> <104p4cr$22dou$1@solani.org> <104p4lv$22dsf$1@solani.org>

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Hi,

Today I had an idea, of some semi-deep Prolog
argument indexing. Just because choice point
elimination is so important and has so many

benefits for performance and the end user
experience, like also debugging. And because it is
tied to indexing. An index and the resulting clause

list, which can be always checked for having reached
its end. This gives a look-ahead information to the
Prolog system  which answers this oracle, concering

clause instantiation:

∃X ( p(X) & X =\= a1 & ... & X =\= ak)

So the idea of semi-deep Prolog argument indexing
would be a hybrid between Scryer Prolog and
SWI-Prolog taking the best of both worls.

It would adopt skip indexes from Scryer Prolog
and deep indexing of SWI-Prolog, but deep indexing
through a Key computation trick. The Key computation

trick is quickly explained.

Normal Key Computations:

p(a, ..)      ~~>  Computed Key: a/0 or sometimes a alone
p(b(x,y), ..) ~~>  Computed Key: b/2 or sometimes b alone
Etc..

Semi Deep Key Computation:

p(a, ..)        ~~>  Computed Key: 'a'
p([a, ..], ..)  ~~>  Computed Key: '.a'
Ect..

Got it?

The Scryer Prolog skip index is needed because
in a DCG the interesting arguments are usually
not the first argument.

Bye

Mild Shock schrieb:
> Hi,
> 
> Now one might ask, if we have a Prolog system
> that anyway juggles with choice points, why
> would we need a logical formula for choice points?
> 
> Well there is a funny correctness criteria,
> for example in the top-level, if the top-level
> doesn't prompt the end user anymore in such a scenario:
> 
> ?- p(X).
> X = a1 ;
> X = a2 ;
> ...
> X = ak-1 ;
> X = ak
> 
> So the end user is not prompted because the
> Prolog system founds CP = []. This is licensed
> by this correctness statement for any choice
> 
> point elimination:
> 
> CP = [] => ~∃X ( p(X) & X =\= a1 & ... & X =\= ak)
> 
> Have Fun!
> 
> Bye
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Now what does a Prolog system do? Well when
>> it prompts the end-user it has somewhere
>> a list of the current query choice points:
>>
>> CPs = [CP1, CP2, .., CPn]
>>
>> This is implementation specific, what choice
>> points a system creates, also the ISO core standard
>> shows a machine in its more procedural explanation,
>>
>> that depicts something that has also somewhere
>> choice points. Since it is implementation specific
>> a Prolog System A and Prolog System B might
>>
>> use different choice points:
>>
>> System A:
>> CPs = [CP1, CP2, .., CPn]
>>
>> System B:
>> CP's = [CP'1, CP'2, .., CP'n]
>>
>> We say a System B could eliminate a choice point CP,
>> relative to a System A, if we have:
>>
>> System A:
>> CP ∈ CPs
>>
>> System B:
>> CP ∉ CPs
>>
>> So System B might have an advantage over System A,
>> since it will not backtrack over CP.
>>
>> When it comes to answer substitution display,
>> it is now very common, that a Prolog system checks
>> its own choice points, and when it finds that
>>
>> CP = []
>>
>> It knows that the query left no choice points,
>> either because there were never any, because
>> there was no branching in the executed code, or
>>
>> because a cut removed branching, or because
>> they were eliminated somehow. Like through
>> some index analysis.
>>
>> Bye
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> This is nothing for Bart Demoen, Physics PhD,
>>> academic fraud. The ideal choice point can
>>> be formulated as a logical formula, involving
>>>
>>> an existential quantifier. Assume we have
>>> a query and already these answers, and the
>>> Prolog system is prompting the interactive user:
>>>
>>> ?- p(X).
>>> X = a1 ;
>>> X = a2 ;
>>> ...
>>> X = ak-1 ;
>>> X = ak
>>>
>>> A mathematical oracle that could indicate whether
>>> it is even necessary to prompt the user could be:
>>>
>>>     ∃X ( p(X) & X =\= a1 & ... & X =\= ak)
>>>
>>> It doesn't match 100% Prolog since Prolog might
>>> give duplicate answers or non-ground answers,
>>> but assume for the moment the query q(X),
>>>
>>> produces only distinct and ground results.
>>> Nice existential FOL formula we have in the above.
>>>
>>> Bye
>>>
>>> Mild Shock schrieb:
>>>>
>>>> Henri Poincaré believed that mathematical
>>>> and scientific creativity came from a deep,
>>>> unconscious intuition that could not be
>>>>
>>>> captured by mechanical reasoning or formal
>>>> systems. He famously wrote about how insights
>>>> came not from plodding logic but from sudden
>>>>
>>>> illuminations — leaps of creative synthesis.
>>>>
>>>> But now we have generative AI — models like GPT — that:
>>>>
>>>> - produce poetry, proofs, stories, and code,
>>>>
>>>> - combine ideas in novel ways,
>>>>
>>>> - and do so by processing patterns in massive
>>>>    datasets, without conscious understanding.
>>>>
>>>> And that does seem to contradict Poincaré's belief
>>>> that true invention cannot come from automation.
>>>>
>>>> Mild Shock schrieb:
>>>>> Hi,
>>>>>
>>>>> But I shouldn't waste too much time.
>>>>> One shouldn't punish people for just
>>>>> being plain stupid.
>>>>>
>>>>> Like for example this clueless french
>>>>> philosopher who had a lot of troubles
>>>>> with non-classical logic.
>>>>>
>>>>> His brain tried to eliminate non-classical
>>>>> logic, it was keen on avoiding non-classical
>>>>> logic. A typical species of a human with
>>>>>
>>>>> an extremly small brain, again working
>>>>> in the wrong place!
>>>>>
>>>>> Bye
>>>>>
>>>>> P.S.: Maybe this a Poincaré thingy? Poincaré
>>>>> was a strong critic of logicism (as championed
>>>>> by Frege and Russell) and of Hilbert’s
>>>>> formalist program.
>>>>>
>>>>> But, he did not formally use or promote systems
>>>>> like intuitionistic logic, modal logic, or
>>>>> relevance logic. His logical framework remained
>>>>> within the bounds of classical logic,
>>>>>
>>>>> though he was skeptical of excessive formalism.
>>>>> He thought formal systems could miss the creative
>>>>> and synthetic nature of mathematical
>>>>> invention. 
>>>>
>>>
>>
>

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