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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.lang.prolog
Subject: Re: A Timeless Confluence [Term Rewriting] (Was: Can we do this with
 ancestral cuts or something?)
Date: Mon, 9 Dec 2024 21:00:17 +0100
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Ok Confluence does indeed ring a bell. Lets show
Declarative (What) versus Procedural (How) in
@emiruz example, as a rewriting problem.

Lets permit that we write the input as [1,2,a,4,5,
b,c,8,9,10] and then have rewriting rules [a->3,b->6,
c->7,d->8] applied, by this little Declarative (What) code:

step(L,R) :- nth1(K,L,a,H), nth1(K,R,3,H).
step(L,R) :- nth1(K,L,b,H), nth1(K,R,6,H).
step(L,R) :- nth1(K,L,c,H), nth1(K,R,7,H).
step(L,R) :- nth1(K,L,d,H), nth1(K,R,8,H).

find(L,L) :- \+ step(L,_).
find(L,R) :- step(L,H), find(H,R).

Each derivation is a Procedural (How) execution:

?- find([1,2,a,4,5,b,c,8,9,10],X).
X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Etc..

Can we count the number of Hows to solve the What?

?- aggregate_all(count, find([1,2,a,4,5,b,c,8,9,10],X), C).
C = 6.

So there are 6 different Procedures that tell
us which steps to exactly use when, to solve the
Declaratively given problem which leaves open

when to use each step.

Mild Shock schrieb:
> A Timeless Confluence
> 
> By the banks of thought where rivers entwine,
> Emmy Noether walked through a realm divine.
> Her algebra wove the fabric of laws,
> While echoes of logic gave her pause.
> 
> There stood Michael Kohlhase, a seeker of form,
> Shaping machines through a digital storm.
> “Madame,” he began, with respect in his tone,
> “Your ideals still guide what we’ve come to own.
> 
> Noetherian rings, your towering art,
> Anchor the systems of which I’m a part.
> In rewriting paths, your truth remains,
> Simplifying chaos, dissolving chains.”
> 
> Emmy smiled, her brilliance aglow,
> "Through eras, the seeds of knowledge grow.
> Yet tell me, dear traveler, in your machine’s frame,
> Do ideals endure, or fade like a flame?”
> 
> Michael replied, “Your vision holds,
> In logic’s rewrite, it gently unfolds.
> Past meets the present where structures align,
> A confluence of thought, eternal, divine.”
> 
> And so they stood, two eras combined,
> Bound by the currents of the infinite mind.
> 
> https://en.m.wikipedia.org/wiki/Emmy_Noether
> 
> https://en.m.wikipedia.org/wiki/Michael_Kohlhase
> 
> Julio Di Egidio schrieb:
>> On 09/12/2024 16:47, Julio Di Egidio wrote:
>>
>>> term rewriting also can do the trick and quite more simply so...
>>
>> I take that back, too.  I cannot find a way out of ancestral cuts in 
>> the recursive case.  Some term rewriting could rather be useful *in 
>> conjunction* with that `scut`, since that as written messes up with 
>> the stack trace...  Anyway, that's another story.
>>
>> -Julio
>>
>