Maybe real Prologers that could code it correctly,
are now an endangered species, on the brink of getting
extinct? I easily find a 40 year old reference that

shows how to symbolically compute with multivariate
polynomials. It doesn’t have the same problem as the
bug in PRESS that it cannot render (1+x) + -1 as x:

Haygood, R. (1989): A Prolog Benchmark Suite for Aquarius,
Computer Science Division, University of California
Berkely, April 30, 1989, See “poly”

The Prolog code is rooted in some Lisp code by
R.P. Gabriel. The Python code of sympy wont do much
else in its class Poly, than using a recursive dense
representations and term orderings.

If only simplification and no division is needed,
then only canonicalization is needed. Handing over
expressions to Python might be useful to factorize
polynomials or to compute Gröbner basis,

since Prolog libraries for that are more rare. On
the other hand I think the entry level for a simplification
in Prolog itself, should not be so high. But education in
this direction could have been already died out.

Mild Shock schrieb:

Hi,

Not only $TSLA is on fire sale! Also
Prolog system have capitualted long ago.
Scryer Prolog and Trealla Prolog copy

some old CLP(X) nonsense based on attributed
variables. SWI-Prolog isn't better off.
Basically the USA and their ICLP venue

is dumbing down all of Prolog development,
so that nonsense such as this is published:

Automatic Differentiation in Prolog
Schrijvers Tom et. al - 2023
https://arxiv.org/pdf/2305.07878

It has the most stupid conclusion.

"In future work we plan to explore Prolog’s meta-
programming facilities (e.g., term expansion) to
implement partial evaluation of revad/5 calls on
known expressions. We also wish to develop further
applications on top of our AD approach, such as
Prolog-based neural networks and integration with
existing probabilistic logic programming languages."

As if term expansion would do anything good
concerning the evaluation or training of neural
networks. They are totally clueless!

Bye

P.S.: The stupidity is even topped, that people
have unlearned how to do symbolic algebra
in Prolog itself. They are not able to code it:

?- simplify(x+x+y-y,E).
E = number(2)*x+y-y

Simplification is hard (IMO).

Instead they are now calling Python:

sym(A * B, S) :-
    !, sym(A, A1),
    sym(B, B1),
    py_call(operator:mul(A1, B1), S).

mys(S, A * B) :-
    py_call(sympy:'Mul', Mul),
    py_call(isinstance(S, Mul), @(true)),
    !, py_call(S:args, A0-B0),
    mys(A0, A),
    mys(B0, B).

Etc..

sympy(A, R) :-
    sym(A, S),
    mys(S, R).

?- sympy(x + y + 1 + x + y + -1, S).
S = 2*x+2*y ;

This is the final nail in the coffin, the declaration
of the complete decline of Prolog. Full proof that
SWI-Prolog Janus is indicative that we have reached

the valley of idiocracy in Prolog. And that there
are no more capable Prologers around.

Mild Shock schrieb:

Hi,

But its funny that people still work on UNSAT,
because its known that SAT is NP complete.

But don't worry, I sometimes do the same.
Imogen seems to chocke on SYJ202:

   SYJ202+1.005.imo     Provable.    Time: 2.129
   SYJ202+1.006.imo     Provable.    Time: 3.790
   SYJ202+1.007.imo     Provable.    Time: 16.222
   SYJ202+1.008.imo     Provable.    Time: 143.802

I assume its just the same problem linearly growing,
but the time is exponential or something.

BTW: Complexity for intuitionistic propositional logic
is even worse, its PSPACE complete. Here a recent

attempt featuring intuitRIL and SuperL

Implementing Intermediate Logics
https://iltp.de/ARQNL-2024/download/proceedings_preli/2_ARQNL_2024_paper_8.pdf


Have Fun!

Bye


Mild Shock schrieb:

This code here doesn’t make much sense:

prove(L --> R):-
     member(A => B,L),
     del(A => B,L,NewL),!,

One can combine member/2 and del/3 into select/3. select/3
together with member/2 is part of the Prologue to Prolog:

*A Prologue for Prolog (working draft)*
https://www.complang.tuwien.ac.at/ulrich/iso-prolog/prologue

So if I further strip away using a two sided sequent,
I can implement Hoa Wangs implication fagment:

P1. Initial rule: if λ, ζ are strings of atomic
formulae, then λ -> ζ is a theorem if some atomic
formula occurs an both sides of the arrow.

P5a. Rule —> =>    If ζ, φ -> λ, ψ, ρ, then ζ -> λ, φ => ψ, ρ
P5b. Rule => -> If λ, ψ, ρ -> π and λ, ρ -> π, φ then λ, φ => ψ, ρ -> π

(Hao Wang. Toward Mechanical Mathematics. IBM
Journal of Research and Development 4:1 (1960), 15.)

as follows in 3 lines:

prove(L) :- select((A->B),L,R), !, prove([-A,B|R]).
prove(L) :- select(-(A->B),L,R), !, prove([A|R]), prove([-B|R]).
prove(L) :- select(-A,L,R), member(A,R), !.

Seems to work, I can prove Peirce Law:

?- prove([(((p->q)->p)->p)]).
true.
See also:

*Hao Wang on the formalisation of mathematics*
Lawrence C. Paulson 26 Jul 2023
https://lawrencecpaulson.github.io/2023/07/26/Wang.html

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