Mathematics currently hates Computer Science because of AI (Was: SWI-Prolog as a Test Bed for Copilots)

Hi,
What you are adressing here, in purely
symbolic form, without some helpful natural
language rephrasing:
 > Let (H, <) be the standard total oder an the
 > Prolog finite terms. Let R be the set of rational
 > term. H c R. Then there is total order
 > extention (R, <') of (H, <).
Is the problem of a compare/3 for rational trees,
that is a extension of the compare/3 for finite aka
acyclic terms with the submodel property. This is
quite possible, for example representation
based compare/3 that uses a collation key:
S @<' T :<=> rep(S) @< rep(T)
It has trivially acyclic comparison as a submodel,
when rep(S) = S for acyclic terms S. The inverse
rep^-1 itself is the homomorphism, its even an
embedding, since identity would be injective.
You might even forget about the plot, and endlessly
go down the rabbit hole of mathematics, and write a
100 pages paper, and prove Fermat’s Last Theorem
in passing again.
I can only assume mathematics currently hates
computer science because of AI.
Bye
Mild Shock schrieb:

Hi,
 Create a ChatGPT for cyclic terms? It seems
that the SWI-Prolog discourse contains a lot
of recent exploration of about cyclic terms.
Yet humans don’t remember them,
 or are too lazy to recall them, look them
up again. Maybe to offload some of the cognitive
load and have a easier way forward, one might
use GPT builder and
 create a cyclic term assistant. One could
then ask the artificial intelligece (AI) for
the following things:
 - Automated Testing:
   please perform some monkey testing
   on my news compare/3 idea
 - Automated Proving:
   please suggest a proof for my newest
   lemma about compare/3
 - Code Refactor:
   please refactor my code, I would like to
   use (==)/2 instead of same_time/2
 - Auto Comment:
   please auto comment my code, I was too
   lazy to write comments
 - What else?
   ChatGPT itself gave me a list when I ask
   what will be between now and AGI. Could
   look it up, as a few interesting items as well
   mainly targeting automated summarizing ideas.
 Is SWI-Prolog discourse part of the SWI-Prolog
assistant building process. Its less a static
resource, has ongoing discussions. Needs periodic
retraining of the AI.
 Also the above vision includes some scenarios
where the Assistant would be better integrated
into an IDE, but these Assistants have usually
more expensive price plans.
 Will this IDE be XPCE, who knows?