Turing computable functions

Cannot possibly derive any outputs not computed from
their inputs.
A Turing machine halt decider cannot possibly report
on the behavior of any directly executing process.
No Turing machine can every do this. This has always
been beyond what any Turing machine can ever do.
The best that any Turing machine halt decider can
possibly do is determine the behavior that an input
finite string specifies.
When we make these things 100% concrete in a language
that has been fully operational for many years...
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
When an input finite string specifies a pathological
relationship with its simulating halt decider the actual
behavior that pathological relationship derives must
be reported because THAT IS THE BEHAVIOR THAT IS SPECIFIED
BY THIS INPUT FINITE STRING.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer