Re: Halting Problem: How my refutation differs to Peter Olcott's

On 5/11/25 7:52 AM, Mr Flibble wrote:

On Sun, 11 May 2025 11:49:50 +0000, joes wrote:
 

Am Sat, 10 May 2025 23:56:36 +0000 schrieb Mr Flibble:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:

On 5/10/25 4:38 PM, Mr Flibble wrote:

>

How my refutation differs to Peter's:
* Peter refutes the halting problem based on pathological input
manifesting in a simulating halt decider as infinite recursion, this
being treated as non-halting.
* Flibble refutes the halting problem based on patholgical input
manifesting as decider/input self-referencial conflation, resulting
in the contradiction at the heart of the halting problem being a
category (type) error, i.e. ill-formed.
These two refutations are related but not exactly the same.

>
And the problem is that you use incorrect categories.
The decider needs to be of the category "Program".
The input also needs to be of the category "Program", but provided via
a representation. The act of representation lets us convert items of
category Program to the category of Finite String which can be an
input.

>
Those two categories you have identified are different hence the
category error.

No. HHH has a string representation, like every program.

 No. Conflating a program with a string representation of the same program
in the manner of a self-referential dependency is a category (type) error.

But the problem doesn't do that.
Olcott might in his implementation, but the actual problem doesn't.
Don't use Olcott's work as an example of what is actually being asked, he is just totally ignorant of the actual problem, and most of his terms are at least slightly (if not grossly) mis defined.

 

>

The "Pathological Input" *IS* a Program, built by the simple rules of
composition that are allowed in the system.

Such composition is invalid.

No. DDD has only a function call, a condition, and an infinite loop.

 No. It is ill-formed due to the category error.
 /Flibble

WHAT categoryt error. You don't get to make up categories limiting thing more than the problem does.
Halt Decider BY DEFINITION, need to be able to decide on the representation of *ANY* program, and that includes programs that are built using the algorithm of the decider within themselves.
Trying to restrict that category, is just an admission that the original task is just impossible.