Refuting the Peter Linz Halting Problem Proof V4

[Skepdick]

I refute the whole class of proofs that are based on this trick:
For any program H that might determine if programs halt, a "pathological" program P, called with some input, can pass its own source and its input to H and then specifically do the opposite of what H predicts P will do. No H can exist that handles this case.

That's precisely the implication of a proof by contradiction! H does not and cannot exist.

Which is what makes the problem unsolvable.

Now if you happen to be the type of person who only insists on having constructive proofs - fine.
If you are the type or person who doesn't recognise proof by contradiction as a valid method of proving anything - fine.

Any proofs of the halting problem can only be semi-decidable. I can agree with that.

Instead of a contradiction all you have to recognise is that you will end up with two mutually-dependent functions P and H which will recursively (and infinitely) continue calling each other. Indeed, that's a circular dependency, but so what? It's also called Mutual recursion. It's a valid model of computation and it's precisely how LISP is implemented. Using an eval-apply loop.

[PeteOlcott]

I refute the whole class of proofs that are based on this trick:
For any program H that might determine if programs halt, a "pathological" program P, called with some input, can pass its own source and its input to H and then specifically do the opposite of what H predicts P will do. No H can exist that handles this case.

That's precisely the implication of a proof by contradiction! H does not and cannot exist.

Which is what makes the problem unsolvable.

Now if you happen to be the type of person who only insists on constructive proofs; the type or person who doesn't recognise proof by contradiction as a valid method of proving anything - fine. I can agree with that.

Instead of a contradiction all you have to recognise is that you will end up with two mutually-dependent functions P and H which will recursively (and infinitely) continue calling each other. Indeed, that's a circular dependency, but so what? It's also called Mutual recursion. It's a valid model of computation and it's precisely how LISP is implemented. Using an eval-apply loop.

The when the halt decider bases its halt status decision on its correct simulation of its input the contradiction is never reached. It took from 2004 until 2016 to inadvertently notice that.

When infinite recursion occurs it derives the pattern that the same function is called from the same machine address with identical parameters. H can see this.

[Skepdick]

And if you care to grok the difference between nested/embedded evaluation of a procedure, and passing control of evaluation to an external procedure (what you call a "library call") read this...

https://www.cs.rpi.edu/academics/course ... tml#SEC160

[Skepdick]

The when the halt decider bases its halt status decision on its correct simulation of its input the contradiction is never reached. It took from 2004 until 2016 to inadvertently notice that.

The halt decider doesn't exist. It is a fictitious entity.

If H existed, and if P depended on H then P will always do the opposite of what H predicted.

See above post for difference between nested execution of a procedure vs passing control to an external copy of a procedure.

[PeteOlcott]

The when the halt decider bases its halt status decision on its correct simulation of its input the contradiction is never reached. It took from 2004 until 2016 to inadvertently notice that.

The halt decider doesn't exist.

It is a fictitious, contradictory entity.

If H existed, and if P depended on H then P will always do the opposite of what H predicted.

See above post for difference between nested execution of a procedure vs passing control to an external copy of a procedure.

That you say that on the basis of the willful ignorance of refusing to read my paper is flat out dishonest.

[Skepdick]

That you say that on the basis of the willful ignorance of refusing to read my paper is flat out dishonest.

Sue me.

[PeteOlcott]

That you say that on the basis of the willful ignorance of refusing to read my paper is flat out dishonest.

Sue me.

I will simply stop responding to anyone that indicates that they are not interested in an honest dialogue.

[Skepdick]

I will simply stop responding to anyone that indicates that they are not interested in an honest dialogue.

If we held that as a general principle we'd all ignore you.