Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT

On 16/04/2025 21:10, Mr Flibble wrote:

On Wed, 16 Apr 2025 20:56:13 +0100, Richard Heathfield wrote:
 

On 16/04/2025 20:42, Mr Flibble wrote:

<snip>

the category error associated with pathological input.  One simply has
to add a third halting result of "pathological input" and we are fine.

>
That's just another way of saying that the universal termination
analyser as specified (determining whether P(D) does or does not
eventually halt) can't be written. If it can't determine whether P(D)
halts, no matter how pathological, it isn't universal.

 You forget that I have already solved this problem:

You forget that Turing has already proved otherwise.
<snip>

Obviously my idea necessitates extending the definition of a halt
decider:
 1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.

And equally obviously you have answered a different question. The Halting Problem requires a universal termination analyser that correctly classifies all P(D) as halting or non-halting, and those are your only choices. You don't have a solution to the Halting Problem; you have solved the Flibble Problem.

Thoughts?  I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.

What you are missing is a program that meets the spec. Yeah, that's pretty obvious.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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