Re: Overcoming the proof of undecidability of the Halting Problem by a simple example in C

On 19/05/2025 03:36, olcott wrote:

On 5/18/2025 9:08 PM, Richard Heathfield wrote:

On 19/05/2025 02:24, olcott wrote:

It was stipulated that HHH does simulate DDD.

>
That's all right then.
>
It's stipulated that you are correct.
>

 Unless is it known that one C function
cannot possibly simulate another the
stipulation must be accepted by anyone
wanting an honest dialogue.

  There is a way it could be done within the rules of C, but the way that you do it is not that way.
We know that programs exist that can translate C source code. The obvious examples are compilers and interpreters. (Your HHH is neither, because you don't actually give it C source to lex.)
We can therefore envisage the possibility of encapsulating an interpreter's capability within a C function, and handing it a C function to be interpreted - something like eval(char *c_function_source), where c_function_source points to the first byte of the source code of the function definition you wish to simulate, given as C source in a \n-separated and null-terminated array of printable, readable characters.
eval() would lex the C (break it into individual tokens), parse it, construct an abstract syntax tree, and finally walk the tree interpreting the code as it went.
It would be a lot more complicated than that in practice, but that's the gist of how you'd do it within the rules of C.
All this is true, so we may reasonably deduce that it is at least in theory possible for a C function to simulate another, but in no way does that imply either that HHH is a C function (indeed, over a third of it consists of assembly language directives) nor that it correctly simulates anything. The stipulation that HHH correctly simulates C has not been shown to be true, and is very likely to be false. Trying to trick honest people into accepting a false stipulation by attempting to smear a refusal as 'dishonest' is a mere shyster trick.
You can stipulate whatever you like, and use that stipulation to make deductions. You could stipulate that a tail is a leg and deduce that a horse has five legs. The logic would be impeccable, but it's still nonsense, and a horse still only has four legs, because stipulating that a tail is a leg doesn't make it a leg.
You can stipulate that HHH correctly simulates DDD, but that doesn't mean that HHH correctly simulates DDD; it only means that you have stipulated that it does.
You can stipulate that you're right, of course, and as far as you're concerned that would be the end of the argument because anyone who disagrees with you is stipulated to be wrong.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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