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From: Mikko <mikko.levanto@iki.fi>
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Subject: =?utf-8?Q?Re:_Analysis_of_Flibble=E2=80=99s_Latest:_Detecting_vs._Simulating_Infinite_Recursion_ZFC?=
Date: Mon, 26 May 2025 12:43:27 +0300
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On 2025-05-25 15:55:42 +0000, olcott said:

> On 5/25/2025 5:19 AM, Richard Heathfield wrote:
>> On 24/05/2025 17:13, olcott wrote:
>>> No HHH can report on the behavior of its caller
>> 
>> From Halt7.c:
>> 
>> void DDD()
>> {
>>   HHH(DDD);
>>   return;
>> }
>> 
>> Since (as you say) no HHH can report on the behaviour of its caller, 
>> and since (as your code shows) DDD is HHH's caller, we deduce that HHH 
>> cannot report on DDD.
>> 
>> So HHH is not (according to you) a halt analyser for DDD.
>> 
>> I'm not sure you've left anything to discuss, have you?
> 
> HHH(DDD) does correctly reject
> *ITS INPUT THUS NOT ITS CALLER*
> as non-halting.

If the caller is DDD then the input specifies a halting behaviour because
DDD calls HHH with an input that specifies a halting behavour. But HHH
cannot correctly reject a halting input as non-halting.

The requirements of a halting decider cannot be met if the decider reports
differently dependig on who calls it. Consequently, HHH is required to
return true also when the following FFF calls it:

void FFF(void) {
  HHH(DDD);
  return;
}

-- 
Mikko