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From: olcott <polcott333@gmail.com>
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Date: Thu, 22 May 2025 12:13:39 -0500
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On 5/22/2025 11:59 AM, Richard Heathfield wrote:
> On 22/05/2025 17:45, olcott wrote:
> 
> <snip>
> 
>> You don't have a clue:
> 
> Righty-ho.
> 
>> https://en.wikipedia.org/wiki/Halting_problem#Proof_concept
> 
> Is it this bit you mean?
> 
> There are programs (interpreters) that simulate the execution of 
> whatever source code they are given. Such programs can demonstrate that 
> a program does halt if this is the case: the interpreter itself will 
> eventually halt its simulation, which shows that the original program 
> halted. However, an interpreter will not halt if its input program does 
> not halt, so this approach cannot solve the halting problem as stated; 
> it does not successfully answer "does not halt" for programs that do not 
> halt.
> 

*The part that the actual link links to*
https://en.wikipedia.org/wiki/Halting_problem#Proof_concept

Christopher Strachey outlined a proof by contradiction that the halting 
problem is not solvable.[28][29] The proof proceeds as follows: Suppose 
that there exists a total computable function halts(f) that returns true 
if the subroutine f halts (when run with no inputs) and returns false 
otherwise. Now consider the following subroutine:

def g():
     if halts(g):
         loop_forever()

halts(g) must either return true or false, because halts was assumed to 
be total. If halts(g) returns true, then g will call loop_forever and 
never halt, which is a contradiction. If halts(g) returns false, then g 
will halt, because it will not call loop_forever; this is also a 
contradiction. Overall, g does the opposite of what halts says g should 
do, so halts(g) can not return a truth value that is consistent with 
whether g halts. Therefore, the initial assumption that halts is a total 
computable function must be false.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer