Re: Analysis of Flibble’s Latest: Detecting vs. Simulating Infinite Recursion ZFC

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