XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-17, olcott  wrote:   
   > On 11/15/2025 8:48 PM, Kaz Kylheku wrote:   
   >> On 2025-11-16, olcott  wrote:   
   >>> HHH cannot possibly report on the behavior   
   >>> of its caller because HHH has no way of   
   >>> knowing what function is calling it.   
   >>>   
   >>> This means that when the halting problem   
   >>> requires HHH to report on the behavior of   
   >>> its caller: DD() that its is requiring   
   >>> something outside the scope of computation.   
   >>   
   >> That's dumber than the Witch scene in Monty Python and The Holy Grail.   
   >>   
   >   
   > *I will be utterly relentless about this*   
   > *I will be utterly relentless about this*   
   > *I will be utterly relentless about this*   
   > *I will be utterly relentless about this*   
   >   
   > Yes and now if you could just translate that   
   > mere baseless rhetoric into actual reasoning   
   > with a sound basis.   
   >   
   > Not to denigrate you but I think that this   
   > would be totally out of your depth as it   
   > would be for most everyone.   
      
   I am certainly not smarter than Turing, but you think you are.   
      
   I do not believe that HHH is required to report on the behavior   
   of its caller. There is no such thing.   
      
   In the computing environment you have devised, the top activation of HHH   
   has a caller, which is the (one and only) activation of main. That   
   observation is not interesting or relevant, and, more importantly,   
   /must/ not be relevant.   
      
   Pure functions do not have a context. Given an expression f(x, y),   
   it denotes eactly the same calculation no matter where it is placed,   
   provided that the placement does not override the meaning of the   
   symbol f (that is to say, there isn't a lexically enclosing   
   shadowing redefinition of f).   
      
   This property is called "referential transparency" in CS.   
      
   The test case D can incorporate any one of an infinite number   
   of possible representations of the /algorithm/ on which H is based.   
      
   It uses that algorithm, but does not call H.   
      
   The circumstances of the halting problem are not limited to the narrow   
   conception that is embodied in just your C programming experiment.   
      
   It is about algorithms, not specific functions in a programming   
   language, which are all in the same image, such that D   
   calls the same address H that is the procedure deciding it.   
      
   You've not acknowledged your mistakes, such as:   
      
   - continuing to use impure functions (e.g. mutating global   
     execution trace buffer; distinguishing "Root == 1" H   
     functions from "Root == 0").   
      
   - treating unequal addresses as necessarily unequal functions.   
      
   - conflating the instruction events from multiple simulations   
     into a single execution trace buffer.   
      
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