XPost: comp.theory, sci.logic, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-19, Tristan Wibberley  wrote:   
   > On 19/11/2025 17:48, Kaz Kylheku wrote:   
   >   
   >> Recursive functions and Turing machines are equivalent. The halting   
   >> problem is about recursive functions too.   
   >   
   > There exists an equivalent ...   
   >   
   >   
   >> In any case, topics in the halting problem cannot be properly explored   
   >> using impure procedures --- not in such a way that we assume that those   
   >> procedures directly correspond to recursive functions.   
   >   
   > No. The Halting Theorem has no problems demonstrable with leaky   
   > simulation (emulation) sandboxes.   
      
   That is correct, but what you cannot say is that specific stateful   
   procedures in that leaky simulation correspond to pure recursive   
   functions in the theory of computation. (And, therefore, to   
   individual Turing Machines.)   
      
   You can build a model of your leaky sandbox in whch you identify   
   what the Turing Machines or functions are.   
      
   (Once you do that, it would probably make sense for your claims about   
   halting to revolve around that.)   
      
   > Topics can be explored with leaky sandboxes, topics such as "How can   
   > leaky sandboxes and their effects be characterised?" and "What are the   
   > relationships between various recursive functions and various Turing   
   > Machines and their generalisations?"   
      
   Olcott's leaky Halt7.obj/x86utm_exe sandbox /cannot/ be   
   characterized in such a way we refer to the stateful C procedure   
   HHH as a recursive primitive function.   
      
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