From: wyniijj5@gmail.com   
      
   On Sat, 2025-07-19 at 16:05 -0500, olcott wrote:   
   > On 7/19/2025 3:57 PM, wij wrote:   
   > > On Sat, 2025-07-19 at 15:41 -0500, olcott wrote:   
   > > > On 7/19/2025 3:14 PM, wij wrote:   
   > > > >    
   > > > > HP is very simple: H(D)=1 if D halts, H(D)=0 if D does not halt.   
   > > > >    
   > > >    
   > > > The standard proof assumes a decider   
   > > > H(M,x) that determines whether machine   
   > > > M halts on input x.   
   > > >    
   > > > But this formulation is flawed, because:   
   > >    
   > > Whatever the 'formulation' is, the HP result is a fact that no H can decide   
   > > the halting status of any given D.   
   > >    
   >    
   > And that is wrong because H(⟨D⟩) is correctly determined.   
   > It has always been a type mismatch error when H(D) was   
   > assumed.   
      
   Yes, there is type mismatch problems in nearly all discussions.   
   But I don't think you will understand what it is.   
      
   > > > Turing machines can only process finite encodings   
   > > > (e.g. ⟨M⟩), not executable entities like M.   
   > > >    
   > > > So the valid formulation must be   
   > > > H(⟨M⟩,x), where ⟨M⟩ is a string.   
   > >    
   > > Halting Problem::= H(D)=1 if D halts, H(D)=0 if D does not halt.   
   > > The conclusion is, no such H exists.   
   > >    
   >    
   > And that is wrong because H(⟨D⟩) is correctly determined.   
   > It has always been a type mismatch error when H(D) was   
   > assumed.   
   >    
   > int DD()   
   > {   
   >    int Halt_Status = HHH(DD);   
   >    if (Halt_Status)   
   >      HERE: goto HERE;   
   >    return Halt_Status;   
   > }   
   >    
      
   A type mismatch: HHH(DD) or HHH()?   
      
   > DD correctly simulated by HHH cannot reach past   
   > the "if" statement thus cannot reach the "return"   
   > statement. T   
      
   That is roughly what HP proof says.   
      
   > his makes HHH(DD)==0 correct.   
      
   How is this statement from? HHH(DD) above shows it cannot return to report 0.   
   (I guess you might say something and doing another, again)   
      
   > > 'formulation' does not really matter.   
   > > If 'formulation' matters, it is another problem.   
   > >    
   >    
   >    
      
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