H_Hat is proved to be halting decidable (current consensus)

[olcott]

If we assume that Simulate is functionally equivalent to the following
code (even if Simulate is an x86 emulator that emulates the x86 machine
code of its input):

int Simulate(u32 P, u32 I)
{
((void(*)(int))P)(I);
return 1;
}

Then because the execution trace shown below shows that H_Hat() invokes
Simulate() with the same data two times in sequence we can conclude that
H_Hat() is invoked in infinite recursion entirely based on this
execution trace and the assumption that Simulate() does nothing besides
execute or emulate it input.

// P has the machine address of H_Hat()
void H_Hat(u32 P)
{
u32 Input_Halts = Simulate(P, P);
if (Input_Halts)
HERE: goto HERE;
return;
}

_H_Hat()
[00000858](01) 55 push ebp
[00000859](02) 8bec mov ebp,esp
[0000085b](01) 51 push ecx
[0000085c](03) 8b4508 mov eax,[ebp+08]
[0000085f](01) 50 push eax
[00000860](03) 8b4d08 mov ecx,[ebp+08]
[00000863](01) 51 push ecx
[00000864](05) e80ffcffff call 00000478
[00000869](03) 83c408 add esp,+08
[0000086c](03) 8945fc mov [ebp-04],eax
[0000086f](04) 837dfc00 cmp dword [ebp-04],+00
[00000873](02) 7402 jz 00000877
[00000875](02) ebfe jmp 00000875
[00000877](02) 8be5 mov esp,ebp
[00000879](01) 5d pop ebp
[0000087a](01) c3 ret

Push instructions have already pushed the value shown in their in the
third column. The two push instructions preceding the call to Simulate()
are its second and first parameters respectively.

Columns
(1) Machine address of instruction
(2) Machine address of top of stack
(3) Value of top of stack after instruction executed
(4) Number of bytes of machine code
(5) Machine language bytes
(6) Assembly language text
...[00000858][000111c5][000111d1](01) 55 push ebp
...[00000859][000111c5][000111d1](02) 8bec mov ebp,esp
...[0000085b][000111c1][00000000](01) 51 push ecx
...[0000085c][000111c1][00000000](03) 8b4508 mov eax,[ebp+08]
...[0000085f][000111bd][00000858](01) 50 push eax
...[00000860][000111bd][00000858](03) 8b4d08 mov ecx,[ebp+08]
...[00000863][000111b9][00000858](01) 51 push ecx
; Call Simulate(0x858, 0x858);
...[00000864][000111b5][00000869](05) e80ffcffff call 00000478
...[00000858][000111a5][000111b1](01) 55 push ebp
...[00000859][000111a5][000111b1](02) 8bec mov ebp,esp
...[0000085b][000111a1][00000858](01) 51 push ecx
...[0000085c][000111a1][00000858](03) 8b4508 mov eax,[ebp+08]
...[0000085f][0001119d][00000858](01) 50 push eax
...[00000860][0001119d][00000858](03) 8b4d08 mov ecx,[ebp+08]
...[00000863][00011199][00000858](01) 51 push ecx
; Call Simulate(0x858, 0x858);
...[00000864][00011195][00000869](05) e80ffcffff call 00000478


--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein