HGFTSNOA/Turing-Completeness proof

:
HGFTSNOA is able to interpret a Turing-complete variation of brainfuck, and is thus itself Turing-complete.
==HGF==
HGF is a version of brainfuck with no input. The conversion table is as follows:
Brainfuck	HGF
+ 	1
- 	2
< 	3
> 	4
. 	5
[ 	T
] 	t
Note that the 5 command outputs the current cell as a number rather than an ASCII character.
===HGFTSNOA implementation===
The following is an implementation of HGF in HGFTSNOA. It uses wrapping eight-bit cells, and its tape is unbounded in both directions. The string on the second line contains the program to be executed; the current program (converted from this Code Golf answer) prints the ASCII values of the string Hello, World!.
T
 tttttt TTTTT "241444144222T1111111111T41111114111413332t231t4141545242255424254T4533t4T14t3354115"
 tttttt TTTTT t tttttt 0 "000" 0
TT
t TTTTT tttttt ttttttt tttttttt ttttttttt T
 tttttttttt TTTTT tttttt TTTT ttttttt
 TTT tttttttttt TTTTT ""
 TTT 0 TTTTTT
 TTTT ""
 TTTTTT
 TTT tttttttttt TTTTT "1"
 tttttttt TTTTT tt tttttttt ttttttttt
 TTTTTT
 TTT tttttttttt TTTTT "2"
 tttttttt TTTTT ttt tttttttt ttttttttt
 TTTTTT
 TTT tttttttttt TTTTT "3"
 ttttttttt TTTTT ttttttttt TTTTTTTT -3
 TTT ttttttttt TTTTT -3
 tttttttt TTTTT "000" TTTTTTTT tttttttt
 ttttttttt TTTTT 0
 TTTTTT
 TTTTTT
 TTT tttttttttt TTTTT "4"
 ttttttttt TTTTT ttttttttt TTTTTTTT 3
 TTT tttttttt TTTT ttttttttt TTTTT ""
 tttttttt TTTTT tttttttt TTTTTTTT "000"
 TTTTTT
 TTTTTT
 TTT tttttttttt TTTTT "5"
 ttttt tttttttt ttttttttt
 TTTTTT
 TTT tttttttttt TTTTT "T"
 TTT 0 TTTTT ttttt tttttttt ttttttttt
 ttttttt TTTTT tttttttttttt tttttt ttttttt 1 "T" "t" 0
 TTTTTT
 TTTTTT
 TTT tttttttttt TTTTT "t"
 TTT ttttt tttttttt ttttttttt
 ttttttt TTTTT tttttttttttt tttttt ttttttt -1 "t" "T" 0
 TTTTTT
 TTTTTT
 TTTT t tttttt ttttttt TTTTTTTT 1 tttttttt ttttttttt
TT
tt TTTTT tttttt ttttttt T
 tttttttt TTTTT tttttt TTTT ttttttt
 ttttttttt TTTTT ttttttt TTTTTTTT 1
 ttttttttt TTTTT tttttt TTTT ttttttttt
 tttttttttt TTTTT ttttttt TTTTTTTT 2
 tttttttttt TTTTT tttttt TTTT tttttttttt
 ttttttttttt TTTTT tttttttt TTTTTTTT ttttttttt TTTTTTTT tttttttttt
 ttttttttttt TTTTT 1 TTTTTTTT ttttttttttt
 TTT ttttttttttt TTTTTTTT -256
 ttttttttttt TTTTT "" TTTTTTTT ttttttttttt
 tttttttt TTTTT ttttttttttt TTTT 0
 ttttttttt TTTTT ttttttttttt TTTT 1
 tttttttttt TTTTT ttttttttttt TTTT 2
 ttttttttttt TTTTT tttttttt
 TTT ttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT ttttttttt
 TTT tttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT tttttttttt
 TTTTTTT
 ttttttttttt TTTTT "0" TTTTTTTT ttttttttttt
 TTTTTT
 TTTTTTT
 ttttttttttt TTTTT "00" TTTTTTTT ttttttttttt
 TTTTTT
 TTTTTTT
 ttttttttttt TTTTT "000"
 TTTTTT
 tttttt TTTTT tttt tttttt 0 ttttttt ttttttttttt TTTT 0
 tttttt TTTTT tttt tttttt 0 ttttttt TTTTTTTT 1 ttttttttttt TTTT 1
 tttttt TTTTT tttt tttttt 0 ttttttt TTTTTTTT 2 ttttttttttt TTTT 2
 TTT 0 TTTTTT
 TTTT tttttt
TT
ttt TTTTT tttttt ttttttt T
 tttttttt TTTTT tttttt TTTT ttttttt
 ttttttttt TTTTT ttttttt TTTTTTTT 1
 ttttttttt TTTTT tttttt TTTT ttttttttt
 tttttttttt TTTTT ttttttt TTTTTTTT 2
 tttttttttt TTTTT tttttt TTTT tttttttttt
 ttttttttttt TTTTT tttttttt TTTTTTTT ttttttttt TTTTTTTT tttttttttt
 ttttttttttt TTTTT -1 TTTTTTTT ttttttttttt
 TTT ttttttttttt TTTTTTTT 1
 ttttttttttt TTTTT "" TTTTTTTT ttttttttttt
 tttttttt TTTTT ttttttttttt TTTT 0
 ttttttttt TTTTT ttttttttttt TTTT 1
 tttttttttt TTTTT ttttttttttt TTTT 2
 ttttttttttt TTTTT tttttttt
 TTT ttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT ttttttttt
 TTT tttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT tttttttttt
 TTTTTTT
 ttttttttttt TTTTT "0" TTTTTTTT ttttttttttt
 TTTTTT
 TTTTTTT
 ttttttttttt TTTTT "00" TTTTTTTT ttttttttttt
 TTTTTT
 TTTTTTT
 ttttttttttt TTTTT "255"
 TTTTTT
 tttttt TTTTT tttt tttttt 0 ttttttt ttttttttttt TTTT 0
 tttttt TTTTT tttt tttttt 0 ttttttt TTTTTTTT 1 ttttttttttt TTTT 1
 tttttt TTTTT tttt tttttt 0 ttttttt TTTTTTTT 2 ttttttttttt TTTT 2
 TTT 0 TTTTTT
 TTTT tttttt
TT
tttt TTTTT tttttt ttttttt tttttttt ttttttttt T
 TTT tttttt TTTT ttttttt
 TTT ttttttt TTTTT tttttttt
 tttttttttt TTTTT ttttttttt
 TTTTTTT
 tttttttttt TTTTT tttttt TTTT ttttttt
 TTTTTT
 TTTT tttttttttt TTTTTTTT tttt tttttt ttttttt TTTTTTTT 1 tttttttt ttttttttt
 TTTTTTT
 TTTT ""
 TTTTTT
TT
ttttt TTTTT tttttt ttttttt T
 tttttttt TTTTT tttttt TTTT ttttttt
 ttttttttt TTTTT ttttttt TTTTTTTT 1
 ttttttttt TTTTT tttttt TTTT ttttttttt
 tttttttttt TTTTT ttttttt TTTTTTTT 2
 tttttttttt TTTTT tttttt TTTT tttttttttt
 tttttttt TTTTT tttttttt TTTTTTTT ttttttttt TTTTTTTT tttttttttt
 TTT 0 TTTTTT
 TTTT 0 TTTTTTTT tttttttt
TT
tttttttttttt TTTTT tttttt ttttttt tttttttt ttttttttt tttttttttt ttttttttttt T
 TTT tttttt TTTT ttttttt TTTTT ttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT 1
 TTTTTTT
 TTT tttttt TTTT ttttttt TTTTT tttttttttt
 ttttttttttt TTTTT ttttttttttt TTTTTTTT -1
 TTT ttttttttttt TTTTT 0
 TTT 0 TTTTTT
 TTTT ttttttt
 TTTTTT
 TTTTTTT
 TTT tttttt TTTT ttttttt TTTTT ""
 TTT tttttttt TTTTT -1
 tttttt TTTTT " T"
 TTTTTTT
 tttttt TTTTT " t"
 TTTTTT
 tttttt TTTTT -"TT" TTTT 3 TTTTTTTT tttttt
 tttttt TTTTT -"TTTTTT" TTTT 3 TTTTTTTT tttttt
 tttttt TTTTT -"TTT" TTTT 0 TTTTTTTT tttttt
 tttttt TTTTT -"TTT" TTTT 1 TTTTTTTT tttttt
 tttttt TTTTT -"TTTT" TTTT 1 TTTTTTTT " " TTTTTTTT tttttt
 tttttt TTTTT -"T" TTTT 4 TTTTTTTT tttttt
 tttttt TTTTT -"TTTTTTTT" TTTT 1 TTTTTTTT tttttt
 tttttt TTTTT -"TT" TTTT 3 TTTTTTTT " " TTTTTTTT tttttt
 tttttt TTTTT -"TTT" TTTT 0 TTTTTTTT tttttt
 tttttt TTTTT -"TT" TTTT 3 TTTTTTTT tttttt
 tttttt 42 TTTT 42
 TTTTTT
 TTTTTT
 TTTTTT
 TTTT tttttttttttt
 tttttt
 ttttttt TTTTTTTT tttttttt
 tttttttt
 ttttttttt
 tttttttttt
 ttttttttttt
TT
===Conversion script===
The following JavaScript program functions as a converter from brainfuck to HGF.
const program = "->+>>>+>>---[++++++++++[>++++++>+++>+<<<-]-<+]>+>+.>.->--..>->-.>[>.<<]>[+>]<<.>++.";
if(program.indexOf(",") > -1)
{
 throw new Error("Input is not supported");
}
else
{
 console.log(program.replace(/[^<>.\[\]+-]/g, "")
 .replace(/\+/g, "1")
 .replace(/-/g, "2")
 .replace(/</g, "3")
 .replace(/>/g, "4")
 .replace(/\./g, "5")
 .replace(/\[/g, "T")
 .replace(/\]/g, "t"));
}
Category:Proofs Category:Examples