Jumpmin
Jumpmin is a minimalized version of Jumplang created by User:PythonshellDebugwindow. The goal of this language is to remain a Turing-complete simple translation of Jumplang.
The original commands
We start with a hefty 10 commands, so a minimalization will be welcome among avid Jumplangers.
| Jumplang Command | Description | 
|---|---|
| + | Increment the current cell by 1 | 
| - | Decrement the current cell by 1 | 
| > | Increment the cell pointer | 
| < | Decrement the cell pointer | 
| , | Input an ASCII character to the current cell | 
| . | Output the current cell as an ASCII character | 
| ^ | Increment the current cell by 2 | 
| v | Decrement the current cell by 2 | 
| ? | Skips the next command if the current cell is 0 | 
| ! | Performs an absolute jump to the 0-based Nth character in the source, where N is the cell pointer + 1th cell (jumping negative or out of bounds halts the program) | 
All others are nops.
Minimalization
Our 10 instructions include I/O (, and .), which is unnecessary for Turing-completeness, so it can be removed, leaving 8 instructions. The ^ and v can now be used for all your incrementing and decrementing needs (their only real advantages over + and - were I/O-related—they were good for printing characters with odd ASCII values and for zeroing characters with odd ASCII values—but since I/O is now removed, they have no advantage over the increment-by-2 and decrement-by-2 commands), so + and - can be removed. We now have 6 instructions:
| Intermediate Command | Description | 
|---|---|
| > | Increment the cell pointer | 
| < | Decrement the cell pointer | 
| ^ | Increment the current cell by 2 | 
| v | Decrement the current cell by 2 | 
| ? | Skips the next command if the current cell is 0 | 
| ! | Performs an absolute jump to the 0-based Nth character in the source, where N is the cell pointer + 1th cell (jumping negative or out of bounds halts the program) | 
?! can be merged into one instruction, ‽, which is a conditional jump (the current cell is used for the condition, and the cell after that is used for the jump address), leaving us with a 5-command Turing-complete Jumplang minimalization.
Minimized commands
| Minimalized Command | Description | 
|---|---|
| > | Increment the cell pointer | 
| < | Decrement the cell pointer | 
| ^ | Increment the current cell by 2 | 
| v | Decrement the current cell by 2 | 
| ‽ | If the current cell is 0, performs an absolute jump to the 0-based Nth character in the source, where N is the cell pointer + 1th cell (jumping negative or out of bounds halts the program) | 
Simple translation to Jumplang
| Jumpmin | Jumplang | 
|---|---|
> | 
> | 
< | 
< | 
^ | 
^ | 
v | 
v | 
‽ | 
?! | 
As you can see, not much has changed (except, of course, the 4 completely removed commands).
Translator to Jumplang
def jumpmin_to_jumplang(jm):
  jl = ""
  for c in jm:
    if c == "‽": jl += "?!"
    else: jl += c
  return jl
Further development
If you have any ideas of how to further minimize the language while keeping it TC, you can put them on the talk page.