Cantor
- This is still a work in progress. It may be changed in the future.
| Paradigm(s) | Stack-based |
|---|---|
| Designed by | User:Joe |
| Appeared in | 2024 |
| Computational class | Turing complete |
| Major implementations | In Factor (GitHub) |
| File extension(s) | .cntr |
Cantor is an esolang created by User:Joe, in 2024, after imagining a stack based language with minimal/no stack shuffling. It is named after George Cantor for his work on infinities.
Overview
Cantor consists of access to infinitely many stacks, and there are only a few operations you can do on these stacks. There is a catch though. To encourage the use of varying stacks, every stack can only store 7 items (so people just don't use the first 2 stacks).
Its basically a tape of stacks. Kinda a weird brainf***.
Commands
The integers can be both positive and negative. Positive numbers indication movement to the right, and negative to the left.
The number 0 can be used to refer to the current stack. For instance, >0 wont move the stack, and =0 dups the top item on the stack.
If an item is copied or moved to a full stack, it is removed.
(...) can be used for comments.
- >n :
- moves the current stack n away.
- =n :
- copies the value at the top of the current stack to the top of stack n away
- #m :
- moves the value at the top of the current stack to the top of stack n away (the value on the top of the current stack is popped off)
- [...] :
- push string (the text within the brackets) to the top of the current stack
- ! :
- include the string on the current stack into the actual program (to evaluate it)
- + :
- concatenate the top two strings on the current stack.
- ^ :
- output the top string on the current stack, popping it (I view this as an extra command just for IO. not necessary for the spirit of cantor)
Turing Completeness
WARNING: NOT A CORRECT PROOF
(I am not too sure if this is a full proof yet, because it doesn't take into account that each stack can only hold 7 items)
On the Underload page, it is shown that :()^ is a Turing Complete reduction. And for Cantor, we can show that it can perform these operations.
- : = n=n
- where n is an arbitrary stack. (n=n copies its top value to the top of the stack)
- () = []n
- ^ = !n
We are done. (I think)
Example Programs
Hello, world!
[Hello, world!]^
Infinite Loop
[=0!]=0!
Truth Machine
(Based off of the Underload Truth Machine)
There is no input, so [] on the top of the stack represents 0, and a [#7] represents 1. There example below has an input of 1.
[#7][[1]^=0!]#1#2>1#-1>1#-2>-2[[0]^]#1#2>1#-1>1#-2>-2!=0! (7 is the garbage stack)
Implementations
Factor implementation https://github.com/JosephOziel/cantor