Transet

Transet

Paradigm(s)	Markov Algorithm & Set
Designed by	User:GUAqwq
Appeared in	2023
Computational class	Turing complete
Major implementations	Implemented
File extension(s)	.ts_

Transet is a Set Rewriting System. There are no integers or characters in Transet, but only sets. It's the 2nd esolang of TS Series by User:GUAqwq

Overview

The systax is similar to wikipedia:Markov algorithm. This is a example for the rules:

{{_}} -> {_}

Which means transform the set in the form {{_}} to {_}

The "_" means any set. In this case, if the input is:

{{{{{{}}}}}}

Then the process will be:

{{{{{{}}}}}} ->  {{{{{}}}}} // _ = {{{{}}}}
{{{{{}}}}}   ->  {{{}}}     // _ = {{}}
{{{}}}       ->  {{}}       // _ = {}
{{}}                        // END

The output is the set after process.

The algorithm will always matches the outermost set in form.

Syntactic Sugar

These are the set brackets which can be used (the brackets must be matched):

{} () [] <>

These are the identefiers which can be used (at most 1 of them in the same rule):

_?*#A-Za-z

Computational class

Transet is Turing complete because the rules are wikipedia:Markov algorithm-like and any string(in another way, list) can be encoded to set using the following method:

Integer:

0 : {}
successor of n : {n}

List/String:

List : {[value],([rest_of_list],<>)}
Nil : <>

In this way, every wikipedia:Markov algorithm rules can be corresponding to two list which end with *

Examples

Binary numbers to integer

Input : a binary string which is encoded to set

Output : integer which is encoded to set

{[<<<>>>],([{[<>],([*],<>)}],<>)} -> {[<>],([{[<<<>>>],([{[<<<>>>],([*],<>)}],<>)}],<>)}
{[<<>>],([*],<>)} -> {[<>],([{[<<<>>>],([*],<>)}],<>)}
{[<>],([*],<>)} -> *

{[<<<>>>],([<>],<>)} -> {[<<>>],(<>,<<>>,<<>,<<>>>)}
{[<<<>>>],([{[x],(<>,<<>>,<<>,<<>>>)}],<>)} -> {[<x>],(<>,<<>>,<<>,<<>>>)}
{[x],(<>,<<>>,<<>,<<>>>)} -> x

Rule 1,2,3 is equivalent to the following Markov Algorithm program: ( "0":<> , "1":<<>> , "|":<<<>>> )

"|0" -> "0||"
"1" -> "0|"
"0" -> ""

Rule 4,5,6 means: (Protect by the form you see in Rule 5)

the last "|" -> Protected 1
"|" (Protected x) -> Protected (x+1)
Protected x -> x

You can just not using Rule 4,5,6. In that way you'll get the String-form anwser which includes many 2s

Interpreters

• Interpreter written in Haskell by User:Hakerh400