Halticopter
| Paradigm(s) | Declarative |
|---|---|
| Designed by | Hakerh400 |
| Appeared in | 2020 |
| Computational class | Unknown |
| Major implementations | Unimplemented |
| File extension(s) | .txt |
Halticopter is an esoteric programming language.
Overview
Source code consists of a single Turing machine (we call it Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} ). Input is also a Turing machine (we call it Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} ). Output is a single bit.
Halticopter assumes that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} does not halt. From that assumption only, it tries to determine whether Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} halts. If the program can conclude that halts, the program outputs Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1} and halts. If the program can conclude that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} does not halt, the program outputs Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0} and halts. If the program cannot determine whether Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} halts or not, the program does not halt. If Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} halts, the result is undefined (the program may either output Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1} , or may not halt).
Syntax
Both source code and input represent Turing machines. The syntax of the Turing machine is the following: it is an array of states separated by new lines and each state is represented either as the "HALT" string (for halting states), or as two groups of 3 space-separated decimal non-negative integers enclosed in parentheses (for non-halting states) - the first group is for the current pointed bit being 0 and the second is for 1. In each group, the first number is 0 or 1 (0 - do not invert the memory bit, 1 - invert the memory bit), the second one is 0 or 1 (0 - go left, 1 - go right), and the third one is the next state (0-indexed). The initial state is the state with index 0. Invalid syntax (either in the source code, or in the input) triggers a syntax error.
Examples
Example 1
Source code:
HALT
Input: (anything)
Output: undefined (because Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} halts)
Example 2
Source code:
(0 0 0) (0 0 0)
Input: (anything)
Output: If the input is literally the same as the source code, the output is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0} . For any other input, the output depends on the inference rules used to determine whether Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} halts or not (see the "Further research" section).
Example 3
Source code: (a Turing machine that halts iff ZF is inconcistent)[1]
Input: (a Turing machine that tries to prove a ZF statement starting from the ZF axioms)
Output: If ZF is consistent: if the statement is provable, then the output is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1} , otherwise the output is either Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0} , or the program does not halt. If ZF is inconsistent, the result is undefined.
Further research
The language does not seem to be precisely defined. The statement "assuming that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} does not halt, we conclude that..." is pretty vague. The language specification can be improved by defining some formal computable inference rules for deducing whether Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle Y} halts based on the assumption that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle X} does not halt (if such rules even exist), but without assuming anything else (such as the consistency of ZF or any other formal mathematical system). The author did not come up with any such rules so far.