Wunnel

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Wunnel is a two-dimensional esoteric programming language designed by Chris Pressey (mostly) on February 13, 2011. It is a turning tarpit which draws from the 1L family of languages. The name is both a pun on the pronunciation of "1L", and a recursive portmanteau of the words Wunnel and tunnel which is used to describe the long sequences of identical instructions (often Nops) used in Wunnel programs to sync up remote parts of the program.

Program structure[edit]

(This is the part that is like 1L.) Instructions are presented in a finite two-dimensional grid (called the playfield). There is an instruction pointer (IP); it starts in the upper-left (northwest) corner of the playfield, travelling down (south). It may only travel in cardinal directions, one playfield cell at a time. If it travels outside the bounds of the playfield, the program halts.

Storage is done on a tape, unbounded in both directions. Each cell of the tape may contain one of the three "sign" integers -1, 0, or 1. Every cell of the tape is initially zero. There are also two special registers ix and iy; each of these may hold any value from 0 to 5 inclusive, and are both initially zero.

There are only two instructions in Wunnel: zero genus and positive genus. (This is where it diverges from 1L a bit.) Any character which has a genus of zero represents the genus zero instruction; any character which has a genus greater than zero represents the positive genus instruction.

Aside: Character Genus[edit]

The genus of a character is computed like the topological genus of a shape, with the following special consideration. Because a single character may consist of separate disconnected shapes, the genus of a character is the sum of the topological geni of each disconnected shape within the character. For example, the percent sign, as typically rendered, is one genus-zero shape (the slash) and two genus-one shapes (the circles); thus its character genus is two. This also means that blank characters have genus zero, as they are the sum of an empty set of individual geni.

Having instructions be distinguished by character genus has some implications for the representation of Wunnel programs. Unlike most programming languages, the concrete rendering of the source code affects the interpretation of the program. For example, in a "military stencil" typeface, all characters would have genus zero; a program in this typeface would have a different meaning from the "same" program rendered in a font such as Comic Sans.

Implementations may invoke a sort of "topological wimpmode" by accepting plain text files and asserting that they assume them to be rendered in a font with such-and-such characteristics. (We will do similarly in the remainder of this article by assuming that the reader's font renders blank spaces as truly blank, and that lower-case "o" renders as a shape with genus one.) However, a really high-fidelity implementation might wish to accept source code in a bitmap or vector graphics format instead of plain text to overcome the fragility of this assumption.

Additionally, the term "symbol" is explicitly avoided in Wunnel because it doesn't matter what these characters symbolize, only how many holes they have.

Instructions[edit]

(This is the turning tarpit part.) One instruction selects an operation from a table, and the other instruction executes that operation. (This is where it diverges from a conventional turning tarpit.) The table is two-dimensional.

The effect of the zero genus instruction depends on which direction the IP is travelling:

  • North: decrement iy register (mod 6)
  • South: increment iy register (mod 6)
  • East: increment ix register (mod 6)
  • West: decrement ix register (mod 6)

The effect of the positive genus instruction is to use the ix and iy registers to look up an operation from the following table, and execute it:

iy ix=0 ix=1 ix=2 ix=3 ix=4 ix=5
0 Rotate Rotate Shunt Negitive Posative Nop
1 Left Shunt Right Blank Nop Blank
2 Right Input Left Nop Posative Negitive
3 Nop Output Shunt Shunt Left Halt
4 Shunt Halt Nop Right Shunt Halt
5 Rotate Nop Rotate Rotate Rotate Rotate

The meaning of each of these operations is:

  • Halt: cease executing the program.
  • Right: move the tape head right one cell.
  • Left: move the tape head left one cell.
  • Posative: write +1 to the current tape cell.
  • Blank: write 0 to the current tape cell.
  • Negitive: write -1 to the current tape cell.
  • Rotate: rotate the IP's direction of travel 90 degrees counterclockwise.
  • Shunt: alter the left/right position of the IP's line of travel by the amount in the current tape cell, where negative values mean to the left. For example, if the tape cell contains 1 and the IP is travelling west on the 9th row, and shunt is executed, the IP will now be travelling west on the 8th row. If the IP was instead travelling east, it would after executing Shunt be travelling east on the 10th row. If it was travelling south in the 10th column, it would change to travelling south in the 9th column.
  • Input: accept a single bit (0 or 1) of input and write it to the current tape cell.
  • Output: output the absolute value of the current tape cell as a bit.

Examples[edit]

A bitwise cat program:

          o   ooo  o


o
o
o
o         o
o         o
o         o
o         o
o
o        o     o
o         o
o
o        o
o              o
o        o     o
o              o

         o
o oooooooo     o
         o
         o
         o

         o    oooo o

Every contiguous line of multiple o characters in this example is a wunnel. All of these wunnels except the horizontal one at the very top execute Nop repeatedly; the one at the very top executes Posative repeatedly (which has the same effect as executing Posative only once.) Note also how two wunnels overlap at the middle of the source nearer the bottom.

Computational Class[edit]

The author suspects Wunnel to be Turing-complete. The above example shows how Shunt can be used to construct a loop. In the example, the direction of the Shunt is fixed, but in general it is conditional. And although there is no instruction to alter a cell relative to its current state (say by incrementing it), it should be possible to use Shunt to select one of three paths based on the cell's value, alter the tape cell as desired in each of those paths, and merge back together with another set of Shunts, this time fixed ones.

The main open question is whether the chosen operation matrix supports an arbitrary effect at an arbitrary point. The first version that was tried had all the Rotate operations arranged in a center diagonal; this restricted the instruction set to only row 0 and column 0 instead of the entire table. The second version put all the Rotate operations on row 5, but it was decided it was much more convenient for every row and every column to contain at least one Nop, so a different arrangement of Rotates which still allow every row and every column to be used, was chosen. The author is fairly confident that the current table allows one to access every operation, and that, with sufficiently long wunnels, they can be executed with sufficient freedom to construct arbitrary programs.