Switchboard

Switchboard is a Turing tarpit with zero instructions and one operation. It is comprised of data in a "board" and a data pointer which moves and operates according the board. It was created in September 2025 by User:CreeperBomb.

Execution

The board is an array of cells with some dimension, each cell storing a some valid position on the board. A cell's "neighbor" is the cell to its right - that is, if a cell is located at $P=\left(p_{1},p_{2},\ldots \right)$, its neighbor is the cell at $P'=\left(p_{1}+1,p_{2},\ldots \right)$. Unspecified cells are assumed to exist with a value pointing to the origin, and there can only be finitely many nonzero cells. If a coordinate is 0 across all cells, its dimension is effectively nonexistent; as such, all boards are considered to have infinitely many dimensions that are unused. Each step, the data pointer piecewise-adds the current cell's nieghbor's value to the current cell's value, and then goes to the cell whose position matches the current cell's (updated) value; in other words, the language repeatedly executes *P += *(P + (1,0,0,…)); P = *P;. The data pointer begins at the origin.

Note that there is no specification in this description for what each coordinate can be. In fact, a coordinate's value can come from any computable near-semiring with a multiplicative identity (computability here applying to both the operations and the set elements). The origin is the cell whose coordinates are all the additive identity, and a cell's neighbor is found by right-adding the multiplicative identity to the lowest dimensional coordinate. "Infinite dimensions" also does not place a restriction on the dimensions being limited to positive integers; in fact, there can be any cardinality of dimensions as long as a minimal dimension exists. Thus, a board with a dimension for every real number and each coordinate of a dimension being a 2x2 complex matrix is just as valid a board as one with two dimensions and integer coordinates. Another example is a 1-dimensional board with boolean coordinates who operate under $\oplus$ as addition and $\wedge$ as multiplication. In fact, within a board, a dimension may have a different near-semiring than another dimension.

Turing completeness

Switchboard is Turing complete, as it can iterate on arbitrary functions:

1. Assume a 1-dimensional board operating in the near-semiring satisfying:
   • Reverse function composition $\circ$ as the additive operation whose identity is the indentity function ${\text{id}}_{\circ }$
   • An operation $\ast$ as the multiplicative operation whose identity is some function ${\text{id}}_{\ast }$ and is defined by $f\ast g={\text{id}}_{\circ }$, ${\text{id}}_{\ast }\ast f=f\ast {\text{id}}_{\ast }=f$ for $f,g\neq {\text{id}}_{\ast }$
   • ${\text{id}}_{\ast }$ has no additive inverse within the near-semiring
2. The origin's neighbor has the value ${\text{id}}_{\ast }$, the origin has some constant function as its value, and all other cells have the identity function as their value (the identity function being the near-semiring's 0)

The choice of ${\text{id}}_{\ast }$ determines the function being iterated.