Cyclifford

Cyclifford is a silly idea of a language by User:arseniiv, based on Clifford algebras.

The program is an expression consisting of integer literals, variables, additions, subtractions, multiplications and applications of two non-principal (anti)automorphisms. Variables $v_{i}$ are referenced by their positive integer indices $i\in \{1,\ldots ,N\}$.

At runtime, the input is treated as a desctiption of a Clifford algebra (over integers): its length in bits is the generator count, and for each generator $v_{i}^{2}$ is taken to be +1 when the $i$-th bit is 0, and −1 when that bit is 1. The state of computation $S$ initially is taken to be the program. Then the Procedure A is applied to $S$ until it’s self-conjugate, i. e. applying principal automorphism to $S$ returns $S$ itself.

Procedure A is as follows. In $S$, replace each $v_{i}$ with $v_{i+1}$ treating indices modulo the input length, and name the result $T$. Then assign $S:=ST$.

If the computation halts, the output is the scalar (grade-0) part of the final $S$.

Example of operation

I’m fairly confident no one understood anything above so an example will come soon. Or will it?..