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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 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/":): v_i^2 is taken to be +1 when the 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/":): i -th bit is 0, and −1 when that bit is 1. The state of computation 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/":): S initially is taken to be the program. Then the Procedure A is applied to 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/":): S until it’s self-conjugate, i. e. applying principal automorphism to 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/":): S returns $ S $ itself.
Procedure A is as follows. In 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/":): S , replace each 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/":): v_i with 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/":): v_{i+1} treating indices modulo the input length, and name the result 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/":): T . Then assign 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/":): S := ST .
If the computation halts, the output is the scalar (grade-0) part of the final 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/":): S .
Example of operation
I’m fairly confident no one understood anything above so an example will come soon. Or will it?..