I'm not sure how what you are proposing is any better than sed. I said math envy since you resorted to using algebraic ring theory when there was a much simpler solution. xD
There are many Turing Complete languages. There are many stream-based languages. Moreover, there are many Turing Complete stream-based languages. These are instances of the presented stream ring algebra. I wanted to understand the foundation of such languages so as to have the algebraic toolkit to generate more instances.