Stream Ring Theory – A Turing-Complete Stream Algebra

I wrote the article on a boat with only an abstract algebra book, a LISP book, and a few articles that I had printed before I left. Thus, my references are my references. To then go back and back fill with references would not be an accurate representation of what I was truly referencing at the time.

But yes, there is a lot of related work out there. Hopefully, my approach and introduced novelties can inspire in a way others have not.

Ditto jq. jq is a very simple functional programming language built around streaming of objects.

I wrote the paper for technically savvy individuals who are not versed in abstract algebra. While writing the first 5 pages, I constantly asked myself: "Will my mom be able to follow what I'm saying?" Fortunately, after reading it, she said: "I get the general idea."

At page 5, the stream ring is defined as a product of the coefficient ring and the function ring and from there, the notation gets heavy and there was little I could do. Hopefully by building confidence in the reader up to page 5, they would have the patience to forge ahead because the true nuggets of value are in the latter parts of the article.

Finally, to the "Captain" comment -- this article was written while in the Sea of Cortez aboard the S/V Red Herring: http://svredherring.com and https://twitter.com/SV_RedHerring.

Marko Rodriguez is one of the main authors of Apache TinkerPop [http://tinkerpop.apache.org/]. This paper is the theoretical groundwork for future, more efficient implementations of the gremlin traversal machine, as appears from the last sentence of the paper: "In general, the algebra can be used to develop both languages and underlying execution systems that are functional, universal, and can be reasoned on algebraically."

A colleague of mine who gets confused by "all the symbols" said that they appreciated the verbose stream notation that I build throughout the article. I would recommend giving the article a earnest try up through to page 5. Then after that, jump to page 17 and read Section 5C on Set Operations. See if the standard concepts of union, intersection, difference, etc. mixed with the verbose stream notation gives you insight and ultimately, the confidence to keep trying to tackle the work.