

Fun with semirings (2013) [pdf] - jordigh
http://www.cl.cam.ac.uk/~sd601/papers/semirings-slides.pdf

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jacobolus
This link is the talk slides. There’s also a paper, which is probably a bit
more useful if you aren’t listening to a presenter.
[http://www.cl.cam.ac.uk/~sd601/papers/semirings.pdf](http://www.cl.cam.ac.uk/~sd601/papers/semirings.pdf)

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agumonkey
A lot more detailed indeed.

ps: also the author of `mov is Turing complete`.

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sjolsen
>Our focus will be on closed semirings, which are semirings with an additional
operation called closure (denoted * ) which satisfies the axiom: a* = 1 + a *
a* = 1 + a* * a

>In semirings where summing an infinite series makes sense, we can define a*
as: 1 + a + a^2 + a^3 + ...

>In other semirings where subtraction and reciprocals make sense we can define
a* as (1 - a)^-1

Suddenly the "generating functions" from my combinatorics course make _so_
much more sense. It was never about functions at all! It was about reusing our
knowledge of algebra on the real field and power series to manipulate a closed
semiring of combinations.

In retrospect, I think it would have been less confusing to use the abstract
algebra from the outset.

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Sniffnoy
The term you're looking for here is "formal power series".

[https://en.wikipedia.org/wiki/Formal_power_series](https://en.wikipedia.org/wiki/Formal_power_series)

