[brianberns]

This idea comes from a functional pearl called "Power Series, Power Serious" [0], which is well worth reading.

I implemented the same thing myself in F#. [1]

[0]: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&d...

[1]: https://github.com/brianberns/PowerSeries

[abeppu]

Huh, there must have been something in the water leading up to this. Also from 1998 is this paper, "Calculus in coinductive form" and neither of these cites the other. https://ieeexplore.ieee.org/document/705675

[brianberns]

These are indeed very similar. Thanks for the link!

The math is a bit over my head, but this formulation seems more difficult than the one I'm familiar with. For example, x^2 is represented as 0::0::2 instead of 0::0::1 (because 2! = 2) and x^3 is represented as 0::0::0::6 instead of 0::0::0::1 (because 3! = 6). Is there a benefit to that?

[barrenko]

I was introduced to the notion of power series two weeks ago, and now it's seemingly everywhere...

[angra_mainyu]

Power series are possibly one of the most powerful tools in analysis.

[coliveira]

Power series have been everywhere for 200 years!

[barrenko]

I am learning that indeed.