It looks to me like the authors attempt to develop a method to automatically make any program memoizable, similarly to how you can automatically differentiate a huge family of differentiable functions in your favorite symbolic math program (Mathematica, maybe?)

Are there more examples of differential plugins (that to me look akin to the table of derivatives in your Calculus I book)?

From the paper:

Users of our approach need to (1) choose which base types and primitives they need (2) implement suitable differentiation plugins for these base types and primitives (3) rewrite (relevant parts of) their programs in terms of these primitives (4) arrange for their program to be called on changes instead of updated inputs.

Anyone seen some more examples other than they toy example in the paper?

Not a PL person, sorry if I misunderstood something.