Stuff like this is so cool. It reminds me of umbral calculus, another place where identities we’re used to from single variable calc apply correctly in other su

Stuff like this is so cool. It reminds me of umbral calculus, another place where identities we’re used to from single variable calc apply correctly in other surprising places. It’s especially amazing how we can invent “illegal operations” like the square root of a datatype (or the square root of minus one) and prove that we’ll get the right answer in the original domain if it exists. I’d bet I miss lots of opportunities to take advantage of inventing nonsensical operations to solve hard problems. It seems like a lot of the logic we use for reasoning about complex systems has the same combinatorial underpinnings (e.g. continuous systems in calc, recurrence relations and polynomials elsewhere, and algebraic datatypes in OP). I’d love to see an intro to all these variations of “calculus” written up from those combinatorial foundations that applies to all of the different applications, rather than via epsilon-delta derivations that only apply to continuous systems. Anybody seen a write-up like that anywhere?