Iverson usually expresses the derivative as an operator, which ties into Heaviside's operational calculus[0] but doesn't have multiplication rules like dx/dy (I

Iverson usually expresses the derivative as an operator, which ties into Heaviside's operational calculus[0] but doesn't have multiplication rules like dx/dy (I'd probably be more on your side here, in favor of dx and dy). I don't think he was too comfortable with mathematical concepts that don't resolve into specific calculations. Which may be why his notation ended up being so easy to turn into a programming language. To me, Iverson's suggestivity would be more about unifying or making analogies between established concepts. For example, APL uses * for exponentiation and ⍣ for repeated function application. [0] https://en.wikipedia.org/wiki/Operational_calculus https://en.wikipedia.org/wiki/Operational_calculus