Differentiation (of functions) is a product-preserving functor, which makes the Chain Rule the rule by which it respects function composition, which makes autom

Differentiation (of functions) is a product-preserving functor, which makes the Chain Rule the rule by which it respects function composition, which makes automatic differentiation a matter of writing out the syntax tree of functions and "folding it up" via a catamorphism (a generalized fold). https://jtobin.io/ad-via-recursion-schemes https://jtobin.io/ad-via-recursion-schemes Yes, really. I wasn't making that up. Automatic differentiation is a page or two of code given enough categorical background.