How do you define something 'like' calculus? How do you define 'number' system? If by number system you mean arbitrary ring and by calculus you mean the derivat

How do you define something 'like' calculus? How do you define 'number' system? If by number system you mean arbitrary ring and by calculus you mean the derivative for example, then yes, but it's not super interesting. For example, the structure of algebraic data types forms a ring, and you can define an operation 'like' the derivative on it. However, given that only two operations (multiplication and addition) are commonly defined here, it's not particularly involved, although the result itself is quite useful (the derivative of the algebraic form of a data type is the type of one-holed versions of that same data type).