Lambda the Ultimate

Say we have a program: F -> G. Under what situations can we generate a program which operates on *deltas* of F and G?

That is, say that dF is an efficiently stored delta value between an old and new value of F, and dG is a delta between values of G. Are there many situations where we can derive the program dF -> dG given F -> G ?

It seems like this is probably a topic with existing research, but I'm having trouble figuring out what to search for. This would be interesting in the context of a framework like React.js, where there is user code that modifies the user-interface state based on external events, then more user code which translates that state into a virtual DOM value, then finally the real DOM is modified using the virtual DOM. If we were able to derive a delta-based version of the user's code, then we could directly translate external events into real DOM manipulation, without generating an entire virtual DOM along the way.