What you're describing is akin to a basic pull-based incremental engine, akin to salsa. The base design is straightforward, but you need some additional logic to avoid following the whole execution tree when hashing. Their downsides is that sometimes you do have to follow the whole execution tree, even if nothing changed.

Push-based designs instead "push" changes to their dependants, which can be quite efficient especially in the case where the update doesn't propagate much. However it has the downside of potentially requiring to update nodes that are no longer used, or updating nodes multiple times.