[ruricolist]

There is a fair amount of academic work on bidirectional tree transformation with lenses, e.g. <https://www.cs.cornell.edu/~jnfoster/papers/lenses.pdf>. It breaks down to proving three operations (Get, Put, Create) that observe three laws (called GetPut, PutGet, and CreateGet); these give you bidirectional transformations you can compose arbitrarily. Later work introduces concepts like "quotienting" (for when you actually want the transformation to be lossy in certain ways) or "discerning" (non-total) lenses.

[lucasluitjes]

OP here, we actually considered using the GetPut/Putget/CreateGet terminology during a refactor, but it didn't seem to map perfectly. As I understand it, with lenses you generally define them through a DSL. Monocle lets you define them through example code. The goal was to make it as easy as possible for a decent programmer to write a lot of them. I couldn't find that type abstraction in academic work, but it's entirely possible I didn't use the right search terms.