Theory, examples of reversible parsers?

Question

Does anyone out there know about examples and the theory behind parsers that will take (maybe) an abstract syntax tree and produce code, instead of vice-versa. Mathematicall

Answer 1

I rather like lewap's response:

find a mathematical way to express a visitor and you have a dual to the parser

But you asked for a sample, so try this on for size: Visual Studio contains a UML editor with excellent symmetry. The way both it and the editors are implemented, all constitute views of the model, and editing either modifies the model resulting in all remaining in synch.