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

Actually, generating code from a parse tree is strictly easier than parsing code, at least in a mathematical sense. There are many grammars which are ambiguous, that is, there is no unique way to parse them, but a parse tree can always be converted to a string in a unique way, modulo whitespace.

The Dragon book gives a good description of the theory of parsers.