There are parser generators (some of which are limited to certain classes of grammars) which, given a grammar, automatically generate a parser for that grammar.
Would it be possible to make a general-purpose translator generator to automatically translate from onea string in the language with production rules described by grammar $G_1$ to a string in the otherlanguage with production rules described by grammar $G_2$? If so, what rules would have to be imposed? E.gFor practical purposes let's say these grammars must both be CFGs., would Would a formalization of semantic rules for the grammars also have to formally specified for the translator generator?
An example of this hypothetical, general-purpose translator generator: the translator generator is given grammar $G_1$ (which is a CFG representing a context-insenitive adaptation of the C programming language), $G_2$ (which is a CFG representing a context-insenitive adaptation of the JavaScript programming language), and a formalization of the semantic rules of the language with production rules described by grammar $G_2$1. The translator generator is expected to produce a translator which takes as input a string in the language with production rules described by grammar $G_1$ and translates that string to a string in the language with production rules described by grammar $G_2$.
1 I am not entirely sure of what this formalization of the language's semantic rules would look like, so if there exists some formalization which would make the existence of this general-purpose translator generator decidable, then I would also welcome suggestions on what this formalization would look like.
