20121002: The Multilanguage Nirvana
The source for this post is online at 20121002multilanguagenirvana.scrbl.
A student and I are working on a verified linearlogic theorem prover, in Coq. We came up with a very cute way to integrate many languages in the production of this tool and this post is about that multilanguage nirvana.

The first language we use in this project is Coq, the wonderful proof assistant that I used for my dissertation and use whenever possible. The main linear logic theorem prover is written in Coq. It’s divided into three pieces: (1) an embedding of linear logic as an inductive theory; (2) a set of decision procedures, one for each kind of linear logic proof, that independently reach true conclusions, assuming an oracle that can handle all other kinds of proofs; and (3) the glue that ties them all together that we prove sound overall.
The set up gives us a function that when given a linear logic problem, expressed as a list of assumptions, it will return a list of all formulas that can be proved from it. However, we’d like to run this program efficiently with Ocaml, so we extract it, giving the normal Ocaml types as replacements for the normal Coq types, such as booleans and lists.
However, this program isn’t really useful by itself, because it needs to (a) have a specified problem and (b) be called with input and then the output printed in some way. Rather than go through the pain of creating a module, we use the wonderful C preprocessor to stitch together these various pieces: the prover, the problem specification, and the code that calls them.
However, it is inconvenient to specify the problem directly in the Ocaml data type syntax, because it is very verbose. We’d prefer to specify it using simple Sexpressions. So, we combine that with a simple Racket program that reformats the Sexpression as Ocaml.
The beautiful make language is used to manage this process and keep everything in sync whenever we change one of the pieces.
I like this little program because it shows how convenient it can be to use many different languages, each for its own little purpose. The only way that this could be better, I think, would be if all the languages were actually just Racket underneath. Maybe some day...