Desugar global variables away

[oflatt]

This PR adds a brand new, type-preserving pass that gets rid of all global variables by tuning them into functions. This does not yet resolve the issue about declare: #334 Example:

(let x 3)
(Add x x)

becomes

(function x () i64)
(set (x) 3)
(Add (x) (x))

Most of this PR is helpers, such as map_exprs, which allows us to map over all exprs in the whole egglog program.

Here are some questions we need to resolve before this is merged:

• [ ] While refactoring map_exprs, I had to add a lot of type constraints throughout the ast. It's a lot of boilerplate- is there a way to get rid of them?
• [x] How does this affect visualizations? Right now the function is unextractable, but probably still shows up in the viz which is incorrect
• [ ] Can we remove AtomTerm::Global? Seems like the typechecker uses core actions so maybe not? Right now we have several panics in the back end when we see a global.

[oflatt]

Assigning @yihozhang to review, added @saulshanabrook in case they wanted to take a look

[saulshanabrook]

Is there a feature/bug this resolves or is it mainly meant to make the implementation cleaner?

[oflatt]

It just makes it cleaner Also will help with adding proofs

[oflatt]

This PR is ready to merge The two other remaining TODOs are optional

[oflatt]

Just had another pass. This is great and the code is easy to follow. Besides questions in the comments, I have a higher-level question:

• Have you thought about removing global variables during the desugaring phase before the type checking? This way ResolvedVar does not need to carry an is_global_ref field around. Currently, this field makes sense only for the typechecking and the globals removal passes.

  • If we can do this, then the typechecking and passes after this will only be dealing with local variables, and we can entirely remove AtomTerm::Global.
  • Instead of having TypeInfo to track the set of global variables, we can have Desugar responsible for managing a set of globals to be desugared.

I've thought of this, and I agree it would be much nicer. The problem is, this pass actually does depend on type information: it needs to know the type of the global being desugared.

[oflatt]

@yihozhang is this ready to merge?

[oflatt]

Thanks for fixing up, I must have lost the commit where I fixed those

[oflatt]

@yihozhang I've refactored this PR to not look up values in actions. It adds to the query instead. I'm going to refactor generating fresh symbols next.