[don't merge] Speed up typechecking

[ChrisPenner]

Don't merge this, it's only a proof of concept.

Choose your PR title well: Your pull request title is what's used to create release notes, so please make it descriptive of the change itself, which may be different from the initial motivation to make the change.

Overview

What does this change accomplish and why?
i.e. How does it change the user experience?
i.e. What was the old behavior/API and what is the new behavior/API?

Feel free to include "before and after" examples if appropriate. (You can copy/paste screenshots directly into this editor.)

If relevant, which Github issues does it close? (See closing-issues-using-keywords.)

Implementation notes

How does it accomplish it, in broad strokes? i.e. How does it change the Haskell codebase?

Interesting/controversial decisions

Include anything that you thought twice about, debated, chose arbitrarily, etc.
What could have been done differently, but wasn't? And why?

Test coverage

Have you included tests (which could be a transcript) for this change, or is it somehow covered by existing tests?

Would you recommend improving the test coverage (either as part of this PR or as a separate issue) or do you think it’s adequate?

If you only tested by hand, because that's all that's practical to do for this change, mention that.

Loose ends

Link to related issues that address things you didn't get to. Stuff you encountered on the way and decided not to include in this PR.

[aryairani]

@ChrisPenner you should work with @dolio to vet any typechecker improvements, and merge them if they are safe