Add a "Core" intermediate representation

[brendanzab]

At the moment our concrete syntax is highly coupled to the syntax we use for type checking and our proofs. It might make sense to separate these to allow for cleaner proofs and type checking, and allow us to add new features without altering the core language too much.

For example, PADS/ML has DDC:

The tricky thing is doing this in such a way that preserves good error messages (see #2).

[mikeday]

It's inevitable that we will want to add some helpful syntax that gets desugared in the core representation.

[brendanzab]

One idea to get around the error reporting problem is to do what GHC does: implement a type checker+inference on the complex AST and a simple, more elegant type checker on the fully explicit core representation as a sanity check for debugging purposes.

[brendanzab]

Could be as close to a direct port of the typechecker in the formal specification, perhaps, seeing as that would have progress, preservation, and soundness already verified:

https://github.com/yeslogic/ddl/blob/06ffee90a00b119a145babd1f9339fcd960f519c/experiments/lean/ddl.lean#L275-L296

In the future we could also have specifications of how the high level code is 'lowered' into the desugared representation.

[mikeday]

Fun!