It turns out the special case that I added initially for this PR was unnecessary. Changing the base environment types is enough.

Unfortunately, the tests don't pass yet because the change to the type of first causes this type error:

unit-tests/typecheck-tests.rkt:3081:22: Type Checker: Polymorphic function `first' could not be applied to arguments:
Argument 1:
  Expected: (U '() (Pairof a (Listof b)))
  Given:    (List g4803 ... B)

which boils down to this inference test failure (a new test that I added):

--------------------
All inference tests > Tests for infer > ((U '() (Pairof X (Listof Y)))) ((List A ... B))
((U '() (Pairof X (Listof Y)))) ((List A ... B))
FAILURE
location:   <pkgs>/typed-racket-test/unit-tests/infer-tests.rkt:274:4
Could not infer a substitution
--------------------

It seems like this case should succeed though, so I'm not sure what's going on. I'll look into it, but if anyone else has any ideas let me know.

@takikawa what's the status here?

@samth the status is that I'm stuck on the inference problem above. I'll update this PR when I fix it.

Note that this is a backwards incompatible change, because instantiating the functions with A Any ... no longer extracts an A in many cases. If we are going to break backwards compatibility in this tiny case we should at least make the functions a lot simpler by making the types like cadr : (All (a) (Pair Any (Pair a Any))) with the appropriate Nulls.

Is this worth keeping open at this point?

This PR and the associated discussion may be useful to reference in the future, but leaving it as "open" seems incorrect at this point.