[Bug][move-compiler-v2] Function-valued argument type error message is confusing

[brmataptos]

🐛 Bug

    public inline fun pass_mut_ref<T>(v: &mut vector<T>, action: |&mut T|&mut T): &mut T {
        action(vector::borrow_mut(v, 0))
    }

    public fun consume_mut_freeze() {
        let v = vector[1, 2, 3];
        let r = pass_mut_ref(&mut v, |x| (freeze(x)));
    }

yields the error message:

error: the function takes `&mut` but `&` was provided
   ┌─ tests/checking/typing/lambda_widen_result.move:43:38
   │
43 │         let r = pass_mut_ref(&mut v, |x| (freeze(x)));
   │                                      ^^^^^^^^^^^^^^^

Which is very confusing. The problem here is that

• The type of parameter action is |&mut T|&mut T.
• The value provided is a lambda of ambiguous type, either |&mut T|&T or |&T|&T.
• So the type checker is trying to unify |&mut T|&T with |&mut T|&mut T and finds that the
  return type &T is not compatible with &mut T.
• But:
  • saying that "the function takes &mut" is wrong: it takes a function value with result type &mut.
  • No & was provided: rather, a function value with result type & was provided.
• BTW, the type checker probably tries both parameter types and gets one right.

For the parameter type of the function-valued parameter, it's difficult to engineer a similar situation without PR #14254, which adds type declarations for lambda parameters.

But changing the test case to

    public fun consume_mut_mut() {
        let v = vector[1, 2, 3];
        let r = pass_mut_ref(&mut v, |a, b| a);
    }

leads to the more reasonable error message:

error: cannot pass `|(_, _)|_` to a function which expects argument of type `|&mut integer|&mut integer`
   ┌─ tests/checking/typing/lambda_widen_result.move:28:38
   │
28 │         let r = pass_mut_ref(&mut v, |a, b| a);
   │                                      ^^^^^^^^

which would be better for the result case.

[brmataptos]

@rahxephon89 and @wrwg this is Urgent because I will need this cleaned up for more general-purpose lambda parameters. I've spent a few minutes looking at the code, and hope one of you can give some insight into how to fix it.