ADT constructors in a type-checking mode

In a bidirectional type-checker we can take advantage of a type-checking mode in case of constructors of ADTs, and do not require the full module path to be provided by the programmer. However, we treat constructors as regular functions in expressions, and we switch from a type-checking mode to a type-inferring mode in case of a function application. This two decisions in combination make type-checking of shadowed or not imported constructors more challenging. Consider the following code, which could be considered valid.
```
data A = A
data B = A of A
data C = A of B

let _ = A (A A)
```
At the moment I do not see any *simple* solution to this problem, so any ideas are welcome.