Nobody ever cared to use tests to replicate what a type system does. That's a straw man. Tests go straight for the actual goal by testing actual values. Correct values are what are necessary. Types on the other hand are neither necessary nor sufficient.
Frankly, I don't even know what to do with such a statement. What is your definition of "internal" ?
I just did a very large re-factor of a codebase a few days ago where I changed a lot of event handler (method) types in a codebase of around 200K lines of code (Object Pascal). This means that the method signature of every single event handler could have been wrong in some way if I made a mistake, and it would have introduced a pretty egregious, non-internal bug in every case. How would you test such a massive change without replicating every single thing that a static type system and compiler already do for you ?
None of these projects had unit tests, but that's fine - you don't really need them for this sort of modification, just some patience, a tolerance for boredom (that, or the ability to suck it up anyway), and a complete lack of concern about messages such as 'ERROR: 0/1,577 file(s) built. NOTE: Error limit exceeded - only showing the first 99,999'.
I haven't touched OO Pascal in 15 years, so I can't speak to how you would write tests for it, or if there's even a testing framework. I will tell you that I left the if-it-compiles-it-works attitude around that time too though.
Re: your definition of "internal": I suspected that this was what you meant. I also disagree with this particular version of "correctness". If the developer intended that a particular function accept an integer, then accepting anything else is essentially a bug, and the fact that it works at all is down to pure coincidence.
As for writing tests in OP: you write tests in the same manner that you do with Java, C++, C#, etc.
Your statement that "nobody ever cared to use tests to replicate what the type system does" is trivially false, have you ever tested what happens when you pass "null" into a function that probably shouldn't take null? If so, you just did. Some type systems allow you to even specify valid subranges of types, and combined with algebraic data types, it's effectively impossible to misuse.
That's not necessarily true though is it? If the "1" in the "1 hour ago" message in the header of your reply wasn't the expected type of the writer of the output function but ultimately still shows up as "1 hour ago" to the user, there's no user-facing defect. I can promise you that this happens all the time in javascript. You're in a thread about Javascript.
> have you ever tested what happens when you pass "null" into a function
Not that I recall. Javascript will throw an appropriate error when it detects that your duck isn't quacking correctly. No one writes validation logic everywhere on internal units, so there's no functionality to verify with a test.
With that said, null is decidedly not "just a type". It's also a value. I generally avoid using null everywhere as much as possible too, because it's a pretty terrible concept.
> Some type systems allow you to even specify valid subranges of types, and combined with algebraic data types, it's effectively impossible to misuse.
Sure but you're in a thread about javascript and typescript. And let's be honest: the vast majority of type systems do not support that.