Industry will choose not to verify that your function does not produce NullPointerException wasting hours of the client's work, because in order to do that they would have to have actual requirements for software developers, and in order to do that they would have to 1 - have the managers be actually technically literate, and 2 - pay the developers properly That's it. That's the theorems. The "formal verification" we're talking about here are those of the likes of "this value is a damn integer", or as you could interpret it "your code is not stupidly broken".

To be clear, I'm not writing this big comment for you, I know you're trolling or whatever you're into, I'm writing this to inform other readers. ✌🏻

Op here back from the dead. This is in fact not a stab at dynamically typed languages, or at least not only: statically typed languages such as Java also support this kind of construct. In fact, one could develop a technically type safe programming language where an instanceof construct has sound semantics.

What instanceof breaks is something called polymorphic parametricity, i.e. the fact that generic functions don't know anything specific about the types they are generic over. This is the fundamental condition for what in the community is dubbed "theorems for free", that is, naturality of generic functions between generic types.