Nonmathematical problems are difficult to answer when you try to find mathematical answers. It should be obvious, why it doesn't work.

Mentioning Scala is ironic, it's very light on math spik and to begin with was created to unify object oriented with functional programming, which is mathematically meaningless, because both are Turing complete and thus equivalent, tautological.

>So what I hear is "How programming languages helps with programming languages?"

Oh, right, in mathematics axiom is argument, but in reality it isn't. In programming you should assert what you assume, otherwise your assumptions can be wrong due to divergence from reality, but there no reality in mathematics, only fantasy, so you can't understand this with mathematics alone.