Yes, it's a programming language. That's the extra advantage: you can execute your specifications. For an example of how it works, take a look at "Functional Specification of JPEG Decompression, and an Implementation for Free" (1995, Jeroen Fokker).

C++ is 80's technology, and as such filled ugliness that was considered sexy at the time. Just like 80s pubic hairdressing it's just too much to see the essence. Try to compare Haskell's polymorphism to C++ templates and you will get the picture. Anyway, to you really think 30 years of computer science since C++ could not come up with anything better? Why not take advantage of the fact that you are very late in taking up a new technology and skip a few decades?

If they teach you only one programming language, yes, they damage you.

In the course of my CS education (early 90s), they started with Pascal when they explained algorithmical basics.
Later courses were in C for OS and networking, while other courses used about everything from PROLOG to ADA.

You learn that some paradigms map to certain types of problems better (or worse) than others. So don't open sockets in
Prolog (I have seen'em do it man) , and don't do AI in C.

a quote: "if the only tool you have is a hammer, every problem looks like a nail".