This is not a persuasive argument because, by your logic, function implementations are also mathematical formulas and everyone agrees that they are copyrightable.
Also, you are distorting the argument by making it about one method signature instead of thousands of interconnected types and methods that work together to present an ergonomic interface for the developer.
A table of baseball batting averages or telephone numbers is not copyrightable, no matter how good or bad it is organized.
There's a reason the Supreme Court didn't adopt the argument you are pushing and instead ruled on fair use grounds: It's a bad argument because a large API is clearly a creative work.
Two equally good programmers may come up with radically different interfaces. Whereas if given an interface and instructed to implement it, they are likely to converge to a similar implementation.
It’s when you see an actual mathematical syntax that you realize how different programming really is.
Not try to be tedious here, just pointing out that actually programming is different than math, even for a language like Haskell.
A formula is an idea. It describes the nature of something computable. It does not explain how to compute.
For example: https://en.wikipedia.org/wiki/Euclidean_algorithm
The programmer must understand the formula in order to write computer code that implements it. The result is a creative/expressive work which is copyrightable.
gcd(X, Y) = X if X == Y or gcd(X - Y, Y) if Y < X or gcd(X, Y - X) otherwhise.
Is this a formula? Should this be copyright-able?
It would have made perfect sense to Euclid.
Some computers can understand this and execute it as if it were computer code. That's amazing! Kudos to those compute language designers and compiler authors. But their ingenuity does not suddenly grant copyright protection to anything their clever compilers can now understand.
If you code GCD in a low-level computer programming language then of course you can claim a copyright on that code, but nobody owns the idea of the Euclidean algorithm.