I have three different functions, and what you wrote is not their type, that's their signature. Actually they are really only two different functions - a < b and b > a are the same thing for this integer type - but whether or not the optimiser knows that will not always be obvious.

Yes, the C++ type system doesn't express this, that's the defect (well, it's the consequence here of a larger defect).

Once they have different types there are two different interesting things we can do, we could just coerce them into a function pointer type based on the signature which is what you've seen in C++ and seem to assume is just naturally the only possibility. Or, we can use parametric polymorphism.