The domain of the variables is the real numbers. This is the default, so the declaration is optional. real(X) is equivalent to X :: -inf..inf.
Note that the notion of real numbers is used here in the pure mathematical sense, where real numbers subsume the integers. A variable of type real can therefore be instantated to either a floating point or an integer number. If the variables are already instantiated, this call checks that the variable is instantiated to a number.