I don't think "curry" is quite the right name for that function. For a function

    int f(int, int, int);

the curried version of f,

    auto f_curried = curry(f);

must be able to take multiple arguments one-at-a-time, so

    f_curried(x)(y)(z) == f(x, y, z)

The code at https://dpaste.de/a8g9D/ just partially applies the function to one set of arguments, which isn't enough -- you have to keep partially applying until you get them all.