C++ curried function

curry.cpp

// (a0 -> a1 -> ... -> r) -> (a0 -> (a1 -> ... -> r))
template <typename F>
auto curry_1(F f)
{
	return [f](auto a) {
		return [f, a](auto... args) {
			return f(a, args...);
		};
	};
}

// (a0 -> ... -> r) -> (a0 -> ... -> ak) -> (ak' -> ... -> r)
template <typename F>
auto curry_n(F f)
{
	return f;
}
template <typename F, typename T, typename... Ts>
auto curry_n(F f, T a, Ts... args)
{
	auto f1 = curry_1(f)(a);
	return curry_n(f1, args...);
}

// (a0 -> a1 -> ... -> r) -> (a0 -> a1 -> ... -> r)
template <typename F, int N>
struct curry_r
{
	auto operator()(F f)
	{
		return [f](auto... args) {
			auto f1 = curry_n(f, args...);
			return curry_r<decltype(f1), N - sizeof...(args)>{}(f1);
		};
	}
};
template <typename F>
struct curry_r<F, 1>
{
	auto operator()(F f)
	{
		return [f](auto a) {
			return f(a);
		};
	}
};
template <typename F>
struct curry_r<F, 0>
{
	auto operator()(F f)
	{
		return f();
	}
};

// (a0 -> a1 -> ... -> r) -> (a0 -> a1 -> ... -> r)
template <typename R, typename... Args>
auto curry(R f(Args...))
{
	return curry_r<R(Args...), sizeof...(Args)>{}(f);
}

/************************
    test code
************************/

#include <iostream>
#include <string>

std::string f(std::string x, std::string y, std::string z)
{
	return x + y + z;
}

int main()
{
	std::cout << curry(f)("a")("b")("c") << std::endl;
	std::cout << curry(f)("a", "b")("c") << std::endl;
	std::cout << curry(f)("a")("b", "c") << std::endl;
	std::cout << curry(f)("a", "b", "c") << std::endl;
	return 0;
}