Is it possible in C++11 to combine functions into a new function?

Question

This is more a kind of theoretical question. Is it possible in C++11 to combine functions into a new function? For example :

auto f = [](int i){return i * 2;};
auto g = [](int i){return i + 10;};

So this works:

auto c = f(g(20)); // = 60

But I want an object that stores the combination, like

auto c = f(g);
std::cout << c(20) << std::endl; //prints 60

Edit: Additionally what i want to create is a function a, which you can give a function b and an int n, and which returns the n'th combination of the given function b. For example (not compilable)

template<typename T>
auto combine(T b, int i) -> decltype(T)
{
   if (i == 0)
      return b;

   return combine(b, i - 1);      
}

auto c = combine(f, 2); //c = f(f(f(int)))

Answer 1

You can write something along the lines of:

#include <functional>
#include <iostream>

template<class F>
F compose(F f, F g)
{
  return [=](int x) { return f(g(x)); };
}

int main()
{
  std::function<int (int)> f = [](int i) { return i * 2; };
  std::function<int (int)> g = [](int i) { return i + 10; };

  auto c = compose(f, g);
  std::cout << c(20) << '\n';  // prints 60
}

The code can be simply extended to cover the second half of the question:

template<class F>
F compose(F f, unsigned n)
{
  auto g = f;

  for (unsigned i = 0; i < n; ++i)
    g = compose(g, f);

  return g;
}

int main()
{
  std::function<int (int)> h = [](int i) { return i * i; };

  auto d = compose(h, 1);
  auto e = compose(h, 2);
  std::cout << d(3) << "\n"    // prints 81
            << e(3) << "\n";   // prints 6561
}

NOTE. Here using std::function. It isn't a lambda but wraps a lambda with a performance cost.