How to use std::function with a template argument

Why does this not work (in C++11) and how can I fix it:

#include <iostream>
#include <functional>

using namespace std;

template <typename T>
int apply(string x, const function<int(T)>& fn)
{
    T t = { x };
    return fn(t);
}

struct S {
    string data;
};

int process_s(const S& s)
{
    return s.data.size();
}

int main()
{
    cout << apply("abc", process_s);
}

The error is

prog.cc:21:8: error: no matching function for call to 'apply'
        cout<<apply("abc", process_s);
              ^~~~~
prog.cc:7:5: note: candidate template ignored: 
  could not match 'function<int (type-parameter-0-0)>'
  against 'int (const S &)'
int apply(string x, const function<int(T)>& fn) {
    ^
1 error generated.

I tried the approach from here, but it doesn't work either:

#include <iostream>
#include <functional>

using namespace std;

template <typename T>
struct id {
    typedef T type;
};

template <typename T>
using nondeduced = typename id<T>::type;

template <typename T>
int apply(string x, const function<nondeduced<int(T)> >& fn)
{
    T t = { x };
    return fn(t);
}

struct S {
    string data;
};

int process_s(const S& s)
{
    return s.data.size();
}

int main()
{
    cout << apply("abc", process_s);
}