How to convert a lambda to an std::function using templates

You can't pass a lambda function object as an argument of type std::function<T> without explicitly specifying the template argument T. Template type deduction tries to match the type of your lambda function to the std::function<T> which it just can't do in this case - these types are not the same. Template type deduction doesn't consider conversions between types.

It is possible if you can give it some other way to deduce the type. You can do this by wrapping the function argument in an identity type so that it doesn't fail on trying to match the lambda to std::function (because dependent types are just ignored by type deduction) and giving some other arguments.

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

template <typename... T>
void func(typename identity<std::function<void(T...)>>::type f, T... values) {
  f(values...);
}

int main() {
  func([](int x, int y, int z) { std::cout << (x*y*z) << std::endl; }, 3, 6, 8);
  return 0;
}

This is obviously not useful in your situation though because you don't want to pass the values until later.

Since you don't want to specify the template parameters, nor do you want to pass other arguments from which the template parameters can be deduced, the compiler won't be able to deduce the type of your std::function argument.

You can use a dedicated/retrospective cast. Once you have a tool like this

#include <functional>

using namespace std;

template<typename T>
struct memfun_type
{
    using type = void;
};

template<typename Ret, typename Class, typename... Args>
struct memfun_type<Ret(Class::*)(Args...) const>
{
    using type = std::function<Ret(Args...)>;
};

template<typename F>
typename memfun_type<decltype(&F::operator())>::type
FFL(F const &func)
{ // Function from lambda !
    return func;
}

you can say FFL() to all lambda types to have them converted to what would be the correct version of std::function

template <typename... Args> void Callback(std::function<void(Args...)> f){
    // store f and call later
}

int main()
{
    Callback(FFL([](int a, float b){
        // do something
    }));

    return 0;
}

Display

As shown at Inferring the call signature of a lambda or arbitrary callable for "make_function", you can infer the calling signature of a lambda (or any other functor with a single calling signature) from its (single) operator():

template<typename T> struct remove_class { };
template<typename C, typename R, typename... A>
struct remove_class<R(C::*)(A...)> { using type = R(A...); };
template<typename C, typename R, typename... A>
struct remove_class<R(C::*)(A...) const> { using type = R(A...); };
template<typename C, typename R, typename... A>
struct remove_class<R(C::*)(A...) volatile> { using type = R(A...); };
template<typename C, typename R, typename... A>
struct remove_class<R(C::*)(A...) const volatile> { using type = R(A...); };

template<typename T>
struct get_signature_impl { using type = typename remove_class<
    decltype(&std::remove_reference<T>::type::operator())>::type; };
template<typename R, typename... A>
struct get_signature_impl<R(A...)> { using type = R(A...); };
template<typename R, typename... A>
struct get_signature_impl<R(&)(A...)> { using type = R(A...); };
template<typename R, typename... A>
struct get_signature_impl<R(*)(A...)> { using type = R(A...); };
template<typename T> using get_signature = typename get_signature_impl<T>::type;

This is a rather inflexible approach, though; as R. Martinho Fernandes says, it won't work for functors with multiple operator()s, nor for functors with templated operator() or for (C++14) polymorphic lambdas. This is why bind defers inference of its result type until the eventual call attempt.