Is it possible to figure out the parameter type and return type of a lambda?

Given a lambda, is it possible to figure out it's parameter type and return type? If yes, how?

Basically, I want lambda_traits which can be used in following ways:

auto lambda = [](int i) { return long(i*10); };

lambda_traits<decltype(lambda)>::param_type  i; //i should be int
lambda_traits<decltype(lambda)>::return_type l; //l should be long

The motivation behind is that I want to use lambda_traits in a function template which accepts a lambda as argument, and I need to know it's parameter type and return type inside the function:

template<typename TLambda>
void f(TLambda lambda)
{
   typedef typename lambda_traits<TLambda>::param_type  P;
   typedef typename lambda_traits<TLambda>::return_type R;
  
   std::function<R(P)> fun = lambda; //I want to do this!
   //...
}

For the time being, we can assume that the lambda takes exactly one argument.

Initially, I tried to work with std::function as:

template<typename T>
A<T> f(std::function<bool(T)> fun)
{
   return A<T>(fun);
}

f([](int){return true;}); //error

But it obviously would give error. So I changed it to TLambda version of the function template and want to construct the std::function object inside the function (as shown above).

Funny, I've just written a function_traits implementation based on https://stackoverflow.com/questions/2562320/specializing-a-template-on-a-lambda-in-c0x which can give the parameter types. The trick, as described in the answer in that question, is to use the decltype of the lambda's operator().

template <typename T>
struct function_traits
    : public function_traits<decltype(&T::operator())>
{};
// For generic types, directly use the result of the signature of its 'operator()'

template <typename ClassType, typename ReturnType, typename... Args>
struct function_traits<ReturnType(ClassType::*)(Args...) const>
// we specialize for pointers to member function
{
    enum { arity = sizeof...(Args) };
    // arity is the number of arguments.

    typedef ReturnType result_type;

    template <size_t i>
    struct arg
    {
        typedef typename std::tuple_element<i, std::tuple<Args...>>::type type;
        // the i-th argument is equivalent to the i-th tuple element of a tuple
        // composed of those arguments.
    };
};

// test code below:
int main()
{
    auto lambda = [](int i) { return long(i*10); };

    typedef function_traits<decltype(lambda)> traits;

    static_assert(std::is_same<long, traits::result_type>::value, "err");
    static_assert(std::is_same<int, traits::arg<0>::type>::value, "err");

    return 0;
}

Note that this solution does not work for generic lambda like [](auto x) {}.

Though I'm not sure this is strictly standard conforming, ideone compiled the following code:

template< class > struct mem_type;

template< class C, class T > struct mem_type< T C::* > {
  typedef T type;
};

template< class T > struct lambda_func_type {
  typedef typename mem_type< decltype( &T::operator() ) >::type type;
};

int main() {
  auto l = [](int i) { return long(i); };
  typedef lambda_func_type< decltype(l) >::type T;
  static_assert( std::is_same< T, long( int )const >::value, "" );
}

However, this provides only the function type, so the result and parameter types have to be extracted from it. If you can use boost::function_traits, result_type and arg1_type will meet the purpose. Since ideone seems not to provide boost in C++11 mode, I couldn't post the actual code, sorry.

The specialization method shown in @KennyTMs answer can be extended to cover all cases, including variadic and mutable lambdas:

template <typename T>
struct closure_traits : closure_traits<decltype(&T::operator())> {};

#define REM_CTOR(...) __VA_ARGS__
#define SPEC(cv, var, is_var)                                              \
template <typename C, typename R, typename... Args>                        \
struct closure_traits<R (C::*) (Args... REM_CTOR var) cv>                  \
{                                                                          \
    using arity = std::integral_constant<std::size_t, sizeof...(Args) >;   \
    using is_variadic = std::integral_constant<bool, is_var>;              \
    using is_const    = std::is_const<int cv>;                             \
                                                                           \
    using result_type = R;                                                 \
                                                                           \
    template <std::size_t i>                                               \
    using arg = typename std::tuple_element<i, std::tuple<Args...>>::type; \
};

SPEC(const, (,...), 1)
SPEC(const, (), 0)
SPEC(, (,...), 1)
SPEC(, (), 0)

Demo.

Note that the arity is not adjusted for variadic operator()s. Instead one can also consider is_variadic.

The answer provided by @KennyTMs works great, however if a lambda has no parameters, using the index arg<0> does not compile. If anyone else was having this problem, I have a simple solution (simpler than using SFINAE related solutions, that is).

Just add void to the end of the tuple in the arg struct after the variadic argument types. i.e.

template <size_t i>
    struct arg
    {
        typedef typename std::tuple_element<i, std::tuple<Args...,void>>::type type;
    };

since the arity isn't dependent on the actual number of template parameters, the actual won't be incorrect, and if it's 0 then at least arg<0> will still exist and you can do with it what you will. If you already plan to not exceed the index arg<arity-1> then it shouldn't interfere with your current implementation.