How to make generic computations over heterogeneous argument packs of a variadic template function?

Since I was not happy with what I found, I tried to work out a solution myself and ended up writing a small library which allows formulating generic operations on argument packs. My solution has the following features:

• Allows iterating over all or some elements of an argument pack, possibly specified by computing their indices on the pack;
• Allows forwarding computed portions of an argument pack to variadic functors;
• Only requires including one relatively short header file;
• Makes extensive use of perfect forwarding to allow for heavy inlining and avoids unnecessary copies/moves to allow for minimum performance loss;
• The internal implementation of the iterating algorithms relies on Empty Base Class Optimization for minimizing memory consumption;
• It is easy (relatively, considering it’s template meta-programming) to extend and adapt.

I will first show what can be done with the library, then post its implementation.

USE CASES

Here is an example of how the for_each_in_arg_pack() function can be used to iterate through all the arguments of a pack and pass each argument in input to some client-supplied functor (of course, the functor must have a generic call operator if the argument pack contains values of heterogenous types):

// Simple functor with a generic call operator that prints its input. This is used by the
// following functors and by some demonstrative test cases in the main() routine.
struct print
{
    template<typename T>
    void operator () (T&& t)
    {
        cout << t << endl;
    }
};

// This shows how a for_each_*** helper can be used inside a variadic template function
template<typename... Ts>
void print_all(Ts&&... args)
{
    for_each_in_arg_pack(print(), forward<Ts>(args)...);
}

The print functor above can also be used in more complex computations. In particular, here is how one would iterate on a subset (in this case, a sub-range) of the arguments in a pack:

// Shows how to select portions of an argument pack and 
// invoke a functor for each of the selected elements
template<typename... Ts>
void split_and_print(Ts&&... args)
{
    constexpr size_t packSize = sizeof...(args);
    constexpr size_t halfSize = packSize / 2;

    cout << "Printing first half:" << endl;
    for_each_in_arg_pack_subset(
        print(), // The functor to invoke for each element
        index_range<0, halfSize>(), // The indices to select
        forward<Ts>(args)... // The argument pack
        );

    cout << "Printing second half:" << endl;
    for_each_in_arg_pack_subset(
        print(), // The functor to invoke for each element
        index_range<halfSize, packSize>(), // The indices to select
        forward<Ts>(args)... // The argument pack
        );
}

Sometimes, one may just want to forward a portion of an argument pack to some other variadic functor instead of iterating through its elements and pass each of them individually to a non-variadic functor. This is what the forward_subpack() algorithm allows doing:

// Functor with variadic call operator that shows the usage of for_each_*** 
// to print all the arguments of a heterogeneous pack
struct my_func
{
    template<typename... Ts>
    void operator ()(Ts&&... args)
    {
        print_all(forward<Ts>(args)...);
    }
};

// Shows how to forward only a portion of an argument pack 
// to another variadic functor
template<typename... Ts>
void split_and_print(Ts&&... args)
{
    constexpr size_t packSize = sizeof...(args);
    constexpr size_t halfSize = packSize / 2;

    cout << "Printing first half:" << endl;
    forward_subpack(my_func(), index_range<0, halfSize>(), forward<Ts>(args)...);

    cout << "Printing second half:" << endl;
    forward_subpack(my_func(), index_range<halfSize, packSize>(), forward<Ts>(args)...);
}

For more specific tasks, it is of course possible to retrieve specific arguments in a pack by indexing them. This is what the nth_value_of() function allows doing, together with its helpers first_value_of() and last_value_of():

// Shows that arguments in a pack can be indexed
template<unsigned I, typename... Ts>
void print_first_last_and_indexed(Ts&&... args)
{
    cout << "First argument: " << first_value_of(forward<Ts>(args)...) << endl;
    cout << "Last argument: " << last_value_of(forward<Ts>(args)...) << endl;
    cout << "Argument #" << I << ": " << nth_value_of<I>(forward<Ts>(args)...) << endl;
}

If the argument pack is homogeneous on the other hand (i.e. all arguments have the same type), a formulation such as the one below might be preferable. The is_homogeneous_pack<> meta-function allows determining whether all the types in a parameter pack are homogeneous, and is mainly meant to be used in static_assert() statements:

// Shows the use of range-based for loops to iterate over a
// homogeneous argument pack
template<typename... Ts>
void print_all(Ts&&... args)
{
    static_assert(
        is_homogeneous_pack<Ts...>::value, 
        "Template parameter pack not homogeneous!"
        );

    for (auto&& x : { args... })
    {
        // Do something with x...
    }

    cout << endl;
}

Finally, since lambdas are just syntactic sugar for functors, they can be used as well in combination with the algorithms above; however, until generic lambdas will be supported by C++, this is only possible for homogeneous argument packs. The following example also shows the usage of the homogeneous-type<> meta-function, which returns the type of all arguments in a homogeneous pack:

 // ...
 static_assert(
     is_homogeneous_pack<Ts...>::value, 
     "Template parameter pack not homogeneous!"
     );
 using type = homogeneous_type<Ts...>::type;
 for_each_in_arg_pack([] (type const& x) { cout << x << endl; }, forward<Ts>(args)...);

This is basically what the library allows doing, but I believe it could even be extended to carry out more complex tasks.

IMPLEMENTATION

Now comes the implementation, which is a bit tricky in itself so I will rely on comments to explain the code and avoid making this post too long (perhaps it already is):

#include <type_traits>
#include <utility>

//===============================================================================
// META-FUNCTIONS FOR EXTRACTING THE n-th TYPE OF A PARAMETER PACK

// Declare primary template
template<int I, typename... Ts>
struct nth_type_of
{
};

// Base step
template<typename T, typename... Ts>
struct nth_type_of<0, T, Ts...>
{
    using type = T;
};

// Induction step
template<int I, typename T, typename... Ts>
struct nth_type_of<I, T, Ts...>
{
    using type = typename nth_type_of<I - 1, Ts...>::type;
};

// Helper meta-function for retrieving the first type in a parameter pack
template<typename... Ts>
struct first_type_of
{
    using type = typename nth_type_of<0, Ts...>::type;
};

// Helper meta-function for retrieving the last type in a parameter pack
template<typename... Ts>
struct last_type_of
{
    using type = typename nth_type_of<sizeof...(Ts) - 1, Ts...>::type;
};

//===============================================================================
// FUNCTIONS FOR EXTRACTING THE n-th VALUE OF AN ARGUMENT PACK

// Base step
template<int I, typename T, typename... Ts>
auto nth_value_of(T&& t, Ts&&... args) ->
    typename std::enable_if<(I == 0), decltype(std::forward<T>(t))>::type
{
    return std::forward<T>(t);
}

// Induction step
template<int I, typename T, typename... Ts>
auto nth_value_of(T&& t, Ts&&... args) ->
    typename std::enable_if<(I > 0), decltype(
        std::forward<typename nth_type_of<I, T, Ts...>::type>(
            std::declval<typename nth_type_of<I, T, Ts...>::type>()
            )
        )>::type
{
    using return_type = typename nth_type_of<I, T, Ts...>::type;
    return std::forward<return_type>(nth_value_of<I - 1>((std::forward<Ts>(args))...));
}

// Helper function for retrieving the first value of an argument pack
template<typename... Ts>
auto first_value_of(Ts&&... args) ->
    decltype(
        std::forward<typename first_type_of<Ts...>::type>(
            std::declval<typename first_type_of<Ts...>::type>()
            )
        )
{
    using return_type = typename first_type_of<Ts...>::type;
    return std::forward<return_type>(nth_value_of<0>((std::forward<Ts>(args))...));
}

// Helper function for retrieving the last value of an argument pack
template<typename... Ts>
auto last_value_of(Ts&&... args) ->
    decltype(
        std::forward<typename last_type_of<Ts...>::type>(
            std::declval<typename last_type_of<Ts...>::type>()
            )
        )
{
    using return_type = typename last_type_of<Ts...>::type;
    return std::forward<return_type>(nth_value_of<sizeof...(Ts) - 1>((std::forward<Ts>(args))...));
}

//===============================================================================
// METAFUNCTION FOR COMPUTING THE UNDERLYING TYPE OF HOMOGENEOUS PARAMETER PACKS

// Used as the underlying type of non-homogeneous parameter packs
struct null_type
{
};

// Declare primary template
template<typename... Ts>
struct homogeneous_type;

// Base step
template<typename T>
struct homogeneous_type<T>
{
    using type = T;
    static const bool isHomogeneous = true;
};

// Induction step
template<typename T, typename... Ts>
struct homogeneous_type<T, Ts...>
{
    // The underlying type of the tail of the parameter pack
    using type_of_remaining_parameters = typename homogeneous_type<Ts...>::type;

    // True if each parameter in the pack has the same type
    static const bool isHomogeneous = std::is_same<T, type_of_remaining_parameters>::value;

    // If isHomogeneous is "false", the underlying type is the fictitious null_type
    using type = typename std::conditional<isHomogeneous, T, null_type>::type;
};

// Meta-function to determine if a parameter pack is homogeneous
template<typename... Ts>
struct is_homogeneous_pack
{
    static const bool value = homogeneous_type<Ts...>::isHomogeneous;
};

//===============================================================================
// META-FUNCTIONS FOR CREATING INDEX LISTS

// The structure that encapsulates index lists
template <unsigned... Is>
struct index_list
{
};

// Collects internal details for generating index ranges [MIN, MAX)
namespace detail
{
    // Declare primary template for index range builder
    template <unsigned MIN, unsigned N, unsigned... Is>
    struct range_builder;

    // Base step
    template <unsigned MIN, unsigned... Is>
    struct range_builder<MIN, MIN, Is...>
    {
        typedef index_list<Is...> type;
    };

    // Induction step
    template <unsigned MIN, unsigned N, unsigned... Is>
    struct range_builder : public range_builder<MIN, N - 1, N - 1, Is...>
    {
    };
}

// Meta-function that returns a [MIN, MAX) index range
template<unsigned MIN, unsigned MAX>
using index_range = typename detail::range_builder<MIN, MAX>::type;

//===============================================================================
// CLASSES AND FUNCTIONS FOR REALIZING LOOPS ON ARGUMENT PACKS

// Implementation inspired by @jogojapan's answer to this question:
// http://stackoverflow.com/questions/14089637/return-several-arguments-for-another-function-by-a-single-function

// Collects internal details for implementing functor invocation
namespace detail
{
    // Functor invocation is realized through variadic inheritance.
    // The constructor of each base class invokes an input functor.
    // An functor invoker for an argument pack has one base class
    // for each argument in the pack

    // Realizes the invocation of the functor for one parameter
    template<unsigned I, typename T>
    struct invoker_base
    {
        template<typename F, typename U>
        invoker_base(F&& f, U&& u) { f(u); }
    };

    // Necessary because a class cannot inherit the same class twice
    template<unsigned I, typename T>
    struct indexed_type
    {
        static const unsigned int index = I;
        using type = T;
    };

    // The functor invoker: inherits from a list of base classes.
    // The constructor of each of these classes invokes the input
    // functor with one of the arguments in the pack.
    template<typename... Ts>
    struct invoker : public invoker_base<Ts::index, typename Ts::type>...
    {
        template<typename F, typename... Us>
        invoker(F&& f, Us&&... args)
            :
            invoker_base<Ts::index, typename Ts::type>(std::forward<F>(f), std::forward<Us>(args))...
        {
        }
    };
}

// The functor provided in the first argument is invoked for each
// argument in the pack whose index is contained in the index list
// specified in the second argument
template<typename F, unsigned... Is, typename... Ts>
void for_each_in_arg_pack_subset(F&& f, index_list<Is...> const& i, Ts&&... args)
{
    // Constructors of invoker's sub-objects will invoke the functor.
    // Note that argument types must be paired with numbers because the
    // implementation is based on inheritance, and one class cannot
    // inherit the same base class twice.
    detail::invoker<detail::indexed_type<Is, typename nth_type_of<Is, Ts...>::type>...> invoker(
        f,
        (nth_value_of<Is>(std::forward<Ts>(args)...))...
        );
}

// The functor provided in the first argument is invoked for each
// argument in the pack
template<typename F, typename... Ts>
void for_each_in_arg_pack(F&& f, Ts&&... args)
{
    for_each_in_arg_pack_subset(f, index_range<0, sizeof...(Ts)>(), std::forward<Ts>(args)...);
}

// The functor provided in the first argument is given in input the
// arguments in whose index is contained in the index list specified
// as the second argument.
template<typename F, unsigned... Is, typename... Ts>
void forward_subpack(F&& f, index_list<Is...> const& i, Ts&&... args)
{
    f((nth_value_of<Is>(std::forward<Ts>(args)...))...);
}

// The functor provided in the first argument is given in input all the
// arguments in the pack.
template<typename F, typename... Ts>
void forward_pack(F&& f, Ts&&... args)
{
    f(std::forward<Ts>(args)...);
}

CONCLUSION

Of course, even though I provided my own answer to this question (and actually because of this fact), I am curious to hear if alternative or better solutions exist which I have missed – apart from the ones mentioned in the “Related Works” section of the question.