Is it possible to generate types with all combinations of template arguments?

Question

I have a templated class

template<class U, class V, class W> 
class S
{
//... implementations 
};

and some stock type implementations for type U, V and W:

typedef boost::mpl::vector<U0, U1> u_types;
typedef boost::mpl::vector<V0, V1, V2, V3, V4> u_types;
typedef boost::mpl::vector<W0, W1, W2, W3, W4> w_types;

I want to test class S with all possible combinations of the template arguments,

typedef boost::mpl::vector<
    S<U0,V0,W0>, 
    S<U0,V0,W1>,
    // ...
    S<U1,V4,W4>,
    > s_types;

like this:

boost::mpl::for_each<s_types>(test_func).

The only problem is there are 2 ** 5 ** 5 = 50 combinations that I do not wish to type in one by one.

Is there a way to generate all the combinations(s_types) with Boost::mpl or Boost.Preprocessor?

thanks.

---

Added my initial failed attempts:

I was trying to resort to indexes(hence defining u_types and the like) and partial template specialization like this

namespace wrapper
{
  template <int Uidx, int Vidx, int Widx> 
  struct S_Wrapper
  {
    typedef S<Uidx, Vidx, Widx> type;

    S_Wrapper() // auto test in the ctor
    {
      cout << "test result = " << test(type());
    }

    // test with S<Uidx, Vidx, Widx>
    static bool test(type t)
    {
      // implementations
    }

    // get stuck here, 
    S_Wrapper<Uidx-1, Vidx, Widx> s; // temp varible to invoke recursive-ness
    // what else to complete all recursive path?
  };

  // specializations       
  template <0, 0, 0> 
  struct S_Wrapper
  {
    typedef S<0, 0, 0> type;

    // test with S<Uidx, Vidx, Widx>
    //
    static bool test(type t)
    {
      // implementations
    }  
  };

  // get stuck here, too
  // what other specializations are ?
  // other specializations
}

then with

wrapper::S_Wrapper< 
  mpl::size<u_types>::type::value, 
  mpl::size<v_types>::type::value, 
  mpl::size<w_types>::type::value
> s;

all S types should be gengerated and tested ;

However I failed to cover all the combination by determining

1) the proper specializations and
2) recursive-ness triggers in struct S_Wrapper

All my trials either ended up in partial coverage of the combinations at runtime or deduction failure at compile time.

Any thoughts?

---

Solution

Inspired by Matthieu, I've come up with a templated class Combine so that I could achieve my goal in 2 lines like this:

typedef Combine<
            u_types,
            v_types,
            w_type,
            print_typeid
        >::Generate<> base_generator_type;
base_generator_type::Run();

which will print all generated types.

---

Code

// example test implementation
struct print_typeid
{
    template<
        class U, 
        class V, 
        class W
    >
    static void run()
    {
        // print the typeinfo
        std::cout 
            <<  total_recursions << ":"
            << typeid(U).name() << ","
            << typeid(V).name() << ","
            << typeid(W).name()
            << std::endl;  
    }            
}; 

// solution implemented in one wrapper class
namespace argument_combination
{
    using boost::is_same;
    using boost::mpl::begin;
    using boost::mpl::end;
    using boost::mpl::next;        
    using boost::mpl::if_;  
    using boost::mpl::deref;    

    unsigned int total_recursions = 0;

    struct end_of_recursion_tag 
    {
        static void Run()
        {
            std::cout << "end of " 
                 << total_recursions 
                 << " recursions\n"
                ;
        }
    };

    template <
        class UTypes,    // Forward Sequence, e.g. boost::mpl::vector
        class VTypes,    // Forward Sequence, e.g. boost::mpl::vector
        class WTypes,    // Forward Sequence, e.g. boost::mpl::vector
        class TestFunc  // class type that has a nested templated run() member function
    >
    struct Combine
    {
        // forward declaration
        template <
            class UIterator,
            class VIterator,
            class WIterator 
        >   
        class Generate;

        // this class implements recursion body 
        template <
            class UIterator,
            class VIterator,
            class WIterator
        >            
        struct Next
        {
            // u_begin is not necessary ;)
            // it would be cheaper not to pre-declare all of them since we force evaluation
            // however this dramatically increase the readability
            typedef typename begin<VTypes>::type v_begin;
            typedef typename begin<WTypes>::type w_begin;

            typedef typename end<UTypes>::type u_end;
            typedef typename end<VTypes>::type v_end;
            typedef typename end<WTypes>::type w_end;

            typedef typename next<UIterator>::type u_next;
            typedef typename next<VIterator>::type v_next;
            typedef typename next<WIterator>::type w_next;

            typedef typename if_< is_same<typename w_next, w_end>,
                                typename if_< is_same<v_next, v_end>,
                                    typename if_< is_same<u_next, u_end>,
                                        end_of_recursion_tag,
                                        Generate< 
                                            u_next, 
                                            v_begin, 
                                            w_begin 
                                        >
                                    >::type,
                                    Generate< 
                                        UIterator, 
                                        v_next,
                                        w_begin 
                                    >
                                >::type,
                                Generate< 
                                    UIterator, 
                                    VIterator, 
                                    w_next
                                    >
                            >::type type;
        };

        //  this class run test on generated types in thos round and go to next*/
        template <
            class UIterator = typename begin<UTypes>::type,
            class VIterator = typename begin<VTypes>::type,
            class WIterator = typename begin<WTypes>::type
        >
        struct Generate
        {
            //  generate <<next>> target type         
            typedef typename Next<
                    UIterator, 
                    VIterator, 
                    WIterator 
                >::type next_type;

            static void Run()
            {
                // increment recursion counter                
                ++total_recursions;

                // test on the generated types of this round of recursion
                TestFunc::run<
                     typename deref<UIterator>::type,
                     typename deref<VIterator>::type,
                     typename deref<WIterator>::type
                 >();

                // go to the next round of recursion
                next_type::Run();
            }
        };
    };

}//  namespace argument_combination

Answer 1

If what you really want to do is generating the vector of all possibles solutions and then test them, you will have to use the preprocessor to generate them all for you.

However, another solution would consist into using a generator: a wrapper class which will instantiate all your solutions and test them. You might want to consult the Hierarchy Generators of Loki (detailed in the book).

// never remember where they put boost::same_type :x
#include <boost/mpl/if.hpp>
#include <boost/mpl/deref.hpp>
#include <boost/mpl/begin.hpp>
#include <boost/mpl/end.hpp>
#include <boost/mpl/next.hpp>

using namespace boost::mpl;

struct None
{
   static void test() {}
};

template <class UIterator, class UTypes,
          class VIterator, class VTypes,
          class WIterator, class WTypes>
class Generator;

template <class UIterator, class UTypes,
          class VIterator, class VTypes,
          class WIterator, class WTypes>
struct Next
{
  // u_begin is not necessary ;)
  // it would be cheaper not to pre-declare all of them since we force evaluation
  // however this dramatically increase the readability
  typedef typename begin<VIterator>::type v_begin;
  typedef typename begin<WIterator>::type w_begin;

  typedef typename next<UIterator>::type u_next;
  typedef typename next<VIterator>::type v_next;
  typedef typename next<WIterator>::type w_next;

  typedef typename end<UIterator>::type u_end;
  typedef typename end<VIterator>::type v_end;
  typedef typename end<WIterator>::type w_end;


  typedef if_< boost::same_type<w_next, w_end>,
               if_< boost::same_type<v_next, v_end>,
                    if_< boost::same_type<u_next, u_end>,
                         None,
                         Generator< u_next, UTypes,
                                    v_begin, VTypes,
                                    w_begin, WTypes >
                    >,
                    Generator< UIterator, UTypes,
                               v_next, VTypes,
                               w_begin, WTypes >
                >,
                Generator< UIterator, UTypes,
                           VIterator, VTypes,
                           w_next, WTypes>
           >::type type;
};

template <class UIterator, class UTypes,
          class VIterator, class VTypes,
          class WIterator, class WTypes>
struct Generator
{
   typedef S< deref<UIterator>::type,
              deref<VIterator>::type,
              deref<WIterator>::type > S_type;

   typedef Next<UIterator, UTypes,
                VIterator, VTypes,
                WIterator, WTypes>::type next_type;

   static void test()
   {
     // test my variation of S
     S_Type my_S;
     test_func(my_S);

     // test the variations of my next and its next and... you get the idea :)
     next_type::test();
   }
};

// And finally
int main(int argc, char* argv[])
{
  typedef Generator< begin<u_types>::type, u_types,
                     begin<v_types>::type, v_types,
                     begin<w_types>::type, w_types > base_generator_type;

  base_generator_type::test();
}

Disclaimer: this code has not been compiled and may lack some include / typename / use directives... nevertheless I hope you get my point.

If you have any idea of what the Design Patterns are, it is highly similar to a 'decorator' or a 'composite' design in its way of adding another round of tests at each step layer.

I would also like to note that this takes more that 50 lines of code... but at least it will grow nicely with the vectors :)