How can I create a n way Cartesian product of type lists in C++?

With Boost.Mp11, this is a short one-liner (as always):

using result = mp_product<
    type_list,
    type_list_1, type_list_2, type_list_3>;

Demo.

Fold expressions to the rescue again

template<typename... Ts>
typelist<typelist<Ts>...> layered(typelist<Ts...>);

template<typename... Ts, typename... Us>
auto operator+(typelist<Ts...>, typelist<Us...>)
    -> typelist<Ts..., Us...>;

template<typename T, typename... Us>
auto operator*(typelist<T>, typelist<Us...>)
    -> typelist<decltype(T{} + Us{})...>;

template<typename... Ts, typename TL>
auto operator^(typelist<Ts...>, TL tl)
    -> decltype(((typelist<Ts>{} * tl) + ...));

template<typename... TLs>
using product_t = decltype((layered(TLs{}) ^ ...));

And you're done. This has the additional benefit over recursion of having O(1) instantiation depth.

struct A0;
struct A1;
struct B0;
struct B1;
struct C0;
struct C1;
struct C2;

using t1 = typelist<A0, A1>;
using t2 = typelist<B0, B1>;
using t3 = typelist<C0, C1, C2>; 

using p1 = product_t<t1, t2>;
using p2 = product_t<t1, t2, t3>;

using expect1 = typelist<typelist<A0, B0>,
                         typelist<A0, B1>,
                         typelist<A1, B0>,
                         typelist<A1, B1>>;

using expect2 = typelist<typelist<A0, B0, C0>,
                         typelist<A0, B0, C1>,
                         typelist<A0, B0, C2>,
                         typelist<A0, B1, C0>,
                         typelist<A0, B1, C1>,
                         typelist<A0, B1, C2>,
                         typelist<A1, B0, C0>,
                         typelist<A1, B0, C1>,
                         typelist<A1, B0, C2>,
                         typelist<A1, B1, C0>,
                         typelist<A1, B1, C1>,
                         typelist<A1, B1, C2>>;

static_assert(std::is_same_v<p1, expect1>);
static_assert(std::is_same_v<p2, expect2>);

Ok, got it. It's not pretty but it works:

template<class ... T>
struct type_list{};

struct somestructA{};
struct somestructB{};

using type_list_1 = type_list<int, somestructA, char>;
using type_list_2 = type_list<somestructB>;
using type_list_3 = type_list<double, short, float>;

template<class TL1, class TL2>
struct add;

template<class ... T1s, class ... T2s>
struct add<type_list<T1s...>, type_list<T2s...>>
{
    using type = type_list<T1s..., T2s...>;
};

template<class ... TL>
struct concat;

template<class TL, class ... TLs>
struct concat<TL, TLs...>
{
    using type = typename add<TL, typename concat<TLs...>::type>::type;
};

template<class TL>
struct concat<TL>
{
    using type = TL;
};

static_assert(std::is_same_v<type_list<int, somestructA, char, double, short, float>, typename add<type_list_1, type_list_3>::type>);

template<class TL1, class TL2>
struct multiply_one;

// Prepends each element of T1 to the list T2.
template<class ... T1s, class ... T2s>
struct multiply_one<type_list<T1s...>, type_list<T2s...>>
{
    using type = typename concat<type_list<type_list<T1s, T2s...>...>>::type;
};

static_assert(std::is_same_v<
    type_list<
        type_list<int, double, short, float>,
        type_list<somestructA, double, short, float>,
        type_list<char, double, short, float>
        >,
    typename multiply_one<type_list_1, type_list_3>::type>);

// Prepends each element of TL to all type lists in TLL.
template<class TL, class TLL>
struct multiply_all;

template<class TL, class ... TLs>
struct multiply_all<TL, type_list<TLs...>>
{
    using type = typename concat<typename multiply_one<TL, TLs>::type...>::type;
};

static_assert(std::is_same_v<
    type_list<
        type_list<int, double, short, float>,
        type_list<somestructA, double, short, float>,
        type_list<char, double, short, float>
        >,
    typename multiply_all<type_list_1, type_list<type_list_3>>::type>);

static_assert(std::is_same_v<
    type_list<
        type_list<int, somestructB>,
        type_list<somestructA, somestructB>,
        type_list<char, somestructB>,
        type_list<int, double, short, float>,
        type_list<somestructA, double, short, float>,
        type_list<char, double, short, float>
        >,
    typename multiply_all<type_list_1, type_list<type_list_2, type_list_3>>::type>);

template<class TL, class ... TLs>
struct cartesian_product
{
    using type = typename multiply_all<TL, typename cartesian_product<TLs...>::type>::type;
};

template<class ... Ts>
struct cartesian_product<type_list<Ts...>>
{
    using type = type_list<type_list<Ts>...>;
};


using expected_result = type_list<
    type_list<int, somestructB, double>,
    type_list<somestructA, somestructB, double>,
    type_list<char, somestructB, double>,
    type_list<int, somestructB, short>,
    type_list<somestructA, somestructB, short>,
    type_list<char, somestructB, short>,
    type_list<int, somestructB, float>,
    type_list<somestructA, somestructB, float>,
    type_list<char, somestructB, float>
>;

static_assert(std::is_same_v<expected_result,
    cartesian_product<type_list_1, type_list_2, type_list_3>::type>);

https://godbolt.org/z/L5eamT

I left my own static_assert tests in there for... Well, I hope they help.

Also, I'm sure there has to be a nicer solution. But this was the obvious "I know this will eventually lead to the goal" path. I eventually had to resort to adding a concat or sorts, I'm sure that it could be used much earlier to skip most of the cruft.