Getting partial template types from nested templates

Give a series of nested template structs, I'd like to be able to extract the outer most template and "assign" it in a template using statement.

ie:

struct s0 { };

template<typename T>
struct s1 { };

template<typename T>
struct s2 { };

template<typename T>
using outer = ?????

Such that I can do:

outer<s1<s0>><int> //would be s1<int>
outer<s2<s1<s0>>><int> //would be s1<int>

I've got close by template member variable in a template struct, but I can't then "assign" that to a single using statement as it requires two levels of template statement.

Thanks in advance

You can create your traits with partial specialization. Usage is not outer<s1<s0>><int> but outer<s1<s0>, int>.

Unsure of what you want for outer<s2<s1<s0>>, int>.

So, if you want s2<int>, you might do:

template <typename T, typename Inner>
struct outer_impl;

template <template <typename> class C, typename T, typename Inner>
struct outer_impl<C<T>, Inner>
{
    using type  = C<Inner>;
};

template <typename T, typename Inner>
using outer = typename outer_impl<T, Inner>::type;

Demo

Or, if you want s2<s1<int>>, you might do:

template <typename T, typename Inner>
struct outermost_impl
{
    using type = Inner;
};

template <template <typename> class C, typename T, typename Inner>
struct outermost_impl<C<T>, Inner>
{
    using type  = C<typename outermost_impl<T, Inner>::type>;
};

template <typename T, typename Inner>
using outermost = typename outermost_impl<T, Inner>::type;

Demo