Best way (Or workaround) to specialize a template alias

Question

I'm currently implementing a tiny metaprogramming-based compile-time computations library.

If have defined a base class for operators, which has a result typedef (I have decided to use integral wrappers like std::integral_constant as values instead of raw integral values, to provide an uniform interface along the library), and a n-ary operator base class, that checks if the operators has at least one operand:

template<typename RESULT>
struct operator
{
    using result = RESULT;
};

template<typename RESULT , typename... OPERANDS>
struct nary_operator : public operator<RESULT>
{
    static_assert( sizeof... OPERANDS > 0 , "An operator must take at least one operand" );
};

So I defined alias for unary and binary operators:

template<typename OP , typename RESULT>
using unary_operator = nary_operator<RESULT , OP>;

template<typename LHS , typename RHS , typename RESULT>
using binary_operator = nary_operator<RESULT , LHS , RHS>;

That operator interfaces are used to define custom operators as alias, like comparison operators below:

template<typename LHS , typename RHS>
using equal = binary_operator<LHS,RHS,bool_wrapper<LHS::value == RHS::value>>;

template<typename LHS , typename RHS>
using not_equal = logical_not<equal<LHS,RHS>>;

template<typename LHS , typename RHS>
using less_than = binary_operator<LHS,RHS,bool_wrapper<LHS::value < RHS::value>>;

template<typename LHS , typename RHS>
using bigger_than = less_than<RHS,LHS>;

template<typename LHS , typename RHS>
using less_or_equal = logical_not<bigger_than<LHS,RHS>>;

template<typename LHS , typename RHS>
using bigger_or_equal = logical_not<less_than<LHS,RHS>>;

Now suppose we want to implement our custom equality operator for our own class. For example:

template<typename X , typename Y , typename Z>
struct vec3
{
    using x = X;
    using y = Y;
    using z = Z;
}; 

If the equality operator was made upon inheritance, instead of aliasing, this could be easily done through template specialization:

//Equality comparator implemented through inheritance:
template<typename LHS , typename RHS>
struct equal : public binary_operator<LHS,RHS,bool_wrapper<LHS::value == RHS::value>> {};

//Specialization of the operator for vec3:

template<typename X1 , typename Y1 , typename Z1 , typename X2 , typename Y2 , typename Z2>
struct equal<vec3<X1,Y1,Z1>,vec3<X2,Y2,Z2>> : public binary_operator<vec3<X1,Y1,Z1>,vec3<X2,Y2,Z2> , bool_wrapper<X1 == X2 && Y1 == Y2 && Z1 == Z2>> {}; 

I know that template alias cannot be specialized.
My question is: Is there a way, that is not to use inheritance design instead of template aliases, to specialize this kind of template aliases?

Answer 1

The pattern I use to specialize template aliases (or provide recursive aliases) is to have a corresponding _impl struct. For example:

template <typename T>
struct my_alias_impl { /* def'n */ };

template <>
struct my_alias_impl<int> { /* alternate def'n */ };

template <typename T>
using my_alias = my_alias_impl<T>;

Users would have to specialize on my_alias_impl instead, but the rest of the public interface remains clean.