A template metafunction class is a type with a public nested template metafunction called apply. Since it is a type, it can be passed to template metafunctions as arguments and metafunctions can return it as their result. This makes it possible to implement higher-order template metafunctions, which are template metafunctions taking template metafunctions as arguments or returning template metafunctions as their result.

For example this is the identitiy template metafunction class:

struct identity
{
  template <class T>
  struct apply
  {
    using type = T;
  };
  using type = identity;
};

This metafunction class is called identity. It takes one argument, T. The result of calling this metafunction class is its argument, T. Note that the identity metafunction class is also a template metaprogramming value, so it can be an argument or the result of a template metafunction.

To call this metafunction, one has to call the nested template metafunction. For example:

identity::apply<std::integral_constant<int, 13>>::type

The above example calls the metafunction class identity with std::integral_constant<int, 13> as its argument.