How can I obtain a C++ expression's type, at compile time (i.e. constexpr'ly)?

I would like to use the name of a type at compile time. For example, suppose I've written:

constexpr size_t my_strlen(const char* s)
{
        const char* cp = s;
        while(*cp != '\0') { cp++; };
        return cp - s;
}

and now I want to have:

template <typename T>
constexpr auto type_name_length = my_strlen(typeid(T).name());

But alas, typeid(T).name() is just const char*, not constexpr... is there some other, constexpr way to get a type's name?

_{Edit: Updated based on this answer to the non-constexpr-specific question; it is the result of refinements by several people including @HowardHinnant, @康桓瑋 @Val and myself.}

The C++ language standard, up to and including C++17, does not provide any facility for obtaining type names. So, we resort to compiler-specific approaches. This works with GCC, clang and MSVC.

#include <string_view>
// If you can't use C++17's standard library, you'll need to use the GSL 
// string_view or implement your own struct (which would not be very difficult,
// since we only need a few methods here)

template <typename T> constexpr std::string_view type_name();

template <>
constexpr std::string_view type_name<void>()
{ return "void"; }

namespace detail {

using type_name_prober = void;

template <typename T>
constexpr std::string_view wrapped_type_name() 
{
#ifdef __clang__
    return __PRETTY_FUNCTION__;
#elif defined(__GNUC__)
    return __PRETTY_FUNCTION__;
#elif defined(_MSC_VER)
    return __FUNCSIG__;
#else
#error "Unsupported compiler"
#endif
}

constexpr std::size_t wrapped_type_name_prefix_length() { 
    return wrapped_type_name<type_name_prober>().find(type_name<type_name_prober>()); 
}

constexpr std::size_t wrapped_type_name_suffix_length() { 
    return wrapped_type_name<type_name_prober>().length() 
        - wrapped_type_name_prefix_length() 
        - type_name<type_name_prober>().length();
}

} // namespace detail

template <typename T>
constexpr std::string_view type_name() {
    constexpr auto wrapped_name = detail::wrapped_type_name<T>();
    constexpr auto prefix_length = detail::wrapped_type_name_prefix_length();
    constexpr auto suffix_length = detail::wrapped_type_name_suffix_length();
    constexpr auto type_name_length = wrapped_name.length() - prefix_length - suffix_length;
    return wrapped_name.substr(prefix_length, type_name_length);
}