namespace boost {
  namespace stacktrace {
    class stacktrace;

    // Additional comparison operators for stacktraces that have amortized O(1) complexity. 
    bool operator>(const stacktrace & lhs, const stacktrace & rhs);
    bool operator<=(const stacktrace & lhs, const stacktrace & rhs);
    bool operator>=(const stacktrace & lhs, const stacktrace & rhs);
    bool operator!=(const stacktrace & lhs, const stacktrace & rhs);

    // Hashing support. 
    std::size_t hash_value(const stacktrace & st);

    // Outputs stacktrace::frame in a human readable format to output stream. 
    template<typename CharT, typename TraitsT> 
      std::basic_ostream< CharT, TraitsT > & 
      operator<<(std::basic_ostream< CharT, TraitsT > & os, 
                 const stacktrace::frame & f);

    // Outputs stacktrace in a human readable format to output stream. 
    template<typename CharT, typename TraitsT> 
      std::basic_ostream< CharT, TraitsT > & 
      operator<<(std::basic_ostream< CharT, TraitsT > & os, 
                 const stacktrace & bt);
  }
}