How to combine these two expl3-based functions to show the day of week in English?

Question

I wrote a function \projlib_datetime_calculate_day_of_week_with_year_month_day:nnn to calculate the "day of week" given the year, month and day (the algorithm adopted should work for dates after 1800s), and also a function \projlib_datetime_display_week_english:n to convert a given number from 1 to 7 to English words. However, I don't know how to combine them to show the day of week of a given date in English. I thought \exp_args:Ne would be enough for getting the value of the first one and then passing to the second, but it doesn't.

Below is my code. Thanks in advance for any help!

\documentclass{article}

% \usepackage{projlib-datetime}

\ExplSyntaxOn

\int_new:N \l__projlib_datetime_day_of_week_day_int
\int_new:N \l__projlib_datetime_day_of_week_month_int
\int_new:N \l__projlib_datetime_day_of_week_year_int
\int_new:N \l__projlib_datetime_day_of_week_century_int
\int_new:N \l__projlib_datetime_day_of_week_result_int
\cs_new:Nn \projlib_datetime_calculate_day_of_week_with_year_month_day:nnn
  {
    \int_set:Nn \l__projlib_datetime_day_of_week_day_int { #3 }
    \int_compare:nNnTF { #2 } < { 3 }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_year_int { \int_eval:n { #1 - 1 } }
      }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_year_int { #1 }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_century_int { \int_eval:n { \l__projlib_datetime_day_of_week_year_int / 100 } }
    \int_set:Nn \l__projlib_datetime_day_of_week_year_int { \int_mod:nn { \l__projlib_datetime_day_of_week_year_int } { 100 } }
    \int_set:Nn \l__projlib_datetime_day_of_week_month_int
      {
        \int_case:nnF { #2 }
          {
            {  1 } { 0 }
            {  2 } { 3 }
            {  3 } { 2 }
            {  4 } { 5 }
            {  5 } { 0 }
            {  6 } { 3 }
            {  7 } { 5 }
            {  8 } { 1 }
            {  9 } { 4 }
            { 10 } { 6 }
            { 11 } { 2 }
            { 12 } { 4 }
          }        { 0 }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_result_int
      {
        \int_eval:n
          {
              \l__projlib_datetime_day_of_week_day_int
            + \l__projlib_datetime_day_of_week_month_int
            +\l__projlib_datetime_day_of_week_year_int
            + \int_div_truncate:nn { \l__projlib_datetime_day_of_week_year_int } { 4 }
            + \int_div_truncate:nn { \l__projlib_datetime_day_of_week_century_int } { 4 }
            - 2 * \l__projlib_datetime_day_of_week_century_int
          }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_result_int
      {
        \int_mod:nn { \l__projlib_datetime_day_of_week_result_int } { 7 }
      }
    \int_compare:nNnT { \l__projlib_datetime_day_of_week_result_int } < { 1 }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_result_int
          {
            \int_eval:n { \l__projlib_datetime_day_of_week_result_int + 7 }
          }
      }
    \int_use:N \l__projlib_datetime_day_of_week_result_int
  }



\cs_new:Nn \projlib_datetime_display_week_english:n
  {
    \int_case:nnF { #1 }
      {
        { 1 }  { Monday    }
        { 2 }  { Tuesday   }
        { 3 }  { Wednesday }
        { 4 }  { Thursday  }
        { 5 }  { Friday    }
        { 6 }  { Saturday  }
        { 7 }  { Sunday    }
      } { ??? }
  }


\ExplSyntaxOff

\begin{document}

\ExplSyntaxOn

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 16 }

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 28 }

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 03 } { 01 }

% \exp_args:Ne
% \projlib_datetime_display_week_english:n
%   {
%     \projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 01 }
%   }

\ExplSyntaxOff

\end{document}

Answer 1

As written your first function is not expandable so can not be used in an expansion context such as e argument. You could write it to be expandable by removing all the internal assignments, but simpler is remove the final \use so the result is just left in the local variable, which you can then either use or pass to your second function as required.

\documentclass{article}

% \usepackage{projlib-datetime}

\ExplSyntaxOn

\int_new:N \l__projlib_datetime_day_of_week_day_int
\int_new:N \l__projlib_datetime_day_of_week_month_int
\int_new:N \l__projlib_datetime_day_of_week_year_int
\int_new:N \l__projlib_datetime_day_of_week_century_int
\int_new:N \l__projlib_datetime_day_of_week_result_int
\cs_new:Nn \projlib_datetime_calculate_day_of_week_with_year_month_day:nnn
  {
    \int_set:Nn \l__projlib_datetime_day_of_week_day_int { #3 }
    \int_compare:nNnTF { #2 } < { 3 }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_year_int { \int_eval:n { #1 - 1 } }
      }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_year_int { #1 }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_century_int { \int_eval:n { \l__projlib_datetime_day_of_week_year_int / 100 } }
    \int_set:Nn \l__projlib_datetime_day_of_week_year_int { \int_mod:nn { \l__projlib_datetime_day_of_week_year_int } { 100 } }
    \int_set:Nn \l__projlib_datetime_day_of_week_month_int
      {
        \int_case:nnF { #2 }
          {
            {  1 } { 0 }
            {  2 } { 3 }
            {  3 } { 2 }
            {  4 } { 5 }
            {  5 } { 0 }
            {  6 } { 3 }
            {  7 } { 5 }
            {  8 } { 1 }
            {  9 } { 4 }
            { 10 } { 6 }
            { 11 } { 2 }
            { 12 } { 4 }
          }        { 0 }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_result_int
      {
        \int_eval:n
          {
              \l__projlib_datetime_day_of_week_day_int
            + \l__projlib_datetime_day_of_week_month_int
            +\l__projlib_datetime_day_of_week_year_int
            + \int_div_truncate:nn { \l__projlib_datetime_day_of_week_year_int } { 4 }
            + \int_div_truncate:nn { \l__projlib_datetime_day_of_week_century_int } { 4 }
            - 2 * \l__projlib_datetime_day_of_week_century_int
          }
      }
    \int_set:Nn \l__projlib_datetime_day_of_week_result_int
      {
        \int_mod:nn { \l__projlib_datetime_day_of_week_result_int } { 7 }
      }
    \int_compare:nNnT { \l__projlib_datetime_day_of_week_result_int } < { 1 }
      {
        \int_set:Nn \l__projlib_datetime_day_of_week_result_int
          {
            \int_eval:n { \l__projlib_datetime_day_of_week_result_int + 7 }
          }
      }
%    \int_use:N \l__projlib_datetime_day_of_week_result_int
  }



\cs_new:Nn \projlib_datetime_display_week_english:n
  {
    \int_case:nnF { #1 }
      {
        { 1 }  { Monday    }
        { 2 }  { Tuesday   }
        { 3 }  { Wednesday }
        { 4 }  { Thursday  }
        { 5 }  { Friday    }
        { 6 }  { Saturday  }
        { 7 }  { Sunday    }
      } { ??? }
  }


\ExplSyntaxOff

\begin{document}

\ExplSyntaxOn

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 16 }
\int_use:N \l__projlib_datetime_day_of_week_result_int

\par\bigskip

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 28 }
\int_use:N \l__projlib_datetime_day_of_week_result_int

\par\bigskip

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 03 } { 01 }
\int_use:N \l__projlib_datetime_day_of_week_result_int

\par\bigskip

\projlib_datetime_calculate_day_of_week_with_year_month_day:nnn { 2022 } { 02 } { 01 }
\projlib_datetime_display_week_english:n\l__projlib_datetime_day_of_week_result_int


\ExplSyntaxOff

\end{document}