Replace digits by arbitrary symbols

Question

I want to write some macro that replaces all digits in its argument by previously defined symbols or macros.

I envision something like

\overrideDigits{1234567890}

which should expand to something like

\one\two\three\four\five\six\seven\eight\nine\zero

to be able to define what the output is by overriding these macros. Or an even more advanced version where

\overrideDigits{1234567890 + \otherMacro}

should result in

    \one\two\three\four\five\six\seven\eight\nine\zero + \otherMacro

I thought the easiest solution (for the simpler version) would be to override the catcodes of the digit in the macro. However, all my tries so far ended in the error message

 Missing control sequence inserted.
<inserted text> 
                \inaccessible
l.59 \overrideDigits{1234567890}

?

I already "improved" from the trivial try to this

\def\overrideDigits#1{%
  \begingroup
  \catcode`0=\active
  \def0{\zero}
  % and so on for the other digits
  \scantokens\expandafter{#1\empty}%
  \endgroup}

which I have adapted from this answer.

• What am I doing wrong?
• Is it impossible to \def digits?
• Is there a better way to achieve this?

Answer 1

Changing category codes is the worst method, in my opinion.

Here's a simple implementation with xparse:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\overrideDigits}{m}
 {
  \tl_map_inline:nn { #1 }
   {
    \nobody_digit:n { ##1 }
   }
 }

\cs_new:Npn \nobody_digit:n #1
 {
  \str_case:nn { #1 }
   {
    {0}{Zero}
    {1}{One}
    {2}{Two}
    {3}{Three}
    {4}{Four}
    {5}{Five}
    {6}{Six}
    {7}{Seven}
    {8}{Eight}
    {9}{Nine}
   }
 }
\ExplSyntaxOff

\begin{document}

\overrideDigits{12345}

\overrideDigits{67890}

\end{document}

The input is mapped character by character and each digit is substituted with whatever you choose (recall that spaces need to be input as ~ in the body of the definition for \nobody_digit:n.

A “classical” implementation:

\documentclass{article}

\makeatletter
\newcommand{\overrideDigits}[1]{%
  \@tfor\next:=#1\do{\csname digit\next subs\endcsname}%
}
\@namedef{digit0subs}{Zero}
\@namedef{digit1subs}{One}
\@namedef{digit2subs}{Two}
\@namedef{digit3subs}{Three}
\@namedef{digit4subs}{Four}
\@namedef{digit5subs}{Five}
\@namedef{digit6subs}{Six}
\@namedef{digit7subs}{Seven}
\@namedef{digit8subs}{Eight}
\@namedef{digit9subs}{Nine}
\makeatother

\begin{document}

\overrideDigits{12345}

\overrideDigits{67890}

\end{document}

Another expl3 implementation with different renderings for the digits. You define named lists and each digit chooses the corresponding item.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\overrideDigits}{O{default}m}
 {
  \tl_map_inline:nn { #2 }
   {
    \clist_item:cn { l_nobody_digits_#1_clist } { ##1 + 1 }
   }
 }
\NewDocumentCommand{\definedigits}{mm}
 {
  \clist_clear_new:c { l_nobody_digits_#1_clist }
  \clist_set:cn { l_nobody_digits_#1_clist } { #2 }
 }
\ExplSyntaxOff

\definedigits{default}{0,1,2,3,4,5,6,7,8,9}

\definedigits{names}{
  Zero,
  One,
  Two,
  Three,
  Four,
  Five,
  Six,
  Seven,
  Eight,
  Nine
 }
\definedigits{greek}{
  \ensuremath{\alpha},
  \ensuremath{\beta},
  \ensuremath{\gamma},
  \ensuremath{\delta},
  \ensuremath{\varepsilon},
  \ensuremath{\zeta},
  \ensuremath{\eta},
  \ensuremath{\vartheta},
  \ensuremath{\iota},
  \ensuremath{\kappa}
}

\begin{document}

\overrideDigits{1234567890}

\overrideDigits[names]{0123456789}

\overrideDigits[greek]{0123456789}

\end{document}

---

Why did your attempt fail? Mainly because when you try doing \def0, 0 is not active, because it has been absorbed in the replacement text for \overrideDigits when it's not active.

A possible solution could be

\def\overrideDigits#1{%
  \begingroup
  \catcode`0=\active
  \begingroup\lccode`~=`0 \lowercase{\endgroup\let~}{\zero}%
  % and so on for the other digits
  \scantokens\expandafter{#1\empty}%
  \endgroup
}

Another possibility is

\begingroup
\catcode`0=\active \catcode`1=\active
\catcode`2=\active \catcode`3=\active
\catcode`4=\active \catcode`5=\active
\catcode`6=\active \catcode`7=\active
\catcode`8=\active \catcode`9=\active
\gdef\overrideDigits#1{%
  \catcode`0=\active \catcode`1=\active
  \catcode`2=\active \catcode`3=\active
  \catcode`4=\active \catcode`5=\active
  \catcode`6=\active \catcode`7=\active
  \catcode`8=\active \catcode`9=\active
  \let0\zero \let1\one \let2\two \let3\three \let4\four
  \let5\five \let6\six \let7\seven \let8\eight \let9\nine
  \scantokens{#1\empty}%
}
\endgroup

Answer 2

Here's a LuaLaTeX-based solution. I deliberately didn't optimize the Lua-side code, to make it easy to modify the output of each substitution operation even if you're not at all not familiar with Lua.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{luacode} % for "luacode" environment and "\luastring" macro

%% Lua-side code
\begin{luacode}
function override_digits ( s )  
    -- replace each digit with a macro
    s = string.gsub ( s, "0", "\\zero")
    s = string.gsub ( s, "1", "\\one")
    s = string.gsub ( s, "2", "\\two")
    s = string.gsub ( s, "3", "\\three")
    s = string.gsub ( s, "4", "\\four")
    s = string.gsub ( s, "5", "\\five")
    s = string.gsub ( s, "6", "\\six")
    s = string.gsub ( s, "7", "\\seven")
    s = string.gsub ( s, "8", "\\eight")
    s = string.gsub ( s, "9", "\\nine")
    tex.sprint ( s )
end
\end{luacode}

%% TeX-side code
\newcommand\overrideDigits[1]{%
    \directlua{ override_digits ( \luastring{#1} )}}

%% set up the macros \zero, \one, etc 
\def\zero{0}
\def\one{9}
\def\two{8}
\def\three{7}
\def\four{6}
\def\five{5}
\def\six{4}
\def\seven{3}
\def\eight{2}
\def\nine{1}

\def\otherMacro{9999}

\begin{document}
\overrideDigits{abc123}

\directlua{tex.sprint(\overrideDigits{4321} + \otherMacro)}
\end{document}