How ifthen \equal could compare \relax to another \relax-like command?

Question

I was implementing an ad hoc list data structure inside LaTeX, where \aaa expands value for aaa, \bbb exapnds value for bbb and to show that \bbb is next to \aaa on the list, \NEXTaaa expand to bbb, and I do not define \NEXTbbb. These definitions are done with \@namedef.

Using ifthen macros to work the code, I found a (supposedly) bug. I cannot compare \relax to macros \relax-like, like the one got after expansion of \csname UndefinedCmd\endcsname.

The question is: after \let\abc\relax, how to get a successfully compare \abc with \relax using ifthen macros? I am actually getting \equal{\abc}{\relax} -> false!!! Is this a bug on ifthen?

MWE:

\documentclass{article}
\usepackage{ifthen}
\begin{document}
\let\abc\relax
\ifthenelse{\equal{\abc}{\relax}}
  {Good!}
  {Bad :-(}
%% I read Bad :-( on PDF file.
\end{document}

\equal doesn't actually compare the meaning of \abc and \relax. It does \def\a{\abc}, \def\b{\relax}, then compares \a and \b, which contain different things, so are different. — Phelype Oleinik, Mar 25 '22 at 18:49
A work-around I used: define a boolean and before use \ifthenelse or \whiledo, I set the boolean with \ifx and use the boolean... but I loose ifthen practicality. — Miguel V. S. Frasson, Mar 25 '22 at 18:55
The hands-down best solution to do that with ifthen is to not use ifthen :) — Phelype Oleinik, Mar 25 '22 at 18:57
It would be very handy extend ifthen creating a \equalx{\csA}{\csB} that tests expansion of command sequences \csA and \csB, thai is, a version of \ifx comparison. — Miguel V. S. Frasson, Mar 25 '22 at 19:03

score 5 · Answer 1 · answered Mar 25 '22 at 19:48

Not a drop-in replacement of \ifthenelse, but more powerful.

\documentclass{article}
\ExplSyntaxOn
\NewExpandableDocumentCommand{\xifthenelse}{mmm}
 {
  \bool_if:nTF { #1 } { #2 } { #3 }
 }
\cs_new_eq:NN \numtest     \int_compare_p:n
\cs_new_eq:NN \oddtest     \int_if_odd_p:n
\cs_new_eq:NN \fptest      \fp_compare_p:n
\cs_new_eq:NN \dimtest     \dim_compare_p:n
\cs_new_eq:NN \deftest     \cs_if_exist_p:N
\cs_new_eq:NN \namedeftest \cs_if_exist_p:c
\cs_new_eq:NN \eqdeftest   \token_if_eq_meaning_p:NN
\cs_new_eq:NN \streqtest   \str_if_eq_p:ee
\cs_new_eq:NN \emptytest   \tl_if_empty_p:n
\cs_new_eq:NN \blanktest   \tl_if_blank_p:n
\cs_new_eq:NN \boolean     \legacy_if_p:n
\cs_new:Npn \modetest #1
 {
  \str_case:nnF { #1 }
   {
    {h}{\mode_if_horizontal_p:}
    {v}{\mode_if_vertical_p:}
    {m}{\mode_if_math_p:}
    {i}{\mode_if_inner_p:}
   }
   {\c_false_bool}
 }
\cs_new:Npn \enginetest #1
 {
  \str_case:nnF { #1 }
   {
    {luatex}{\sys_if_engine_luatex_p:}
    {pdftex}{\sys_if_engine_pdftex_p:}
    {ptex}{\sys_if_engine_ptex_p:}
    {uptex}{\sys_if_engine_uptex_p:}
    {xetex}{\sys_if_engine_xetex_p:}
   }
   {\c_false_bool}
 }
\ExplSyntaxOff
\begin{document}
\let\abc\relax
\xifthenelse{\eqdeftest{\abc}{\relax}}{true}{false}
\xifthenelse{\eqdeftest{\abc}{\relax} && \numtest{0>1}}{true}{false}
\xifthenelse{\eqdeftest{\abc}{\relax} || \numtest{0>1}}{true}{false}
\xifthenelse{\enginetest{pdftex} || \enginetest{luatex}}{true}{false}
\end{document}

You can use parentheses, && for “and”, || for “or”, ! for negation.

score 4 · Accepted Answer · answered Mar 25 '22 at 19:03

You should probably not use ifthen. Maybe etoolbox's \ifboolexpr or something more robust. But if you must, here are two options.

Redefine ifthen's \isundefined to consider \relax as undefined:

\documentclass{article}
\usepackage{ifthen}
\makeatletter
\def\TE@undef#1#2{%
  \TE@throw
  \noexpand\ifnum1=%
    \noexpand\ifx\noexpand@undefined\noexpand#11\noexpand\fi
    \noexpand\ifx\relax\noexpand#11\noexpand\fi\space#2}
\makeatother
\begin{document}
\let\abc\relax
\ifthenelse{\isundefined{\abc}}
  {Good!}
  {Bad :-(}
\end{document}

Add a \isdefequal to do an \ifx comparison (the arguments must be two single tokens):

\documentclass{article}
\usepackage{etoolbox}
\usepackage{ifthen}
\makeatletter
\patchcmd\ifthenelse
  {\let\isundefined\TE@undef}
  {\let\isundefined\TE@undef
   \let\isdefequal\TE@isdefequal}
  {}{\FAILED}
\long\def\TE@isdefequal#1#2#3{\TE@throw
  \noexpand\ifx\noexpand#1\noexpand#2#3}
\makeatother
\begin{document}
\let\abc\relax
\ifthenelse{\isdefequal{\abc}{\relax}}
  {Good!}
  {Bad :-(}
\end{document}

Thanks! Second solution is perfect to my application. – Miguel V. S. Frasson Mar 25 '22 at 19:05 — Miguel V. S. Frasson, Mar 25 '22 at 19:05
@MiguelV.S.Frasson Proceed with caution ;-) – Phelype Oleinik Mar 25 '22 at 19:06 — Phelype Oleinik, Mar 25 '22 at 19:06

How ifthen \equal could compare \relax to another \relax-like command?

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