High-order recursive macro to define several similar macro at once does infinite loop

Question

I’m a fan of factorization and hate code repetition. So I was trying to define a macro which defines for me all the common mathematical sets commands (\C, \N, etc.) and made a recursive function inspiring of \slowRomannumeral p. 24 from these TeX and LaTeX programmation notes.

So I did this first:

\def\defsets#1{\defnextset #1@}
\def\defnextset#1{\ifx @#1 \else
    \expandafter\newcommand\csname #1\endcsname{\mathbb{#1}}
    \expandafter\defnextset
  \fi}
\defsets{RDNZQC}

But I soon realised that I needed something alike for my math operators, exactly the same but just with \DeclareMathOperator instead of \newcommand and without \mathbb, so I defined a \defset command and tried to make my main macro high-order:

\newcommand{\defset}[1]{\expandafter\newcommand\csname #1\endcsname{\mathbb{#1}}}
\def\defsets#1{\defnext\defset #1@}
\def\defnext#1#2{\ifx @#2 \else
    #1#2\relax
    \expandafter\defnext#1
  \fi}
\defsets{RDNZQC}

And I checked a lot of things: I put a \relax otherwise for an unkown reason it tries to redefine expandafter, the first \newcommand does work, #1#2 should work, and using \def instead of \newcommand* to define \defset I get the following error:

ERROR: Missing \endcsname inserted.

--- TeX said ---
<to be read again> 
                   \let 
l.68 \defsets{RDNZQC}

and adding an \expandafter makes the same as the actual current code with \newcommand* (and all the same combinations with it): an infinite loop.

So how to make this code work? so I can just make a \defop and do the same thing for my math operators and some code tricks with each operator command between braces (since this currently works for single characters actually).

Answer 1

You cannot skip more than one token by one \expandafter. There are more solutions of your problem. For example, you can set the used def-method by \let first:

\def\defset#1{\expandafter\def\csname#1\endcsname{\mathbb{#1}}}

\def\defsets#1{\let\defnextA=\defset \defnext #1@}
\def\defnext#1{\ifx @#1\else
    \defnextA{#1}%
    \expandafter\defnext
  \fi}

\defsets{RDNZQC}

Second: you can repeat the def-method as #1 but with one more \expandafter:

\def\defset#1{\expandafter\def\csname#1\endcsname{\mathbb{#1}}}

\def\defsets#1{\defnext\defset #1@}
\def\defnext#1#2{\ifx @#2\else
    #1{#2}%
    \expandafter\defnext\expandafter#1%
  \fi}

\defsets{RDNZQC}

Answer 2

You need to expand away the \fi

\RequirePackage{amsmath}

\makeatletter

\newcommand{\defset}[1]{\expandafter\newcommand\csname #1\endcsname{\mathbb{#1}}}
\def\defsets#1{\defnext\defset #1@}
\def\defnext#1#2{\ifx @#2%
    \expandafter\@gobble
   \else
    #1{#2}%
    \expandafter\@firstofone
   \fi    
    {\defnext#1}}
\defsets{RDNZQ{Zzz}C}


\show\Z
\show\Zzz


\newcommand*{\defop}[1]{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}}

\defnext\defop {Vect}{Spec}@

{\let\protect\show\Vect}

\stop

Produces

LaTeX2e <2016/03/31>
Babel <3.9q> and hyphenation patterns for 81 language(s) loaded.
> \Z=\long macro:
->\mathbb {Z}.
l.15 \show\Z

? 
> \Zzz=\long macro:
->\mathbb {Zzz}.
l.16 \show\Zzz

? 
> \Vect =\long macro:
->\qopname \newmcodes@ o{Vect}.
\Vect ->\protect \Vect  

l.23 {\let\protect\show\Vect
                            }
? 

Note you need to re-brace #2 as {#2} to support multiple token arguments.

Answer 3

The problem is of course in \expandafter\defnext#1 that tries to expand whatever is replaced for #1 instead of the intended \fi.

If you hate code repetition, you'll surely like this, where \defsets and \defops are basically one-liners.

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\defsets}{m}
 {
  \tl_map_inline:nn { #1 }
   {
    \cs_new_protected:cpn { ##1 } { \mathbb{##1} }
   }
 }
\NewDocumentCommand{\defops}{m}
 {
  \clist_map_inline:nn { #1 } 
   {
    \galex_declaremathoperator:cn { ##1 } { ##1 }
   }
 }
\cs_set_eq:NN \galex_declaremathoperator:Nn \DeclareMathOperator
\cs_generate_variant:Nn \galex_declaremathoperator:Nn { c }
\ExplSyntaxOff

\defsets{RDNZQC}
\defops{Vect,Spec}

\begin{document}

\texttt{\meaning\R}

\texttt{\meaning\Q}

\texttt{\meaning\Spec}

\texttt{\expandafter\meaning\csname Spec \endcsname}

\end{document}

Only one \expandafter to show that \Spec does the right thing. None in the coding part.

I could have used

\exp_args:Nc \DeclareMathOperator { ##1 } { ##1 }

instead of defining \galex_declaremathoperator:Nn and a variant thereof. But this way all is cleaner and in line with recommendations.

The same is obtained with \@tfor:

\makeatletter
%\let\@xp\expandafter % already done by amsmath
\newcommand{\defsets}[1]{%
  \@tfor\next:=#1\do{%
    \@xp\newcommand\csname\next\@xp\endcsname\@xp{\@xp\mathbb\@xp{\next}}%
  }%
}
\newcommand{\defops}[1]{%
  \@tfor\next:=#1\do{%
    \@xp\DeclareMathOperator\csname\next\@xp\endcsname\@xp{\next}%
  }%
}
\makeatother

\defsets{RDNZQC}
\defops{{Vect}{Spec}}

The \@tfor function is essentially the abstract version of the \slowRomannumeral trick in your variant: it consumes one item at a time from the token list passed between := and \do, doing \def\next{<item>} (\next can be any token). The main difference is exactly this: we need to expand \next if we don't want that it is incorporated in the definition of \N and so on. Therefore the long chain of \expandafter's is needed. An item in this context is a single token or a braced group.

The \tl_map_inline:nn method is much better, because the current item is available “literally” as #1 (so in the body of a definition it must be called ##1).

Answer 4

Seems I wake up after the battle, all dust has settled ...

\documentclass{article}
\usepackage{amsmath}
\usepackage{xinttools}


\makeatletter
\newcommand\defsets [1]
   {\xintFor* ##1 in {#1} \do {\@namedef{##1}{\mathbb{##1}}}}
\makeatother

\newcommand\defops [1]
   {\xintFor ##1 in {#1} \do {\expandafter
           \DeclareMathOperator\csname ##1\endcsname{##1}}}


\defsets{RDNZQC}
\defops{Vect, Spec}

\begin{document}

\texttt{\meaning\R}

\texttt{\meaning\Q}

\texttt{\meaning\Spec}

\texttt{\expandafter\meaning\csname Spec \endcsname}

\end{document}