Define a command (possibly recursively) to wrap text in a command n times

Question

I'm trying to define a new command \multiboxed in LaTeX so that I can put n boxes around an equation without having to manually nest \boxed commands. So far I have (using the pgffor package):

def\multiboxed#1#2{
  \foreach \index in {1, ..., #1} {
      Hello
  }
  #1
  \foreach \index in {1, ..., #1} {
    World
  }
}

which successfully wraps the second argument with Hello and World a number of times equal to the first argument. However, changing this to

def\multiboxed#1#2{
  \foreach \index in {1, ..., #1} {
      \fbox{
  }
  #1
  \foreach \index in {1, ..., #1} {
    }
  }
}

really doesn't work, as expected. As such, I have two questions which I only really need an answer to one of:

1. How do I successfully modify the for loops to achieve the desired behaviour?
2. Alternatively, how do I define a recursive command to achieve the same output?

Obviously an answer to (2) would be better as this is a better way of solving the problem, but I have a feeling I'd better understand an answer to (1). Ideally I'd also not have to rely on the pgffor package. Thanks for any light you can shed on this matter.

Answer 1

Nothing wrong with the the answers so far but they all use big heavyweight packages, this version doesn't use any package at all and needs rather less code.

\documentclass{article}

\def\Fbox#1#2{\ifnum#1=0\mbox{#2}\else\fbox{\Fbox{\numexpr#1-1\relax}{#2}}\fi}


\begin{document}

\Fbox{0}{hello}
\Fbox{1}{hello}
\Fbox{2}{hello} 
\Fbox{3}{hello} 
\Fbox{4}{hello} 
\Fbox{5}{hello} 

\end{document}

Another variant using \@first/@secondoftwo:

\makeatletter
\def\Fbox#1#2{%
  \ifnum#1=0\relax
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
  {\mbox{#2}}{\fbox{\Fbox{\numexpr#1-1\relax}{#2}}}%
}
\makeatother

Answer 2

A token register can collect the nested \fbox commands. \global is needed, because the body of \foreach is executed in a group.

\documentclass{article}
\usepackage{pgffor}

\newtoks\ToksMultiBoxed
\newcommand*{\multiboxed}[2]{%
  \global\ToksMultiBoxed{#2}%
  \ifnum#1>0 %
    \foreach \index in {1,...,#1} {%
      \global\ToksMultiBoxed\expandafter{%
        \expandafter\fbox\expandafter{\the\ToksMultiBoxed}%
      }%
    }%
  \fi
  \the\ToksMultiBoxed
}

\begin{document}

\multiboxed{4}{Hello}
\multiboxed{1}{World}
\multiboxed{0}{!}

\end{document}

\documentclass{article}
\usepackage{loops}[2012/10/16]
\makeatletter
\newcommand*{\multiboxed}[2]{%
  \skvifnumTF#1=\z@{%
    #2%
  }{%
    \@temptokena{#2}%
    \foreachfox {1,...,#1} {%
      \skvexpanded{\@temptokena{\noexpand\fbox{\the\@temptokena}}}%
    }%
    \the\@temptokena
  }%
}
\makeatother  
\begin{document}
\multiboxed{4}{Hello}
\multiboxed{1}{World}
\multiboxed{0}{!}
\end{document}

Answer 3

As David Carlisle says there is nothing wrong with the other answers. That is, as long as you are satisfied with just a plain box. But when it comes to drawing boxes, nothing beats the tikz way:

The extra spacing is achieved by using a white line for two of the boxes.

Code:

\documentclass{article}
\usepackage{tikz}
\usepackage{xstring}

\tikzset{Dotted Red/.style={draw=red, dotted, line width=1pt}}
\tikzset{Dashed Violet/.style={draw=violet, dashed}}

\newcommand{\Boxed}[3][]{
\begin{tikzpicture}[baseline, inner sep=0, outer sep=0]
    \node [thick] (Origin) {#3};
    \foreach \x in {1,...,#2} {%
        \pgfmathsetmacro{\Shift}{0.1*(\x+1)}%
        \StrBetween[\x,\numexpr\x+1\relax]{,#1,}{,}{,}[\LineStyle]
        \draw [thick, draw=black, \LineStyle] 
            ([shift={(-\Shift cm,-\Shift cm)}]Origin.south west) rectangle 
            ([shift={( \Shift cm, \Shift cm)}]Origin.north east) ;
    }%
\end{tikzpicture}
}



\begin{document}
    \Boxed{3}{Hello}
    \hspace{1cm}
    \Boxed[blue,black,green,violet,red]{5}{Hello World}

    \bigskip
    \hspace{1.0cm}\Boxed[blue,black,white,white,Dashed Violet,Dotted Red]{6}{How you doin?}
\end{document}

Answer 4

The opening and closing braces of the argument to \fbox need to be in the same scope. Here's a possible solution:

\documentclass{article}

\usepackage{pgffor}

\newtoks\boxcontenttok

\def\multiboxed#1#2{%
  \boxcontenttok{#2}%
  \foreach \index in {1, ..., #1} {%
    \edef\boxcontent{\noexpand\fbox{\the\boxcontenttok}}%
    \expandafter\global\expandafter\boxcontenttok\expandafter{\boxcontent}%
  }%
  \the\boxcontenttok
}

\begin{document}

\multiboxed{3}{Hello World}

\end{document}

Answer 5

Here's an implementation with xparse and expl3

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\multibox}{mm}
 {
  \multibox_do:nn { #1 } { #2 }
 }

\tl_new:N \l_multibox_tokens_tl
\cs_new_protected:Npn \multibox_do:nn #1 #2
 {
  \tl_set:Nn \l_multibox_tokens_tl { #2 }
  \prg_replicate:nn { #1 }
   {
    \tl_set:Nx \l_multibox_tokens_tl { \exp_not:N \fbox{ \exp_not:V \l_multibox_tokens_tl } }
   }
  \tl_use:N \l_multibox_tokens_tl
 }
\ExplSyntaxOff

\begin{document}
\multibox{5}{Hello}
\multibox{2}{world}
\end{document}

It shows an interesting feature: at each step of the replication, the previous content of \l_multibox_tokens_tl is expanded only once, even in a "complete expansion" context.

Let's see how it works. As the style guidelines recommend, the user level command \multibox is translated into a function, so the first definition is no mystery.

Next we reserve a token list variable that will be set to the text we want to box. After this assignment, we start a simple loop in which some code is repeated a number of times with \prg_replicate:nn{...}{...}. The first argument is the number of repetitions, the second is the code.

This is the important part: the token list variable is reset each time:

\tl_set:Nx \l_multibox_tokens_tl { <tokens> }

expands completely the <tokens> and stores the result in the token list variable. However, this "complete expansion" can be controlled: in this case we pass

\exp_not:N \fbox{ \exp_not:V \l_multibox_tokens_tl }

which means that \fbox will be stored as is (it's "\noexpand"); the open brace is already unexpandable like the closing brace. Now

\exp_not:V \l_multibox_tokens_tl

delivers the current value of the variable, but it will not expanded any more. So the successive values of \l_multibox_tokens_tl while executing \multibox{5}{Hello} will be

Hello
\fbox{Hello}
\fbox{\fbox{Hello}}
\fbox{\fbox{\fbox{Hello}}}
\fbox{\fbox{\fbox{\fbox{Hello}}}}
\fbox{\fbox{\fbox{\fbox{\fbox{Hello}}}}}

and this last value is finally delivered for typesetting.

Thus it's not really much different from Heiko's first solution, which uses token registers and \edef.