Why doesn't this code combining \foreach with \newtheorem work?

Question

Here is an example document.

\documentclass[a4paper]{amsart}

\usepackage{tikz}

\theoremstyle{definition}
\newtheorem{baseTheorem}{Base Theorem}[section]
\foreach \x in                                         % 1
    {conjecture, definition, example}                  % 2
    {\newtheorem{\x}[baseTheorem]{\MakeUppercase{\x}}} % 3

\begin{document}

\section{Even numbers}

\begin{definition}
    A number is called \emph{even} if its remainder on division by $2$ is zero.
\end{definition}

\begin{example}
    $2$ and $0$ are both even numbers.
\end{example}

\begin{conjecture}
    The sum of two even numbers is again an even number.
\end{conjecture}

\end{document}

This document does not compile. It produces the following error:

! Undefined control sequence.
<argument> \x 

l.16    A
          number is called \emph{even} if its remainder on division by $2$ i...

However, if the lines numbered 1, 2 and 3 are replaced with the following lines...

\newtheorem{conjecture}[baseTheorem]{\MakeUppercase{conjecture}}
\newtheorem{definition}[baseTheorem]{\MakeUppercase{definition}}
\newtheorem{example}[baseTheorem]{\MakeUppercase{example}}

... then the document does compile, and looks as I expect. (What I really want is to capitalise the first letter of "Conjecture" etc., not the entire word, but this is a separate problem.)

Additionally, if \x is changed to \t in the original versions of lines 1 and 3, a different error message is obtained:

! Argument of \UseTextAccent has an extra }.
<inserted text> 
                \par 
l.16     A
           number is called \emph{even} if its remainder on division by $2$ ...

I reasoned that the issue might be that the third argument of \newtheorem was being recorded verbatim and only evaluated when it comes time to typeset an individual theorem environment. I tried the following:

\foreach \x in
    {conjecture, definition, example}
    {\def\uppercased\MakeUppercase{\x} \newtheorem{\x}[baseTheorem]{\uppercased}}

But it did not get around the problem:

! Undefined control sequence.
<argument> \uppercased 

l.16     A
           number is called \emph{even} if its remainder on division by $2$ ...

What can I do?

For the capitalization side note, \usepackage{titlecaps} and replace each instance of \MakeUppercase{} with \titlecap{}. — Steven B. Segletes, Sep 16 '13 at 15:29
For the capitalization problem see: Command to uppercase the first letter of each word in a sentence; How to define a command that bolds the first letter of each word in the input argument?; Capitalising first letter of each word in section headings using book class — Qrrbrbirlbel, Sep 16 '13 at 15:31

score 9 · Accepted Answer · edited Sep 16 '13 at 15:15

The commands in the final argument of \newtheorem are expanded as each theorem is set not at the point of definition, so each theorem tries to use the command \x in its title, long after your loop has finished. You need to change the order of evaluation, for example this works:

\documentclass[a4paper]{amsart}

\usepackage{pgffor}

\theoremstyle{definition}
\newtheorem{baseTheorem}{Base Theorem}[section]
\foreach \x in                                         % 1
    {conjecture, definition, example}                  % 2
    {\edef\tmp{\noexpand\newtheorem{\x}[baseTheorem]{\noexpand\MakeUppercase{\x}}}\tmp} % 3

\begin{document}

\section{Even numbers}

\begin{definition}
    A number is called \emph{even} if its remainder on division by $2$ is zero.
\end{definition}

\begin{example}
    $2$ and $0$ are both even numbers.
\end{example}

\begin{conjecture}
    The sum of two even numbers is again an even number.
\end{conjecture}

\end{document}

score 7 · Answer 2 · edited Apr 13 '17 at 12:35

While David Carlisle has given the technical reasons for your problem (\x is expanded to late) in his answer, you can also use the .list handler that uses \foreach internally but

doesn’t group its content (not a problem here because \newtheorem defines the environments globally anyway) and
can be used with the already expanded content as #1 (rather than as a macro sequence).

Code

\documentclass[a4paper]{amsart}

\usepackage{pgffor}
\theoremstyle{definition}
\newtheorem{baseTheorem}{Base Theorem}[section]

\pgfkeys{/utils/my Foreach/.code={\newtheorem{#1}[baseTheorem]{\MakeUppercase{#1}}},
         /utils/my Foreach/.list={conjecture, definition, example}}

\begin{document}
\section{Even numbers}

\begin{definition}
    A number is called \emph{even} if its remainder on division by $2$ is zero.
\end{definition}

\begin{example}
    $2$ and $0$ are both even numbers.
\end{example}

\begin{conjecture}
    The sum of two even numbers is again an even number.
\end{conjecture}
\end{document}

+1 Ah well you'd have to know something about pgf to give this answer:-) — David Carlisle, Sep 16 '13 at 15:24

score 6 · Answer 3 · answered Sep 16 '13 at 15:37

As David has already explained, you need to get the strings, not \x which expands to the strings. It's easy with expl3.

\documentclass[a4paper]{amsart}
\usepackage{expl3}

\ExplSyntaxOn
% provide a "user interface"
\cs_set_eq:NN \Foreach \clist_map_inline:nn
\ExplSyntaxOff

\theoremstyle{definition}
\newtheorem{baseTheorem}{Base Theorem}[section]
\Foreach{conjecture, definition, example}
  {\newtheorem{#1}[baseTheorem]{\MakeUppercase{#1}}}

\begin{document}

\section{Even numbers}

\begin{definition}
    A number is called \emph{even} if its remainder on division by $2$ is zero.
\end{definition}

\begin{example}
    $2$ and $0$ are both even numbers.
\end{example}

\begin{conjecture}
    The sum of two even numbers is again an even number.
\end{conjecture}

\end{document}

enter image description here

+1 Ah well you'd have to know something about pgf to give this answer:-) s/pgf/latex3/ — David Carlisle, Sep 16 '13 at 16:15

score 3 · Answer 4 · 2017-09-03T13:59:37.867

(edit) 2017: since xint 1.1 (2014/10/28) one needs here \usepackage{xinttools}. Code updated for that to replace \usepackage{xint} of initial answer.

The reason was explained by David, here is an alternative to using pgffor, with the (expandable) utility \xintApplyUnbraced of package xint (yes I do some shameless constant advertising of it here). Presumably some future package release will have more tools and more user-friendly syntax, such as using comma separated list of values.

The \Action macro is defined starting with a space: this is done to stop \xintApplyUnbraced which always tries to expand things; the space is gobbled, and \xintApplyUnbraced will be happy. Then, when all the three \newtheorem statements have been prepared, and only then, they are executed.

Note that \xintApplyUnbraced is completely expandable and this can help in some contexts.

For each use of \xintApplyUnbraced one needs some \Action macro, there is no reserved name for it, but a document can use again and again an \Action with each time a new definition. I use \def rather than \newcommand because \Action is more of a low-level helper thing.

\documentclass[a4paper]{amsart}

\usepackage{xinttools}

\theoremstyle{definition}
\newtheorem{baseTheorem}{Base Theorem}[section]

% space at the start could be removed, but in some other situations
% it has its use. It means: don't execute the following code until
% all elements from the initial list have been fed to \Action

\def\Action #1{ \newtheorem{#1}[baseTheorem]{\MakeUppercase{#1}}}

\xintApplyUnbraced\Action{{conjecture}{definition}{example}} 

\begin{document}

\section{Even numbers}

\begin{definition}
    A number is called \emph{even} if its remainder on division by $2$ is zero.
\end{definition}

\begin{example}
    $2$ and $0$ are both even numbers.
\end{example}

\begin{conjecture}
    The sum of two even numbers is again an even number.
\end{conjecture}

\end{document}

Output:

Why doesn't this code combining \foreach with \newtheorem work?

4 Answers4

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