Theorem support

[josephwright]

In beamer, the amsthm package is loaded and various theorem-related stuff is done:

1. Theorem counters are reset in overlays so they make sense
2. Theorems are made overlay-aware
3. Proofs are made overlay-aware
4. Theorems and proofs are set up as block elements with templates
5. Various theorem names are pre-defined

Some of this we definitely want (points 1,2 and likely 3). However, the rest is a bit more tricky. First, do we even want to force loading of amsthm? I could arrange to do the other bits without that. If we do, then adjusting proofs is easy: but what if we don't? Making theorems into blocks links to wider block questions so needs kernel work. Finally, the list of theorem types in beamer feels quite arbitary - so I'm not sure it's ideal.

I'm trying a few things, but would welcome ideas here - I never need this stuff myself!

---

For testing, I took the tutorial example and got it sort-of working

\DocumentMetadata{tagging = on}
\documentclass{xbeamer}
\newtheorem{theorem}{Theorem}
\begin{document}

\begin{frame}
  \frametitle{There Is No Largest Prime Number}
  \framesubtitle{The proof uses \textit{reductio ad absurdum}.}

  \begin{theorem}
    There is no largest prime number.
  \end{theorem}
  \begin{proof}
    \begin{enumerate}
    \item<1-> Suppose $p$ were the largest prime number.
    \item<2-> Let $q$ be the product of the first $p$ numbers.
    \item<3-> Then $q + 1$ is not divisible by any of them.
    \item<1-> But $q + 1$ is greater than $1$, thus divisible by some prime
      number not in the first $p$ numbers.\qedhere
    \end{enumerate}
  \end{proof}
  \uncover<4->{The proof used \textit{reductio ad absurdum}.}
\end{frame}

\end{document}

The fact that proof are not block elements in particular shows up!

---

To save people looking it up, the list of theorem types from the beamer source:

\mode
<all>
{
  \ifbeamer@blocks
    \ifbeamer@countsect
      \newtheorem{theorem}{\translate{Theorem}}[section]
    \else
      \newtheorem{theorem}{\translate{Theorem}}
    \fi
    \newtheorem{corollary}[theorem]{\translate{Corollary}}
    \newtheorem{fact}[theorem]{\translate{Fact}}
    \newtheorem{lemma}[theorem]{\translate{Lemma}}
    \newtheorem{problem}[theorem]{\translate{Problem}}
    \newtheorem{solution}[theorem]{\translate{Solution}}

    \theoremstyle{definition}
    \newtheorem{definition}[theorem]{\translate{Definition}}
    \newtheorem{definitions}[theorem]{\translate{Definitions}}

    \theoremstyle{example}
    \newtheorem{example}[theorem]{\translate{Example}}
    \newtheorem{examples}[theorem]{\translate{Examples}}


    % Compatibility
    \newtheorem{Beispiel}[theorem]{Beispiel}
    \newtheorem{Beispiele}[theorem]{Beispiele}
    \theoremstyle{plain}
    \newtheorem{Loesung}[theorem]{L\"osung}
    \newtheorem{Satz}[theorem]{Satz}
    \newtheorem{Folgerung}[theorem]{Folgerung}
    \newtheorem{Fakt}[theorem]{Fakt}
    \newenvironment{Beweis}{\begin{proof}[Beweis.]}{\end{proof}}
    \newenvironment{Lemma}{\begin{lemma}}{\end{lemma}}
    \newenvironment{Proof}{\begin{proof}}{\end{proof}}
    \newenvironment{Theorem}{\begin{theorem}}{\end{theorem}}
    \newenvironment{Problem}{\begin{problem}}{\end{problem}}
    \newenvironment{Corollary}{\begin{corollary}}{\end{corollary}}
    \newenvironment{Example}{\begin{example}}{\end{example}}
    \newenvironment{Examples}{\begin{examples}}{\end{examples}}
    \newenvironment{Definition}{\begin{definition}}{\end{definition}}
  \fi
}

[davidcarlisle]

on point (1) shouldn't all (latex) counters reset on overlays?

Whatever beamer does, If I have \newcounter{wibble} I wouldn't expect it to increment every overlay.

Oh I just tried it...

\documentclass{beamer}

\newcounter{wibble}
\begin{document}
\begin{frame}{testing...}

one \stepcounter{wibble}\arabic{wibble}

\only<2>{two \stepcounter{wibble}\arabic{wibble}}

\only<1>{three \stepcounter{wibble}\arabic{wibble}}

\end{frame}
\end{document}

This output seems wrong to me:

[josephwright]

The beamer code adds the obvious pre-defined counters to the reset list but others are left to the user to add using resetcounteronoverlays. My guess is the opt-in is as you can't be sure exactly what the semantics of an arbitrary counter are, and there's no 'remove from reset' command. We can of course be a bit more aggressive, say using \newcounter: that still misses direct definition of \c@... but those are likely more specialised cases anyway.

[josephwright]

I've adjusted to cover all counters - we'll see how that goes!

[samcarter]

Just thinking out loud:

• keep some more generally applicable environment names, but make them normal blocks instead of theorems (example, definition,...)
• have some means for users to define new block environments
• (very sketchy...) don't define theorems by default, but provide some means to "blockify" other environments, this way users could create their create their theorems etc. with their favourite theorem package and warp them in blocks (not sure how texnically feasible this would be regarding titles...)

Finally, the list of theorem types in beamer feels quite arbitary - so I'm not sure it's ideal.

You don't use the German environment names, like Loesung, every day? :P

[josephwright]

* keep some more generally applicable environment names, but make them normal blocks instead of theorems (example, definition,...)

Yes, that had crossed my mind too: I think Till used theorem as it provides a handy number and/or similar styling between block envs.

* have some means for users to define new block environments

Plan broadly here is that we want to get the kernel block template extended enough that it's a case of a wrapper around a template instance - in other words, we don't do much at all, rather we say 'the kernel provides this stuff - you can use it following this model'.

* (very sketchy...) don't define theorems by default, but provide some means to "blockify" other environments, this way users could create their create their theorems etc. with their favourite theorem package and warp them in blocks (not sure how texnically feasible this would be regarding titles...)

More tricky - and again I think we likely want to see extended kernel support with blocks there from the start.

Finally, the list of theorem types in beamer feels quite arbitary - so I'm not sure it's ideal.

You don't use the German environment names, like Loesung, every day? :P

:)

[cfr42]

I really don't like the use of translator. One problem with translator is that it seems to support far fewer languages than babel. So whereas I add stuff I need for other documents in babel and biblatex configs, for anything relying on translator, I just set stuff explicitly, if I have to, which is a bit icky.

And, yes, almost every teaching doc I compile issues a string of complaints about the languages I use not being supported by various packages. Even more annoyingly, translator urges me to download the relevant packages from CTAN, even though they don't exist.

[While I admit my use of Welsh is uncommon, it can't be that unusual to need Greek, can it?]

[josephwright]

The example only includes use of translator as I copy-pasted the code from beamer - if we need string translations, it will be translations or babel (I suspect the latter covers theorems out-of-the-box).

[josephwright]

In another channel, @davidcarlisle points out

amsthm [is] part of the ams house styling [...] It's not really related to math as such, it's far more related to class level heading and text styling.

which makes me wonder about loading it at all - perhaps better to stick to the kernel version and create proof, etc., as block envs.

[josephwright]

Indeed, re-reading the beamer manual in this area, I'm pretty convinced that on reflection we don't want amsthm and likely few-to-no theorem envs. Dealing with proof is still more tricky (though that might just need \qedhere sorting)

[cfr42]

Beamer makes some very specific choices which don't obviously have anything to do with presentations per se. Not just here, but why are quotations italicised, for example? I think it would be better if Beamer did much less non-presentation stuff.

[u-fischer]

@josephwright

Indeed, re-reading the beamer manual in this area, I'm pretty convinced that on reflection we don't want amsthm

No I think not. There is a firstaid that makes it more or less tagging aware, but it is not perfect (there is an open issue) and imho currently it only complicates things if you load it on top of the block code . It is imho better to try to implement everything with the templates in the block code. If needed the code there should be improve and extended, e.g. to support more theorem styles.

to save people looking it up, the list of theorem types from the beamer source:

;-). You can certainly drop all this german compability environments ;-)