X-VM-v5-Data: ([nil nil nil nil nil nil nil t nil] [nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil nil]) Date: Tue, 20 Mar 90 18:06:33 CET Reply-To: LaTeX-L Mailing list Sender: LaTeX-L Mailing list From: bbeeton Subject: theorem considerations To: Rainer Schoepf Status: R X-Status: X-Keywords: X-UID: 55 At the AMS, we are constructing a LaTeX substyle that will provide the features of AMS-TeX to LaTeX users. The following comments have been provided by Mike Downes, who is coordinating that work. The first paragraph is from the rough draft of the AMS-LaTeX user documentation). Lack of time prevented us from doing certain things which might be candidates for future improvements: \begin{itemize} ... \item A generalized and more flexible enunciation environment in the {\tt amsart} documentstyle with three or four levels instead of the current theorem environment with one. For example, level one would include theorems, propositions, and lemmas; level two, definitions, examples, and conjectures; level three, proofs, and level four, remarks, claims, etc. Different levels would have different typographical treatment to provide appropriate emphasis---for example, following the {\tt amsart} style, level one might have boldface names with italic text, level two the same but with roman text, level three italic names and roman text, and so on. ... Proofs are sort of a strange animal because they're usually unnumbered, sometimes they are only a brief paragraph, and other times they can be a whole section, with lemmas, remarks, and other things embedded within them. And there may be a particular ``Q.E.D.'' symbol that should go at the end of each proof. So they might better be classified as a whole different species instead of as a type of enunciation; I only lump them with the rest out of reflex, because that's how our editorial department tends to view them (and I started out in editorial). At the AMS one recent innovation from the editors that gave us some headaches was to require that if a proof followed immediately after a theorem the intervening space would be less than if the proof followed something else (perhaps a remark, say): \smallskipamount instead of \medskipamount. Other than having a few different levels, the flexibility that I would like to see added to theorem-type environments is as follows: 1. Allow theorem-type environments to be unnumbered, either individual instances, or all instances of a given class (e.g., corollary, proof, or remark). 2. Allow a name to be used instead of a number: ``Disjunctivization Theorem'' instead of ``Theorem 3.2''. 3. Allow the numbering to be modified in individual cases---for example: Definition 2.1' in addition to Definition 2.1, or Theorems A and B at the beginning of a paper with all the other theorems numbered in the usual way. This could probably be done as a special case of item 2. 4. Allow the user to suppress the parentheses supplied automatically around the optional argument of \begin{theorem}. Or some other way to add something such as a \cite and not get parentheses---our editorial department would like to see \begin{theorem}[{\cite[Theorem 4]{jones}] produce this: Theorem 3.2 [8, Theorem 4] rather than this: Theorem 3.2 ([8, Theorem 4]) I have one more comment about what seems to be a slightly more general issue. When I started thinking about the enunciation question, I went through some sample (non-LaTeX) papers from our publications and found some unusual numbering schemes that I wouldn't know how to do in the current LaTeX. The most interesting scheme had theorems and other enunciations numbered along with subsections. Here is a sectioning skeleton lifted from a paper that appeared in August 1988, with irrelevant information removed. (If you classify examples, proofs, and remarks as enunciations, then there are practically no non-enunciation subsections here.) {1. Introduction} {2. The CLT with non-Gaussian limits in $l^\infty(\Scr F)$} {2.1. Definition} {2.1$'$. Definition} {2.2. Proposition} {Proof} {2.3. Corollary} {2.4. Remark} {2.5. Proposition} {2.6. Notation} {Proof of Proposition 2.5 (Sketch)} {2.7. Remark} {3. An exponential bound for sums of positive, bounded random ...} {3.1. Theorem} {Proof} {4. The central limit theorem, non-i.i.d\. case} {4.1. Examples} {4.2. Theorem} {Proof} {4.3. Proposition} {4.4. Example} {4.5. Example} {5. The CLT with stable limits} {5.1. Examples} {5.2. Theorem} {Proof} {5.3. Remarks} {5.4. Theorem} {5.5. Remark} {5.6. Example} {5.7. Proposition} {5.8. Proposition} {5.9. Example} {5.10. Proposition} {5.11. Lemma} {Proof} {Proof of {\rm (ii)} from Proposition 5.10} {6. A law of the iterated logarithm} {6.1. Theorem (Ledoux and Talagrand (1986))} {6.2. Theorem} {Proof} {7. Some additional examples: $\BL^*$ norms, weighted empiricals} {7.1. Theorem} {Proof} {7.2. Remark} {7.3. Theorem} {Proof} While this kind of scheme is rare, it is not idiosyncratic to one or two authors. In two issues pulled at random from our library three articles (out of 39 total) used such a scheme. From past experience that's pretty much what I expected. In extreme cases some authors even have the displayed equations numbered consecutively with everything else. In the example that I looked at, the author put parentheses around the numbers for theorems and subsections so that they had the same form as the equation numbers. The chief difficulty of using such a scheme in LaTeX is getting the number of a theorem to appear to the left of the word ``Theorem'' instead of to the right; currently in LaTeX the ordinary user can't get 7.3. Theorem instead of Theorem 7.3 because the form is determined by \@begintheorem. In terms of the document structure, the trouble is that we seem to be trying to make one thing serve two purposes at the same time---subsection title and theorem title. One possibility is to say this is simply poor writing, but I don't think that's true. Instead, you could consider ``7.3. Theorem'' to be a subsection heading ``7.3.'' with no text, followed immediately by a theorem, under the convention that two such entities will be run together if nothing intervenes. This is more or less the same as the idea of the run-in item in AMSTeX's \roster. Then the vertical space would be the pre-subsection space and the pre-theorem space and indention might be understood to be present behind the scenes, but elided---an extension in some sense of the idea of \addvspace. Finally, this understanding means that the input file should have something like \section{}\begin{theorem} but I'm not sure how this part ought to look. I have another hypothesis about the underlying logic of what these authors are trying to do, which is to consider the numbers to be simply pointers into the text, to be dropped into various places as needed: drop one into a section title here, drop another one into a theorem title here. In that case the vertical space preceding ``7.3. Theorem'' would be the pre-theorem space rather than the pre-subsection space. At first glance it seemed bad logic to me to allow subsection numbers to be applied to theorems in this sense, but from a strictly utilitarian point of view it is arguably better than other more common number schemes, if you just want to locate a particular item within a particular paper. More to the point, the axiom that numbers of a particular form and sequence must be reserved to a particular level of sectioning need not be taken as an axiom. Suppose you decide to consider that the information ``this is a subsection'' is conveyed by vertical spacing, font, and indention, but that the . form and sequence used for subsections is not restricted to subsections and can be used for pointing to just about any non-negligible piece of the document smaller than a section. -------