93 lines
3.3 KiB
TeX
93 lines
3.3 KiB
TeX
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\section{Meta: Typesetting}
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This appendix is a meta-document describing typographic considerations for
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this document.
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It is intended to be included in debug/developer builds,
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not to be included as official documentation for the software.
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\subsection{$\Classify$}
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\index{classification!\ensuremath{\Classify} design}
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The symbol representing classification is defined in \secref{class}.
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It uses the capital Fraktur letter~`C',
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typeset as~$\Classify\!\!$.
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Compare this side-by-side with the summation operator Sigma:
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\def\EXSUM{\sum_k^n k}
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\def\EXCLASS{\Classify^\texttt{as}_\texttt{yields} P}
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\begin{equation*}
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\EXSUM \mspace{50mu} \EXCLASS.
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\end{equation*}
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These are both written inline, respectively, as
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$\EXSUM$ and $\EXCLASS$.
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Classifications are canonically referred to by their \xmlattr{as}~name,
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which makes for a bit of an awkward-looking construction when the
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superscript is provided but not the subscript.
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For example, consider the classification $\Classify^\texttt{foo-bar}$ inline,
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compared to~$\Classify_\texttt{foo-bar}$.
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Now compare the display style
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\begin{equation*}
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\Classify^\texttt{foo-bar}
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\mspace{25mu}\text{vs.}\mspace{25mu}
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\Classify_\texttt{foo-bar}.
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\end{equation*}
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Of course,
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referring to the \xmlattr{yields}~name will use the subscript,
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which (at least to the author) feels more natural.
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Why not swap them, then?
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The superscript always denotes a scalar Boolean value.
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The subscript,
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however,
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has a more complex type that's dependent on the predicates of the classification.
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Let's say we wanted to denote a classification with a dimensionality of~$2$:
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$\Classify^\texttt{foo-bar}_{\texttt{fooBar}^2}$ versus
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$\Classify_\texttt{foo-bar}^{\texttt{fooBar}^2}$,
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typeset in display style as
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\begin{equation*}
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\Classify^\texttt{foo-bar}_{\texttt{fooBar}^2}
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\mspace{25mu}\text{vs.}\mspace{25mu}
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\Classify_\texttt{foo-bar}^{\texttt{fooBar}^2}.
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\end{equation*}
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The amount of vertical space taken up by the first style is unchanged by the
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superscript on the subscript,
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but that's not true of the second style.
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The final consideration is that the subscript of the summation,
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when the superscript is omitted,
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denotes the range or set of values for the sum.
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For example,
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one may have $\sum_{0\leq k \leq n}$ or
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$\sum_{a\in A}$.
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Having the subscript of $\Classify$ represent the more complex set of values
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is therefore more analogous to the sum,
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and better fits readers' intuitive notational expectations.
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It is also worth noting that the distinction between the two is historical---%
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\xmlattr{as} used to represent an accumulator,
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which is a long-removed feature;
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references to~\xmlattr{as} in \tame{} today end up resolving
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to~\xmlattr{yields} anyway.
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If that name is repurposed,
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one potential option is to have it take the place of~\xmlattr{yields},
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in which case the superscript in~$\Classify$ goes away and the
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notational awkwardness is removed.
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A final note on the choice of character:
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Admittedly, $\Classify$ does look a bit threatening,
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but one could also interpret it as ``bold and distinguished''.
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$\mathcal{C}$ was considered,
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but it looks too childish (and perhaps Comic Sans-like) when typeset large:
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\begin{equation*}
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\displaystyle\mathop{\hbox{\huge$\mathcal{C}$}}^\texttt{rejected}_\texttt{style}.
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\end{equation*}
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It's easy enough to change in the future if we change our minds.
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