design/tpl (Matches): Add light clarifying text
This is just some plain English to go along with and help rationalize the text. Further rationale will be provided in a dedicated section in the future; such information is vitally important to understand why the system evolved as it did.master
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@ 391,7 +391,20 @@ For example,


This is conceptually like a symbol table lookup in the compiler.}








\subsection{Matches}


A classification consists of a set of binary predicates called


\emph{matches}.


Matches may reference any values,


including the results of other classifications


(as in \thmpref{classcompose}),


allowing for the construction of complex abstractions over the data being


classified.




Matches are intended to act intuitively across inputs of different ranks%


that is,


one can match on any combination of matrix, vector, and scalar values.




\begin{axiom}[Match Input Translation]\axmlabel{matchinput}


Let $j$ and $k$ be free variables intended to be bound in the


context of \axmref{classpred}.



@ 441,6 +454,14 @@ For example,


\end{align*}


\end{axiom}






\index{package!core/match@\tamepkg{core/match}}


Matches are represented by \xmlnode{match} nodes in \tame{}.


Since the primitive is rather verbose,


\tamepkg{core/match} also defines templates providing a more concise


notation


(\xmlnode{t:match$\zeta$} below).




\index{classification!match@\xmlnode{match}}


\begin{axiom}[Match Introduction]\axmlabel{matchintro}


\begin{alignat*}{2}



@ 593,6 +614,7 @@ We therefore establish a relationship to the notation of linear algebra




% This must be an axiom because it defines how the connectives operate; see


% the remark.


\index{classification!matrix notation}


\begin{axiom}[Classification Matrix Notation]\axmlabel{classmatnot}


Let $\Gamma^2$ be defined by \axmref{classyield}.


Then,



@ 614,9 +636,21 @@ We therefore establish a relationship to the notation of linear algebra


combined.


\end{remark}




\index{classification!intuition}


\axmref{classmatnot} makes it easy to visualize classification


operations simply by drawing horizontal boxes across the predicates,


as demonstrated by \spref{f:classmatboxes}.


This visualization helps to show intuitively how the classification system


is intended to function,


with matrices serving as higherresolution vectors.\footnote{%


For example,


with insurance,


one may have a vector of data by risk location,


and a matrix of chosen class codes by location.


Consequently,


we expect $M_j$ to be the set of class codes associated with


location~$j$ so that it can be easily matched against locationlevel


data~$v_j$.}




% NB: Give this formatting extra attention if the document's formatting is


% substantially changed, since it's not exactly responsible with it's




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