design/tpl: Use \{emph=>dfn} for term introductions
This uses \textsl rather than \emph.master
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@ -1,7 +1,7 @@
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\section{Classification System}\seclabel{class}
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\index{classification}
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A \emph{classification} is a user-defined abstraction that describes
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A \dfn{classification} is a user-defined abstraction that describes
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(``classifies'') arbitrary data.
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Classifications can be used as predicates, generating functions, and can be
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composed into more complex classifications.
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@ -9,12 +9,12 @@ Nearly all conditions in \tame{} are specified using classifications.
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\index{first-order logic!sentence}
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\index{classification!coupling}
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All classifications represent \emph{first-order sentences}---%
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All classifications represent \dfn{first-order sentences}---%
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that is,
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they contain no \emph{free variables}.
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they contain no \dfn{free variables}.
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Intuitively,
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this means that all variables within a~classification are
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\emph{tightly coupled} to the classification itself.
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\dfn{tightly coupled} to the classification itself.
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This limitation is mitigated through use of the template system.
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\begin{axiom}[Classification Introduction]\axmlabel{class-intro}
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@ -74,7 +74,7 @@ A $\land$-classification is pronounced ``conjunctive classification'',
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and $\lor$ ``disjunctive''.\footnote{%
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Conjunctive and disjunctive classifications used to be referred to,
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respectively,
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as \emph{universal} and \emph{existential},
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as \dfn{universal} and \dfn{existential},
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referring to fact that
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$\forall\Set{a_0,\ldots,a_n}(a) \equiv a_0\land\ldots\land a_n$,
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and similarly for $\exists$.
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@ -392,7 +392,7 @@ Then,
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& \equiv \true.
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\end{align*}
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Each \xmlnode{match} of a classification is a~\emph{predicate}.
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Each \xmlnode{match} of a classification is a~\dfn{predicate}.
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Multiple predicates are by default joined by conjunction:
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\begin{lstlisting}
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@ -231,7 +231,7 @@ For example,
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\indexsym{[\,]}{function, image}
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\index{function!image (\ensuremath{[\,]})}
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\index{function!as a set}
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The set of values over which some function~$f$ ranges is its \emph{image},
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The set of values over which some function~$f$ ranges is its \dfn{image},
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which is a subset of its codomain.
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In the example above,
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both the domain and codomain are the set of integers~$\Int$,
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@ -253,9 +253,9 @@ We therefore have
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\indexsym{()}{tuple}
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\index{tuple (\ensuremath{()})}
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\index{relation|see {function}}
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An ordered pair $(x,y)$ is also called a \emph{$2$-tuple}.
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An ordered pair $(x,y)$ is also called a \dfn{$2$-tuple}.
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Generally,
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an \emph{$n$-tuple} is used to represent an $n$-ary function,
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an \dfn{$n$-tuple} is used to represent an $n$-ary function,
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where by convention we have $(x)=x$.
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So $f(x,y) = f((x,y)) = x+y$.
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If we let $t=(x,y)$,
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@ -264,7 +264,7 @@ If we let $t=(x,y)$,
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necessary and where parenthesis may add too much noise;
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this notation is especially well-suited to indexes,
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as in $f_1$.
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Binary functions are often written using \emph{infix} notation;
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Binary functions are often written using \dfn{infix} notation;
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for example, we have $x+y$ rather than $+(x,y)$.
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\begin{equation}
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@ -322,7 +322,7 @@ Given that, we have $f\bicomp{[]} = f\bicomp{[A]}$ for functions returning
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\index{abstract algebra!monoid}
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\index{monoid|see abstract algebra, monoid}
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\begin{definition}[Monoid]\dfnlabel{monoid}
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Let $S$ be some set. A \emph{monoid} is a triple $\Monoid S\bullet e$
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Let $S$ be some set. A \dfn{monoid} is a triple $\Monoid S\bullet e$
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with the axioms
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\begin{align}
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@ -438,7 +438,7 @@ A vector is a sequence of values, defined as a function of
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\index{index set (\ensuremath{\Fam{a}jJ})}
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\begin{definition}[Vector]\dfnlabel{vec}
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Let $J\subset\Int$ represent an index set.
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A \emph{vector}~$v\in\Vectors^\Real$ is a totally ordered sequence of
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A \dfn{vector}~$v\in\Vectors^\Real$ is a totally ordered sequence of
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elements represented as a function of an element of its index set:
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\begin{equation}\label{vec}
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v = \Vector{v_0,\ldots,v_j}^{\Real}_{j\in J}
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@ -454,7 +454,7 @@ We may omit the superscript such that $\Vectors^\Real=\Vectors$
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\index{vector!matrix}
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\begin{definition}[Matrix]\dfnlabel{matrix}
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Let $J\subset\Int$ represent an index set.
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A \emph{matrix}~$M\in\Matrices$ is a totally ordered sequence of
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A \dfn{matrix}~$M\in\Matrices$ is a totally ordered sequence of
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elements represented as a function of an element of its index set:
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\begin{equation}
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M = \Vector{M_0,\ldots,M_j}^{\Vectors^\Real}_{j\in J}
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