doc-src/Logics/CTT.tex
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   176 The notation for~{\CTT} (Fig.\ts\ref{ctt-syntax}) is based on that of
   176 The notation for~{\CTT} (Fig.\ts\ref{ctt-syntax}) is based on that of
   177 Nordstr\"om et al.~\cite{nordstrom90}.  The empty type is called $F$ and
   177 Nordstr\"om et al.~\cite{nordstrom90}.  The empty type is called $F$ and
   178 the one-element type is $T$; other finite types are built as $T+T+T$, etc.
   178 the one-element type is $T$; other finite types are built as $T+T+T$, etc.
   179 
   179 
   180 \index{*SUM symbol}\index{*PROD symbol}
   180 \index{*SUM symbol}\index{*PROD symbol}
   181 Quantification is expressed using general sums $\sum@{x\in A}B[x]$ and
   181 Quantification is expressed by sums $\sum@{x\in A}B[x]$ and
   182 products $\prod@{x\in A}B[x]$.  Instead of {\tt Sum($A$,$B$)} and {\tt
   182 products $\prod@{x\in A}B[x]$.  Instead of {\tt Sum($A$,$B$)} and {\tt
   183   Prod($A$,$B$)} we may write \hbox{\tt SUM $x$:$A$. $B[x]$} and \hbox{\tt
   183   Prod($A$,$B$)} we may write \hbox{\tt SUM $x$:$A$.\ $B[x]$} and \hbox{\tt
   184   PROD $x$:$A$. $B[x]$}.  For example, we may write
   184   PROD $x$:$A$.\ $B[x]$}.  For example, we may write
   185 \begin{ttbox}
   185 \begin{ttbox}
   186 SUM y:B. PROD x:A. C(x,y)   {\rm for}   Sum(B, \%y. Prod(A, \%x. C(x,y)))
   186 SUM y:B. PROD x:A. C(x,y)   {\rm for}   Sum(B, \%y. Prod(A, \%x. C(x,y)))
   187 \end{ttbox}
   187 \end{ttbox}
   188 The special cases as \hbox{\tt$A$*$B$} and \hbox{\tt$A$-->$B$} abbreviate
   188 The special cases as \hbox{\tt$A$*$B$} and \hbox{\tt$A$-->$B$} abbreviate
   189 general sums and products over a constant family.\footnote{Unlike normal
   189 general sums and products over a constant family.\footnote{Unlike normal