diff --git a/APCCM2017_Stanger.tex b/APCCM2017_Stanger.tex index 6d23062..1bb98eb 100644 --- a/APCCM2017_Stanger.tex +++ b/APCCM2017_Stanger.tex @@ -709,7 +709,7 @@ \subsubsection{Schema \(\SC{1}\)} \label{sec-sigs-s-i} -\noindent The SIG for \(\SC{1}\) will not just be that for relvar \(S\!\) (see Figure~\ref{fig-sig-s-alone}), as that schema did not incorporate the constraints implicit in \(\SC{0}\). The process for constructing the SIG will be similar to that for the earlier example, however. The constraints appearing in \(\SC{1}\) are \Constraint{\ref{constraint-key}}(a), \Constraint[\SC{1}]{\ref{constraint-key}}(b), \Constraint[\SC{1}]{\ref{constraint-key}}(c), \Constraint[\SC{1}]{\ref{constraint-union}}--\Constraint[\SC{1}]{\ref{constraint-tuple-types}}, and \Constraint{\ref{constraint-implied-types-london}}--\Constraint{\ref{constraint-implied-types-TSSNL}}. +\noindent The SIG for \(\SC{1}\) will not just be that for relvar \(S\!\) (see Figure~\ref{fig-sig-s-alone}), as that schema did not incorporate all the constraints implicit in \(\SC{0}\). The process for constructing the SIG will be similar to that for the earlier example, however. The constraints appearing in \(\SC{1}\) are \Constraint{\ref{constraint-key}}(a), \Constraint[\SC{1}]{\ref{constraint-key}}(b), \Constraint[\SC{1}]{\ref{constraint-key}}(c), \Constraint[\SC{1}]{\ref{constraint-union}}--\Constraint[\SC{1}]{\ref{constraint-tuple-types}}, and \Constraint{\ref{constraint-implied-types-london}}--\Constraint{\ref{constraint-implied-types-TSSNL}}. The SIG will include all of the edges that appear in Figure~\ref{fig-sig-s-alone}. \(\T{S} \SurTotal \TT{S}\) implies \(\T{\LSsub} \SurTotal \TT{\LSsub}\) and \(\T{\NLSsub} \SurTotal \TT{\NLSsub}\). Constraints \Constraint{\ref{constraint-implied-types-london}}--\Constraint{\ref{constraint-implied-types-TSSNL}} imply the existence of several subtype nodes, plus corresponding selection and projection edges: \begin{itemize} @@ -730,9 +730,15 @@ \item \(\TSSNL \ProjectionEdge \T{\Status}\) - \item \(\TSSNL \ProjectionEdge \T{\City} -\) \newline \(\CityLondon\) + \item \(\TSSNL \ProjectionEdge \T{\City} \setminus \CityLondon\) \end{itemize} + +% \begin{tabular}{ll} +% \textbf{Constraint} & \textbf{Implied edge(s)} \\ +% {\Constraint{\ref{constraint-implied-types-london}}} & \(\TSSL \ProjectionEdge\,\CityLondon\) \\ +% \end{tabular} + \Constraint[\SC{1}]{\ref{constraint-key}}(b) and \Constraint[\SC{1}]{\ref{constraint-key}}(c) imply two additional key edges: \begin{itemize} @@ -757,7 +763,7 @@ \item \(\TSSC \SelectionEdge\) \(\TSSL\) - \item \(\TSSC \SelectionEdge \T{\Sname} \times \T{\Status} \times \T{\City} -\) \newline \(\CityLondon\) + \item \(\TSSC \SelectionEdge \T{\Sname} \times \T{\Status} \times \T{\City} \setminus \CityLondon\) \end{itemize} The complete SIG for \(\SC{1}\) is shown in Figure~\ref{fig-sig-s}.