\begin{frame}[fragile]
  \frametitle{Relations as Query Results}

  \begin{goal}{}
    \emph{Query:}
    PID and Name of everybody who has chatted.
  \end{goal}
  \pause
  
  \begin{exampleblock}{Relational Model}
    \vspace{-1ex}
    \begin{talign}
      &\{\; \pair{x}{y} \;\mid\; \mpause[1]{ \myex{z}{\text{\textit{Person}}(x,y,z)} } \\
      &\hspace{1.3cm} \mpause{ \;\wedge\; \myex{c_1,c_2,c_3}{(\, \text{Chat}(c_1,x,c_2,c_3) \vee \text{Chat}(c_1,c_2,x,c_3)\,) }} \; \} 
    \end{talign}
  \end{exampleblock}
  \pause\pause\pause

  \begin{exampleblock}{Tuple Model}
    \vspace{-1ex}
    \begin{talign}
      &\{\; \pair{\,\text{PID}(p)}{\,\text{Name}(p)\,} \;\mid\; \text{\textit{Person}}(p) \\
      &\hspace{.9cm} \mpause[1]{ \;\wedge\; \myex{c}{(\, \text{Chat}(c) \wedge (\;\text{P1}(c) = \text{PID}(p) \vee \text{P2}(c) = \text{PID}(p)\;)\,) }} \; \} 
    \end{talign}
  \end{exampleblock}
  \pause\pause
  
  \begin{exampleblock}{SQL Query}
    {\small
    \begin{verbatim}SELECT P.PID, P.Name FROM Person as P 
WHERE EXISTS (
  SELECT * FROM Chats as C
  WHERE C.P1 = P.PID OR C.P2 = P.PID
)\end{verbatim}%
}
  \end{exampleblock}

\end{frame}