Fix schema, relation and attribute representations (#51)

Changes also include preliminary editing of the relational model section. * Fix todo in relational model introduction * Fix relation and attribute styles * Fix schema definition * Change relation and attribute font * Proof read the definition of schema * Proof read the definition for a tuple * Add some labels to dictionary --------- Signed-off-by: Matteo Bongiovanni <[email protected]>
MatBon01 · Jun 15, 2023 · 69dd944 · 69dd944
1 parent 393f57a
commit 69dd944
Show file tree

Hide file tree

Showing 3 changed files with 46 additions and 24 deletions.
diff --git a/report/.hunspell b/report/.hunspell
@@ -35,6 +35,8 @@ secondmarker
 counit
 verticalcomposition
 BagRelAlgOps
+peopleSchema
+peopleTuple
 OLTP
 DebitCredit
 TPC
diff --git a/report/background/relationalmodel.tex b/report/background/relationalmodel.tex
@@ -1,50 +1,68 @@
 \section{The relational model of a database}\label{sec:relationalmodel}
-We briefly describe the relational model of a database so that we can introduce the key operators we are modelling using category theory. \todo{not modelling, think of better word}
+We briefly describe the relational model of a database so that we can introduce
+the key operators we seek to describe using category theory.
 \subsection{Introduction to the relational model}
 There are several different data models to choose from when designing a database that specify important aspects of the design such as the structure, operations and constraints on the data \cite{DatabaseSystems}. For this project we concern ourselves with the relational model and its associated algebra.
 
-The relational model represents data through two dimensional tables, called \emph{relations}. Each relation contains several \emph{attributes}, denoting the columns of the table. We call the name of the relation and the set of its attributes a \emph{schema} and they are denoted by the name of the relation followed by the set of attributes in parentheses.\cite{DatabaseSystems} For instance: 
+The relational model represents data through two dimensional tables, called
+\emph{relations}. The columns of the ``table'' are called its \emph{attributes}
+and the name of the relation with the set of its attributes is its
+\emph{schema} \cite{DatabaseSystems}. We denote the schema of a relation
+\relation{R} with attributes $\attribute{A_1}, \attribute{A_2}, \ldots,
+\attribute{A_n}$ as: 
 \begin{center}
-\begin{verbatim}
-  R(a1, a2,..., an)
-\end{verbatim}
+    \schema{\relation{R}}{\attribute{A_1}, \attribute{A_2}, \ldots,
+    \attribute{A_n}}
 \end{center}
-is a relation \relation{R} with $n$ attributes \attribute{a1}, \attribute{a2}, \ldots, \attribute{an}. A more practical example is the schema
-\begin{figure}[!h]
-\begin{verbatim}
-  People(firstName, surname, age)
-\end{verbatim}
-\caption[Schema for the \relation{People} relation]{Example of a schema for the relation \relation{People}}
-\label{fig:peopleSchema}
+
+
+A more practical example is the schema found in \fref{fig:peopleSchema}.
+It describes the schema for the relation \relation{People} with the attributes \attribute{firstName}, \attribute{surname} and \attribute{age}.
+An (empty) tabular representation for the \relation{People} relation can be found on \fref{tab:peopleRelationHeadings}.
+
+\begin{figure}[h]
+    \centering
+    \schema{\relation{People}}{\attribute{firstName},\ \attribute{surname},\
+    \attribute{age}}
+    \caption[Schema for the \relation{People} relation]{Example of a schema for the relation \relation{People}}
+    \label{fig:peopleSchema}
 \end{figure}
-This describes a schema for the relation \relation{People} and the attributes \attribute{firstName}, \attribute{surname} and \attribute{age}.
-An empty table showing the relation can be found on \fref{tab:peopleRelationHeadings}.
-\begin{table}[h]
+
+\begin{table}[t]
   \centering
   \begin{tabular}{l|l|l}
     \attribute{firstName} & \attribute{surname} & \attribute{age} \\
     \hline\hline
     & &\\
   \end{tabular}
-  \caption[\relation{People} relation's headings]{A tabular representation of the \relation{People} relation's attributes.}
+  \caption[\relation{People} relation's headings]{A tabular representation of the \relation{People} relation.}
   \label{tab:peopleRelationHeadings}
 \end{table}
 
-A row of the table\footnote{Excluding the row with the headings.} is called a \emph{tuple} and it consists of \emph{components}, one per attribute. A tuple is simply denoted by a comma separated list of its components within parentheses. For instance a tuple for the \relation{People} relation would be:
+A row of the table\footnote{Excluding any row representing the name of the
+attributes} is called a \emph{tuple} which consists of \emph{components}, one
+per attribute. A tuple is simply denoted by a comma separated list of its
+components within parentheses. For instance a tuple for the \relation{People}
+relation could be:
 \begin{figure}[!h]
   \centering
-  (\verb|Jim|, \verb|Smith|, 32).
+  (Jim, Smith, 32).
+  \caption{An example tuple in the \relation{People} relation.}
+  \label{fig:peopleTuple}
 \end{figure}
 
-With this table we can now represent the \relation{People} in a tabular form in \fref{tab:peopleRelationWithTuple}:
-\begin{table}[h]
+We can now represent the \relation{People} relation containing the tuple in
+\fref{fig:peopleTuple} as \fref{tab:peopleRelationWithTuple}.
+
+\begin{table}[b]
   \centering
   \begin{tabular}{l|l|l}
     \attribute{firstName} & \attribute{surname} & \attribute{age} \\
     \hline\hline
     Jim & Smith & 32\\
   \end{tabular}
-  \caption[\relation{People} relation with tuple]{A tabular representation of the \relation{People} relation and its associated tuple.}
+  \caption[\relation{People} relation with tuple]{A tabular representation of
+  the \relation{People} relation with a tuple.}
   \label{tab:peopleRelationWithTuple}
 \end{table}
 
@@ -116,7 +134,7 @@ \subsubsection{Selections}
   \caption[Example of selection on \relation{People} relation]{People relation with the selection \select{\attribute{age}\:>\:30}{People} applied to it.}
   \label{tab:peopleRelationSelection}
 \end{table}
-b
+
 \subsubsection{Products}\label{sec:products}
 The product of two relations \relation{R} and \relation{S} is simply the Cartesian product of the set of tuples of each relation, where instead of a binary tuple of tuples, the result is a single longer tuple. Typically, the result of $\relation{R} \times \relation{S}$ has the elements of tuples in $R$ before those in $S$. \cite{DatabaseSystems}
 

diff --git a/report/background/utils.sty b/report/background/utils.sty
@@ -43,15 +43,17 @@
 \newcommand{\finitemap}[2]{\ensuremath{\mathrm{Map}_*\ #1\;#2}}
 
 % Relational model
-\newcommand{\relation}[1]{\ensuremath{\mathrm{#1}}}
-\newcommand{\attribute}[1]{\ensuremath{\mathnormal{#1}}}
+\newcommand{\relation}[1]{\ensuremath{\mathtt{#1}}}
+\newcommand{\attribute}[1]{\ensuremath{\mathtt{#1}}}
 \newcommand{\projsymb}[1]{\ensuremath{\pi_{#1}}}
 \newcommand{\proj}[2]{\ensuremath{\projsymb{#1}\!\left(\relation{#2}\right)}}
 \newcommand{\selectsymb}[1]{\ensuremath{\sigma_{#1}}}
 \newcommand{\select}[2]{\ensuremath{\selectsymb{#1}\!\left(\relation{#2}\right)}}
 \newcommand{\natjoin}[2]{\ensuremath{\relation{#1}\bowtie\relation{#2}}}
 \newcommand{\thetajoin}[3]{\ensuremath{\relation{#2}\bowtie_{#1}\relation{#3}}}
 \newcommand{\equijoin}[4]{\ensuremath{\relation{#1}\,{}_{#2}\!\bowtie_{\:#4}\relation{#3}}}
+% note no \relation or \attribute commands
+\newcommand{\schema}[2]{\ensuremath{\mathtt{#1\left(#2\right)}}}
 
 % Temporary function to show italicised code similar to maths
 % TODO: Change