\section{\label{sec:notation}Notation}
We write $\forall a \in A, b \in B . p~a~b$ to mean ``for all $a$ in $A$
and $b$ in $B$, $p~a~b$ holds''.
We will be defining some relations which relate pairs and singles of
values. In order to be clear about what the relation is acting on,
we will write the single value $v$ as $\single{v}$, and the pair of
values $v$ and $w$ as $\pair{v}{w}$.
There are certain letters that we use to represent certain types of
thing. These things may not be familiar to you yet, but you can refer
back to this section as you need to later on. They are:\\
\begin{tabular}{ll}
Patches & $p$, $q$, $r$, $s$, $t$, $u$, $v$\\
Contexted patches & $w$, $x$, $y$, $z$\\
Catches & $c$, $d$, $e$, $f$, $g$\\
\end{tabular}
If we are using $a$ to represent a thing, then we will use $\seq{a}$ to
represent a sequence of things, and $A$ to represent a set of things.
We use subsections of \textit{italic text} when giving intuition about
what the formal description means.