diff --git a/macros.tex b/macros.tex
index efee607..28d3f6c 100644
--- a/macros.tex
+++ b/macros.tex
@@ -705,4 +705,142 @@
     edge from parent {}
     }
 ;
-\end{tikzpicture}}
\ No newline at end of file
+\end{tikzpicture}}
+
+\newcommand{\smath}[1]{\ensuremath{{\scriptstyle #1}}}
+
+\newcommand{\InfiniteModel}{%
+\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 3.0cm/##1,
+    level distance = 1.0cm}]
+\node (root) [draw=none] { }
+  child { node [opnode] {$\smath{\query 0}$}
+    child { node [opnode] {$\smath{\query 0}$}
+      child { node [draw=none,rotate=165] {$\vdots$}
+        edge from parent node { }
+      }
+      child { node[leaf] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    child { node [leaf] {$\smath{\ans\False}$}
+      edge from parent node { }
+    }
+    edge from parent node { }
+  }
+;
+\end{tikzpicture}}
+%
+\newcommand{\ShortConjModel}{%
+\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 3.5cm/##1,
+    level distance = 1.0cm}]
+\node (root) [draw=none] { }
+  child { node [opnode] {$\smath{\query 0}$}
+    child { node [opnode] {$\smath{\query 0}$}
+      child { node [treenode] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      child { node[treenode] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    child { node [treenode] {$\smath{\ans\False}$}
+      edge from parent node { }
+    }
+    edge from parent node { }
+  }
+;
+\end{tikzpicture}}
+%
+
+\newcommand{\TTTwoModel}{%
+\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 8cm/##1,
+    level distance = 1.5cm}]
+\node (root) [draw=none] { }
+  child { node [opnode] {$\smath{\query 0}$}
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [leaf] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      child { node[leaf] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [leaf] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      child { node[leaf] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    edge from parent node { }
+  }
+;
+\end{tikzpicture}}
+%
+\newcommand{\XORTwoModel}{%
+\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 5.5cm/##1,
+    level distance = 1cm}]
+\node (root) [draw=none] { }
+  child { node [opnode] {$\smath{\query 0}$}
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [treenode] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      child { node[treenode] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [treenode] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      child { node[treenode] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    edge from parent node { }
+  }
+;
+\end{tikzpicture}}
+%
+\newcommand{\SXORTwoModel}{%
+\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 2.5cm/##1,
+    level distance = 1cm}]
+\node (root) [opnode] {$\smath{\query 0}$}
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [treenode] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      child { node[treenode] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+    child { node [opnode] {$\smath{\query 1}$}
+      child { node [treenode] {$\smath{\ans\True}$}
+        edge from parent node { }
+      }
+      child { node[treenode] {$\smath{\ans\False}$}
+        edge from parent node { }
+      }
+      edge from parent node { }
+    }
+;
+\end{tikzpicture}}
+%
+\newcommand{\TTZeroModel}{%
+  \begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 1cm/##1,
+    level distance = 1cm}]
+  \node (root) [draw=none] { }
+  child { node [treenode] {$\smath{\ans\True}$}
+    edge from parent node { }
+  }
+;
+\end{tikzpicture}}%
\ No newline at end of file
diff --git a/thesis.bib b/thesis.bib
index eb8692d..3f2a5a4 100644
--- a/thesis.bib
+++ b/thesis.bib
@@ -3749,4 +3749,4 @@
    editor   = {Andrew M. Pitts and Peter Dybjer},
    pages    = {131--184},
    year     = 1997
-}
+}
\ No newline at end of file
diff --git a/thesis.tex b/thesis.tex
index 150bba6..960a5dc 100644
--- a/thesis.tex
+++ b/thesis.tex
@@ -4855,11 +4855,12 @@ designed by \citet{Longley09} in 2008~\cite{LongleyW08}. Its origin is
 in game semantics, in which program evaluation is viewed as an
 interactive dialogue with the ambient environment~\cite{Hyland97} ---
 this view aligns neatly with the view of effect handler oriented
-programming. Curiously, \citeauthor{Longley09} and
-\citeauthor{PlotkinP09} developed catchcont and effect handlers,
-respectively, during the same time, in the same country, in the same
-city, in the same building. Despite all of this the two operators have
-not yet been related formally.
+programming. Curiously, we can view catchcont and effect handlers as
+``siblings'' in the sense that \citeauthor{Longley09} and
+\citeauthor{PlotkinP09} them respectively, during the same time,
+whilst working in the same department. However, the relationship is
+presently just `spiritual' as no formal connections have been drawn
+between the two operators.
 
 The catchcont operator appears as a computation form in our calculus.
 %
@@ -4913,10 +4914,105 @@ the second component of the returned pair. Importantly, the second
 $\lambda$-abstraction makes sure to bind any instances of $f$ in the
 captured evaluation context once it has been reinstated by the
 \slab{Resume} rule.
+
+Let us consider an example use of catchcont to compute a tree
+representing the interaction between a second-order function and its
+first-order parameter.
+%
+\[
+  \bl
+    \dec{odd} : (\Int \to \Bool) \to \Bool \times \UnitType\\
+    \dec{odd}~f \defas \Record{\dec{xor}\,(f~0)\,(f~1); \Unit}
+  \el
+\]
+%
+The function $\dec{odd}$ expects its environment to provide it with an
+implementation of a single operation of type $\Int \to \Bool$. The
+body of $\dec{odd}$ invokes, or queries, this operation twice with
+arguments $0$ and $1$, respectively. The results are then tested using
+exclusive-or.
+
+Now, let us implement the environment for $\dec{odd}$.
+%
+\[
+  \bl
+  \dec{Dialogue} \defas [!:\Int;?:\Record{\Bool,\dec{Dialogue},\dec{Dialogue}}] \smallskip\\
+    \dec{env} : ((\Int \to \Bool) \to \Bool \times \UnitType) \to \dec{Dialogue}\\
+    \dec{env}~m \defas
+    \bl
+      \Case\;\Catchcont~f.m~f\;\{
+         \ba[t]{@{}l@{~}c@{~}l}
+           \Inl~\Record{ans;\Unit} &\mapsto& \dec{!}ans;\\
+           \Inr~\Record{q;k}       &\mapsto& \dec{?}q\,(\dec{env}~k~\True)\,(\dec{env}~k~\False)\}
+         \ea
+    \el
+  \el
+\]
+%
+We allow ourselves to use recursive data types to make the example
+concise. Type $\dec{Dialogue}$ represents the dialogue between
+$\dec{odd}$ and its parameter. The data structure is a standard binary
+tree with two constructors: $!$ constructs a leaf holding a value of
+type $\Int$ and $?$ constructs an interior node holding a value of
+type $\Bool$ and two subtrees. The function $\dec{env}$ implements the
+environment that $\dec{odd}$ will be run in. This function evaluates
+its parameter $m$ under $\Catchcont$ which injects the operation
+$f$. If $m$ returns, then the left component gets tagged with $!$,
+otherwise the argument to the operation $q$ gets tagged with a $?$
+along with the subtrees constructed by the two recursive applications
+of $\dec{env}$.
+%
+% The primitive structure of catchcont makes it somewhat fiddly to
+% program with it compared to other control operators as we have to
+% manually unpack the data.
+
+The following derivation gives the high-level details of how
+evaluation proceeds.
 %
 \begin{derivation}
-  1 + (\Catchcont~f. 
+  &\dec{env}~\dec{odd}\\
+  \reducesto^+ & \reason{$\beta$-reduction}\\
+  &\bl
+      \Case\;\Catchcont~f.\;\Record{\dec{xor}\,(f~0)\,(f~1);\Unit}\{\cdots\}
+         % \ba[t]{@{}l@{~}c@{~}l}
+         %   \Inl~\Record{ans;\Unit} &\mapsto& \dec{!}ans;\\
+         %   \Inr~\Record{q;k}       &\mapsto& \dec{?}q\,(\dec{env}~k~\True)\,(\dec{env}~k~\False)\}
+         % \ea
+     \el\\
+  \reducesto& \reason{\slab{Capture} $\EC = \Record{\dec{xor}\,[\,]\,(f~1),\Unit}$}\\
+  &\bl
+      \Case\;\Inr\,\Record{0;\lambda x.\lambda f.\qq{\cont_{\EC}}\,x}\;\{\cdots\}
+         % \ba[t]{@{}l@{~}c@{~}l}
+         %   \Inl~\Record{ans;\Unit} &\mapsto& \dec{!}ans;\\
+         %   \Inr~\Record{q;k}       &\mapsto& \dec{?}q\,\bl (\dec{env}~\qq{\cont_{\EC}}~\True)\\(\dec{env}~\qq{\cont_{\EC}}~\False)\}\el
+         % \ea
+  \el\\
+  \reducesto^+& \reason{\slab{Resume} $\EC$ with $\True$}\\
+  &\dec{?}0\,(\Case\;\Catchcont~f.\;\Record{\dec{xor}~\True\,(f~1);\Unit}\{\cdots\})\,(\dec{env}~\qq{\cont_{\EC}}~\False)\\
+  \reducesto^+& \reason{\slab{Capture} $\EC' = \Record{\dec{xor}~\True\,[\,], \Unit}$}\\
+  &\dec{?}0\,(\dec{?}1\,(\dec{env}~\qq{\cont_{\EC'}}~\True)\,(\dec{env}~\qq{\cont_{\EC'}}~\False))\,(\dec{env}~\qq{\cont_{\EC}}~\False)\\
+  \reducesto^+& \reason{\slab{Resume} $\EC'$ with $\True$}\\
+  &\dec{?}0\,\bl(\dec{?}1\,(\Case\;\Catchcont~f.\Record{\dec{xor}~\True~\True;\Unit}\;\{\cdots\})\,(\dec{env}~\qq{\cont_{\EC'}}~\False))\\(\dec{env}~\qq{\cont_{\EC}}~\False)\el\\
+  \reducesto^+& \reason{\slab{Value}}\\
+  &\dec{?}0\,\bl(\dec{?}1\,(\Case\;\Inl~\Record{\False;\Unit}\;\{\cdots\})\,(\dec{env}~\qq{\cont_{\EC'}}~\False))\\(\dec{env}~\qq{\cont_{\EC}}~\False)\el\\
+  \reducesto& \reason{$\beta$-reduction}\\
+  &\dec{?}0\,\bl(\dec{?}1\,\dec{!}\False\,(\dec{env}~\qq{\cont_{\EC'}}~\False))\,(\dec{env}~\qq{\cont_{\EC}}~\False)\el\\
+  \reducesto^+&\reason{Same reasoning}\\
+  &?0\,(?1\,!\False\,!\True)\,(?1\,!\True\,!\False)
 \end{derivation}
+%
+Figure~\ref{fig:decision-tree-cc} visualises this result as a binary
+tree. The example here does not make use of the `continuation
+component', the interested reader may consult \citet{LongleyW08} for
+an example usage.
+%
+\begin{figure}
+\begin{center}
+    \scalebox{1.3}{\SXORTwoModel}
+  \end{center}
+  \caption{Visualisation of the result obtained by
+    $\dec{env}~\dec{odd}$.}\label{fig:decision-tree-cc}
+\end{figure}
 % \subsection{Second-class control operators}
 % Coroutines, async/await, generators/iterators, amb.
 
@@ -17080,118 +17176,6 @@ applying it to $\dec{q}_1$ or $\dec{q}_2$ yields $\True$.
 %
 \medskip
 
-\newcommand{\smath}[1]{\ensuremath{{\scriptstyle #1}}}
-
-\newcommand{\InfiniteModel}{%
-\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 3.0cm/##1,
-    level distance = 1.0cm}]
-\node (root) [draw=none] { }
-  child { node [opnode] {$\smath{\query 0}$}
-    child { node [opnode] {$\smath{\query 0}$}
-      child { node [draw=none,rotate=165] {$\vdots$}
-        edge from parent node { }
-      }
-      child { node[leaf] {$\smath{\ans\False}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    child { node [leaf] {$\smath{\ans\False}$}
-      edge from parent node { }
-    }
-    edge from parent node { }
-  }
-;
-\end{tikzpicture}}
-%
-\newcommand{\ShortConjModel}{%
-\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 3.5cm/##1,
-    level distance = 1.0cm}]
-\node (root) [draw=none] { }
-  child { node [opnode] {$\smath{\query 0}$}
-    child { node [opnode] {$\smath{\query 0}$}
-      child { node [treenode] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      child { node[treenode] {$\smath{\ans\False}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    child { node [treenode] {$\smath{\ans\False}$}
-      edge from parent node { }
-    }
-    edge from parent node { }
-  }
-;
-\end{tikzpicture}}
-%
-
-\newcommand{\TTTwoModel}{%
-\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 8cm/##1,
-    level distance = 1.5cm}]
-\node (root) [draw=none] { }
-  child { node [opnode] {$\smath{\query 0}$}
-    child { node [opnode] {$\smath{\query 1}$}
-      child { node [leaf] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      child { node[leaf] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    child { node [opnode] {$\smath{\query 1}$}
-      child { node [leaf] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      child { node[leaf] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    edge from parent node { }
-  }
-;
-\end{tikzpicture}}
-%
-\newcommand{\XORTwoModel}{%
-\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 5.5cm/##1,
-    level distance = 1cm}]
-\node (root) [draw=none] { }
-  child { node [opnode] {$\smath{\query 0}$}
-    child { node [opnode] {$\smath{\query 1}$}
-      child { node [treenode] {$\smath{\ans\False}$}
-        edge from parent node { }
-      }
-      child { node[treenode] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    child { node [opnode] {$\smath{\query 1}$}
-      child { node [treenode] {$\smath{\ans\True}$}
-        edge from parent node { }
-      }
-      child { node[treenode] {$\smath{\ans\False}$}
-        edge from parent node { }
-      }
-      edge from parent node { }
-    }
-    edge from parent node { }
-  }
-;
-\end{tikzpicture}}
-%
-\newcommand{\TTZeroModel}{%
-  \begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 1cm/##1,
-    level distance = 1cm}]
-  \node (root) [draw=none] { }
-  child { node [treenode] {$\smath{\ans\True}$}
-    edge from parent node { }
-  }
-;
-\end{tikzpicture}}%
 %
 \begin{figure}
   \centering
@@ -17279,7 +17263,7 @@ is precisely the number of $\ans \True$ leaves in the tree.
 
 Of the examples we have given, the tree for $\dec{T}_0$ is 0-standard;
 those for $\dec{I}_0$ and $\dec{I}_1$ are 1-standard; that for
-$\dec{Odd}_n$ is $n$-standard; and the rest are not $n$-standard for
+$\dec{odd}_n$ is $n$-standard; and the rest are not $n$-standard for
 any $n$.
 
 \subsection{Formal definitions}