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+\section{The Abstract Syntax Tree}
+\label{sec:ast}
+
+In functional programming languages it is trivial to create new types. A
+formally defined syntax as we have seen for While in \autoref{sec:intro:while}
+translates almost directly to a type definition:
+
+\lstinputlisting[firstline=12,lastline=24]{While/WhileCommon.dcl}
+\lstinputlisting[firstline=6,lastline=10]{While/Simple.dcl}
+
+Note that we have added common binary operators like \CI{Lt} that did not exist
+in the grammar of \autoref{sec:intro:while}. These operators could also be
+constructed from other boolean expressions. We have also added \CI{Div} for
+integer division. It is a useful addition in this example, as it will force us
+to implement error handling in the evaluation of arithmetic expressions when we
+divide by zero.
+
+As an example, the example program from \autoref{sec:intro:while} would be
+stored in the AST as follows:
+
+\begin{lstlisting}
+Compose
+	(Ass "x" (Var "y"))
+	(While
+		(Not (Comp (Var "x") Le (Lit 0)))
+		(Compose
+			(Ass "x" (Op (Var "x") Sub (Lit 2)))
+			(Ass "y" (Op (Var "y") Sub (Lit 1)))
+		)
+	)
+\end{lstlisting}