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book.tex

@@ -5202,9 +5202,23 @@ programs.
 This chapter studies lexically scoped functions as they appear in
 functional languages such as Racket. By lexical scoping we mean that a
 function's body may refer to variables whose binding site is outside
-of the function, in an enclosing scope. Consider the example in
-Figure~\ref{fig:lexical-scoping} featuring an anonymous function
-defined using the \key{lambda} form.
+of the function, in an enclosing scope.
+%
+Consider the example in Figure~\ref{fig:lexical-scoping} featuring an
+anonymous function defined using the \key{lambda} form.  The body of
+the \key{lambda}, refers to three variables: \code{x}, \code{y}, and
+\code{z}. The binding sites for \code{x} and \code{y} are outside of
+the \key{lambda}. Variable \code{y} is bound by the enclosing
+\key{let} and \code{x} is a parameter of \code{f}. The \key{lambda} is
+returned from the function \code{f}. Below the definition of \code{f},
+we have two calls to \code{f} with different arguments for \code{x},
+first \code{5} then \code{3}. The functions returned from \code{f} are
+bound to variables \code{g} and \code{h}. Even though these two
+functions were created by the same \code{lambda}, they are really
+different functions because they use different values for
+\code{x}. Finally, we apply \code{g} to \code{11} (producing
+\code{20}) and apply \code{h} to \code{15} (producing \code{22}) so
+the result of this program is \code{42}.
 
 \begin{figure}[btp]
 \begin{lstlisting}
@@ -5221,27 +5235,16 @@ defined using the \key{lambda} form.
 \label{fig:lexical-scoping}
 \end{figure}
 
-The body of the \key{lambda}, \code{(+ x (+ y z))}, refers to three
-variables. The binding sites for \code{x} and \code{y} are outside of
-the \key{lambda}: \code{y} is bound by the enclosing \key{let} and
-\code{x} is a parameter of \code{f}. The \key{lambda} is returned from
-the function \code{f}. Below the definition of \code{f}, we have two
-calls to \code{f} with different arguments for \code{x}, first
-\code{5} then \code{3}. The functions returned from \code{f} are bound
-to \code{g} and \code{h}. Even though these two functions were created
-by the same \code{lambda}, they are really different functions because
-they use different values for \code{x}. Finally, we apply \code{g} to
-\code{11} (producing \code{20}) and apply \code{h} to \code{15}
-(producing \code{22}) so the result of this program is \code{42}.
 
 \section{The $R_5$ Language}
 
-The syntax for this language with lexical scoping, $R_5$, is defined
-in Figure~\ref{fig:r5-syntax}. It adds the \key{lambda} form to the
-grammar for $R_4$, which already has syntax for function application.
-In this chapter we shall descibe how to compile $R_5$ back into $R_4$,
-compiling lexically-scoped functions into a combination of functions
-(as in $R_4$) and tuples (as in $R_3$).
+The syntax for this language with anonymous functions and lexical
+scoping, $R_5$, is defined in Figure~\ref{fig:r5-syntax}. It adds the
+\key{lambda} form to the grammar for $R_4$, which already has syntax
+for function application.  In this chapter we shall descibe how to
+compile $R_5$ back into $R_4$, compiling lexically-scoped functions
+into a combination of functions (as in $R_4$) and tuples (as in
+$R_3$).
 
 \begin{figure}[tp]
 \centering
@@ -5274,8 +5277,10 @@ compiling lexically-scoped functions into a combination of functions
 \label{fig:r5-syntax}
 \end{figure}
 
-Our compiler must provide special treatment to variable occurences
-such as \code{x} and \code{y} in the body of the \code{lambda} of
+We shall describe how to compile $R_5$ to $R_4$, replacing anonymous
+functions with top-level function definitions.  However, our compiler
+must provide special treatment to variable occurences such as \code{x}
+and \code{y} in the body of the \code{lambda} of
 Figure~\ref{fig:lexical-scoping}, for the functions of $R_4$ may not
 refer to variables defined outside the function. To identify such
 variable occurences, we review the standard notion of free variable.