closure pic

book.tex

@@ -4661,16 +4661,18 @@ paragraphs. The register \code{rax} is for the return value of the
 function.
 
 Recall from Section~\ref{sec:x86} that the stack is also used for
-local variables, and that at the beginning of a function we move the
-stack pointer \code{rsp} down to make room for them.  To make
-additional room for passing arguments, we shall move the stack pointer
-even further down. We count how many stack arguments are needed for
-each function call that occurs inside the body of the function and
-find their maximum. Adding this number to the number of local variables
-gives us how much the \code{rsp} should be moved at the beginning of
-the function. In preparation for a function call, we offset from
-\code{rsp} to set up the stack arguments. We put the first stack
-argument in \code{0(\%rsp)}, the second in \code{8(\%rsp)}, and so on.
+local variables and for storing the values of caller-save registers
+(we shall refer to all of these collectively as ``locals''), and that
+at the beginning of a function we move the stack pointer \code{rsp}
+down to make room for them.  To make additional room for passing
+arguments, we shall move the stack pointer even further down. We count
+how many stack arguments are needed for each function call that occurs
+inside the body of the function and find their maximum. Adding this
+number to the number of locals gives us how much the \code{rsp} should
+be moved at the beginning of the function. In preparation for a
+function call, we offset from \code{rsp} to set up the stack
+arguments. We put the first stack argument in \code{0(\%rsp)}, the
+second in \code{8(\%rsp)}, and so on.
 
 Upon calling the function, the stack arguments are retrieved by the
 callee using the base pointer \code{rbp}. The address \code{16(\%rbp)}
@@ -4699,18 +4701,18 @@ caller.
 Caller View & Callee View & Contents       & Frame \\ \hline
 8(\key{\%rbp})  & & return address & \multirow{5}{*}{Caller}\\
 0(\key{\%rbp})  &  & old \key{rbp} \\
--8(\key{\%rbp}) &  & variable $1$ \\
+-8(\key{\%rbp}) &  & local $1$ \\
 \ldots & & \ldots \\
-$-8k$(\key{\%rbp}) &  & variable $k$ \\
+$-8k$(\key{\%rbp}) &  & local $k$ \\
  & &  \\
 $8n-8$\key{(\%rsp)} & $8n+8$(\key{\%rbp})& argument $n$ \\
 & \ldots           & \ldots \\
 0\key{(\%rsp)} & 16(\key{\%rbp})  & argument $1$   & \\ \hline
 & 8(\key{\%rbp})   & return address & \multirow{5}{*}{Callee}\\
 & 0(\key{\%rbp})   & old \key{rbp} \\
-& -8(\key{\%rbp})  & variable $1$ \\
+& -8(\key{\%rbp})  & local $1$ \\
 &  \ldots          & \ldots \\
-& $-8m$(\key{\%rsp})   & variable $m$\\ \hline
+& $-8m$(\key{\%rsp})   & local $m$\\ \hline
 \end{tabular}
 
 \caption{Memory layout of caller and callee frames.}
@@ -5017,9 +5019,9 @@ refer to variables defined outside the function. To identify such
 variable occurences, we review the standard notion of free variable.
 
 \begin{definition}
-A variable is \textbf{\emph{free with respect to an expression}} $e$
-if the variable occurs inside $e$ but does not have an enclosing
-binding in $e$.
+A variable is \emph{free with respect to an expression} $e$ if the
+variable occurs inside $e$ but does not have an enclosing binding in
+$e$.
 \end{definition}
 
 For example, the variables \code{x}, \code{y}, and \code{z} are all
@@ -5038,9 +5040,24 @@ point where the \code{lambda} is applied. Referring again to
 Figure~\ref{fig:lexical-scoping}, the binding of \code{x} to \code{5}
 needs to be used in the application of \code{g} to \code{11}, but the
 binding of \code{x} to \code{3} needs to be used in the application of
-\code{h} to \code{15}.
+\code{h} to \code{15}. The solution is to bundle the values of the
+free variables together with the function pointer for the lambda's
+code into a data structure called a \emph{closure}. Fortunately, we
+already have the appropriate ingredients to make closures,
+Chapter~\ref{ch:tuples} gave us tuples and Chapter~\ref{ch:functions}
+gave us function pointers. The function pointer shall reside at index
+$0$ and the values for free variables will fill in the rest of the
+tuple.
+
+
+\begin{figure}[tbp]
+\centering \includegraphics[width=0.8\textwidth]{closures}
+\caption{Example closure representation for the \key{lambda}'s
+  in Figure~\ref{fig:lexical-scoping}.}
+\label{fig:tuple-rep}
+\end{figure}
+
 
-UNDER CONSTRUCTION
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -5052,6 +5069,27 @@ UNDER CONSTRUCTION
 \label{ch:type-dynamic}
 
 
+\begin{figure}[tbp]
+\centering
+\fbox{
+\begin{minipage}{0.96\textwidth}
+\[
+\begin{array}{lcl}
+  \Type &::=& \ldots \mid \key{Any} \\
+  \Exp &::=& \ldots \mid (\key{inject}\; \Exp \; \Type) \mid (\key{project}\;\Exp\;\Type)\\
+  \Def &::=& \ldots \\
+  R_4 &::=& (\key{program} \; \Def^{*} \; \Exp)
+\end{array}
+\]
+\end{minipage}
+}
+\caption{The $R_6$ language, an extension of $R_5$
+  (Figure~\ref{fig:r5-syntax}).}
+\label{fig:r6-syntax}
+\end{figure}
+
+Figure~\ref{fig:r6-syntax}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \chapter{Parametric Polymorphism}
 \label{ch:parametric-polymorphism}