check

book.tex

@@ -13153,10 +13153,12 @@ an array:
   that none of the elements are pointers to the heap and a $1$
   indicates that all of the elements are pointers.
 
-\item The next $61$ bits store the length of the array.
+\item The next $60$ bits store the length of the array.
 
-\item The left-most bit distinguishes between a tuple ($0$) versus an
-  array ($1$).
+\item The bit at position $62$ distinguishes between a tuple ($0$)
+  versus an array ($1$).
+
+\item The left-most bit is reserved for use in Chapter~\ref{ch:Lgrad}.
 \end{itemize}
 
 
@@ -13182,8 +13184,8 @@ when the argument's type is \CARRAYTY{T}.
 
 We recommend inserting a new pass named \code{check\_bounds} that
 inserts code around each \racket{\code{vector-ref} and \code{vector-set!}}
-\python{subscript} operation to ensure that the index is greater than or equal to zero
-and less than the array's length.
+\python{subscript} operation to ensure that the index is greater than or
+equal to zero and less than the array's length.
 
 %% \subsection{Reveal Casts}
 
@@ -19845,7 +19847,7 @@ and a target type, and translates it to expression in \LangProxy{} that has
 the same behavior as casting the expression from the source to the
 target type in the interpreter.
 
-The \code{lower-cast} function can follow a code structure similar to
+The \code{lower\_cast} function can follow a code structure similar to
 the \code{apply\_cast} function (Figure~\ref{fig:apply_cast}) used in
 the interpreter for \LangCast{} because it must handle the same cases as
 \code{apply\_cast} and it needs to mimic the behavior of
@@ -19855,15 +19857,17 @@ casts between two tuple types and between two function types.
 As mentioned in Section~\ref{sec:interp-casts}, a cast from one tuple
 type to another tuple type is accomplished by creating a proxy that
 intercepts the operations on the underlying tuple. Here we make the
-creation of the proxy explicit with the \code{vector-proxy} primitive
-operation. It takes three arguments, the first is an expression for
+creation of the proxy explicit with the
+\racket{\code{vector-proxy}}\python{\code{tuple\_proxy}}
+primitive operation. It takes three arguments, the first is an expression for
 the tuple, the second is a tuple of functions for casting an element
 that is being read from the tuple, and the third is a tuple of
 functions for casting an element that is being written to the tuple.
 You can create the functions using \code{Lambda}. Also, as we shall
 see in the next section, we need to differentiate these tuples from
-the user-created ones, so we recommend using a new primitive operator
-named \code{raw-vector} instead of \code{vector} to create these
+the user-created ones, so we recommend using a new primitive function
+named \racket{\code{raw-vector}}\python{\code{raw\_tuple}} instead of
+\racket{\code{vector}}\python{\code{Tuple}} to create these
 tuples of functions. Figure~\ref{fig:map-bang-lower-cast} shows
 the output of \code{lower\_casts} on the example in
 Figure~\ref{fig:map-bang} that involved casting a tuple of