Update intro-text for Section 7.4

thesis.tex

@@ -2495,14 +2495,26 @@ We can determine whether a redex is administrative in the image by
 determining whether it corresponds to a redex in the preimage. If
 there is no corresponding redex, then the redex is said to be
 administrative. We can further classify an administrative redex as to
-whether it is \emph{static} or \emph{dynamic}. A static administrative
+whether it is \emph{static} or \emph{dynamic}.
-redex is a by-product of the translation that does not contribute to
+
-the implementation of the dynamic behaviour of the preimage.
+A static administrative redex is a by-product of the translation that
+does not contribute to the implementation of the dynamic behaviour of
+the preimage.
 %
-In contrast, a dynamic administrative redex is a genuine
+The separation between value and computation terms in fine-grain
-implementation detail that supports some part of the dynamic behaviour
+call-by-value makes it evident where static administrative redexes can
-of the preimage. An example of such a detail is the implementation of
+arise. They arise from computation terms, which can clearly be seen
-effect forwarding. In $\HCalc$ effect forwarding involves no auxiliary
+from the translation where each computation term induces a
+$\lambda$-abstraction. Each induced $\lambda$-abstraction must
+necessarily be eliminated by a unary application. These unary
+applications are administrative; they do not correspond to reductions
+in the preimage. The applications that do correspond to reductions in
+the preimage are the binary (continuation) applications.
+
+A dynamic administrative redex is a genuine implementation detail that
+supports some part of the dynamic behaviour of the preimage. An
+example of such a detail is the implementation of effect
+forwarding. In $\HCalc$ effect forwarding involves no auxiliary
 reductions, any operation invocation is instantaneously dispatched to
 a suitable handler (if such one exists).
 %
@@ -2517,11 +2529,6 @@ Section~\ref{sec:first-order-explicit-resump} administrative
 reductions due to resumption invocation can be dealt with by choosing
 a more clever implementation of resumptions.
 
-% We can characterise static administrative redexes\dots
-% \dhil{Characterise static redexes\dots}
-
-% \dhil{Discuss dynamic and static administrative redex.}
-
 \subsection{Resumptions as explicit reversed stacks}
 \label{sec:first-order-explicit-resump}
 %
@@ -3168,25 +3175,36 @@ If $M \reducesto N$ then $\pcps{M} \reducesto^+ \areducesto^* \pcps{N}$.
 
 In this section we will continue to build upon the higher-order
 uncurried CPS translation
-(Section~\ref{sec:higher-order-uncurried-deep-handlers-cps}). Specifically,
+(Section~\ref{sec:higher-order-uncurried-deep-handlers-cps}) in order
-we will adapt it to be able to translate shallow effect handlers. The
+to add support for shallow handlers. The dynamic nature of shallow
-dynamic nature of shallow handlers pose an interesting challenge as
+handlers pose an interesting challenge, because unlike deep resumption
-shallow resumption invocation discards its handler. Consequently
+capture, a shallow resumption capture discards the handler leaving
-evaluation after resumption may occur under a potentially different
+behind a dangling pure continuation. The dangling pure continuation
-handler which is determined dynamically by the context. This means
+must be `adopted' by whichever handler the resumption invocation occur
-that the CPS translation must be able to update the current
+under. This handler is determined dynamically by the context, meaning
-continuation pair.
+the CPS translation must be able to modify continuation pairs.
-\dhil{Fix the text}
+
+In Section~\ref{sec:cps-shallow-flawed} I will discuss an attempt at a
+`natural' extension of the higher-order uncurried CPS translation for
+deep handlers, but for various reasons this extension is
+flawed. However, the insights gained by attempting this extension
+leads to yet another change of the continuation representation
+(Section~\ref{sec:generalised-continuations}) resulting in the notion
+of a \emph{generalised continuation}.
+%
+In Section~\ref{sec:cps-gen-conts} we will see how generalised
+continuations provide a basis for implementing deep and shallow effect
+handlers simultaneously, solving all of the problems encountered thus
+far uniformly.
 
 \subsection{A specious attempt}
 \label{sec:cps-shallow-flawed}
 %
 Initially it is tempting to try to extend the interpretation of the
 continuation representation in the higher-order uncurried CPS
-translation for deep handlers to squeeze in shallow handlers. The
+translation for deep handlers to squeeze in shallow handlers. The main
-first obstacle one encounters is how to decouple a pure continuation
+obstacle one encounters is how to decouple a pure continuation from
-from its handler such that it can later be `adopted' by another
+its handler such that a it can later be picked up by another handler.
-handler.
 
 To fully uninstall a handler, we must uninstall both the pure
 continuation function corresponding to its return clause and the
@@ -3476,6 +3494,7 @@ presentation relatively concise.
 \dhil{Remark that a `generalised continuation' is a defunctionalised continuation.}
 
 \subsection{Dynamic terms: the target calculus revisited}
+\label{sec:target-calculus-revisited}
 
 \begin{figure}[t]
 \textbf{Syntax}