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Update intro-text for Section 7.4

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Daniel Hillerström
2020-09-23 15:26:17 +01:00
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@@ -2495,9 +2495,11 @@ We can determine whether a redex is administrative in the image by
determining whether it corresponds to a redex in the preimage. If determining whether it corresponds to a redex in the preimage. If
there is no corresponding redex, then the redex is said to be there is no corresponding redex, then the redex is said to be
administrative. We can further classify an administrative redex as to 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.
% %
The separation between value and computation terms in fine-grain The separation between value and computation terms in fine-grain
call-by-value makes it evident where static administrative redexes can call-by-value makes it evident where static administrative redexes can
@@ -2506,8 +2508,8 @@ from the translation where each computation term induces a
$\lambda$-abstraction. Each induced $\lambda$-abstraction must $\lambda$-abstraction. Each induced $\lambda$-abstraction must
necessarily be eliminated by a unary application. These unary necessarily be eliminated by a unary application. These unary
applications are administrative; they do not correspond to reductions applications are administrative; they do not correspond to reductions
in the preimage. Instead the applications that do correspond to in the preimage. The applications that do correspond to reductions in
reductions in the preimage are the binary continuation applications. the preimage are the binary (continuation) applications.
A dynamic administrative redex is a genuine implementation detail that A dynamic administrative redex is a genuine implementation detail that
supports some part of the dynamic behaviour of the preimage. An supports some part of the dynamic behaviour of the preimage. An
@@ -3173,25 +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 In this section we will continue to build upon the higher-order
uncurried CPS translation 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} \subsection{A specious attempt}
\label{sec:cps-shallow-flawed} \label{sec:cps-shallow-flawed}
% %
Initially it is tempting to try to extend the interpretation of the Initially it is tempting to try to extend the interpretation of the
continuation representation in the higher-order uncurried CPS 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 To fully uninstall a handler, we must uninstall both the pure
continuation function corresponding to its return clause and the continuation function corresponding to its return clause and the
@@ -3481,6 +3494,7 @@ presentation relatively concise.
\dhil{Remark that a `generalised continuation' is a defunctionalised continuation.} \dhil{Remark that a `generalised continuation' is a defunctionalised continuation.}
\subsection{Dynamic terms: the target calculus revisited} \subsection{Dynamic terms: the target calculus revisited}
\label{sec:target-calculus-revisited}
\begin{figure}[t] \begin{figure}[t]
\textbf{Syntax} \textbf{Syntax}