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Another example

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Daniel Hillerström
2021-05-28 19:03:55 +01:00
parent 3cb5e3622f
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thesis.tex
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@@ -4189,6 +4189,8 @@ $\abort$ and $\calldc$ is only well-defined within the dynamic extent
of $\splitter$. Since the prompt is eliminated after use of either of $\splitter$. Since the prompt is eliminated after use of either
operation subsequent operation invocations must be guarded by a new operation subsequent operation invocations must be guarded by a new
instance of $\splitter$. instance of $\splitter$.
Let us consider an example using both $\calldc$ and $\abort$.
% %
\begin{derivation} \begin{derivation}
&2 + \splitter\,(\lambda p.2 + \splitter\,(\lambda p'.3 + \calldc\,\Record{p;\lambda k. k~0 + \abort\,\Record{p';\lambda\Unit.k~1}})),\emptyset\\ &2 + \splitter\,(\lambda p.2 + \splitter\,(\lambda p'.3 + \calldc\,\Record{p;\lambda k. k~0 + \abort\,\Record{p';\lambda\Unit.k~1}})),\emptyset\\
@@ -4210,11 +4212,12 @@ instance of $\splitter$.
% %
The important thing to observe here is that the application of The important thing to observe here is that the application of
$\calldc$ skips over the inner prompt and reifies it as part of the $\calldc$ skips over the inner prompt and reifies it as part of the
continuation. The first application of $k$ restores the context with continuation. This behaviour stands differ from the original
the prompt. The $\abort$ application erases the evaluation context up formulations of control/prompt, shift/reset. The first application of
to this prompt, however, the body of the functional argument to $k$ restores the context with the prompt. The $\abort$ application
$\abort$ reinvokes the continuation $k$ which restores the prompt erases the evaluation context up to this prompt, however, the body of
context once again. the functional argument to $\abort$ reinvokes the continuation $k$
which restores the prompt context once again.
% \begin{derivation} % \begin{derivation}
% &1 + \splitter\,(\lambda p.2 + \splitter\,(\lambda p'.3 + \calldc\,\Record{p';\lambda k. k\,0 + \calldc\,\Record{p';\lambda k'. k\,(k'\,1)}}))), \emptyset\\ % &1 + \splitter\,(\lambda p.2 + \splitter\,(\lambda p'.3 + \calldc\,\Record{p';\lambda k. k\,0 + \calldc\,\Record{p';\lambda k'. k\,(k'\,1)}}))), \emptyset\\
% \reducesto& \reason{\slab{AppSplitter}}\\ % \reducesto& \reason{\slab{AppSplitter}}\\
@@ -4295,8 +4298,29 @@ rules. The interesting rule is the $\slab{Capture}$. When $\fcontrol$
is applied to some value $W$ the enclosing context $\EC$ gets reified is applied to some value $W$ the enclosing context $\EC$ gets reified
and aborted up to the nearest enclosing prompt, which invokes the and aborted up to the nearest enclosing prompt, which invokes the
handler $V$ with the argument $W$ and the continuation. handler $V$ with the argument $W$ and the continuation.
Consider the following, slightly involved, example.
% %
\dhil{Show an example\dots} \begin{derivation}
&2 + \fprompt\,(\lambda y~k'.1 + k'~y).\fprompt\,(\lambda x~k. x + k\,(\fcontrol~k)).3 + \fcontrol~1\\
\reducesto& \reason{\slab{Capture} $\EC = 3 + [\,]$}\\
&2 + \fprompt\,(\lambda y~k'.1 + k'~y).(\lambda x~k. x + k\,(\fcontrol~k))\,1\,\qq{\cont_{\EC}}\\
\reducesto^+& \reason{\slab{Capture} $\EC' = 1 + \qq{\cont_{\EC}}\,[\,]$}\\
&2 + (\lambda k~k'.k'\,(k~1))\,\qq{\cont_{\EC}}\,\qq{\cont_{\EC'}}\\
\reducesto^+& \reason{\slab{Resume} $\EC$ with $1$}\\
&2 + \qq{\cont{\EC'}}\,(3 + 1)\\
\reducesto^+& \reason{\slab{Resume} $\EC'$ with $4$}\\
&2 + 1 + \qq{\cont_{\EC}}\,4\\
\reducesto^+& \reason{\slab{Resume} $\EC$ with 4}\\
&3 + 3 + 4 \reducesto^+ 10
\end{derivation}
%
This example makes use of nontrivial control manipulation as it passes
a captured continuation around. However, the point is that the
separation of the handling of continuations from their capture makes
it considerably easier to implement complicated control idioms,
because the handling code is compartmentalised.
\paragraph{Cupto} The control operator cupto is a variation of \paragraph{Cupto} The control operator cupto is a variation of
control0/prompt0 designed to fit into the typed ML-family of control0/prompt0 designed to fit into the typed ML-family of