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Daniel Hillerström
2021-05-28 12:21:14 +01:00
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12
thesis.bib
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@@ -1802,6 +1802,18 @@
year = {1990} year = {1990}
} }
@inproceedings{KameyamaY08,
author = {Yukiyoshi Kameyama and
Takuo Yonezawa},
title = {Typed Dynamic Control Operators for Delimited Continuations},
booktitle = {{FLOPS}},
series = {{LNCS}},
volume = {4989},
pages = {239--254},
publisher = {Springer},
year = {2008}
}
# Escape # Escape
@article{Reynolds98a, @article{Reynolds98a,
author = {John C. Reynolds}, author = {John C. Reynolds},

68
thesis.tex
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@@ -3718,14 +3718,22 @@ is same as $\FelleisenF$. However, the presentation here is close to
actual implementations of $\Control$. actual implementations of $\Control$.
The static semantics of control and prompt were absent in The static semantics of control and prompt were absent in
\citeauthor{Felleisen88}'s original treatment. \citeauthor{Felleisen88}'s original treatment. Later,
\citet{KameyamaY08} have given a polymorphic type system with answer
type modifications for control and prompt (we will discuss answer type
modification when discussing shift/reset). It is also worth mentioning
that \citet{DybvigJS07} present a typed embedding of control and
prompts in Haskell (actually, they present an entire general monadic
framework for implementing control operators based on the idea of
\emph{multi-prompts}, which are a slight generalisation of prompts ---
we will revisit multi-prompts when we discuss cupto).
% %
\dhil{Mention Yonezawa and Kameyama's type system.} % \dhil{Mention Yonezawa and Kameyama's type system.}
% % %
\citet{DybvigJS07} gave a typed embedding of multi-prompts in % \citet{DybvigJS07} gave a typed embedding of multi-prompts in
Haskell. In the multi-prompt setting the prompts are named and an % Haskell. In the multi-prompt setting the prompts are named and an
instance of $\Control$ is indexed by the prompt name of its designated % instance of $\Control$ is indexed by the prompt name of its designated
delimiter. % delimiter.
% Typing them, particularly using a simple type system, % Typing them, particularly using a simple type system,
% affect their expressivity, because the type of the continuation object % affect their expressivity, because the type of the continuation object
@@ -3855,12 +3863,37 @@ second application of $\Control$ captures the remainder of the
computation of to $\Prompt$. However, the captured context gets computation of to $\Prompt$. However, the captured context gets
discarded, because the continuation $k'$ is never invoked. discarded, because the continuation $k'$ is never invoked.
% %
\dhil{Mention control0/prompt0 and the control hierarchy}
A slight variation on control and prompt is $\Controlz$ and
$\Promptz$~\cite{Shan04}. The main difference is that $\Controlz$
removes its corresponding prompt, i.e.
%
\begin{reductions}
% \slab{Value} &
% \Prompt~V &\reducesto& V\\
\slab{Capture_0} &
\Promptz~\EC[\Controlz~k.M] &\reducesto& M[\qq{\cont_{\EC}}/k], \text{ where $\EC$ contains no \Promptz}\\
% \slab{Resume} & \Continue~\cont_{\EC}~V &\reducesto& \EC[V]
\end{reductions}
%
Higher-order programming with control and prompt (and delimited
control in general) is fragile, because the body of a higher-order
function may inadvertently trap instances of control in its functional
arguments.
%
This observation led \citet{SitaramF90} to define an indexed family of
control and prompt pairs such that instances of control and prompt can
be layered on top of one another. The idea is that the index on each
pair denotes their level $i$ such that $\Control^i$ matches
$\Prompt^i$ and may capture any other instances of $\Prompt^j$ where
$j < i$.
% \dhil{Mention control0/prompt0 and
% the control hierarchy}
\paragraph{\citeauthor{DanvyF90}'s shift and reset} Shift and reset \paragraph{\citeauthor{DanvyF90}'s shift and reset} Shift and reset
first appeared in a technical report by \citeauthor{DanvyF89} in first appeared in a technical report by \citeauthor{DanvyF89} in
1989. Although, perhaps the most widely known account of shift and 1989. Although, perhaps the most widely known account of shift and
reset appeared in \citeauthor{DanvyF90}'s treatise on abstracting reset appeared in \citeauthor{DanvyF90}'s seminal work on abstracting
control the following year~\cite{DanvyF90}. control the following year~\cite{DanvyF90}.
% %
Shift and reset differ from control and prompt in that the contexts Shift and reset differ from control and prompt in that the contexts
@@ -3928,7 +3961,7 @@ substructural type system with answer type modification, whilst
language with answer type modification into a system without using language with answer type modification into a system without using
typed multi-prompts. typed multi-prompts.
Differences between shift/reset and control/prompt manifests in the Differences between shift/reset and control/prompt manifest in the
dynamic semantics as well. dynamic semantics as well.
% %
\begin{reductions} \begin{reductions}
@@ -3966,12 +3999,11 @@ previous continuation invocation.
This difference naturally raises the question whether shift/reset and This difference naturally raises the question whether shift/reset and
control/prompt are interdefinable or exhibit essential expressivity control/prompt are interdefinable or exhibit essential expressivity
differences. This question was answered by \citet{Shan04}, who differences. \citet{Shan04} answered this question demonstrating that
demonstrated that shift/reset and control/prompt are shift/reset and control/prompt are macro-expressible. The translations
macro-expressible. The translations are too intricate to be reproduced are too intricate to be reproduced here, however, it is worth noting
here, however, it is worth noting that \citeauthor{Shan04} were that \citeauthor{Shan04} were working in the untyped setting of Scheme
working in the untyped setting of Scheme and the translation of and the translation of control/prompt made use of recursive
control/prompt made use of recursive
continuations. \citet{BiernackiDS05} typed and reimplemented this continuations. \citet{BiernackiDS05} typed and reimplemented this
translation in Standard ML New Jersey~\cite{AppelM91}, using translation in Standard ML New Jersey~\cite{AppelM91}, using
\citeauthor{Filinski94}'s encoding of shift/reset in terms of callcc \citeauthor{Filinski94}'s encoding of shift/reset in terms of callcc
@@ -4007,7 +4039,7 @@ Splitter and the two operations abort and calldc are value forms.
V,W ::= \cdots \mid \splitter \mid \abort \mid \calldc V,W ::= \cdots \mid \splitter \mid \abort \mid \calldc
\] \]
% %
In their treatise of splitter, \citeauthor{QueinnecS91} gave three In their treatment of splitter, \citeauthor{QueinnecS91} gave three
different presentations of splitter. The presentation that I have different presentations of splitter. The presentation that I have
opted for here is close to their second presentation, which is in opted for here is close to their second presentation, which is in
terms of multi-prompt continuations. This variation of splitter admits terms of multi-prompt continuations. This variation of splitter admits
@@ -4518,7 +4550,7 @@ The $\slab{Capture}$ reifies the continuation up to the handler, and
thus the $\slab{Resume}$ rule can only reinstate the captured thus the $\slab{Resume}$ rule can only reinstate the captured
continuation without the handler. continuation without the handler.
% %
\dhil{Revisit the toss example with shallow handlers} %\dhil{Revisit the toss example with shallow handlers}
% \begin{reductions} % \begin{reductions}
% \slab{Capture} & \Handle\;\EC[\Do\;\ell~V] \;\With\; H &\reducesto& M[V/p,\qq{\cont_{\EC}}/k],\\ % \slab{Capture} & \Handle\;\EC[\Do\;\ell~V] \;\With\; H &\reducesto& M[V/p,\qq{\cont_{\EC}}/k],\\
% \multicolumn{4}{l}{\hfill\bl\text{where $\ell$ is not handled in $\EC$}\\\text{and }\{\ell~p~k \mapsto M\} \in H\el}\\ % \multicolumn{4}{l}{\hfill\bl\text{where $\ell$ is not handled in $\EC$}\\\text{and }\{\ell~p~k \mapsto M\} \in H\el}\\