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Change control into a computation form.

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Daniel Hillerström 5 years ago
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  1. 13
      thesis.bib
  2. 113
      thesis.tex

13
thesis.bib
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@ -2233,3 +2233,16 @@
pages = {395--410},
year = {2001}
}
# Typed multi prompts
@article{DybvigJS07,
author = {R. Kent Dybvig and
Simon L. Peyton Jones and
Amr Sabry},
title = {A monadic framework for delimited continuations},
journal = {J. Funct. Program.},
volume = {17},
number = {6},
pages = {687--730},
year = {2007}
}

113
thesis.tex
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@ -1393,54 +1393,64 @@ connections to shell prompts, and how they act as barriers between the
user and operating system.
%
A prompt is a computation form, whilst control is a value.
In this presentation both control and prompt appear as computation
forms.
%
\begin{syntax}
&V,W \in \ValCat &::=& \cdots \mid \Control\\
&M,W \in \CompCat &::=& \cdots \mid \Prompt~M
&M,W \in \CompCat &::=& \cdots \mid \Control~k.M \mid \Prompt~M
\end{syntax}
%
A prompt is written using the sharp ($\Prompt$) symbol. An application
of $\Control$ reifies the current continuation up to the nearest,
dynamically determined, enclosing $\Prompt$.
The $\Control~k.M$ expression reifies the context up to the nearest,
dynamically determined, enclosing prompt and binds it to $k$ inside of
$M$. A prompt is written using the sharp ($\Prompt$) symbol.
%
The prompt remains in place after the reification, and thus any
subsequent application of $\Control$ will be delimited by the same
prompt.
%
\citeauthor{Felleisen88}'s original treatment of control and prompt
was untyped. Typing them, particularly using a simple type system,
affect their expressivity, because the type of the continuation object
produced by $\Control$ must be compatible with the type of its nearest
enclosing prompt -- this type is often called the \emph{answer} type
(this terminology is adopted from typed continuation passing style
transforms, where the codomain of every function is transformed to
yield the type of whatever answer the entire program
yields~\cite{MeyerW85}).
The static semantics of control and prompt were absent in
\citeauthor{Felleisen88}'s original treatment.
%
\dhil{Give intuition for why soundness requires the answer type to be fixed.}
\dhil{Mention Yonezawa and Kameyama's type system.}
%
\citet{DybvigJS07} gave a typed embedding of multi-prompts in
Haskell. In the multi-prompt setting the prompts are named and an
instance of $\Control$ is indexed by the prompt name of its designated
delimiter.
In the static semantics we extend the typing judgement relation to
contain an up front fixed answer type $A$.
%
\begin{mathpar}
\inferrule*
{\typ{\Gamma;A}{M : A}}
{\typ{\Gamma;A}{\Prompt~M : A}}
% Typing them, particularly using a simple type system,
% affect their expressivity, because the type of the continuation object
% produced by $\Control$ must be compatible with the type of its nearest
% enclosing prompt -- this type is often called the \emph{answer} type
% (this terminology is adopted from typed continuation passing style
% transforms, where the codomain of every function is transformed to
% yield the type of whatever answer the entire program
% yields~\cite{MeyerW85}).
% %
% \dhil{Give intuition for why soundness requires the answer type to be fixed.}
% %
\inferrule*
{~}
{\typ{\Gamma;A}{\Control : (\Cont\,\Record{A;A} \to A) \to A}}
\end{mathpar}
%
A prompt has the same type as its computation constituent, which in
turn must have the same type as fixed answer type.
%
Similarly, the type of $\Control$ is governed by the fixed answer
type. Discarding the answer type reveals that $\Control$ has the same
typing judgement as $\FelleisenF$.
%
% In the static semantics we extend the typing judgement relation to
% contain an up front fixed answer type $A$.
% %
% \begin{mathpar}
% \inferrule*
% {\typ{\Gamma;A}{M : A}}
% {\typ{\Gamma;A}{\Prompt~M : A}}
% \inferrule*
% {~}
% {\typ{\Gamma;A}{\Control : (\Cont\,\Record{A;A} \to A) \to A}}
% \end{mathpar}
% %
% A prompt has the same type as its computation constituent, which in
% turn must have the same type as fixed answer type.
% %
% Similarly, the type of $\Control$ is governed by the fixed answer
% type. Discarding the answer type reveals that $\Control$ has the same
% typing judgement as $\FelleisenF$.
% %
The dynamic semantics for control and prompt consist of three rules:
1) handle return through a prompt, 2) continuation capture, and 3)
@ -1450,7 +1460,7 @@ continuation invocation.
\slab{Value} &
\Prompt~V &\reducesto& V\\
\slab{Capture} &
\Prompt~\EC[\Control~V] &\reducesto& \Prompt~(V~\qq{\cont_{\EC}}), \text{ where $\EC$ contains no \Prompt}\\
\Prompt~\EC[\Control~k.M] &\reducesto& \Prompt~M[\qq{\cont_{\EC}}/k], \text{ where $\EC$ contains no \Prompt}\\
\slab{Resume} & \Continue~\cont_{\EC}~V &\reducesto& \EC[V]
\end{reductions}
%
@ -1473,13 +1483,11 @@ To illustrate $\Prompt$ and $\Control$ in action, let us consider a
few simple examples.
%
\begin{derivation}
& 1 + \Prompt~2 + \Control\,(\lambda k.\Continue~k~(\Continue~k~0))\\
& 1 + \Prompt~2 + (\Control~k.\Continue~k~(\Continue~k~0))\\
\reducesto^+& \reason{Capture $\EC = 2 + [\,]$}\\
& 1 + \Prompt~(\lambda k.\Continue~k~(\Continue~k~0))\,\cont_{2 + [\,]}\\
\reducesto & \reason{$\beta$-reduction}\\
& 1 + \Prompt~\Continue~\cont_{2+[\,]}~(\Continue~\cont_{2 + [\,]}~0)\\
& 1 + \Prompt~\Continue~\cont_{\EC}~(\Continue~\cont_{\EC]}~0))\,\\
\reducesto & \reason{Resume with 0}\\
& 1 + \Prompt~\Continue~\cont_{2+[\,]}~(2 + 0)\\
& 1 + \Prompt~\Continue~\cont_{\EC}~(2 + 0)\\
\reducesto^+ & \reason{Resume with 2}\\
& 1 + \Prompt~2 + 2\\
\reducesto^+ & \reason{\slab{Value} rule}\\
@ -1498,11 +1506,11 @@ $4$, which is (implicitly) supplied to the continuation of $\Prompt$.
Let us consider a slight variation of the previous example.
%
\begin{derivation}
& 1 + \Prompt~2 + \Control\,(\lambda k.\Continue~k~0) + \Control\,(\lambda k'. 0)\\
\reducesto^+& \reason{Capture $\EC = 2 + [\,] + \Control\,(\lambda k'.0)$}\\
& 1 + \Prompt~2 + (\Control~k.\Continue~k~0) + (\Control~k'. 0)\\
\reducesto^+& \reason{Capture $\EC = 2 + [\,] + (\Control~k'.0)$}\\
& 1 + \Prompt~\Continue~\cont_{\EC}~0\\
\reducesto & \reason{Resume with 0}\\
& 1 + \Prompt~2 + 0 + \Control\,(\lambda k'. 0)\\
& 1 + \Prompt~2 + 0 + (\Control~k'. 0)\\
\reducesto^+ & \reason{Capture $\EC' = 2 + [\,]$}\\
& 1 + \Prompt~0 \\
\reducesto & \reason{\slab{Value} rule}\\
@ -2101,9 +2109,20 @@ programs~\cite{Knuth97}. Canonical reference for implementing
coroutines with call/cc~\cite{HaynesFW86}.
\section{Programming continuations}
Blind vs non-blind backtracking. Engines. Web
programming. Asynchronous
programming. Coroutines. Meta-programming~\cite{LawallD94,KameyamaKS11,OishiK17,Yallop17}.
%Blind vs non-blind backtracking. Engines. Web
% programming. Asynchronous
% programming. Coroutines.
Amongst the first uses of continuations were modelling of unrestricted
jumps, such as \citeauthor{Landin98}'s modelling of \Algol{} labels
and gotos using the J
operator~\cite{Landin65,Landin65a,Landin98,Reynolds93}.
Backtracking is another early and prominent use of
continuations. \citet{Burstall69} used the J operator to implement a
backtracking mechanism to facilitate tree-based search.
Meta-programming~\cite{LawallD94,KameyamaKS11,OishiK17,Yallop17}.
\section{Constraining continuations}
For example callec is a variation of callcc where the continuation

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