|
|
@ -488,9 +488,9 @@ handlers. |
|
|
\section{Typed programming languages} |
|
|
\section{Typed programming languages} |
|
|
\label{sec:pls} |
|
|
\label{sec:pls} |
|
|
% |
|
|
% |
|
|
\dhil{Definition of (typed) programming language, conservative extension, macro-expressiveness} |
|
|
|
|
|
|
|
|
\dhil{Definition of (typed) programming language, conservative extension, macro-expressiveness~\cite{Felleisen90,Felleisen91}} |
|
|
|
|
|
|
|
|
\chapter{The state of effectful programming} |
|
|
|
|
|
|
|
|
\chapter{State of effectful programming} |
|
|
\label{ch:related-work} |
|
|
\label{ch:related-work} |
|
|
|
|
|
|
|
|
\section{Type and effect systems} |
|
|
\section{Type and effect systems} |
|
|
@ -502,42 +502,170 @@ handlers. |
|
|
|
|
|
|
|
|
\chapter{Controlling continuations} |
|
|
\chapter{Controlling continuations} |
|
|
\label{ch:continuations} |
|
|
\label{ch:continuations} |
|
|
|
|
|
% The significance of continuations in the programming languages |
|
|
|
|
|
% literature is inescapable as continuations have found widespread use . |
|
|
|
|
|
% |
|
|
|
|
|
|
|
|
Undelimited control: Landin's J~\cite{Landin98}, Reynolds' |
|
|
|
|
|
escape~\cite{Reynolds98a}, Scheme75's catch~\cite{SussmanS75} --- |
|
|
|
|
|
which was based the less expressive MacLisp catch~\cite{Moon74}, |
|
|
|
|
|
callcc is a procedural variation of catch. It was invented in |
|
|
|
|
|
1982~\cite{AbelsonHAKBOBPCRFRHSHW85}. |
|
|
|
|
|
|
|
|
|
|
|
Delimited control: Control delimiters form the basis for delimited |
|
|
|
|
|
control. \citeauthor{Felleisen88} introduced control delimiters in |
|
|
|
|
|
1988, although allusions to control delimiters were made a year |
|
|
|
|
|
earlier by \citet{FelleisenFDM87} and in \citeauthor{Felleisen87}'s |
|
|
|
|
|
PhD dissertation~\cite{Felleisen87}. The basic idea was teased even |
|
|
|
|
|
earlier in \citeauthor{Talcott85}'s teased the idea of control |
|
|
|
|
|
delimiters in her PhD dissertation~\cite{Talcott85}. |
|
|
|
|
|
|
|
|
A continuation is an abstract data structure that captures the |
|
|
|
|
|
remainder of the computation from some given point in the computation. |
|
|
% |
|
|
% |
|
|
Common Lisp resumable exceptions (condition system)~\cite{Steele90}, |
|
|
|
|
|
F~\cite{FelleisenFDM87,Felleisen88}, control/prompt~\cite{SitaramF90}, |
|
|
|
|
|
shift/reset~\cite{DanvyF89,DanvyF90}, splitter~\cite{QueinnecS91}, |
|
|
|
|
|
fcontrol~\cite{Sitaram93}, catchcont~\cite{LongleyW08}, effect |
|
|
|
|
|
handlers~\cite{PlotkinP09}. |
|
|
|
|
|
|
|
|
The exact nature of the data structure and the precise point at which |
|
|
|
|
|
the remainder of the computation is captured depends largely on the |
|
|
|
|
|
exact notion of continuation under consideration. |
|
|
|
|
|
% |
|
|
|
|
|
It can be difficult to navigate the existing literature on |
|
|
|
|
|
continuations as sometimes the terminologies for different notions of |
|
|
|
|
|
continuations are overloaded or even conflated. |
|
|
|
|
|
% |
|
|
|
|
|
As there exist several notions of continuations, there exist several |
|
|
|
|
|
mechanisms for programmatic manipulation of continuations. These |
|
|
|
|
|
mechanisms are known as control operators. |
|
|
|
|
|
% |
|
|
|
|
|
A substantial amount of existing literature has been devoted to |
|
|
|
|
|
understand how to program with individual control operators, and to a |
|
|
|
|
|
lesser extent how the various operators compare. |
|
|
|
|
|
|
|
|
|
|
|
The purpose of this chapter is to provide a contemporary and |
|
|
|
|
|
unambiguous characterisation of the notions of continuations in |
|
|
|
|
|
literature. This characterisation is used to classify and discuss a |
|
|
|
|
|
wide range of control operators from the literature. |
|
|
|
|
|
|
|
|
|
|
|
% Undelimited control: Landin's J~\cite{Landin98}, Reynolds' |
|
|
|
|
|
% escape~\cite{Reynolds98a}, Scheme75's catch~\cite{SussmanS75} --- |
|
|
|
|
|
% which was based the less expressive MacLisp catch~\cite{Moon74}, |
|
|
|
|
|
% callcc is a procedural variation of catch. It was invented in |
|
|
|
|
|
% 1982~\cite{AbelsonHAKBOBPCRFRHSHW85}. |
|
|
|
|
|
|
|
|
\section{Notions of continuations} |
|
|
\section{Notions of continuations} |
|
|
|
|
|
|
|
|
|
|
|
% \citeauthor{Reynolds93} has written a historical account of the |
|
|
|
|
|
% various early discoveries of continuations~\cite{Reynolds93}. |
|
|
|
|
|
|
|
|
|
|
|
In the literature the term ``continuation'' is often accompanied by a |
|
|
|
|
|
qualifier such as full~\cite{JohnsonD88}, partial~\cite{JohnsonD88}, |
|
|
|
|
|
abortive, escape, undelimited, delimited, composable, or functional. |
|
|
|
|
|
% |
|
|
|
|
|
Some of these qualifiers are synonyms, and hence redundant, e.g. the |
|
|
|
|
|
terms ``full'' and ``undelimited'' refer to the same notion of |
|
|
|
|
|
continuation, likewise the terms ``partial'' and ``delimited'' mean |
|
|
|
|
|
the same thing, the notions of ``abortive'' and ``escape'' are |
|
|
|
|
|
interchangeable too, and ``composable'' and ``functional'' also refer |
|
|
|
|
|
to the same notion. |
|
|
|
|
|
% |
|
|
|
|
|
|
|
|
|
|
|
Thus the peloton of distinct continuation notions can be pruned to |
|
|
|
|
|
``undelimited'', ``delimited'', ``abortive'', and ``composable''. |
|
|
|
|
|
% |
|
|
|
|
|
The first two notions concern the introduction of continuations, that |
|
|
|
|
|
is how continuations are captured. Dually, the latter two notions |
|
|
|
|
|
concern the elimination of continuations, that is how continuations |
|
|
|
|
|
interact with the enclosing context. |
|
|
|
|
|
% |
|
|
|
|
|
Consequently, it is not meaningful to contrast, say, ``undelimited'' |
|
|
|
|
|
with ``abortive'' continuations, because they are orthogonal notions. |
|
|
|
|
|
% |
|
|
|
|
|
A common confusion in the literature is to conflate ``undelimited'' |
|
|
|
|
|
continuations with ``abortive'' continuations. |
|
|
|
|
|
% Similarly, often times ``composable'' is taken to imply ``delimited''. |
|
|
|
|
|
However, it is perfectly possible to conceive of a continuation that |
|
|
|
|
|
is undelimited but not abortive. |
|
|
|
|
|
% |
|
|
|
|
|
% An educated guess as to why this confusion occurs in the literature |
|
|
|
|
|
% may be that it is due to the introduction |
|
|
|
|
|
|
|
|
|
|
|
To make each notion of continuation concrete I will present its |
|
|
|
|
|
characteristic reduction rule. To facilitate this presentation I will |
|
|
|
|
|
make use of an abstract control operator $\CC$ to perform an abstract |
|
|
|
|
|
capture of continuations, i.e. informally $C\,k.M$ is to be understood |
|
|
|
|
|
as a syntactic construct that captures the continuation and reifies it |
|
|
|
|
|
as a function which it binds to $k$ in the computation $M$. The |
|
|
|
|
|
precise extent of the capture will be given by the characteristic |
|
|
|
|
|
reduction rule. I will also make use of an abstract control delimiter |
|
|
|
|
|
$\Delim{-}$. The term $\Delim{M}$ encloses the computation $M$ in a |
|
|
|
|
|
syntactically identifiable marker. For the intent and purposes of this |
|
|
|
|
|
presentation enclosing a value in a delimiter is an idempotent |
|
|
|
|
|
operation, i.e. $\Delim{V} \reducesto V$. I will write $\EC$ to |
|
|
|
|
|
denote an evaluation context~\cite{Felleisen87}. |
|
|
|
|
|
|
|
|
|
|
|
\paragraph{Undelimited continuation} |
|
|
|
|
|
% |
|
|
|
|
|
\[ |
|
|
|
|
|
\EC[\CC\,k.M] \reducesto \EC[M[(\lambda x.\EC[x])/k]] |
|
|
|
|
|
\] |
|
|
|
|
|
% |
|
|
|
|
|
\begin{derivation} |
|
|
|
|
|
& 3 * (\CC\,k. 2 + k\,(k\,1))\\ |
|
|
|
|
|
\reducesto& \reason{captures the context $k = 3 * [~]$}\\ |
|
|
|
|
|
& 3 * (2 + k\,(k~1))[(\lambda x. 3 * x)/k]\\ |
|
|
|
|
|
=& \reason{substitution}\\ |
|
|
|
|
|
& 3 * (2 + (\lambda x. 3 * x)((\lambda x. 3 * x)\,1))\\ |
|
|
|
|
|
\reducesto& \reason{$\beta$-reduction}\\ |
|
|
|
|
|
& 3 * (2 + (\lambda x. 3 * x)(3 * 1))\\ |
|
|
|
|
|
\reducesto& \reason{$\beta$-reduction}\\ |
|
|
|
|
|
& 3 * (2 + (\lambda x. 3 * x)\,3)\\ |
|
|
|
|
|
\reducesto^4& \reason{$\beta$-reductions}\\ |
|
|
|
|
|
& 33 |
|
|
|
|
|
\end{derivation} |
|
|
|
|
|
|
|
|
|
|
|
\paragraph{Delimited continuation} |
|
|
|
|
|
% |
|
|
|
|
|
\[ |
|
|
|
|
|
\Delim{\EC[\CC\,k.M]} \reducesto \Delim{M[(\lambda x.\Delim{\EC[x]})/k]} |
|
|
|
|
|
\] |
|
|
|
|
|
% |
|
|
|
|
|
\[ |
|
|
|
|
|
\Delim{\EC[\CC\,k.M]} \reducesto M[(\lambda x.\Delim{\EC[x]})/k] |
|
|
|
|
|
\] |
|
|
|
|
|
|
|
|
|
|
|
\paragraph{Abortive continuation} An abortive continuation discards the current context.Like delimited continuations, an |
|
|
|
|
|
abortive continuation is accompanied by a delimiter. The |
|
|
|
|
|
characteristic property of an abortive continuation is that it |
|
|
|
|
|
discards its invocation context up to its enclosing delimiter. |
|
|
|
|
|
% |
|
|
|
|
|
\[ |
|
|
|
|
|
\EC[k\,V] \reducesto V, \quad \text{where } k = (\lambda x. \keyw{abort}\;x). |
|
|
|
|
|
\] |
|
|
|
|
|
% |
|
|
|
|
|
Consequently, composing an abortive continuation with itself is |
|
|
|
|
|
meaningless, e.g. in $k (k\,V)$ the innermost application erases the |
|
|
|
|
|
outermost application. |
|
|
|
|
|
|
|
|
|
|
|
\paragraph{Composable continuation} The defining characteristic of a |
|
|
|
|
|
composable continuation is that it composes the captured context with |
|
|
|
|
|
current context, i.e. |
|
|
|
|
|
% |
|
|
|
|
|
\[ |
|
|
|
|
|
\EC[k\,V] \reducesto \EC[\EC'[V]], \quad \text{where } k = (\lambda x. \EC'[x]) |
|
|
|
|
|
\] |
|
|
|
|
|
|
|
|
Escape continuations, undelimited continuations, delimited |
|
|
Escape continuations, undelimited continuations, delimited |
|
|
continuations, composable continuations. |
|
|
continuations, composable continuations. |
|
|
|
|
|
|
|
|
|
|
|
Downward and upward use of continuations. |
|
|
|
|
|
|
|
|
\section{First-Class control operators} |
|
|
\section{First-Class control operators} |
|
|
Describe how effect handlers fit amongst shift/reset, prompt/control, |
|
|
Describe how effect handlers fit amongst shift/reset, prompt/control, |
|
|
callcc, J, catchcont, etc. |
|
|
callcc, J, catchcont, etc. |
|
|
|
|
|
|
|
|
\subsection{Escape operators} |
|
|
|
|
|
|
|
|
\subsection{Abortive operators} |
|
|
|
|
|
|
|
|
\subsection{Undelimited operators} |
|
|
\subsection{Undelimited operators} |
|
|
|
|
|
|
|
|
\subsection{Delimited operators} |
|
|
\subsection{Delimited operators} |
|
|
|
|
|
Delimited control: Control delimiters form the basis for delimited |
|
|
|
|
|
control. \citeauthor{Felleisen88} introduced control delimiters in |
|
|
|
|
|
1988, although allusions to control delimiters were made a year |
|
|
|
|
|
earlier by \citet{FelleisenFDM87} and in \citeauthor{Felleisen87}'s |
|
|
|
|
|
PhD dissertation~\cite{Felleisen87}. The basic idea was teased even |
|
|
|
|
|
earlier in \citeauthor{Talcott85}'s teased the idea of control |
|
|
|
|
|
delimiters in her PhD dissertation~\cite{Talcott85}. |
|
|
|
|
|
% |
|
|
|
|
|
Common Lisp resumable exceptions (condition system)~\cite{Steele90}, |
|
|
|
|
|
F~\cite{FelleisenFDM87,Felleisen88}, control/prompt~\cite{SitaramF90}, |
|
|
|
|
|
shift/reset~\cite{DanvyF89,DanvyF90}, splitter~\cite{QueinnecS91}, |
|
|
|
|
|
fcontrol~\cite{Sitaram93}, catchcont~\cite{LongleyW08}, effect |
|
|
|
|
|
handlers~\cite{PlotkinP09}. |
|
|
|
|
|
|
|
|
Comparison of various delimited control |
|
|
Comparison of various delimited control |
|
|
operators~\cite{Shan04}. Simulation of delimited control using |
|
|
operators~\cite{Shan04}. Simulation of delimited control using |
|
|
undelimited control~\cite{Filinski94} |
|
|
undelimited control~\cite{Filinski94} |
|
|
@ -550,7 +678,8 @@ Backtracking: Amb~\cite{McCarthy63}. |
|
|
Coroutines~\cite{DahlDH72} as introduced by Simula |
|
|
Coroutines~\cite{DahlDH72} as introduced by Simula |
|
|
67~\cite{DahlMN68}. The notion of coroutines was coined by Melvin |
|
|
67~\cite{DahlMN68}. The notion of coroutines was coined by Melvin |
|
|
Conway, who used coroutines as a code idiom in assembly |
|
|
Conway, who used coroutines as a code idiom in assembly |
|
|
programs~\cite{Knuth97}. |
|
|
|
|
|
|
|
|
programs~\cite{Knuth97}. Canonical reference for implementing |
|
|
|
|
|
coroutines with call/cc~\cite{HaynesFW86}. |
|
|
|
|
|
|
|
|
\section{Implementation strategies} |
|
|
\section{Implementation strategies} |
|
|
Continuation marks. CPS. Stack inspection. |
|
|
Continuation marks. CPS. Stack inspection. |
|
|
@ -7202,16 +7331,16 @@ If $\typc{}{M : A}{E}$ and $M \reducesto^+ N \not\reducesto$, then $M |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\part{Expressiveness} |
|
|
\part{Expressiveness} |
|
|
\chapter{Computability, complexity, and expressivness} |
|
|
|
|
|
\label{ch:expressiveness} |
|
|
|
|
|
\section{Notions of expressiveness} |
|
|
|
|
|
Felleisen's macro-expressiveness, Longley's type-respecting |
|
|
|
|
|
expressiveness, Kammar's typability-preserving expressiveness. |
|
|
|
|
|
|
|
|
% \chapter{Computability, complexity, and expressivness} |
|
|
|
|
|
% \label{ch:expressiveness} |
|
|
|
|
|
% \section{Notions of expressiveness} |
|
|
|
|
|
% Felleisen's macro-expressiveness, Longley's type-respecting |
|
|
|
|
|
% expressiveness, Kammar's typability-preserving expressiveness. |
|
|
|
|
|
|
|
|
\section{Interdefinability of deep and shallow Handlers} |
|
|
|
|
|
\section{Encoding parameterised handlers} |
|
|
|
|
|
|
|
|
% \section{Interdefinability of deep and shallow Handlers} |
|
|
|
|
|
% \section{Encoding parameterised handlers} |
|
|
|
|
|
|
|
|
\chapter{The asymptotic power of control} |
|
|
|
|
|
|
|
|
\chapter{Asymptotic speedup with first-class control} |
|
|
\label{ch:handlers-efficiency} |
|
|
\label{ch:handlers-efficiency} |
|
|
Describe the methodology\dots |
|
|
Describe the methodology\dots |
|
|
\section{Generic search} |
|
|
\section{Generic search} |
|
|
@ -7229,7 +7358,7 @@ Describe the methodology\dots |
|
|
\subsection{No shortcuts} |
|
|
\subsection{No shortcuts} |
|
|
\subsection{No sharing} |
|
|
\subsection{No sharing} |
|
|
|
|
|
|
|
|
\chapter{Robustness of the asymptotic power of control} |
|
|
|
|
|
|
|
|
\chapter{Speeding up programs in ML-like programming languages} |
|
|
\section{Mutable state} |
|
|
\section{Mutable state} |
|
|
\section{Exception handling} |
|
|
\section{Exception handling} |
|
|
\section{Effect system} |
|
|
\section{Effect system} |
|
|
|
