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Controlling continuations [WIP]

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macros.tex
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@@ -13,6 +13,9 @@
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\B}{\ensuremath{\mathbb{B}}}
\newcommand{\BB}[1]{\ensuremath{\mathbf{#1}}}
\newcommand{\CC}{\keyw{C}}
% \newcommand{\Delim}[1]{\ensuremath{\langle\!\!\mkern-1.5mu\langle#1\rangle\!\!\mkern-1.5mu\rangle}}
\newcommand{\Delim}[1]{\ensuremath{\langle#1\rangle}}
%%
%% Partiality

159
thesis.bib
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@@ -16,7 +16,7 @@
address = {Scotland, {UK}},
optmonth = aug,
year = 2016,
type = {{MSc(R)} Dissertation}
type = {{MSc(R)} thesis}
}
# OCaml handlers
@@ -43,7 +43,8 @@
Leo White},
title = {Concurrent System Programming with Effect Handlers},
booktitle = {{TFP}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {10788},
pages = {98--117},
publisher = {Springer},
@@ -107,7 +108,8 @@
Matija Pretnar},
title = {Handlers of Algebraic Effects},
booktitle = {{ESOP}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {5502},
pages = {80--94},
publisher = {Springer},
@@ -123,10 +125,7 @@
number = {4},
year = {2013},
OPTurl = {http://dx.doi.org/10.2168/LMCS-9(4:23)2013},
OPTdoi = {10.2168/LMCS-9(4:23)2013},
timestamp = {Thu, 31 Aug 4448958 16:06:56 +},
biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/PlotkinP13},
bibsource = {dblp computer science bibliography, http://dblp.org}
OPTdoi = {10.2168/LMCS-9(4:23)2013}
}
@article{PlotkinP03,
@@ -397,7 +396,8 @@
Andrej Bauer},
title = {Runners in Action},
booktitle = {{ESOP}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {12075},
pages = {29--55},
publisher = {Springer},
@@ -551,7 +551,8 @@
Tom Schrijvers},
title = {Fusion for Free - Efficient Algebraic Effect Handlers},
booktitle = {{MPC}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {9129},
pages = {302--322},
publisher = {Springer},
@@ -675,7 +676,8 @@
Shin{-}Cheng Mu},
title = {Handling Local State with Global State},
booktitle = {{MPC}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {11825},
pages = {18--44},
publisher = {Springer},
@@ -925,7 +927,8 @@
Sam Lindley},
title = {Shallow Effect Handlers},
booktitle = {{APLAS}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {11275},
pages = {415--435},
publisher = {Springer},
@@ -976,7 +979,8 @@
Tom Schrijvers},
title = {Explicit Effect Subtyping},
booktitle = {{ESOP}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {10801},
pages = {327--354},
publisher = {Springer},
@@ -1032,7 +1036,8 @@
title = {The {OCaml} System Release 4.11: Documentation and user's manual},
year = 2020,
month = aug,
publisher = {Institut National de Recherche en Informatique et en Automatique}
OPTpublisher = {Institut National de Recherche en Informatique et en Automatique},
publisher = {INRIA}
}
# Lisp
@@ -1193,7 +1198,7 @@
# Landin's J operator
@article{Landin65,
author = {Peter J. Landin},
title = {Correspondence between {ALGOL} 60 and Church's Lambda-notation: part
title = {Correspondence between {ALGOL} 60 and {C}hurch's {L}ambda-notation: part
{I}},
journal = {Commun. {ACM}},
volume = {8},
@@ -1204,7 +1209,7 @@
@article{Landin65a,
author = {Peter J. Landin},
title = {A correspondence between {ALGOL} 60 and Church's Lambda-notations:
title = {A correspondence between {ALGOL} 60 and {C}hurch's {L}ambda-notations:
Part {II}},
journal = {Commun. {ACM}},
volume = {8},
@@ -1321,7 +1326,7 @@
# Simula (coroutines)
@inproceedings{DahlMN68,
author = {Ole-Johan Dahl and Bj\o{}rn Myhrhaug and Kristen Nygaard},
title = {Some Features of the SIMULA 67 Language},
title = {Some Features of the {SIMULA} 67 Language},
year = {1968},
publisher = {Winter Simulation Conference},
booktitle = {Proceedings of the Second Conference on Applications of Simulations},
@@ -1351,28 +1356,28 @@
# Second-hand reference for call/cc
@techreport{AbelsonHAKBOBPCRFRHSHW85,
author = {Hal Abelson
and Chris Haynes
and Norman Adams
and Eugene Kohlbecker
and David Bartley
and Don Oxley
and Gary Brooks
and Kent Pitman
and William Clinger
and Jonathan Rees
and Dan Friedman
and Bill Rozas
and Robert Halstead
and Gerald Jey Sussman
and Chris Hanson
and Mitchell Wand},
author = {William D. Clinger and others},
@Comment = {Hal Abelson
@Comment and Chris Haynes
@Comment and Norman Adams
@Comment and Eugene Kohlbecker
@Comment and David Bartley
@Comment and Don Oxley
@Comment and Gary Brooks
@Comment and Kent Pitman
@Comment and William Clinger
@Comment and Jonathan Rees
@Comment and Dan Friedman
@Comment and Bill Rozas
@Comment and Robert Halstead
@Comment and Gerald Jey Sussman
@Comment and Chris Hanson
@Comment and Mitchell Wand},
title = {The Revised Revised Report on {Scheme} or An {UnCommon} {Lisp}},
year = {1985},
institution = {MIT},
number = {No. 848},
month = aug,
type = {AI Memo}
number = {AIM-848},
month = aug
}
# Splitter
@@ -1426,7 +1431,8 @@
author = {John C. Reynolds},
title = {Towards a theory of type structure},
booktitle = {Symposium on Programming},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {19},
pages = {408--423},
publisher = {Springer},
@@ -1474,22 +1480,46 @@
# GNU coreutils
@book{MacKenzieMPPBYS20,
author = {David MacKenzie
and Jim Meyering
and Ross Paterson
and François Pinard
and Karl Berry
and Brian Youmans
and Richard Stallman},
author = {David MacKenzie and others},
@Comment = {David MacKenzie
@Comment and Jim Meyering
@Comment and Ross Paterson
@Comment and François Pinard
@Comment and Karl Berry
@Comment and Brian Youmans
@Comment and Richard Stallman},
title = {{GNU} {Coreutils}},
note = {For version 8.32},
month = feb,
year = 2020,
publisher = {Free Software Foundation},
address = {Boston, MA, USA}
OPTaddress = {Boston, MA, USA}
}
# Expressiveness
@inproceedings{Felleisen90,
author = {Matthias Felleisen},
title = {On the Expressive Power of Programming Languages},
booktitle = {{ESOP}},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {432},
pages = {134--151},
publisher = {Springer},
year = {1990}
}
@article{Felleisen91,
author = {Matthias Felleisen},
title = {On the Expressive Power of Programming Languages},
journal = {Sci. Comput. Program.},
volume = {17},
number = {1-3},
pages = {35--75},
year = {1991},
note = {Revised version}
}
@inproceedings{CartwrightF92,
author = {Robert Cartwright and
Matthias Felleisen},
@@ -1514,7 +1544,8 @@
title = {Interpreting Localized Computational Effects Using Operators of Higher
Type},
booktitle = {CiE},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {5028},
pages = {389--402},
publisher = {Springer},
@@ -1638,6 +1669,18 @@
year = {1984}
}
@article{HaynesFW86,
author = {Christopher T. Haynes and
Daniel P. Friedman and
Mitchell Wand},
title = {Obtaining Coroutines with Continuations},
journal = {Comput. Lang.},
volume = {11},
number = {3/4},
pages = {143--153},
year = {1986}
}
@techreport{Moggi90,
title = {An Abstract View of Programming Languages},
author = {Eugenio Moggi},
@@ -1679,7 +1722,8 @@
author = {William L. Harrison},
title = {The Essence of Multitasking},
booktitle = {{AMAST}},
series = {Lecture Notes in Computer Science},
OPTseries = {Lecture Notes in Computer Science},
series = {LNCS},
volume = {4019},
pages = {158--172},
publisher = {Springer},
@@ -1694,3 +1738,26 @@
volume = {25},
year = {2015}
}
# History of continuations
@article{Reynolds93,
author = {John C. Reynolds},
title = {The Discoveries of Continuations},
journal = {{LISP} Symb. Comput.},
volume = {6},
number = {3-4},
pages = {233--248},
year = {1993}
}
# Terminology: 'partial' and 'full' continuations
@inproceedings{JohnsonD88,
author = {Gregory F. Johnson and
Dominic Duggan},
title = {Stores and Partial Continuations as First-Class Objects in a Language
and its Environment},
booktitle = {{POPL}},
pages = {158--168},
publisher = {{ACM} Press},
year = {1988}
}

193
thesis.tex
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@@ -488,9 +488,9 @@ handlers.
\section{Typed programming languages}
\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}
\section{Type and effect systems}
@@ -502,13 +502,156 @@ handlers.
\chapter{Controlling 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}.
A continuation is an abstract data structure that captures the
remainder of the computation from some given point in the computation.
%
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}
% \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
continuations, composable continuations.
Downward and upward use of continuations.
\section{First-Class control operators}
Describe how effect handlers fit amongst shift/reset, prompt/control,
callcc, J, catchcont, etc.
\subsection{Abortive operators}
\subsection{Undelimited 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
@@ -523,21 +666,6 @@ shift/reset~\cite{DanvyF89,DanvyF90}, splitter~\cite{QueinnecS91},
fcontrol~\cite{Sitaram93}, catchcont~\cite{LongleyW08}, effect
handlers~\cite{PlotkinP09}.
\section{Notions of continuations}
Escape continuations, undelimited continuations, delimited
continuations, composable continuations.
\section{First-Class control operators}
Describe how effect handlers fit amongst shift/reset, prompt/control,
callcc, J, catchcont, etc.
\subsection{Escape operators}
\subsection{Undelimited operators}
\subsection{Delimited operators}
Comparison of various delimited control
operators~\cite{Shan04}. Simulation of delimited control using
undelimited control~\cite{Filinski94}
@@ -550,7 +678,8 @@ Backtracking: Amb~\cite{McCarthy63}.
Coroutines~\cite{DahlDH72} as introduced by Simula
67~\cite{DahlMN68}. The notion of coroutines was coined by Melvin
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}
Continuation marks. CPS. Stack inspection.
@@ -7202,16 +7331,16 @@ If $\typc{}{M : A}{E}$ and $M \reducesto^+ N \not\reducesto$, then $M
\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}
Describe the methodology\dots
\section{Generic search}
@@ -7229,7 +7358,7 @@ Describe the methodology\dots
\subsection{No shortcuts}
\subsection{No sharing}
\chapter{Robustness of the asymptotic power of control}
\chapter{Speeding up programs in ML-like programming languages}
\section{Mutable state}
\section{Exception handling}
\section{Effect system}