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Fix typos in introduction

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Daniel Hillerström 5 years ago
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      thesis.tex

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thesis.tex
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@ -611,16 +611,33 @@ efficiency.
% expressiveness.
\section{Why first-class control matters}
First things first, let us settle on the meaning of the qualifier
`first-class'. A programming language entity (or citizen) is regarded
as being first-class if it can be used on an equal footing with other
entities.
%
A familiar example is functions as first-class values. A first-class
function may be treated like any other primitive value, i.e. passed as
an argument to other functions, returned from functions, stored in
data structures, or let-bound.
First-class control makes the control state of the program available
as a first-class value known as a continuation object at any point
during evaluation~\cite{FriedmanHK84}. This object comes equipped with
at least one operation for restoring the control state. As such the
control flow of the program becomes a first-class entity that the
programmer may manipulate to implement interesting control phenomena.
From the perspective of programmers first-class control is a valuable
programming feature because it enables them to implement their own
control idioms as if they were native to the programming language (in
fact this is the very definition of first-class control). More
important, with first-class control programmer-defined control idioms
are local phenomena which can be encapsulated in a library such that
the rest of the program does not need to be made aware of their
existence. Conversely, without first-class control some control idioms
can only be implemented using global program restructuring techniques
such as continuation passing style.
control idioms, such as async/await~\cite{SymePL11}, as if they were
native to the programming language. More important, with first-class
control programmer-defined control idioms are local phenomena which
can be encapsulated in a library such that the rest of the program
does not need to be made aware of their existence. Conversely, without
first-class control some control idioms can only be implemented using
global program restructuring techniques such as continuation passing
style.
From the perspective of compiler engineers first-class control is
valuable because it unifies several control-related constructs under
@ -678,9 +695,12 @@ intended purpose.
In contrast, effect handlers provide a structured form of delimited
control, where programmers can give distinct names to control reifying
operations and separate the from their handling.
operations and separate them from their handling. Throughout this
dissertation we will see numerous examples of how effect handlers
makes programming with delimited structured (c.f. the following
section, Chapter~\ref{ch:continuations}, and
Chapter~\ref{ch:unary-handlers}).
%
\dhil{Maybe expand this a bit more to really sell it}
\section{State of effectful programming}
\label{sec:state-of-effprog}
@ -690,7 +710,8 @@ boxes, whose outputs are determined entirely by their
inputs~\cite{Hughes89,Howard80}. This is a compelling view which
admits a canonical mathematical model of
computation~\cite{Church32,Church41}. Alas, this view does not capture
the reality of practical programs, which interact their environment.
the reality of practical programs, which interact with their
environment.
%
Functional programming prominently features two distinct, but related,
approaches to effectful programming, which \citet{Filinski96}
@ -705,11 +726,11 @@ style~\cite{JonesW93}. The latter retains the usual direct style of
programming either by hard-wiring the semantics of the effects into
the language or by more flexible means via first-class control.
In this section I will provide a brief programming perspective on
different approaches to programming with effects along with an
informal introduction to the related concepts. We will look at each
approach through the lens of global mutable state --- which is the
``hello world'' example of effectful programming.
In this section I will provide a brief perspective on different
approaches to programming with effects along with an informal
introduction to the related concepts. We will look at each approach
through the lens of global mutable state --- the ``hello world'' of
effectful programming.
% how
% effectful programming has evolved as well as providing an informal
@ -730,9 +751,9 @@ approach through the lens of global mutable state --- which is the
%
We can realise stateful behaviour by either using language-supported
state primitives, globally structure our program to follow a certain
style, or use first-class control in the form of delimited control to
simulate state. We do not consider undelimited control, because it is
insufficient to express mutable state~\cite{FriedmanS00}.
style, or using first-class control in the form of delimited control
to simulate state. We do not consider undelimited control, because it
is insufficient to express mutable state~\cite{FriedmanS00}.
% Programming in its infancy was effectful as the idea of first-class
% control was conceived already during the design of the programming
% language Algol~\cite{BackusBGKMPRSVWWW60} -- one of the early
@ -777,13 +798,14 @@ It is common to find mutable state builtin into the semantics of
mainstream programming languages. However, different languages vary in
their approach to mutable state. For instance, state mutation
underpins the foundations of imperative programming languages
belonging to the C family of languages. They do typically not
belonging to the C family of languages. They typically do not
distinguish between mutable and immutable values at the level of
types. Contrary, programming languages belonging to the ML family of
languages use types to differentiate between mutable and immutable
values. They reflect mutable values in types by using a special unary
type constructor $\PCFRef^{\Type \to \Type}$. Furthermore, ML
languages equip the $\PCFRef$ constructor with three operations.
types. On the contrary, programming languages belonging to the ML
family of languages use types to differentiate between mutable and
immutable values. They reflect mutable values in types by using a
special unary type constructor $\PCFRef^{\Type \to
\Type}$. Furthermore, ML languages equip the $\PCFRef$ constructor
with three operations.
%
\[
\refv : S \to \PCFRef~S \qquad\quad
@ -815,7 +837,7 @@ The body of the function first retrieves the current value of the
state cell and binds it to $st$. Subsequently, it destructively
increments the value of the state cell. Finally, it applies the
predicate $\even : \Int \to \Bool$ to the original state value to test
whether its parity is even (remark: this example function is a slight
whether its parity is even (this example function is a slight
variation of an example by \citet{Gibbons12}).
%
We can run this computation as a subcomputation in the context of
@ -913,8 +935,9 @@ represents the continuation of the invocation of $\shift$ (up to the
innermost reset); it gets passed as a function to the argument of
$\shift$.
Both primitives are defined over some (globally) fixed result type
$R$.
We define both primitives over some fixed return type $R$ (an actual
practical implementation would use polymorphism to make them more
flexible).
%
By instantiating $R = S \to A \times S$, where $S$ is the type of
state and $A$ is the type of return values, then we can use shift and
@ -970,11 +993,12 @@ Modulo naming of operations, this version is similar to the version
that uses builtin state. The type signature of the function is even
the same.
%
Before we can apply this function we must first a state initialiser.
Before we can apply this function we must first implement a state
initialiser.
%
\[
\bl
\runState : (\UnitType \to R) \to S \to R \times S\\
\runState : (\UnitType \to A) \to S \to A \times S\\
\runState~m~st_0 \defas \reset{\lambda\Unit.\Let\;x \revto m\,\Unit\;\In\;\lambda st. \Record{x;st}}\,st_0
\bl
\el
@ -994,7 +1018,7 @@ the state-accepting function returned by the reset instance. The
application of the reset instance to $st_0$ effectively causes
evaluation of each function in this chain to start.
After instantiating $R = \Bool$ and $S = \Int$ we can use the
After instantiating $A = \Bool$ and $S = \Int$ we can use the
$\runState$ function to apply the $\incrEven$ function.
%
\[
@ -1056,8 +1080,8 @@ Haskell~\cite{JonesABBBFHHHHJJLMPRRW99}.
\el
\]
%
Interactions between $\Return$ and $\bind$ are governed by the
so-called `monad laws'.
Interactions between $\Return$ and $\bind$ are governed by the monad
laws.
\begin{reductions}
\slab{Left\textrm{ }identity} & \Return\;x \bind k &=& k~x\\
\slab{Right\textrm{ }identity} & m \bind \Return &=& m\\
@ -1397,7 +1421,7 @@ operation is another computation tree node.
%
\[
\bl
\ba{@{~}l@{\qquad}@{~}r}
\ba{@{~}l@{\,\quad}@{~}r}
\multicolumn{2}{l}{T~A \defas \Free~F~A} \smallskip\\
\multirow{2}{*}{
\bl
@ -1894,10 +1918,13 @@ polymorphic $\lambda$-calculi for which I give computational
interpretations in terms of contextual operational semantics and
realise using two foundational operational techniques: continuation
passing style and abstract machine semantics. When it comes to
expressivity studies there are multiple complementary notions of
expressiveness available in the literature; in this dissertation I
work with typed macro-expressiveness and type-respecting
expressiveness notions.
expressiveness there are multiple possible dimensions to investigate
and multiple different notions of expressivity available. I focus on
two questions: `are deep, shallow, and parameterised handlers
interdefinable?' which I investigate via a syntactic notion of
expressiveness due \citet{Felleisen91}. And, `does effect handlers
admit any essential computational efficiency?' which I investigate
using a semantic notion of expressiveness due to \citet{LongleyN15}.
\subsection{Scope extrusion}
The literature on effect handlers is rich, and my dissertation is but
@ -1941,8 +1968,11 @@ theory of scoped effect operations, whilst \citet{BiernackiPPS20}
study them in conjunction with ordinary handlers from a programming
perspective.
% \citet{WuSH14} study scoped effects, which are effects whose payloads
% are effectful computations
% \citet{WuSH14} study scoped effects, which are effects whose
% payloads are effectful computations. Scoped effects are
% non-algebraic, Thinking in terms of computation trees, a scoped
% effect is not an internal node of some computation tree, rather, it
% is itself a whole computation tree.
% Effect handlers were conceived in the realm of category theory to give
% an algebraic treatment of exception handling~\cite{PlotkinP09}. They
@ -1963,9 +1993,9 @@ handlers extension to Prolog; and \citet{Leijen17b} has an imperative
take on effect handlers in C.
\section{Contributions}
The key contributions of this dissertation are scattered across the
four main parts. The following listing summarises the contributions of
each part.
The key contributions of this dissertation are spread across the four
main parts. The following listing summarises the contributions of each
part.
\paragraph{Background}
\begin{itemize}
\item A comprehensive operational characterisation of various
@ -2010,35 +2040,40 @@ The following is a summary of the chapters belonging to each part of
this dissertation.
\paragraph{Background}
Chapter~\ref{ch:maths-prep} defines some basic mathematical
\begin{itemize}
\item Chapter~\ref{ch:maths-prep} defines some basic mathematical
notation and constructions that are they pervasively throughout this
dissertation.
Chapter~\ref{ch:continuations} presents a literature survey of
\item Chapter~\ref{ch:continuations} presents a literature survey of
continuations and first-class control. I classify continuations
according to their operational behaviour and provide an overview of
the various first-class sequential control operators that appear in
the literature. The application spectrum of continuations is discussed
as well as implementation strategies for first-class control.
\end{itemize}
\paragraph{Programming}
Chapter~\ref{ch:base-language} introduces a polymorphic fine-grain
\begin{itemize}
\item Chapter~\ref{ch:base-language} introduces a polymorphic fine-grain
call-by-value core calculus, $\BCalc$, which makes key use of
\citeauthor{Remy93}-style row polymorphism to implement polymorphic
variants, structural records, and a structural effect system. The
calculus distils the essence of the core of the Links programming
language.
Chapter~\ref{ch:unary-handlers} presents three extensions of $\BCalc$,
\item Chapter~\ref{ch:unary-handlers} presents three extensions of $\BCalc$,
which are $\HCalc$ that adds deep handlers, $\SCalc$ that adds shallow
handlers, and $\HPCalc$ that adds parameterised handlers. The chapter
also contains a running case study that demonstrates effect handler
oriented programming in practice by implementing a small operating
system dubbed \OSname{} based on \citeauthor{RitchieT74}'s original
\UNIX{}.
\end{itemize}
\paragraph{Implementation}
Chapter~\ref{ch:cps} develops a higher-order continuation passing
\begin{itemize}
\item Chapter~\ref{ch:cps} develops a higher-order continuation passing
style translation for effect handlers through a series of step-wise
refinements of an initial standard continuation passing style
translation for $\BCalc$. Each refinement slightly modifies the notion
@ -2047,18 +2082,20 @@ ultimately leads to the key invention of generalised continuation,
which is used to give a continuation passing style semantics to deep,
shallow, and parameterised handlers.
Chapter~\ref{ch:abstract-machine} demonstrates an application of
\item Chapter~\ref{ch:abstract-machine} demonstrates an application of
generalised continuations to abstract machine as we plug generalised
continuations into \citeauthor{FelleisenF86}'s CEK machine to obtain
an adequate abstract runtime with simultaneous support for deep,
shallow, and parameterised handlers.
\end{itemize}
\paragraph{Expressiveness}
Chapter~\ref{ch:deep-vs-shallow} shows that deep, shallow, and
\begin{itemize}
\item Chapter~\ref{ch:deep-vs-shallow} shows that deep, shallow, and
parameterised notions of handlers can simulate one another up to
specific notions of administrative reduction.
Chapter~\ref{ch:handlers-efficiency} studies the fundamental efficiency of effect
\item Chapter~\ref{ch:handlers-efficiency} studies the fundamental efficiency of effect
handlers. In this chapter, we show that effect handlers enable an
asymptotic improvement in runtime complexity for a certain class of
functions. Specifically, we consider the \emph{generic count} problem
@ -2068,9 +2105,12 @@ of $\BCalc$) and its extension with effect handlers $\HPCF$.
We show that $\HPCF$ admits an asymptotically more efficient
implementation of generic count than any $\BPCF$ implementation.
%
\end{itemize}
\paragraph{Conclusions}
Chapter~\ref{ch:conclusions} concludes and discusses future work.
\begin{itemize}
\item Chapter~\ref{ch:conclusions} concludes and discusses future work.
\end{itemize}
\part{Background}
@ -15114,8 +15154,9 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
% By case analysis on $\reducesto$ and induction on $\approxa$ using
% Lemma~\ref{lem:sdtrans-subst} and Lemma~\ref{lem:sdtrans-admin}.
%
By induction on $M' \approxa \sdtrans{M}$ and side induction on
$M \reducesto N$ using Lemma~\ref{lem:sdtrans-subst} and Lemma~\ref{lem:sdtrans-admin}.
By induction on $M' \approxa \sdtrans{M}$ and case analysis on
$M \reducesto N$ using Lemma~\ref{lem:sdtrans-subst} and
Lemma~\ref{lem:sdtrans-admin}.
%
The interesting case is reflexivity of $\approxa$ where
$M \reducesto N$ is an application of $\semlab{Op^\dagger}$, which

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