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Exceptions example and figures.

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Daniel Hillerström
2020-10-07 16:51:08 +01:00
parent d30ffb2a39
commit 39824fcf18
2 changed files with 86 additions and 34 deletions
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1
macros.tex
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@@ -348,6 +348,7 @@
\newcommand{\iter}{\dec{iter}} \newcommand{\iter}{\dec{iter}}
\newcommand{\stdout}{\dec{stdout}} \newcommand{\stdout}{\dec{stdout}}
\newcommand{\IO}{\dec{IO}} \newcommand{\IO}{\dec{IO}}
\newcommand{\BIO}{\dec{BIO}}
\newcommand{\Alice}{\dec{Alice}} \newcommand{\Alice}{\dec{Alice}}
\newcommand{\Bob}{\dec{Bob}} \newcommand{\Bob}{\dec{Bob}}
\newcommand{\Root}{\dec{Root}} \newcommand{\Root}{\dec{Root}}

119
thesis.tex
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@@ -2051,10 +2051,10 @@ model for strings, $\String \defas \List~\Char$, such that we can use
string literal notation to denote the $\strlit{contents of a file}$. string literal notation to denote the $\strlit{contents of a file}$.
% %
The signature of the basic file system will consist of a single The signature of the basic file system will consist of a single
operation $\Putc$ for writing a single character to the file. operation $\Write$ for writing a list of characters to the file.
% %
\[ \[
\IO \defas \{\Putc : \Record{\UFD;\Char} \opto \UnitType\} \BIO \defas \{\Write : \Record{\UFD;\String} \opto \UnitType\}
\] \]
% %
The operation is parameterised by a file descriptor ($\UFD$) and a The operation is parameterised by a file descriptor ($\UFD$) and a
@@ -2067,51 +2067,52 @@ Let us define a suitable handler for this operation.
% %
\[ \[
\bl \bl
\basicIO : (\UnitType \to \alpha \eff \IO) \to \Record{\alpha; \UFile}\\ \basicIO : (\UnitType \to \alpha \eff \BIO) \to \Record{\alpha; \UFile}\\
\basicIO~m \defas \basicIO~m \defas
\ba[t]{@{~}l} \ba[t]{@{~}l}
\Handle\;m\,\Unit\;\With\\ \Handle\;m\,\Unit\;\With\\
~\ba{@{~}l@{~}c@{~}l} ~\ba{@{~}l@{~}c@{~}l}
\Return\;res &\mapsto& \Record{res;\nil}\\ \Return\;res &\mapsto& \Record{res;\nil}\\
\OpCase{\Putc}{\Record{\_;c}}{resume} &\mapsto& \OpCase{\Write}{\Record{\_;cs}}{resume} &\mapsto&
\Let\; \Record{res;file} = resume\,\Unit\;\In\; \ba[t]{@{}l}
\Record{res; c \cons file} \Let\; \Record{res;file} = resume\,\Unit\;\In\\
\Record{res; cs \concat file}
\ea
\ea \ea
\ea \ea
\el \el
\] \]
% %
The handler takes as input a computation that produces some value The handler takes as input a computation that produces some value
$\alpha$, and in doing so may perform the $\IO$ effect. $\alpha$, and in doing so may perform the $\BIO$ effect.
% %
The handler ultimately returns a pair consisting of the return value The handler ultimately returns a pair consisting of the return value
$\alpha$ and the final state of the file. $\alpha$ and the final state of the file.
% %
The $\Return$-case pairs the result $res$ with the empty file $\nil$ The $\Return$-case pairs the result $res$ with the empty file $\nil$
which models the scenario where the computation $m$ performed no which models the scenario where the computation $m$ performed no
$\Putc$-operations, e.g. $\Write$-operations, e.g.
$\basicIO\,(\lambda\Unit.\Unit) \reducesto^+ $\basicIO\,(\lambda\Unit.\Unit) \reducesto^+
\Record{\Unit;\strlit{}}$. \Record{\Unit;\strlit{}}$.
% %
The $\Putc$-case extends the file by first invoking the resumption, The $\Write$-case extends the file by first invoking the resumption,
whose return type is the same as the handler's return type, thus it whose return type is the same as the handler's return type, thus it
returns a pair containing the result of $m$ and the file state. The returns a pair containing the result of $m$ and the file state. The
file gets extended with the character $c$ before it is returned along file gets extended with the character sequence $cs$ before it is
with the original result of $m$. The file is effectively built bottom returned along with the original result of $m$.% The file is
up starting with the last character. % effectively built bottom up starting with the last character.
Let us define an auxiliary function that writes a string to a given Let us define an auxiliary function that writes a string to the $\stdout$ file.
file.
% %
\[ \[
\bl \bl
\echo : \String \to \UnitType \eff \{\Putc : \Record{\UFD;\Char} \opto \UnitType\}\\ \echo : \String \to \UnitType \eff\, \BIO\\%\{\Write : \Record{\UFD;\String} \opto \UnitType\}\\
\echo~cs \defas \iter\,(\lambda c.\Do\;\Putc\,\Record{\stdout;c})\,cs \echo~cs \defas \Do\;\Write\,\Record{\stdout;cs}
\el \el
\] \]
% %
The function $\echo$ invokes the operation $\Putc$ point-wise on the The function $\echo$ is a simple wrapper around an invocation of
list of characters $cs$ by using the list iteration function $\iter$. $\Write$.
% %
We can now write some contents to the file and observe the effects. We can now write some contents to the file and observe the effects.
% %
@@ -2125,17 +2126,44 @@ We can now write some contents to the file and observe the effects.
\subsection{Exceptions: non-local exits} \subsection{Exceptions: non-local exits}
\label{sec:tiny-unix-exit} \label{sec:tiny-unix-exit}
A process may terminate successfully by running to completion, or it
may terminate with success or failure in the middle of some
computation by performing an \emph{exit} system call. The exit system
call is typically parameterised by an integer value intended to
indicate whether the exit was due to success or failure. By
convention, \UNIX{} interprets the integer zero as success and any
nonzero integer as failure, where the specific value is supposed to
correspond to some known error code.
%
We can model the exit system call by way of a single operation
$\Exit$.
%
\[ \[
\Status \defas \{\Exit : \Int \opto \Zero\} \Status \defas \{\Exit : \Int \opto \Zero\}
\] \]
%
The operation is parameterised by an integer value, however, an
invocation of $\Exit$ can never return, because the type $\Zero$ is
uninhabited. Thus $\Exit$ acts like an exception.
%
It is convenient to abstract invocations of $\Exit$ to make it
possible to invoke the operation in any context.
%
\[ \[
\bl \bl
\exit : \Int \to \alpha \eff \Status\\ \exit : \Int \to \alpha \eff \Status\\
\exit~n \defas \Absurd\;(\Do\;\Exit~n) \exit~n \defas \Absurd\;(\Do\;\Exit~n)
\el \el
\] \]
%
The $\Absurd$ computation term is used to coerce the return type
$\Zero$ of $\Fail$ into $\alpha$. This coercion is safe, because
$\Zero$ is an uninhabited type.
%
An interpretation of $\Fail$ amounts to implementing an exception
handler.
%
\[ \[
\bl \bl
\status : (\UnitType \to \alpha \eff \Status) \to \Int\\ \status : (\UnitType \to \alpha \eff \Status) \to \Int\\
@@ -2149,7 +2177,17 @@ We can now write some contents to the file and observe the effects.
\ea \ea
\el \el
\] \]
%
Following the \UNIX{} convention, the $\Return$-case interprets a
successful completion of $m$ as the integer $0$. The operation case
returns whatever payload the $\Exit$ operation was carrying. As a
consequence, outside of $\status$, an invocation of $\Exit~0$ in $m$
is indistinguishable from $m$ returning normally, e.g.
$\status\,(\lambda\Unit.\exit~0) = \status\,(\lambda\Unit.\Unit)$.
To illustrate $\status$ and $\exit$ in action consider the following
example, where the computation gets terminated mid-way.
%
\[ \[
\ba{@{~}l@{~}l} \ba{@{~}l@{~}l}
&\bl &\bl
@@ -2160,6 +2198,8 @@ We can now write some contents to the file and observe the effects.
\reducesto^+& \Record{1;\strlit{dead}} : \Record{\Int;\UFile} \reducesto^+& \Record{1;\strlit{dead}} : \Record{\Int;\UFile}
\ea \ea
\] \]
%
The (delimited) continuation of $\exit~1$ is effectively dead code.
\subsection{Dynamic binding: user-specific environments} \subsection{Dynamic binding: user-specific environments}
\label{sec:tiny-unix-env} \label{sec:tiny-unix-env}
@@ -2315,6 +2355,8 @@ string.
\el \el
\] \]
\dhil{This is an instance of non-blind backtracking}
\[ \[
\bl \bl
\interrupt : \UnitType \to \UnitType \eff \{\Interrupt : \UnitType \opto \UnitType\}\\ \interrupt : \UnitType \to \UnitType \eff \{\Interrupt : \UnitType \opto \UnitType\}\\
@@ -2377,15 +2419,15 @@ string.
\hline \hline
\strlit{hamlet}\tikzmark{hamlet}\\ \strlit{hamlet}\tikzmark{hamlet}\\
\hline \hline
\strlit{ritchie.txt}\\ \strlit{ritchie.txt}\tikzmark{ritchie}\\
\hline \hline
\multicolumn{1}{| c |}{$\cdots$}\\ \multicolumn{1}{| c |}{$\cdots$}\\
\hline \hline
\strlit{act3}\\ \strlit{stdout}\tikzmark{stdout}\\
\hline \hline
\multicolumn{1}{| c |}{$\cdots$}\\ \multicolumn{1}{| c |}{$\cdots$}\\
\hline \hline
\strlit{stdout}\\ \strlit{act3}\tikzmark{act3}\\
\hline \hline
\end{tabular} \end{tabular}
\hspace{1.5cm} \hspace{1.5cm}
@@ -2393,13 +2435,13 @@ string.
\hline \hline
\multicolumn{1}{| c |}{\textbf{I-List}} \\ \multicolumn{1}{| c |}{\textbf{I-List}} \\
\hline \hline
2\\ 1\tikzmark{ritchieino}\\
\hline \hline
1\tikzmark{hamletino}\\ 2\tikzmark{hamletino}\\
\hline \hline
\multicolumn{1}{| c |}{$\cdots$}\\ \multicolumn{1}{| c |}{$\cdots$}\\
\hline \hline
1\\ 1\tikzmark{stdoutino}\\
\hline \hline
\end{tabular} \end{tabular}
\hspace{1.5cm} \hspace{1.5cm}
@@ -2407,18 +2449,27 @@ string.
\hline \hline
\multicolumn{1}{| c |}{\textbf{Data region}} \\ \multicolumn{1}{| c |}{\textbf{Data region}} \\
\hline \hline
\strlit{UNIX is basically...}\\ \tikzmark{stdoutdr}\strlit{}\\
\hline \hline
\tikzmark{hamletdr}\strlit{To be, or not to be...}\\ \tikzmark{hamletdr}\strlit{To be, or not to be...}\\
\hline \hline
\multicolumn{1}{| c |}{$\cdots$}\\ \multicolumn{1}{| c |}{$\cdots$}\\
\hline \hline
\strlit{}\\ \tikzmark{ritchiedr}\strlit{UNIX is basically...}\\
\hline \hline
\end{tabular} \end{tabular}
\tikz[remember picture,overlay]\draw[->,thick] ([xshift=1.3cm,yshift=0.1cm]pic cs:hamlet) -- ([xshift=-0.85cm,yshift=0.1cm]pic cs:hamletino) node[] {}; %% Hamlet arrows.
\tikz[remember picture,overlay]\draw[->,thick] ([xshift=0.62cm,yshift=0.1cm]pic cs:hamletino) -- ([xshift=-0.23cm,yshift=0.1cm]pic cs:hamletdr) node[] {}; \tikz[remember picture,overlay]\draw[->,thick,out=30,in=160] ([xshift=1.3cm,yshift=0.1cm]pic cs:hamlet) to ([xshift=-0.85cm,yshift=0.1cm]pic cs:hamletino) node[] {};
\caption{\UNIX{} directory, i-list, and data region mappings}\label{fig:unix-mappings} \tikz[remember picture,overlay]\draw[->,thick,out=30,in=180] ([xshift=0.62cm,yshift=0.1cm]pic cs:hamletino) to ([xshift=-0.23cm,yshift=0.1cm]pic cs:hamletdr) node[] {};
%% Ritchie arrows.
\tikz[remember picture,overlay]\draw[->,thick,out=-30,in=180] ([xshift=0.22cm,yshift=0.1cm]pic cs:ritchie) to ([xshift=-0.85cm,yshift=0.1cm]pic cs:ritchieino) node[] {};
\tikz[remember picture,overlay]\draw[->,thick,out=30,in=180] ([xshift=0.62cm,yshift=0.1cm]pic cs:ritchieino) to ([xshift=-0.23cm,yshift=0.1cm]pic cs:ritchiedr) node[] {};
%% Act3 arrow.
\tikz[remember picture,overlay]\draw[->,thick,out=10,in=210] ([xshift=1.73cm,yshift=0.1cm]pic cs:act3) to ([xshift=-0.85cm,yshift=-0.5mm]pic cs:hamletino) node[] {};
%% Stdout arrows.
\tikz[remember picture,overlay]\draw[->,thick,out=30,in=180] ([xshift=1.3cm,yshift=0.1cm]pic cs:stdout) to ([xshift=-0.85cm,yshift=0.1cm]pic cs:stdoutino) node[] {};
\tikz[remember picture,overlay]\draw[->,thick,out=30,in=180] ([xshift=0.62cm,yshift=0.1cm]pic cs:stdoutino) to ([xshift=-0.23cm,yshift=0.1cm]pic cs:stdoutdr) node[] {};
\caption{\UNIX{} directory, i-list, and data region mappings.}\label{fig:unix-mappings}
\end{figure} \end{figure}
@@ -2465,9 +2516,9 @@ string.
% %
\draw (client) -- (client_ground); \draw (client) -- (client_ground);
\draw (server) -- (server_ground); \draw (server) -- (server_ground);
\draw[->] ($(client)!0.25!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{SYN 42} ($(server)!0.40!(server_ground)$); \draw[->,thick] ($(client)!0.25!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{SYN 42} ($(server)!0.40!(server_ground)$);
\draw[<-] ($(client)!0.56!(client_ground)$) -- node[rotate=6,above,scale=0.7,midway]{SYN 84;ACK 43} ($(server)!0.41!(server_ground)$); \draw[<-,thick] ($(client)!0.56!(client_ground)$) -- node[rotate=6,above,scale=0.7,midway]{SYN 84;ACK 43} ($(server)!0.41!(server_ground)$);
\draw[->] ($(client)!0.57!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{ACK 44} ($(server)!0.72!(server_ground)$); \draw[->,thick] ($(client)!0.57!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{ACK 85} ($(server)!0.72!(server_ground)$);
\end{tikzpicture} \end{tikzpicture}
\caption{Sequence diagram for the TCP handshake example.}\label{fig:tcp-handshake} \caption{Sequence diagram for the TCP handshake example.}\label{fig:tcp-handshake}
\end{figure} \end{figure}