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Exceptions example and figures.

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Daniel Hillerström 5 years ago
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  1. 1
      macros.tex
  2. 119
      thesis.tex

1
macros.tex
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@ -348,6 +348,7 @@
\newcommand{\iter}{\dec{iter}}
\newcommand{\stdout}{\dec{stdout}}
\newcommand{\IO}{\dec{IO}}
\newcommand{\BIO}{\dec{BIO}}
\newcommand{\Alice}{\dec{Alice}}
\newcommand{\Bob}{\dec{Bob}}
\newcommand{\Root}{\dec{Root}}

119
thesis.tex
View File

@ -2051,10 +2051,10 @@ model for strings, $\String \defas \List~\Char$, such that we can use
string literal notation to denote the $\strlit{contents of a file}$.
%
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
@ -2067,51 +2067,52 @@ Let us define a suitable handler for this operation.
%
\[
\bl
\basicIO : (\UnitType \to \alpha \eff \IO) \to \Record{\alpha; \UFile}\\
\basicIO : (\UnitType \to \alpha \eff \BIO) \to \Record{\alpha; \UFile}\\
\basicIO~m \defas
\ba[t]{@{~}l}
\Handle\;m\,\Unit\;\With\\
~\ba{@{~}l@{~}c@{~}l}
\Return\;res &\mapsto& \Record{res;\nil}\\
\OpCase{\Putc}{\Record{\_;c}}{resume} &\mapsto&
\Let\; \Record{res;file} = resume\,\Unit\;\In\;
\Record{res; c \cons file}
\OpCase{\Write}{\Record{\_;cs}}{resume} &\mapsto&
\ba[t]{@{}l}
\Let\; \Record{res;file} = resume\,\Unit\;\In\\
\Record{res; cs \concat file}
\ea
\ea
\ea
\el
\]
%
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
$\alpha$ and the final state of the file.
%
The $\Return$-case pairs the result $res$ with the empty file $\nil$
which models the scenario where the computation $m$ performed no
$\Putc$-operations, e.g.
$\Write$-operations, e.g.
$\basicIO\,(\lambda\Unit.\Unit) \reducesto^+
\Record{\Unit;\strlit{}}$.
%
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
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
with the original result of $m$. The file is effectively built bottom
up starting with the last character.
file gets extended with the character sequence $cs$ before it is
returned along with the original result of $m$.% The file is
% effectively built bottom up starting with the last character.
Let us define an auxiliary function that writes a string to a given
file.
Let us define an auxiliary function that writes a string to the $\stdout$ file.
%
\[
\bl
\echo : \String \to \UnitType \eff \{\Putc : \Record{\UFD;\Char} \opto \UnitType\}\\
\echo~cs \defas \iter\,(\lambda c.\Do\;\Putc\,\Record{\stdout;c})\,cs
\echo : \String \to \UnitType \eff\, \BIO\\%\{\Write : \Record{\UFD;\String} \opto \UnitType\}\\
\echo~cs \defas \Do\;\Write\,\Record{\stdout;cs}
\el
\]
%
The function $\echo$ invokes the operation $\Putc$ point-wise on the
list of characters $cs$ by using the list iteration function $\iter$.
The function $\echo$ is a simple wrapper around an invocation of
$\Write$.
%
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}
\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
$\Exit$.
%
\[
\Status \defas \{\Exit : \Int \opto \Zero\}
\]
%
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.
%
\[
\bl
\exit : \Int \to \alpha \eff \Status\\
\exit~n \defas \Absurd\;(\Do\;\Exit~n)
\el
\]
%
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.
%
\[
\bl
\status : (\UnitType \to \alpha \eff \Status) \to \Int\\
@ -2149,7 +2177,17 @@ We can now write some contents to the file and observe the effects.
\ea
\el
\]
%
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.
%
\[
\ba{@{~}l@{~}l}
&\bl
@ -2160,6 +2198,8 @@ We can now write some contents to the file and observe the effects.
\reducesto^+& \Record{1;\strlit{dead}} : \Record{\Int;\UFile}
\ea
\]
%
The (delimited) continuation of $\exit~1$ is effectively dead code.
\subsection{Dynamic binding: user-specific environments}
\label{sec:tiny-unix-env}
@ -2315,6 +2355,8 @@ string.
\el
\]
\dhil{This is an instance of non-blind backtracking}
\[
\bl
\interrupt : \UnitType \to \UnitType \eff \{\Interrupt : \UnitType \opto \UnitType\}\\
@ -2377,15 +2419,15 @@ string.
\hline
\strlit{hamlet}\tikzmark{hamlet}\\
\hline
\strlit{ritchie.txt}\\
\strlit{ritchie.txt}\tikzmark{ritchie}\\
\hline
\multicolumn{1}{| c |}{$\cdots$}\\
\hline
\strlit{act3}\\
\strlit{stdout}\tikzmark{stdout}\\
\hline
\multicolumn{1}{| c |}{$\cdots$}\\
\hline
\strlit{stdout}\\
\strlit{act3}\tikzmark{act3}\\
\hline
\end{tabular}
\hspace{1.5cm}
@ -2393,13 +2435,13 @@ string.
\hline
\multicolumn{1}{| c |}{\textbf{I-List}} \\
\hline
2\\
1\tikzmark{ritchieino}\\
\hline
1\tikzmark{hamletino}\\
2\tikzmark{hamletino}\\
\hline
\multicolumn{1}{| c |}{$\cdots$}\\
\hline
1\\
1\tikzmark{stdoutino}\\
\hline
\end{tabular}
\hspace{1.5cm}
@ -2407,18 +2449,27 @@ string.
\hline
\multicolumn{1}{| c |}{\textbf{Data region}} \\
\hline
\strlit{UNIX is basically...}\\
\tikzmark{stdoutdr}\strlit{}\\
\hline
\tikzmark{hamletdr}\strlit{To be, or not to be...}\\
\hline
\multicolumn{1}{| c |}{$\cdots$}\\
\hline
\strlit{}\\
\tikzmark{ritchiedr}\strlit{UNIX is basically...}\\
\hline
\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[] {};
\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[] {};
\caption{\UNIX{} directory, i-list, and data region mappings}\label{fig:unix-mappings}
%% Hamlet arrows.
\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[] {};
\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}
@ -2465,9 +2516,9 @@ string.
%
\draw (client) -- (client_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[<-] ($(client)!0.56!(client_ground)$) -- 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] ($(client)!0.25!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{SYN 42} ($(server)!0.40!(server_ground)$);
\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[->,thick] ($(client)!0.57!(client_ground)$) -- node[rotate=-6,above,scale=0.7,midway]{ACK 85} ($(server)!0.72!(server_ground)$);
\end{tikzpicture}
\caption{Sequence diagram for the TCP handshake example.}\label{fig:tcp-handshake}
\end{figure}

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