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phd-dissertation
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Time-sharing code.

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Daniel Hillerström 5 years ago
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  1. 16
      macros.tex
  2. 107
      thesis.tex

16
macros.tex
View File

@ -353,4 +353,18 @@
\newcommand{\whoami}{\dec{whoami}}
\newcommand{\Su}{\dec{Su}}
\newcommand{\su}{\dec{su}}
\newcommand{\sessionmgr}{\dec{sessionmgr}}
\newcommand{\sessionmgr}{\dec{sessionmgr}}
\newcommand{\echo}{\dec{echo}}
\newcommand{\strlit}[1]{\texttt{"#1"}}
\newcommand{\nondet}{\dec{nondet}}
\newcommand{\Fork}{\dec{Fork}}
\newcommand{\fork}{\dec{fork}}
\newcommand{\Interrupt}{\dec{Interrupt}}
\newcommand{\interrupt}{\dec{interrupt}}
\newcommand{\Pstate}{\dec{Pstate}}
\newcommand{\Done}{\dec{Done}}
\newcommand{\Suspended}{\dec{Paused}}
\newcommand{\slice}{\dec{slice}}
\newcommand{\timeshare}{\dec{timeshare}}
\newcommand{\runNext}{\dec{runNext}}
\newcommand{\concatMap}{\dec{concatMap}}

107
thesis.tex
View File

@ -22,6 +22,7 @@
\DeclareCaptionFormat{underlinedfigure}{#1#2#3\hrulefill}
\captionsetup[figure]{format=underlinedfigure}
\usepackage[T1]{fontenc} % Fixes issues with accented characters
\usepackage[scaled=0.85]{beramono}
%\usepackage{libertine}
%\usepackage{lmodern}
%\usepackage{palatino}
@ -2044,7 +2045,7 @@ Section~\ref{sec:tiny-unix-io}.
Much like UNIX we shall model a file as a list of characters, that is
$\UFile \defas \List~\Char$. For convenience we will use the same
model for strings, $\String \defas \List~\Char$, such that we can use
string literal notation to denote the $\texttt{"contents of a file"}$.
string literal notation to denote the $\strlit{contents of a file}$.
%
The signature of the basic file system will consist of a single
operation $\Putc$ for writing a single character to the file.
@ -2087,7 +2088,7 @@ 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.
$\basicIO\,(\lambda\Unit.\Unit) \reducesto^+
\Record{\Unit;\texttt{""}}$.
\Record{\Unit;\strlit{}}$.
%
The $\Putc$-case extends the file by first invoking the resumption,
whose return type is the same as the handler's return type, thus it
@ -2101,20 +2102,20 @@ file.
%
\[
\bl
\fwrite : \Record{\UFD;\String} \to \UnitType \eff \{\Putc : \Record{\UFD;\Char} \opto \UnitType\}\\
\fwrite~\Record{fd;cs} \defas \iter\,(\lambda c.\Do\;\Putc\,\Record{fd;c})\,cs
\echo : \String \to \UnitType \eff \{\Putc : \Record{\UFD;\Char} \opto \UnitType\}\\
\echo~cs \defas \iter\,(\lambda c.\Do\;\Putc\,\Record{\stdout;c})\,cs
\el
\]
%
The function $\fwrite$ invokes the operation $\Putc$ point-wise on the
The function $\echo$ invokes the operation $\Putc$ point-wise on the
list of characters $cs$ by using the list iteration function $\iter$.
%
We can now write some contents to the file and observe the effects.
%
\[
\ba{@{~}l@{~}l}
&\basicIO\,(\lambda\Unit. \fwrite\,\Record{\stdout;\texttt{"Hello"}}; \fwrite\,\Record{\stdout;\texttt{"World"}})\\
\reducesto^+& \Record{\Unit;\texttt{"HelloWorld"}} : \Record{\UnitType;\UFile}
&\basicIO\,(\lambda\Unit. \echo~\strlit{Hello}; \echo~\strlit{World})\\
\reducesto^+& \Record{\Unit;\strlit{HelloWorld}} : \Record{\UnitType;\UFile}
\ea
\]
@ -2151,9 +2152,9 @@ We can now write some contents to the file and observe the effects.
&\bl
\basicIO\,(\lambda\Unit.
\status\,(\lambda\Unit.
\fwrite\,\Record{\stdout;\texttt{"dead"}};\exit~1;\fwrite\,\Record{\stdout;\texttt{"code"}}))
\echo~\strlit{dead};\exit~1;\echo~\strlit{code}))
\el\\
\reducesto^+& \Record{1;\texttt{"dead"}} : \Record{\Int;\UFile}
\reducesto^+& \Record{1;\strlit{dead}} : \Record{\Int;\UFile}
\ea
\]
@ -2216,9 +2217,9 @@ The following handler implements the environment.
\bl
\Case\;user\,\{
\ba[t]{@{}l@{~}c@{~}l}
\Alice &\mapsto& resume~\texttt{"alice"}\\
\Bob &\mapsto& resume~\texttt{"bob"}\\
\Root &\mapsto& resume~\texttt{"root"}\}
\Alice &\mapsto& resume~\strlit{alice}\\
\Bob &\mapsto& resume~\strlit{bob}\\
\Root &\mapsto& resume~\strlit{root}\}
\ea
\el
\ea
@ -2233,7 +2234,7 @@ string representation of the user. With this implementation we can
interpret an application of $\whoami$.
%
\[
\environment~\Record{\Root;\whoami} \reducesto^+ \texttt{"root"} : \String
\environment~\Record{\Root;\whoami} \reducesto^+ \strlit{root} : \String
\]
%
It is not difficult to extend this basic environment model to support
@ -2279,17 +2280,89 @@ string.
\qquad\sessionmgr\,\Record{\Root;\lambda\Unit.\\
\qquad\qquad\status\,(\lambda\Unit.
\ba[t]{@{}l@{~}l}
\su~\Alice;&\fwrite\,\Record{\stdout;\whoami\,\Unit};~\fwrite\,\Record{\stdout;\texttt{" "}};\\
\su~\Bob;&\fwrite\,\Record{\stdout;\whoami\,\Unit};~\fwrite\,\Record{\stdout;\texttt{" "}};\\
\su~\Root;&\fwrite\,\Record{\stdout;\whoami\,\Unit})})
\su~\Alice;&\echo\,(\whoami\,\Unit);~\echo~\strlit{ };\\
\su~\Bob; &\echo\,(\whoami\,\Unit);~\echo~\strlit{ };\\
\su~\Root; &\echo\,(\whoami\,\Unit))})
\ea
\el \smallskip\\
\reducesto^+& \Record{0;\texttt{"alice bob root"}} : \Record{\Int;\UFile}
\reducesto^+& \Record{0;\strlit{alice bob root}} : \Record{\Int;\UFile}
\ea
\]
\subsection{Nondeterminism: time sharing}
\label{sec:tiny-unix-time}
\[
\bl
\fork : \UnitType \to \Bool \eff \{\Fork : \UnitType \opto \Bool\}\\
\fork~\Unit \defas \Do\;\Fork~\Unit
\el
\]
\[
\bl
\nondet : (\UnitType \to \alpha \eff \{\Fork:\UnitType \opto \Bool\}) \to \List~\alpha\\
\nondet~m \defas
\ba[t]{@{}l}
\Handle\;m\,\Unit\;\With\\
~\ba{@{~}l@{~}c@{~}l}
\Return\;res &\mapsto& [res]\\
\Fork~\Unit~resume &\mapsto& resume~\True \concat resume~\False
\ea
\ea
\el
\]
\[
\bl
\interrupt : \UnitType \to \UnitType \eff \{\Interrupt : \UnitType \opto \UnitType\}\\
\interrupt~\Unit \defas \Do\;\Interrupt~\Unit
\el
\]
\[
\Pstate~\alpha~\varepsilon \defas \forall \theta.
\ba[t]{@{}l@{}l}
[&\Done:\alpha;\\
&\Suspended:\UnitType \to \Pstate~\alpha~\varepsilon \eff \{\Interrupt:\theta';\varepsilon\} ]
\ea
\]
\[
\bl
\slice : (\UnitType \to \alpha \eff \{\Interrupt:\UnitType \opto \UnitType;\varepsilon\}) \to \Pstate~\alpha~\varepsilon\\
\slice~m \defas
\ba[t]{@{}l}
\Handle\;m\,\Unit\;\With\\
~\ba{@{~}l@{~}c@{~}l}
\Return\;res &\mapsto& \Done~res\\
\Interrupt~\Unit~resume &\mapsto& \Suspended~resume
\ea
\ea
\el
\]
\[
\bl
\runNext : \List~(\Pstate~\alpha~\{\Fork:\Bool;\varepsilon\}) \to \List~\alpha \eff \varepsilon\\
\runNext~ps \defas
\concatMap\,(\lambda p.
\ba[t]{@{}l}
\Case\;p\;\{
\ba[t]{@{}l@{~}c@{~}l}
\Done~res &\mapsto& [res]\\
\Suspended~m &\mapsto& \runNext\,(\nondet~m) \})\,ps
\ea
\ea
\el
\]
\[
\bl
\timeshare : (\UnitType \to \alpha \eff \{\Fork:\UnitType \opto \Bool;\Interrupt:\UnitType \opto \UnitType;\epsilon\}) \to (\List~\alpha) \eff \epsilon\\
\timeshare~m \defas \runNext\,[\Suspended\,(\lambda\Unit.\slice~m)]
\el
\]
\subsection{State: file i/o}
\label{sec:tiny-unix-io}

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