dhil
/
phd-dissertation
mirror of https://github.com/dhil/phd-dissertation
1
0
Fork 0
Code Issues Releases Wiki Activity
Browse Source

Time-sharing code.

master
Daniel Hillerström 5 years ago
parent
495258cf0b
commit
70ebcde70a
2 changed files with 105 additions and 18 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 14
      macros.tex
  2. 107
      thesis.tex

14
macros.tex
View File

@ -354,3 +354,17 @@
\newcommand{\Su}{\dec{Su}}
\newcommand{\su}{\dec{su}}
\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}

Write Preview
Loading…
Cancel
Save