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phd-dissertation
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File system example code.

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Daniel Hillerström 5 years ago
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  1. 7
      macros.tex
  2. 344
      thesis.tex

7
macros.tex
View File

@ -402,14 +402,19 @@
\newcommand{\INode}{\dec{INode}} \newcommand{\INode}{\dec{INode}}
\newcommand{\IList}{\dec{IList}} \newcommand{\IList}{\dec{IList}}
\newcommand{\fileRW}{\dec{fileRW}} \newcommand{\fileRW}{\dec{fileRW}}
\newcommand{\fileAlloc}{\dec{fileAlloc}}
\newcommand{\fileAlloc}{\dec{fileCO}}
\newcommand{\URead}{\dec{Read}} \newcommand{\URead}{\dec{Read}}
\newcommand{\UWrite}{\dec{Write}} \newcommand{\UWrite}{\dec{Write}}
\newcommand{\UCreate}{\dec{Create}} \newcommand{\UCreate}{\dec{Create}}
\newcommand{\UOpen}{\dec{Open}}
\newcommand{\fread}{\dec{fread}} \newcommand{\fread}{\dec{fread}}
\newcommand{\fcreate}{\dec{fcreate}} \newcommand{\fcreate}{\dec{fcreate}}
\newcommand{\Ucreate}{\dec{create}} \newcommand{\Ucreate}{\dec{create}}
\newcommand{\redirect}{\texttt{>}} \newcommand{\redirect}{\texttt{>}}
\newcommand{\fopen}{\dec{fopen}}
\newcommand{\lookup}{\dec{lookup}}
\newcommand{\modify}{\dec{modify}}
\newcommand{\fileIO}{\dec{fileIO}}
%% %%
%% Some control operators %% Some control operators

344
thesis.tex
View File

@ -3132,9 +3132,9 @@ happens.
Evidently, each write operation has been interleaved, resulting in a Evidently, each write operation has been interleaved, resulting in a
mishmash poetry of Shakespeare and \UNIX{}. mishmash poetry of Shakespeare and \UNIX{}.
% %
To some this may be a shambolic treatment of classical arts, whilst to
others this may be a modern contemporaneous treatment. As the saying
goes: art is in the eye of the beholder.
% To some this may be a shambolic treatment of classical arts, whilst to
% others this may be a modern contemporaneous treatment. As the saying
% goes: art is in the eye of the beholder.
\subsection{State: file i/o} \subsection{State: file i/o}
\label{sec:tiny-unix-io} \label{sec:tiny-unix-io}
@ -3423,13 +3423,116 @@ system.
\] \]
% %
Initially the file system contains a single, empty file with the name Initially the file system contains a single, empty file with the name
$\texttt{stdout}$.
$\texttt{stdout}$. Next we will implement the basic operations on the
file system separately.
\paragraph{File reading and writing} \paragraph{File reading and writing}
% %
Let us begin by giving a semantics to file reading and writing. We
need an abstract operation for each file operation.
%
\[
\dec{FileRW} \defas \{\URead : \Int \opto \Option~\String;\UWrite : \Record{\Int;\String} \opto \UnitType\}
\]
%
The operation $\URead$ is parameterised by an i-node number
(i.e. index into the i-list) and possibly returns the contents of the
file pointed to by the i-node. The operation may fail if it is
provided with a stale i-node number. Thus the option type is used to
signal failure or success to the caller.
%
The $\UWrite$ operation is parameterised by an i-node number and some
strings to be appended onto the file pointed to by the i-node. The
operation returns unit, and thus the operation does not signal to its
caller whether it failed or succeed.
%
Before we implement a handler for the operations, we will implement
primitive read and write operations that operate directly on the file
system. We will use the primitive operations to implement the
semantics for $\URead$ and $\UWrite$. To implement the primitive the
operations we will need two basic functions on association lists. I
will only their signatures here.
%
\[
\bl
\lookup : \Record{\alpha;\List\,\Record{\alpha;\beta}} \to \beta \eff \{\Fail : \UnitType \opto \Zero\} \smallskip\\
\modify : \Record{\alpha;\beta;\List\,\Record{\alpha;\beta}} \to \Record{\alpha;\beta}
\el
\]
%
Given a key of type $\alpha$ the $\lookup$ function returns the
corresponding value of type $\beta$ in the given association list. If
the key does not exists, then the function invokes the $\Fail$
operation to signal failure.
%
The $\modify$ function takes a key and a value. If the key exists in
the provided association list, then it replaces the value bound by the
key with the provided value.
%
Using these functions we can implement the primitive read and write
operations.
%
\[
\bl
\fread : \Record{\Int;\FileSystem} \to \String \eff \{\Fail : \UnitType \opto \Zero\}\\
\fread\,\Record{ino;fs} \defas
\ba[t]{@{}l}
\Let\;inode \revto \lookup\,\Record{ino; fs.ilist}\;\In\\
\lookup\,\Record{inode.loc; fs.dreg}
\el
\el
\]
%
The function $\fread$ takes as input the i-node number for the file to
be read and a file system. First it looks up the i-node structure in
the i-list, and then it uses the location in the i-node to look up the
file contents in the data region. Since $\fread$ performs no exception
handling it will fail if either look up fails. The implementation of
the primitive write operation is similar.
%
\[
\bl
\fwrite : \Record{\Int;\String;\FileSystem} \to \FileSystem \eff \{\Fail : \UnitType \opto \Zero\}\\
\fwrite\,\Record{ino;cs;fs} \defas
\ba[t]{@{}l}
\Let\;inode \revto \lookup\,\Record{ino; fs.ilist}\;\In\\
\Let\;file \revto \lookup\,\Record{inode.loc; fs.dreg}\;\In\\
\Record{\,fs\;\keyw{with}\;dreg = \modify\,\Record{inode.loc;file \concat cs;fs}}
\el
\el
\]
%
The first two lines grab hold of the file, whilst the last line
updates the data region in file system by appending the string $cs$
onto the file.
%
Before we can implement the handler, we need an exception handling
mechanism. The following exception handler interprets $\Fail$ as some
default value.
%
\[
\bl
\faild : \Record{\alpha;\UnitType \to \alpha \eff \{\Fail : \UnitType \opto \Zero\}} \to \alpha\\
\faild\,\Record{default;m} \defas
\ba[t]{@{~}l}
\Handle\;m~\Unit\;\With\\
~\ba{@{~}l@{~}c@{~}l}
\Return\;x &\mapsto& x\\
\OpCase{\Fail}{\Unit}{\_} &\mapsto& default
\ea
\ea
\el
\]
%
The $\Fail$-case is simply the default value, whilst the
$\Return$-case is the identity.
%
Now we can use all the above pieces to implement a handler for the
$\URead$ and $\UWrite$ operations.
%
\[ \[
\bl \bl
\fileRW : (\UnitType \to \alpha \eff \{\URead : \Int \opto \Option\,\String;\UWrite : \Record{\Int;\String} \opto \UnitType\}) \to \alpha \eff \{\State~\FileSystem\}\\
\fileRW : (\UnitType \to \alpha \eff \dec{FileRW}) \to \alpha \eff \State~\FileSystem\\
\fileRW~m \defas \fileRW~m \defas
\ba[t]{@{}l} \ba[t]{@{}l}
\Handle\;m\,\Unit\;\With\\ \Handle\;m\,\Unit\;\With\\
@ -3445,7 +3548,7 @@ $\texttt{stdout}$.
\ba[t]{@{}l} \ba[t]{@{}l}
\faild~\Record{\Unit; \lambda \Unit.\\ \faild~\Record{\Unit; \lambda \Unit.\\
\quad\bl \quad\bl
\Let\;fs \revto \fwrite\,\Record{ino;cs;\Uget~\Unit}\\
\Let\;fs \revto \fwrite\,\Record{ino;cs;\Uget\,\Unit}\\
\In\;\Uput~fs};\,resume\,\Unit \In\;\Uput~fs};\,resume\,\Unit
\el \el
\ea \ea
@ -3453,12 +3556,29 @@ $\texttt{stdout}$.
\ea \ea
\el \el
\] \]
%
The $\URead$-case uses the $\fread$ function to implement reading a
file. The file system state is retrieved using the state operation
$\Uget$. The possible failure of $\fread$ is dealt with by the
$\faild$ handler by interpreting failure as $\None$.
%
The $\UWrite$-case makes use of the $\fwrite$ function to implement
writing to a file. Again the file system state is retrieved using
$\Uget$. The $\Uput$ operation is used to update the file system state
with the state produced by the successful invocation of
$\fwrite$. Failure is interpreted as unit, meaning that from the
caller perspective the operation fails silently.
\paragraph{File allocation}
\paragraph{File creation and opening}
%
\dhil{TODO}
\[
\dec{FileCO} \defas \{\UCreate : \String \opto \Int; \UOpen : \String \opto \Option~\Int\}
\]
% %
\[ \[
\bl \bl
\fileAlloc : (\UnitType \to \alpha \eff \{\UCreate : \String \opto \Int\}) \to \alpha \eff \{\State~\FileSystem\}\\
\fileAlloc : (\UnitType \to \alpha \eff \dec{FileCO}) \to \alpha \eff \State~\FileSystem\\
\fileAlloc~m \defas \fileAlloc~m \defas
\ba[t]{@{}l} \ba[t]{@{}l}
\Handle\;m\,\Unit\;\With\\ \Handle\;m\,\Unit\;\With\\
@ -3472,17 +3592,52 @@ $\texttt{stdout}$.
\In\;\Uput~fs;\,ino} \In\;\Uput~fs;\,ino}
\el\\ \el\\
\In\; resume\,ino \In\; resume\,ino
\el
\el\\
\OpCase{\UOpen}{fname}{resume} &\mapsto&
\ba[t]{@{}l}
\Let\; ino \revto \faild~\Record{\None; \lambda \Unit.\\
\quad\Some\,(\fopen\,\Record{fname;\Uget\,\Unit})}\\
\In\;resume\,ino
\ea
\ea \ea
\ea \ea
\el \el
\] \]
%
There is no file close operation in \fsname{}, because it would be a no-op.
\paragraph{File linking and unlinking}
\dhil{Maybe axe\dots} \medskip\\
The composition of $\fileRW$ and $\fileAlloc$ give a semantics to file
i/o.
%
\[
\bl
\fileIO : (\UnitType \to \alpha \eff \{\dec{FileCO},\dec{FileRW}\}) \to \alpha \eff \State~\FileSystem \\
\fileIO~m \defas \dec{fileCO}\,(\lambda\Unit. \dec{fileRW}\,m)
\el
\]
%
The two handlers may as well be implemented as a single monolithic
handler, since they implement different operations, return the same
value, and make use of the same state cell. In practice a monolithic
handler may have better performance. However, a sufficient clever
compiler would be able to use the fusion technique of \citet{WuS15} to
fuse the two handlers into one, and thus allow modular composition
without remorse.
\paragraph{Stream redirection} \paragraph{Stream redirection}
% %
\dhil{TODO}
%
\[ \[
\bl \bl
\redirect : \Record{\UnitType \to \alpha \eff \{\Write : \Record{\Int;\String} \opto \UnitType\}; \String} \to \alpha \eff \{\UCreate : \String \opto \Int;\Write : \Record{\Int;\String}\}\\
\redirect :
\bl
\Record{\UnitType \to \alpha \eff \{\Write : \Record{\Int;\String} \opto \UnitType\}; \String}\\
\to \alpha \eff \{\UCreate : \String \opto \Int;\Write : \Record{\Int;\String} \opto \UnitType\}
\el\\
m~\redirect~fname \defas m~\redirect~fname \defas
\ba[t]{@{}l} \ba[t]{@{}l}
\Let\;ino \revto \Ucreate~fname\;\In\\ \Let\;ino \revto \Ucreate~fname\;\In\\
@ -3495,10 +3650,85 @@ $\texttt{stdout}$.
\el \el
\] \]
% %
\paragraph{File linking and unlinking}
\dhil{Maybe axe\dots}
\medskip\\
% ([0, 0, 0],
% (dir = [("hamlet", 2), ("ritchie.txt", 1), ("stdout", 0)],
% dregion = [(2, "To be, or not to be,
% that is the question:
% Whether 'tis nobler in the mind to suffer
% "),
% (1, "UNIX is basically a simple operating system, but you have to be a genius to understand the simplicity.
% "), (
% 0, "")],
% inext = 3,
% inodes = [(2, (lno = 1, loc = 2)), (1, (lno = 1, loc = 1)), (0, (lno = 1, loc = 0))],
% lnext = 3)) : ([Int], FileSystem)
% links> init(fsys0, example7);
% ([0, 0, 0],
% (dir = [("hamlet", 2), ("ritchie.txt", 1), ("stdout", 0)],
% dregion = [(2, "To be, or not to be,
% that is the question:
% Whether 'tis nobler in the mind to suffer
% "),
% (1, "UNIX is basically a simple operating system, but you have to be a genius to understand the simplicity.
% "), (
% 0, "")],
% inext = 3,
% inodes = [(2, (lno = 1, loc = 2)), (1, (lno = 1, loc = 1)), (0, (lno = 1, loc = 0))],
% lnext = 3)) : ([Int], FileSystem)
We can now plug everything together.
%
\[
\ba{@{~}l@{~}l}
&\bl
\runState\,\Record{\dec{fs}_0;\fileIO\,(\lambda\Unit.\\
\qquad\timeshare\,(\lambda\Unit.\\
\qquad\qquad\dec{interruptWrite}\,(\lambda\Unit.\\
\qquad\qquad\qquad\sessionmgr\,\Record{\Root;\lambda\Unit.\\
\qquad\qquad\qquad\qquad\status\,(\lambda\Unit.
\ba[t]{@{}l}
\If\;\fork~\Unit\;\Then\;
\su~\Alice;\,
\quoteRitchie~\redirect~\strlit{ritchie.txt}\\
\Else\;
\su~\Bob;\,
\quoteHamlet~\redirect~\strlit{hamlet})})))}
\ea
\el \smallskip\\
\reducesto^+&
\bl
\Record{
\ba[t]{@{}l}
[0, 0];\\
\Record{
\ba[t]{@{}l}
dir=[\Record{\strlit{hamlet};2},
\Record{\strlit{ritchie.txt};1},
\Record{\strlit{stdout};0}];\\
ilist=[\Record{2;\Record{lno=1;loc=2}},
\Record{1;\Record{lno=1;loc=1}},
\Record{0;\Record{lno=1;loc=0}}];\\
dreg=[
\ba[t]{@{}l}
\Record{2;
\ba[t]{@{}l@{}l}
\texttt{"}&\texttt{To be, or not to be,\nl{}that is the question:\nl{}}\\
&\texttt{Whether 'tis nobler in the mind to suffer\nl{}}};
\ea\\
\Record{1;
\ba[t]{@{}l@{}l}
\texttt{"}&\texttt{UNIX is basically a simple operating system, }\\
&\texttt{but you have to be a genius to understand the simplicity.\nl{}}};
\ea\\
\Record{0; \strlit{}}]}}
\ea
\ea
\ea\\
: \Record{\List~\Int; \FileSystem}
\el
\ea
\]
% \begin{figure}[t] % \begin{figure}[t]
% \centering % \centering
% \begin{tikzpicture}[node distance=4cm,auto,>=stealth'] % \begin{tikzpicture}[node distance=4cm,auto,>=stealth']
@ -3904,10 +4134,10 @@ extension of the following equations to all terms.
\dstrans{N_\ell} \}_{\ell \in \mathcal{L}} \dstrans{N_\ell} \}_{\ell \in \mathcal{L}}
\end{equations} \end{equations}
\paragraph{Example} We illustrate the translation $\dstrans{-}$ on the
EXAMPLE handler from Section~\ref{sec:strategies} (recall that the
variable $m$ is bound to the input computation). The example here is
reproduced in ANF notation.
% \paragraph{Example} We illustrate the translation $\dstrans{-}$ on the
% EXAMPLE handler from Section~\ref{sec:strategies} (recall that the
% variable $m$ is bound to the input computation). The example here is
% reproduced in ANF notation.
% \[ % \[
% \ba{@{~}l@{~}l@{}l} % \ba{@{~}l@{~}l@{}l}
% &\mathcal{S}&\left\llbracket % &\mathcal{S}&\left\llbracket
@ -4014,45 +4244,45 @@ of thunks. The first forwards all operations, acting as the identity
on computations. The second interprets a single operation before on computations. The second interprets a single operation before
reverting to forwarding. reverting to forwarding.
\paragraph{Example} We demonstrate the translation $\sdtrans{-}$ on
the $\Pipe$ handler from Section~\ref{sec:shallow-handlers-tutorial}
(recall that the variables $c$ and $p$ are bound to the consumer and
producer functions respectively). The example is reproduced in ANF
notation.
%
\[
\ba{@{~}l@{~}l@{}l}
&\mathcal{D}&\left\llbracket
\ba[m]{@{~}l}
\ShallowHandle\; c\,\Unit \;\With\; \\
\quad
\ba[m]{@{}l@{~}c@{~}l@{}}
\Return~x &\mapsto& \Return\; x \\
\Await~\Unit~resume &\mapsto& \Copipe\; \Record{resume; p} \\
\ea \\
\ea\right\rrbracket = \\
&
&\ba[t]{@{~}l}
\Let\; z \revto
\ba[t]{@{~}l}
\Handle\; c~\Unit \; \With\\
\quad \ba[m]{@{~}l}
\ba[m]{@{~}l@{~}l}
\Return~x &\mapsto \Return\; \Record{\lambda\Unit. \Return\; x; \lambda\Unit. \Return\;x}\\
\Await~\Unit~resume &\mapsto
\ea\\
\qquad\ba[t]{@{~}l}
\Let\;r \revto \lambda x.\Let\; z \revto resume~x\;
\In\; \Let\; \Record{f; g} = z \;\In\; f~\Unit\; \In\\
\Return\;\Record{\lambda \Unit. \Let\; x \revto \Do\; \ell~p \;\In\; r~x;
\lambda\Unit.\sdtrans{\Copipe}\Record{r; p}}
\ea
\ea
\ea\\
\In\;\Let\;\Record{f; g} = z\; \In\; g~\Unit
\ea
\ea
\]
% \paragraph{Example} We demonstrate the translation $\sdtrans{-}$ on
% the $\Pipe$ handler from Section~\ref{sec:shallow-handlers-tutorial}
% (recall that the variables $c$ and $p$ are bound to the consumer and
% producer functions respectively). The example is reproduced in ANF
% notation.
% %
% \[
% \ba{@{~}l@{~}l@{}l}
% &\mathcal{D}&\left\llbracket
% \ba[m]{@{~}l}
% \ShallowHandle\; c\,\Unit \;\With\; \\
% \quad
% \ba[m]{@{}l@{~}c@{~}l@{}}
% \Return~x &\mapsto& \Return\; x \\
% \Await~\Unit~resume &\mapsto& \Copipe\; \Record{resume; p} \\
% \ea \\
% \ea\right\rrbracket = \\
% &
% &\ba[t]{@{~}l}
% \Let\; z \revto
% \ba[t]{@{~}l}
% \Handle\; c~\Unit \; \With\\
% \quad \ba[m]{@{~}l}
% \ba[m]{@{~}l@{~}l}
% \Return~x &\mapsto \Return\; \Record{\lambda\Unit. \Return\; x; \lambda\Unit. \Return\;x}\\
% \Await~\Unit~resume &\mapsto
% \ea\\
% \qquad\ba[t]{@{~}l}
% \Let\;r \revto \lambda x.\Let\; z \revto resume~x\;
% \In\; \Let\; \Record{f; g} = z \;\In\; f~\Unit\; \In\\
% \Return\;\Record{\lambda \Unit. \Let\; x \revto \Do\; \ell~p \;\In\; r~x;
% \lambda\Unit.\sdtrans{\Copipe}\Record{r; p}}
% \ea
% \ea
% \ea\\
% \In\;\Let\;\Record{f; g} = z\; \In\; g~\Unit
% \ea
% \ea
% \]
% %
\begin{theorem} \begin{theorem}

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