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Fixed mutability bug

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Dmitry Boulytchev 2018-11-13 09:54:04 +03:00
parent 6279f44f71
commit 5f6726930b
12 changed files with 181 additions and 747 deletions
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122
doc/01.tex
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@ -1,114 +1,6 @@
\documentclass{article}
\section{Introduction: Languages, Semantics, Interpreters, Compilers}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\newcommand{\set}[1]{\{#1\}}
\newcommand{\angled}[1]{\langle {#1} \rangle}
\newcommand{\fib}{\rightarrow_{\mathit{fib}}}
\newcommand{\fibm}{\Rightarrow_{\mathit{fib}}}
\newcommand{\oo}[1]{{#1}^o}
\newcommand{\inml}[1]{\mbox{\lstinline{#1}}}
\newcommand{\goal}{\mathfrak G}
\newcommand{\inmath}[1]{\mbox{$#1$}}
\newcommand{\sembr}[1]{\llbracket{#1}\rrbracket}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\ruleno}[1]{\eqno[\textsc{#1}]}
\newcommand{\trule}[2]{\dfrac{#1}{#2}}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\newcommand{\nredrule}[3]{
\begin{array}{cl}
\textsf{[{#1}]}&
\begin{array}{c}
#2 \\
\hline
\raisebox{-1pt}{\ensuremath{#3}}
\end{array}
\end{array}}
\newcommand{\naxiom}[2]{
\begin{array}{cl}
\textsf{[{#1}]} & \raisebox{-1pt}{\ensuremath{#2}}
\end{array}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={fun}{{$\lambda$}}1 {->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Introduction: Languages, Semantics, Interpreters, Compilers\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\section{Language and semantics}
\subsection{Language and semantics}
A language is a collection of programs. A program is an \emph{abstract syntax tree} (AST), which describes the hierarchy of constructs. An abstract
syntax of a programming language describes the format of abstract syntax trees of programs in this language. Thus, a language is a set of constructive
@ -123,7 +15,7 @@ $$
where $\mathscr D$ is some \emph{semantic domain}. The choice of the domain is at our command; for example, for Turing-complete languages $\mathscr D$ can
be the set of all partially-recursive (computable) functions.
\section{Interpreters}
\subsection{Interpreters}
In reality, the semantics often is described using \emph{interpreters}:
@ -155,7 +47,7 @@ operational, denotational or game semantics, etc.)
Pragmatically: if you have a good implementation of a good programming language you trust, you can write interpreters of other languages.
\section{Compilers}
\subsection{Compilers}
A compiler is just a language transformer
@ -176,7 +68,7 @@ And, again, we expect compilers to be defined in terms of some implementation la
its semantics in ocaml possesses the following property (fill the rest yourself).
\section{The first example: language of expressions}
\subsection{The first example: language of expressions}
Abstract syntax:
@ -250,7 +142,3 @@ Important observations:
\item This concrete semantics is \emph{strict}: for a binary operator both its arguments are evaluated unconditionally; thus,
for example, \lstinline|1 !! x| is undefined in empty state.
\end{enumerate}
\end{document}

120
doc/02.tex
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@ -1,118 +1,6 @@
\documentclass{article}
\section{Statements, Stack Machine, Stack Machine Compiler}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\def\transarrow{\xrightarrow}
\newcommand{\setarrow}[1]{\def\transarrow{#1}}
\def\padding{\phantom{X}}
\newcommand{\setpadding}[1]{\def\padding{#1}}
\newcommand{\trule}[2]{\frac{#1}{#2}}
\newcommand{\crule}[3]{\frac{#1}{#2},\;{#3}}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\trans}[3]{{#1}\transarrow{\padding#2\padding}{#3}}
\newcommand{\ctrans}[4]{{#1}\transarrow{\padding#2\padding}{#3},\;{#4}}
\newcommand{\llang}[1]{\mbox{\lstinline[mathescape]|#1|}}
\newcommand{\pair}[2]{\inbr{{#1}\mid{#2}}}
\newcommand{\inbr}[1]{\left<{#1}\right>}
\newcommand{\highlight}[1]{\color{red}{#1}}
\newcommand{\ruleno}[1]{\eqno[\scriptsize\textsc{#1}]}
\newcommand{\rulename}[1]{\textsc{#1}}
\newcommand{\inmath}[1]{\mbox{$#1$}}
\newcommand{\lfp}[1]{fix_{#1}}
\newcommand{\gfp}[1]{Fix_{#1}}
\newcommand{\vsep}{\vspace{-2mm}}
\newcommand{\supp}[1]{\scriptsize{#1}}
\newcommand{\sembr}[1]{\llbracket{#1}\rrbracket}
\newcommand{\cd}[1]{\texttt{#1}}
\newcommand{\free}[1]{\boxed{#1}}
\newcommand{\binds}{\;\mapsto\;}
\newcommand{\dbi}[1]{\mbox{\bf{#1}}}
\newcommand{\sv}[1]{\mbox{\textbf{#1}}}
\newcommand{\bnd}[2]{{#1}\mkern-9mu\binds\mkern-9mu{#2}}
\newcommand{\meta}[1]{{\mathcal{#1}}}
\renewcommand{\emptyset}{\varnothing}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={fun}{{$\lambda$}}1 {->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Statements, Stack Machine, Stack Machine Compiler\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\section{Statements}
\subsection{Statements}
More interesting language~--- a language of simple statements:
@ -225,7 +113,7 @@ As for the statement, with the aid of the relation ``$\Rightarrow$'' we can defi
\label{bs_sm}
\end{figure}
\section{A Compiler for the Stack Machine}
\subsection{A Compiler for the Stack Machine}
A compiler of the statement language into the stack machine is a total mapping
@ -257,5 +145,3 @@ And now the main dish:
\sembr{\llang{$S_1$;$\;S_2$}}_{comp}&=&\sembr{S_1}_{comp}\llang{@}\sembr{S_2}_{comp}
\end{array}
\]
\end{document}

122
doc/03.tex
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@ -1,122 +1,4 @@
\documentclass{article}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\usepackage{subcaption}
\usepackage{placeins}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\def\transarrow{\xrightarrow}
\newcommand{\setarrow}[1]{\def\transarrow{#1}}
\def\padding{\phantom{X}}
\newcommand{\setpadding}[1]{\def\padding{#1}}
\newcommand{\trule}[2]{\frac{#1}{#2}}
\newcommand{\crule}[3]{\frac{#1}{#2},\;{#3}}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\trans}[3]{{#1}\transarrow{\padding#2\padding}{#3}}
\newcommand{\ctrans}[4]{{#1}\transarrow{\padding#2\padding}{#3},\;{#4}}
\newcommand{\llang}[1]{\mbox{\lstinline[mathescape]|#1|}}
\newcommand{\pair}[2]{\inbr{{#1}\mid{#2}}}
\newcommand{\inbr}[1]{\left<{#1}\right>}
\newcommand{\highlight}[1]{\color{red}{#1}}
\newcommand{\ruleno}[1]{\eqno[\scriptsize\textsc{#1}]}
\newcommand{\rulename}[1]{\textsc{#1}}
\newcommand{\inmath}[1]{\mbox{$#1$}}
\newcommand{\lfp}[1]{fix_{#1}}
\newcommand{\gfp}[1]{Fix_{#1}}
\newcommand{\vsep}{\vspace{-2mm}}
\newcommand{\supp}[1]{\scriptsize{#1}}
\newcommand{\sembr}[1]{\llbracket{#1}\rrbracket}
\newcommand{\cd}[1]{\texttt{#1}}
\newcommand{\free}[1]{\boxed{#1}}
\newcommand{\binds}{\;\mapsto\;}
\newcommand{\dbi}[1]{\mbox{\bf{#1}}}
\newcommand{\sv}[1]{\mbox{\textbf{#1}}}
\newcommand{\bnd}[2]{{#1}\mkern-9mu\binds\mkern-9mu{#2}}
\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newcommand{\meta}[1]{{\mathcal{#1}}}
\renewcommand{\emptyset}{\varnothing}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={fun}{{$\lambda$}}1 {->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Structural Induction\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
%\section{Structural Induction}
\section{Structural Induction}
\begin{figure}
\begin{subfigure}{\textwidth}
@ -285,5 +167,3 @@ configurations, since they are never affected by the remaining instructions.
Taking into account the semantics of \llang{BINOP $\otimes$} and applying the compositionality lemma, the theorem follows.
\end{itemize}
\end{proof}
\end{document}

133
doc/04.tex
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@ -1,121 +1,6 @@
\documentclass{article}
\title{Control Flow Constructs}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\usepackage{subcaption}
\usepackage{placeins}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\def\transarrow{\xrightarrow}
\newcommand{\setarrow}[1]{\def\transarrow{#1}}
\def\padding{\phantom{X}}
\newcommand{\setpadding}[1]{\def\padding{#1}}
\newcommand{\trule}[2]{\frac{#1}{#2}}
\newcommand{\crule}[3]{\frac{#1}{#2},\;{#3}}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\trans}[3]{{#1}\transarrow{\padding#2\padding}{#3}}
\newcommand{\ctrans}[4]{{#1}\transarrow{\padding#2\padding}{#3},\;{#4}}
\newcommand{\llang}[1]{\mbox{\lstinline[mathescape]|#1|}}
\newcommand{\pair}[2]{\inbr{{#1}\mid{#2}}}
\newcommand{\inbr}[1]{\left<{#1}\right>}
\newcommand{\highlight}[1]{\color{red}{#1}}
\newcommand{\ruleno}[1]{\eqno[\scriptsize\textsc{#1}]}
\newcommand{\rulename}[1]{\textsc{#1}}
\newcommand{\inmath}[1]{\mbox{$#1$}}
\newcommand{\lfp}[1]{fix_{#1}}
\newcommand{\gfp}[1]{Fix_{#1}}
\newcommand{\vsep}{\vspace{-2mm}}
\newcommand{\supp}[1]{\scriptsize{#1}}
\newcommand{\sembr}[1]{\llbracket{#1}\rrbracket}
\newcommand{\cd}[1]{\texttt{#1}}
\newcommand{\free}[1]{\boxed{#1}}
\newcommand{\binds}{\;\mapsto\;}
\newcommand{\dbi}[1]{\mbox{\bf{#1}}}
\newcommand{\sv}[1]{\mbox{\textbf{#1}}}
\newcommand{\bnd}[2]{{#1}\mkern-9mu\binds\mkern-9mu{#2}}
\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newcommand{\meta}[1]{{\mathcal{#1}}}
\renewcommand{\emptyset}{\varnothing}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh, skip, od, fi, elif, for},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={fun}{{$\lambda$}}1 {->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Control Flow Constructs\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\section{Structural Control Flow}
\subsection{Structural Control Flow}
We add a few structural control flow constructs to the language:
@ -143,27 +28,27 @@ In the concrete syntax for the constructs we add the closing keywords ``\llang{i
\[\trans{c}{\llang{skip}}{c}\ruleno{Skip$_{bs}$}\]
\[
\crule{\trans{c}{\mbox{$S_1$}}{c^\prime}}
{\trans{c}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\sembr{e}\;s\ne 0}\ruleno{If-True$_{bs}$}
\]
\[
\crule{\trans{c}{\mbox{$S_2$}}{c^\prime}}
{\trans{c}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\trans{c=\inbr{s, \_, \_}}{\llang{if $\;e\;$ then $\;S_1\;$ else $\;S_2\;$}}{c^\prime}}
{\sembr{e}\;s=0}\ruleno{If-False$_{bs}$}
\]
\[
\crule{\trans{c}{\llang{$S$}}{c^\prime},\;\trans{c^\prime}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
{\trans{c}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
{\trans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c^{\prime\prime}}}
{\sembr{e}\;s\ne 0}\ruleno{While-True$_{bs}$}
\]
\[
\ctrans{c}{\llang{while $\;e\;$ do $\;S\;$}}{c}{\sembr{e}\;s=0}\ruleno{While-False$_{bs}$}
\ctrans{c=\inbr{s, \_, \_}}{\llang{while $\;e\;$ do $\;S\;$}}{c}{\sembr{e}\;s=0}\ruleno{While-False$_{bs}$}
\]
\caption{Big-step operational semantics for control flow statements}
\label{bs_stmt_cf}
\end{figure}
\section{Extended Stack Machine}
\subsection{Extended Stack Machine}
In order to compile the extended language into a program for the stack machine the latter has to be extended. First, we introduce a set of label names
@ -223,7 +108,7 @@ Finally, the top-level semantics for the extended stack machine can be redefined
\forall p\in\mathscr P,\,\forall i\in\mathbb Z^*\;:\;\sembr{p}_{SM}\;i=o\Leftrightarrow\withenv{p}{\trans{\inbr{\epsilon, \inbr{\bot, i, \epsilon}}}{p}{\inbr{\_, \inbr{\_, \_, o}}}}
\]
\section{Syntax Extensions}
\subsection{Syntax Extensions}
With the structural control flow constructs already implemented, it is rather simple to ``saturate'' the language with more elaborated control constructs, using
the method of \emph{syntactic extension}. Namely, we may introduce the following constructs
@ -331,5 +216,3 @@ loop using syntax extension:
\end{tabular}
However, for nested \lstinline{repeat} constructs the size of extended program is exponential w.r.t. the nesting depth, which makes the whole idea unreasonable.
\end{document}

118
doc/05.tex
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@ -1,120 +1,3 @@
\documentclass{article}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\usepackage{subcaption}
\usepackage{placeins}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\def\transarrow{\xrightarrow}
\newcommand{\setarrow}[1]{\def\transarrow{#1}}
\def\padding{\phantom{X}}
\newcommand{\setpadding}[1]{\def\padding{#1}}
\newcommand{\trule}[2]{\frac{#1}{#2}}
\newcommand{\crule}[3]{\frac{#1}{#2},\;{#3}}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\trans}[3]{{#1}\transarrow{\padding#2\padding}{#3}}
\newcommand{\ctrans}[4]{{#1}\transarrow{\padding#2\padding}{#3},\;{#4}}
\newcommand{\llang}[1]{\mbox{\lstinline[mathescape]|#1|}}
\newcommand{\pair}[2]{\inbr{{#1}\mid{#2}}}
\newcommand{\inbr}[1]{\left<{#1}\right>}
\newcommand{\highlight}[1]{\color{red}{#1}}
\newcommand{\ruleno}[1]{\eqno[\scriptsize\textsc{#1}]}
\newcommand{\rulename}[1]{\textsc{#1}}
\newcommand{\inmath}[1]{\mbox{$#1$}}
\newcommand{\lfp}[1]{fix_{#1}}
\newcommand{\gfp}[1]{Fix_{#1}}
\newcommand{\vsep}{\vspace{-2mm}}
\newcommand{\supp}[1]{\scriptsize{#1}}
\newcommand{\sembr}[1]{\llbracket{#1}\rrbracket}
\newcommand{\cd}[1]{\texttt{#1}}
\newcommand{\free}[1]{\boxed{#1}}
\newcommand{\binds}{\;\mapsto\;}
\newcommand{\dbi}[1]{\mbox{\bf{#1}}}
\newcommand{\sv}[1]{\mbox{\textbf{#1}}}
\newcommand{\bnd}[2]{{#1}\mkern-9mu\binds\mkern-9mu{#2}}
\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newcommand{\meta}[1]{{\mathcal{#1}}}
\renewcommand{\emptyset}{\varnothing}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh, skip, od, fi, elif, for, local},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Procedures\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\section{Procedures}
Procedures are unit-returning functions. We consider adding procedures as a separate step, since introducing full-fledged functions would require
@ -283,4 +166,3 @@ Now we specify additional rules for the new instructions:
\[
\withenv{P}{\trans{\inbr{\epsilon,\,st,\,c}}{\llang{END}p}{\inbr{\epsilon,\,st,\,c}}}\ruleno{EndStop$_{SM}$}
\]
\end{document}

134
doc/06.tex
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@ -1,124 +1,6 @@
\documentclass{article}
\section{Functions}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
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\usepackage{color}
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\usepackage{mathrsfs}
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\usepackage{subcaption}
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\newtheorem{theorem}{Theorem}
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\renewcommand{\emptyset}{\varnothing}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh, skip, od, fi, elif, for, local, return, read, write},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
morecomment=[s]{(*}{*)}
}
\lstset{
mathescape=true,
%basicstyle=\small,
identifierstyle=\ttfamily,
keywordstyle=\bfseries,
commentstyle=\scriptsize\rmfamily,
basewidth={0.5em,0.5em},
fontadjust=true,
escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Functions\\
(the first draft)
}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\section{Functions in Expressions}
\subsection{Functions in Expressions}
At the syntax level function calls are introduced with the following construct:
@ -177,7 +59,7 @@ The rules inself are summarized in the Fig.~\ref{bs_expr}. Note the use of doubl
\label{bs_expr}
\end{figure}
\section{Return Statement}
\subsection{Return Statement}
In order to make it possible to return values from procedures we add a return statement to the language of statements:
@ -271,10 +153,10 @@ The rules themselves are shown on Fig.~\ref{bs_cps}. Note, the rule for the call
\[\trule{\begin{array}{c}
{\setsubarrow{_{\mathscr E}}\withenv{\Phi}{\trans{c_{j-1}}{e_j}{c_j=\inbr{\sigma_j,\,i_j,\,o_j,\,v_j}}}}\\
\Phi\;f = \llang{fun $\;f\;$ ($\overline{a}$) local $\;\overline{l}\;$ \{$s$\}} \\
\withenv{\llang{skip},\,\Phi}{\trans{\inbr{\mbox{\textbf{enter}}\;\sigma_k\; (\overline{a}@\overline{l})\; [\overline{a_j\gets v_j}],i_k,o_k,\hbox{---}}}{s}{\inbr{\sigma^\prime, i^\prime, o^\prime, n}}}
\end{array}
}
{\withenv{K,\,\Phi}{\trans{c_0=\inbr{\sigma_0,\,\_,\,\_,\,\_}}{f (\overline{e_k})}{\inbr{\mbox{\textbf{leave}}\;\sigma^\prime\;\sigma_0, i^\prime, o^\prime, n}}}}
\withenv{\llang{skip},\,\Phi}{\trans{\inbr{\mbox{\textbf{enter}}\;\sigma_k\; (\overline{a}@\overline{l})\; [\overline{a_j\gets v_j}],i_k,o_k,\hbox{---}}}{s}{\inbr{\sigma^\prime, i^\prime, o^\prime, \hbox{---}}}}\\
\withenv{\llang{skip},\,\Phi}{\trans{\inbr{\mbox{\textbf{leave}}\;\sigma^\prime\;\sigma_0, i^\prime, o^\prime, \hbox{---}}}{K}{\inbr{\sigma^{\prime\prime}, i^{\prime\prime}, o^{\prime\prime}, n}}}
\end{array}}
{\withenv{K,\,\Phi}{\trans{c_0=\inbr{\sigma_0,\,\_,\,\_,\,\_}}{f (\overline{e_k})}{\inbr{\sigma^{\prime\prime}, i^{\prime\prime}, o^{\prime\prime}, n}}}}
\ruleno{Call}
\]
@ -292,5 +174,3 @@ The rules themselves are shown on Fig.~\ref{bs_cps}. Note, the rule for the call
\caption{Continuation-passing Style Semantics for Statements}
\label{bs_cps}
\end{figure}
\end{document}

128
doc/lectures.tex Normal file
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@ -0,0 +1,128 @@
\documentclass{article}
\usepackage{amssymb, amsmath}
\usepackage{alltt}
\usepackage{pslatex}
\usepackage{epigraph}
\usepackage{verbatim}
\usepackage{latexsym}
\usepackage{array}
\usepackage{comment}
\usepackage{makeidx}
\usepackage{listings}
\usepackage{indentfirst}
\usepackage{verbatim}
\usepackage{color}
\usepackage{url}
\usepackage{xspace}
\usepackage{hyperref}
\usepackage{stmaryrd}
\usepackage{amsmath, amsthm, amssymb}
\usepackage{graphicx}
\usepackage{euscript}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{multirow,bigdelim}
\usepackage{subcaption}
\usepackage{placeins}
\makeatletter
\makeatother
\definecolor{shadecolor}{gray}{1.00}
\definecolor{darkgray}{gray}{0.30}
\def\transarrow{\xrightarrow}
\newcommand{\setarrow}[1]{\def\transarrow{#1}}
\def\padding{\phantom{X}}
\newcommand{\setpadding}[1]{\def\padding{#1}}
\def\subarrow{}
\newcommand{\setsubarrow}[1]{\def\subarrow{#1}}
\newcommand{\trule}[2]{\frac{#1}{#2}}
\newcommand{\crule}[3]{\frac{#1}{#2},\;{#3}}
\newcommand{\withenv}[2]{{#1}\vdash{#2}}
\newcommand{\trans}[3]{{#1}\transarrow{\padding#2\padding}\subarrow{#3}}
\newcommand{\ctrans}[4]{{#1}\transarrow{\padding#2\padding}\subarrow{#3},\;{#4}}
\newcommand{\llang}[1]{\mbox{\lstinline[mathescape]|#1|}}
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\newcommand{\highlight}[1]{\color{red}{#1}}
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\newcommand{\rulename}[1]{\textsc{#1}}
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\newtheorem{theorem}{Theorem}
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\newcommand{\dom}[1]{\mathtt{dom}\;{#1}}
\definecolor{light-gray}{gray}{0.90}
\newcommand{\graybox}[1]{\colorbox{light-gray}{#1}}
\lstdefinelanguage{ocaml}{
keywords={let, begin, end, in, match, type, and, fun,
function, try, with, class, object, method, of, rec, repeat, until,
while, not, do, done, as, val, inherit, module, sig, @type, struct,
if, then, else, open, virtual, new, fresh, skip, od, fi, elif, for, local, return, read, write},
sensitive=true,
%basicstyle=\small,
commentstyle=\scriptsize\rmfamily,
keywordstyle=\ttfamily\bfseries,
identifierstyle=\ttfamily,
basewidth={0.5em,0.5em},
columns=fixed,
fontadjust=true,
literate={->}{{$\to$}}3 {===}{{$\equiv$}}1 {=/=}{{$\not\equiv$}}1 {|>}{{$\triangleright$}}3 {\&\&\&}{{$\wedge$}}2 {|||}{{$\vee$}}2 {^}{{$\uparrow$}}1,
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}
\lstset{
mathescape=true,
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escapechar=!,
language=ocaml
}
\sloppy
\newcommand{\ocaml}{\texttt{OCaml}\xspace}
\theoremstyle{definition}
\title{Introduction to Programming Languages, Compilers and Tools}
\author{Dmitry Boulytchev}
\begin{document}
\maketitle
\input{01}
\input{02}
\input{03}
\input{04}
\input{05}
\input{06}
\input{07}
\end{document}

1
regression/orig/test050.log Normal file
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@ -0,0 +1 @@
> 2

5
regression/test050.expr Normal file
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@ -0,0 +1,5 @@
n := read ();
x := [1];
y := [x, x];
y[1][0] := 2;
write (y[0][0])

1
regression/test050.input Normal file
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@ -0,0 +1 @@
0

32
src/Language.ml
View file

@ -11,7 +11,7 @@ open Combinators
module Value =
struct
@type t = Int of int | String of string | Array of t list | Sexp of string * t list with show
@type t = Int of int | String of bytes | Array of t array | Sexp of string * t list (*with show*)
let to_int = function
| Int n -> n
@ -34,22 +34,22 @@ module Value =
| Sexp (t, _) -> t
| _ -> failwith "symbolic expression expected"
let update_string s i x = String.init (String.length s) (fun j -> if j = i then x else s.[j])
let update_array a i x = List.init (List.length a) (fun j -> if j = i then x else List.nth a j)
let update_string s i x = Bytes.set s i x; s
let update_array a i x = a.(i) <- x; a
let string_val v =
let buf = Buffer.create 128 in
let append s = Buffer.add_string buf s in
let rec inner = function
| Int n -> append (string_of_int n)
| String s -> append "\""; append s; append "\""
| Array a -> let n = List.length a in
append "["; List.iteri (fun i a -> (if i > 0 then append ", "); inner a) a; append "]"
| String s -> append "\""; append @@ Bytes.to_string s; append "\""
| Array a -> let n = Array.length a in
append "["; Array.iteri (fun i a -> (if i > 0 then append ", "); inner a) a; append "]"
| Sexp (t, a) -> let n = List.length a in
append "`"; append t; (if n > 0 then (append " ("; List.iteri (fun i a -> (if i > 0 then append ", "); inner a) a; append ")"))
in
inner v;
Buffer.contents buf
Bytes.of_string @@ Buffer.contents buf
end
@ -125,13 +125,13 @@ module Builtin =
| ".elem" -> let [b; j] = args in
(st, i, o, let i = Value.to_int j in
Some (match b with
| Value.String s -> Value.of_int @@ Char.code s.[i]
| Value.Array a -> List.nth a i
| Value.String s -> Value.of_int @@ Char.code (Bytes.get s i)
| Value.Array a -> a.(i)
| Value.Sexp (_, a) -> List.nth a i
)
)
| ".length" -> (st, i, o, Some (Value.of_int (match List.hd args with Value.Sexp (_, a) | Value.Array a -> List.length a | Value.String s -> String.length s)))
| ".array" -> (st, i, o, Some (Value.of_array args))
| ".length" -> (st, i, o, Some (Value.of_int (match List.hd args with Value.Sexp (_, a) -> List.length a | Value.Array a -> Array.length a | Value.String s -> Bytes.length s)))
| ".array" -> (st, i, o, Some (Value.of_array @@ Array.of_list args))
| ".stringval" -> let [a] = args in (st, i, o, Some (Value.of_string @@ Value.string_val a))
end
@ -202,7 +202,7 @@ module Expr =
let rec eval env ((st, i, o, r) as conf) expr =
match expr with
| Const n -> (st, i, o, Some (Value.of_int n))
| String s -> (st, i, o, Some (Value.of_string s))
| String s -> (st, i, o, Some (Value.of_string @@ Bytes.of_string s))
| StringVal s ->
let (st, i, o, Some s) = eval env conf s in
(st, i, o, Some (Value.of_string @@ Value.string_val s))
@ -351,7 +351,7 @@ module Stmt =
let i = Value.to_int i in
(match a with
| Value.String s when tl = [] -> Value.String (Value.update_string s i (Char.chr @@ Value.to_int v))
| Value.Array a -> Value.Array (Value.update_array a i (update (List.nth a i) v tl))
| Value.Array a -> Value.Array (Value.update_array a i (update a.(i) v tl))
)
in
State.update x (match is with [] -> v | _ -> update (State.eval st x) v is) st
@ -378,7 +378,7 @@ module Stmt =
| Case (e, bs) ->
let (_, _, _, Some v) as conf' = Expr.eval env conf e in
let rec branch ((st, i, o, _) as conf) = function
| [] -> failwith (Printf.sprintf "Pattern matching failed: no branch is selected while matching %s\n" (show(Value.t) v))
| [] -> failwith (Printf.sprintf "Pattern matching failed: no branch is selected while matching %s\n" "" (*show(Value.t) v*))
| (patt, body)::tl ->
let rec match_patt patt v st =
let update x v = function
@ -389,9 +389,9 @@ module Stmt =
| Pattern.Named (x, p), v -> update x v (match_patt p v st )
| Pattern.Wildcard , _ -> st
| Pattern.Sexp (t, ps), Value.Sexp (t', vs) when t = t' && List.length ps = List.length vs -> match_list ps vs st
| Pattern.Array ps , Value.Array vs when List.length ps = List.length vs -> match_list ps vs st
| Pattern.Array ps , Value.Array vs when List.length ps = Array.length vs -> match_list ps (Array.to_list vs) st
| Pattern.Const n , Value.Int n' when n = n' -> st
| Pattern.String s , Value.String s' when s = s' -> st
| Pattern.String s , Value.String s' when s = Bytes.to_string s' -> st
| Pattern.Boxed , Value.String _
| Pattern.Boxed , Value.Array _
| Pattern.UnBoxed , Value.Int _

4
src/SM.ml
View file

@ -60,7 +60,7 @@ let rec eval env ((cstack, stack, ((st, i, o) as c)) as conf) = function
(match insn with
| BINOP op -> let y::x::stack' = stack in eval env (cstack, (Value.of_int @@ Expr.to_func op (Value.to_int x) (Value.to_int y)) :: stack', c) prg'
| CONST i -> eval env (cstack, (Value.of_int i)::stack, c) prg'
| STRING s -> eval env (cstack, (Value.of_string s)::stack, c) prg'
| STRING s -> eval env (cstack, (Value.of_string @@ Bytes.of_string s)::stack, c) prg'
| SEXP (s, n) -> let vs, stack' = split n stack in
eval env (cstack, (Value.sexp s @@ List.rev vs)::stack', c) prg'
| LD x -> eval env (cstack, State.eval st x :: stack, c) prg'
@ -87,7 +87,7 @@ let rec eval env ((cstack, stack, ((st, i, o) as c)) as conf) = function
| TAG (t, n) -> let x::stack' = stack in
eval env (cstack, (Value.of_int @@ match x with Value.Sexp (t', a) when t' = t && List.length a = n -> 1 | _ -> 0) :: stack', c) prg'
| ARRAY n -> let x::stack' = stack in
eval env (cstack, (Value.of_int @@ match x with Value.Array a when List.length a = n -> 1 | _ -> 0) :: stack', c) prg'
eval env (cstack, (Value.of_int @@ match x with Value.Array a when Array.length a = n -> 1 | _ -> 0) :: stack', c) prg'
| PATT StrCmp -> let x::y::stack' = stack in
eval env (cstack, (Value.of_int @@ match x, y with (Value.String xs, Value.String ys) when xs = ys -> 1 | _ -> 0) :: stack', c) prg'
| PATT Array -> let x::stack' = stack in