unicode latex
This commit is contained in:
Francesco Mecca
parent
8bd79b8e39
commit
6febde620a
10 changed files with 2545 additions and 1165 deletions
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@ -1,9 +1,9 @@
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SRC = prova.tex
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SRC = tesi.tex
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AUX = prova.aux
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AUX = tesi.aux
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DEL = prova.aux prova.bbl prova.blg prova.log prova.out
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DEL = tesi.aux tesi.bbl tesi.blg tesi.log tesi.out
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NAME = prova
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NAME = tesi
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prova:
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tesi:
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@echo
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@echo
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@echo "=== Removing temporary files ==="
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@echo "=== Removing temporary files ==="
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rm -f $(DEL)
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rm -f $(DEL)
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21
tesi/conv.py
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21
tesi/conv.py
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import json
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from sys import argv
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allsymbols = json.load(open('./unicode-latex.json'))
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symbols = ['≼', '→', '⊀', '⋠', '≺', '∀', '∈', '₂', '₁', 'ₐ', 'ₘ', 'ₙ', 'ᵢ' ]
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symbols = {s: allsymbols[s] for s in symbols}
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print(symbols)
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def read_by_char(fname):
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with open(fname, 'r') as fp:
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for line in fp.readlines():
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for ch in line:
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yield ch
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def convert(ch):
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return symbols[ch] if ch in symbols else ch
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newfile = [convert(ch) for ch in read_by_char(argv[1])]
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with open(argv[2], 'w') as f:
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f.writelines(newfile)
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\relax
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\providecommand\hyper@newdestlabel[2]{}
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\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
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\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
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\global\let\oldcontentsline\contentsline
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\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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\global\let\oldnewlabel\newlabel
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\gdef\newlabel#1#2{\newlabelxx{#1}#2}
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\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
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\AtEndDocument{\ifx\hyper@anchor\@undefined
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\let\contentsline\oldcontentsline
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\let\newlabel\oldnewlabel
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\fi}
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\fi}
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\global\let\hyper@last\relax
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\gdef\HyperFirstAtBeginDocument#1{#1}
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\providecommand*\HyPL@Entry[1]{}
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\HyPL@Entry{0<</S/D>>}
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\@writefile{toc}{\contentsline {section}{\numberline {1}{\bfseries \sffamily TODO} Scaletta [1/2]}{1}{section.1}\protected@file@percent }
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\newlabel{sec:org6c3943f}{{1}{1}{{\bfseries \sffamily TODO} Scaletta [1/2]}{section.1}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {2}1. Background}{2}{section.2}\protected@file@percent }
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\newlabel{sec:orgad08c62}{{2}{2}{1. Background}{section.2}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}1.1 OCaml}{2}{subsection.2.1}\protected@file@percent }
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\newlabel{sec:orgca8d200}{{2.1}{2}{1.1 OCaml}{subsection.2.1}{}}
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\newlabel{sec:org83a2e95}{{1}{3}{1.1 OCaml}{Item.1}{}}
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\newlabel{sec:org2127ffb}{{2}{5}{1.1 OCaml}{Item.2}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}1.2.1.1 Initial state of the compilation}{6}{subsection.2.2}\protected@file@percent }
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\newlabel{sec:org0b0c254}{{2.2}{6}{1.2.1.1 Initial state of the compilation}{subsection.2.2}{}}
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771
tesi/prova.log
771
tesi/prova.log
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This is XeTeX, Version 3.14159265-2.6-0.999991 (TeX Live 2019 Gentoo Linux) (preloaded format=xelatex 2020.2.19) 19 FEB 2020 16:42
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entering extended mode
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restricted \write18 enabled.
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%&-line parsing enabled.
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**prova.tex
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(./prova.tex
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Package inputenc Warning: inputenc package ignored with utf8 based engines.
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Package: fontenc 2018/08/11 v2.0j Standard LaTeX package
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% Created 2020-02-19 Wed 16:42
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\author{Francesco Mecca}
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\date{}
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\title{Translation Verification of the OCaml pattern matching compiler}
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\hypersetup{
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||||||
pdfauthor={Francesco Mecca},
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||||||
pdftitle={Translation Verification of the OCaml pattern matching compiler},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 26.3 (Org mode 9.1.9)},
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pdflang={English}}
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\begin{document}
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\maketitle
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\section{{\bfseries\sffamily TODO} Scaletta [1/2]}
|
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\label{sec:org6c3943f}
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\begin{itemize}
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\item[{$\boxtimes$}] Abstract
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\item[{$\boxminus$}] Background [25\%]
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\begin{itemize}
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\item[{$\boxtimes$}] Ocaml
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\item[{$\square$}] Lambda code
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\item[{$\square$}] Pattern matching
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\item[{$\square$}] Translation Verification
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||||||
\item[{$\square$}] Symbolic execution
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\end{itemize}
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\end{itemize}
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\begin{abstract}
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||||||
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||||||
This dissertation presents an algorithm for the translation validation of the OCaml
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||||||
pattern matching compiler. Given the source representation of the target program and the
|
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||||||
target program compiled in untyped lambda form, the algoritmhm is capable of modelling
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||||||
the source program in terms of symbolic constraints on it's branches and apply symbolic
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execution on the untyped lambda representation in order to validate wheter the compilation
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||||||
produced a valid result.
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program the untyped lambda translation produces the same output as the source program.
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The input of the program is modelled in terms of symbolic constraints closely related to
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the runtime representation of OCaml objects and the output consists of OCaml code
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blackboxes that are not evaluated in the context of the verification.
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\end{abstract}
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\section{1. Background}
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\label{sec:orgad08c62}
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\subsection{1.1 OCaml}
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\label{sec:orgca8d200}
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Objective Caml (OCaml) is a dialect of the ML (Meta-Language) family of programming
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languages.
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\end{itemize}
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type for the input parameters. For example a function that computes the lenght of a
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time templates and function overloading.
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\begin{itemize}
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||||||
\item Strong typing: Languages such as C and C++ allow the programmer to operate on data
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\end{itemize}
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||||||
without considering its type, mainly through pointers. Other languages such as C\#
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|
||||||
\begin{itemize}
|
|
||||||
\item Type Inference: the principal type of a well formed term can be inferred without any
|
|
||||||
\end{itemize}
|
|
||||||
annotation or declaration.
|
|
||||||
\begin{itemize}
|
|
||||||
\item Algebraic data types: types that are modelled by the use of two
|
|
||||||
\end{itemize}
|
|
||||||
algebraic operations, sum and product.
|
|
||||||
A sum type is a type that can hold of many different types of
|
|
||||||
objects, but only one at a time. For example the sum type defined
|
|
||||||
as \emph{A + B} can hold at any moment a value of type A or a value of
|
|
||||||
type B. Sum types are also called tagged union or variants.
|
|
||||||
A product type is a type constructed as a direct product
|
|
||||||
of multiple types and contains at any moment one instance for
|
|
||||||
every type of its operands. Product types are also called tuples
|
|
||||||
or records. Algebraic data types can be recursive
|
|
||||||
in their definition and can be combined.
|
|
||||||
Moreover ML languages are functional, meaning that functions are
|
|
||||||
treated as first class citizens and variables are immutable,
|
|
||||||
although mutable statements and imperative constructs are permitted.
|
|
||||||
In addition to that OCaml features an object system, that provides
|
|
||||||
inheritance, subtyping and dynamic binding, and modules, that
|
|
||||||
provide a way to encapsulate definitions. Modules are checked
|
|
||||||
statically and can be reificated through functors.
|
|
||||||
|
|
||||||
\begin{enumerate}
|
|
||||||
\item {\bfseries\sffamily TODO} 1.2 Pattern matching [37\%]
|
|
||||||
\label{sec:org83a2e95}
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] capisci come mettere gli esempi uno accanto all'altro
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
Pattern matching is a widely adopted mechanism to interact with ADT.
|
|
||||||
C family languages provide branching on predicates through the use of
|
|
||||||
if statements and switch statements.
|
|
||||||
Pattern matching is a mechanism for destructuring and analyzing data
|
|
||||||
structures for the presence of values simbolically represented as
|
|
||||||
tokens. One common example of pattern matching is the use of regular
|
|
||||||
expressions on strings. OCaml provides pattern matching on ADT,
|
|
||||||
primitive data types.
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\boxtimes$}] Esempio enum, C e Ocaml
|
|
||||||
\end{itemize}
|
|
||||||
\begin{verbatim}
|
|
||||||
type color = | Red | Blue | Green
|
|
||||||
|
|
||||||
begin match color with
|
|
||||||
| Red -> print "red"
|
|
||||||
| Blue -> print "red"
|
|
||||||
| Green -> print "red"
|
|
||||||
|
|
||||||
\end{verbatim}
|
|
||||||
|
|
||||||
OCaml provides tokens to express data destructoring
|
|
||||||
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\boxtimes$}] Esempio destructor list
|
|
||||||
\end{itemize}
|
|
||||||
\begin{verbatim}
|
|
||||||
|
|
||||||
begin match list with
|
|
||||||
| [ ] -> print "empty list"
|
|
||||||
| element1 :: [ ] -> print "one element"
|
|
||||||
| element1 :: element2 :: [ ] -> print "two elements"
|
|
||||||
| head :: tail-> print "head followed by many elements"
|
|
||||||
\end{verbatim}
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\boxtimes$}] Esempio destructor tuples
|
|
||||||
\end{itemize}
|
|
||||||
\begin{verbatim}
|
|
||||||
|
|
||||||
begin match tuple with
|
|
||||||
| (Some _, Some _) -> print "Pair of optional types"
|
|
||||||
| (Some _, None) -> print "Pair of optional types, last null"
|
|
||||||
| (None, Some _) -> print "Pair of optional types, first null"
|
|
||||||
| (None, None) -> print "Pair of optional types, both null"
|
|
||||||
\end{verbatim}
|
|
||||||
|
|
||||||
Pattern clauses can make the use of \emph{guards} to test predicates and
|
|
||||||
variables can be binded in scope.
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] Esempio binding e guards
|
|
||||||
\end{itemize}
|
|
||||||
\begin{verbatim}
|
|
||||||
|
|
||||||
begin match token_list with
|
|
||||||
| "switch"::var::"{"::rest ->
|
|
||||||
| "case"::":"::var::rest when is_int var ->
|
|
||||||
| "case"::":"::var::rest when is_string var ->
|
|
||||||
| "}"::[ ] -> stop ()
|
|
||||||
| "}"::rest -> error "syntax error: " rest
|
|
||||||
|
|
||||||
\end{verbatim}
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] Un altro esempio con destructors e tutto i lresto
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
In general pattern matching on primitive and algebraic data types takes the
|
|
||||||
following form.
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] Esempio informale
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
It can be described more formally through a BNF grammar.
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] BNF
|
|
||||||
|
|
||||||
\item[{$\square$}] Come funziona il pattern matching?
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
\item {\bfseries\sffamily TODO} 1.2.1 Pattern matching compilation to lambda code
|
|
||||||
\label{sec:org2127ffb}
|
|
||||||
|
|
||||||
\begin{itemize}
|
|
||||||
\item[{$\square$}] Da tabella a matrice
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
Formally, pattern are defined as follows:
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{ll}
|
|
||||||
pattern ::= & Patterns\\
|
|
||||||
\hline
|
|
||||||
\_ & wildcard\\
|
|
||||||
x & variable\\
|
|
||||||
c(p₁,p₂,\ldots{},pₙ & constructor pattern\\
|
|
||||||
(p₁\(\vert{}\) p₂) & or-pattern\\
|
|
||||||
\end{tabular}
|
|
||||||
\end{center}
|
|
||||||
|
|
||||||
Values are defined as follows:
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{ll}
|
|
||||||
values ::= & Values\\
|
|
||||||
\hline
|
|
||||||
c(v₁, v₂, \ldots{}, vₙ) & constructor value\\
|
|
||||||
\end{tabular}
|
|
||||||
\end{center}
|
|
||||||
|
|
||||||
The entire pattern matching code can be represented as a clause matrix
|
|
||||||
that associates rows of patterns (p\(_{\text{i,1}}\), p\(_{\text{i,2}}\), \ldots{}, p\(_{\text{i,n}}\)) to
|
|
||||||
lambda code action lⁱ
|
|
||||||
\begin{equation*}
|
|
||||||
(P → L) =
|
|
||||||
\begin{pmatrix}
|
|
||||||
p_{1,1} & p_{1,2} & \cdots & p_{1,n} → l₁ \\
|
|
||||||
p_{2,1} & p_{2,2} & \cdots & p_{2,n} → l₂ \\
|
|
||||||
\vdots & \vdots & \ddots \vdots → \vdots \\
|
|
||||||
p_{m,1} & p_{m,2} & \cdots & p_{m,n} → lₘ
|
|
||||||
\end{pmatrix}
|
|
||||||
\end{equation*}
|
|
||||||
|
|
||||||
Most native data types in OCaml, such as integers, tuples, lists,
|
|
||||||
records, can be seen as instances of the following definition
|
|
||||||
|
|
||||||
\begin{verbatim}
|
|
||||||
type t = Nil | One of int | Cons of int * t
|
|
||||||
\end{verbatim}
|
|
||||||
that is a type \emph{t} with three constructors that define its complete
|
|
||||||
signature.
|
|
||||||
Every constructor has an arity. Nil, a constructor of arity 0, is
|
|
||||||
called a constant constructor.
|
|
||||||
|
|
||||||
The pattern \emph{p} matches a value \emph{v}, written as p ≼ v, when
|
|
||||||
one of the following rules apply
|
|
||||||
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{llll}
|
|
||||||
\_ & ≼ & v & \\
|
|
||||||
x & ≼ & v & \\
|
|
||||||
(p₁ \(\vert{}\)$\backslash$ p₂) & ≼ & v & iff p₁ ≼ v or p₂ ≼ v\\
|
|
||||||
c(p₁, p₂, \ldots{}, pₐ) & ≼ & c(v₁, v₂, \ldots{}, vₐ) & iff (p₁, p₂, \ldots{}, pₐ) ≼ (v₁, v₂, \ldots{}, vₐ)\\
|
|
||||||
(p₁, p₂, \ldots{}, pₐ) & ≼ & (v₁, v₂, \ldots{}, vₐ) & iff pᵢ ≼ vᵢ ∀i ∈ [1..a]\\
|
|
||||||
\end{tabular}
|
|
||||||
\end{center}
|
|
||||||
We can also say that \emph{v} is an \emph{instance} of \emph{p}.
|
|
||||||
|
|
||||||
When we consider the pattern matrix P we say that the value vector
|
|
||||||
\vv{v} = (v₁, v₂, \ldots{}, vᵢ) matches the line number i in P if and only if the following two
|
|
||||||
conditions are satisfied:
|
|
||||||
\begin{itemize}
|
|
||||||
\item \[ p_{i,1} & p_{i,2} & \cdots & p_{i,n} \] ≼ (v₁, v₂, \ldots{}, vᵢ)
|
|
||||||
\item \[ ∀j < i p_{j,1} & p_{j,2} & \cdots & p_{j,n} \] ⋠ (v₁, v₂, \ldots{}, vᵢ)
|
|
||||||
\end{itemize}
|
|
||||||
|
|
||||||
We can define the following three relations with respect to patterns:
|
|
||||||
\begin{itemize}
|
|
||||||
\item Patter p is less precise than pattern q, writtens p ≼ q when all
|
|
||||||
instances of q are instances of p
|
|
||||||
\item Pattern p and q are equivalent, written p ≡ q, when their instances
|
|
||||||
are the same
|
|
||||||
\item Patterns p and q are compatible when they share a common instance
|
|
||||||
\end{itemize}
|
|
||||||
\end{enumerate}
|
|
||||||
|
|
||||||
\subsection{1.2.1.1 Initial state of the compilation}
|
|
||||||
\label{sec:org0b0c254}
|
|
||||||
|
|
||||||
Given a source of the following form:
|
|
||||||
|
|
||||||
\#+BEGIN\_SRC ocaml
|
|
||||||
match x with
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{l}
|
|
||||||
p₁ -> e₁\\
|
|
||||||
p₂ -> e₂\\
|
|
||||||
\end{tabular}
|
|
||||||
\end{center}
|
|
||||||
\ldots{}
|
|
||||||
\begin{center}
|
|
||||||
\begin{tabular}{l}
|
|
||||||
pₘ -> eₘ\\
|
|
||||||
\end{tabular}
|
|
||||||
\end{center}
|
|
||||||
\#+END\_SRC ocaml
|
|
||||||
|
|
||||||
the initial input of the algorithm consists of a vector of variables
|
|
||||||
\vv{x} = (x₁, x₂, \ldots{}, xₙ) of size n
|
|
||||||
and a clause matrix P → L of width n and height m.
|
|
||||||
|
|
||||||
\begin{equation*}
|
|
||||||
(P → L) =
|
|
||||||
\begin{pmatrix}
|
|
||||||
p_{1,1} & p_{1,2} & \cdots & p_{1,n} → l₁ \\
|
|
||||||
p_{2,1} & p_{2,2} & \cdots & p_{2,n} → l₂ \\
|
|
||||||
\vdots & \vdots & \ddots \vdots → \vdots \\
|
|
||||||
p_{m,1} & p_{m,2} & \cdots & p_{m,n} → lₘ
|
|
||||||
\end{pmatrix}
|
|
||||||
\end{equation*}
|
|
||||||
\end{document}
|
|
||||||
|
|
@ -1,21 +0,0 @@
|
||||||
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019 Gentoo Linux) (preloaded format=pdflatex 2020.2.15) 17 FEB 2020 16:31
|
|
||||||
entering extended mode
|
|
||||||
restricted \write18 enabled.
|
|
||||||
%&-line parsing enabled.
|
|
||||||
**tesi.tex
|
|
||||||
|
|
||||||
! Emergency stop.
|
|
||||||
<*> tesi.tex
|
|
||||||
|
|
||||||
End of file on the terminal!
|
|
||||||
|
|
||||||
|
|
||||||
Here is how much of TeX's memory you used:
|
|
||||||
3 strings out of 494553
|
|
||||||
112 string characters out of 6177841
|
|
||||||
52201 words of memory out of 5000000
|
|
||||||
3775 multiletter control sequences out of 15000+600000
|
|
||||||
3640 words of font info for 14 fonts, out of 8000000 for 9000
|
|
||||||
14 hyphenation exceptions out of 8191
|
|
||||||
0i,0n,0p,11b,6s stack positions out of 5000i,500n,10000p,200000b,80000s
|
|
||||||
! ==> Fatal error occurred, no output PDF file produced!
|
|
||||||
2519
tesi/unicode-latex.json
Normal file
2519
tesi/unicode-latex.json
Normal file
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Reference in a new issue