diff --git a/report/UF_FRED_paper_style.sty b/report/UF_FRED_paper_style.sty
new file mode 100644
index 0000000..6668526
--- /dev/null
+++ b/report/UF_FRED_paper_style.sty
@@ -0,0 +1,24 @@
+\usepackage[utf8]{inputenc}
+\usepackage{hyperref}
+\usepackage{setspace}
+\usepackage{palatino}
+\usepackage{graphicx}
+\usepackage{float}
+\usepackage{titling} % drop vertical space before the title
+\usepackage{multirow}
+\usepackage{lscape}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{subcaption}
+\usepackage[a4paper, total={6in, 9.5in}]{geometry}
+\fontfamily{ppl}\selectfont 
+
+\usepackage[american]{babel}
+
+\usepackage{setspace}
+\renewcommand{\baselinestretch}{1.5} 
+
+% BIBLIOGRAPHY %%%%%%%%%%%%%%
+\usepackage[natbibapa]{apacite} % to enable '\citet' and '\citep' macros
+\bibliographystyle{apacite}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/report/main.aux b/report/main.aux
new file mode 100644
index 0000000..0e65cdb
--- /dev/null
+++ b/report/main.aux
@@ -0,0 +1,29 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\bibstyle{apacite}
+\babel@aux{american}{}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction to the new constructs}{1}{section.1}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Scanner}{2}{section.2}}
+\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
+\newlabel{tab:1}{{\caption@xref {tab:1}{ on input line 111}}{2}{Scanner}{table.caption.1}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Parser}{3}{section.3}}
+\@writefile{toc}{\contentsline {section}{\numberline {4}Code Generation}{4}{section.4}}
+\@writefile{toc}{\contentsline {section}{\numberline {5}An example Program}{6}{section.5}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Computation of the n-th Fibonacci number}{6}{subsection.5.1}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Optimization and static analysis}{6}{section.6}}
diff --git a/report/main.log b/report/main.log
new file mode 100644
index 0000000..acfa9b8
--- /dev/null
+++ b/report/main.log
@@ -0,0 +1,1043 @@
+This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2018.10.11)  1 MAR 2020 12:56
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**main.tex
+(./main.tex
+LaTeX2e <2017-04-15>
+Babel <3.18> and hyphenation patterns for 84 language(s) loaded.
+(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
+Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
+(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo
+File: size11.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
+)
+\c@part=\count79
+\c@section=\count80
+\c@subsection=\count81
+\c@subsubsection=\count82
+\c@paragraph=\count83
+\c@subparagraph=\count84
+\c@figure=\count85
+\c@table=\count86
+\abovecaptionskip=\skip41
+\belowcaptionskip=\skip42
+\bibindent=\dimen102
+)
+(./UF_FRED_paper_style.sty
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+   defining Unicode char U+00D1 (decimal 209)
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+   defining Unicode char U+00E2 (decimal 226)
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+   defining Unicode char U+00F0 (decimal 240)
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+   defining Unicode char U+00F2 (decimal 242)
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+   defining Unicode char U+00F4 (decimal 244)
+   defining Unicode char U+00F5 (decimal 245)
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+   defining Unicode char U+00F8 (decimal 248)
+   defining Unicode char U+00F9 (decimal 249)
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+   defining Unicode char U+00FF (decimal 255)
+   defining Unicode char U+0100 (decimal 256)
+   defining Unicode char U+0101 (decimal 257)
+   defining Unicode char U+0102 (decimal 258)
+   defining Unicode char U+0103 (decimal 259)
+   defining Unicode char U+0104 (decimal 260)
+   defining Unicode char U+0105 (decimal 261)
+   defining Unicode char U+0106 (decimal 262)
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+   defining Unicode char U+0108 (decimal 264)
+   defining Unicode char U+0109 (decimal 265)
+   defining Unicode char U+010A (decimal 266)
+   defining Unicode char U+010B (decimal 267)
+   defining Unicode char U+010C (decimal 268)
+   defining Unicode char U+010D (decimal 269)
+   defining Unicode char U+010E (decimal 270)
+   defining Unicode char U+010F (decimal 271)
+   defining Unicode char U+0110 (decimal 272)
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+   defining Unicode char U+0112 (decimal 274)
+   defining Unicode char U+0113 (decimal 275)
+   defining Unicode char U+0114 (decimal 276)
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+   defining Unicode char U+0116 (decimal 278)
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+   defining Unicode char U+011B (decimal 283)
+   defining Unicode char U+011C (decimal 284)
+   defining Unicode char U+011D (decimal 285)
+   defining Unicode char U+011E (decimal 286)
+   defining Unicode char U+011F (decimal 287)
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+   defining Unicode char U+0121 (decimal 289)
+   defining Unicode char U+0122 (decimal 290)
+   defining Unicode char U+0123 (decimal 291)
+   defining Unicode char U+0124 (decimal 292)
+   defining Unicode char U+0125 (decimal 293)
+   defining Unicode char U+0128 (decimal 296)
+   defining Unicode char U+0129 (decimal 297)
+   defining Unicode char U+012A (decimal 298)
+   defining Unicode char U+012B (decimal 299)
+   defining Unicode char U+012C (decimal 300)
+   defining Unicode char U+012D (decimal 301)
+   defining Unicode char U+012E (decimal 302)
+   defining Unicode char U+012F (decimal 303)
+   defining Unicode char U+0130 (decimal 304)
+   defining Unicode char U+0131 (decimal 305)
+   defining Unicode char U+0132 (decimal 306)
+   defining Unicode char U+0133 (decimal 307)
+   defining Unicode char U+0134 (decimal 308)
+   defining Unicode char U+0135 (decimal 309)
+   defining Unicode char U+0136 (decimal 310)
+   defining Unicode char U+0137 (decimal 311)
+   defining Unicode char U+0139 (decimal 313)
+   defining Unicode char U+013A (decimal 314)
+   defining Unicode char U+013B (decimal 315)
+   defining Unicode char U+013C (decimal 316)
+   defining Unicode char U+013D (decimal 317)
+   defining Unicode char U+013E (decimal 318)
+   defining Unicode char U+0141 (decimal 321)
+   defining Unicode char U+0142 (decimal 322)
+   defining Unicode char U+0143 (decimal 323)
+   defining Unicode char U+0144 (decimal 324)
+   defining Unicode char U+0145 (decimal 325)
+   defining Unicode char U+0146 (decimal 326)
+   defining Unicode char U+0147 (decimal 327)
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+   defining Unicode char U+014B (decimal 331)
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+   defining Unicode char U+014D (decimal 333)
+   defining Unicode char U+014E (decimal 334)
+   defining Unicode char U+014F (decimal 335)
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+   defining Unicode char U+0151 (decimal 337)
+   defining Unicode char U+0152 (decimal 338)
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+   defining Unicode char U+0154 (decimal 340)
+   defining Unicode char U+0155 (decimal 341)
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+   defining Unicode char U+0157 (decimal 343)
+   defining Unicode char U+0158 (decimal 344)
+   defining Unicode char U+0159 (decimal 345)
+   defining Unicode char U+015A (decimal 346)
+   defining Unicode char U+015B (decimal 347)
+   defining Unicode char U+015C (decimal 348)
+   defining Unicode char U+015D (decimal 349)
+   defining Unicode char U+015E (decimal 350)
+   defining Unicode char U+015F (decimal 351)
+   defining Unicode char U+0160 (decimal 352)
+   defining Unicode char U+0161 (decimal 353)
+   defining Unicode char U+0162 (decimal 354)
+   defining Unicode char U+0163 (decimal 355)
+   defining Unicode char U+0164 (decimal 356)
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+   defining Unicode char U+0168 (decimal 360)
+   defining Unicode char U+0169 (decimal 361)
+   defining Unicode char U+016A (decimal 362)
+   defining Unicode char U+016B (decimal 363)
+   defining Unicode char U+016C (decimal 364)
+   defining Unicode char U+016D (decimal 365)
+   defining Unicode char U+016E (decimal 366)
+   defining Unicode char U+016F (decimal 367)
+   defining Unicode char U+0170 (decimal 368)
+   defining Unicode char U+0171 (decimal 369)
+   defining Unicode char U+0172 (decimal 370)
+   defining Unicode char U+0173 (decimal 371)
+   defining Unicode char U+0174 (decimal 372)
+   defining Unicode char U+0175 (decimal 373)
+   defining Unicode char U+0176 (decimal 374)
+   defining Unicode char U+0177 (decimal 375)
+   defining Unicode char U+0178 (decimal 376)
+   defining Unicode char U+0179 (decimal 377)
+   defining Unicode char U+017A (decimal 378)
+   defining Unicode char U+017B (decimal 379)
+   defining Unicode char U+017C (decimal 380)
+   defining Unicode char U+017D (decimal 381)
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+   defining Unicode char U+01CD (decimal 461)
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+   defining Unicode char U+01D0 (decimal 464)
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+   defining Unicode char U+01D2 (decimal 466)
+   defining Unicode char U+01D3 (decimal 467)
+   defining Unicode char U+01D4 (decimal 468)
+   defining Unicode char U+01E2 (decimal 482)
+   defining Unicode char U+01E3 (decimal 483)
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+   defining Unicode char U+01E8 (decimal 488)
+   defining Unicode char U+01E9 (decimal 489)
+   defining Unicode char U+01EA (decimal 490)
+   defining Unicode char U+01EB (decimal 491)
+   defining Unicode char U+01F0 (decimal 496)
+   defining Unicode char U+01F4 (decimal 500)
+   defining Unicode char U+01F5 (decimal 501)
+   defining Unicode char U+0218 (decimal 536)
+   defining Unicode char U+0219 (decimal 537)
+   defining Unicode char U+021A (decimal 538)
+   defining Unicode char U+021B (decimal 539)
+   defining Unicode char U+0232 (decimal 562)
+   defining Unicode char U+0233 (decimal 563)
+   defining Unicode char U+1E02 (decimal 7682)
+   defining Unicode char U+1E03 (decimal 7683)
+   defining Unicode char U+200C (decimal 8204)
+   defining Unicode char U+2010 (decimal 8208)
+   defining Unicode char U+2011 (decimal 8209)
+   defining Unicode char U+2012 (decimal 8210)
+   defining Unicode char U+2013 (decimal 8211)
+   defining Unicode char U+2014 (decimal 8212)
+   defining Unicode char U+2015 (decimal 8213)
+   defining Unicode char U+2018 (decimal 8216)
+   defining Unicode char U+2019 (decimal 8217)
+   defining Unicode char U+201A (decimal 8218)
+   defining Unicode char U+201C (decimal 8220)
+   defining Unicode char U+201D (decimal 8221)
+   defining Unicode char U+201E (decimal 8222)
+   defining Unicode char U+2030 (decimal 8240)
+   defining Unicode char U+2031 (decimal 8241)
+   defining Unicode char U+2039 (decimal 8249)
+   defining Unicode char U+203A (decimal 8250)
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+   defining Unicode char U+1E21 (decimal 7713)
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+   defining Unicode char U+00A0 (decimal 160)
+   defining Unicode char U+00A1 (decimal 161)
+   defining Unicode char U+00A3 (decimal 163)
+   defining Unicode char U+00AD (decimal 173)
+   defining Unicode char U+00B8 (decimal 184)
+   defining Unicode char U+00BF (decimal 191)
+   defining Unicode char U+00C5 (decimal 197)
+   defining Unicode char U+00C6 (decimal 198)
+   defining Unicode char U+00D8 (decimal 216)
+   defining Unicode char U+00DF (decimal 223)
+   defining Unicode char U+00E6 (decimal 230)
+   defining Unicode char U+00EC (decimal 236)
+   defining Unicode char U+00ED (decimal 237)
+   defining Unicode char U+00EE (decimal 238)
+   defining Unicode char U+00EF (decimal 239)
+   defining Unicode char U+00F8 (decimal 248)
+   defining Unicode char U+0131 (decimal 305)
+   defining Unicode char U+0141 (decimal 321)
+   defining Unicode char U+0142 (decimal 322)
+   defining Unicode char U+0152 (decimal 338)
+   defining Unicode char U+0153 (decimal 339)
+   defining Unicode char U+0174 (decimal 372)
+   defining Unicode char U+0175 (decimal 373)
+   defining Unicode char U+0176 (decimal 374)
+   defining Unicode char U+0177 (decimal 375)
+   defining Unicode char U+0218 (decimal 536)
+   defining Unicode char U+0219 (decimal 537)
+   defining Unicode char U+021A (decimal 538)
+   defining Unicode char U+021B (decimal 539)
+   defining Unicode char U+2013 (decimal 8211)
+   defining Unicode char U+2014 (decimal 8212)
+   defining Unicode char U+2018 (decimal 8216)
+   defining Unicode char U+2019 (decimal 8217)
+   defining Unicode char U+201C (decimal 8220)
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+   defining Unicode char U+00A7 (decimal 167)
+   defining Unicode char U+00B6 (decimal 182)
+   defining Unicode char U+00B7 (decimal 183)
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+   defining Unicode char U+2021 (decimal 8225)
+   defining Unicode char U+2022 (decimal 8226)
+)
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+   defining Unicode char U+00A9 (decimal 169)
+   defining Unicode char U+00AA (decimal 170)
+   defining Unicode char U+00AE (decimal 174)
+   defining Unicode char U+00BA (decimal 186)
+   defining Unicode char U+02C6 (decimal 710)
+   defining Unicode char U+02DC (decimal 732)
+   defining Unicode char U+200C (decimal 8204)
+   defining Unicode char U+2026 (decimal 8230)
+   defining Unicode char U+2122 (decimal 8482)
+   defining Unicode char U+2423 (decimal 9251)
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+
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+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+
+! Missing } inserted.
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+                }
+l.124     \end{tabular}}
+                        
+I've inserted something that you may have forgotten.
+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+
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+l.131 ...ew non-terminal symbol \textbf{vect_elem}
+                                                  , delimited by square brac...
+I've inserted a begin-math/end-math symbol since I think
+you left one out. Proceed, with fingers crossed.
+
+! Extra }, or forgotten $.
+<recently read> \egroup 
+                        
+l.131 ...ew non-terminal symbol \textbf{vect_elem}
+                                                  , delimited by square brac...
+I've deleted a group-closing symbol because it seems to be
+spurious, as in `$x}$'. But perhaps the } is legitimate and
+you forgot something else, as in `\hbox{$x}'. In such cases
+the way to recover is to insert both the forgotten and the
+deleted material, e.g., by typing `I$}'.
+
+! Missing $ inserted.
+<inserted text> 
+                $
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+                      
+I've inserted a begin-math/end-math symbol since I think
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+
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+<inserted text> 
+                \endgroup 
+l.132 \begin{verbatim}
+                      
+I've inserted something that you may have forgotten.
+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+
+
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+ []
+
+[2]
+
+! LaTeX Error: \begin{document} ended by \end{verbatim}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
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+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
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+I've inserted something that you may have forgotten.
+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+
+! Extra \endgroup.
+<recently read> \endgroup 
+                          
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+                    {}
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+= %body, %entry[] 
+ []
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+= %else, %then[] 
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diff --git a/report/main.out b/report/main.out
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+\BOOKMARK [1][-]{section.1}{Introduction to the new constructs}{}% 1
+\BOOKMARK [1][-]{section.2}{Scanner}{}% 2
+\BOOKMARK [1][-]{section.3}{Parser}{}% 3
+\BOOKMARK [1][-]{section.4}{Code Generation}{}% 4
+\BOOKMARK [1][-]{section.5}{An example Program}{}% 5
+\BOOKMARK [2][-]{subsection.5.1}{Computation of the n-th Fibonacci number}{section.5}% 6
+\BOOKMARK [1][-]{section.6}{Optimization and static analysis}{}% 7
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+\documentclass[11pt]{article}
+\usepackage{UF_FRED_paper_style}
+
+\onehalfspacing
+%% ===============================================
+
+\setlength{\droptitle}{-5em} %% Don't touch
+
+
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% SET THE TITLE
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% TITLE:
+\title{Introducing array-like structures in an expression-based toy-programming language}
+
+% AUTHORS:
+\author{Lapo Toloni \\% Name author
+    \href{l.toloni-at-studenti.unipi.it}{\texttt{l.toloni-at-studenti.unipi.it}}} 
+
+    
+% DATE:
+\date{\today}
+
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% ABSTRACT
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\maketitle
+% %%%%%%%%%%%%%%%%%%
+
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% BODY OF THE DOCUMENT
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% --------------------
+\section{Introduction to the new constructs}
+% --------------------
+The focus of this project is to introduce in the language array-like structures and operations to play with them. All along the codebase\footnote{\href{}{https://github.com/lapotolo/languages-interpreters-compilers-unipi}} 
+and in this report we will refer to these linear structures as \textbf{vectors}. In particular the newly implemented features are:
+
+\begin{itemize}
+
+  \item Declaration and evaluation of a vector of expressions. Multidimensional vectors are supported too.\\
+  As an example we are now allowed to write and have evaluated:
+  \begin{verbatim}
+      [1,2,3]
+      [let x = 5 in if ( x < 5) then x-2 else x+1, 1*4-2, 42]
+      let base = 1 in [base+1, base+2, base+3]
+  \end{verbatim}{}
+  The only constraint is that every element must evaluate to a value of the same type.
+  
+  \item Vector access. For example:
+  \begin{verbatim}
+      let ve = [1,2,3,4,5,6] in ve[0] - ve[5]
+      let mat = [[1,2,3],[4,5,6],[7,8,9]] in mat[1][2]
+  \end{verbatim}{}
+  Note that in this status any check is performed on indices out of bounds. LLVM library calls returns 0 when we access a not allocated piece of memory
+  
+  \item Vector update. For example:
+  \begin{verbatim}
+      var mat = [[1,2,3],[4,5,6],[7,8,9]] in
+        mat[0]:= [42,42,42]
+  \end{verbatim}{}
+  
+  \item vector concatenation. For example:
+  \begin{verbatim}
+    let ve1 = [0,1,1,2] in
+    let ve2 = [3,5,8] in
+      ve1 ++ ve2  // gives the list [0,1,1,2,3,5,8]
+  \end{verbatim}{}
+  
+  \item syntactic sugar to ease the declaration of a vector. For example:
+  \begin{verbatim}
+      [[1,2,3]] times 10 // gives a list of 10 lists whose elements are
+                         // [1,2,3]
+  \end{verbatim}{}
+  
+  \item shortcircuit evaluation model for boolean AND and OR. For example:
+  \begin{verbatim}
+      (10 < 3) & (1 = 1)  // right-hand-side is not evaluated 
+      (5 != 3) | (false)  // right-hand-side is not evaluated
+  \end{verbatim}{}
+  
+  \item evaluation of a sequence of expressions. For example:
+  \begin{verbatim}
+     var i = 0 in
+     var c = 1 in
+     while (i < 10) do
+       seq
+       c := c * c + i;
+       i := i + 1. 
+  \end{verbatim}{}
+  
+  \item support for the modulo binary operation. For example:
+  \begin{verbatim}
+      42 mod 9
+  \end{verbatim}{}
+\end{itemize}
+
+\section{Scanner}
+Here the extension is trivial. The following table subsumes the addition to the lex scanner:
+\begin{table}[H]
+  \centering
+  \label{tab:1}
+  \scalebox{.8}{
+    \begin{tabular}{rll}
+    \hline
+    \multicolumn{1}{c}{\textbf{lexeme}} & \multicolumn{1}{c}{\textbf{token}} & \multicolumn{1}{c}{\textbf{associated semantics}}\\ \hline
+    \multicolumn{1}{l}{++} & CONCAT\_KW & vector concatenation\\
+
+    \multicolumn{1}{l}{times} & TIMES\_KW & syntactic sugar for vector declaration\\
+    \multicolumn{1}{l}{\&} & AND\_SC & short-circuited AND\\
+    \multicolumn{1}{l}{\|} & OR\_SC & short-circuited OR\\
+    \multicolumn{1}{l}{seq} & SEQ\_KW & expression sequence\\
+    \multicolumn{1}{l}{mod} & MOD & modulo operation\\
+    \hline
+    \end{tabular}}
+\end{table}
+Moreover, square brackets are used to delimit vectors and to access them; commas separate vector elements, semicolons separate expressions in a sequence while dots terminate an expression sequence.
+
+
+\section{Parser}
+Regarding the syntactic analysis phase, the only non-trivial extensions are those implemented to parse vectors and related operations.\\
+The LALR(1) parser built with Bison is enhanced with new productions recognizing vector of expressions. An expression may now derive a new non-terminal symbol \textbf{vect_elem}, delimited by square brackets:
+\begin{verbatim}
+expr : ...
+     | '[' vect_elem ']'   { $$ = make_vect($2); }
+\end{verbatim}{}
+
+The computation associated with this production is the call to
+\textbf{make\_vect()}, an internal function taking as argument a value of type \textbf{struct expr\_vect} and producing a value of type \textbf{expr} with type tag \textbf{VECT}.\\
+
+\textbf{struct expr\_vect} is a new possible form of the internal struct used to represent a node of the abstract syntax tree. This kind of node holds the result of the evaluation of the current expression and a pointer to the following expression of the vector.\\
+
+Four other new productions are related with it. These encode vector elements and vector continuation (and termination):
+\begin{verbatim}     
+vect_elem: expr vect_elem_continuation 
+         | %empty   
+
+vect_elem_continuation: ',' expr vect_elem_continuation
+                      | %empty        
+\end{verbatim}{}
+
+The two \%empty productions produces a \textbf{NULL} and are respectively used to deal with empty vectors and termination of vectors. More interestingly both the first productions of the two rules have as associated computation a call to \textbf{make\_expr\_vect()} that is the function that produce the value of type \textbf{struct expr\_vect} that will be eaten by the function \textbf{make\_vect()}.\\
+
+The possibility of binding a vector to a name using the \textbf{let} construct or of storing it in memory as a variable using the \textbf{var} construct comes for free because of a vector of expressions is an expression itself.
+\\
+\medskip
+To support the standard operations of arrays we add two more possible productions starting from the non-terminal expr:
+\begin{verbatim}
+expr: ...
+    | expr '[' expr ']'                
+    | expr '[' expr ']' ASSIGN_OP expr
+\end{verbatim}{}
+By not specifying that we require an IDENT token standing in front of a square bracket and a VAL token to index a vector, we keep the representation homogeneus at the syntactic level. In addition, we let the back-end of the compiler decide how to interpret malformed phrases. \\
+For example, if the first expression in the vector access rule does not evaluate to a valid name, then the compilation will fail because of the failure of the C function that resolves the names in the environment (arguments will not match!). \\
+A less typing intensive form used to obtain an expression yielding a vector of a desired size is associated to the production.
+\begin{verbatim}
+expr: ...
+    | '[' vect_elem ']' TIMES_KW expr
+\end{verbatim}{}
+
+The last thing to note about syntactic design choices is related to how we can sequence a block of expressions:
+\begin{verbatim}
+expr: ...
+    | SEQ_KW expr_sequence
+
+expr_sequence : expr expr_seq_cont
+
+expr_seq_cont : ';' expr expr_seq_cont
+              | '.'                   
+\end{verbatim}{}
+We can note that this solution is almost the same as the one used for vectors of expressions. However to keep a functional flavour in the language we decided to avoid using curl brackets to enclose a sequence of expressions.\\
+
+Internally at the level of the abstract syntax tree a sequence of expressions is represented just as a vector of expression. Deeper in the back-end, when LLVM API comes into play, this two features cannot be the same anymore since a vector is represented through a LLVMArrayType and so every element must evaluate to an object of the same type, while in a sequence every element can evaluate to a different type.
+\\
+Finally note that every possible check on types (integers, booleans, vectors) is left to the back-end. It is a waste of time to make the front-end more complex to deal with them while being quite sure that the chosen back-end library will perform a better job.
+
+\section{Code Generation}
+The code generation phase consists in translating to some intermediate representation the tree structure generated by the parser. In this project this is achieved via calls to the LLVM API.\\
+In particular to generate the IR code for a vector of expressions it is needed to:
+\begin{itemize}
+    \item compute the length of the vector;
+    \item create a C array to temporarily keep in memory the result of the evaluation of each expression in the vector together with its IR code;
+    \item use a LLVMBuildAlloca call to allocate the required space to store that vector  of expressions in memory and obtain the base address of the allocated space;
+    \item for each expression in the vector (already evaluated and whose result is stored in the C array "expressions"):
+        \begin{itemize}
+            \item use LLVMBuildInBoundsGEP to compute the offset indicating the location of memory where to store the current expression. The return value of LLVMBuildInBoundsGEP is the pointer to the memory location indicating the next free block in a contiguous segment of memory bounded by $base\ address$ and $base\ address+vector\ length$. 
+            \item use LLVMBuildStore to generate code to actually store that expression to the correct location.
+        \end{itemize}{}
+\end{itemize}{}
+Both for vector accesses and vector updates the pattern to generate the code is similar to the one used to create a vector of expressions. In fact in LLVM, every time we have to deal with array-like structures, the crucial point is the computation of the correct pointer to the required element indicated by a given index. This is always done via LLVMBuildInBoundsGEP and similar library calls.\\
+Code generation for the "seq" construct is based on a simple loop over the internal C structure holding the sequence of expressions. In this case we do not have to generate code to store contiguously in memory the results of each evaluation since every expression is evaluated but only the result of the evaluation of the last expression in the sequence is returned.\\
+Then we extended the "codegen\_expr" function for the "bin\_op" case to make the compiler capable of generating IR code for short-circuited AND and OR and for vector concatenation.\\
+Let's take as an example the implementation of the short-circuited AND. We have to create LLVM basic blocks that encode the fact that the first operand is true or false and one last basic block representing the continuation of the program.
+Since we have to evaluate the second operand only in the case that the first is true, we conditionally branch on the result of the evaluation of the left-hand-side expression.\\
+If it is true, then we continue the computation in the basic block that contains the calls to generate the code for the right-hand side.
+Otherwise, from the branching point the computation follows a path going through an empty basic blocks, encoding the fact that the left-hand-side expression was false and no code has to be generated.
+Both blocks have a single outgoing edge sinking in the continuation basic block.
+The last thing to note is the presence of a LLVMBuildPhi call as the first instruction of the continuation basic block. \\
+Vector concatenation instead follows a pattern similar to the one used for vector creation. Some more effort is required to compute the length of the concatenated vector starting from an integer that is wrapped into a LLVMValueRef.
+Next, we perform two loops to draw first from the left-hand-side vector and then from the right-hand-side. The body of these two loops is almost the same as the one used in the vector creation part. The single difference regards the use of LLVMBuildStructGEP and LLVMBuildLoad to load from memory the elements of the two vectors that will be concatenated. \\
+Excluding future optimization passes, these sets of load are present even if the two vectors were not previously stored in memory, since the model of computation is eager and every expression is always evaluated as soon as it is encountered.
+Note that a unique form of laziness is introduced in the language through short-circuited boolean operations.    \\
+\section{An example Program}
+We list a simple program to show the new features of the language.
+
+\subsection{Computation of the n-th Fibonacci number}
+This is a standard example of a dynamic programming algorithm to compute in linear time and space the n-th Fibonacci number:
+\begin{verbatim}
+let n = 10 in
+var i = 2 in
+var x = [0] times n in
+  seq 
+    x[0] := 0;
+    x[1] := 1;
+    while i < n do
+      seq
+        x[i] := x[i-1] + x[i-2];
+        i := i+1.;
+    x[n-1]. \\ n := 10 implies x[n-1] = 34
+\end{verbatim}
+
+\section{Optimization and static analysis}
+LLVM provides optimization and static analysis through an object called LLVMPassManager. Optimizations are realized as passes traversing some portion of the program to gather information or to transform it. Transform passes mutate the generated IR code mantaining its semantics.
+One common optimization pass is the one provided by \textbf{LLVMAddInstructionCombiningPass}. A first example of the transformation performed by this pass is the following:
+\begin{verbatim}
+var x = [1,2,3] in
+  seq
+    x[0] := x[1];
+    x[0].
+
+generating code...
+
+define i32 @main() {
+entry:
+  %x = alloca [3 x i32]*
+  %0 = alloca [3 x i32]
+  %1 = getelementptr inbounds i32, [3 x i32]* %0, i32 0
+  store i32 1, i32* %1
+  %2 = getelementptr inbounds i32, [3 x i32]* %0, i32 1
+  store i32 2, i32* %2
+  %3 = getelementptr inbounds i32, [3 x i32]* %0, i32 2
+  store i32 3, i32* %3
+  store [3 x i32]* %0, [3 x i32]** %x
+  %4 = load [3 x i32]*, [3 x i32]** %x
+  %5 = load [3 x i32]*, [3 x i32]** %x
+  %6 = getelementptr inbounds [3 x i32], [3 x i32]* %5, i32 0, i32 1
+  %7 = load i32, i32* %6
+  %8 = getelementptr inbounds [3 x i32], [3 x i32]* %4, i32 0, i32 0
+  store i32 %7, i32* %8
+  %9 = load [3 x i32]*, [3 x i32]** %x
+  %10 = getelementptr inbounds [3 x i32], [3 x i32]* %9, i32 0, i32 0
+  %11 = load i32, i32* %10
+  ret i32 %11
+}
+
+generating optimised code...
+
+define i32 @main() {
+entry:
+  %0 = alloca [3 x i32], align 4
+  %1 = getelementptr inbounds i32, [3 x i32]* %0, i64 0
+  store i32 1, i32* %1, align 4
+  %2 = getelementptr inbounds i32, [3 x i32]* %0, i64 1
+  store i32 2, i32* %2, align 4
+  %3 = getelementptr inbounds i32, [3 x i32]* %0, i64 2
+  store i32 3, i32* %3, align 4
+  %4 = getelementptr inbounds [3 x i32], [3 x i32]* %0, i64 0, i64 1
+  %5 = load i32, i32* %4, align 4
+  %6 = getelementptr inbounds [3 x i32], [3 x i32]* %0, i64 0, i64 0
+  store i32 %5, i32* %6, align 4
+  ret i32 %5
+}
+
+running...
+-> 2    
+\end{verbatim}
+
+Note that the two virtual registers \textbf{\%4} and \textbf{\%5} holds the same address in the non optimised code. In the end, by avoiding repeated computation of already known addresses and reducing registers spilling, we spare five virtual registers. \\
+The same pass also enables the elimination of redudant variables as if it is performing a live variable data-flow analysis:
+\begin{verbatim}
+var n = 10 in
+var c = 1 in
+var b = 0 in
+var a = 0 in
+seq
+  while a < n do
+    seq
+      b:= a+1;
+      c:= c+b;
+      a:= b*2.;
+  c.
+
+generating code...
+
+define i32 @main() {
+entry:
+  %a = alloca i32
+  %b = alloca i32
+  %c = alloca i32
+  %n = alloca i32
+  store i32 10, i32* %n
+  store i32 1, i32* %c
+  store i32 0, i32* %b
+  store i32 0, i32* %a
+  br label %cond
+
+cond:                                             ; preds = %body, %entry
+  %0 = load i32, i32* %a
+  %1 = load i32, i32* %n
+  %2 = icmp slt i32 %0, %1
+  br i1 %2, label %body, label %cont
+
+body:                                             ; preds = %cond
+  %3 = load i32, i32* %a
+  %4 = add i32 %3, 1
+  store i32 %4, i32* %b
+  %5 = load i32, i32* %c
+  %6 = load i32, i32* %b
+  %7 = add i32 %5, %6
+  store i32 %7, i32* %c
+  %8 = load i32, i32* %b
+  %9 = mul i32 %8, 2
+  store i32 %9, i32* %a
+  br label %cond
+
+cont:                                             ; preds = %cond
+  %10 = load i32, i32* %c
+  ret i32 %10
+}
+
+generating optimised code...
+
+define i32 @main() {
+entry:
+  %a = alloca i32, align 4
+  %c = alloca i32, align 4
+  %n = alloca i32, align 4
+  store i32 10, i32* %n, align 4
+  store i32 1, i32* %c, align 4
+  br label %cond
+
+cond:                                             ; preds = %body, %entry
+  %storemerge = phi i32 [ %6, %body ], [ 0, %entry ]
+  store i32 %storemerge, i32* %a, align 4
+  %0 = load i32, i32* %n, align 4
+  %1 = icmp slt i32 %storemerge, %0
+  br i1 %1, label %body, label %cont
+
+body:                                             ; preds = %cond
+  %2 = load i32, i32* %a, align 4
+  %3 = add i32 %2, 1
+  %4 = load i32, i32* %c, align 4
+  %5 = add i32 %4, %3
+  store i32 %5, i32* %c, align 4
+  %6 = shl i32 %3, 1
+  br label %cond
+
+cont:                                             ; preds = %cond
+  %7 = load i32, i32* %c, align 4
+  ret i32 %7
+}
+
+running...
+-> 12
+\end{verbatim}
+We can see how the two variables $a$ and $b$ are merged in the single variable/register $a$ in the optimized code. \\
+In addition the LLVMAddInstructionCombiningPass forces 4-byte aligned address, the replacement of multiplications and divisions with shifts and other simple peephole optimizations. \\
+Another possible pass to add is LLVMAddCFGSimplificationPass. This extension makes LLVM delete unreachable blocks by simplifying the control flow graph of the program, as we can see in:
+\begin{verbatim}
+let x = 5 in 
+if x < 2 then x+1 else x-1
+
+generating code...
+
+define i32 @main() {
+entry:
+  br i1 false, label %then, label %else
+
+then:                                             ; preds = %entry
+  br label %cont
+
+else:                                             ; preds = %entry
+  br label %cont
+
+cont:                                             ; preds = %else, %then
+  %0 = phi i32 [ 6, %then ], [ 4, %else ]
+  ret i32 %0
+}
+
+generating optimised code...
+
+define i32 @main() {
+entry:
+  ret i32 4
+}
+\end{verbatim}
+Since the value of $x$ is known at compile time, it can be propagated forward through the program. This implies that the compiler is be able to infer that the "then" branch will never be an actual computation path and so that portion of code is useless and will not be generated.
+% ==========================
+% ==========================
+% ==========================
+
+
+\end{document}
\ No newline at end of file
diff --git a/src/ast.c b/src/ast.c
index fa356b3..2cfbe43 100644
--- a/src/ast.c
+++ b/src/ast.c
@@ -474,7 +474,7 @@ LLVMValueRef codegen_expr(
       // left_true and left_false as possible successors blocks
       LLVMBuildCondBr(builder, left_val, left_true_bb, left_false_bb);
 
-      // in the case left is true it is left to evaluate the right hand side
+      // in the case left is true we need to evaluate the right hand side
       LLVMPositionBuilderAtEnd(builder, left_true_bb);
       LLVMValueRef right_val = codegen_expr(e->binop.rhs, env, module, builder);
       LLVMBuildBr(builder, cont_bb);
@@ -761,14 +761,23 @@ void jit_eval(struct expr *expr)
 
   // NEW
   // Setup optimizations using a pass manager
+  
   LLVMPassManagerRef pass_manager = LLVMCreateFunctionPassManagerForModule(module);
-  LLVMAddPromoteMemoryToRegisterPass(pass_manager);
-  //LLVMAddInstructionCombiningPass(pass_manager);
-  LLVMInitializeFunctionPassManager(pass_manager);;
   
-  //LLVMAddReassociatePass(pass_manager);
-  //LLVMAddGVNPass(pass_manager);
-  //LLVMAddCFGSimplificationPass(pass_manager);
+  // Do simple "peephole" optimizations and bit-twiddling opti.
+  // LLVMAddInstructionCombiningPass(pass_manager);
+  
+  // Reassociate expressions.
+  // LLVMAddReassociatePass(pass_manager);
+  
+  // Eliminate Common SubExpressions.
+  // LLVMAddGVNPass(pass_manager);
+  
+  // Simplify the control flow graph (deleting unreachable blocks, etc).
+  LLVMAddCFGSimplificationPass(pass_manager);
+
+  //LLVMAddPromoteMemoryToRegisterPass(pass_manager);
+  LLVMInitializeFunctionPassManager(pass_manager);;
   
   char *error;
   if (LLVMCreateExecutionEngineForModule(&engine, module, &error)) {
@@ -783,7 +792,6 @@ void jit_eval(struct expr *expr)
 
   // visit expression to get its LLVM type
   LLVMTypeRef bad_f_type = LLVMFunctionType(LLVMVoidType(), NULL, 0, 0);
-
   LLVMValueRef typing_f = LLVMAddFunction(module, "typing_f", bad_f_type);
   
   LLVMBasicBlockRef typing_entry_bb = LLVMAppendBasicBlock(typing_f, "entry");
@@ -796,7 +804,7 @@ void jit_eval(struct expr *expr)
 
   // emit expression as function body
   LLVMTypeRef actual_f_type = LLVMFunctionType(type, NULL, 0, 0);
-  LLVMValueRef f = LLVMAddFunction(module, "f", actual_f_type);
+  LLVMValueRef f = LLVMAddFunction(module, "main", actual_f_type);
   LLVMBasicBlockRef entry_bb = LLVMAppendBasicBlock(f, "entry");
   LLVMPositionBuilderAtEnd(builder, entry_bb);
   LLVMValueRef ret = codegen_expr(expr, NULL, module, builder);
diff --git a/src/examples/code/sugared-fibo.code b/src/examples/code/sugared-fibo.code
index d7e7a83..67e2642 100644
--- a/src/examples/code/sugared-fibo.code
+++ b/src/examples/code/sugared-fibo.code
@@ -8,4 +8,4 @@ var x = [0] times n in
       seq
         x[i] := x[i-1] + x[i-2];
         i := i+1.;
-    x[9].
\ No newline at end of file
+    x[n-1].
\ No newline at end of file
diff --git a/src/examples/transformations/dead-code-elimination.code b/src/examples/transformations/dead-code-elimination.code
new file mode 100644
index 0000000..49a92d7
--- /dev/null
+++ b/src/examples/transformations/dead-code-elimination.code
@@ -0,0 +1,2 @@
+let x = 5 in 
+if x < 2 then x+1 else x-1
\ No newline at end of file
diff --git a/src/examples/transformations/liveness-ab-merge.code b/src/examples/transformations/liveness-ab-merge.code
new file mode 100644
index 0000000..f334fe0
--- /dev/null
+++ b/src/examples/transformations/liveness-ab-merge.code
@@ -0,0 +1,11 @@
+var n = 10 in
+var c = 1 in
+var b = 0 in
+var a = 0 in
+seq
+  while a < n do
+    seq
+      b:= a+1;
+      c:=c+b;
+      a:= b*2.;
+  c.
\ No newline at end of file
diff --git a/src/examples/transformations/opt-test-vect-vect.code b/src/examples/transformations/opt-test-vect-vect.code
deleted file mode 100644
index b3bcd23..0000000
--- a/src/examples/transformations/opt-test-vect-vect.code
+++ /dev/null
@@ -1,46 +0,0 @@
-let x = [1,2,3] in [x,x,x]
-
-generating code...
-
-define [3 x [3 x i32]*]* @f() {
-entry:
-  %0 = alloca [3 x i32]
-  %1 = getelementptr inbounds i32, [3 x i32]* %0, i32 0
-  store i32 1, i32* %1
-  %2 = getelementptr inbounds i32, [3 x i32]* %0, i32 1
-  store i32 2, i32* %2
-  %3 = getelementptr inbounds i32, [3 x i32]* %0, i32 2
-  store i32 3, i32* %3
-  %4 = alloca [3 x [3 x i32]*]
-  %5 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i32 0
-  store [3 x i32]* %0, [3 x i32]** %5
-  %6 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i32 1
-  store [3 x i32]* %0, [3 x i32]** %6
-  %7 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i32 2
-  store [3 x i32]* %0, [3 x i32]** %7
-  ret [3 x [3 x i32]*]* %4
-}
-
-generating optimised code...
-
-define [3 x [3 x i32]*]* @f() {
-entry:
-  %0 = alloca [3 x i32], align 4
-  %1 = getelementptr inbounds i32, [3 x i32]* %0, i64 0
-  store i32 1, i32* %1, align 4
-  %2 = getelementptr inbounds i32, [3 x i32]* %0, i64 1
-  store i32 2, i32* %2, align 4
-  %3 = getelementptr inbounds i32, [3 x i32]* %0, i64 2
-  store i32 3, i32* %3, align 4
-  %4 = alloca [3 x [3 x i32]*], align 8
-  %5 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i64 0
-  store [3 x i32]* %0, [3 x i32]** %5, align 8
-  %6 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i64 1
-  store [3 x i32]* %0, [3 x i32]** %6, align 8
-  %7 = getelementptr inbounds [3 x i32]*, [3 x [3 x i32]*]* %4, i64 2
-  store [3 x i32]* %0, [3 x i32]** %7, align 8
-  ret [3 x [3 x i32]*]* %4
-}
-
-running...
--> 0
\ No newline at end of file
diff --git a/src/examples/transformations/test-instr-comb.code b/src/examples/transformations/test-instr-comb.code
index d313020..c3140e7 100644
--- a/src/examples/transformations/test-instr-comb.code
+++ b/src/examples/transformations/test-instr-comb.code
@@ -1,15 +1,4 @@
-let x = [1,2,3] in
-[x[0]+1,x[0]+2]
-
-var x = 5 in 
-x + x
-
-define i32 @f() {
-entry:
-  %x = alloca i32
-  store i32 5, i32* %x
-  %0 = load i32, i32* %x
-  %1 = load i32, i32* %x
-  %2 = add i32 %0, %1
-  ret i32 %2
-}
\ No newline at end of file
+var x = [1,2,3] in
+  seq
+    x[0] := x[1];
+    x[0].
\ No newline at end of file