From 3d818d28c8a97c933e8f5732fd35d5424ecf213d Mon Sep 17 00:00:00 2001
From: sebastien <sebastien@ac1d8469-bf42-47a9-8791-bf33cf982152>
Date: Fri, 19 Oct 2007 15:03:37 +0000
Subject: [PATCH] v4 doc: added slides about preprocessor

git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1433 ac1d8469-bf42-47a9-8791-bf33cf982152
---
 doc/preprocessor/expr-sharing.dia |  Bin 0 -> 1887 bytes
 doc/preprocessor/expr-sharing.png |  Bin 0 -> 27510 bytes
 doc/preprocessor/expr.dia         |  Bin 0 -> 1652 bytes
 doc/preprocessor/expr.png         |  Bin 0 -> 11248 bytes
 doc/preprocessor/matrices.dia     |  Bin 0 -> 1804 bytes
 doc/preprocessor/matrices.png     |  Bin 0 -> 26428 bytes
 doc/preprocessor/overview.dia     |  Bin 0 -> 2572 bytes
 doc/preprocessor/overview.png     |  Bin 0 -> 48909 bytes
 doc/preprocessor/preprocessor.pdf |  Bin 0 -> 638297 bytes
 doc/preprocessor/preprocessor.tex | 1165 +++++++++++++++++++++++++++++
 10 files changed, 1165 insertions(+)
 create mode 100644 doc/preprocessor/expr-sharing.dia
 create mode 100644 doc/preprocessor/expr-sharing.png
 create mode 100644 doc/preprocessor/expr.dia
 create mode 100644 doc/preprocessor/expr.png
 create mode 100644 doc/preprocessor/matrices.dia
 create mode 100644 doc/preprocessor/matrices.png
 create mode 100644 doc/preprocessor/overview.dia
 create mode 100644 doc/preprocessor/overview.png
 create mode 100644 doc/preprocessor/preprocessor.pdf
 create mode 100644 doc/preprocessor/preprocessor.tex

diff --git a/doc/preprocessor/expr-sharing.dia b/doc/preprocessor/expr-sharing.dia
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diff --git a/doc/preprocessor/matrices.dia b/doc/preprocessor/matrices.dia
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diff --git a/doc/preprocessor/overview.png b/doc/preprocessor/overview.png
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diff --git a/doc/preprocessor/preprocessor.pdf b/doc/preprocessor/preprocessor.pdf
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diff --git a/doc/preprocessor/preprocessor.tex b/doc/preprocessor/preprocessor.tex
new file mode 100644
index 0000000000..3eed856851
--- /dev/null
+++ b/doc/preprocessor/preprocessor.tex
@@ -0,0 +1,1165 @@
+\documentclass{beamer}
+%\documentclass[draft]{beamer}
+%\documentclass[handout]{beamer}
+
+
+\mode<handout>
+{
+  \usepackage{pgfpages}
+  \pgfpagesuselayout{4 on 1}[a4paper,border shrink=3mm,landscape]
+  \usetheme{Madrid}
+  \usecolortheme{seagull}
+}
+
+\mode<beamer>
+{
+  \usetheme{Madrid}
+  \setbeamercovered{transparent}
+}
+
+
+\usepackage[english]{babel}
+\usepackage[utf8]{inputenc}
+
+\usepackage{times}
+
+
+\title{The Dynare Preprocessor}
+
+\author[S. Villemot]{Sébastien Villemot}
+
+\institute{CEPREMAP}
+
+\date{October 19, 2007}
+
+\AtBeginSection[]
+{
+  \begin{frame}{Outline}
+    \tableofcontents[currentsection]
+  \end{frame}
+}
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}
+  \frametitle{General overview}
+  \begin{center}
+    \includegraphics[width=11cm]{overview.png}
+  \end{center}
+\end{frame}
+
+\begin{frame}{Outline}
+  \tableofcontents
+\end{frame}
+
+\section{Introduction to object-oriented programming in C++}
+
+\begin{frame}
+  \frametitle{Object-oriented programming (OOP)}
+  \begin{itemize}
+  \item Traditional way of programming: a program is a list of instructions (organized in functions) which manipulate data
+  \item OOP is an alternative programming paradigm that uses \alert{objects} and their interactions to design programs
+    \pause
+  \item With OOP, programming becomes a kind of modelization: each object of the program should modelize a real world object, or a mathematical object (\textit{e.g.} a matrix, an equation, a model...)
+  \item Each object can be viewed as an independent little machine with a distinct role or responsibility
+  \item Each object is capable of receiving messages, processing data, and sending messages to other objects
+    \pause
+  \item Main advantage of OOP is \alert{modularity}, which leads to greater reusability, flexibility and maintainability
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Object}
+  \framesubtitle{Definition and example}
+  \begin{itemize}
+  \item An \alert{object} is the bundle of:
+    \begin{itemize} 
+    \item several variables (called its \alert{attributes}), which modelize the characteristics (or the state) of the object
+    \item several functions (called its \alert{methods}) which operate on the attributes, and which modelize the behaviour of the object (the actions it can perform)
+    \end{itemize}
+    \pause
+  \item Example: suppose we want to modelize a coffee machine
+    \begin{itemize}
+    \item The coffee machine (in real life) is a box, with an internal counter for the credit balance, a slot to put coins in, and a button to get a coffee
+    \item The corresponding object will have one attribute (the current credit balance) and two methods (one which modelizes the introduction of money, and the other the making of a coffee)
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{A coffee machine}
+  \framesubtitle{Class definition}
+  \begin{block}{C++ header file (\texttt{CoffeeMachine.hh})}
+    \begin{scriptsize}
+\begin{verbatim}
+class CoffeeMachine {
+public:
+  int credit;
+  CoffeeMachine();
+  void put_coin(int coin_value);
+  void get_coffee();
+};
+\end{verbatim}
+      \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item A \alert{class} is a template (or a blueprint) of an object
+  \item Collectively, the attributes and methods defined by a class are called \alert{members}
+  \item A class definition creates a new \alert{type} (\texttt{CoffeeMachine}) that can be used like other C++ types (\textit{e.g.} \texttt{int}, \texttt{string}, ...)
+  \item In C++, class definitions are put in header files (\texttt{.hh} extension)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{A coffee machine}
+  \framesubtitle{Method bodies}
+  \begin{block}{C++ source file (\texttt{CoffeeMachine.cc})}
+    \begin{scriptsize}
+\begin{verbatim}
+void CoffeeMachine::put_coin(int coin_value)
+{
+  credit += coin_value;
+  cout << "Credit is now " << credit << endl;
+}
+
+void CoffeeMachine::get_coffee()
+{
+  if (credit == 0)
+    cout << "No credit!" << endl;
+  else {
+      credit--;
+      cout << "Your coffee is ready, credit is now " << credit << endl;
+  }
+}
+\end{verbatim}
+    \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item Methods can refer to other members (here the two methods modify the \texttt{credit} attribute)
+  \item Method bodies are put in source files (\texttt{.cc} extension)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Constructors and destructors}
+  \begin{itemize}
+  \item In our class header, there is a special method called \texttt{CoffeeMachine()} (same name than the class)
+  \item It is a \alert{constructor}: called when the object is created, used to initalize the attributes of the class
+  \end{itemize}
+  \begin{block}{C++ source file (\texttt{CoffeeMachine.cc}, continued)}
+    \begin{scriptsize}
+\begin{verbatim}
+CoffeeMachine::CoffeeMachine()
+{
+  credit = 0;
+}
+\end{verbatim}
+    \end{scriptsize}   
+  \end{block}
+  \begin{itemize}
+  \item It is possible to create constructors with arguments
+  \item It is also possible to define a \alert{destructor} (method name is the class name prepended by a tilde, like \texttt{$\sim$CoffeeMachine}): called when the object is destroyed, used to do cleaning tasks (\textit{e.g.} freeing memory)
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{Instantiation and method invocation}
+  \begin{block}{Program main function}
+    \begin{scriptsize}
+\begin{verbatim}
+#include "CoffeeMachine.hh"
+
+int main()
+{
+  CoffeeMachine A, B;
+
+  A.put_coin(2);
+  A.get_coffee();
+
+  B.put_coin(1);
+  B.get_coffee();
+  B.get_coffee();
+}
+\end{verbatim}
+    \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item Creates two machines: at the end, \texttt{A} has 1 credit, \texttt{B} has no credit and refused last coffee
+  \item \texttt{A} and \texttt{B} are called \alert{instances} of class \texttt{CoffeeMachine}
+  \item Methods are invoked by appending a dot and the method name to the instance variable name
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Dynamic instantiation with \texttt{new}}
+  \begin{block}{Program main function}
+    \begin{scriptsize}
+\begin{verbatim}
+#include "CoffeeMachine.hh"
+
+void main()
+{
+  CoffeeMachine *A;
+
+  A = new CoffeeMachine();
+
+  A->put_coin(2);
+  A->get_coffee();
+
+  delete A;
+}
+\end{verbatim}
+    \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item Here \texttt{A} is a pointer to an instance of class \texttt{CoffeeMachine}
+  \item Dynamic creation of instances is done with \texttt{new}, dynamic deletion with \texttt{delete} (analogous to \texttt{malloc} and \texttt{free})
+  \item Since \texttt{A} is a pointer, methods are called with \texttt{->} instead of a dot
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Access modifiers}
+  \begin{itemize}
+  \item In our coffee machine example, all attributes and methods were marked as \texttt{public}
+  \item Means that those attributes and methods can be accessed from anywhere in the program
+  \item Here, one can gain credit without putting money in the machine, with something like \texttt{A.credit = 1000;}
+  \item The solution is to declare it \alert{private}: such members can only be accessed from methods within the class
+  \end{itemize}
+  \begin{block}{C++ header file (\texttt{CoffeeMachine.hh})}
+    \begin{scriptsize}
+\begin{verbatim}
+class CoffeeMachine {
+private:
+  int credit;
+public:
+  CoffeeMachine();
+  void put_coin(int coin_value);
+  void get_coffee();
+};
+\end{verbatim}
+      \end{scriptsize}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Interface}
+  \begin{itemize}
+  \item The public members of a class form its \alert{interface}: they describe how the class interacts with its environment
+  \item Seen from outside, an object is a ``black box'', receiving and sending messages through its interface
+  \item Particular attention should be given to the interface design: an external programmer should be able to work with an class by only studying its interface, but not its internals
+  \item A good design pratice is to limit the set of public members to the strict minimum:
+    \begin{itemize}
+    \item enhances code understandability by making clear the interface
+    \item limits the risk that an internal change in the object requires a change in the rest of the program: \alert{loose coupling}
+    \item prevents the disruption of the coherence of the object by an external action: principle of \alert{isolation}
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Why isolation is important}
+  \begin{itemize}
+  \item Consider a class \texttt{Circle} with the following attributes:
+    \begin{itemize}
+    \item coordinates of the center
+    \item radius
+    \item surface
+    \end{itemize}
+  \item If all members are public, it is possible to modify the radius but not the surface, therefore disrupting internal coherence
+  \item The solution is to make radius and surface private, and to create a public method \texttt{changeRadius} which modifies both simultaneously
+  \item \textit{Conclusion:} Creating a clear interface and isolating the rest diminishes the risk of introducing bugs
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Inheritance (1/2)}
+
+  \begin{block}{Matrices and positive definite matrices}
+    \begin{scriptsize}
+      \begin{columns}[t]
+        \begin{column}{4.8cm}
+\begin{verbatim}
+class Matrix
+{
+protected:
+  int height, width;
+  double[] elements;
+public:
+  Matrix(int n, int p,
+         double[] e);
+  virtual ~Matrix();
+  double det();
+};
+\end{verbatim}
+        \end{column}
+        \begin{column}{6cm}
+\begin{verbatim}
+class PositDefMatrix : public Matrix
+{
+public:
+  PositDefMatrix(int n, int p,
+                 double[] e);
+  Matrix cholesky();
+};
+\end{verbatim}
+        \end{column}
+      \end{columns}
+    \end{scriptsize}
+    
+  \end{block}
+  \begin{itemize}
+  \item \texttt{PositDefMatrix} is a \alert{subclass} (or \alert{derived class}) of \texttt{Matrix}
+  \item Conversely \texttt{Matrix} is the \alert{superclass} of \texttt{PositDefMatrix}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Inheritance (2/2)}
+  \begin{itemize}
+  \item \texttt{PositDefMatrix} inherits \texttt{width}, \texttt{height}, \texttt{elements} and \texttt{det} from \texttt{Matrix}
+  \item Method \texttt{cholesky} can be called on an instance of \texttt{PositDefMatrix}, but not of \texttt{Matrix}
+  \item The keyword \texttt{protected} means: public for subclasses, but private for other classes
+  \item \alert{Type casts} are legal when going upward in the derivation tree:
+    \begin{itemize}
+    \item a pointer to \texttt{PositDefMatrix} can be safely cast to a \texttt{Matrix*}
+    \item the converse is faulty and leads to unpredictable results
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Constructors and destructors (bis)}
+  \begin{block}{C++ code snippet}
+    \begin{scriptsize}
+\begin{verbatim}
+Matrix::Matrix(int n, int p, double[] e) : height(n), width(p)
+{
+  elements = new double[n*p];
+  memcpy(elements, e, n*p*sizeof(double));
+}
+
+Matrix::~Matrix()
+{
+  delete[] elements;
+}
+
+PositDefMatrix::PositDefMatrix(int n, int p, double[] e) :
+  Matrix(n, p, e)
+{
+  // Check that matrix is really positive definite
+}
+\end{verbatim}
+    \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item Constructor of \texttt{PositDefMatrix} calls constructor of \texttt{Matrix}
+  \item Note the abbreviated syntax with colon
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Possible derivation tree for real matrices}
+  \framesubtitle{Arrow means \textit{...is a subclass of...}}
+  \begin{center}
+    \includegraphics[width=10cm]{matrices.png}
+  \end{center}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Polymorphism (1/3)}
+  \begin{itemize}
+  \item In previous example, determinant computation method uses the same algorithm for both classes
+  \item But for positive definite matrices, a faster algorithm exists (using the cholesky)
+  \item \alert{Polymorphism} offers an elegant solution:
+    \begin{itemize}
+    \item declare \texttt{det} as a \alert{virtual method} in class \texttt{Matrix}
+    \item \alert{override} it in \texttt{PositDefMatrix}, and provide the corresponding implementation
+    \end{itemize}
+  \item When method \texttt{det} will be invoked, the correct implementation will be selected, depending on the type of the instance (this is done through a runtime type test)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Polymorphism (2/3)}
+
+  \begin{block}{Class headers}
+    \begin{scriptsize}
+      \begin{columns}[t]
+        \begin{column}{4.8cm}
+\begin{verbatim}
+class Matrix
+{
+protected:
+  int height, width;
+  double[] elements;
+public:
+  Matrix(int n, int p,
+         double[] e);
+  virtual ~Matrix();
+  virtual double det();
+  bool is_invertible();
+};
+\end{verbatim}
+        \end{column}
+        \begin{column}{6cm}
+\begin{verbatim}
+class PositDefMatrix : public Matrix
+{
+public:
+  PositDefMatrix(int n, int p,
+                 double[] e);
+  Matrix cholesky();
+  virtual double det();
+};
+\end{verbatim}
+        \end{column}
+      \end{columns}
+    \end{scriptsize}
+    
+  \end{block}
+  \begin{itemize}
+  \item Note the \texttt{virtual} keyword
+  \item A method has been added to determine if matrix is invertible
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Polymorphism (3/3)}
+  \begin{block}{C++ code snippet}
+    \begin{scriptsize}
+\begin{verbatim}
+bool Matrix::is_invertible()
+{
+  return(det() != 0);
+}
+
+double PositDefMatrix::det()
+{
+  // Square product of diagonal terms of cholesky decomposition
+}
+\end{verbatim}
+    \end{scriptsize}
+  \end{block}
+  \begin{itemize}
+  \item A call to \texttt{is\_invertible} on a instance of \texttt{Matrix} will use the generic determinant computation
+  \item The same call on an instance of \texttt{PositDefMatrix} will call the specialized determinant computation
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Abstract classes}
+  \begin{itemize}
+  \item It is possible to create classes which don't provide an implementation for some virtual methods
+  \item Syntax in the header: \\
+    \texttt{virtual int method\_name() = 0;}
+  \item As a consequence, such classes can never be instantiated
+  \item Generally used as the root of a derivation tree, when classes of the tree share behaviours but not implementations
+  \item Such classes are called \alert{abstract classes}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Some programming rules (1/2)}
+  \begin{itemize}
+  \item Don't repeat yourself (DRY): if several functions contain similar portions of code, \alert{factorize} that code into a new function
+    \begin{itemize}
+    \item makes code shorter
+    \item reduces the risk of introducing inconsistencies
+    \item makes easier the propagation of enhancements and bug corrections
+    \end{itemize}
+  \item Make short functions
+    \begin{itemize}
+    \item often difficult to grasp what a long function does
+    \item structuring the code by dividing it into short functions makes the logical structure more apparent
+    \item enhances code readability and maintainability
+    \end{itemize}
+  \item Use explicit variable names (except for loop indexes)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Some programming rules (2/2)}
+  \begin{itemize}
+  \item Global variables are evil
+    \begin{itemize}
+    \item a global variable can be modified from anywhere in the code (nonlocality problem)
+    \item creates a potentially unlimited number of dependencies between all portions of the code
+    \item makes bugs difficult to localize (any part of the code could have created the trouble)
+    \item to summarize, goes against the principle of modularity
+    \item in addition, global variables are not thread safe (unless used with locks/mutexes)
+    \end{itemize}
+  \item Document your code when it doesn't speak by itself
+    \begin{itemize}
+    \item Dynare preprocessor code is documented using Doxygen
+    \item done through special comments beginning with an exclamation mark
+    \item run \texttt{doxygen} from the source directory to create a bunch of HTML files documenting the code
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\section{Parsing}
+
+\begin{frame}
+\frametitle{Parsing overview}
+\begin{itemize}
+\item Parsing is the action of transforming an input text (a \texttt{mod} file in our case) into a data structure suitable for computation
+\item The parser consists of three components:
+  \begin{itemize}
+  \item the \alert{lexical analyzer}, which recognizes the ``words'' of the \texttt{mod} file (analog to the \textit{vocabulary} of a language)
+  \item the \alert{syntax analyzer}, which recognizes the ``sentences'' of the \texttt{mod} file (analog to the \textit{grammar} of a language)
+  \item the \alert{parsing driver}, which coordinates the whole process and constructs the data structure using the results of the lexical and syntax analyses
+  \end{itemize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}
+\frametitle{Lexical analysis}
+\begin{itemize}
+\item The lexical analyzer recognizes the ``words'' (or \alert{lexemes}) of the language
+\item Lexical analyzer is described in \texttt{DynareFlex.ll}. This file is transformed into C++ source code by the program \texttt{flex}
+\item This file gives the list of the known lexemes (described by regular expressions), and gives the associated \alert{token} for each of them
+\item For punctuation (semicolon, parentheses, ...), operators (+, -, ...) or fixed keywords (\textit{e.g.} \texttt{model}, \texttt{varexo}, ...), the token is simply an integer uniquely identifying the lexeme
+\item For variable names or numbers, the token also contains the associated string for further processing
+%\item \textit{Note:} the list of tokens can be found at the beginning of \texttt{DynareBison.yy}
+\item When invoked, the lexical analyzer reads the next characters of the input, tries to recognize a lexeme, and either produces an error or returns the associated token
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Lexical analysis}
+\framesubtitle{An example}
+\begin{itemize}
+\item Suppose the \texttt{mod} file contains the following:
+\begin{verbatim}
+model;
+x = log(3.5);
+end;
+\end{verbatim}
+\item Before lexical analysis, it is only a sequence of characters
+\item The lexical analysis produces the following stream of tokens:
+
+\begin{footnotesize}
+\begin{verbatim}
+MODEL
+SEMICOLON
+NAME "x"
+EQUAL
+LOG
+LEFT_PARENTHESIS
+FLOAT_NUMBER "3.5"
+RIGHT_PARENTHESIS
+SEMICOLON
+END
+SEMICOLON
+\end{verbatim}
+\end{footnotesize}
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Syntax analysis}
+Using the list of tokens produced by lexical analysis, the syntax analyzer determines which ``sentences'' are valid in the language, according to a \alert{grammar} composed of \alert{rules}.
+\begin{block}{A grammar for lists of additive and multiplicative expressions}
+\begin{footnotesize}
+\begin{verbatim}
+%start expression_list;
+
+expression_list := expression SEMICOLON
+                 | expression_list expression SEMICOLON;
+
+expression := expression PLUS expression
+            | expression TIMES expression
+            | LEFT_PAREN expression RIGHT_PAREN
+            | INT_NUMBER;
+\end{verbatim}
+\end{footnotesize}
+\end{block}
+\begin{itemize}
+\item \texttt{(1+3)*2; 4+5;} will pass the syntax analysis without error
+\item \texttt{1++2;} will fail the syntax analysis, even though it has passed the lexical analysis
+\end{itemize}
+\end{frame}
+
+\begin{frame}
+\frametitle{Syntax analysis}
+\framesubtitle{In Dynare}
+\begin{itemize}
+\item The \texttt{mod} file grammar is described in \texttt{DynareBison.yy}
+\item The grammar is transformed into C++ source code by the program \texttt{bison}
+\item The grammar tells a story which looks like:
+  \begin{itemize}
+  \item A \texttt{mod} file is a list of statements
+  \item A statement can be a \texttt{var} statement, a \texttt{varexo} statement, a \texttt{model} block, an \texttt{initval} block, ...
+  \item A \texttt{var} statement begins with the token \texttt{VAR}, then a list of \texttt{NAME}s, then a semicolon
+  \item A \texttt{model} block begins with the token \texttt{MODEL}, then a semicolon, then a list of equations separated by semicolons, then an \texttt{END} token
+  \item An equation can be either an expression, or an expression followed by an \texttt{EQUAL} token and another expression
+  \item An expression can be a \texttt{NAME}, or a \texttt{FLOAT\_NUMBER}, or an expression followed by a \texttt{PLUS} and another expression, ...
+  \end{itemize}
+\end{itemize}
+\end{frame}
+
+
+\begin{frame}
+\frametitle{Semantic actions}
+\begin{itemize}
+\item So far we have only described how to accept valid \texttt{mod} files and to reject others
+\item But validating is not enough: one need to do something about what has been parsed
+\item Each rule of the grammar can have a \alert{semantic action} associated to it: C/C++ code enclosed in curly braces
+\item Each rule can return a semantic value (referenced to by \texttt{\$\$} in the action)
+\item In the action, it is possible to refer to semantic values returned by components of the rule (using \texttt{\$1}, \texttt{\$2}, ...)
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Semantic actions}
+\framesubtitle{An example}
+\begin{block}{A simple calculator which prints its results}
+\begin{footnotesize}
+\begin{verbatim}
+%start expression_list
+%type <int> expression
+
+expression_list := expression SEMICOLON
+                   { cout << $1; }
+                 | expression_list expression SEMICOLON
+                   { cout << $2; };
+
+expression := expression PLUS expression
+              { $$ = $1 + $3; }
+            | expression TIMES expression
+              { $$ = $1 * $3; }
+            | LEFT_PAREN expression RIGHT_PAREN
+              { $$ = $2; }
+            | INT_NUMBER
+              { $$ = $1; };
+\end{verbatim}
+\end{footnotesize}
+\end{block}
+\end{frame}
+
+\begin{frame}
+\frametitle{Parsing driver}
+
+The class \texttt{ParsingDriver} has the following roles:
+\begin{itemize}
+\item Given the \texttt{mod} filename, it opens the file and launches the lexical and syntaxic analyzers on it
+\item It implements most of the semantic actions of the grammar
+\item By doing so, it creates an object of type \texttt{ModFile}, which is the data structure representing the \texttt{mod} file
+\item Or, if there is a parsing error (unknown keyword, undeclared symbol, syntax error), it displays the line and column numbers where the error occurred, and exits
+\end{itemize}
+\end{frame}
+
+\section{Data structure representing a \texttt{mod} file}
+
+\begin{frame}
+  \frametitle{The \texttt{ModFile} class}
+  \begin{itemize}
+  \item This class is the internal data structure used to store all the informations contained in a \texttt{mod} file
+  \item One instance of the class represents one \texttt{mod} file
+  \item The class contains the following elements (as class members):
+    \begin{itemize}
+    \item a symbol table
+    \item a numerical constants table
+    \item two trees of expressions: one for the model, and one for the expressions outside the model
+    \item the list of the statements (parameter initializations, shocks block, \texttt{check}, \texttt{steady}, \texttt{simul}, ...)
+    \item an evaluation context
+    \end{itemize}
+  \item An instance of \texttt{ModFile} is the output of the parsing process (return value of \texttt{ParsingDriver::parse()})
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The symbol table (1/3)}
+  \begin{itemize}
+  \item A \alert{symbol} is simply the name of a variable, of a parameter or of a function unknown to the preprocessor: actually everything that is not recognized as a Dynare keyword
+  \item The \alert{symbol table} is a simple structure used to maintain the list of the symbols used in the \texttt{mod} file
+  \item For each symbol, stores:
+    \begin{itemize}
+    \item its name (a string)
+    \item its type (an integer)
+    \item a unique integer identifier (unique for a given type, but not across types)
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The symbol table (2/3)}
+  Existing types of symbols:
+  \begin{itemize}
+  \item Endogenous variables
+  \item Exogenous variables
+  \item Exogenous deterministic variables
+  \item Parameters
+  \item Local variables inside model: declared with a pound sign (\#) construction
+  \item Local variables outside model: no declaration needed, not interpreted by the preprocessor (\textit{e.g.} Matlab loop indexes)
+  \item Names of functions unknown to the preprocessor: no declaration needed, not interpreted by the preprocessor, only allowed outside model (until we create an interface for providing custom functions with their derivatives)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The symbol table (2/3)}
+  \begin{itemize}
+  \item Symbol table filled in:
+    \begin{itemize}
+    \item using the \texttt{var}, \texttt{varexo}, \texttt{varexo\_det}, \texttt{parameter} declarations
+    \item using pound sign (\#) constructions in the model block
+    \item on the fly during parsing: local variables outside models or unknown functions when an undeclared symbol is encountered
+    \end{itemize}
+  \item Roles of the symbol table:
+    \begin{itemize}
+    \item permits parcimonious and more efficient representation of expressions (no need to duplicate or compare strings, only handle a pair of integers)
+    \item ensures that a given symbol is used with only one type
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Expression trees (1/2)}
+  \begin{itemize}
+  \item The data structure used to store expressions is essentially a \alert{tree}
+  \item Graphically, the tree representation of $(1+z)*\log(y)$ is:
+    \begin{center}
+      \includegraphics[width=4cm]{expr.png}
+    \end{center}
+  \item No need to store parentheses
+  \item Each circle represents a \alert{node}
+  \item A node has at most one parent and at most two children
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Expression trees (2/2)}
+  \begin{itemize}
+  \item In Dynare preprocessor, a tree node is a represented by an instance of the abstract class \texttt{ExprNode}
+  \item This class has 5 sub-classes, corresponding to the 5 types of nodes:
+    \begin{itemize}
+    \item \texttt{NumConstNode} for constant nodes: contains the identifier of the numerical constants it represents
+    \item \texttt{VariableNode} for variable/parameters nodes: contains the identifier of the variable or parameter it represents
+    \item \texttt{UnaryOpNode} for unary operators (\textit{e.g.} unary minus, $\log$, $\sin$): contains an integer representing the operator, and a pointer to its child
+    \item \texttt{BinaryOpNode} for binary operators (\textit{e.g.} $+$, $*$, pow): contains an integer representing the operator, and pointers to its two children
+    \item \texttt{UnknownFunctionNode} for functions unknown to the parser (\textit{e.g.} user defined functions): contains the identifier of the function name, and a vector containing an arbitrary number of children (the function arguments)
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Classes \texttt{DataTree} and \texttt{ModelTree}}
+  \begin{itemize}
+  \item Class \texttt{DataTree} is a container for storing a set of expression trees
+  \item Class \texttt{ModelTree} is a sub-class of \texttt{DataTree}, specialized for storing a set of model equations (among other things, contains symbolic derivation algorithm)
+  \item Class \texttt{ModFile} contains:
+    \begin{itemize}
+    \item one instance of \texttt{ModelTree} for storing the equations of model block
+    \item one instance of \texttt{DataTree} for storing all expressions outside model block
+    \end{itemize}
+  \item Expression storage is optimized through three mechanisms:
+    \begin{itemize}
+    \item pre-computing of numerical constants
+    \item symbolic simplification rules
+    \item sub-expression sharing
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Constructing expression trees}
+  \begin{itemize}
+  \item Class \texttt{DataTree} contains a set of methods for constructing expression trees
+  \item Construction is done bottom-up, node by node:
+    \begin{itemize}
+    \item one method for adding a constant node (\texttt{AddPossiblyNegativeConstant(double)})
+    \item one method for a log node (\texttt{AddLog(arg)})
+    \item one method for a plus node (\texttt{AddPlus(arg1, arg2)})
+    \end{itemize}
+  \item These methods take pointers to \texttt{ExprNode}, allocate the memory for the node, construct it, and return its pointer
+  \item These methods are called:
+    \begin{itemize}
+    \item from \texttt{ParsingDriver} in the semantic actions associated to the parsing of expressions
+    \item during symbolic derivation, to create derivatives expressions
+    \end{itemize}
+  \item Note that \texttt{NodeID} is an alias (typedef) for \texttt{ExprNode*}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Reduction of constants and symbolic simplifications}
+  \begin{itemize}
+  \item The construction methods compute constants whenever it is possible
+    \begin{itemize}
+    \item Suppose you ask to construct the node $1+1$
+    \item The \texttt{AddPlus()} method will return a pointer to a constant node containing 2
+    \end{itemize}
+  \item The construction methods also apply a set of simplification rules, such as:
+    \begin{itemize}
+    \item $0+0=0$
+    \item $x+0 = x$
+    \item $0-x = -x$
+    \item $-(-x) = x$
+    \item $x*0 = 0$
+    \item $x/1 = x$
+    \item $x^0 = 1$
+    \end{itemize}
+  \item When a simplification rule applies, no new node is created
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Sub-expression sharing (1/2)}
+  \begin{itemize}
+  \item Consider the two following expressions: $(1+z)*\log(y)$ and $2^{(1+z)}$
+  \item Expressions share a common sub-expression: $1+z$
+  \item The internal representation of these expressions is:
+    \begin{center}
+      \includegraphics[width=6cm]{expr-sharing.png}
+    \end{center}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Sub-expression sharing (2/2)}
+  \begin{itemize}
+  \item Construction methods implement a simple algorithm which achieves maximal expression sharing
+  \item Algorithm uses the fact that each node has a unique memory address (pointer to the corresponding instance of \texttt{ExprNode})
+  \item It maintains 5 tables which keep track of the already constructed nodes: one table by type of node (constants, variables, unary ops, binary ops, unknown functions)
+  \item Suppose you want to create the node $e_1+e_2$ (where $e_1$ and $e_2$ are sub-expressions):
+    \begin{itemize}
+    \item the algorithm searches the binary ops table for the tuple equal to (address of $e_1$, address of $e_2$, op code of +) (it is the \alert{search key})
+    \item if the tuple is found in the table, the node already exists, and its memory address is returned
+    \item otherwise, the node is created, and is added to the table with its search key
+    \end{itemize}
+  \item Maximum sharing is achieved, because expression trees are constructed bottom-up
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Final remarks about expressions}
+  \begin{itemize}
+  \item Storage of negative constants
+    \begin{itemize}
+    \item class \texttt{NumConstNode} only accepts positive constants
+    \item a negative constant is stored as a unary minus applied to a positive constant
+    \item this is a kind of identification constraint to avoid having two ways of representing negative constants: $(-2)$ and $-(2)$
+    \end{itemize}
+  \item Widely used constants
+    \begin{itemize}
+    \item class \texttt{DataTree} has attributes containing pointers to one, zero, and minus one constants
+    \item these constants are used in many places (in simplification rules, in derivation algorithm...)
+    \item sub-expression sharing algorithm ensures that those constants will never be duplicated
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{List of statements}
+  \begin{itemize}
+  \item A statement is represented by an instance of a subclass of the abstract class \texttt{Statement}
+  \item Three groups of statements:
+    \begin{itemize}
+    \item initialization statements (parameter initialization with $p = \ldots$, \texttt{initval}, \texttt{histval} or \texttt{endval} block)
+    \item shocks blocks
+    \item computing tasks (\texttt{check}, \texttt{simul}, ...)
+    \end{itemize}
+  \item Each type of statement has its own class (\textit{e.g.} \texttt{InitValStatement}, \texttt{SimulStatement}, ...)
+  \item The class \texttt{ModFile} stores a list of pointers of type \texttt{Statement*}, corresponding to the statements of the \texttt{mod} file, in their order of declaration
+  \item Heavy use of polymorphism in the check pass, computing pass, and when writing outputs: abstract class \texttt{Statement} provides a virtual method for these 3 actions
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Evaluation context}
+  \begin{itemize}
+  \item The \texttt{ModFile} class contains an \alert{evaluation context}
+  \item It is a map associating a numerical value to some symbols
+  \item Filled in with \texttt{initval} block, and with parameters initializations
+  \item Used during equation normalization (in the block decomposition), for finding non-zero entries in the jacobian
+  \end{itemize}
+\end{frame}
+
+\section{Check pass}
+
+\begin{frame}
+  \frametitle{Error checking during parsing}
+  \begin{itemize}
+  \item Some errors in the \texttt{mod} file can be detected during the parsing:
+    \begin{itemize}
+    \item syntax errors
+    \item use of undeclared symbol in model block, initval block...
+    \item use of a symbol incompatible with its type (\textit{e.g.} parameter in initval, local variable used both in model and outside model)
+    \item multiple shocks declaration for the same variable
+    \end{itemize}
+  \item But some other checks can only be done when parsing is completed
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Check pass}
+  \begin{itemize}
+  \item The check pass is implemented through method \texttt{ModFile::checkPass()}
+  \item Does the following checks:
+    \begin{itemize}
+    \item check there is at least one equation in the model (except if doing a standalone BVAR estimation)
+    \item check there is not both a \texttt{simul} and a \texttt{stoch\_simul} (or another command triggering local approximation)
+    \end{itemize}
+  \item Other checks could be added in the future, for example:
+    \begin{itemize}
+    \item check that every endogenous variable is used at least once in current period
+    \item check there is a single \texttt{initval} (or \texttt{histval}, \texttt{endval}) block
+    \item check that \texttt{varobs} is used if there is an estimation
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\section{Computing pass}
+
+\begin{frame}
+  \frametitle{Overview of the computing pass}
+  \begin{itemize}
+  \item Computing pass implemented in \texttt{ModFile::computingPass()}
+  \item Begins with a determination of which derivatives to compute
+  \item Then, calls \texttt{ModelTree::computingPass()}, which computes:
+    \begin{itemize}
+    \item leag/lag variable incidence matrix
+    \item symbolic derivatives
+    \item equation normalization + block decomposition (only in \texttt{sparse\_dll} mode)
+    \item temporary terms
+    \item symbolic gaussian elimination (only in \texttt{sparse\_dll} mode) \textit{(actually this is done in the output writing pass, but should be moved to the computing pass)}
+    \end{itemize}
+  \item Finally, calls \texttt{Statement::computingPass()} on all statements
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The variable table}
+  \begin{itemize}
+  \item In the context of class \texttt{ModelTree}, a \alert{variable} is a pair (symbol, lead/lag)
+  \item The symbol must correspond to an endogenous or exogenous variable (in the sense of the model)
+  \item The class \texttt{VariableTable} keeps track of those pairs
+  \item An instance of \texttt{ModelTree} contains an instance of \texttt{VariableTable}
+  \item Each pair (\texttt{symbol\_id}, lead/lag) is given a unique \texttt{variable\_id}
+  \item After the computing pass, the class \texttt{VariableTable} writes the leag/lag incidence matrix:
+    \begin{itemize}
+    \item endogenous symbols in row
+    \item leads/lags in column
+    \item elements of the matrix are either 0 or correspond to a variable ID, depending on whether the pair (symbol, lead/lag) is used or not in the model
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Static versus dynamic model}
+  \begin{itemize}
+  \item The static model is simply the (dynamic) model from which the leads/lags have been omitted
+  \item Static model used to characterize the steady state
+  \item The jacobian of the static model is used in the (Matlab) solver for determining the steady state
+  \item No need to derive static and dynamic models independently: \\
+    static derivatives can be easily deduced from dynamic derivatives
+  \end{itemize}
+  \begin{block}{Example}
+    \begin{itemize}
+    \item suppose dynamic model is $2x \cdot x_{-1} = 0$
+    \item static model is $2x^2 = 0$, whose derivative w.r. to $x$ is $4x$
+    \item dynamic derivative w.r. to $x$ is $2x_{-1}$, and w.r. to $x_{-1}$ is $2x$
+    \item removing leads/lags from dynamic derivatives and summing over the two partial derivatives w.r. to $x$ and $x_{-1}$ gives $4x$
+    \end{itemize}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Which derivatives to compute ?}
+  \begin{itemize}
+  \item In deterministic mode:
+    \begin{itemize}
+    \item static jacobian (w.r. to endogenous variables only)
+    \item dynamic jacobian (w.r. to endogenous variables only)
+    \end{itemize}
+  \item In stochastic mode:
+    \begin{itemize}
+    \item static jacobian (w.r. to endogenous variables only)
+    \item dynamic jacobian (w.r. to all variables)
+    \item possibly dynamic hessian (if \texttt{order} option $\geq 2$)
+    \item possibly dynamic 3rd derivatives (if \texttt{order} option $\geq 3$)
+    \end{itemize}
+  \item For ramsey policy: the same as above, but with one further order of derivation than declared by the user with \texttt{order} option (the derivation order is determined in the check pass, see \texttt{RamseyPolicyStatement::checkPass()})
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Derivation algorithm (1/2)}
+  \begin{itemize}
+  \item Derivation of the model implemented in \texttt{ModelTree::derive()}
+  \item Simply calls \texttt{ExprNode::getDerivative(varID)} on each equation node
+  \item Use of polymorphism:
+    \begin{itemize}
+    \item for a constant or variable node, derivative is straightforward (0 or 1)
+    \item for a unary or binary op node, recursively calls method \texttt{getDerivative()} on children to construct derivative of parent, using usual derivation rules, such as:
+      \begin{itemize}
+      \item $(log(e))' = \frac{e'}{e}$
+      \item $(e_1 + e_2)' = e'_1 + e'_2$
+      \item $(e_1 \cdot e_2)' = e'_1\cdot e_2 + e_1\cdot e'_2$
+      \item $\ldots$
+      \end{itemize}
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Derivation algorithm (2/2)}
+  \framesubtitle{Optimizations}
+  \begin{itemize}
+  \item Caching of derivation results
+    \begin{itemize}
+    \item method \texttt{ExprNode::getDerivative(varID)} memorizes its result in a member attribute the first time it is called
+    \item so that the second time it is called (with the same argument), simply returns the cached value without recomputation
+    \item caching is useful because of sub-expression sharing
+    \end{itemize}
+    \pause
+  \item Symbolic \textit{a priori}
+    \begin{itemize}
+    \item consider the expression $x+y^2$
+    \item without any computation, you know its derivative w.r. to $z$ is zero
+    \item each node stores in an attribute the set of variables which appear in the expression it represents ($\{x,y\}$ in the example)
+    \item that set is computed in the constructor (straigthforwardly for a variable or a constant, recursively for other nodes, using the sets of the children)
+    \item when \texttt{getDerivative(varID)} is called, immediately returns zero if \texttt{varID} is not in that set
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Temporary terms (1/2)}
+  \begin{itemize}
+  \item When the preprocessor writes equations and derivatives in its outputs, it takes advantage of sub-expression sharing
+  \item In Matlab static and dynamic output files, equations are preceded by a list of \alert{temporary terms}
+  \item Those terms are temporary variables containing expressions shared by several equations or derivatives
+  \item Doing so greatly enhances the computing speed of model residual, jacobian or hessian
+  \end{itemize}
+  \begin{block}{Example}
+    \begin{columns}[t]
+      \begin{column}{6cm}
+        The equations:
+\begin{verbatim}
+residual(0)=x+y^2-z^3;
+residual(1)=3*(x+y^2)+1;
+\end{verbatim}
+      \end{column}
+      \begin{column}{4.8cm}
+        Can be optimized in:
+\begin{verbatim}
+T01=x+y^2;
+residual(0)=T01-z^3;
+residual(1)=3*T01+1;
+\end{verbatim}
+      \end{column}
+    \end{columns}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Temporary terms (2/2)}
+  \begin{itemize}
+  \item Expression storage in the preprocessor implements maximal sharing...
+  \item ...but it is not optimal for the Matlab output files, because creating a temporary variable also has a cost (in terms of CPU and of memory)
+  \item Computation of temporary terms implements a trade-off between:
+    \begin{itemize}
+    \item cost of duplicating sub-expressions
+    \item cost of creating new variables
+    \end{itemize}
+  \item Algorithm uses a recursive cost calculation, which marks some nodes as being ``temporary''
+  \item \textit{Problem}: redundant with optimizations done by the C/C++ compiler (when Dynare is in DLL mode) $\Rightarrow$ compilation very slow on big models
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The special case of Ramsey policy}
+  \begin{itemize}
+  \item For most statements, the method \texttt{computingPass()} is a no-op...
+  \item ...except for \texttt{planner\_objective} statement, which serves to declare planner objective when doing optimal policy under commitment
+  \item Class \texttt{PlannerObjectiveStatement} contains an instance of \texttt{ModelTree}: used to store the objective (only one equation in the tree)
+  \item During the computing pass, triggers the computation of the first and second order (static) derivatives of the objective
+  \end{itemize}
+\end{frame}
+
+\section{Writing outputs}
+
+\begin{frame}
+  \frametitle{Output overview}
+  \begin{itemize}
+  \item Implemented in \texttt{ModFile::writeOutputFiles()}
+  \item If \texttt{mod} file is \texttt{model.mod}, all created filenames will begin with \texttt{model}
+  \item Main output file is \texttt{model.m}, containing:
+    \begin{itemize}
+    \item general initialization commands
+    \item symbol table output (from \texttt{SymbolTable::writeOutput()})
+    \item lead/lag incidence matrix (from \texttt{ModelTree::writeOutput()})
+    \item call to Matlab functions corresponding to the statements of the \texttt{mod} file (written by calling \texttt{Statement::writeOutput()} on all statements through polymorphism)
+    \end{itemize}
+  \item Subsidiary output files:
+    \begin{itemize}
+    \item one for the static model
+    \item one for the dynamic model
+    \item and one for the planner objective (if relevant)
+    \item written through \texttt{ModelTree} methods: \texttt{writeStaticFile()} and \texttt{writeDynamicFile()}
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Model output files}
+  Three possibles modes for \texttt{ModelTree} (see \texttt{mode} attribute):
+  \begin{itemize}
+  \item Standard mode: static and dynamic files in Matlab
+  \item DLL mode:
+    \begin{itemize}
+    \item static and dynamic files in C++ source code (with corresponding headers)
+    \item compiled through \texttt{mex} to allow execution from within Matlab
+    \end{itemize}
+  \item Sparse DLL mode:
+    \begin{itemize}
+    \item static file in Matlab
+    \item two possibilities for dynamic file:
+      \begin{itemize}
+      \item by default, a C++ source file (with header) and a binary file, to be read from the C++ code
+      \item or, with \texttt{no\_compiler} option, a binary file in custom format, executed from Matlab through \texttt{simulate} DLL
+      \item the second option serves to bypass compilation of C++ file which can be very slow
+      \end{itemize}
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\section{Conclusion}
+
+\begin{frame}
+  \frametitle{Future work (1/2)}
+  \framesubtitle{Enhancements, optimizations}
+  \begin{itemize}
+  \item Refactor and reorganize some portions of the code
+  \item Create a testsuite (with unitary tests)
+  \item Separate computation of temporary terms between static and dynamic outputs
+  \item Enhance sub-expression sharing algorithm (using associativity, commutativity and factorization rules)
+  \item Add many checks on the structure of the \texttt{mod} file
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Future work (2/2)}
+  \framesubtitle{Features}
+  \begin{itemize}
+  \item Add precompiler macros (\#include, \#define, \#if)
+  \item Add handling for several (sub-)models
+  \item Add indexed variables and control statements (if, loops) both in models and command language
+  \item Add sum, diff, prod operators
+  \item For unknown functions in the model: let user provide a derivative, or trigger numerical derivation
+  \item Generalize binary code output
+  \item Generalize block decomposition ?
+  \end{itemize}
+\end{frame}
+
+
+
+\end{document}
-- 
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