From 2aeb02623decb815bfd0c459113a1db294142925 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Laure=CE=B7t?= <laurentfainsin@protonmail.com>
Date: Fri, 3 Dec 2021 15:52:36 +0100
Subject: [PATCH] =?UTF-8?q?fin=20de=20s=C3=A9ance?=
MIME-Version: 1.0
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---
 AccesVariable.java              |  22 +++++
 Addition.java                   |  13 +++
 AfficheurInfixe.java            |  58 ++++++++++++
 AfficheurInfixeMinimalTest.java |  53 +++++++++++
 AfficheurInfixeTest.java        |  58 ++++++++++++
 AfficheurPostfixe.java          |  43 +++++++++
 AfficheurPostfixeTest.java      |  53 +++++++++++
 CalculHauteur.java              |  47 ++++++++++
 CalculHauteurTest.java          |  66 +++++++++++++
 Constante.java                  |  23 +++++
 EvaluateurExpression.java       |  67 +++++++++++++
 EvaluateurExpressionTest.java   |  74 +++++++++++++++
 ExemplesAffichage.java          |  50 ++++++++++
 Expression.java                 |  15 +++
 ExpressionBinaire.java          |  40 ++++++++
 ExpressionTernaire.java         |  37 ++++++++
 ExpressionTestSetup.java        |  59 ++++++++++++
 ExpressionUnaire.java           |  32 +++++++
 Let.java                        |  13 +++
 Multiplication.java             |  13 +++
 Negation.java                   |  14 +++
 OperateurBinaire.java           |  11 +++
 OperateurTernaire.java          |  11 +++
 OperateurUnaire.java            |  11 +++
 Soustraction.java               |  14 +++
 VisiteurExpression.java         |  59 ++++++++++++
 expressions.dot                 | 121 ++++++++++++++++++++++++
 expressions.fig                 | 161 ++++++++++++++++++++++++++++++++
 expressions.pdf                 | Bin 0 -> 18120 bytes
 sujet.pdf                       | Bin 0 -> 94854 bytes
 30 files changed, 1238 insertions(+)
 create mode 100755 AccesVariable.java
 create mode 100755 Addition.java
 create mode 100755 AfficheurInfixe.java
 create mode 100755 AfficheurInfixeMinimalTest.java
 create mode 100755 AfficheurInfixeTest.java
 create mode 100755 AfficheurPostfixe.java
 create mode 100755 AfficheurPostfixeTest.java
 create mode 100755 CalculHauteur.java
 create mode 100755 CalculHauteurTest.java
 create mode 100755 Constante.java
 create mode 100755 EvaluateurExpression.java
 create mode 100755 EvaluateurExpressionTest.java
 create mode 100755 ExemplesAffichage.java
 create mode 100755 Expression.java
 create mode 100755 ExpressionBinaire.java
 create mode 100755 ExpressionTernaire.java
 create mode 100755 ExpressionTestSetup.java
 create mode 100755 ExpressionUnaire.java
 create mode 100755 Let.java
 create mode 100755 Multiplication.java
 create mode 100755 Negation.java
 create mode 100755 OperateurBinaire.java
 create mode 100755 OperateurTernaire.java
 create mode 100755 OperateurUnaire.java
 create mode 100755 Soustraction.java
 create mode 100755 VisiteurExpression.java
 create mode 100755 expressions.dot
 create mode 100755 expressions.fig
 create mode 100755 expressions.pdf
 create mode 100755 sujet.pdf

diff --git a/AccesVariable.java b/AccesVariable.java
new file mode 100755
index 0000000..8b6f481
--- /dev/null
+++ b/AccesVariable.java
@@ -0,0 +1,22 @@
+/**
+  * AccesVariable représente l'accès à une variable.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class AccesVariable implements Expression {
+	private String nom;
+
+	public AccesVariable(String nom) {
+		this.nom = nom;
+	}
+
+	public String getNom() {
+		return this.nom;
+	}
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterAccesVariable(this);
+	}
+
+}
diff --git a/Addition.java b/Addition.java
new file mode 100755
index 0000000..4641968
--- /dev/null
+++ b/Addition.java
@@ -0,0 +1,13 @@
+/**
+  * Opérateur binaire d'addition.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class Addition implements OperateurBinaire {
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterAddition(this);
+	}
+
+}
diff --git a/AfficheurInfixe.java b/AfficheurInfixe.java
new file mode 100755
index 0000000..1a1429d
--- /dev/null
+++ b/AfficheurInfixe.java
@@ -0,0 +1,58 @@
+/** Afficheur infixe, complètement parenthésé, d'une expression arithmétique.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class AfficheurInfixe implements VisiteurExpression<String> {
+
+	public String visiterAccesVariable(AccesVariable v) {
+		return "(" + v.getNom() + ")";
+	}
+
+	public String visiterConstante(Constante c) {
+		return "(" + String.valueOf(c.getValeur()) + ")";
+	}
+
+	public String visiterExpressionTernaire(ExpressionTernaire e) {
+		return "("
+			+ "let" + e.getOperateur().accepter(this)
+			+ " " + e.getOperande1().accepter(this)
+			+ "=" + e.getOperande2().accepter(this)
+			+ " in " + e.getOperande3().accepter(this)
+			+ ")" ;
+	}
+
+	public String visiterLet(Let l) {
+		return "";
+	}
+
+
+	public String visiterExpressionBinaire(ExpressionBinaire e) {
+		return "(" + e.getOperandeGauche().accepter(this)
+			+ " " + e.getOperateur().accepter(this)
+			+ " " + e.getOperandeDroite().accepter(this)
+			+ ")" ;
+	}
+
+	public String visiterAddition(Addition a) {
+		return "+";
+	}
+
+	public String visiterSoustraction(Soustraction a) {
+		return "-";
+	}
+
+	public String visiterMultiplication(Multiplication m) {
+		return "*";
+	}
+
+	public String visiterExpressionUnaire(ExpressionUnaire e) {
+		return "(" + e.getOperateur().accepter(this)
+			+ " " + e.getOperande().accepter(this) + ")";
+	}
+
+	public String visiterNegation(Negation n) {
+		return "~";
+	}
+
+}
diff --git a/AfficheurInfixeMinimalTest.java b/AfficheurInfixeMinimalTest.java
new file mode 100755
index 0000000..6eb1968
--- /dev/null
+++ b/AfficheurInfixeMinimalTest.java
@@ -0,0 +1,53 @@
+/**
+  * AfficheurInfixeMinimalTest :
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public class AfficheurInfixeMinimalTest extends ExpressionTestSetup {
+
+	private void verifier(String valeurAttendue, Expression e) {
+		AfficheurInfixe affInfixe = new AfficheurInfixeMinimal();
+		String resultat = e.accepter(affInfixe);
+		assertEquals(valeurAttendue, resultat.replaceAll("\\s+", " "));
+	}
+
+	public void testerConstante() {
+		verifier("10", cte);
+	}
+
+	public void testerAccesVariable1() {
+		verifier("x", av);
+	}
+
+	public void testerE1() {
+		verifier("2 + x", e1);
+	}
+
+	public void testerE2() {
+		verifier("(2 + x) * 3", e2);
+	}
+
+	public void testerE3() {
+		verifier("7 * (2 + x)", e3);
+	}
+
+	public void testerE4() {
+		verifier("x + y + z", e4);
+	}
+
+	public void testerE5() {
+		verifier("x + (y + z)", e5);
+	}
+
+	public void testerE6() {
+		verifier("- - (2 + x)", e6);
+	}
+
+	public static void main(String[] args) {
+		junit.textui.TestRunner.run(
+				new junit.framework.TestSuite(AfficheurInfixeMinimalTest.class));
+	}
+
+}
diff --git a/AfficheurInfixeTest.java b/AfficheurInfixeTest.java
new file mode 100755
index 0000000..a510c76
--- /dev/null
+++ b/AfficheurInfixeTest.java
@@ -0,0 +1,58 @@
+/**
+  * AfficheurInfixeTest :
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public class AfficheurInfixeTest extends ExpressionTestSetup {
+
+
+	private void verifier(String valeurAttendue, Expression e) {
+		AfficheurInfixe affInfixe = new AfficheurInfixe();
+		String resultat = e.accepter(affInfixe);
+		assertEquals(valeurAttendue, resultat.replaceAll("\\s+", " "));
+	}
+
+	public void testerConstante() {
+		verifier("(10)", cte);
+	}
+
+	public void testerAccesVariable1() {
+		verifier("(x)", av);
+	}
+
+	public void testerE1() {
+		verifier("((2) + (x))", e1);
+	}
+
+	public void testerE2() {
+		verifier("(((2) + (x)) * (3))", e2);
+	}
+
+	public void testerE3() {
+		verifier("((7) * ((2) + (x)))", e3);
+	}
+
+	public void testerE4() {
+		verifier("(((x) + (y)) + (z))", e4);
+	}
+
+	public void testerE5() {
+		verifier("((x) + ((y) + (z)))", e5);
+	}
+
+	public void testerE6() {
+		verifier("(~ (~ ((2) + (x))))", e6);
+	}
+
+	public void testerE7() {
+		verifier("(let (x)=((2) + (x)) in ((2) + (x)))", e7);
+	}
+
+	public static void main(String[] args) {
+		junit.textui.TestRunner.run(
+				new junit.framework.TestSuite(AfficheurInfixeTest.class));
+	}
+
+}
diff --git a/AfficheurPostfixe.java b/AfficheurPostfixe.java
new file mode 100755
index 0000000..7b1f390
--- /dev/null
+++ b/AfficheurPostfixe.java
@@ -0,0 +1,43 @@
+/** Afficheur infixe, complètement parenthésé, d'une expression arithmétique.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class AfficheurPostfixe implements VisiteurExpression<String> {
+
+	public String visiterAccesVariable(AccesVariable v) {
+		return v.getNom();
+	}
+
+	public String visiterConstante(Constante c) {
+		return String.valueOf(c.getValeur());
+	}
+
+	public String visiterExpressionBinaire(ExpressionBinaire e) {
+		return e.getOperandeGauche().accepter(this)
+			+ " " + e.getOperandeDroite().accepter(this)
+			+ " " + e.getOperateur().accepter(this);
+	}
+
+	public String visiterAddition(Addition a) {
+		return "+";
+	}
+
+	public String visiterSoustraction(Soustraction a) {
+		return "-";
+	}
+
+	public String visiterMultiplication(Multiplication m) {
+		return "*";
+	}
+
+	public String visiterExpressionUnaire(ExpressionUnaire e) {
+		return e.getOperande().accepter(this)
+			+ " " + e.getOperateur().accepter(this);
+	}
+
+	public String visiterNegation(Negation n) {
+		return "~";
+	}
+
+}
diff --git a/AfficheurPostfixeTest.java b/AfficheurPostfixeTest.java
new file mode 100755
index 0000000..259d620
--- /dev/null
+++ b/AfficheurPostfixeTest.java
@@ -0,0 +1,53 @@
+/**
+  * AfficheurPostfixeTest :
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public class AfficheurPostfixeTest extends ExpressionTestSetup {
+
+
+	private void verifier(String valeurAttendue, Expression e) {
+		AfficheurPostfixe affPostfixe = new AfficheurPostfixe();
+		assertEquals(valeurAttendue, e.accepter(affPostfixe));
+	}
+
+	public void testerConstante() {
+		verifier("10", cte);
+	}
+
+	public void testerAccesVariable1() {
+		verifier("x", av);
+	}
+
+	public void testerE1() {
+		verifier("2 x +", e1);
+	}
+
+	public void testerE2() {
+		verifier("2 x + 3 *", e2);
+	}
+
+	public void testerE3() {
+		verifier("7 2 x + *", e3);
+	}
+
+	public void testerE4() {
+		verifier("x y + z +", e4);
+	}
+
+	public void testerE5() {
+		verifier("x y z + +", e5);
+	}
+
+	public void testerE6() {
+		verifier("2 x + ~ ~", e6);
+	}
+
+	public static void main(String[] args) {
+		junit.textui.TestRunner.run(
+				new junit.framework.TestSuite(AfficheurPostfixeTest.class));
+	}
+
+}
diff --git a/CalculHauteur.java b/CalculHauteur.java
new file mode 100755
index 0000000..e804e8b
--- /dev/null
+++ b/CalculHauteur.java
@@ -0,0 +1,47 @@
+/** Afficheur infixe, complètement parenthésé, d'une expression arithmétique.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+import java.lang.*;
+
+public class CalculHauteur implements VisiteurExpression<Integer> {
+
+	public Integer visiterAccesVariable(AccesVariable v) {
+		return 1;
+	}
+
+	public Integer visiterConstante(Constante c) {
+		return 1;
+	}
+
+	public Integer visiterExpressionBinaire(ExpressionBinaire e) {
+		return Math.max(
+            e.getOperandeGauche().accepter(this),
+            e.getOperandeDroite().accepter(this)
+        ) + e.getOperateur().accepter(this);
+	}
+
+	public Integer visiterAddition(Addition a) {
+		return 1;
+	}
+
+	public Integer visiterSoustraction(Soustraction a) {
+		return 1;
+	}
+
+	public Integer visiterMultiplication(Multiplication m) {
+		return 1;
+	}
+
+	public Integer visiterExpressionUnaire(ExpressionUnaire e) {
+		return e.getOperateur().accepter(this)
+            + e.getOperande().accepter(this);
+	}
+
+	public Integer visiterNegation(Negation n) {
+		return 1;
+	}
+
+}
diff --git a/CalculHauteurTest.java b/CalculHauteurTest.java
new file mode 100755
index 0000000..5b005b2
--- /dev/null
+++ b/CalculHauteurTest.java
@@ -0,0 +1,66 @@
+/** Tester CalculHauteur.
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class CalculHauteurTest extends ExpressionTestSetup {
+
+	private void verifierHauteur(int hauteurAttentdue, Expression e) {
+		CalculHauteur v = new CalculHauteur();
+		verifierHauteur(hauteurAttentdue, e, v);
+	}
+
+	private void verifierHauteur(int hauteurAttentdue, Expression e,
+			CalculHauteur v) {
+		int hauteur = e.accepter(v);
+		assertEquals(hauteurAttentdue, hauteur);
+	}
+
+	public void testerConstante() {
+		verifierHauteur(1, cte);
+	}
+
+	public void testerAccesVariable() {
+		verifierHauteur(1, av);
+	}
+
+	public void testerE1() {
+		verifierHauteur(2, e1);
+	}
+
+	public void testerE2() {
+		verifierHauteur(3, e2);
+	}
+
+	public void testerE3() {
+		verifierHauteur(3, e3);
+	}
+
+	public void testerE4() {
+		verifierHauteur(3, e4);
+	}
+
+	public void testerE5() {
+		verifierHauteur(3, e5);
+	}
+
+	public void testerE6() {
+		verifierHauteur(4, e6);
+	}
+
+	public void testerReutilisationVisiteur() {
+		CalculHauteur v = new CalculHauteur();
+		verifierHauteur(1, cte, v);
+		verifierHauteur(3, e3, v);
+		verifierHauteur(3, e4, v);
+		verifierHauteur(3, e4, v);
+		verifierHauteur(3, e5, v);
+		verifierHauteur(4, e6, v);
+	}
+
+
+	public static void main(String[] args) {
+		junit.textui.TestRunner.run(
+				new junit.framework.TestSuite(CalculHauteurTest.class));
+	}
+
+}
diff --git a/Constante.java b/Constante.java
new file mode 100755
index 0000000..bc5e37a
--- /dev/null
+++ b/Constante.java
@@ -0,0 +1,23 @@
+/**
+  * Constante entière.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class Constante implements Expression {
+
+	private int valeur;
+
+	public Constante(int valeur) {
+		this.valeur = valeur;
+	}
+
+	public int getValeur() {
+		return this.valeur;
+	}
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterConstante(this);
+	}
+
+}
diff --git a/EvaluateurExpression.java b/EvaluateurExpression.java
new file mode 100755
index 0000000..44a89c8
--- /dev/null
+++ b/EvaluateurExpression.java
@@ -0,0 +1,67 @@
+/** Afficheur infixe, complètement parenthésé, d'une expression arithmétique.
+  *
+  * @author    Xavier Crégut
+  * @version    $Revision$
+  */
+
+  import java.util.*;
+
+  public class EvaluateurExpression implements VisiteurExpression<Integer> {
+
+    private Map<String,Integer> env;
+
+    public EvaluateurExpression(Map<String,Integer> env) {
+        this.env = env;
+    }
+
+    public Integer visiterAccesVariable(AccesVariable v) {
+        return env.get(v.getNom());
+    }
+
+    public Integer visiterConstante(Constante c) {
+        return c.getValeur();
+    }
+
+    public Integer visiterExpressionBinaire(ExpressionBinaire e) {
+        switch (e.getOperateur().accepter(this)) {
+            case 0:
+                return e.getOperandeGauche().accepter(this) + e.getOperandeDroite().accepter(this);
+                
+            case 1:
+                return e.getOperandeGauche().accepter(this) - e.getOperandeDroite().accepter(this);
+                
+            case 2:
+                return e.getOperandeGauche().accepter(this) * e.getOperandeDroite().accepter(this);
+                  
+            default:
+                return 0;
+        }
+    }
+
+    public Integer visiterAddition(Addition a) {
+        return 0;
+    }
+
+    public Integer visiterSoustraction(Soustraction a) {
+        return 1;
+    }
+
+    public Integer visiterMultiplication(Multiplication m) {
+        return 2;
+    }
+
+    public Integer visiterExpressionUnaire(ExpressionUnaire e) {
+        switch (e.getOperateur().accepter(this)) {
+            case 0:
+                return -e.getOperande().accepter(this);
+                        
+            default:
+                return 0;
+        }
+    }
+
+    public Integer visiterNegation(Negation n) {
+        return 0;
+    }
+
+}
\ No newline at end of file
diff --git a/EvaluateurExpressionTest.java b/EvaluateurExpressionTest.java
new file mode 100755
index 0000000..7d0707f
--- /dev/null
+++ b/EvaluateurExpressionTest.java
@@ -0,0 +1,74 @@
+import java.util.HashMap;
+
+/** Tester EvaluateurExpression.
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class EvaluateurExpressionTest extends ExpressionTestSetup {
+
+	protected HashMap<String, Integer> environnement;
+
+	protected void setUp() {
+		super.setUp();
+		this.environnement = new HashMap<String, Integer>();
+		this.environnement.put("x", 5);
+		this.environnement.put("y", 7);
+		this.environnement.put("z", 2);
+	}
+
+	private void verifierValeur(int valeurAttendue, Expression e) {
+		EvaluateurExpression v = new EvaluateurExpression(this.environnement);
+		assertEquals(valeurAttendue, e.accepter(v).intValue());
+	}
+
+	public void testerConstante() {
+		verifierValeur(10, cte);
+	}
+
+	public void testerAccesVariable1() {
+		verifierValeur(5, av);
+	}
+
+	public void testerAccesVariable2() {
+		verifierValeur(7, new AccesVariable("y"));
+	}
+
+	public void testerAccesVariableNonDefinie() {
+		try {
+			verifierValeur(5, new AccesVariable("t"));
+			fail();
+		} catch (RuntimeException e) {
+			// OK.
+		}
+	}
+
+	public void testerE1() {
+		verifierValeur(7, e1);
+	}
+
+	public void testerE2() {
+		verifierValeur(21, e2);
+	}
+
+	public void testerE3() {
+		verifierValeur(49, e3);
+	}
+
+	public void testerE4() {
+		verifierValeur(14, e4);
+	}
+
+	public void testerE5() {
+		verifierValeur(14, e5);
+	}
+
+	public void testerE6() {
+		verifierValeur(7, e6);
+	}
+
+	public static void main(String[] args) {
+		junit.textui.TestRunner.run(
+				new junit.framework.TestSuite(EvaluateurExpressionTest.class));
+	}
+
+}
diff --git a/ExemplesAffichage.java b/ExemplesAffichage.java
new file mode 100755
index 0000000..b4e1af1
--- /dev/null
+++ b/ExemplesAffichage.java
@@ -0,0 +1,50 @@
+/**
+  * Exemples d'affichage d'expressions arithmétiques
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public class ExemplesAffichage {
+
+    static final private OperateurBinaire plus = new Addition();
+    static final private OperateurBinaire fois = new Multiplication();
+    static final private OperateurUnaire negation = new Negation();
+
+    static public Expression expression1() {
+        return new ExpressionUnaire(negation,
+                    new ExpressionBinaire(fois,
+                        new Constante(2),
+                        new ExpressionBinaire(plus,
+                            new Constante(1),
+                            new AccesVariable("x"))));
+    }
+
+    static public Expression expression2() {
+        return new ExpressionBinaire(plus,
+                    new Constante(5),
+                    new ExpressionBinaire(fois,
+                            new AccesVariable("x"),
+                            new Constante(4)));
+    }
+
+    static public Expression expression3() {
+        return new ExpressionBinaire(plus,
+                    new Constante(5),
+                    new ExpressionBinaire(fois,
+                            new AccesVariable("x"),
+                            new Constante(4)));
+    }
+
+    public static void main(String[] args) {
+        // Afficher expression 1
+        AfficheurInfixe infixe = new AfficheurInfixe();
+        String e1infixe = expression1().accepter(infixe);
+        System.out.println("e1 = " + e1infixe);
+
+        // Afficher expression2
+        String e2infixe = expression2().accepter(infixe);
+        System.out.println("e2 = " + e2infixe);
+    }
+}
+
diff --git a/Expression.java b/Expression.java
new file mode 100755
index 0000000..e109553
--- /dev/null
+++ b/Expression.java
@@ -0,0 +1,15 @@
+/**
+  * Expression entière.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public interface Expression {
+
+	/** Accepter un visiteur.
+	 * @param visiteur le visiteur accepté
+	 */
+	<R> R accepter(VisiteurExpression<R> visiteur);
+
+}
diff --git a/ExpressionBinaire.java b/ExpressionBinaire.java
new file mode 100755
index 0000000..f730f6f
--- /dev/null
+++ b/ExpressionBinaire.java
@@ -0,0 +1,40 @@
+/**
+  * Expression binaire avec donc deux opérandes droit et gauche et un opérateur
+  * binaire.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  * @composed 1 "" "operateur" OperateurBinaire
+  * @has 1 - "gauche" Expression
+  * @has 1 - "droite" Expression
+  */
+public class ExpressionBinaire implements Expression {
+
+	private Expression operandegauche;
+	private Expression operandedroite;
+	private OperateurBinaire operateur;
+
+	public ExpressionBinaire(OperateurBinaire op, Expression gauche, Expression droite)
+	{
+		this.operateur = op;
+		this.operandegauche = gauche;
+		this.operandedroite = droite;
+	}
+
+	public Expression getOperandeGauche() {
+		return this.operandegauche;
+	}
+
+	public Expression getOperandeDroite() {
+		return this.operandedroite;
+	}
+
+	public OperateurBinaire getOperateur() {
+		return this.operateur;
+	}
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterExpressionBinaire(this);
+	}
+
+}
diff --git a/ExpressionTernaire.java b/ExpressionTernaire.java
new file mode 100755
index 0000000..f005c8b
--- /dev/null
+++ b/ExpressionTernaire.java
@@ -0,0 +1,37 @@
+
+public class ExpressionTernaire implements Expression {
+
+	private AccesVariable operande1;
+	private Expression operande2;
+	private Expression operande3;
+	private OperateurTernaire operateur;
+
+	public ExpressionTernaire(OperateurTernaire op, AccesVariable e1, Expression e2, Expression e3)
+	{
+		this.operateur = op;
+		this.operande1 = e1;
+		this.operande2 = e2;
+		this.operande3 = e3;
+	}
+
+	public AccesVariable getOperande1() {
+		return this.operande1;
+	}
+
+	public Expression getOperande2() {
+		return this.operande2;
+	}
+
+	public Expression getOperande3() {
+		return this.operande3;
+	}
+
+	public OperateurTernaire getOperateur() {
+		return this.operateur;
+	}
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterExpressionTernaire(this);
+	}
+
+}
diff --git a/ExpressionTestSetup.java b/ExpressionTestSetup.java
new file mode 100755
index 0000000..eb5d5d1
--- /dev/null
+++ b/ExpressionTestSetup.java
@@ -0,0 +1,59 @@
+/**
+  * ExpressionTest :
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public abstract class ExpressionTestSetup extends junit.framework.TestCase {
+
+	protected Constante cte;
+	protected AccesVariable av;
+	protected Expression e1, e2, e3;	// Expressions du sujet
+	protected Expression e4, e5, e6;
+	protected Expression e7;
+
+	protected void setUp() {
+		// 10
+		this.cte = new Constante(10);
+		// x
+		this.av = new AccesVariable("x") ;
+
+		// 2 + x
+		this.e1 = new ExpressionBinaire(new Addition(),
+				new Constante(2),
+				av);
+
+		// (2 + x) * 3
+		this.e2	= new ExpressionBinaire(new Multiplication(),
+				this.e1,
+				new Constante(3));
+
+		// 7 * (2 + x)
+		this.e3 = new ExpressionBinaire(new Multiplication(),
+				new Constante(7),
+				this.e1) ;
+
+		// (x + y) + z
+		this.e4 = new ExpressionBinaire(new Addition(),
+				new ExpressionBinaire(new Addition(),
+					new AccesVariable("x"), new AccesVariable("y")),
+				new AccesVariable("z"));
+
+		// x + (y + z)
+		this.e5 = new ExpressionBinaire(new Addition(),
+				new AccesVariable("x"),
+				new ExpressionBinaire(new Addition(),
+					new AccesVariable("y"), new AccesVariable("z")));
+
+		// - - (2 + x)
+		this.e6 = new ExpressionUnaire(new Negation(),
+				new ExpressionUnaire(new Negation(),
+					this.e1));
+
+		// let x=(2+x) in (2+x)
+		this.e7 = new ExpressionTernaire(new Let(), av, e1, e1);
+	}
+
+}
+
diff --git a/ExpressionUnaire.java b/ExpressionUnaire.java
new file mode 100755
index 0000000..3b27101
--- /dev/null
+++ b/ExpressionUnaire.java
@@ -0,0 +1,32 @@
+/**
+  * Expression unaire avec un opérateur unaire appliqué sur un opérande.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  * @composed 1 "" "operateur" OperateurUnaire
+  * @has 1 "" "operande" Expression
+  */
+public class ExpressionUnaire implements Expression {
+
+	private Expression operande;
+	private OperateurUnaire operateur;
+
+	public ExpressionUnaire(OperateurUnaire operateur, Expression operande)
+	{
+		this.operande = operande;
+		this.operateur = operateur;
+	}
+
+	public Expression getOperande() {
+		return this.operande;
+	}
+
+	public OperateurUnaire getOperateur() {
+		return this.operateur;
+	}
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterExpressionUnaire(this);
+	}
+
+}
diff --git a/Let.java b/Let.java
new file mode 100755
index 0000000..7848279
--- /dev/null
+++ b/Let.java
@@ -0,0 +1,13 @@
+/**
+  * Opérateur ternaire de let.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class Let implements OperateurTernaire {
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterLet(this);
+	}
+
+}
diff --git a/Multiplication.java b/Multiplication.java
new file mode 100755
index 0000000..c4a7619
--- /dev/null
+++ b/Multiplication.java
@@ -0,0 +1,13 @@
+/**
+  * Opérateur binaire de multiplication.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public class Multiplication implements OperateurBinaire {
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterMultiplication(this);
+	}
+
+}
diff --git a/Negation.java b/Negation.java
new file mode 100755
index 0000000..163efc3
--- /dev/null
+++ b/Negation.java
@@ -0,0 +1,14 @@
+/**
+  * Opérateur unaire correspondant à la négation.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+
+public class Negation implements OperateurUnaire {
+
+	public <R> R accepter(VisiteurExpression<R> visiteur) {
+		return visiteur.visiterNegation(this);
+	}
+
+}
diff --git a/OperateurBinaire.java b/OperateurBinaire.java
new file mode 100755
index 0000000..4489c3d
--- /dev/null
+++ b/OperateurBinaire.java
@@ -0,0 +1,11 @@
+/**
+  * Opérateur binaire.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public interface OperateurBinaire {
+
+	<R> R accepter(VisiteurExpression<R> visiteur);
+
+}
diff --git a/OperateurTernaire.java b/OperateurTernaire.java
new file mode 100755
index 0000000..a854e0d
--- /dev/null
+++ b/OperateurTernaire.java
@@ -0,0 +1,11 @@
+/**
+  * Opérateur ternaire.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public interface OperateurTernaire {
+
+	<R> R accepter(VisiteurExpression<R> visiteur);
+
+}
diff --git a/OperateurUnaire.java b/OperateurUnaire.java
new file mode 100755
index 0000000..3f2ee66
--- /dev/null
+++ b/OperateurUnaire.java
@@ -0,0 +1,11 @@
+/**
+  * Opérateur unaire.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public interface OperateurUnaire {
+
+	<R> R accepter(VisiteurExpression<R> visiteur);
+
+}
diff --git a/Soustraction.java b/Soustraction.java
new file mode 100755
index 0000000..5736e7f
--- /dev/null
+++ b/Soustraction.java
@@ -0,0 +1,14 @@
+/**
+  * Opérateur binaire de soustraction.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+  public class Soustraction implements OperateurBinaire {
+
+    public <R> R accepter(VisiteurExpression<R> visiteur) {
+      return visiteur.visiterSoustraction(this);
+    }
+  
+  }
+  
\ No newline at end of file
diff --git a/VisiteurExpression.java b/VisiteurExpression.java
new file mode 100755
index 0000000..046dbba
--- /dev/null
+++ b/VisiteurExpression.java
@@ -0,0 +1,59 @@
+/**
+  * Visiteur sur une expression arithmétique.
+  *
+  * @author	Xavier Crégut
+  * @version	$Revision$
+  */
+public interface VisiteurExpression<R> {
+
+	/** Visiter un accès à une variable.
+	  * @param v l'accès à une variable à visiter
+	  */
+	R visiterAccesVariable(AccesVariable v);
+
+	/** Visiter une constante.
+	  * @param c la constante à visiter
+	  */
+	R visiterConstante(Constante c);
+
+	/** Visiter une expression binaire.
+	  * @param e l'expression binaire à visiter
+	  */
+	R visiterExpressionBinaire(ExpressionBinaire e);
+
+	/** Visiter l'opérateur binaire addition.
+	  * @param a l'opérateur à visiter
+	  */
+	R visiterAddition(Addition a);
+
+	/** Visiter l'opérateur binaire soustraction.
+	  * @param a l'opérateur à visiter
+	  */
+	  R visiterSoustraction(Soustraction a);
+
+	/** Visiter l'opérateur binaire multiplication.
+	  * @param m l'opérateur à visiter
+	  */
+	R visiterMultiplication(Multiplication m);
+
+	/** Visiter une expression unaire.
+	  * @param v l'expression unaire à visiter
+	  */
+	R visiterExpressionUnaire(ExpressionUnaire e);
+
+	/** Visiter un opérateur unaire négation.
+	  * @param n l'opérateur unaire à visiter
+	  */
+	R visiterNegation(Negation n);
+
+	/** Visiter une expression ternaire.
+	  * @param e l'expression ternaire à visiter
+	  */
+	  R visiterExpressionTernaire(ExpressionTernaire e);
+
+	/** Visiter un opérateur ternaire let.
+	  * @param n l'opérateur ternaire à visiter
+	  */
+	  R visiterLet(Let n);
+
+}
diff --git a/expressions.dot b/expressions.dot
new file mode 100755
index 0000000..eeab00c
--- /dev/null
+++ b/expressions.dot
@@ -0,0 +1,121 @@
+#!/usr/local/bin/dot
+#
+# Class diagram 
+# Generated by UMLGraph version R5_7_2-23-gd0ede4 (http://www.spinellis.gr/umlgraph/)
+#
+
+digraph G {
+	edge [fontname="Helvetica",fontsize=10,labelfontname="Helvetica",labelfontsize=10];
+	node [fontname="Helvetica",fontsize=10,shape=plaintext];
+	nodesep=0.25;
+	ranksep=0.5;
+	// VisiteurExpression<R>
+	c0 [label=<<table title="VisiteurExpression" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> &#171;interface&#187; </td></tr>
+<tr><td align="center" balign="center"> VisiteurExpression&lt;R&gt; </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// AccesVariable
+	c1 [label=<<table title="AccesVariable" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> AccesVariable </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// Addition
+	c2 [label=<<table title="Addition" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> Addition </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// AfficheurInfixe
+	c3 [label=<<table title="AfficheurInfixe" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> AfficheurInfixe </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// Constante
+	c4 [label=<<table title="Constante" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> Constante </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// ExemplesAffichage
+	c5 [label=<<table title="ExemplesAffichage" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> ExemplesAffichage </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// ExpressionBinaire
+	c6 [label=<<table title="ExpressionBinaire" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> ExpressionBinaire </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// Expression
+	c7 [label=<<table title="Expression" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> &#171;interface&#187; </td></tr>
+<tr><td align="center" balign="center"> Expression </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// ExpressionUnaire
+	c8 [label=<<table title="ExpressionUnaire" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> ExpressionUnaire </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// Multiplication
+	c9 [label=<<table title="Multiplication" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> Multiplication </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// Negation
+	c10 [label=<<table title="Negation" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> Negation </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// OperateurBinaire
+	c11 [label=<<table title="OperateurBinaire" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> &#171;interface&#187; </td></tr>
+<tr><td align="center" balign="center"> OperateurBinaire </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	// OperateurUnaire
+	c12 [label=<<table title="OperateurUnaire" border="0" cellborder="1" cellspacing="0" cellpadding="2" port="p">
+		<tr><td><table border="0" cellspacing="0" cellpadding="1">
+<tr><td align="center" balign="center"> &#171;interface&#187; </td></tr>
+<tr><td align="center" balign="center"> OperateurUnaire </td></tr>
+		</table></td></tr>
+		</table>>, URL="null", fontname="Helvetica", fontcolor="black", fontsize=10.0];
+	//AccesVariable implements Expression
+	c7:p -> c1:p [dir=back,arrowtail=empty,style=dashed];
+	//Addition implements OperateurBinaire
+	c11:p -> c2:p [dir=back,arrowtail=empty,style=dashed];
+	//AfficheurInfixe implements VisiteurExpression<R>
+	c0:p -> c3:p [dir=back,arrowtail=empty,style=dashed];
+	//Constante implements Expression
+	c7:p -> c4:p [dir=back,arrowtail=empty,style=dashed];
+	//ExpressionBinaire implements Expression
+	c7:p -> c6:p [dir=back,arrowtail=empty,style=dashed];
+	// ExpressionBinaire HAS Expression
+	c6:p -> c7:p [taillabel="1", label="", headlabel="gauche", fontname="Helvetica", fontcolor="black", fontsize=10.0, color="black", arrowhead=none, arrowtail=ediamond, dir=both];
+	// ExpressionBinaire HAS Expression
+	c6:p -> c7:p [taillabel="1", label="", headlabel="droite", fontname="Helvetica", fontcolor="black", fontsize=10.0, color="black", arrowhead=none, arrowtail=ediamond, dir=both];
+	// ExpressionBinaire COMPOSED OperateurBinaire
+	c6:p -> c11:p [taillabel="1", label="", headlabel="operateur", fontname="Helvetica", fontcolor="black", fontsize=10.0, color="black", arrowhead=none, arrowtail=diamond, dir=both];
+	//ExpressionUnaire implements Expression
+	c7:p -> c8:p [dir=back,arrowtail=empty,style=dashed];
+	// ExpressionUnaire HAS Expression
+	c8:p -> c7:p [taillabel="1", label="", headlabel="operande", fontname="Helvetica", fontcolor="black", fontsize=10.0, color="black", arrowhead=none, arrowtail=ediamond, dir=both];
+	// ExpressionUnaire COMPOSED OperateurUnaire
+	c8:p -> c12:p [taillabel="1", label="", headlabel="operateur", fontname="Helvetica", fontcolor="black", fontsize=10.0, color="black", arrowhead=none, arrowtail=diamond, dir=both];
+	//Multiplication implements OperateurBinaire
+	c11:p -> c9:p [dir=back,arrowtail=empty,style=dashed];
+	//Negation implements OperateurUnaire
+	c12:p -> c10:p [dir=back,arrowtail=empty,style=dashed];
+}
+
diff --git a/expressions.fig b/expressions.fig
new file mode 100755
index 0000000..cfbfc68
--- /dev/null
+++ b/expressions.fig
@@ -0,0 +1,161 @@
+#FIG 3.2
+# Generated by graphviz version 2.43.0 (0)
+# Title: G
+# Pages: 1
+Portrait
+Center
+Inches
+Letter
+100.00
+Single
+-2
+1200 2
+0 32 #d3d3d3
+0 33 #fffffe
+2 3 0 1 33 7 2 0 20 0.0 0 0 0 0 0 5
+ 0 5360 0 0 12330 0 12330 5360 0 5360
+# c0
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 250 800 250 160 2830 160 2830 800 250 800
+4 0 0 1 0 16 10.0 0.0000 6 10.0 50.0 920 368  \302\253interface\302\273 \001
+4 0 0 1 0 16 10.0 0.0000 6 10.0 76.7 330 628  VisiteurExpression<R> \001
+# c3
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 690 2160 690 1780 2370 1780 2370 2160 690 2160
+4 0 0 1 0 16 10.0 0.0000 6 10.0 56.7 770 1988  AfficheurInfixe \001
+# c0->c3
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  1530 1012 1530 1146 1530 1282 1530 1415 1530 1543 1530 1660 1530 1762
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 1460 1005 1530 805 1600 1005 1460 1005
+# c1
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 5790 2160 5790 1780 7450 1780 7450 2160 5790 2160
+4 0 0 1 0 16 10.0 0.0000 6 10.0 50.0 5870 1988  AccesVariable \001
+# c2
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 2510 5120 2510 4740 3610 4740 3610 5120 2510 5120
+4 0 0 1 0 16 10.0 0.0000 6 10.0 33.3 2590 4948  Addition \001
+# c4
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 8130 2160 8130 1780 9410 1780 9410 2160 8130 2160
+4 0 0 1 0 16 10.0 0.0000 6 10.0 36.7 8210 1988  Constante \001
+# c5
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 7990 680 7990 300 10150 300 10150 680 7990 680
+4 0 0 1 0 16 10.0 0.0000 6 10.0 63.3 8070 508  ExemplesAffichage \001
+# c6
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 3050 2160 3050 1780 5090 1780 5090 2160 3050 2160
+4 0 0 1 0 16 10.0 0.0000 6 10.0 63.3 3130 1988  ExpressionBinaire \001
+# c7
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 5910 800 5910 160 7310 160 7310 800 5910 800
+4 0 0 1 0 16 10.0 0.0000 6 10.0 50.0 5990 368  \302\253interface\302\273 \001
+4 0 0 1 0 16 10.0 0.0000 6 10.0 40.0 6010 628  Expression \001
+# c6->c7
+3 4 0 1 0 0 0 0 -1 0.0 0 0 0 7
+  4585 1648 4816 1517 5068 1374 5330 1226 5592 1077 5845 934 6078 802
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 5
+ 4580 1651 4436 1640 4371 1769 4515 1780 4580 1651
+4 1 0 0 0 16 10.0 0.0000 6 10.0 20.0 5718 930 gauche\001
+4 1 0 0 0 16 10.0 0.0000 6 10.0 3.3 4301 1677 1\001
+# c6->c7
+3 4 0 1 0 0 0 0 -1 0.0 0 0 0 7
+  4773 1665 5034 1533 5307 1388 5581 1236 5846 1084 6090 937 6302 802
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 5
+ 4770 1666 4628 1645 4553 1769 4696 1790 4770 1666
+4 1 0 0 0 16 10.0 0.0000 6 10.0 20.0 6592 930 droite\001
+4 1 0 0 0 16 10.0 0.0000 6 10.0 3.3 4483 1677 1\001
+# c11
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 3090 3760 3090 3120 5050 3120 5050 3760 3090 3760
+4 0 0 1 0 16 10.0 0.0000 6 10.0 50.0 3450 3328  \302\253interface\302\273 \001
+4 0 0 1 0 16 10.0 0.0000 6 10.0 60.0 3170 3588  OperateurBinaire \001
+# c6->c11
+3 4 0 1 0 0 0 0 -1 0.0 0 0 0 7
+  4070 2391 4070 2511 4070 2636 4070 2763 4070 2888 4070 3008 4070 3119
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 20 0.0 0 0 0 0 0 5
+ 4070 2391 4150 2271 4070 2151 3990 2271 4070 2391
+4 1 0 0 0 16 10.0 0.0000 6 10.0 30.0 3590 3027 operateur\001
+4 1 0 0 0 16 10.0 0.0000 6 10.0 3.3 4000 2279 1\001
+# c7->c1
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  6610 1012 6610 1146 6610 1282 6610 1415 6610 1543 6610 1660 6610 1762
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 6540 1005 6610 805 6680 1005 6540 1005
+# c7->c4
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  7231 914 7452 1062 7683 1215 7914 1370 8136 1518 8339 1653 8514 1769
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 7190 971 7063 802 7268 855 7190 971
+# c7->c6
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  5730 864 5440 1016 5146 1177 4861 1340 4599 1498 4371 1642 4193 1766
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 5699 801 5909 774 5761 926 5699 801
+# c8
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 10090 2160 10090 1780 12090 1780 12090 2160 10090 2160
+4 0 0 1 0 16 10.0 0.0000 6 10.0 60.0 10170 1988  ExpressionUnaire \001
+# c7->c8
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 13
+  7435 868 7441 870 7447 872 7452 874 7458 876 7464 878 7470 880 7979 1048 8501 1214 9018 1374 9514 1523 9971 1656 10374 1769
+ 0 1 1 1 1 1 1 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 7407 933 7241 801 7453 800 7407 933
+# c8->c7
+3 4 0 1 0 0 0 0 -1 0.0 0 0 0 13
+  10396 1695 10037 1583 9632 1457 9195 1321 8740 1177 8280 1029 7830 880 7746 851 7661 822 7574 792 7487 761 7400 731 7314 701
+ 0 1 1 1 1 1 1 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 5
+ 10403 1697 10493 1809 10632 1769 10541 1657 10403 1697
+4 1 0 0 0 16 10.0 0.0000 6 10.0 26.7 7774 829 operande\001
+4 1 0 0 0 16 10.0 0.0000 6 10.0 3.3 10562 1677 1\001
+# c12
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 10130 3760 10130 3120 12050 3120 12050 3760 10130 3760
+4 0 0 1 0 16 10.0 0.0000 6 10.0 50.0 10470 3328  \302\253interface\302\273 \001
+4 0 0 1 0 16 10.0 0.0000 6 10.0 56.7 10210 3588  OperateurUnaire \001
+# c8->c12
+3 4 0 1 0 0 0 0 -1 0.0 0 0 0 7
+  11090 2391 11090 2511 11090 2636 11090 2763 11090 2888 11090 3008 11090 3119
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 20 0.0 0 0 0 0 0 5
+ 11090 2391 11170 2271 11090 2151 11010 2271 11090 2391
+4 1 0 0 0 16 10.0 0.0000 6 10.0 30.0 10610 3027 operateur\001
+4 1 0 0 0 16 10.0 0.0000 6 10.0 3.3 11125 2279 1\001
+# c9
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 4290 5120 4290 4740 5910 4740 5910 5120 4290 5120
+4 0 0 1 0 16 10.0 0.0000 6 10.0 53.3 4370 4948  Multiplication \001
+# c10
+2 3 0 1 0 7 1 0 -1 0.0 0 0 0 0 0 5
+ 10510 5120 10510 4740 11690 4740 11690 5120 10510 5120
+4 0 0 1 0 16 10.0 0.0000 6 10.0 33.3 10590 4948  Negation \001
+# c11->c2
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  3735 3933 3637 4072 3536 4214 3436 4356 3340 4491 3252 4614 3176 4722
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 3681 3888 3854 3765 3795 3969 3681 3888
+# c11->c9
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  4405 3933 4503 4072 4604 4214 4704 4356 4800 4491 4888 4614 4964 4722
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 4345 3969 4286 3765 4459 3888 4345 3969
+# c12->c10
+3 4 1 1 0 0 0 0 -1 10.0 0 0 0 7
+  11090 3972 11090 4106 11090 4242 11090 4375 11090 4503 11090 4620 11090 4722
+ 0 1 1 1 1 1 0
+2 3 0 1 0 0 0 0 -1 0.0 0 0 0 0 0 4
+ 11020 3965 11090 3765 11160 3965 11020 3965
+# end of FIG file
diff --git a/expressions.pdf b/expressions.pdf
new file mode 100755
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