diff --git a/poincare/src/simplify/rules_generation/Makefile b/poincare/src/simplify/rules_generation/Makefile
index 8c6b823e9..c552b6cd4 100644
--- a/poincare/src/simplify/rules_generation/Makefile
+++ b/poincare/src/simplify/rules_generation/Makefile
@@ -3,10 +3,8 @@ dir=poincare/src/simplify/rules_generation
 rulegen_objs := $(addprefix $(dir)/,\
   rules_parser.o\
   rules_lexer.o\
-  builder.o\
   node.o\
   rule.o\
-  selector.o\
 )
 
 $(dir)/rules_parser.cpp: $(dir)/rules_parser.y
diff --git a/poincare/src/simplify/rules_generation/builder.cpp b/poincare/src/simplify/rules_generation/builder.cpp
deleted file mode 100644
index 3b69a150d..000000000
--- a/poincare/src/simplify/rules_generation/builder.cpp
+++ /dev/null
@@ -1,33 +0,0 @@
-#include "builder.h"
-#include "rule.h"
-#include <iostream>
-#include <cassert>
-
-Builder::Builder(Type type, std::string * name, std::vector<Builder *> * children) :
-  Node(name, (std::vector<Node *> *)children),
-  m_type(type)
-{
-}
-
-void Builder::generateFields(Rule * context, std::string &indentation) {
-  Selector * selector = context->selector();
-  switch (m_type) {
-    case Type::ExpressionType:
-      std::cout << indentation << ".m_action = ExpressionBuilder::Action::BuildFromTypeAndValue," << std::endl;
-      std::cout << indentation << ".m_expressionType = Expression::Type::" << *m_name << "," << std::endl;
-      break;
-    case Type::Variable:
-      std::cout << indentation << ".m_action = ExpressionBuilder::Action::Clone," << std::endl;
-      assert(m_children->size() == 0);
-      std::cout << indentation << ".m_matchIndex = " << selector->flatIndexOfChildNamed(*m_name) << "," << std::endl;
-      break;
-    case Type::Wildcard:
-      std::cout << indentation << ".m_action = ExpressionBuilder::Action::BringUpWildcard," << std::endl;
-      assert(m_children->size() == 0);
-      std::cout << indentation << ".m_matchIndex = " << selector->flatIndexOfChildNamed(*m_name) << "," << std::endl;
-      break;
-    case Type::ExpressionGenerator:
-      assert(false); // Not implemented yet.
-      break;
-  }
-}
diff --git a/poincare/src/simplify/rules_generation/builder.h b/poincare/src/simplify/rules_generation/builder.h
deleted file mode 100644
index 45c923273..000000000
--- a/poincare/src/simplify/rules_generation/builder.h
+++ /dev/null
@@ -1,22 +0,0 @@
-#ifndef POINCARE_SIMPLIFY_RULES_GENERATION_BUILDER_H
-#define POINCARE_SIMPLIFY_RULES_GENERATION_BUILDER_H
-
-#include "node.h"
-#include <string>
-
-class Builder : public Node {
-public:
-  enum class Type {
-    ExpressionGenerator,
-    ExpressionType,
-    Variable,
-    Wildcard
-  };
-  Builder(Type type, std::string * name, std::vector<Builder *> * children = nullptr);
-protected:
-  void generateFields(Rule * context, std::string &indentation) override;
-private:
-  Type m_type;
-};
-
-#endif
diff --git a/poincare/src/simplify/rules_generation/node.cpp b/poincare/src/simplify/rules_generation/node.cpp
index 76f64d5c5..94eea90f8 100644
--- a/poincare/src/simplify/rules_generation/node.cpp
+++ b/poincare/src/simplify/rules_generation/node.cpp
@@ -1,25 +1,113 @@
-#include "builder.h"
+#include "node.h"
+#include "rule.h"
 #include <iostream>
+#include <sstream>
 #include <cassert>
 
-Node::Node(std::string * name, std::vector<Node *> * children) :
-  m_name(name),
-  m_children(children)
+Node::Node(Type type, std::string * typeName) :
+  m_type(type),
+  m_typeName(typeName),
+  m_referenceMode(ReferenceMode::None),
+  m_referenceName(nullptr),
+  m_value(nullptr),
+  m_parent(nullptr)
 {
-  if (children == nullptr) {
-    m_children = new std::vector<Node *>();
-  }
-  for (Node * child : *m_children) {
-    child->m_parent = this;
-  }
+  m_children = new std::vector<Node *>();
 }
 
 Node::~Node() {
   delete m_children;
 }
 
+void Node::setReference(ReferenceMode mode, std::string * referenceName) {
+  assert(m_referenceName == nullptr);
+  m_referenceName = referenceName;
+  m_referenceMode = mode;
+}
+
+void Node::setValue(std::string * value) {
+  assert(m_value == nullptr);
+  m_value = value;
+}
+
+void Node::setChildren(std::vector<Node *> * children) {
+  assert(m_children->size() == 0);
+  delete m_children;
+  m_children = children;
+  for (Node * child : *m_children) {
+    child->m_parent = this;
+  }
+}
+
+// Generation
+
+std::string Node::generateSelectorConstructor(Rule * context) {
+  std::ostringstream result;
+  switch (m_type) {
+    case Node::Type::Any:
+      switch (m_referenceMode) {
+        case Node::ReferenceMode::None:
+        case Node::ReferenceMode::SingleNode:
+          result << "ExpressionSelector::Any(";
+          break;
+        case Node::ReferenceMode::Wildcard:
+          result << "ExpressionSelector::Wildcard(";
+          break;
+      }
+      break;
+    case Node::Type::Expression:
+      if (m_value == nullptr) {
+        result << "ExpressionSelector::Type(Expression::Type::" << *m_typeName << ", ";
+      } else {
+        result << "ExpressionSelector::TypeAndValue(Expression::Type::" << *m_typeName << ", " << *m_value << ",";
+      }
+      break;
+    case Node::Type::Generator:
+      //assert(false);
+      break;
+  }
+  result << m_children->size() << ")";
+  return result.str();
+}
+
+std::string Node::generateBuilderConstructor(Rule * context) {
+  Node * selector = context->selector();
+  std::ostringstream result;
+  switch (m_type) {
+    case Node::Type::Any:
+      switch (m_referenceMode) {
+        case Node::ReferenceMode::None:
+          assert(false);
+          break;
+        case Node::ReferenceMode::SingleNode:
+          assert(m_referenceName != nullptr);
+          result << "ExpressionBuilder::Clone(" << selector->flatIndexOfChildNamed(*m_referenceName) << ", " ;
+          break;
+        case Node::ReferenceMode::Wildcard:
+          result << "ExpressionBuilder::BringUpWildcard(" << selector->flatIndexOfChildNamed(*m_referenceName) << ", ";
+          break;
+      }
+      break;
+    case Node::Type::Expression:
+      if (m_value == nullptr) {
+        // Here we could assert that m_typeName is among the kinds that expect no value
+        result << "ExpressionBuilder::BuildFromType(Expression::Type::" << *m_typeName << ", ";
+      } else {
+        // Here we could assert that m_typeName is among the kinds that expect a value
+        result << "ExpressionBuilder::BuildFromTypeAndValue(Expression::Type::" << *m_typeName << ", " << *m_value << ", ";
+      }
+      break;
+    case Node::Type::Generator:
+      result << "ExpressionBuilder::CallExternalGenerator(SimplificationGenerator::" << *m_typeName << ", ";
+      //assert(false);
+      break;
+  }
+  result << m_children->size() << ")";
+  return result.str();
+}
+
 int Node::flatIndexOfChildNamed(std::string name) {
-  if (name == *m_name) {
+  if (m_referenceName != nullptr && *m_referenceName == name) {
     return 0;
   }
   int sum=1;
@@ -54,17 +142,26 @@ std::string indentation_string(int i) {
     return result;
 }
 
-int Node::generate(Rule * context, int index, int indentationLevel) {
+void Node::generateSelectorTree(Rule * context) {
+  generateTree(true, context, 0, 0);
+}
+
+void Node::generateBuilderTree(Rule * context) {
+  generateTree(false, context, 0, 0);
+}
+
+int Node::generateTree(bool selector, Rule * context, int index, int indentationLevel) {
   std::string indentation = indentation_string(indentationLevel);
-  std::string nextIndentation = indentation_string(indentationLevel+1);
-  std::cout << indentation << "{" << std::endl;
-  std::cout << nextIndentation << "// #" << index << std::endl;
-  this->generateFields(context, nextIndentation);
-  std::cout << nextIndentation << ".m_numberOfChildren = " << m_children->size() << "," << std::endl;
-  std::cout << indentation << "}," << std::endl;
+  std::cout << indentation;
+  if (selector) {
+    std::cout << generateSelectorConstructor(context);
+  } else {
+    std::cout << generateBuilderConstructor(context);
+  }
+  std::cout << ", // #" << index << std::endl;
   int generatedCount = 1;
   for (Node * child : *m_children) {
-    generatedCount += child->generate(context, index+generatedCount, indentationLevel+1);
+    generatedCount += child->generateTree(selector, context, index+generatedCount, indentationLevel+1);
   }
   return generatedCount;
 }
diff --git a/poincare/src/simplify/rules_generation/node.h b/poincare/src/simplify/rules_generation/node.h
index fb2a689bb..2f070f510 100644
--- a/poincare/src/simplify/rules_generation/node.h
+++ b/poincare/src/simplify/rules_generation/node.h
@@ -8,14 +8,39 @@ class Rule;
 
 class Node {
 public:
-  Node(std::string * name, std::vector<Node *> * m_children);
+  enum class Type {
+    Expression,
+    Generator,
+    Any
+  };
+  enum class ReferenceMode {
+    None,
+    SingleNode,
+    Wildcard
+  };
+
+  // Creating Nodes
+  Node(Type type, std::string * typeName = nullptr);
   ~Node();
-  int generate(Rule * context = nullptr, int index = 0, int indentationLevel = 0);
+  void setReference(ReferenceMode mode, std::string * referenceName);
+  void setValue(std::string * value);
+  void setChildren(std::vector<Node *> * children);
+
   int totalDescendantCountIncludingSelf();
   int flatIndexOfChildNamed(std::string name);
-protected:
-  virtual void generateFields(Rule * context, std::string &indentation) = 0;
-  std::string * m_name;
+
+  void generateSelectorTree(Rule * context);
+  void generateBuilderTree(Rule * context);
+private:
+  int generateTree(bool selector, Rule * context, int index, int indentationLevel);
+  std::string generateSelectorConstructor(Rule * context);
+  std::string generateBuilderConstructor(Rule * context);
+
+  Type m_type;
+  std::string * m_typeName;
+  ReferenceMode m_referenceMode;
+  std::string * m_referenceName;
+  std::string * m_value;
   std::vector<Node *> * m_children;
   Node * m_parent;
 };
diff --git a/poincare/src/simplify/rules_generation/rule.cpp b/poincare/src/simplify/rules_generation/rule.cpp
index e01f5d319..176d3bde8 100644
--- a/poincare/src/simplify/rules_generation/rule.cpp
+++ b/poincare/src/simplify/rules_generation/rule.cpp
@@ -1,7 +1,7 @@
 #include "rule.h"
 #include <iostream>
 
-Rule::Rule(Selector * selector, Builder * builder) :
+Rule::Rule(Node * selector, Node * builder) :
   m_selector(selector), m_builder(builder) {
 }
 
@@ -10,16 +10,16 @@ Rule::~Rule() {
   delete m_selector;
 }
 
-Selector * Rule::selector() {
+Node * Rule::selector() {
   return m_selector;
 }
 
 void Rule::generate(std::string rule_name) {
-  std::cout << "const ExpressionSelector " << rule_name << "Selector[" << m_selector->totalDescendantCountIncludingSelf() << "] = {" << std::endl;
-  m_selector->generate(this);
+  std::cout << "constexpr ExpressionSelector " << rule_name << "Selector[" << m_selector->totalDescendantCountIncludingSelf() << "] = {" << std::endl;
+  m_selector->generateSelectorTree(this);
   std::cout << "};" << std::endl;
 
-  std::cout << "const ExpressionBuilder " << rule_name << "Builder[" << m_builder->totalDescendantCountIncludingSelf() << "] = {" << std::endl;
-  m_builder->generate(this);
+  std::cout << "constexpr ExpressionBuilder " << rule_name << "Builder[" << m_builder->totalDescendantCountIncludingSelf() << "] = {" << std::endl;
+  m_builder->generateBuilderTree(this);
   std::cout << "};" << std::endl;
 }
diff --git a/poincare/src/simplify/rules_generation/rule.h b/poincare/src/simplify/rules_generation/rule.h
index de303e794..f6c57ae6f 100644
--- a/poincare/src/simplify/rules_generation/rule.h
+++ b/poincare/src/simplify/rules_generation/rule.h
@@ -1,18 +1,17 @@
 #ifndef POINCARE_SIMPLIFY_RULES_GENERATION_RULE_H
 #define POINCARE_SIMPLIFY_RULES_GENERATION_RULE_H
 
-#include "selector.h"
-#include "builder.h"
+#include "node.h"
 
 class Rule {
 public:
-  Rule(Selector * selector, Builder * builder);
+  Rule(Node * selector, Node * builder);
   ~Rule();
   void generate(std::string rule_name);
-  Selector * selector();
+  Node * selector();
 private:
-  Selector * m_selector;
-  Builder * m_builder;
+  Node * m_selector;
+  Node * m_builder;
 };
 
 #endif
diff --git a/poincare/src/simplify/rules_generation/rules_lexer.l b/poincare/src/simplify/rules_generation/rules_lexer.l
index 748a688ce..76d96f184 100644
--- a/poincare/src/simplify/rules_generation/rules_lexer.l
+++ b/poincare/src/simplify/rules_generation/rules_lexer.l
@@ -9,14 +9,18 @@
 
 %%
 
-[A-Z][a-z]+ { yylval.string = new std::string(yytext); return(EXPRESSION_TYPE); }
-\$[a-zA-Z]+ { yylval.string = new std::string(yytext); return(EXPRESSION_GENERATOR); }
-[a-z]+\* { yylval.string = new std::string(yytext); return(WILDCARD); }
-[a-z]+ { yylval.string = new std::string(yytext); return(VARIABLE); }
+[a-z]+ { yylval.string = new std::string(yytext); return (IDENTIFIER); }
+[A-Za-z]+ { yylval.string = new std::string(yytext); return (CAPITALIZED_IDENTIFIER); }
+[0-9]+ { yylval.string = new std::string(yytext); return (VALUE); }
+\$ { return(DOLLAR); }
+\* { return (ASTERISK); }
 \-\> { return(SIMPLIFIES_TO); }
 \( { return(LEFT_PARENTHESIS); }
 \) { return(RIGHT_PARENTHESIS); }
+\[ { return(LEFT_BRACKET); }
+\] { return(RIGHT_BRACKET); }
 \, { return(COMMA); }
 \; { return(SEMICOLON); }
+\. { return(PERIOD); }
 
 %%
diff --git a/poincare/src/simplify/rules_generation/rules_parser.y b/poincare/src/simplify/rules_generation/rules_parser.y
index 497e562cb..2b369824a 100644
--- a/poincare/src/simplify/rules_generation/rules_parser.y
+++ b/poincare/src/simplify/rules_generation/rules_parser.y
@@ -23,39 +23,38 @@ int yyerror(std::vector<Rule *> ** rules, const char *s);
  * when parsing (a/b) we want to create a new Fraction), or a string (this will
  * be useful to retrieve the value of Integers for example). */
 %union {
-  std::vector<Builder *> * builder_list;
-  std::vector<Selector *> * selector_list;
   std::vector<Rule *> * rule_list;
+  std::vector<Node *> * node_list;
   Rule * rule;
-  Selector * selector;
-  Builder * builder;
+  Node * node;
   std::string * string;
 }
 
-/* The INTEGER token uses the "string" part of the union to store its value */
-%token <string> INTEGER
-%token <string> SYMBOL
+/* The IDENTIFIER, CAPITALIZED_IDENTIFIER and VALUE token uses the "string" part
+ * of the union to store their value */
 
-%token <string> EXPRESSION_TYPE
-%token <string> EXPRESSION_GENERATOR
-%token <string> WILDCARD
-%token <string> VARIABLE
+%token <string> IDENTIFIER
+%token <string> CAPITALIZED_IDENTIFIER
+%token <string> VALUE
+
+/* Some tokens don't store any value */
 
 %token SIMPLIFIES_TO
 %token LEFT_PARENTHESIS
 %token RIGHT_PARENTHESIS
+%token LEFT_BRACKET
+%token RIGHT_BRACKET
 %token COMMA
 %token SEMICOLON
+%token PERIOD
+%token DOLLAR
+%token ASTERISK
 
+/* The "rule_list" symbol uses the "rule_list" part of the union, and so on */
 %type <rule_list> rule_list;
 %type <rule> rule;
-%type <selector> selector;
-%type <selector_list> selector_list;
-%type <builder> builder;
-%type <builder_list> builder_list;
-
-/* The "exp" symbol uses the "expression" part of the union. */
-/*%type <expression> exp;*/
+%type <node> node;
+%type <node_list> node_list;
 
 %%
 
@@ -67,32 +66,39 @@ rule_list:
   | rule_list rule { $1->push_back($2); $$ = $1; }
 
 rule:
-  selector SIMPLIFIES_TO builder SEMICOLON { $$ = new Rule($1, $3); }
+  node SIMPLIFIES_TO node SEMICOLON { $$ = new Rule($1, $3); }
 
-selector:
-  VARIABLE { $$ = new Selector(Selector::Type::Variable, $1); }
-  | WILDCARD { $$ = new Selector(Selector::Type::Wildcard, $1); }
-  | EXPRESSION_TYPE LEFT_PARENTHESIS selector_list RIGHT_PARENTHESIS {
-      $$ = new Selector(Selector::Type::ExpressionType, $1, $3);
+node:
+  CAPITALIZED_IDENTIFIER {
+      $$ = new Node(Node::Type::Expression, $1);
+    }
+  | DOLLAR CAPITALIZED_IDENTIFIER {
+      $$ = new Node(Node::Type::Generator, $2);
+    }
+  | IDENTIFIER {
+      $$ = new Node(Node::Type::Any);
+      $$->setReference(Node::ReferenceMode::SingleNode, $1);
+    }
+  | IDENTIFIER ASTERISK {
+      $$ = new Node(Node::Type::Any);
+      $$->setReference(Node::ReferenceMode::Wildcard, $1);
+    }
+  | node PERIOD IDENTIFIER {
+      $$ = $1;
+      $$->setReference(Node::ReferenceMode::SingleNode, $3);
+    }
+  | node LEFT_BRACKET IDENTIFIER RIGHT_BRACKET {
+      $$ = $1;
+      $$->setValue($3);
+    }
+  | node LEFT_PARENTHESIS node_list RIGHT_PARENTHESIS {
+      $$ = $1;
+      $$->setChildren($3);
     }
 
-selector_list:
-  selector { $$ = new std::vector<Selector *>(); $$->push_back($1); }
-  | selector_list COMMA selector { $1->push_back($3); $$ = $1; }
-
-builder:
-  VARIABLE { $$ = new Builder(Builder::Type::Variable, $1); }
-  | WILDCARD { $$ = new Builder(Builder::Type::Wildcard, $1); }
-  | EXPRESSION_GENERATOR LEFT_PARENTHESIS builder_list RIGHT_PARENTHESIS {
-      $$ = new Builder(Builder::Type::ExpressionGenerator, $1, $3);
-    }
-  | EXPRESSION_TYPE LEFT_PARENTHESIS builder_list RIGHT_PARENTHESIS {
-      $$ = new Builder(Builder::Type::ExpressionType, $1, $3);
-    }
-
-builder_list:
-  builder { $$ = new std::vector<Builder *>(); $$->push_back($1); }
-  | builder_list COMMA builder { $1->push_back($3); $$ = $1; }
+node_list:
+  node { $$ = new std::vector<Node *>(); $$->push_back($1); }
+  | node_list COMMA node { $1->push_back($3); $$ = $1; }
 
 %%
 
@@ -120,20 +126,16 @@ int main(void) {
     rules->at(i)->generate(name.str());
     std::cout << std::endl;
   }
-  std::cout << "const Simplification simplifications[" << rules->size() << "] = {" << std::endl;
+  std::cout << "constexpr Simplification simplifications[" << rules->size() << "] = {" << std::endl;
   for (int i=0; i<rules->size(); i++) {
     std::stringstream name;
     name << "rule" << i;
-    std::cout << "  {" << std::endl;
-    std::cout << "    .m_selector = (ExpressionSelector *)" << name.str() << "Selector," << std::endl;
-    std::cout << "    .m_builder = (ExpressionBuilder *)" << name.str() << "Builder," << std::endl;
-    std::cout << "  }," << std::endl;
+std::cout << "  Simplification((ExpressionSelector *)" << name.str() << "Selector, (ExpressionBuilder *)" << name.str() << "Builder)," << std::endl;
   }
   std::cout << "};" << std::endl;
 
   std::cout << std::endl;
-  std::cout << "const int knumberOfSimplifications = " << rules->size() << ";" << std::endl;
-
+  std::cout << "constexpr int knumberOfSimplifications = " << rules->size() << ";" << std::endl;
 
   delete rules;
   return 0;
diff --git a/poincare/src/simplify/rules_generation/selector.cpp b/poincare/src/simplify/rules_generation/selector.cpp
deleted file mode 100644
index ef700302c..000000000
--- a/poincare/src/simplify/rules_generation/selector.cpp
+++ /dev/null
@@ -1,27 +0,0 @@
-#include "selector.h"
-#include <iostream>
-#include <cassert>
-
-Selector::Selector(Type type, std::string * name, std::vector<Selector *> * children) :
-  Node(name, (std::vector<Node *> *)children),
-  m_type(type)
-{
-}
-
-void Selector::generateFields(Rule * context, std::string &indentation) {
-  Selector * parent = (Selector *)m_parent;
-  switch (m_type) {
-    case Type::Variable:
-      std::cout << indentation << ".m_match = ExpressionSelector::Match::Any," << std::endl;
-      break;
-    case Type::Wildcard:
-      std::cout << indentation << ".m_match = ExpressionSelector::Match::Wildcard," << std::endl;
-      // Wildcard should always be the last element of a parent
-      assert(parent->m_children->back() == this);
-      break;
-    case Type::ExpressionType:
-      std::cout << indentation << ".m_match = ExpressionSelector::Match::Type," << std::endl;
-      std::cout << indentation << ".m_expressionType = Expression::Type::" << *m_name << "," << std::endl;
-      break;
-  }
-}
diff --git a/poincare/src/simplify/rules_generation/selector.h b/poincare/src/simplify/rules_generation/selector.h
deleted file mode 100644
index 730610e62..000000000
--- a/poincare/src/simplify/rules_generation/selector.h
+++ /dev/null
@@ -1,21 +0,0 @@
-#ifndef POINCARE_SIMPLIFY_RULES_GENERATION_SELECTOR_H
-#define POINCARE_SIMPLIFY_RULES_GENERATION_SELECTOR_H
-
-#include "node.h"
-#include <string>
-
-class Selector : public Node {
-public:
-  enum class Type {
-    Variable,
-    Wildcard,
-    ExpressionType
-  };
-  Selector(Type type, std::string * name, std::vector<Selector *> * children = nullptr);
-protected:
-  void generateFields(Rule * context, std::string &indentation) override;
-private:
-  Type m_type;
-};
-
-#endif