diff --git a/poincare/src/simplify/expression_builder.cpp b/poincare/src/simplify/expression_builder.cpp
index ebe0161c4..e8ebb4359 100644
--- a/poincare/src/simplify/expression_builder.cpp
+++ b/poincare/src/simplify/expression_builder.cpp
@@ -16,7 +16,7 @@ Expression * ExpressionBuilder::build(ExpressionMatch matches[]) {
   int numberOfChildrenExpressions = 0;
 
   for (int i=0; i<m_numberOfChildren; i++) {
-    ExpressionBuilder * child = this->child(i);
+    ExpressionBuilder * child = (ExpressionBuilder *)this->child(i);
     if (child->m_action == ExpressionBuilder::Action::BringUpWildcard) {
       for (int j=0; j<matches[child->m_matchIndex].numberOfExpressions(); j++) {
         children_expressions[numberOfChildrenExpressions++] =
@@ -62,14 +62,3 @@ Expression * ExpressionBuilder::build(ExpressionMatch matches[]) {
   }
   return result;
 }
-
-// Extrude in a class
-ExpressionBuilder * ExpressionBuilder::child(int index) {
-  assert(index>=0 && index<m_numberOfChildren);
-  if (index == 0) {
-    return (this+1); // Pointer arithmetics
-  } else {
-    ExpressionBuilder * previousChild = this->child(index-1);
-    return previousChild+previousChild->m_numberOfChildren+1; // Pointer arithm.
-  }
-}
diff --git a/poincare/src/simplify/expression_builder.h b/poincare/src/simplify/expression_builder.h
index 77b18ef6e..bb42b92b7 100644
--- a/poincare/src/simplify/expression_builder.h
+++ b/poincare/src/simplify/expression_builder.h
@@ -2,18 +2,25 @@
 #define POINCARE_SIMPLIFY_EXPRESSION_BUILDER_H
 
 #include <poincare/expression.h>
+#include "contiguous_tree.h"
 #include "expression_match.h"
 extern "C" {
 #include <stdint.h>
 }
 
 
-class ExpressionBuilder {
-  typedef Expression * (ExternalGenerator)(Expression ** parameters, int numberOfParameters);
+class ExpressionBuilder : public ContiguousTree {
+public:
+  static constexpr ExpressionBuilder BuildFromType(Expression::Type type, uint8_t numberOfChildren);
+  static constexpr ExpressionBuilder BuildFromTypeAndValue(Expression::Type type, int32_t value, uint8_t numberOfChildren);
+  static constexpr ExpressionBuilder Clone(uint8_t matchIndex, uint8_t numberOfChildren);
+  static constexpr ExpressionBuilder BringUpWildcard(uint8_t matchIndex, uint8_t numberOfChildren);
+  typedef Expression * (ExternalGenerator)(Expression ** parameters, int numberOfParameters);
+  static constexpr ExpressionBuilder CallExternalGenerator(ExternalGenerator * generator, uint8_t numberOfChildren);
 public:
-  ExpressionBuilder * child(int i);
   Expression * build(ExpressionMatch matches[]);
 
+private:
   enum class Action {
     BuildFromTypeAndValue,
     Clone,
@@ -21,6 +28,10 @@ public:
     CallExternalGenerator
   };
 
+  constexpr ExpressionBuilder(Expression::Type type, int32_t integerValue, uint8_t numberOfChildren);
+  constexpr ExpressionBuilder(Action action, uint8_t matchIndex, uint8_t numberOfChildren);
+  constexpr ExpressionBuilder(ExternalGenerator * generator, uint8_t numberOfChildren);
+
   Action m_action;
 
   union {
@@ -39,8 +50,67 @@ public:
     // m_action == CallExternalGenerator
     ExternalGenerator * m_generator;
   };
-
-  uint8_t m_numberOfChildren;
 };
 
+/* Since they have to be evaluated at compile time, constexpr functions are
+ * implicitely defined inline. Therefore we have to provide their implementation
+ * in this header. */
+
+constexpr ExpressionBuilder ExpressionBuilder::BuildFromType(
+  Expression::Type type,
+  uint8_t numberOfChildren) {
+  return ExpressionBuilder(type, 0, numberOfChildren);
+}
+constexpr ExpressionBuilder ExpressionBuilder::BuildFromTypeAndValue(
+  Expression::Type type,
+  int32_t value,
+  uint8_t numberOfChildren) {
+  return ExpressionBuilder(type, value, numberOfChildren);
+}
+
+constexpr ExpressionBuilder ExpressionBuilder::Clone(
+  uint8_t matchIndex,
+  uint8_t numberOfChildren) {
+  return ExpressionBuilder(ExpressionBuilder::Action::Clone, matchIndex, numberOfChildren);
+}
+
+constexpr ExpressionBuilder ExpressionBuilder::BringUpWildcard(
+  uint8_t matchIndex,
+  uint8_t numberOfChildren) {
+  return ExpressionBuilder(ExpressionBuilder::Action::BringUpWildcard, matchIndex, numberOfChildren);
+}
+
+constexpr ExpressionBuilder ExpressionBuilder::CallExternalGenerator(
+  ExternalGenerator * generator,
+  uint8_t numberOfChildren) {
+  return ExpressionBuilder(generator, numberOfChildren);
+}
+
+constexpr ExpressionBuilder::ExpressionBuilder(Expression::Type type,
+  int32_t integerValue,
+  uint8_t numberOfChildren)
+  :
+  ContiguousTree(numberOfChildren),
+  m_action(ExpressionBuilder::Action::BuildFromTypeAndValue),
+  m_expressionType(type),
+  m_integerValue(integerValue) {
+}
+
+constexpr ExpressionBuilder::ExpressionBuilder(Action action,
+  uint8_t matchIndex,
+  uint8_t numberOfChildren)
+  :
+  ContiguousTree(numberOfChildren),
+  m_action(action),
+  m_matchIndex(matchIndex) {
+}
+
+constexpr ExpressionBuilder::ExpressionBuilder(ExternalGenerator * generator,
+  uint8_t numberOfChildren)
+  :
+  ContiguousTree(numberOfChildren),
+  m_action(ExpressionBuilder::Action::CallExternalGenerator),
+  m_generator(generator) {
+}
+
 #endif
diff --git a/poincare/src/simplify/expression_selector.h b/poincare/src/simplify/expression_selector.h
index 63bfaf38b..bf30f13cd 100644
--- a/poincare/src/simplify/expression_selector.h
+++ b/poincare/src/simplify/expression_selector.h
@@ -2,21 +2,27 @@
 #define POINCARE_SIMPLIFY_EXPRESSION_SELECTOR_H
 
 #include <poincare/expression.h>
+#include "contiguous_tree.h"
 #include "expression_match.h"
 extern "C" {
 #include <stdint.h>
 }
 
-class ExpressionSelector {
-  /* Everything must be made public otherwise we cannot static-initialize an
-   * array of ExpressionSelectors. */
+class ExpressionSelector : public ContiguousTree {
 public:
-  enum class Match {
-    Any,
-    Type,
-    Wildcard,
-    TypeAndValue,
-  };
+  static constexpr ExpressionSelector Any(uint8_t numberOfChildren) {
+    return ExpressionSelector(Match::Any, (Expression::Type)0, 0, numberOfChildren);
+  }
+  static constexpr ExpressionSelector Wildcard(uint8_t numberOfChildren) {
+    return ExpressionSelector(Match::Wildcard, (Expression::Type)0, 0, numberOfChildren);
+  }
+  static constexpr ExpressionSelector Type(Expression::Type type, uint8_t numberOfChildren) {
+    return ExpressionSelector(Match::Type, type, 0, numberOfChildren);
+  }
+  static constexpr ExpressionSelector TypeAndValue(Expression::Type type, int32_t value, uint8_t numberOfChildren) {
+    return ExpressionSelector(Match::TypeAndValue, type, value, numberOfChildren);
+  }
+
   ExpressionSelector * child(int i);
   /* The match function is interesting
    * - It returns 0 if the selector didn't match the expression
@@ -25,6 +31,25 @@ public:
    * value is zero.
    */
   int match(Expression * e, ExpressionMatch * matches);
+private:
+  enum class Match {
+    Any,
+    Type,
+    Wildcard,
+    TypeAndValue,
+  };
+
+  constexpr ExpressionSelector(Match match,
+      Expression::Type type,
+      int32_t integerValue,
+      uint8_t numberOfChildren)
+    :
+      ContiguousTree(numberOfChildren),
+      m_match(match),
+      m_expressionType(type),
+      m_integerValue(integerValue)
+  {
+  }
 
   Match m_match;
   union {
@@ -41,7 +66,6 @@ public:
       };
     };
   };
-  uint8_t m_numberOfChildren;
 };
 
 #endif