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C++ Template and derived class, no match for function

I try to compile the following code :

#include "Fraction.cpp"
#include "Pile.cpp"
#include "Plus.cpp"
#include <iostream>

using namespace std;

Nombre calcul(Element* tab [], int nbElement){

  Pile<Nombre> pile  = Pile<Nombre>(30);
  for(int i = 0 ; i < nbElement ; i++){
      if( tab[i]->getType() == "o" ){
        Fraction f = (*tab[i])(pile.pop(),pile.pop());
        pile.push(f);
      }
      else if(tab[i]->getType() == "n"){
        pile.push(*(tab[i]));
      }
  }
  return pile.pop();

}

int main(){

}

Here are the needed classes:

Fraction.hpp:

#include <iostream>
#include "Element.cpp"
using namespace std;


class Fraction : public Nombre{

private:
  int nume;
  int deno;
  static int pgcd(int x, int y);

public:
  Fraction(int n, int d);
  Fraction(int n);
  int getNume() const;
  int getDeno() const;
  virtual string getType();
  Fraction operator+(const Fraction &) const;
  Fraction operator-(const Fraction &) const;

};

ostream &operator<<(ostream &os,const Fraction &f);
Fraction operator+(const int &n,const Fraction &f);

Pile.hpp:

template <typename T> class Pile{

  private:
    int size;
    int top;
    T* stacktab;

  public:
    Pile<T>();
    Pile<T>(int s);
    bool isEmpty();
    bool isFull();
    bool push(T elt);
    T pop();
    void afficher(ostream &flux);

};

Element.cpp:

#include <string>
using namespace std;

class Element{

public:
  virtual string getType() = 0;
};


class Operateur : public Element{
public:
    virtual string getType() ;
};

class Nombre : public Element{
public:
    virtual string getType() ;
};

string Operateur::getType() {
  return "o";
}

string Nombre::getType() {
  return "n";
}

Plus.cpp:

class Plus : public Operateur{
public:
  Fraction operator()(Fraction f1, Fraction f2);
};

class Moins : public Operateur{
public:
  Fraction operator()(Fraction f1, Fraction f2);
};

Fraction Plus::operator()(Fraction f1,Fraction f2){
  return f1 + f2;
}

Fraction Moins::operator()(Fraction f1, Fraction f2){
  return f1 - f2;
}

I get 2 errors when i try to compile this code:

1) error: no match for call to ‘(Element) (Nombre, Nombre)’
         Fraction f = (*tab[i])(pile.pop(),pile.pop());

Here, *tab[i] is a pointer on Element but the instance are supposed to be Plus or Moins ( which are both derived from Operateur, and Operateur derived from Element). I understand the problem: i only implemented operator() in Plus and Moins classes so the compiler can't find it in Element, but how can i fix this ?

2) error: no matching function for call to ‘Pile<Nombre>::push(Element&)’
         pile.push(*(tab[i]));
note: candidate: bool Pile<T>::push(T) [with T = Nombre]
template <typename T>  bool Pile<T>::push(T elt){
                             ^
note:   no known conversion for argument 1 from ‘Element’ to ‘Nombre’

I use Pile and i try to push() with an Element object. As Nombre is derivated from Element, shouldn't i be able to use an Element object instead of a Nombre object ?

I have been looking for answers for hours, but i still don't understand. I feel like i have not understood something very basic.

You need to have a virtual Fraction operator()(Fraction f1, Fraction f2); in Element.

But that won't work so easily, because Fraction is derived from Element, so has not been declared yet. You could try virtual Element operator()(Element e1, Element e2); . But you will find that returning a non-homogenous type from Plus and Moins will be another issue.

You are pushing non-homogenous types onto the Pile. That won't work. Even though Fraction is derived from Nombre, it isn't exactly a Nombre, and will slice.

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