// Expression template to parse sum a+b+c...
// Following Todd Veldhuizen
#include<iostream>
#include<vector>

// The "+" operation.
class plus 
{
public:
  static double apply(double a, double b) { return a+b; };
};

// Node "Left Op Right"
template<typename Left, typename Op, typename Right>
class X {
  Left left;
  Right right;
public:
  X(Left l, Right r) : left(l), right(r)  { } // initialization list
  double operator[](int i) { return Op::apply(left[i],right[i]); } // node is indexed with [] !
};


// Simple array class:
class Array {
  std::vector<double> data;
public:
  Array(std::vector<double> d) : data{d} {}
  // Assign an expression to the array
  template<typename Left, typename Op, typename Right>
  void operator=(X<Left,Op,Right> expression)
  {
    for (unsigned i=0; i < data.size(); ++i)
      data[i] = expression[i];
  }
  double operator[](int i) { return data[i]; } // Array is indexed with [] !
  // overload <<
  friend std::ostream& operator <<(std::ostream& os, const Array& obj);
};

// overload << for Array output
std::ostream& operator<<(std::ostream & os, const Array& obj)
{
  for(auto ele:obj.data) os<<ele<<" ";
  os<<"\n";
  return os;
}


template<typename Left>
X<Left, plus, Array> operator+(Left a, Array b)
{
  return X<Left, plus, Array>(a,b);
}

int main()
{
  using std::cout;  
  Array a{{2,3,5,9}}, b{{1,0,0,1}}, c{{3,0,2,5}}, d{{0,0,0,0}};
  
  cout<<a;
  cout<<b;
  cout<<c; 
  
  cout<<"----------  + "<<"\n";
  d = a+b+c;
  cout<< d ;

  cout<<"a[0]="<<a[0]<<"\n";
  cout<<"(a+b)[0]="<<(a+b)[0]<<"\n";
  cout<<"(a+b+c)[0]="<<(a+b+c)[0]<<"\n";

  // try:: 
  //   cout<<a+b+c; 
  // you get error, but see that the expression a+b+c is parsed as
  //  X<X<Array, plus, Array>, plus, Array>
  // second way: compile a.out and type
  // nm -C a.out
}