Static constant string (class member)

In C++11 you can do now:

class A {
 private:
  static constexpr const char* STRING = "some useful string constant";
};

You have to define your static member outside the class definition and provide the initializer there.

First

// In a header file (if it is in a header file in your case)
class A {   
private:      
  static const string RECTANGLE;
};

and then

// In one of the implementation files
const string A::RECTANGLE = "rectangle";

The syntax you were originally trying to use (initializer inside class definition) is only allowed with integral and enum types.

Starting from C++17 you have another option, which is quite similar to your original declaration: inline variables

// In a header file (if it is in a header file in your case)
class A {   
private:      
  inline static const string RECTANGLE = "rectangle";
};

No additional definition is needed.

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