More C++ Idioms/Algebraic Hierarchy

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[edit]

Algebraic Hierarchy

[edit] Intent

To hide multiple closely related algebraic abstractions (numbers) behind a single generic abstraction and provide a generic interface to it.

[edit] Also Known As

  • State (Gamma et al.)

[edit] Motivation

In pure object-oriented languages like Smalltalk, variables are run-time bindings to objects that act like labels. Binding a variable to an object is like sticking a label on it. Assignment in these languages is analogous to peeling a label off one object and putting it on another. On the other hand, in C and C++, variables are synonyms for addresses or offsets instead of being labels for objects. Assignment does not mean re-labelling, it means overwriting old contents with new one. Algebraic Hierarchy idiom uses delegated polymorphism to simulate weak variable to object binding in C++. Algebraic Hierarchy uses Envelope Letter idiom in its implementation. The motivation behind this idiom is to be able write code like the one below.

Number n1 = Complex (1, 2); // Label n1 for a complex number
Number n2 = Real (10); // Label n2 for a real number
Number n3 = n1 + n2; // Result of addition is labelled n3
Number n2 = n3; // Re-labelling

[edit] Solution and Sample Code

Complete code showing implementation of Algebraic Hierarchy idiom is shown below.

#include <iostream>
 
using namespace std;
 
struct BaseConstructor { BaseConstructor(int=0) {} };
 
class RealNumber;
class Complex;
class Number;
 
class Number
{
    friend class RealNumber;
    friend class Complex;
 
  public:
    Number ();
    Number & operator = (const Number &n);
    Number (const Number &n);
    virtual ~Number();
 
    virtual Number operator + (Number const &n) const;
    void swap (Number &n) throw ();
 
    static Number makeReal (double r);
    static Number makeComplex (double rpart, double ipart);
 
  protected:
    Number (BaseConstructor);
 
  private:
    void redefine (Number *n);
    virtual Number complexAdd (Number const &n) const;
    virtual Number realAdd (Number const &n) const;
 
    Number *rep;
    short referenceCount;
};
 
class Complex : public Number
{
  friend class RealNumber;
  friend class Number;
 
  Complex (double d, double e);
  Complex (const Complex &c);
  virtual ~Complex ();
 
  virtual Number operator + (Number const &n) const;
  virtual Number realAdd (Number const &n) const;
  virtual Number complexAdd (Number const &n) const;
 
  double rpart, ipart;
};
 
class RealNumber : public Number
{
  friend class Complex;
  friend class Number;
 
  RealNumber (double r);
  RealNumber (const RealNumber &r);
  virtual ~RealNumber ();
 
  virtual Number operator + (Number const &n) const;
  virtual Number realAdd (Number const &n) const;
  virtual Number complexAdd (Number const &n) const;
 
  double val;
};
 
/// Used only by the letters.
Number::Number (BaseConstructor)
: rep (0),
  referenceCount (1)
{}
 
/// Used by user and static factory functions.
Number::Number () 
  : rep (0),
    referenceCount (0)
{}
 
/// Used by user and static factory functions.
Number::Number (const Number &n)
: rep (n.rep),
  referenceCount (0)
{
  cout << "Constructing a Number using Number::Number\n";
  if (n.rep)
    n.rep->referenceCount++;
}
 
Number Number::makeReal (double r)
{
  Number n;
  n.redefine (new RealNumber (r));
  return n;
}
 
Number Number::makeComplex (double rpart, double ipart)
{
  Number n;
  n.redefine (new Complex (rpart, ipart));
  return n;
}
 
Number::~Number()
{
  if (rep && --rep->referenceCount == 0)
    delete rep;
}
 
Number & Number::operator = (const Number &n)
{
  cout << "Assigning a Number using Number::operator=\n";
  Number temp (n);
  this->swap (temp);
  return *this;
}
 
void Number::swap (Number &n) throw ()
{
  std::swap (this->rep, n.rep);
}
 
Number Number::operator + (Number const &n) const
{
  return rep->operator + (n);
}
 
Number Number::complexAdd (Number const &n) const 
{
  return rep->complexAdd (n);
}
 
Number Number::realAdd (Number const &n) const
{
  return rep->realAdd (n);
}
 
void Number::redefine (Number *n)
{
  if (rep && --rep->referenceCount == 0)
    delete rep;
  rep = n;
}
 
Complex::Complex (double d, double e)
  : Number (BaseConstructor()),
    rpart (d),
    ipart (e)
{
  cout << "Constructing a Complex\n";
}
 
Complex::Complex (const Complex &c)
  : Number (BaseConstructor()),
    rpart (c.rpart),
    ipart (c.ipart)
{
  cout << "Constructing a Complex using Complex::Complex\n";
}
 
Complex::~Complex()
{
  cout << "Inside Complex::~Complex()\n";
}
 
Number Complex::operator + (Number const &n) const
{ 
  return n.complexAdd (*this); 
}
 
Number Complex::realAdd (Number const &n) const
{
  cout << "Complex::realAdd\n";
  RealNumber const *rn = dynamic_cast <RealNumber const *> (&n);
  return Number::makeComplex (this->rpart + rn->val, 
                              this->ipart);
}
 
Number Complex::complexAdd (Number const &n) const
{
  cout << "Complex::complexAdd\n";
  Complex const *cn = dynamic_cast <Complex const *> (&n);
  return Number::makeComplex (this->rpart + cn->rpart, 
                              this->ipart + cn->ipart);
}
 
RealNumber::RealNumber (double r)
  : Number (BaseConstructor()),
    val (r)
{
  cout << "Constructing a RealNumber\n";
}
 
RealNumber::RealNumber (const RealNumber &r)
  : Number (BaseConstructor()),
    val (r.val)
{
  cout << "Constructing a RealNumber using RealNumber::RealNumber\n";
}
 
RealNumber::~RealNumber()
{
  cout << "Inside RealNumber::~RealNumber()\n";
}
 
Number RealNumber::operator + (Number const &n) const
{ 
  return n.realAdd (*this); 
}
 
Number RealNumber::realAdd (Number const &n) const
{
  cout << "RealNumber::realAdd\n";
  RealNumber const *rn = dynamic_cast <RealNumber const *> (&n);
  return Number::makeReal (this->val + rn->val);
}
 
Number RealNumber::complexAdd (Number const &n) const
{
  cout << "RealNumber::complexAdd\n";
  Complex const *cn = dynamic_cast <Complex const *> (&n);
  return Number::makeComplex (this->val + cn->rpart, cn->ipart);
}
namespace std
{
template <>
void swap (Number & n1, Number & n2)
{
  n1.swap (n2);
}
}
int main (void)
{
  Number n1 = Number::makeComplex (1, 2);
  Number n2 = Number::makeReal (10);
  Number n3 = n1 + n2;
  cout << "Finished\n";
 
  return 0;
}

[edit] Known Uses

[edit] Related Idioms

[edit] References

Advanced C++ Programming Styles and Idioms by James Coplien, Addison Wesley, 1992.

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