Principles of Object-Oriented Software Development
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Decomposition -- modules versus objects

subsections:
Abstract data types allow the programmer to define a complex data structure and an associated collection of functions, operating on that structure, in a consistent way. Historically, the idea of data abstraction was originally not type-oriented but arose from a more pragmatic concern with information hiding and representation abstraction, see  [Parnas72b]. The first realization of the idea of data abstraction was in the form of modules grouping a collection of functions and allowing the actual representation of the data structures underlying the values of the (abstract) type domain to be hidden, see also  [Parnas72a]. In  [Cook90], a comparison is made between the way in which abstract data types are realized traditionally (as modules) and the way abstract data types may be realized using object-oriented programming techniques. According to  [Cook90], these approaches must be regarded as being orthogonal to one another and, being to some extent complementary, deserve to be integrated in a common framework. After presenting an example highlighting the differences between the two approaches, we will further explore these differences and study the trade-offs with respect to possible extensions and reuse of code.

Decomposition -- matrix

data abstraction

nil cons(h,t)
empty(l) true false
head(l) error h
tail(l) error t

Modules -- operation oriented

ADT

  • organized around observers -- representation hiding

Objects -- data oriented

OOP

  • organized around generators -- method interface
slide: Decomposition and data abstraction
Recall that abstract data types may be completely characterized by a finite collection of generators and a number of observer functions that are defined with respect to each possible generator. Following this idea, we may approach the specification of a data abstraction by constructing a matrix listing the generators column-wise and the observers row-wise, which for each observer/generator pair specifies the value of the observer for that particular generator. Incidentally, the definition of such a matrix allows us to check in an easy way whether we have given a complete characterization of the data type. Above, an example is given of the specification of a list, with generators nil and cons, and observers empty, head and tail. (Note that we group the secondary producer tail with the observers.) Now, the traditional way of realizing abstract data types as modules may be characterized as operation oriented, in the sense that the module realization of the type is organized around the observers, resulting in a horizontal decomposition of the matrix. On the other hand, an object-oriented approach may be characterized as data oriented, since the object realization of a type is based on specifying a method interface for each possible generator (sub)type, resulting in a vertical decomposition of the matrix. See slide 8-decomposition. Note, however, that in practice, different generators need not necessarily correspond to different (sub)classes. Behavior may be subsumed in variables, as an object cannot change its class/type.

Abstract interfaces

When choosing for the module realization of the data abstraction list in C style, we are likely to have an abstract functional interface as specified in slide mod-face.

Modules -- a functional interface

ADT 



  typedef int element; 
  struct list;
  
  extern list* nil();
  extern list* cons(element e, list* l);
  extern element head(list* l);
  extern list* tail(list* l);
  extern bool equal(list* l, list* m);
slide: Modules -- a functional interface
For convenience, the list has been restricted to contain integer elements only. However, at the expense of additional notation, we could also easily define a generic list by employing template functions as provided by C++. This is left as an exercise for the reader. The interface of the abstract class list given in slide obj-face has been defined generically by employing templates.

Objects -- a method interface

OOP 



  template< class E > 
  class list {
  public:
  list() { }
  virtual ~list() { }
  virtual bool empty() = 0;
  virtual E head()  = 0;
  virtual list* tail() = 0;
  virtual bool operator==(list* m) = 0;
  };
slide: Objects -- a method interface
Note that the equal function in the ADT interface takes two arguments, whereas the operator== function in the OOP interface takes only one, since the other is implicitly provided by the object itself.

Representation and implementation

The realization of abstract data types as modules with functions requires additional means to hide the representation of the list type. In contrast, with an object-oriented approach, data hiding is effected by employing the encapsulation facilities of classes.

Modules -- representation hiding

Modules provide a syntactic means to group related pieces of code and to hide particular aspects of that code. In slide 8-modules an example is given of the representation and the generator functions for a list of integers.

Modules -- representation hiding

ADT 



  typedef int element;
  
  enum { NIL, CONS };
  
  struct list {
  int tag;
  element e;
  list* next;
  };

Generators

 

  list* nil()  { 
  nil  


  list* l = new list; l->tag = NIL; return l;
  }
  
  list* cons( element e, list* l) { 
  cons  


  list* x = new list; 
  x->tag = CONS; x->e = e; x->next = l;
  return x;
  }
slide: Data abstraction and modules
For implementing the list as a collection of functions (ADT style), we employ a struct with an explicit tag field, indicating whether the list corresponds to nil or a cons. The functions corresponding with the generators create a new structure and initialize the tag field. In addition, the cons operator sets the element and next field of the structure to the arguments of cons. The implementation of the observers is given in slide 8-mod-impl.

Modules -- observers

ADT 



  int empty(list* lst) { return !lst || lst->tag == NIL; }
  
  element head(list* l) {  
  head  


  require( ! empty(l) );
  return l->e;
  }
  
  
  
  list* tail(list* l) { 
  tail  


  require( ! empty(l) );
  return l->next;
  }
  
  
  
  bool equal(list* l, list* m) { 
  equal  


  switch( l->tag) {
    case NIL: return empty(m);
    case CONS: return !empty(m) && 
  		head(l) == head(m) &&
  		tail(l) == tail(m);
    }
  }
slide: Modules -- observers
To determine whether the list is empty it suffices to check whether the tag of the list is equal to NIL. For both head and tail the pre-condition is that the list given as an argument is not empty. If the pre-condition holds, the appropriate field of the list structure is returned. The equality operator, finally, performs an explicit switch on the tag field, stating for each case under what conditions the lists are equal. Below, a program fragment is given that illustrates the use of the list. 
  list* r = cons(1,cons(2,nil()));
  while (!empty(r)) { 
  	cout << head(r) << endl;
  	r = tail(r);
  	}
Note that both the generator functions nil and cons take care of creating a new list structure. Writing a function to destroy a list is left as an exercise for the reader.

Objects -- method interface

The idea underlying an object-oriented decomposition of the specification matrix of an abstract type is to make a distinction between the (syntactic) subtypes of the data type (corresponding with its generators) and to specify for each subtype the value of all possible observer functions. (We speak of syntactic subtypes, following  [Dahl92], since these subtypes correspond to the generators defining the value domain of the data type. See  [Dahl92] for a more extensive treatment.)

Method interface -- list

OOP 



  template< class E >
  class nil : public list< E > { 
  nil  


  public:
  nil() {}
  bool empty() { return 1; }
  E head() { require( false ); return E(); }
  list< E >* tail() { require( 0 ); return 0; }
  bool operator==(list* m) { return m->empty(); }
  };
  
  
  template< class E >
  class cons : public list< E > { 
  cons  


  public:
  cons(E e, list* l) : _e(e), next(l) {}
  ~cons() { delete next; }
  bool empty() { return 0; }
  E head() { return _e; }
  list* tail() { return next; }
  bool operator==(list* m);
  protected:
  E _e;
  list* next;
  };
slide: Data abstraction and objects
In the object realization in slide 8-objects, each subtype element is defined as a class inheriting from the list class. For both generator types nil and cons the observer functions are defined in a straightforward way. Note that, in contrast to the ADT realization, the distinction between the various cases is implicit in the member function definitions of the generator classes. As an example of using the list classes consider the program fragment below. 
  list<int>* r = new cons<int>(1, new cons<int>(2, new nil<int>)); 
  while (! r->empty()) { 
  	cout << r->head() << endl;
  	r = r->tail();
  	}
  delete r;
For deleting a list we may employ the (virtual) destructor of list, which recursively destroys the tail of a list.

Adding new generators

Abstract data types were developed with correctness and security in mind, and not so much from a concern with extensibility and reuse. Nevertheless, it is interesting to compare the traditional approach of realizing abstract data types (employing modules) and the object-oriented approach (employing objects as generator subtypes) with regard to the ease with which a specification may be extended, either by adding new generators or by adding new observers.

Adding new generators -- representation

ADT 



  typedef int element;
  
  enum { NIL, CONS, INTERVAL };
  
  struct list {
  int tag;
  element e; 
  union { element z; list* next; };
  };

Generator 


  list* interval( element x, element y ) {
  	list* l = new list;
  	if ( x <= y ) {
  		l->tag = INTERVAL;
  		l->e = x; l->z = y;
  		}
  	else l->tag = NIL;
  	return l;
  	}
slide: Modules and generators
Let us first look at what happens when we add a new generator to a data type, such as an interval list subtype, containing the integers in the interval between two given integers. For the module realization of the list, adding an interval(x,y) generator will result in an extension of the (hidden) representation types with an additional representation tag type INTERVAL and the definition of a suitable generator function. To represent the interval list type, we employ a union to select between the next field, which is used by the cons generator, and the z field, which indicates the end of the interval.

Modifying the observers

ADT 



  element head(list* l) {  
  head  


    require( ! empty(l) );
    return l->e; // for both CONS and INTERVAL
    }
  
  
  list* tail(list* l) { 
  tail  


    require( ! empty(l) );
    switch( l->tag ) {
      case CONS: return l->next;
      case INTERVAL:
  	 return interval((l->e)+1,l->z);
  	}
    }
slide: Modifying the observers
Also, we need to modify the observer functions by adding an appropriate case for the new interval representation type, as pictured in slide 8-mod-xx. Clearly, unless special constructs are provided, the addition of a new generator case requires disrupting the code implementing the given data type manually, to extend the definition of the observers with the new case. In contrast, not surprisingly, when we wish to add a new generator case to the object realization of the list, we do not need to disrupt the given code, but we may simply add the definition of the generator subtype as given in slide 8-oop-gen.

Adding new generators

OOP 



  class interval : public list<int> { 
  interval  


  public:
  interval(int x, int y) : _x(x), _y(y) { require( x <= y ); }
  bool empty() { return 0; }
  int head() { return _x; }
  list< int >* tail() {
    return (_x+1 <= _y)?
  	new interval(_x+1,_y):
  	new nil<int>;
    }
  
  
  bool operator==(list@lt;int>* m) { 
    return !m->empty() &&
    _x == m->head() && tail() == m->tail();
    }
  protected:
  int _x; int _y;
  };
slide: Objects and generators
Adding a new generator subtype corresponds to defining the realization for an abstract interface class, which gives a method interface that its subclasses must respect. Observe, however, that we cannot exploit the fact that a list is defined by an interval when testing equality, since we cannot inspect the type of the list as for the ADT implementation.

Adding new observers

Now, for the complementary case, what happens when we add new observers to the specification of a data type? Somewhat surprisingly, the object-oriented approach now seems to be at a disadvantage. Since in a module realization of an abstract data type the code is organized around observers, adding a new observer function amounts simply to adding a new operation with a case for each of the possible generator types, as shown in slide 8-mod-obs.

Adding new observers

ADT 



  int length( list* l ) { 
  length  


        switch( l->tag ) {
        case NIL: return 0;
        case CONS: return 1 + length(l->next);
        case INTERVAL: return l->z - l->e + 1;
        };
  }
slide: Modules and observers
When we look at how we may extend a given object realization of an abstract data type with a new observer we are facing a problem. The obvious solution is to modify the source code and add the length function to the list interface class and each of the generator classes. This is, however, against the spirit of object orientation and may not always be feasible. Another, rather awkward solution, is to extend the collection of possible generator subtypes with a number of new generator subtypes that explicitly incorporate the new observer function. However, this also means redefining the tail function since it must deliver an instance of a list with length class. As a workaround, one may define a function length and an extended version of the list template class supporting only the length (observer) member function as depicted in slide 8-oop-obs.

Adding new observers

OOP 



  template< class E >  
  int length(list< E >* l) { 
  length  


     return l->empty() ? 0 : 1 + length( l->tail() );
   }
  
  
  template< class E >
  class listWL : public list<E> {  
  listWL  


  public:
  int length() { return ::length( this ); }
  };
slide: Objects and observers
A program fragment illustrating the use of the listWL class is given below. 


  list<int>* r = new cons<int>(1,new cons<int>(2,new interval(3,7))); 
  while (! r->empty()) { 
  	cout << ((listWL< int >*)r)->length() << endl;
  	r = r->tail();
  	}
  delete r;
Evidently, we need to employ a cast whenever we wish to apply the length observer function. Hence, this seems not to be the right solution. Alternatively, we may use the function length directly. However, we are then forced to mix method syntax of the form ref->op(args) with function syntax of the form fun(ref,args), which may easily lead to confusion.

Discussion

 We may wonder why an object-oriented approach, that is supposed to support extensibility, is at a disadvantage here when compared to a more traditional module-based approach. As observed in  [Cook90], the problem lies in the fact that neither of the two approaches reflect the full potential and flexibility of the matrix specification of an abstract data type. Each of the approaches represents a particular choice with respect to the decomposition of the matrix, into either an operations-oriented (horizontal) decomposition or a data-oriented (vertical) decomposition. The apparent misbehavior of an object realization with respect to extending the specification with observer functions explains why in some cases we prefer the use of overloaded functions rather than methods, since overloaded functions allow for implicit dispatching to take place on multiple arguments, whereas method dispatching behavior is determined only by the type of the object. However, it must be noted that the dispatching behavior of overloaded functions in C++ is of a purely syntactic nature. This means that we cannot exploit the information specific for a class type as we can when using virtual functions. Hence, to employ this information we would be required to write as many variants of overloaded functions as there are combinations of argument types. Dynamic dispatching on multiple arguments is supported by multi-methods in CLOS, see  [Paepcke93]. According to  [Cook90], the need for such methods might be taken as a hint that objects only partially realize the true potential of data abstraction.
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eliens@cs.vu.nl

draft version 0.1 (15/7/2001)