If you take a closer look, there is only a subtle difference between these two patterns. IEnumerable<T> can be considered the pull-based equivalent of the push-based IObservable<T>. In fact, they are duals. When two entities exchange information, one entity's pull corresponds to another entity pushing the information. This duality is illustrated in the following diagram:

Let's understand this duality by looking at this sample code, a number sequence generator:

#include <iostream>
#include <vector>
#include <iterator>
#include <memory>
#include "../Common2.h"
using namespace std;

class ConcreteEnumberable : public IEnumerable<int>
{
      int *numberlist,_count;
public:
      ConcreteEnumberable(int numbers[], int count):
            numberlist(numbers),_count(count){}
      ~ConcreteEnumberable() {}

      class Enumerator : public IEnumerator<int>
      {
      int *inumbers, icount, index;
      public:
      Enumerator(int *numbers,
            int count):inumbers(numbers),icount(count),index(0) {}
      bool HasMore() { return index < icount; }
      //---------- ideally speaking, the next function should throw
      //---------- an exception...instead it just returns -1 when the 
      //---------- bound has reached
      int next() { return (index < icount) ?
                   inumbers[index++] : -1; }
      ~Enumerator() {}
      };
      IEnumerator<int> *GetEnumerator()
            { return new Enumerator(numberlist, _count); }
};

The preceding class takes an array of integers as a parameter and we can enumerate over the elements as we have implemented the IEnumerable<T> interface. The Enumeration logic is implemented by the nested class, which implements the IEnumerator<T> interface:

int main()
{
      int x[] = { 1,2,3,4,5 };
      //-------- Has used Raw pointers on purpose here as we have
      //------- not introduced unique_ptr,shared_ptr,weak_ptr yet
      //-------- using auto_ptr will be confusting...otherwise
      //-------- need to use boost library here... ( an overkill)
      ConcreteEnumberable *t = new ConcreteEnumberable(x, 5);
      IEnumerator<int> * numbers = t->GetEnumerator();
      while (numbers->HasMore())
            cout << numbers->next() << endl;
      delete numbers;delete t;
      return 0;
}

The main program instantiates an implementation of the ConcreteEnuerable class and walks through each element.

We will write an even number sequence generator to demonstrate how these data types work together in converting a pull-based program to a push program. The robustness aspect is given low priority to keep the listing terse:

#include "stdafx.h"
#include <iostream>
#include <vector>
#include <iterator>
#include <memory>
#include "../Common2.h"
using namespace std;

class EvenNumberObservable : IObservable<int>{
      int *_numbers,_count;
public:
      EvenNumberObservable(int numbers[],
            int count):_numbers(numbers),_count(count){}
      bool Subscribe(IObserver<int>& observer){
            for (int i = 0; i < _count; ++i)
                  if (_numbers[i] % 2 == 0)
                        observer.OnNext(_numbers[i]);
            observer.OnCompleted();
            return true;
      }
};

The preceding program takes an array of integers, filters out of the odd numbers, and notifies Observer<T> if an even integer is encountered. In this particular case, the data source is pushing data to observer. The implementation of Observer<T> is given as follows:

class SimpleObserver : public IObserver<int>{
public:
      void OnNext(int value) { cout << value << endl; }
      void OnCompleted() { cout << _T("hello completed") << endl; }
      void OnError( CustomException * ex) {}
};

The SimpleObserver class implements the IObserver<T> interface and it has the capability to receive notifications and react to them:

int main()
{
      int x[] = { 1,2,3,4,5 };
      EvenNumberObservable *t = new EvenNumberObservable(x, 5);
      IObserver<int>> *xy = new SimpleObserver();
      t->Subscribe(*xy);
      delete xy; delete t;
      return 0;
}

From the preceding example, you see how one can naturally subscribe for even numbers from an Observable sequence of natural numbers. The system will automatically push (publish) the values to the observer (subscriber) when an even number is detected. The code gives explicit implementations for key interfaces so that one can understand, or speculate what really happens under the hood.