Find all occurences of Old' and replace them by New'. This is an O(n) operation. Additionally the heap has to be rebuilt as soon as there is more than one replacement made.

If New' is Null, then the entry will be deleted.

Missing closing '`'

The search for objects is done by identity and not by using the _compare() method. "By identity" means that if two objects are to be compared and both have a special _identity() method returning a Variant, the return values of these methods are compared.

If one of the objects does not implement the _identity() method, the default is comparison by object addresses in memory. This strategy lets you save primitive data types (Integer, Boolean, String), etc. in the heap. But you can also distinct objects in equivalence classes. The _compare() method defines your equivalence relation, the identity comparison enables to discern different objects.

If we are a heap of objects whose _compare() methods compare some sort of priority, and Old' is the same object as New', this can be used to propagate a priority change made to the object and will correct its position in the heap.

This has an application in Dijkstra's algorithm (or any priority first search like Prim or A*) where you would update a node's priority.