From: ptkwt@...1.aracnet.com (Phil Tomson)
Date: 2002-10-10T05:12:28+09:00
Subject: Polymorphism, Isomorphism

Consider this a bit of public pondering...

Polymorphism is considered a central idea in Object Oriented Programming.  
In typed languages like C++, polymorphism can only happen within a class 
hierarchy - there must be some kind of ISA relationship.  In dynamic 
languages like Ruby no ISA relationship is needed - if two different 
classes respond to the same methods they can (often, but not always of 
course due to things like return values and semantics) be used in the same 
places.  I'm wondering if this relation might actually be called 
Isomorphism - two classes with the ability to respond to the same set of 
methods but having no relationship to each other. (a 1 to 1 mapping of 
methods)

If we look at a class as a set of methods (actually, maybe a module could 
be called a set of methods) then perhaps we could talk about whether 
another class _contains_ the same set of methods (subset and proper subset 
relationships could be defined).  I guess what I'm leading up to would be 
something like being able to do: 
ClassA.isomorphic?(ClassB) #returns true if there is a 1:1 correspondence
                           #between methods in ClassA and ClassB
ClassA.containsMethods?(ClassB) #returns true if ClassA defines all of the   
                           # same methods that ClassB has defined (but
                           # ClassA could define methods not defined in
                           # ClassB

The same operations would be applicable to objects which are members of 
these classes.

Does the term Isomorphism work here?  It seems that it might provide us 
with a distinction from Polymorphism (which people coming from a C++/Java 
world see as being distinctly related to inheritance).  

Also, what about this idea of set operations on Classes (where we look at 
classes and modules as sets of methods)?  Would it buy us anything?

....just thinking 'out loud'.
Phil