Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!cornell!uw-beaver!uw-june!rkr
From: rkr@cs.washington.edu (R. K. Raj)
Newsgroups: comp.lang.smalltalk
Subject: Re: Smalltalk types
Message-ID: <9138@june.cs.washington.edu>
Date: 7 Sep 89 18:10:42 GMT
References: <56929@aerospace.AERO.ORG> <7784@charlie.OZ> <7785@charlie.OZ> <9120@june.cs.washington.edu> <7792@charlie.OZ>
Reply-To: rkr@june.cs.washington.edu.cs.washington.edu (R. K. Raj)
Organization: Computer Science Department, U Wash in Sea
Lines: 39

In <7792@charlie.OZ> rad@aragorn.UUCP (Robert Alan Dew) writes:
 >#>
 >#>Two objects o1 and o2 are of the same type iff
 >#>		T(o1) = T(o2).
 >#
 >#The concept of conformity is useful in object-oriented languages in
 >#extending the notion of type equivalence. We should be interested in knowing
 >#when one object can be used in place of another.
 >#For instance, using the
 >#above notation, we can say that o1 can be used in place of o2 iff
 >#        T(o1) is a superset of T(o2).  
 >
 >I disagree.  The definition for replacement must be stronger.
 >Care should be taken when o1 replaces o2, this is because o1 can have a
 >completely different behaviour when recieving the same message.
 >
 >The message does not imply the same behaviour for objects of the same type.
 >
 >Robert Dew            rad@aragorn.cm.deakin.oz

Notice that I only said that o1 can be used in place of o2 and did not
guarantee that you'd get the same behavior.  What one would like is to say
that o1 can be used in place of o2 iff
        B(o1) is a superset of B(o2).  (B = Behavior)

Unfortunately, the problem is: how do you (or the compiler) figure out what
is equivalent behavior? It therefore makes sense to relax the behavior
requirement and accept the weaker requirement of mere conforming types.

This isn't much different from what is done in more traditional languages.
For example, when a procedure call such as SORT(A) is made in a Pascal
program, there is no simple way of determining that the actual procedure
body of SORT does what it is intuitively expected to do: all the programmer
and the compiler do is to ensure that procedure call and procedure header
interfaces match. While techniques based on program verification can be
used, they typically are not used. Why? That's another story.

  - R. K. Raj
    rkr@cs.washington.edu,     rkr@uw-june.UUCP