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From: rad@aragorn.cm.deakin.oz.au (Robert Alan Dew)
Newsgroups: comp.lang.smalltalk
Subject: Re: Smalltalk types
Message-ID: <7792@charlie.OZ>
Date: 6 Sep 89 14:22:09 GMT
References: <56929@aerospace.AERO.ORG> <7784@charlie.OZ> <7785@charlie.OZ> <9120@june.cs.washington.edu>
Sender: root@charlie.OZ
Reply-To: rad@aragorn.UUCP (Robert Alan Dew)
Organization: Department of Computing & Mathematics - Deakin University
Lines: 32

In article <9120@june.cs.washington.edu> rkr@june.cs.washington.edu.cs.washington.edu (R. K. Raj) writes:
  [  ...  ]
#Just one more thing. Robert Dew (rad@aragorn.cm.deakin.oz) has suggested
#the following definition of type equivalence:
#
#>Let O be the set of all objects.
#>Let M be the set of all messages.
#>Let S denote a subset of M.
#>Let T:O -> S be a mapping from an object to a set of all messages the object
#>understands.
#>
#>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.

I agree, but knowing whether the objects are of the same type is
only part of the solution.

#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