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From: alan@ux.cs.man.ac.uk (Alan Wills)
Newsgroups: comp.lang.smalltalk
Subject: Re: Smalltalk types
Message-ID: <6483@ux.cs.man.ac.uk>
Date: 8 Sep 89 10:42:27 GMT
References: <7793@charlie.OZ>
Organization: Dept. of Computer Science, University of Manchester, UK.
Lines: 26
In-reply-to: rad@aragorn.cm.deakin.oz.au's message of 6 Sep 89 14:24:51 GMT

Robert Dew's list of sets of Smalltalk classes which understand the same set of
messages is worth contrasting with the notion of a type as being the set of
objects which understand a particular set of messages.  For example, in
Smalltalk, if we look at the set of all objects which understand the
messages "<", "=<", ">", ">=", "=" : we get all instances of Magnitude (and
its subclasses) and all instances of String (and its subclasses).  Even
more interesting is that, although the implementations of these functions
are different in the two inheritance subtrees, this correspondence isn't just a mere
overloading of names: the relations obey the same rules about how they're
interrelated. For example:
   if I know     and also          then I can infer
   x < y                             (y < x) not
   x =< y       (x = y) not           x < y
   x > y                              y < x
   x < y         y < z                x < z
etc

I guess this helps to illustrate that this notion of type --- equivalence
sets wrt parts of behaviours --- is useful when into the nitty-gritty of
reasoning about programs to check they're going to do the right things.

Alan Wills
Manchester University, UK
-- 
Alan Wills
+44-61-273 7121 x5699