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From: boehm@parc.xerox.com (Hans Boehm)
Newsgroups: comp.object,comp.lang.misc,comp.lang.eiffel
Subject: Re: A Hard Problem for Static Type Systems
Message-ID: <boehm.673043278@siria>
Date: 30 Apr 91 20:27:58 GMT
References: <1991Apr20.010347.28984@leland.Stanford.EDU> <554@eiffel.UUCP> <1991Apr26.203642.17387@leland.Stanford.EDU> <556@eiffel.UUCP> <1146@tetrauk.UUCP>
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rick@tetrauk.UUCP (Rick Jones) writes:
>...  It is worth noting that
>Craig Chambers' "hard problem" is only irresolvable in a static type system if
>you demand contravariance (which he did in his initial posting) - but then most
>problems are irresolvable in a useful way with contravariance...

Craig Chambers' problem is resolvable in at least some statically typed
languages, as is the Polygon-Rectangle example. There are elegant solutions
that don't involve inheritance at all.  See the discussion in comp.object.

(There may also be some that do use inheritance.
I'm less of an expert on those. But I haven't seen any discussion of the
more aggressive type systems that incorporate inheritance, but obey the
contravariance rule,  e.g. Cardelli's Quest, or Cook's system.) 

The original sentence strikes me as a substantial overgeneralization.  The
problem appears to be unsolvable in a straightforward way using a version of
Eiffel's type system that enforces contravariance.  Nothing else has been
established.

Hans
(boehm@xerox.com)

Usual disclaimers ...