From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 23412 invoked by alias); 25 Jan 2002 21:49:35 -0000 Mailing-List: contact gcc-help@gcc.gnu.org; run by ezmlm Precedence: bulk List-Archive: List-Post: List-Help: Sender: gcc-owner@gcc.gnu.org Received: (qmail 23339 invoked from network); 25 Jan 2002 21:49:32 -0000 Received: from unknown (HELO pcp736370pcs.reston01.va.comcast.net) (68.48.241.178) by sources.redhat.com with SMTP; 25 Jan 2002 21:49:32 -0000 Received: (from tim@localhost) by pcp736370pcs.reston01.va.comcast.net (8.9.3/8.9.3) id RAA03886; Fri, 25 Jan 2002 17:08:13 -0500 Date: Fri, 25 Jan 2002 14:47:00 -0000 From: Tim Hollebeek To: Gabriel Dos Reis Cc: Daniel Berlin , Richard Kenner , pcarlini@unitus.it, gcc@gcc.gnu.org Subject: Re: g++ and aliasing bools Message-ID: <20020125170813.A3838@pcp736370pcs.reston01.va.comcast.net> Reply-To: tim@hollebeek.com References: Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Mailer: Mutt 1.0pre3us In-Reply-To: X-SW-Source: 2002-01/txt/msg01694.txt.bz2 > > | Mark's claim that if the underlying algorithm is easy, reasoning about it > | should be, is also not quite right. > > A claim I completely agree with. > > | Take Fermat's theorem, for instance. > > Oh, come on. > > Proof by analogy is fraud. Secondly, Fermat's theorem is *not* an > algorithm -- it is an *existential* (or non-existential) theorem > without any algorithm specification --- there is no remote relation > about the Fermat's theorem and the concrete issue we have at hand. Replace Fermat's theorem with Collatz's sequence (aka Hasse's _algorithm_). It's even simpler to state than Fermat, but harder to prove [1]. The only way to get around this fact is to claim that either (1) reasoning about recursion is generally hard, or (2) proving an algorithm terminates is generally hard, which gives me a sense of deja vu ... =) So, it is definitely true that reasoning about simple algorithms may be very difficult. Q.E.D. [1] based on the fact it is still unproved, while Fermat is not.