From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-0.3 required=5.0 tests=BAYES_00, REPLYTO_WITHOUT_TO_CC autolearn=no autolearn_force=no version=3.4.4 X-Google-Thread: 103376,2ff5c149712ec0eb X-Google-Attributes: gid103376,public,usenet X-Google-Language: ENGLISH,ASCII-7-bit Path: g2news1.google.com!news4.google.com!news.germany.com!news.belwue.de!newsfeed.arcor.de!newsspool2.arcor-online.net!news.arcor.de.POSTED!not-for-mail From: "Dmitry A. Kazakov" Subject: Re: Ada Interfaces and the Liskov Substitution Principle Newsgroups: comp.lang.ada User-Agent: 40tude_Dialog/2.0.15.1 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Reply-To: mailbox@dmitry-kazakov.de Organization: cbb software GmbH References: <1179953657.839272.160320@a26g2000pre.googlegroups.com> <1179991769.376381.252010@m36g2000hse.googlegroups.com> <12h6mi42jcha0.7f9vfsnihjwr$.dlg@40tude.net> <1180003336.1163.29.camel@kartoffel> <83abvs7sa9.fsf@hod.lan.m-e-leypold.de> <465aa5ba$0$23147$9b4e6d93@newsspool1.arcor-online.net> <465b6606$0$10188$9b4e6d93@newsspool4.arcor-online.net> <1180445634.5664.23.camel@kartoffel> Date: Tue, 29 May 2007 19:29:08 +0200 Message-ID: <39viqigjwhrb$.gz67xvpinyjr.dlg@40tude.net> NNTP-Posting-Date: 29 May 2007 19:28:54 CEST NNTP-Posting-Host: 6a41a3b2.newsspool4.arcor-online.net X-Trace: DXC=;2fbJSbWe7SAX0F2i> On Tue, 29 May 2007 15:33:54 +0200, Georg Bauhaus wrote: > On Tue, 2007-05-29 at 14:05 +0200, Dmitry A. Kazakov wrote: > >>> In fact, this is happening. For example, timing properties of >>> co-operating procedures are captured in mathematical models. This is >>> different from the ubiquitously alleged mathematicality of programming: >>> that programs model mathematical functions. Some programs do, but is this >>> all that matters? >> >> Yes, because application programming deals with mathematical models of the >> reality. I doubt you could skip this abstraction layer. > > Programming deals with models of reality and, empirically, most of the > time these models have properties that can be described using > mathematics. Which is a good thing. > However, asking for *mathematical* models of reality is asking for > a clean room definition of the physical model in terms of mathematics. Any mathematical model is still an approximation. The reason why mathematics is better here than ad-hocery of outsourced programmers, is that the mathematical "hardware" is far more powerful than one of Intel. Hence there is a far less constraints imposed upon you when you model it mathematically. So even if you had a very good mathematical model it might be quite difficult to implement it on the machine hardware. This is all programming is about - porting mathematics. (:-)) To model the reality in just one hop might be just impossible for a normal programmer. You cannot rely on Nobel Price laureates, they are rare, expensive and uninterested in our problems. > Many programs just happen to be a model of reality, and they still > work well, even though they were not mathematically designed. > The programmers are hardly aware of every conceivable mathematical > property of their model. Still, they write sound programs. How can you know that? (:-)) Let's take the braking control system for your next car... >>> Shouldn't the relation between programs and mathematical >>> functions be reversed? Wait, it is! >> >> You can consider mathematics or parts of as programming on some "axiomatic >> hardware". > > What I want is the mathematics of program models, more than programming > to satisfy mathematics. BTW, what is the best suited mathematical > structure that (minimally) describes the loop > > while k < 100 loop > k := Integer'succ(k); > end loop; Ordered set, mathematical induction etc. > and how does it help? A lot. For example it can tell the code reviewer that the above program is equivalent to: if k < 100 then k := 100; end if; -- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.de