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-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,cafc372bafbed3f1 X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2003-05-19 16:12:09 PST From: jatwood@cvpjaws03.dhcp.cv.hp.com (John Atwood) Newsgroups: comp.lang.ada Subject: Re: writing an "artful" algorithm Date: Mon, 19 May 2003 23:19:50 +0000 (UTC) Organization: A poorly-installed InterNetNews site Message-ID: References: Reply-To: john.atwood@hp.com NNTP-Posting-Host: cvpjaws03.dhcp.cv.hp.com X-Trace: usenet01.boi.hp.com 1053386860 15.253.27.238 (19 May 2003 17:27:40 -0700) Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!nntp.cs.ubc.ca!nntp-relay.ihug.net!ihug.co.nz!news.compaq.com!usenet01.boi.hp.com!cvpjaws03.dhcp.cv.hp.com!not-for-mail Xref: archiver1.google.com comp.lang.ada:37540 Date: 2003-05-19T23:19:50+00:00 List-Id: John Stoneham wrote: >For those who like puzzles and have a little bit of free time, you may > > >This does seem like the imperative way to work out the problem, and I >think just about any other imperative approach would look about the >same, even if it used vectors or records in its representation. It would >still need to test individual digits and generate and test every >possible combination. But what about the functional approach? Would it >be more "artful" here? Would it even be possible to use a functional >approach for such a problem? Here's a functional solution to a similar problem: http://www.cs.nott.ac.uk/~gmh/bib.html#countdown Graham Hutton. Journal of Functional Programming, 12(6):609-616, Cambridge University Press, November 2002. We systematically develop a functional program that solves the countdown problem, a numbers game in which the aim is to construct arithmetic expressions satisfying certain constraints. Starting from a formal specification of the problem, we present a simple but inefficient program that solves the problem, and prove that this program is correct. We then use program fusion to calculate an equivalent but more efficient program, which is then further improved by exploiting arithmetic properties. John