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=-1.9 required=5.0 tests=BAYES_00 autolearn=ham autolearn_force=no version=3.4.4 X-Google-Thread: 103376,24d7acf9b853aac8 X-Google-NewGroupId: yes X-Google-Attributes: gida07f3367d7,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII Path: g2news1.google.com!news1.google.com!npeer02.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!nntp.club.cc.cmu.edu!micro-heart-of-gold.mit.edu!newsswitch.lcs.mit.edu!nntp.TheWorld.com!not-for-mail From: Robert A Duff Newsgroups: comp.lang.ada Subject: Re: S-expression I/O in Ada Date: Mon, 09 Aug 2010 15:19:58 -0400 Organization: The World Public Access UNIX, Brookline, MA Message-ID: References: <547afa6b-731e-475f-a7f2-eaefefb25861@k8g2000prh.googlegroups.com> <1qk2k63kzh7yv$.3jgc403xcqdw$.dlg@40tude.net> <8ae8e899-9eef-4c8c-982e-bfdfc10072f1@h17g2000pri.googlegroups.com> <258zlxrv4fn6.1vszho1rtmf48$.dlg@40tude.net> <984db477-973c-4a66-9bf6-e5348c9b95f2@n19g2000prf.googlegroups.com> <46866b8yq8nn$.151lqiwa0y2k6.dlg@40tude.net> <13b07f2c-2f35-43e0-83c5-1b572c65d323@y11g2000yqm.googlegroups.com> <13tpf7ya3evig$.h05p3x08059s$.dlg@40tude.net> <1omt2srxtpsga$.c3hbxthzo6cf.dlg@40tude.net> <1e4cch2df5uyb.18brqdd16dhv8.dlg@40tude.net> <85bc3155-69b3-4803-978a-c24a5ac089e0@p7g2000yqa.googlegroups.com> NNTP-Posting-Host: shell01.theworld.com Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: pcls6.std.com 1281381583 19650 192.74.137.71 (9 Aug 2010 19:19:43 GMT) X-Complaints-To: abuse@TheWorld.com NNTP-Posting-Date: Mon, 9 Aug 2010 19:19:43 +0000 (UTC) User-Agent: Gnus/5.1008 (Gnus v5.10.8) Emacs/21.3 (irix) Cancel-Lock: sha1:/73vFz5xH6h70gg92DXO4d+Ao2Q= Xref: g2news1.google.com comp.lang.ada:13010 Date: 2010-08-09T15:19:58-04:00 List-Id: Natacha Kerensikova writes: > On Aug 8, 11:08�pm, Robert A Duff > wrote: >> "Dmitry A. Kazakov" writes: >> By the way, one defense of modular types I've heard is that >> they are used in mathematics. �True. �But mathematicians do >> not use _implicit_ mod. �They say things like "X = Y (mod N)", >> which is pronounced "X is congruent to Y (modulo N)". >> Congruent, not equal. > > Actually past a certain level, they don't explicit mod anymore. Interesting. I never reached that level of math! >... I > don't remember hearing many "modulo" in Galois field classes. And > neither when dealing with stuff like an n-bit integer representing a > member of Z/2Z [X] quotiented by a n+1 degree polynomial (Reed-Solomon > stuff). And then you're overloading "+" with something very xor-like - Bob