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: 103376,73057f1a3ca11607 X-Google-Attributes: gid103376,public X-Google-Language: ENGLISH,ASCII Path: g2news1.google.com!news1.google.com!news.glorb.com!npeer.de.kpn-eurorings.net!news.tele.dk!news.tele.dk!small.news.tele.dk!newspeer1.se.telia.net!se.telia.net!masternews.telia.net.!newsb.telia.net.POSTED!not-for-mail From: =?ISO-8859-1?Q?Bj=F6rn_Persson?= User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.4.1) Gecko/20031114 X-Accept-Language: sv, sv-se, sv-fi, en-gb, en-us, en MIME-Version: 1.0 Newsgroups: comp.lang.ada Subject: Re: Is T an ancestor of T? References: In-Reply-To: Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable Message-ID: Date: Sat, 23 Oct 2004 16:55:40 GMT NNTP-Posting-Host: 217.209.116.179 X-Complaints-To: abuse@telia.com X-Trace: newsb.telia.net 1098550540 217.209.116.179 (Sat, 23 Oct 2004 18:55:40 CEST) NNTP-Posting-Date: Sat, 23 Oct 2004 18:55:40 CEST Organization: Telia Internet Xref: g2news1.google.com comp.lang.ada:5661 Date: 2004-10-23T16:55:40+00:00 List-Id: Georg Bauhaus wrote: > Bj=F6rn Persson wrote: > : Georg Bauhaus wrote: > :=20 > :> By the last sentence of (10), > :> the ultimate ancestor (T) "is not a descendant of any other type". > :> So if T is the ultimate ancestor, it is not a descendant of T. > :> Which it is by the first sentence of (10). > :> I must be missing something. Specific types? > :=20 > : Maybe it's the word "other" you're missing? >=20 > I don't speak English. Is there a mix of defined (linguistic) > "ambiguity" (T descends from itself) and assumed clarity of "other" > in this paragraph? (Is there a well defined mathematical meaning of > "other" in general, not just in paragraph 3.4.1(10)? What is the set > of "not any other types"?) Oh come on! I'm sure German has the same construct. "Other" implies=20 "other than X", and X has got to be mentioned or otherwise apparent from = the context. The sentence is as follows: "The ultimate ancestor of a type is the ancestor of the type that is not = a descendant of any other type." There are two types mentioned that are possible candidates for X. One,=20 T1, is being defined as "the ultimate ancestor". The other, T2, is=20 spoken of as "a type" and "the type". It is stated that T1 is an=20 ancestor of T2, which means that T2 is a descendant of T1. It is also=20 stated that T1 is not a descendant of any type except X. So which of T1=20 and T2 is X? If T1 and T2 are the same type, then they are both X, and the sentence=20 says that the ultimate ancestor T of a type T is the ancestor T of the=20 type T that is not a descendant of any type except T. No problem. If T1 and T2 are not the same, and T1 is X, then it says that in order=20 to be the ultimate ancestor, T1 must not be a descendant of any type=20 except T1. That is, "other" means "other than itself". If T1 and T2 are not the same, and T2 is X, then it says that in order=20 to be the ultimate ancestor, T1 must not be a descendant of any type=20 except T2. But T1 is an ancestor of T2 so it can't be a descendant of=20 T2, and then T1 isn't allowed to be a descendant of any type at all. Not = only does this cause a contradiction, but it's also terribly=20 convoluted. Why would anyone write "any other type" if "any type" would=20 mean the same thing? Obviously they don't mean that T2 is X. > : By the way, did you notice that class-wide types aren't ancestors or = > : descendants of themselves? >=20 > Yes, and class-wide types don't have parents or ancestors at all, > do they? Yes they have. T is an ancestor of T'Class. I'd assume it's the parent=20 too, but I haven't found a proof for that. --=20 Bj=F6rn Persson PGP key A88682FD omb jor ers @sv ge. r o.b n.p son eri nu