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=-0.9 required=5.0 tests=BAYES_00,FORGED_GMAIL_RCVD, FREEMAIL_FROM autolearn=no autolearn_force=no version=3.4.4 X-Google-Thread: 103376,7b207d193114a9 X-Google-Attributes: gid103376,public,usenet X-Google-Language: ENGLISH,ASCII-7-bit Path: g2news1.google.com!news2.google.com!postnews.google.com!s12g2000prg.googlegroups.com!not-for-mail From: Eric Hughes Newsgroups: comp.lang.ada Subject: Re: Partial type specifications and their ordering Date: Tue, 18 Mar 2008 07:30:19 -0700 (PDT) Organization: http://groups.google.com Message-ID: References: <4yntq9j6q827.kusbb0olb916.dlg@40tude.net> NNTP-Posting-Host: 166.70.57.218 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: posting.google.com 1205850619 3778 127.0.0.1 (18 Mar 2008 14:30:19 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Tue, 18 Mar 2008 14:30:19 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: s12g2000prg.googlegroups.com; posting-host=166.70.57.218; posting-account=5RIiTwoAAACt_Eu87gmPAJMoMTeMz-rn User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8.1.12) Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) Xref: g2news1.google.com comp.lang.ada:20464 Date: 2008-03-18T07:30:19-07:00 List-Id: On Mar 18, 2:40 am, "Dmitry A. Kazakov" wrote: > Your draft does not explain why certain sets of types (called partial here) > cannot form a proper class. No code. No subprogram definitions. Nothing to execute. The name "partial type" can be taken as an abbreviation for "partial specification of a type". Pretty much every definition of types that I've seen, starting with Godel's 1957 _Dialectica_ paper, uses some kind of algorithm expression to define types. A partial type strips out algorithm expressions and focuses only on assumptions and results of operations and on invariants about data. > My guess is that any set of types can be associated with a class. Any set of partial types can be associated with a least common superclass. That's what a lattice is. See http://en.wikipedia.org/wiki/Lattice_%28order%29. > Consequently, generic types (not Ada term, but the meaning is obvious) are > fully equivalent to classes. Please go find out what Alonzo Church meant by a lambda constructor (which became Lisp, but is far broader than Lisp). Barring degeneracies, a generic type has a higher minimal lambda recursion level than an ordinary type. If you'd rather use a programming language that treats type recursion as basic, try a functional language such as Haskell. Partial types specification are a notion orthogonal to generics. Eric