Path: news.cambrium.nl!textnews.cambrium.nl!feeder3.cambriumusenet.nl!feed.tweaknews.nl!postnews.google.com!a17g2000pre.googlegroups.com!not-for-mail From: Tegiri Nenashi Newsgroups: comp.databases.theory Subject: Re: no names allowed, we serve types only Date: Wed, 17 Feb 2010 10:51:14 -0800 (PST) Organization: http://groups.google.com Lines: 69 Message-ID: <2680fc20-5aad-4325-a770-c6127cfd9e3d@a17g2000pre.googlegroups.com> References: <79770923-7407-4a2f-bae9-adedc37f6aa7@a16g2000pre.googlegroups.com> NNTP-Posting-Host: 70.137.135.62 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1266432674 4173 127.0.0.1 (17 Feb 2010 18:51:14 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Wed, 17 Feb 2010 18:51:14 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: a17g2000pre.googlegroups.com; posting-host=70.137.135.62; posting-account=PBsn8woAAADaWofLEAjNrE17YVrUmBlm User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.1.7) Gecko/20091221 Firefox/3.5.7,gzip(gfe),gzip(gfe) Xref: news.cambrium.nl On Feb 17, 10:14=A0am, David BL wrote: > On Feb 17, 9:15 pm, Nilone wrote: > > > On Feb 17, 1:29 pm, David BL wrote: > > > > Operators can be formalised without a type system too. =A0Simply > > > formalise an operator as a function defined on some domain, where a > > > domain is merely a set (not a "type"). > > > Thanks for the introduction, I haven't seen the typeless model > > before. =A0I don't see how such a system would handle arithmetic > > operators (e.g. + and <) and string operators like concatenation and > > search - could you perhaps give an example? > > In a typeless system a unary function could for example be formalised > as a triple (D,C,G) where D is the domain, C is the co-domain and G is > the graph of the function (a subset of DxC). =A0This is typeless in the > sense that a function value doesn't formally have any concept of a > defined type. =A0Rather the domain and co-domain are formally part of > the function's value as a triple (D,C,G). =A0For example two functions > can have the same domain and graph but different co-domains. =A0That > makes them distinct. =A0This is actually conventional, as when one > determines whether a given function is surjective (i.e. its range > equals its co-domain). =A0It wouldn't make sense to ask whether a > function is surjective if its co-domain isn't part of its value. > > Alternatively a typeless system could instead formalise a unary > function as a set of pairs (i.e. what we above called its graph). =A0In > that case the domain and range is determined from the graph using > projection, but there is no concept of a co-domain. > > Similarly a typeless system could formalise a relation in two > different ways. =A0One allows for attributes to have domains specified > independently of the graph (or "body") of the relation, and these > domains represent part of the relation's value. =A0That means that two > distinct relations can have exactly the same graph. > > Alternatively a relation can be identified with its graph. =A0In that > case the domains are determined as the projection of each attribute. > > In a typeless formalism one is very clear about what it means for two > functions or two relations to be equal. =A0 It seems to require more > effort to understand what equality means in a typed formalism. > > In a D&D type system, a value has a MST, but this actually depends on > the prevailing type system. =A0E.g. two different databases could use > different type systems. =A0Putting it another way, the MST of a value > depends on who you ask :-). > > D&D want to ensure that equality of values is independent of declared > types. =A0That's why they say that a selector for an ellipse value that > happens to specify equal width and height actually returns a value > which has an MST of circle. =A0It's like a "magic downcast". =A0They poin= t > out that OO systems don't normally work that way. =A0E.g. an OO > constructor for ellipse never returns a circle. > > I think D&D end up treating relations with the same body and attribute > names as equal. =A0i.e. in essence the declared attribute domains are > not part of the relation's value. =A0I think they define subtyping of > relation types accordingly. > > It seems to me that D&D spend a lot of effort discussing ideas that > are either eliminated or trivialised in a typeless formalism of the > RM. Formalization is less of an issue here. I interpret the question as how to make a working system operating predicates such as Plus(x,y,z) and Concat(x,y,z). Logical programming provides sort of an answer.