# Re: no names allowed, we serve types only

Date: Wed, 17 Feb 2010 10:51:14 -0800 (PST)

Message-ID: <2680fc20-5aad-4325-a770-c6127cfd9e3d_at_a17g2000pre.googlegroups.com>

On Feb 17, 10:14 am, David BL <davi..._at_iinet.net.au> wrote:

> On Feb 17, 9:15 pm, Nilone <rea..._at_gmail.com> wrote:

*>
**> > On Feb 17, 1:29 pm, David BL <davi..._at_iinet.net.au> wrote:
**>
**> > > Operators can be formalised without a type system too. Simply
**> > > 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. I 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). This is typeless in the
**> sense that a function value doesn't formally have any concept of a
**> defined type. Rather the domain and co-domain are formally part of
**> the function's value as a triple (D,C,G). For example two functions
**> can have the same domain and graph but different co-domains. That
**> makes them distinct. This is actually conventional, as when one
**> determines whether a given function is surjective (i.e. its range
**> equals its co-domain). It 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). In
**> 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. One 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. That means that two
**> distinct relations can have exactly the same graph.
**>
**> Alternatively a relation can be identified with its graph. In 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. 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. E.g. two different databases could use
**> different type systems. Putting 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. That'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. It's like a "magic downcast". They point
**> out that OO systems don't normally work that way. E.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. i.e. in essence the declared attribute domains are
**> not part of the relation's value. I 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. Received on Wed Feb 17 2010 - 19:51:14 CET