Re: no names allowed, we serve types only
Date: Wed, 17 Feb 2010 10:51:14 -0800 (PST)
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
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