Re: RM and definition of relations/tuples

Martin Zapf wrote:
> 2. definition
>
> A relation r for schem R is a set of tuples.
> A tuple t is a function
> t: R -> Union (dom(A_1),dom(A_2),...,dom(A_1))
> t maps each Attribute of R to an value of its domain.
> So a relation is a set of functions, which are called tuples.

I suspect there is (more than one) typo here as well. Let's take care of the obvious one, first

t: R -> Union (dom(A_1),dom(A_2),...,dom(A_n))

Then, what is the "Union" operator in front? Union is a binary operator. Is it the iterative version that applies to more than 2 arguments. (Similar to binary "+" generalized to iterative sigma notation). Then, it has to have a variable to iterate to, but the expression

(dom(A_1),dom(A_2),...,dom(A_n))

doesn't have any free variable.

On the page 32 of the Alice book I see Cartesian product definition for unnamed perspective, and function definition for named perspective, although both are informal ones. This leaves no doubt that you have meant

t: attribute_name -> U_i dom(A_i)

That is

t: attribute_name -> dom(A_1) U ... U dom(A_n) Received on Wed Nov 23 2005 - 21:39:27 CET