Re: Transitive Closure

mikharakiri_nospaum_at_yahoo.com (Mikito Harakiri) wrote in message news:<8a529bb.0405160919.73cf214b_at_posting.google.com>...

> Both TC and selection (I prefer that name that pops up on the first
> page when googling "Relational Algebra")

I prefer restriction. What selection does is a restriction.

> are unary relational operators.

No, even in the page you mention you can see that selection is a binary operator:

R2 = select(R1,P)

BTW it is not a commutative operator:

select(R1, P) <> select(P, R1)

In the second case the operation is undefined.

> So we are talking about composition operation applied to
> operators and commutativity of this operation.

We are talking about the order of the operations, not about the order of the operands.

1+2 = 2+1 thanks to the commutative property of the sum (1+2)+3 = 1+(2+3) thanks to the associative property of the sum

In the first case we have one operation and in the second case we have two.

The commutative property does not make sense with unary operators like TClose. Unary operators are always commutative because there is only one operand's order.  

> In relational world operator commutativity is very important. Although
> Relational Algebra appears to be more procedural than relational
> calculus (apply this selection, then, apply this projection, and so
> on), this syntactic order doesn't really matter as selection and
> projection commute to about every other operator.

No.

(a union b){c, d} = a{c, d} union b{c, d) because projection DISTRIBUTES over union, intersection, and join, but not over difference:

(a minus b){c, d} <> a{c, d) minus b{c, d}

It is trivial to find an example.

> This is why
> select-project-join is expressed in good old SQL as:
>
> select ... from A,B,C where ...

The messy SQL is very confusion prone.

Translated to algebra this is:

Project(Restrict(CartesianProduct(A,B,C), ...), ...)

Projection and restriction distribute over the cartesian product, but try with an EXCEPT clause.

Regards
  Alfredo Received on Mon May 17 2004 - 01:49:21 CEST