Re: a union is always a join!

On Mar 18, 11:43 am, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:
On Mar 17, 10:31 pm, "Brian Selzer" <br...@xxxxxxxxxxxxxxxxxxx> wrote:

Your argument rests on the premise that keys permanently
identify things in the universe of discourse.  But by definition, all that
is required is that no two tuples in the same relation in the same database
have the same key components.  What that means is that what identifies
something in the universe of discourse at t' could identify something
totally different at t''.

Well, there is no such thing as well defined update operation.
Because, it depends on the key. Example

delete {(p=1,q=a)}
insert {(p=1,q=b)}

with key {p} is equivalent to

update where p = 1 set q = b

Therefore, the update relative to key {p,q} is different from update
relative to key {p}. My take is that update is nothing more than
syntactic shorthand for combination of insert and delete.


I don't think so. I think that the delete/insert pair states that
there is a different thing with key p = 1, whereas the update states
that the thing with key p = 1 merely appears different. In other
words, the delete/insert pair describes two distinct things, whereas
the update describes two distinct appearances of the same thing. The
delete/insert pair,

delete {(p=1,q=a)}
insert {(p=1,q=a)}

states that there are two distinct things with exactly the same
components, just during adjacent intervals.

In other words, just because keys are the same at different times doesn't
necessarily mean that they map to the same thing in the universe of
discourse, and similarly, just because keys are different at different times
doesn't necessarily mean that they don't map to the same thing in the
universe of discourse.

Keys were the only option to try to define update formally. Again, if
not through keys, how do you formally define update?


I just don't agree with you on this. I presented an alternative
definition that is independent of keys.


Morale: you
can't possibly define what update is without a key.

Yes, you can:  Consider the equivalence between the two D expressions from
/TTM Third Edition/ pages 112-113:

UPDATE r (Ai := X, Aj := Y)

where i != j is equivalent to

( ( EXTEND r ADD ( X AS Bi, Y AS Bj ) )
        { ALL BUT Ai, Aj } RENAME { Bi AS Bk, Bj AS Aj, Bk AS Ai}

Now let's look a bit more closely at this expression.  The first part

( ( EXTEND r ADD ( X AS Bi, Y AS Bj ) )

results in a relation in which each tuple contains both the old components
and the new components, and from that relation it is possible to determine
exactly what is different--tuple, by tuple.  But then that /stated/
correlation is projected away by

        { ALL BUT Ai, Aj } RENAME { Bi AS Bk, Bj AS Aj, Bk AS Ai},

so clearly, information is lost when translating an update into an
assignment.  Now if we could just shift constraint enforcement to just
before that information is projected away, then we could specify transition
constraints declaratively.

I'm not sure what relational assignment is to form an opinion if it
adequately preserves information to be leveraged in transition
constraints. It is obvious that transition constraint is nothing more
than algebraic-relational expression that includes two variables: the
state of relation before update R(t_1) and the state after R(t_2).- Hide quoted text -

Unfortunately, it just isn't that simple. Since the key components
that identify something can be different at different times yet still
identify that same something, there can be more than one transition
that yields a resulting state. For example, if the guy that had up to
this point been first in line at the bank was wearing a blue hat, and
if the guy that is now first in line is wearing a red hat, then one
possibility is that there is a different guy that is first in line,
the guy wearing the red hat, but another possibility is that the guy
that had up to this point been first in line is still first in line
but just put on a red hat. So which is it? If the transition
consisted of a delete/insert pair, then it's clear that it's the first
possibility, but if the transition consists of an update, then it's
clearly the second.


- Show quoted text -

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