Re: MERGE as the imperative form of aggregation

Marshall wrote:

> On Apr 15, 8:16 pm, "Brian Selzer" <b..._at_selzer-software.com> wrote:
>
>>"Marshall" <marshall.spi..._at_gmail.com> wrote in message >>

[snip]

>>  You can't use a key: [large snip]

Transitions are a distinguishing feature of state machines. I suggest each implies the other. If I recall his argument correctly, Brian's position assumes tuples are implicit state machines.

For a deterministic state machine, a new state is a function of a prior state and some event:

f(S,E): S

S_1 === f(S_0,E_0)
S_n+1 === f(S_n,E_n)

For a non-deterministic state machine, f above is a relation. One can change that into a boolean relation that tests the validity of a state transition:

f'(S,S,E): {true,false}

f'(S_n,S_n+1,E_n) is true iff a transition from S_n to S_n+1 is valid in response to even E_n.

The form of f' is exactly the form of a relation in the relational model.

If we have only partial information about E, a deterministic transition would appear non-deterministic based on the available information. (external predicate) In the degenerate case, we can know nothing about E and still express a transition constraint describing the allowable transitions for any E.

As one can see, a transition constraint is a relation of degree 3.

I see no particular restriction on the domains involved. S could be any domain and E could be any domain. This, of course, means S could be a tuple type.

Brian's position simultaneously acknowledges and ignores logical identity and the information principle.

His logic follows the form of: Suppose we have a relation R(A) and a transition constraint X(A,A,E), it is possible that the attributes of A forming the candidate keys might change. We thus need a special statement that knows which of the values correspond.

However, while his logic acknowledges candidate keys, it ignores what logical identity and the information principle actually say.

While the relational model does not prevent A tuples from participating in transition constraints, logical identity and the information principle require us to identify the A's across the transition, and Brian's position simply ignores this requirement. This requires the designer to change R(A) to R(k,A) where k is a key of R.

Then if we have an imperative statement where R(k,A) becomes R'(k',A'), and a transition relation X(A,A,E) the constraint becomes:

assert (k != k') \/ (exists e | X(A,A',e))

Note that we place no restrictions on the type or form of imperative statement whatsoever. The statement could assign a literal to a relvar and the constraint works the same as it would for an update statement. Received on Mon Apr 16 2007 - 16:57:13 CEST