Final example discussed in class 2/21/00:

Query:  Find the names of customers who have accounts in all branches
located in Princeton

DOMAIN RELATIONAL CALCULUS:
The class developed the following candidate solution (cleaned up a little):

{<N> | EXISTS A ( (<N,A> IN depositor) AND 
                  FORALL(Bn, b) (( NOT (Bn,A,b) IN acct)   OR 
                                   EXISTS(Bc,a) (((Bn,Bc,a) IN branch)
                                                 OR NOT(Bc = `Princeton`))))  }

We appear to be asking that if Bn is the branch name for account A, that the
branch be in Princeton.  But as it is written, any Bc <> `Princeton' 
satisfies the inner "EXISTS(Bc,a) ..."  Closer to what we wanted is:

{<N> | EXISTS A ( (<N.A> IN depositor) AND 
                  FORALL(Bn, b) (( NOT (Bn,A,b) IN acct)   OR 
                                  EXISTS(a) (((Bn,`Princeton',a) IN branch))))}

But this only asks that one account of depositor N be at a branch in Princeton:
the A we choose to satisfy "EXISTS A ...


I offered the solution from my notes:

{<N> | EXISTS A ( (<N.A> IN depositor) AND 
                  FORALL(Bn, Bc, a) (( NOT (Bn,Bc,a) IN branch)   OR 
                                       NOT(Bc = `Princeton`)    OR
                                       EXISTS(b) ((Bn,A, b) IN acct))) }
Here we are asking that there be one account (w/ acct# A) for the 
depositor named N so that if Bn is a branch in Princeton, then A is an 
account in that branch.
But one account (w/ acct# A) cannot be at several branches in Princeton.
Note that this condition is not satisfied if N has no accounts at any branch
in Princeton because in evaluating the FORALL(Bn, Bc,a), we must include
all branches with Bc=`Princeton'; for these EXISTS(b)((Bn,A,b) IN acct)
needs to be true but is not.

Clearly, the account numbers associated with the depositor named N
must vary as well as the branch names.  We cannot ask for a single 
acct# linked to name N.  This example actually came from Silberschatz et. al.
Their solution is:

{<N> | FORALL(Bn,Bc,a)( ((<Bn,Bc,a> IN branch ) AND (Bc = `Princeton')) =>
                  EXISTS(A,b)( (<Bn,A,b> IN acct) AND (<N,A> IN depositor) )) }

This says that for each branch in Princeton there is an account at that 
branch that has N as the depositor`s name.  Note that we do want the
"for all" to precede the "there exists" because we will have a different
account for each branch.  It looks correct to me, but textbook authors can
make mistakes too, so check it out.


TUPLE RELATIONAL CALCULUS:
Following the strategy of the Domain Relational Calculus solution:

{P | FORALL B( ((B IN branch ) AND (B.city = `Princeton' )) =>
                  EXISTS(T,D)( (T IN acct) AND (D IN depositor)  AND
                               (T.bname = B.bname) AND (T.acct# = D.acct#)
                                AND (D.name = P.name) )) }