Show that step 2 of the method used in Section 16.3.1 to perform a join using a semi- join does in fact generate the semi-join. For simplicity, assume that the join we are attempting is a natural join. That is, prove that ?attributes(T1) (T1 T2) = ?attributes(T1)(T1 ?attributes(join-condition)(T2))
What will be an ideal response?
This a special case of the rule for pushing projections through joins in Section 11.2.
For every tuple t ? T1 T2 there is a tuple t
? T1 ?attributes(join-condition)(T2)
that agrees with t on all attributes of T1 and vice versa. Thus the above two expressions
are equivalent.
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