Database Reference
In-Depth Information
Note that in operad's operations
q
3
and
q
4
, we have the relational symbol
Over65
that is not in the source schema
(it was a hidden relation in the SOtgd).
Consequently, the operad's operations generally can have the relational symbols of
the schemas that are different from the source and target schemas. Let us consider
the case when no relational symbols of the source schema are used on the left-hand
side of the tgd's implications:
A
Example 9
Let us consider the previous Example
8
where the mapping
M
AB
is
reduced to
M
AB
={∀
x
p
(
Local
(x
p
)
⇒
Local1
(x
p
))
}
with
=
q
1
,
1
r
∅
,
M
AB
=
MakeOperads(
M
AB
)
where the operation
q
1
∈
⇒
O(
Local
,
Local1
)
is the expression
(
_
)
1
(x
e
)
(
_
)(x
e
)
.
Then, by applying the new algorithm for composition, we obtain the composed
mapping
M
AC
=
M
AB
,
M
BC
)
equal to
Compose(
M
AC
=
∃
f
1
∃
f
Emp
∃
f
Over
65
x
e
f
Emp
(x
e
)
.
1
∧
Local
(x
e
)
⇒
Office
x
e
,f
1
(x
e
)
∀
=
x
e
f
Emp
(x
e
)
.
1
∧
f
Over
65
(x
e
)
.
1
⇒
CanRetire
(x
e
)
.
∧∀
=
=
Note that in the second implication of the composed SOtgd, on the left-hand side of
this implication, we have no any relational symbol from
, so that in step 2 of the
algorithm
MakeOperad
we will introduce the relational symbols
Emp
and
Over65
in this implication.
Then, by transformation into operads, we obtain
A
M
AC
=
MakeOperads(
M
AC
)
={
q
1
,q
2
,
1
r
∅
}
where:
1. The operation
q
1
∈
O(
Emp
,
Local
,
Office
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
(
_
)
x
e
,f
1
(x
e
)
;
∧
2. The operation
q
2
∈
O(
Emp
,
Over65
,
CanRetire
)
is the expression
(
_
)
1
(x
e
)
(
_
)
2
(x
e
)
⇒
∧
(
_
)(x
e
).
Note that the operation
q
2
means that we do not transfer any tuple from
A
into
C
(but
only the tuples from
B
into
C
). Consequently, the information flux transmitted from
A
into
C
by this operation has to be empty, as we will show in the next example.
Based on the equivalence of representation of schema mappings by
SOtgd
and
by mapping-operads, we can introduce the composition of mapping operads analo-
gously to the composition of schema mappings:
