Database Reference
In-Depth Information
of this database-mapping graph (program)
G
. Let us insert a number of tuples
into an instance-database
A
=
α
∗
(
A
)
such that the updated database-instance is
α
1
(
equal to
A
)
and satisfies all three inter-schema mappings above (and
hence
α
1
is a new model of the database mapping system in
G
), with the new
updated databases
B
i
=
=
A
α
1
(
B
i
),i
=
1
,
2
,
3 for the schemas
B
1
,
B
2
and
B
3
, and
a
1
=
Act
(and, analogously, for
a
2
and
a
3
).
Thus, our database process-program
P
, obtained from the algorithm '
DBprog
',
with set of process variables
p
0
,p
1
,...,p
7
∈
Δ(α, MakeOperads(
M
AB
1
))
∈
X
, is the system of guarded
flattened
equations of the program
P
specified by algorithm
DBprog
:
=
p
0
=⊥
0
,
p
1
=
3
(p
2
,p
3
,p
4
)
,(p
2
=
E
a
1
.p
5
),
B
3
)
.
(p
3
=
a
2
.p
6
),(p
4
=
a
3
.p
7
),(p
5
=
B
1
),(p
6
=
B
2
),(p
7
=
=
Hence, for
i
1
,
2
,
3,
=
p
2
,
(p
3
,p
4
)
∈
T
P
(X),
3
(p
2
,p
3
,p
4
)
g
E
(p
1
)
=
g
E
(p
i
+
1
)
=
a
i
.p
i
+
4
,
g
E
(p
i
+
4
)
=
B
i
∈
P
(
Υ
)
=
Act
⊆
T
P
(
∅
)
⊆
T
P
(X)
as follows from the algorithm '
DBprog
' and the fact that
α
1
∈
Mod(
Sch
(G))
.
The solution of this set of equation is given by:
T
s
E
(p
0
)
=⊥
0
,
T
s
E
(p
i
+
4
)
=
B
i
∈T
∞
,i
=
1
,
2
,
3
,
T
s
E
(p
i
+
1
)
=
a
i
⊗
B
i
∈T
∞
,i
=
1
,
2
,
3
,
T
s
E
(p
1
)
=+
a
1
⊗
B
3
)
∈T
∞
.
B
1
,
+
(a
2
⊗
B
2
,a
3
⊗
We have the following equivalence classes:
[
p
i
+
4
]
E
={
p
i
+
4
,B
i
}
[
p
i
+
1
]
E
={
p
i
+
1
,a
i
⊗
B
i
}
=
,
,
for
i
1
,
2
,
3
.
And
[
p
1
]
E
=
3
(p
2
,p
3
,p
4
),
3
(a
1
⊗
B
1
,p
3
,p
4
),
3
(p
2
,a
2
⊗
B
2
,p
4
),
3
(p
2
,p
3
,a
3
⊗
3
(a
1
⊗
3
(a
1
⊗
B
3
),
B
1
,a
2
⊗
B
2
,p
4
),
B
1
,p
3
,a
3
⊗
B
3
),
3
(p
2
,a
2
⊗
3
(a
1
⊗
B
2
,a
3
⊗
B
3
),
B
1
,a
2
⊗
B
2
,a
3
⊗
B
3
),
and all permutations of these tuples
.
At the same time,
p
0
]
E
=
p
0
, nil,
0
[
⊥
∪{
all other terms that are not in the above defined equivalence classes
}
.
