Database Reference
In-Depth Information
@
so that the unique non-recursive solution
is obtained from the cor-
responding unique non-guarded recursive solution
(
of general coinduction
)
ψ
@
[
_
]
:
X
→
D
P
S
:
@
=
ψ
@
T
P
X
→
D
P
S
with
[
_
]
◦
η
X
.
Proof
The triangle (a) commutes from the fact that
g
E
◦
η
X
=
id
X
(from the algo-
rithm
DBprog
and Proposition
34
), and
φ
η
X
(from Proposition
45
), while the
triangle (b) corresponds to the particular definition of the guarded recursive specifi-
cation in this proposition by
φ
=
φ
#
◦
℘
.
From the fact that there is only one
(S
×
B
P
)
-homomorphism from the coalgebra
(X,
=
B
P
(η
X
)
◦
@
ψ
@
[
_
]
)
into the final coalgebra
(
D
P
S
,
B
)
it must be
[
_
]
=
◦
η
X
:
X
→
D
P
S
.
7.6
Review Questions
1. Explain what the main differences between a denotational and an operational
semantics are, and what the relationship between the behavior of the database
mapping programs and observational semantics for RDB based on views and
the power-view operator
T
is. Is this power-view operator
T
obtained from the
initial semantics for the relational SPJRU algebra
Σ
R
in Sect.
5.1.1
a plausi-
ble factor which can determinate the semantic adequateness of these two se-
mantics? Why did we obtain that the Structural Operational Semantics for the
database mapping systems is a kind of the Guarded recursion (GSOS)? What
can be the adequate interpretations for the branching (parallel) composition '
'
and the action prefixing composition '
a.
_' of the GSOS grammar for the DB
theory?
2. Why do we need the process of updates through views in database mapping
systems (programs), that is, for a given update of a view of relational database
how should it be translated to updates on the underlying database (consider
the mapping-interpretation of the schema mappings)? What are the side-effect
