Database Reference
In-Depth Information
need to satisfy these requirements? An exercise: reduce this machine in order to
be able to execute only the terms of the Codd's SPJRU algebra
Σ
R
, and not to
make any update of a given database instance.
6. Why is Theorem
10
a fundamental result for the database mapping denotational
semantics based on the
DB
category? Would it be possible to define the class of
abstract database machines in order to support the operational semantics for the
Big Data Integration (the operational semantics will be formally provided in next
chapter) without it? If yes, provide an alternative class and explain what will be
the difference from this one.
7. Is the categorial approach to SQL embedding (based on the abstraction of the
synchronization process in Fig.
6.3
by using the algorithm
Smap
) sufficient to
represent the fundamental phases of the general database updating, with two
basic processes: variable binding and execution? Take Example
34
(where the
three basic atomic update operations are presented: updating (i), inserting (ii)
and deleting (iii) of tuples in a given instance database
α(
A
)
of a schema
)for
the variable binding and execution in the Categorial Database Machine
M
R
.How
is this database updating synchrony process represented by the “forgetful” func-
torial semantics? What is the meaning of the “embedding” natural transformation
τ
E
?
8. For a given database schema
A
A
, expressed by its sketch category
Sch
(G(
A
))
and
its category of interpretations
Int(G(
))
, explain what is a
transition
from one
to another instance of this database, w.r.t. Example
34
. How is the concept of
an atomic transaction for a Categorial RDB machine
M
R
represented? Explain
the meaning of the vertical composition of the “embedding” and “transaction”
natural transformations, provided by this diagram
A
and how it determines the morphisms in the
DB
category, between two consistent
instance databases of a given updated schema, as a basic transition which can
be used for a definition of the Operational semantics of the database mapping
systems.
9. Which kind of the concurrent control mechanism is used in order to define the
concurrent-categorial RDB machines
M
RC
? What are the principal modifica-
tions of the non-concurrent RDB machines in order to obtain these concurrent
machines? Why do we need a different definition for the composition of user
programs in this concurrent framework, and how is its semantics represented
during a concurrent execution of a number of programs? Explain the semantics
of the vertical composition of the “embedding” and “transaction” natural trans-
formations, provided by the diagram above, but in this new concurrent setting.
