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on two systems that are directly related to the concepts described earlier and also
targeted at schema evolution.
The first system that we will discuss is an implementation of mapping composi-
tion that is reported in
Yu and Popa
[
2005
] and is targeted at the mapping adaptation
problem in the context of schema evolution. This implementation is part of the Clio
system [
Fagin et al. 2009a
] and builds on the schema mapping framework of Clio.
In particular, it is focused on schema mappings that are expressed as SO tgds [
Fagin
et al.
2005b
]. A different implementation of mapping composition that is worth not-
ing, but which we do not discuss in detail in here, is the one reported in
Bernstein
et al. [
2008
]. This system allows a schema mapping to contain not only source-to-
target constraints, but also target constraints, source constraints, and target-to-source
constraints. Furthermore, the focus is on expressing the composition as a first-order
formula (when possible). In this approach, a significant effort is spent on eliminating
second-order features (via deskolemization). As a result, the composition algorithm
is inherently complex and may not always succeed in finding a first-order formula,
even when one exists.
The second system that we will discuss in this section is a more recent one,
reported in
Curino et al.
[
2008
], and includes both composition and inversion as part
of a framework for schema evolution. This system is focused on the query migration
(or adaptation) problem in the context of schema evolution.
6.1
Mapping Composition and Evolution in Clio
The system described in
Yu and Popa
[
2005
] is part of the larger Clio system [
Fagin
et al.
2009a
] and is the first reported implementation of mapping composition in the
context of schema evolution. In this system, both source schema evolution and tar-
get schema evolution are described through mappings, which are given in the same
language as the original schema mapping (that is to be adapted). However, differ-
ently from the earlier diagram shown in Fig.
7.1
, the source evolution is required
to be given as a schema mapping from
S
00
to
S
, and not from
S
to
S
00
. (The latter
would, intuitively, be a more natural way to describe an evolution of
S
into
S
00
.)
The main reason for this requirement is that the system described in
Yu and Popa
[
2005
] preceded the work on mapping inversion. Thus, the only way to apply map-
ping composition techniques was to require that all mappings form a chain, as seen
in Fig.
7.5
.
In the system implemented in
Yu and Popa
[
2005
], the schema mapping language
that is used to specify the input mappings (i.e., the original mapping
M
and the
M
00
) are based on SO tgds [
Fagin et al. 2005b
]. One
reason for this choice is that, as discussed earlier, GLAV mappings are not closed
under composition, while SO tgds form a more expressive language that includes
GLAV mappings and, moreover, is closed under composition. Another reason is that
SO tgds, independently of mapping composition, include features that are desirable
for any schema mapping language. In particular, the Skolem terms that can be used
M
0
and
evolution mappings
