Global Positioning System Reference
In-Depth Information
Relevant Link RLintA-M
A RLintA-M link leads to additional attributes in the fi nal schema, which
are results of methods.
A RLintA-M link binds a set of attributes of a given class (possibly
reduced to a singleton) to a method of the same class. This set of attributes
represents the source attributes and belongs to the initial schema. The
result of the method (here a function) will be added to the fi nal schema as
a new attribute.
This RL is defi ned by the following elements: the class concerned by
this RL (c
i
), the set of source attributes (A
s
), the method (m
k
), its parameter
list (P). Table 5 presents the formal defi nition of RLintA-M.
This defi nition means that in the initial schema where it exists the set
of attributes {a
1
,..., a
n
}, this RL adds in the fi nal schema an attribute that
denotes the result of the method m
k
(a
|A|+1
). Note here that several links
can possibly call the method m
k
.
The recursive defi nition of the set A, with respect to the creation of
attributes denoting the link, leads to establish (recursively or not) links
between methods. One of these methods is considered as a source attribute.
The origin of the recursion is necessarily, by the defi nition of the link, in
the set of non-calculated attributes.
As an example, from a social point of view, we illustrate this type of RL
between the attribute “population” and the method “density (integer, real)”
of the City class. This RL is defi ned by: A_M-> (City, population, density
Table 5.
Formal defi nition of RLintA-M.
Let c
i
= (A
i
, M
i
, K
i
) be a class where c
i
∈ C. Let A
s
= {a
s1
, ... , a
sn
} be a set
of attributes . Let m
k
∈ M
i
be a method.
Let |A| denote the cardinality of
the set of attributes A. Let a
|A|+1
denote the result attribute. Let D be a
domain. Let P be defined as P: D P | M (P) P |
ε
Pre-conditions:
A
s
⊆ A
i
, K
i
⊄ A
s
A RL of
RLintA-M (-A_M->)
type between A
s
and a
|A|+1
is defined by:
-A_M->: C x A x … x A x M x (P) -> A
(c
i
, a
1
, … , a
n
, m
k
, (p
1
, ... , p
q
)) = a
|A|+1
Post-condition:
A = A ∪ {a
|A|+1
}
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