Specification of Reactive Hardware/Software Systems - Electronic ...

252 Data Part of POOSL
The evaluation of an expression as part of the execution of a method is formalised in rule
(e) above. If rule (e) is successively applied to configuration
¡ ¡
¥ s¡ ¥ ¥ Sys until the
E¥
rule is not applicable anymore, the resulting configuration is either stuck, or it is of the
form
¥ Sys . In the latter case, data object ¤ is the result of the evaluation
¡ ¡
¥
¡
¡ ¡ ¥ s¡ ¡ ¥
¤ ¡
of expression E. By axiom (9) this result is at the same time the result of the execution of
method m. This result is inserted at the place of the and the local variable environment
of m is popped s¡ ¡ off stack (at least if this stack is not empty).
8.5.4 The Semantic Function
Now that we have defined the £ transition relation , we will specify what we consider to
be the meaning of a configuration. We define the semantics of a configuration as the set
of all terminal configurations of all its possible derivation sequences. A configuration is
terminal if it is of the form
¡ ¡
¥ s¥ ¥ Sys . Formally, we define a semantic function as
¤ ¥
follows:
where
: Conf £ © (Conf )
( Se £
¡
Sys ¥ ¤ ¥ ¡ ¡
¡ ¥ s¡ ¥ ¡ ¥ Sys ¡
¥ ¡ ¡ ¡
¥ ¥ s¥ ¥ Sys £ ¤ ¥ ¡ ¡
¡ ¥ s¡ ¥ ¡ ¥ Sys ¦
s¥ ¥
© £
£
)
e S
Here, (Conf ) denotes the powerset of Conf , i.e., the set of all subsets of Conf . is
the reflexive-transitive closure of relation and denotes that a configuration can lead
to another configuration in zero or more computation steps.
8.6 Primitive deepCopy Messages
The transition system defined in Appendix A incorporates the definition of so-called
deepCopy messages. A deepCopy of a non-primitive object creates a new object of the
same class. The objects referred to by the instance variables of this newly created object
are again deepCopies of the objects referred to by the instance variables of the original
object. DeepCopies of primitive objects are the primitive objects themselves.
The definition of the semantics of deepCopy messages requires a function copy and
a collection of functions relabel m. Function copy takes a triple ¡
¥ ¤ ¥ ¡
¡ ¤
of an object
(identifier) , a variables state and a type ¡ ¤ and delivers a copy of object . This
copy is again represented by a triple of an object (identifier), a variables state and a type
and is of the form
¡ ¡ ¤£¡ . is the set of identifiers of all objects that are
(indirectly) known to object ¤ . If ¤ denotes a non-primitive object, it is also contained in
¤ ¥ ¡ ¤¢¡ ¥
The collection of functions relabel m is used to relabel all object identifiers in some
triple
by increasing them by m.
¡ . Since primitive objects do not know any other objects, ¡ is empty if ¤ is primitive.
¤ ¥ ¡ ¥
¡
To calculate a proper object-copy, we let the input triple
¤ ¥ ¡ ¥
¡
of function copy be