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

322 Behaviour-Preserving Transformations
One AudibleAlarmImage, one DoorsImage and one ElevatorPassengerImage is
mapped onto each ElevatorCageControlModule.
All ElevatorMechanismHandlers, all IndividualElevators and the CentralControl instance
are mapped onto the ElevatorsControlModule.
One FloorPassengerImage is mapped onto each FloorPassengerInterfaceModule.
The modification of the initial POOSL specification presented in Figure 10.1 requires a
large sequence of successive applications of basic behaviour-preserving transformations.
In this chapter we will only present a global sketch of this sequence and show the result
of its application in graphical form. In [Voe] the transformation sequence is described
in more detail. [Voe] further presents a complete initial elevator specification as well
as a complete transformed elevator specification. An Instance Structure Diagram of the
transformed elevator specification is shown in Figure 10.4.
The transformation sequence is explained in 12 steps. Each step uses one or more basic
behaviour-preserving transformations defined in the previous chapter. Applications of
Proposition 4 (stating that ¢
is a partial congruence) are not mentioned.
¡
¢
1. First transformation 13 is applied to replace the ElevatorControlSystem cluster
by its constituents. The remaining behaviour specification is then of the form
K)) L), where BSpec1 contains the terminator instances and
(BSpec1 (BSpec2
where BSpec2 K is the behaviour specification of the ElevatorControlSystem class.
This class is eliminated from the system of process and cluster classes by applying
12.
¢
¢
¢
¢ ¦
2. Since BSpec1 does not contain any channels that are in K, (BSpec1 (BSpec2 K)) L)
can be transformed into ((BSpec1 K) (BSpec2 K)) L) by 7. Since BSpec1
and BSpec2 do not communicate over channels in L, 11 can be applied to yield
(BSpec1 BSpec2) K L. The two successive channel hidings are combined by 8.
We then obtain (BSpec1 BSpec2) K L.
¢ ¦
¢ ElevatorMechanism(¡ 0¡ )§ ¢ ¦
3. By repeatedly applying 2 and 3, (BSpec1 BSpec2) K L can be transformed
into (BSpec1 f BSpec3) K L.
ElevatorMechanism(¡ 0¡
¢ ((AAI(¡ AAI¡ ¡
¢ DI(¡ DI¡ ¡ 0¡ ¢ EMH(¡ EMH¡ ¡ 0¡ ¢ EMI(¡ EMI¡ ¡ 0¡ M)§ f ¢ BSpec3) ¦ 0¡
4. Using transformation 13, cluster ) is replaced by its internals.
We will use obvious abbreviations for their names: (BSpec1
) ) ) ))
K L
5. Transformations 10 and 6 (with condition NoComChange¡ ) are applied to give
the internal channels of the former ElevatorMechanism(¡ 0¡ ) cluster new and fresh
names. The applied channel renaming function is g. (BSpec1 ¢ ((AAI(¡ AAI¡ ¡ 0¡ )§ g ¢
DI(¡ DI¡ ¡ 0¡ )§ g ¢ EMH(¡ EMH¡ ¡ 0¡ )§ g ¢ EMI(¡ EMI¡ ¡ 0¡ )§ g )
g(M))§ f ¢ BSpec3)
K¦ L