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

324 Behaviour-Preserving Transformations
10. To combine the various communication channels we apply transformation 10 to
the complete specification. 6 is used several times to distribute the applied channel
renaming function over each component of the specification. Unfortunately,
in a number of application steps of 6 transformation condition NoComChange¡ is
not satisfied 4 . In these steps condition NoComChange itself has to be applied. It is a
tedious exercise, but it can be shown that NoComChange is indeed satisfied in each
step. To simplify the resulting channel renaming functions, we repeatedly apply
1, 4 and 5. The resulting Instance Structure Diagram is given in Figure 10.3.
11. A number of process objects of Figure 10.3 contain different channels that are
externally mapped onto the same channel. For example, each FloorPassengerImage
has internal channels fpsl and fpsi (the inner names are fpsl and fpsi). Externally,
these channels are renamed to fpcc (the outer names are both fpcc). Using
transformation 14 it is possible to carry the renaming through internally. Consider
the topmost instance of process class FloorPassengerImage. Its behaviour
specification is given by FloorPassengerImage (¡ FPI¡ ¡ 0¡ ). We apply 14 with C b 1
= FloorPassengerImage, f1 = fpcc/fpsl,fpcc/fpsi,fpfp0/fpfp, C b 2 = FloorPassengerImage1,
f2 = fpcc/fpsi,fpfp0/fpfp, ch fpsl and ch¡ fpcc. The transformed specification
then becomes FloorPassengerImage1 (¡ FPI¡ ¡ 0¡ ) § fpcc© fpsi¥ fpfp0© fpfp , where Floor-
PassengerImage1 is a newly defined process class that is added by means of 12.
When 14 is applied again, this specification transforms into FloorPassengerImage2
(¡ FPI¡ ¡ 0¡ ) § fpfp0© fpfp , where FloorPassengerImage2 is yet another process class. In
a similar way, each remaining FloorPassengerImage is replaced by a corresponding
FloorPassengerImage2 process. We then use 12 to eliminate process classes
FloorPassengerImage and FloorPassengerImage1. Finally, process class FloorPassengerImage2
is renamed to FloorPassengerImage by 15. In an analogous way the
instances of process classes ElevatorPassengerImage and ElevatorMechanismHandler
are modified.
4 This problem is caused by the weakly distributed nature of the elevator specification.